
Marco VILLANI
Professore Associato Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede exFisica

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Pubblicazioni
2022
 AttractorSpecific and Common Expression Values in Random Boolean Network Models (with a Preliminary Look at SingleCell Data)
[Articolo su rivista]
Villani, M.; D'Addese, G.; Kauffman, S. A.; Serra, R.
abstract
Random Boolean Networks (RBNs for short) are strongly simplified models of gene regulatory networks (GRNs), which have also been widely studied as abstract models of complex systems and have been used to simulate different phenomena. We define the “common sea” (CS) as the set of nodes that take the same value in all the attractors of a given network realization, and the “specific part” (SP) as the set of all the other nodes, and we study their properties in different ensembles, generated with different parameter values. Both the CS and of the SP can be composed of one or more weakly connected components, which are emergent intermediatelevel structures. We show that the study of these sets provides very important information about the behavior of the model. The distribution of distances between attractors is also examined. Moreover, we show how the notion of a “common sea” of genes can be used to analyze data from singlecell experiments.
2021
 A Fast and Effective Method to Identify Relevant Sets of Variables in Complex Systems
[Articolo su rivista]
D’Addese, Gianluca; Casari, Martina; Serra, Roberto; Villani, Marco
abstract
In many complex systems one observes the formation of mediumlevel structures, whose detection could allow a highlevel description of the dynamical organization of the system itself, and thus to its better understanding. We have developed in the past a powerful method to achieve this goal, which however requires a heavy computational cost in several realworld cases. In this work we introduce a modified version of our approach, which reduces the computational burden. The design of the new algorithm allowed the realization of an original suite of methods able to work simultaneously at the micro level (that of the binary relationships of the single variables) and at meso level (the identification of dynamically relevant groups). We apply this suite to a particularly relevant case, in which we look for the dynamic organization of a gene regulatory network when it is subject to knockouts. The approach combines information theory, graph analysis, and an iterated sieving algorithm in order to describe rather complex situations. Its application allowed to derive some general observations on the dynamical organization of gene regulatory networks, and to observe interesting characteristics in an experimental case
2021
 Asymptotic InformationTheoretic Detection of Dynamical Organization in Complex Systems
[Articolo su rivista]
D'Addese, Gianluca; Sani, Laura; LA ROCCA, Luca; Serra, Roberto; Villani, Marco
abstract
The identification of emergent structures in complex dynamical systems is a formidable challenge. We propose a computationally efficient methodology to address such a challenge, based on modeling the state of the system as a set of random variables. Specifically, we present a sieving algorithm to navigate the huge space of all subsets of variables and compare them in terms of a simple index that can be computed without resorting to simulations. We obtain such a simple index by studying the asymptotic distribution of an informationtheoretic measure of coordination among variables, when there is no coordination at all, which allows us to fairly compare subsets of variables having different cardinalities. We show that increasing the number of observations allows the identification of larger and larger subsets. As an example of relevant application, we make use of a paradigmatic case regarding the identification of groups in autocatalytic sets of reactions, a chemical situation related to the origin of life problem.
2021
 Dynamical properties and path dependence in a genenetwork model of cell differentiation
[Articolo su rivista]
Braccini, M.; Roli, A.; Villani, M.; Serra, R.
abstract
In this work, we explore the properties of a control mechanism exerted on random Boolean networks that takes inspiration from the methylation mechanisms in cell differentiation and consists in progressively freezing (i.e. clamping to 0) some nodes of the network. We study the main dynamical properties of this mechanism both theoretically and in simulation. In particular, we show that when applied to random Boolean networks, it makes it possible to attain dynamics and path dependence typical of biological cells undergoing differentiation.
2020
 Avalanches of perturbations in modular gene regulatory networks
[Capitolo/Saggio]
Vezzani, A.; Villani, M.; Serra, R.
abstract
A wellknown hypothesis, with farreaching implications, is that biological evolution should preferentially lead to critical dynamic regimes. Useful information about the dynamical regime of gene regulatory networks can be obtained by studying their responses to small perturbations. The interpretation of these data requires the use of suitable models, where it is usually assumed that the system is homogeneous. On the other hand, it is widely acknowledged that biological networks display some degree of modularity, so it is interesting to ascertain how modularity can affect the estimation of their dynamical properties. In this study we introduce a welldefined degree of modularity and we study how it influences the network dynamics. In particular, we show how the estimate of the Derrida parameter from “avalanche” data may be affected by strong modularity.
2020
 Evolving always‐critical networks
[Articolo su rivista]
Villani, M.; Magri, S.; Roli, A.; Serra, R.
abstract
Living beings share several common features at the molecular level, but there are very few large‐scale “operating principles” which hold for all (or almost all) organisms. However, biology is subject to a deluge of data, and as such, general concepts such as this would be extremely valuable. One interesting candidate is the “criticality” principle, which claims that biological evolution favors those dynamical regimes that are intermediaries between ordered and disordered states (i.e., “at the edge of chaos”). The reasons why this should be the case and experimental evidence are briefly discussed, observing that gene regulatory networks are indeed often found on, or close to, the critical boundaries. Therefore, assuming that criticality provides an edge, it is important to ascertain whether systems that are critical can further evolve while remaining critical. In order to explore the possibility of achieving such “always‐critical” evolution, we resort to simulated evolution, by suitably modifying a genetic algorithm in such a way that the newly‐generated individuals are constrained to be critical. It is then shown that these modified genetic algorithms can actually develop critical gene regulatory networks with two interesting (and quite different) features of biological significance, involving, in one case, the average gene activation values and, in the other case, the response to perturbations. These two cases suggest that it is often possible to evolve networks with interesting properties without losing the advantages of criticality. The evolved networks also show some interesting features which are discussed.
2020
 Exploring the Dynamic Organization of Random and Evolved Boolean Networks
[Articolo su rivista]
D’Addese, Gianluca; Magrì, Salvatore; Serra, Roberto; Villani, Marco
abstract
The properties of most systems composed of many interacting elements are neither determined by the topology of the interaction network alone, nor by the dynamical laws in isolation. Rather, they are the outcome of the interplay between topology and dynamics. In this paper, we consider four different types of systems with critical dynamic regime and with increasingly complex dynamical organization (loosely defined as the emergent property of the interactions between topology and dynamics) and analyze them from a structural and dynamic point of view. A first noteworthy result, previously hypothesized but never quantified so far, is that the topology per se induces a notable increase in dynamic organization. A second observation is that evolution does not change dramatically the size distribution of the present dynamic groups, so it seems that it keeps track of the already present organization induced by the topology. Finally, and similarly to what happens in other applications of evolutionary algorithms, the types of dynamic changes strongly depend upon the used fitness functio
2020
 Selecting for positive responses to knock outs in boolean networks
[Capitolo/Saggio]
Villani, M.; Magri, S.; Roli, A.; Serra, R.
abstract
Random Boolean networks are a widely acknowledged model for cell dynamics. Previous studies have shown the possibility of achieving Boolean Networks (BN) with given characteristics by means of evolutionary techniques. In this work we show that it is possible to evolve BNs exhibiting more positive than negative reactions to knockout stresses. It is also interesting to observe that in the observed runs (i) the evolutionary processes can guide the BNs toward different dynamic regimes, depending on their internal structure and that (ii) the BNs forced to evolve by maintaining a critical dynamical regime achieve better results than those that do not have this characteristic; this observation supports the idea that criticality may be beneficial to an evolving population of dynamical systems.
2020
 The detection of dynamical organization in cancer evolution models
[Capitolo/Saggio]
Sani, L.; D'Addese, G.; Graudenzi, A.; Villani, M.
abstract
Many systems in nature, society and technology are composed of numerous interacting parts. Very often these dynamics lead to the formation of mediumlevel structures, whose detection could allow a highlevel description of the dynamical organization of the system itself, and thus to its understanding. In this work we apply this idea to the “cancer evolution” models, of which each individual patient represents a particular instance. This approach  in this paper based on the RI methodology, which is based on entropic measures  allows us to identify distinct independent cancer progression patterns in simulated patients, planning a road towards applications to real cases.
2020
 The effects of a simplified model of chromatin dynamics on attractors robustness in random boolean networks with selfloops: An experimental study
[Capitolo/Saggio]
Braccini, M.; Roli, A.; Villani, M.; Montagna, S.; Serra, R.
abstract
Boolean networks are currently acknowledged as a powerful model for cell dynamics phenomena. Recently, the possibility of modelling methylation mechanisms—involved in cell differentiation—in Random Boolean Networks have been discussed: methylated genes are represented in the network as nodes locked to value 0 (frozen nodes). Preliminary results show that this mechanism can reproduce dynamics with characteristics in agreement with those of cell undergoing differentiation. In a second, parallel work, the effect of nodes with selfloops in Random Boolean Networks has been studied, showing that the average number of attractors may increase with the number of selfloops, whilst the average attractor robustness tends to decrease. As these two studies are aimed at extending the applicability of Random Boolean Networks to model cell differentiation phenomena, in this work we study the combined effect of the previous two approaches. Results in simulation show that frozen nodes tend to partially dampen the effects of selfloops on attractor number and robustness. This outcome suggests that both the variants can indeed be effectively combined in Boolean models for cell differentiation.
2019
 A View of Criticality in the Ising Model Through the Relevance Index
[Capitolo/Saggio]
Roli, Andrea; Villani, Marco; Serra, Roberto
abstract
The Relevance Index has been introduced to detect key features of the
organization of complex dynamical systems. It is based upon Shannon entropies
and can be used to identify groups of variables that change in a coordinated fashion,
while they are less integrated with the rest of the system. In previous work, we have
shown that the average Relevance Index attains its maximum at the phase transition
in both Ising model and random Boolean networks. In this contribution we present a
further study on the Ising model, showing that the relevance index is maximized for
large groups of variables at criticality. These results provide further evidence to the
hypothesis that this index is a powerful measure for capturing criticality.
2019
 A simplified model of chromatin dynamics drives differentiation process in Boolean models of GRN
[Relazione in Atti di Convegno]
Braccini, Michele; Roli, Andrea; Villani, Marco; Montagna, Sara; Serra, Roberto
abstract
Cellular types of multicellular organisms are the stable results
of complex intertwined processes that occur in biological
cells. Among the many others, chromatin dynamics significantly
contributes—by modulating access to genes—to
differential gene expression, and ultimately to determine cell
types. Here, we propose a dynamical model of differentiation
based on a simplified bioinspired methylation mechanism in
Boolean models of GRNs. Preliminary results show that, as
the number of methylated nodes increases, there is a decrease
in attractor number and networks tend to assume dynamical
behaviours typical of ordered ensembles. At the same time,
results show that this mechanism does not affect the possibility
of generating path dependent differentiation: cell types
determined by the specific sequence of methylated genes.
2019
 An improved relevance index method to search important structures in complex systems
[Relazione in Atti di Convegno]
Sani, L.; Bononi, A.; Pecori, R.; Amoretti, M.; Mordonini, M.; Roli, A.; Villani, M.; Cagnoni, S.; Serra, R.
abstract
We present an improvement of a method that aims at detecting important dynamical structures in complex systems, by identifying subsets of elements that show tight and coordinated interactions among themselves, while interplaying much more loosely with the rest of the system. Such subsets are estimated by means of a Relevance Index (RI), which is normalized with respect to a homogeneous system, usually described by independent Gaussian variables, as a reference. The strategy presented herein improves the way the homogeneous system is conceived from a theoretical viewpoint. Firstly, we consider the system components as dependent and with equal pairwise correlations, which implies a nondiagonal correlation matrix of the homogeneous system. Then, we generate the components of the homogeneous system according to a multivariate Bernoulli distribution, by exploiting the NORTA method, which is able to create samples of a desired random vector, given its marginal distributions and its correlation matrix. The proposed improvement on the RI method has been applied to three different case studies, obtaining better results compared with the traditional method based on the homogeneous system with independent Gaussian variables.
2019
 Evolving critical boolean networks
[Relazione in Atti di Convegno]
Magri, S.; Villani, M.; Roli, A.; Serra, R.
abstract
Random Boolean networks are a widely acknowledged model for cell dynamics. Previous studies have shown the possibility of achieving Boolean networks with given characteristics by means of evolutionary techniques. In this work we make a further step towards more biologically plausible models by aiming at evolving networks with a given fraction of active nodes along the attractors, while constraining the evolutionary process to move across critical networks. Results show that this path along criticality does not impede to climb the mount of improbable, yet biologically realistic requirements.
2019
 Preface
[Capitolo/Saggio]
Cagnoni, S.; Mordonini, M.; Pecori, R.; Roli, A.; Villani, M.
abstract
2019
 Sustainable growth and synchronization in protocell models
[Articolo su rivista]
Serra, R.; Villani, M.
abstract
The growth of a population of protocells requires that the two key processes of replication of the protogenetic material and reproduction of the whole protocell take place at the same rate. While in many ODEbased models such synchronization spontaneously develops, this does not happen in the important case of quadratic growth terms. Here we show that spontaneous synchronization can be recovered (i) by requiring that the transmembrane diffusion of precursors takes place at a finite rate, or (ii) by introducing a finite lifetime of the molecular complexes. We then consider reaction networks that grow by the addition of newly synthesized chemicals in a binary polymer model, and analyze their behaviors in growing and dividing protocells, thereby confirming the importance of (i) and (ii) for synchronization. We describe some interesting phenomena (like longterm oscillations of duplication times) and show that the presence of foodgenerated autocatalytic cycles is not sufficient to guarantee synchronization: in the case of cycles with a complex structure, it is often observed that only some subcycles survive and synchronize, while others die out. This shows the importance of truly dynamic models that can uncover effects that cannot be detected by static graph theoretical analyses.
2018
 A comparison between threshold ergodic sets and stochastic simulation of boolean networks for modelling cell differentiation
[Relazione in Atti di Convegno]
Braccini, Michele; Roli, Andrea; Villani, Marco; Serra, Roberto
abstract
Recently a cell differentiation model based on noisy random Boolean networks has been proposed. This mathematical model is able to describe in an elegant way the most relevant features of cell differentiation. Noise plays a key role in this model; the different stages of the differentiation process are emergent dynamical configurations deriving from the control of the intracellular noise level. In this work we compare two approaches to this cell differentiation framework: the first one (already present in the literature) is focused on a network analysis representing the average wandering of the system among its attractors, whereas the second (new) approach takes into consideration the dynamical stories of thousands of individual cells. Results showed that under a particular noise condition the two approaches produce comparable results. Therefore both can be used to model the cell differentiation process in an integrative and complementary manner.
2018
 A relevance index method to infer global properties of biological networks
[Relazione in Atti di Convegno]
Villani, Marco; Sani, Laura; Amoretti, Michele; Vicari, Emilio; Pecori, Riccardo; Mordonini, Monica; Cagnoni, Stefano; Serra, Roberto
abstract
Many complex systems, both natural and artificial, may be represented by networks of interacting nodes. Nevertheless, it is often difficult to find meaningful correspondences between the dynamics expressed by these systems and the topological description of their networks. In contrast, many of these systems may be well described in terms of coordinated behavior of their dynamically relevant parts. In this paper we use the recently proposed Relevance Index approach, based on informationtheoretic measures. Starting from the observation of the dynamical states of any system, the Relevance Index is able to provide information about its organization. Moreover, we show how the application of the proposed approach leads to novel and effective interpretations in the T helper network case study.
2018
 An IntegrationBased Approach to Pattern Clustering and Classification
[Relazione in Atti di Convegno]
Sani, L.; D'Addese, G.; Pecori, R.; Mordonini, M.; Villani, M.; Cagnoni, S.
abstract
Methods based on information theory, such as the Relevance Index (RI), have been employed to study complex systems for their ability to detect significant groups of variables, well integrated among one another and well separated from the others, which provide a functional block description of the system under analysis. The integration (or zI in its standardized form) is a metric that can express the significance of a group of variables for the system under consideration: the higher the zI, the more significant the group. In this paper, we use this metric for an unusual application to a pattern clustering and classification problem. The results show that the centroids of the clusters of patterns identified by the method are effective for distancebased classification algorithms. We compare such a method with other conventional classification approaches to highlight its main features and to address future research towards the refinement of its accuracy and computational efficiency.
2018
 An iterative informationtheoretic approach to the detection of structures in complex systems
[Articolo su rivista]
Villani, Marco; Sani, Laura; Pecori, Riccardo; Amoretti, Michele; Roli, Andrea; Mordonini, Monica; Serra, Roberto; Cagnoni, Stefano
abstract
Systems that exhibit complex behaviours often contain inherent dynamical structures which evolve over time in a coordinated way. In this paper, we present a methodology based on the Relevance Index method aimed at revealing the dynamical structures hidden in complex systems. The method iterates two basic steps: detection of relevant variable sets based on the computation of the Relevance Index, and application of a sieving algorithm, which refines the results. This approach is able to highlight the organization of a complex system into sets of variables, which interact with one another at different hierarchical levels, detected, in turn, in the different iterations of the sieve. The method can be applied directly to systems composed of a small number of variables, whereas it requires the help of a custom metaheuristic in case of systems with larger dimensions. We have evaluated the potential of the method by applying it to three case studies: synthetic data generated by a nonlinear stochastic dynamical system, a smallsized and wellknown system modelling a catalytic reaction, and a larger one, which describes the interactions within a social community, that requires the use of the metaheuristic. The experiments we made to validate the method produced interesting results, effectively uncovering hidden details of the systems to which it was applied.
2018
 Dynamical Criticality in Gene Regulatory Networks
[Articolo su rivista]
Villani, Marco; La Rocca, Luca; Kauffman, Stuart Alan; Serra, Roberto
abstract
A wellknown hypothesis, with farreaching implications, is that biological evolution should preferentially lead to states that are dynamically critical. In previous papers, we showed that a wellknown model of genetic regulatory networks, namely, that of random Boolean networks, allows one to study in depth the relationship between the dynamical regime of a living being's gene network and its response to permanent perturbations. In this paper, we analyze a huge set of new experimental data on single gene knockouts in S. cerevisiae, laying down a statistical framework to determine its dynamical regime. We find that the S. cerevisiae network appears to be slightly ordered, but close to the critical region. Since our analysis relies on dichotomizing continuous data, we carefully consider the issue of an optimal threshold choice.
2018
 Dynamical criticality: overview and open questions
[Articolo su rivista]
Roli, Andrea; Villani, Marco; Filisetti, Alessandro; Serra, Roberto
abstract
Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the socalled criticality hypothesis, which states that systems in a dynamical regime between order and disorder attain the highest level of computational capabilities and achieve an optimal tradeoff between robustness and flexibility. Recent results in cellular and evolutionary biology, neuroscience and computer science have revitalised the interest in the criticality hypothesis, emphasising its role as a viable candidate general law in adaptive complex systems. This paper provides an overview of the works on dynamical criticality that are  to the best of our knowledge  particularly relevant for the criticality hypothesis. The authors review the main contributions concerning dynamics and information processing at the edge of chaos, and illustrate the main achievements in the study of critical dynamics in biological systems. Finally, the authors discuss open questions and propose an agenda for future work.
2018
 Dynamical properties of a geneprotein model
[Relazione in Atti di Convegno]
Sapienza, Davide; Villani, Marco; Serra, Roberto
abstract
A major limitation of the classical random Boolean network model of gene regulatory networks is its synchronous updating, which implies that all the proteins decay at the same rate. Here a model is discussed, where the network is composed of two different sets of nodes, labelled G and P with reference to “genes” and “proteins”. Each gene corresponds to a protein (the one it codes for), while several proteins can simultaneously affect the expression of a gene. Both kinds of nodes take Boolean values. If we look at the genes only, it is like adding some memory terms, so the new state of the gene subnetwork network does no longer depend upon its previous state only. In general, these terms tend to make the dynamics of the network more ordered than that of the corresponding memoryless network. The analysis is focused here mostly on dynamical critical states. It has been shown elsewhere that the usual way of computing the Derrida parameter, starting from purely random initial conditions, can be misleading in strongly nonergodic systems. So here the effects of perturbations on both genes’ and proteins’ levels is analysed, using both the canonical Derrida procedure and an “extended” one. The results are discussed. Moreover, the stability of attractors is also analysed, measured by counting the fraction of perturbations where the system eventually falls back onto the initial attractor.
2018
 Preface
[Relazione in Atti di Convegno]
Pelillo, M.; Poli, I.; Serra, R.; Roli, A.; Slanzi, D.; Villani, M.
abstract
2018
 Simulating populations of protocells with uneven division
[Relazione in Atti di Convegno]
Musa, Martina; Villani, Marco; Serra, Roberto
abstract
Protocells should be similar to presentday biological cells, but much simpler. They are believed to have played a key role in the origin of life, and they may also be the basis of a new technology with tremendous opportunities. In this work we study the effect of uneven division processes on the synchronization of the duplication rates of protocells’ membrane and internal materials.
2017
 A stochastic model of growing and dividing protocells
[Capitolo/Saggio]
Serra, R.; Villani, M.
abstract
In the last two chapters we have shown several interesting results, which will now be brought together in a quite complete (albeit abstract) protocell model. In Chap. 3 we have studied how the presence of genetic memory molecules (GMMs) can affect the growth and fission rate of their lipid container, leading under quite broad assumptions to the important phenomenon of emergent synchronization, i.e. to a condition where protocell fission and duplication of its genetic material take place at the same pace. In that chapter, chemical kinetics has been described with deterministic differential equations (it has also been mentioned that synchronization is somewhat robust even if small fluctuations are considered).
2017
 Automatic design of boolean networks for cell differentiation
[Relazione in Atti di Convegno]
Braccini, Michele; Roli, Andrea; Villani, Marco; Serra, Roberto
abstract
Cell differentiation is the process that denotes a cell type change, typically from a less specialised type to a more specialised one. Recently, a cell differentiation model based on Boolean networks subject to noise has been proposed. This model reproduces the main abstract properties of cell differentiation, such as the attainment of different degrees of differentiation, deterministic and stochastic differentiation, reversibility, induced pluripotency and cell type change. The generic abstract properties of the model have been already shown to match those of the real biological phenomenon. A direct comparison with specific cell differentiation processes and the identification of genetic network features that are linked to specific differentiation traits requires the design of a suitable Boolean network such that its dynamics matches a set of target properties. To the best of our knowledge, the only current method for addressing this problem is a random generate and test procedure. In this work we present an automatic design method for this purpose, based on metaheuristic algorithms. We devised two variants of the method and tested them against random search on typical abstract differentiation trees. Results, although preliminary, show that our technique is far more efficient than both random search and complete enumeration and it is able to find solutions to instances which were not solved by those techniques.
2017
 Conclusions, open questions and perspectives
[Capitolo/Saggio]
Serra, R.; Villani, M.
abstract
In the previous chapters we have discussed some protocell models and we have analysed their behaviour in depth, so now it is time to consider what we have learnt, which questions have been at least partially answered, which questions are still open and which new questions have arisen. In this final chapter we will therefore take the liberty of revisiting and repeating some arguments that have already been dealt with in the previous chapters.
2017
 Dynamical models of protocells and synchronization
[Capitolo/Saggio]
Serra, R.; Villani, M.
abstract
Let us now consider the contributions that a complex systems approach can provide to the research on protocells.
2017
 Dynamical regimes in nonergodic random Boolean networks
[Articolo su rivista]
Villani, Marco; Campioli, Davide; Damiani, Chiara; Roli, Andrea; Filisetti, Alessandro; Serra, Roberto
abstract
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. Random boolean networks not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a theoretical viewpoint, since it is possible to tune their asymptotic behaviour from order to disorder. The usual approach characterizes network families as a whole, either by means of static or dynamic measures. We show here that a more detailed study, based on the properties of system’s attractors, can provide information that makes it possible to predict with higher precision important properties, such as system’s response to gene knockout. A new set of principled measures is introduced, that explains some puzzling behaviours of these networks. These results are not limited to random Boolean network models, but they are general and hold for any discrete model exhibiting similar dynamical characteristics.
2017
 GPUbased parallel search of relevant variable sets in complex systems
[Relazione in Atti di Convegno]
Vicari, Emilio; Amoretti, Michele; Sani, Laura; Mordonini, Monica; Pecori, Riccardo; Roli, Andrea; Villani, Marco; Cagnoni, Stefano; Serra, Roberto
abstract
Various methods have been proposed to identify emergent dynamical structures in complex systems. In this paper, we focus on the Dynamical Cluster Index (DCI), a measure based on information theory which allows one to detect relevant sets, i.e. sets of variables that behave in a coherent and coordinated way while loosely interacting with the rest of the system. The method associates a score to each subset of system variables; therefore, for a thorough analysis of the system, it requires an exhaustive enumeration of all possible subsets. For large systems, the curse of dimensionality makes the problem solvable only using metaheuristics. Even within such approaches, however, DCI computation has to be performed for a huge number of times; thus, an efficient implementation becomes a mandatory requirement. Considering that a candidate relevant set’s DCI can be computed independently of the others, we propose a GPUbased massively parallel implementation of DCI computation. We describe the algorithm’s structure and validate it by assessing the speedup in comparison with a singlethread sequential CPU implementation when analyzing a set of dynamical systems of different sizes.
2017
 Generic properties of dynamical models of protocells
[Capitolo/Saggio]
Serra, R.; Villani, M.
abstract
Models are of great importance for protocell research, not only for the usual reasons why models matter, but also because real protocells are not yet available in the lab. There are indeed some cases where one or a few duplications have been achieved (Hanczyc and Szostak 2004; Luisi et al. 2004; Luisi 2006; Stano et al. 2006; Schrum et al. 2010; Stano and Luisi 2010a) but so far, to the best of our knowledge, a sustained growth of a population of protocells has never been observed.
2017
 Identifying Critical States through the Relevance Index
[Articolo su rivista]
Roli, Andrea; Villani, Marco; Caprari, Riccardo; Serra, Roberto
abstract
The identification of critical states is a major task in complex systems, and the availability of measures to detect such conditions is of utmost importance. In general, criticality refers to the existence of two qualitatively different behaviors that the same system can exhibit, depending on the values of some parameters. In this paper, we show that the relevance index may be effectively used to identify critical states in complex systems. The relevance index was originally developed to identify relevant sets of variables in dynamical systems, but in this paper, we show that it is also able to capture features of criticality. The index is applied to two prominent examples showing slightly different meanings of criticality, namely the Ising model and random Boolean networks. Results show that this index is maximized at critical states and is robust with respect to system size and sampling effort. It can therefore be used to detect criticality.
2017
 Introduction
[Capitolo/Saggio]
Serra, R.; Villani, M.
abstract
Protocells should be similar to presentday biological cells, but somehow simpler (see Rasmussen et al. 2008; Schrum et al. 2010 and further references quoted therein). They are believed to have played a key role in the origin of life, and they may also be the basis of a new technology with tremendous opportunities. So the prefix proto may be interpreted either as indicating ancient times or in the sense of prototype.
2017
 Locating critical regions by the Relevance Index
[Relazione in Atti di Convegno]
Roli, Andrea; Villani, Marco; Serra, Roberto
abstract
The detection of critical states is a task of utmost importance in complex systems; to this aim, measures to identify such conditions are required. In general, the term criticality concerns the existence of two qualitatively different behaviours that a system can exhibit, which depends on some parameter values. In this short communication, we summarise our recent findings on the use of the Relevance Index to identify critical states in complex systems. Although the Relevance Index method was originally developed to identify relevant sets of variables in dynamical systems, we show that it is also able to detect features of criticality. The index is applied to two notable examples showing slightly different meanings of criticality, namely, the Ising model and Random Boolean Networks. Results show that this index is maximised at critical states and is robust with respect to system size and sampling effort.
2017
 Modelling Protocells
[Monografia/Trattato scientifico]
Serra, Roberto; Villani, Marco
abstract
The monograph discusses models of synthetic protocells, which are celllike structures obtained from nonliving matter endowed with some rudimentary kind of metabolism and genetics, but much simpler than biological cells. They should grow and proliferate, generating offsprings that resemble in some way the parent protocells with some variation, so that selection may take place. Sustainable protocell populations have not yet been obtained experimentally and mathematical models are therefore extremely important to address key questions concerning their synthesis and behavior. Different protocell “architectures” have been proposed and highlevel abstract models like those that are presented in this book are particularly relevant to gain a better understanding of the different properites. These models are able to treat all the major dynamical phenomena in a unified framework, so they can be seen as “virtual laboratories” for protocell research. Particular attention is paid to the problem of synchronization of the fission rate of the whole protocell and the duplication rate of its "protogenetic" material, which is shown to be an emergent property that spontaneously develops in successive generations.
The book is of interest for a broad range of scientists working in soft matter physics, chemistry and biology, interested in the role protocells may play on the development of new technologies with medical, environmental and industrial applications as well as scientists interested in the origin of life.
2017
 Models of selfreplication
[Capitolo/Saggio]
Serra, R.; Villani, M.
abstract
A protocell could be schematically described as a selforganized, spatially confined collection of chemical species and chemical reactions, able to support the three main properties of living systems: metabolism, reproduction and inheritance. In living systems, while some chemicals are exclusively dedicated to a single activity, like DNA that is devoted to templatebased replication, it often happens that the same chemical substance can participate (as substrate, product or catalyst) to many different reactions, which in turn can contribute to the different properties mentioned above; moreover the same reaction may be involved in more than one property. The components are not freely fluctuating within the environment, but are spatially confined by membranes in very small containers (cells).
2017
 New paths for the application of DCI in social sciences: Theoretical issues regarding an empirical analysis
[Relazione in Atti di Convegno]
Righi, Riccardo; Roli, Andrea; Russo, Margherita; Serra, Roberto; Villani, Marco
abstract
Starting from the conceptualization of ‘Cluster Index’ (CI), Villani et al. [16, 17] implemented the ‘Dynamic Cluster Index’ (DCI), an algorithm to perform the detection of subsets of agents characterized by patterns of activity that can be considered as integrated over time. DCI methodology makes possible to shift the attention into a new dimension of groups of agents (i.e. communities of agents): the presence of a common function characterizing their actions. In this paper we discuss the implications of the use in the domain of social sciences of this methodology, up to now mainly applied in natural sciences. Developing our considerations thanks to an empirical analysis, we discuss the theoretical implications of its application in such a different field.
2017
 Synchronization in nearmembrane reaction models of protocells
[Relazione in Atti di Convegno]
Calvanese, Giordano; Villani, Marco; Serra, Roberto
abstract
In this paper a new model of growing and dividing protocells is described, whose main features are (i) an autocatalytic set of “genetic memory molecules” (GMMs) whose reactions happen in a thin aqueous phase shell near the membrane and (ii) a lipid container that grows according to the amphiphilic production stimulated by the GMMs. Synchronization occur when the container growth rate is equal to the GMMs selfreplicative one: the behavior of this model is compared with a previous version where reactions occur in the whole internal aqueous volume. Analytical results and simulations has shown that synchronization emerges in both models for the same set of kinetic equations, the main difference being only in the time scale of the process. Moreover the introduction of finite rates in the transmembrane diffusion permits the emergence of synchronization for a significantly wide set of parameters, enough to allow the protocell evolvability (defined as the capability of cumulating novelties, by maintaining the already present capabilities).
2017
 The use of omicsbased approaches in regulatory toxicology: An alternative approach to assess the no observed transcriptional effect level
[Articolo su rivista]
Quercioli, Daniele; Roli, Andrea; Morandi, Elena; Perdichizzi, Stefania; Polacchini, Laura; Rotondo, Francesca; Vaccari, Monica; Villani, Marco; Serra, Roberto; Colacci, Annamaria
abstract
The evaluation of chemical hazard is based on the identification of the quality and the quantity of adverse effects as a consequence of exposure. The adverse effects that do not involve genetic damage are often related to the chemical dose or concentration. The adverse outcome is the consequence of a row of key events, each targeting a different biological trait. The identification of these key events at molecular and cellular level would provide novel biomarkers of exposure and risk. The application of toxicogenomics approaches to experimental models of chemical exposure allows the detection of gene pathways involved in response to low doses of the chemical as an early endpoint of adversity. The use of toxicogenomics would improve the knowledge on the doseresponse relationship, linking the environmental exposure to the effect on the population and allowing a better refinement of the quantitative risk assessment. In this context, the gene modulation data can be used to calculate a No Observed Transcriptional Effect Level (NOTEL).In this paper we present a method for evaluating the NOTEL based on anomaly detection: a classifier is built that discriminates between target class instances, i.e., normal cases, and anomalies, i.e., samples with significant transcriptional effects. The strength of this method is that (i) it can be applied to cases in which few samples are available and the space dimension is high and (ii) it makes use of the complete gene expression profiles.
2016
 Beyond Networks: Search for Relevant Subsets in Complex Systems
[Capitolo/Saggio]
Roli, Andrea; Villani, Marco; Filisetti, Alessandro; Serra, Roberto
abstract
Networks are often used to represent the relations among the variables of a dynamical system. The properties of network topology are usually exploited to understand the organization of the system. Nevertheless, the dynamical organization of a system might considerably differ from its topological one. In this paper, we describe a method to identify “relevant subsets” of variables. The variables belonging to a relevant subset should be strongly integrated and should have a much weaker interaction with the other system variables. Extending previous works on neural networks, an informationtheoretic measure is introduced, i.e., the Dynamical Cluster Index, in order to identify candidate relevant subsets. The method solely relies on observations of the variables’ values in time
2016
 Dynamically critical systems and powerlaw distributions: Avalanches revisited
[Relazione in Atti di Convegno]
Di Stefano, Marina L.; Villani, Marco; LA ROCCA, Luca; Kauffman, Stuart A.; Serra, Roberto
abstract
In this paper we show that a wellknown model of genetic regulatory networks, namely that of Random Boolean Networks (RBNs), allows one to study in depth the relationship between two important properties of complex systems, i.e. dynamical criticality and powerlaw distributions. The study is based upon an analysis of the response of a RBN to permanent perturbations, that may lead to avalanches of changes in activation levels, whose statistical properties are determined by the same parameter that characterizes the dynamical state of the network (ordered, critical or disordered). Under suitable approximations, in the case of large sparse random networks an analytical expression for the probability density of avalanches of different sizes is proposed, and it is shown that for nottoosmall avalanches of critical systems it may be approximated by a power law. In the case of small networks the abovementioned formula does not maintain its validity, because of the phenomenon of selfinterference of avalanches, which is also explored by numerical simulations.
2016
 Efficient search of relevant structures in complex systems
[Relazione in Atti di Convegno]
Sani, Laura; Amoretti, Michele; Vicari, Emilio; Mordonini, Monica; Pecori, Riccardo; Roli, Andrea; Villani, Marco; Cagnoni, Stefano; Serra, Roberto
abstract
In a previous work, Villani et al. introduced a method to identify candidate emergent dynamical structures in complex systems. Such a method detects subsets (clusters) of the system elements which behave in a coherent and coordinated way while loosely interacting with the remainder of the system. Such clusters are assessed in terms of an index that can be associated to each subset, called Dynamical Cluster Index (DCI). When large systems are analyzed, the “curse of dimensionality” makes it impossible to compute the DCI for every possible cluster, even using massively parallel hardware such as GPUs. In this paper, we propose an efficient metaheuristic for searching relevant dynamical structures, which hybridizes an evolutionary algorithm with local search and obtains results comparable to an exhaustive search in a much shorter time. The effectiveness of the method we propose has been evaluated on a set of Boolean models of realworld systems.
2016
 On the dynamics of autocatalytic cycles in protocell models
[Relazione in Atti di Convegno]
Villani, Marco; Filisetti, Alessandro; Nadini, Matthieu; Serra, Roberto
abstract
The emergence of autocatalytic sets of molecules seems to have played an important role in the origin of life, allowing a sustainable systems’ growth and reproduction. Several frameworks have been proposed, one of the most recent and promising being that of RAF (Reflexively AutocatalyticFood generated) sets. As it often happens when topological properties only are taken into account, RAFs are however only potentially able of supporting continuous growth. Dynamics can also play a significant role: it is shown here how dynamical interactions may sometimes lead to unexpected behaviors.
2016
 On the robustness of the detection of relevant sets in complex dynamical systems
[Relazione in Atti di Convegno]
Villani, Marco; Carra, Pietro; Roli, Andrea; Filisetti, Alessandro; Serra, Roberto
abstract
The identification of system’s parts that rule its dynamics and the understanding of its dynamical organisation is a paramount objective in the analysis of complex systems. In previous work we have proposed the Dynamical Cluster Index method, which is based on informationtheoretical measures. This method makes it possible to identify the components of a complex system that are relevant for its dynamics as well as their relation in terms of information flow. Complex systems’ organisation is often characterised by intertwined components. The detection of such dynamical structures is a prerequisite for inferring the hierarchical organisation of the system. The method relies on a ranking based on a statistical index, which depends on a reference system (the homogeneous system) generated according to a parametrised sampling procedure. In this paper we address the issue of assessing the robustness of the method against the homogeneous system generation model. The results show that the method is robust and can be reliably applied to the analysis of data from complex system dynamics in general settings, without requiring particular hypotheses.
2015
 Dynamical Properties of Artificially Evolved Boolean Network Robots
[Relazione in Atti di Convegno]
Roli, Andrea; Villani, Marco; Serra, Roberto; Benedettini, Stefano; Pinciroli, Carlo; Birattari, Mauro
abstract
In this work we investigate the dynamical properties of the Boolean networks (BN) that control a robot performing a composite task. Initially, the robot must perform phototaxis, i.e. move towards a light source located in the environment; upon perceiving a sharp sound, the robot must switch to antiphototaxis, i.e. move away from the light source. The network controlling the robot is subject to an adaptive walk and the process is subdivided in two sequential phases: in the first phase, the learning feedback is an evaluation of the robot’s performance in achieving only phototaxis; in the second phase, the learning feedback is composed of a performance measure accounting for both phototaxis and antiphototaxis. In this way, it is possible to study the properties of the evolution of the robot when its behaviour is adapted to a new operational requirement. We analyse the trajectories followed by the BNs in the state space and find that the best performing BNs (i.e. those able to maintaining the previous learned behaviour while adapting to the new task) are characterised by generalisation capabilities and the emergence of simple behaviours that are dynamically combined to attain the global task. In addition, we also observe a further remarkable property: the complexity of the best performing BNs increases during evolution. This result may provide useful indications for improving the automatic design of robot controllers and it may also help shed light on the relation and interplay among robustness, evolvability and complexity in evolving systems.
2015
 Exploring the organisation of complex systems through the dynamical interactions among their relevant subsets
[Relazione in Atti di Convegno]
Filisetti, Alessandro; Villani, Marco; Roli, Andrea; Fiorucci, Marco; Serra, Roberto
abstract
Complex systems often show forms of organisation where a clearcut hierarchy of levels with a welldefined direction of information flow cannot be found. In this paper we propose an informationtheoretic method aimed at identifying the dynamically relevant parts of a system along with their relationships, interpreting in such a way the system’s dynamical organisation. The analysis is quite general and can be applied to many dynamical systems. We show here its application to two relevant biological examples, the case of mammalian cell cycle network and of Mitogen Activated Protein Kinase (MAPK) cascade. The result of our analysis shows that the elements of the mammalian cell cycle network act as a single compact group, whereas the MAPK system can be decomposed into two dynamically distinct parts, with asymmetric information flows
2015
 The Search for Candidate Relevant Subsets of Variables in Complex Systems
[Articolo su rivista]
Villani, Marco; Roli, Andrea; Filisetti, Alessandro; Fiorucci, Marco; Serra, Roberto; Poli, Irene
abstract
We describe a method to identify relevant subsets of variables, useful to understand the organization of a dynamical system. The variables belonging to a relevant subset should have a strong integration with the other variables of the same relevant subset, and a much weaker interaction with the other system variables. On this basis, extending previous work on neural networks, an informationtheoretic measure, the dynamical cluster index, is
introduced in order to identify good candidate relevant subsets. The method does not require any previous knowledge of the relationships
among the system variables, but relies on observations of their values over time. We show its usefulness in several application domains,
including: (i) random Boolean networks, where the whole network is made of different subnetworks with different topological relationships (independent or interacting subnetworks); (ii) leaderfollower dynamics, subject to noise and fluctuations; (iii) catalytic reaction networks in a flow reactor; (iv) the MAPK signaling pathway in eukaryotes. The validity of the method has been tested in cases where the data are generated by a known dynamical model and the dynamical cluster index is applied in order to uncover significant aspects of its organization; however, it is important that it can also be applied to time series coming from field data without any reference to a model. Given that it is based on relative frequencies of sets of
values, the method could be applied also to cases where the data are not ordered in time. Several indications to improve the scope and effectiveness of the dynamical cluster index to analyze the organization of complex systems are finally given.
2014
 A stochastic model of catalytic reaction networks in protocells
[Articolo su rivista]
Serra, Roberto; Filisetti, Alessandro; Villani, Marco; Graudenzi, Alex; Damiani, Chiara; Panini, Tommaso
abstract
Protocells are supposed to have played a key role in the selforganizing processes leading to the emergence of life. Existing models either (i) describe protocell architecture and dynamics, given the existence of sets of collectively selfreplicating molecules for granted, or (ii) describe the emergence of the aforementioned sets from an ensemble of random molecules in a simple experimental setting (e.g. a closed system or a steadystate flow reactor) that does not properly describe a protocell. In this paper we present a model that goes beyond these limitations by describing the dynamics of sets of replicating molecules within a lipid vesicle. We adopt the simplest possible protocell architecture, by considering a semipermeable membrane that selects the molecular types that are allowed to enter or exit the protocell and by assuming that the reactions take place in the aqueous phase in the internal compartment. As a first approximation, we ignore the protocell growth and division dynamics. The behavior of catalytic reaction networks is then simulated by means of a stochastic model that accounts for the creation and the extinction of species and reactions. While this is not yet an exhaustive protocell model, it already provides clues regarding some processes that are relevant for understanding the conditions that can enable a population of protocells to undergo evolution and selection.
2014
 Attractors Perturbations in Biological Modelling: Avalanches and Cellular Differentiation
[Capitolo/Saggio]
Villani, Marco; Serra, Roberto
abstract
We describe here and discuss in detail the model of random Boolean networks (RBNs). Although these models have been widely studied, they still present some unexpected mathematical features, and we discuss in particular their stability properties, introducing and commenting a new measure (attractor sensitivity) that seems particularly relevant for their application to the dynamics of gene regulatory networks. We also review some results that show that RBNs can properly account for data on perturbations induced by gene knockout in real organisms. Moreover, we show that this comparison between model and data also sheds light on the important hypothesis that living beings tend to live in, or close to, critical states. Last but not least, we show that adding noise to RBNs can lead to a nice model of cell differentiation
2014
 Automatic Design of Boolean Networks for Modelling Cell Differentiation
[Capitolo/Saggio]
Stefano, Benedettini; Andrea, Roli; Serra, Roberto; Villani, Marco
abstract
A mathematical model based on Random Boolean Networks (RBNs) has been recently proposed to describe the main features of cell differentiation. The model captures in a unique framework all the main phenomena involved in cell differentiation and can be subject to experimental testing. A prominent role in the model is played by cellular noise, which somehow controls the cell ontogenetic process from the stem, totipotent state to the mature, completely differentiated one. Noise is high in stem cells and decreases while the cell undergoes the differentiation process. A limitation of the current mathematical model is that RBNs, as an ensemble, are not endowed with the property of showing a smooth relation between noise level and the differentiation stages of cells. In this work, we show that it is possible to generate an ensemble of Boolean networks (BNs) that can satisfy such a requirement, while keeping the other main relevant statistical features of classical RBNs. This ensemble is designed by means of an optimisation process, in which a stochastic local search (SLS) optimises an objective function which accounts for the requirements the network ensemble has to fulfil.
2014
 Evolution, Complexity and Artificial Life
[Curatela]
Stefano, Cagnoni; Marco, Mirolli; Villani, Marco
abstract
Evolution and complexity characterize both biological and artificial life by direct modeling of biological processes and the creation of populations of interacting entities from which complex behaviors can emerge and evolve.
This edited book includes invited chapters from leading scientists in the fields of artificial life, complex systems, and evolutionary computing. The contributions identify both fundamental theoretical issues and stateoftheart realworld applications. The book is intended for researchers and graduate students in the related domains.
2014
 Growth and division in a dynamic protocell model
[Articolo su rivista]
Villani, Marco; Filisetti, Alessandro; Graudenzi, Alex; Damiani, Chiara; Carletti, Timoteo; Serra, Roberto
abstract
In this paper a new model of growing and dividing protocells is described, whose main features are (i) a lipid container that grows according to the composition of the molecular milieu (ii) a set of "genetic memory molecules" (GMMs) that undergo catalytic reactions in the internal aqueous phase and (iii) a set of stochastic kinetic equations for the GMMs. The mass exchange between the external environment and the internal phase is described by simulating a semipermeable membrane and a flow driven by the differences in chemical potentials, thereby avoiding to resort to sometimes misleading simplifications, e.g., that of a flow reactor. Under simple assumptions, it is shown that synchronization takes place between the rate of replication of the GMMs and that of the container, provided that the set of reactions hosts a socalled RAF (Reflexive Autocatalytic, Foodgenerated) set whose influence on synchronization is hereafter discussed. It is also shown that a slight modification of the basic model that takes into account a ratelimiting term, makes possible the growth of novelties, allowing in such a way suitable evolution: so the model represents an effective basis for understanding the main abstract properties of populations of protocells.
2014
 Identifying emergent dynamical structures in network models
[Relazione in Atti di Convegno]
Villani, Marco; Stefano, Benedettini; Andrea, Roli; Lane, David Avra; Irene, Poli; Serra, Roberto
abstract
The identification of emergent structures in dynamical systems is a major challenge in complex systems science. In particular, the formation of intermediatelevel dynamical structures is of particular interest for what concerns biological as well as artificial network models. In this work, we present a new technique aimed at identifying clusters of nodes in a network that behave in a coherent and coordinated way and that loosely interact with the remainder of the system. This method is based on an extension of a measure introduced for detecting clusters in biological neural networks. Even if our results are still preliminary, we have evidence for showing that our approach is able to identify these “emerging things” in some artificial network models and that it is way more powerful than usual measures based on statistical correlation. This method will make it possible to identify mesolevel dynamical structures in network models in general, from biological to social networks
2014
 Investigating the Role of Network Topology and Dynamical Regimes on the Dynamics of a Cell Differentiation Model
[Relazione in Atti di Convegno]
Graudenzi, Alex; Damiani, Chiara; Paroni, Andrea; Filisetti, Alessandro; Villani, Marco; Serra, Roberto; Antoniotti, Marco
abstract
The characterization of the generic properties underlying the complex interplay
ruling cell differentiation is one of the goals of modern biology. To this end, we
rely on a powerful and general dynamical model of cell differentiation, which defines differentiation
hierarchies on the basis of the stability of gene activation patterns against
biological noise.
In particular, in this work we investigate the role of the topology (i.e. scalefree or random)
and of the dynamical regime (i.e. ordered, critical or disordered) of gene regulatory
networks on the model dynamics. Two real lineage commitment trees, i.e. intestinal crypts
and hematopoietic cells, are compared with the hierarchies emerging from the dynamics
of ensembles of randomly simulated networks.
Briefly, critical networks with random topology seem to display a wider range of possible
behaviours as compared to the others, hence suggesting an intrinsic dynamical heterogeneity
that may be fundamental in defining different differentiation trees. Conversely,
scalefree networks show a generally more ordered dynamics, which limit the overall
variability, yet containing the effect of possible genomic perturbations. Interestingly, a
considerable number of networks across all types show emergent trees that are biologically
plausible, suggesting that a relatively wide portion of the networks space may be
suitable, without the need for a fine tuning of the parameters
2014
 Le reti intorno a noi
[Articolo su rivista]
Villani, Marco
abstract
Gran parte dei sistemi naturali – e del resto numerosi sistemi artificiali – sono composti da molte o moltissime parti interagenti fra di loro in modo non lineare (cioè in modo non sempre proporzionato agli stimoli ricevuti). Mentre la scienza negli ultimi secoli ha compiuto notevolissimi progressi nella ricerca della causa delle cose analizzando le singole parti, solo negli ultimi decenni ha realmente iniziato ad interrogarsi su come le medesime parti possono essere collegate per realizzare sistemi collettivi anche molto differenti fra di loro. E solo negli ultimi anni gli scienziati  di molti campi diversi  si sono realmente resi conto di quanto differenti possono essere i modi di mettere insieme le cose per generare un’incredibile varietà di comportamenti: non è solo la “vecchia” diatriba fra due diversi modi di interpretare i sistemi (spiegandoli cioè in funzione delle proprietà delle singole parti, od in funzione dei collegamenti che le parti hanno fra di loro), ma è la constatazione ovvia, ma a volte anche abbastanza sorpresa, di come entrambi gli approcci siano due aspetti della medesima realtà. La rappresentazione dei sistemi tramite reti (insiemi di oggetti collegati fra di loro) soffre di numerosi limiti, ma un suo abile utilizzo può servire a mostrare gli inattesi collegamenti fra la Firenze dei Medici, alcuni sistemi di potere attuali e le line di trasporto aeree, fra comunità di delfini e club sportivi, fra la diffusione del virus dell’HIV e l’attuale strategia di difesa dai “virus” software. A causa della sua intima struttura la stessa “rete democratica” per antonomasia (il WWW) offre enormi zone inaccessibili ai motori di ricerca web, sebbene lo scopo di ogni autore di pagina web sia quella di essere visitato. Il tema sotterraneo dell’articolo è quindi il modo in cui i sistemi naturali ed artificiali processano e diffondono l’informazione, e come tali processi influiscono profondamente la dinamica del sistema stesso: allo scopo verranno presentate alcune misure di rete e le differenze essenziali fra alcune topologie (particolari modalità di disposizione dei collegamenti). Nell’articolo verranno anche accennati i limiti della rappresentazione dei sistemi in forma di rete ed i tentativi attuali di superarla, così come verrà introdotto il tema di una reale rappresentazione dinamica dei sistemi: solo cenni, perché si tratta di un problema tuttora irrisolto. La strada della comprensione dei sistemi complessi (che potrebbe avere come motto il titolo del famoso articolo di Anderson “More is different”) è ancora – eccitantemente  in salita.
2014
 On RAF Sets and Autocatalytic Cycles in Random Reaction Networks
[Relazione in Atti di Convegno]
Filisetti, Alessandro; Villani, Marco; Damiani, Chiara; Graudenzi, Alex; Roli, Andrea; Hordijk, Wim; Serra, Roberto
abstract
The emergence of autocatalytic sets of molecules seems to
have played an important role in the origin of life context. Although the
possibility to reproduce this emergence in laboratory has received considerable
attention, this is still far from being achieved.
In order to unravel some key properties enabling the emergence of structures
potentially able to sustain their own existence and growth, in this
work we investigate the probability to observe them in ensembles of
random catalytic reaction networks characterized by different structural
properties.
From the point of view of network topology, an autocatalytic set have
been defined either in term of strongly connected components (SCCs) or
as re
exively autocatalytic and foodgenerated sets (RAFs).
We observe that the average level of catalysis differently affects the probability
to observe a SCC or a RAF, highlighting the existence of a region
where the former can be observed, whereas the latter cannot. This parameter
also affects the composition of the RAF, which can be further
characterized into linear structures, autocatalysis or SCCs.
Interestingly, we show that the different network topology (uniform as
opposed to powerlaw catalysis systems) does not have a significantly divergent
impact on SCCs and RAFs appearance, whereas the proportion
between cleavages and condensations seems instead to play a role.
A major factor that limits the probability of RAF appearance and that
may explain some of the diffculties encountered in laboratory seems to
be the presence of molecules which can accumulate without being substrate
or catalyst of any reaction.
2014
 On Some Properties of Information Theoretical Measures for the Study of Complex Systems
[Relazione in Atti di Convegno]
Filisetti, Alessandro; Villani, Marco; Roli, Andrea; Fiorucci, Marco; Poli, Irene; Serra, Roberto
abstract
The identification of emergent structures in dynamical sys
tems is a major challenge in complex systems science. In particular, the
formation of intermediatelevel dynamical structures is of particular in
terest for what concerns biological as well as artificial systems. In this
work, we present a set of measures aimed at identifying groups of ele
ments that behave in a coherent and coordinated way and that loosely
interact with the rest of the system (the socalled \relevant sets"). These
measures are based on Shannon entropy, and they are an extension of a
measure introduced for detecting clusters in biological neural networks.
Even if our results are still preliminary, we have evidence for showing
that our approach is able to identify and partially characterise the rele
vant sets in some artificial systems, and that this way is more powerful
than usual measures based on statistical correlation. In this work, the
two measures that contribute to the cluster index, previously adopted in
the analysis of neural networks, i.e. integration and mutual information,
are analysed separately in order to enhance the overall performance of
the socalled dynamical cluster index. Although this latter variable al
ready provides useful information about highly integrated subsystems,
the analysis of the different parts of the index are extremely useful to
better characterise the nature of the subsystems.
2014
 Preface
[Capitolo/Saggio]
Cagnoni, S.; Mirolli, M.; Villani, M.
abstract
2013
 A model of protocell based on the introduction of a semipermeable membrane in a stochastic model of catalytic reaction networks
[Abstract in Rivista]
Serra, Roberto; Alessandro, Filisetti; Alex, Graudenzi; Chiara, Damiani; Villani, Marco
abstract
The theoretical characterization of the selforganizing molecular structures emerging from ensembles of distinct interacting chemicals turns to be very important in revealing those dynamics that led to the transition from the nonliving to the living matter as well as in the design of artificial protocells.
In this work we aim at studying the role of a semipermeable membrane, i.e. a very simple protocell description, in the dynamics of a stochastic model describing randomly generated catalytic reaction sets (CRSs) of molecules
2013
 Dynamical regimes and learning properties of evolved Boolean networks
[Articolo su rivista]
Stefano, Benedettini; Villani, Marco; Andrea, Roli; Serra, Roberto; Mattia, Manfroni; Antonio, Gagliardi; Carlo, Pinciroli; Mauro, Birattari
abstract
Boolean networks (BNs) have been mainly considered as genetic regulatory network modelsand are the subject of notable works in complex systems biology literature. Nevertheless, in spite oftheir similarities with neural networks, their potential as learning systems has not yet been fullyinvestigated and exploited.In this work, we show that by employing metaheuristic methods we can train BNs to deal with to twonotable tasks, namely, the problem of controlling the BN's trajectory to match a set of requirementsand the Density Classification Problem. These tasks represent two important categories of problems inmachine learning. The former is an example of the problems in which a dynamical system has to bedesigned such that its dynamics satisfies given requirements. The latter one is a representative task inclassification.We also analyse the performance of the optimisation techniques as a function of the characteristics ofthe networks and the objective function and we show that the learning process could influence and beinfluenced by the BNs' dynamical condition.
2013
 Emergent properties of gene regulatory networks  models and data
[Capitolo/Saggio]
Serra, Roberto; Villani, Marco
abstract
We emphasize here the importance of generic models of biological systems that aim at describing the features that are common to a wide class of systems, instead of studying in detail a specific subsystem in a specific cell type or organism. Among generic models of gene regulatory networks, Random Boolean networks (RBNs) are reviewed in depth, and it is shown that they can accurately describe some important experimental data, in particular the statistical properties of the perturbations of gene expression levels induced by the knockout of a single gene. It is also shown that this kind of study may shed light on a candidate general dynamical property of biological systems. Several biologically plausible modifications of the original model are reviewed and discussed, and it is also show how RBNs can be applied to describe cell differentiation
2013
 Exaptation in innovation processes: theory and models
[Capitolo/Saggio]
Bonifati, Giovanni; Villani, Marco
abstract
In this chapter we present a contribution to a theory of exaptation phenomena in innovation processes. In section 1 we define exaptations and discuss some related conceptual issues. In order to contribute to the development of an exaptationbased view in the economics of innovation, in the remaining sections we propose a theoretical framework and simulation models for the study of the processes of exaptation. In section 2, we relate exaptation phenomena at different levels of organization and provide a framework for their analysis. In section 3 we argue that in innovation theory an exaptationbased perspective can be considered, at least potentially, an alternative to the “adaptation through selection” perspective. In sections 46 we represent and clarify the theory presented above, by means of two agentbased simulation models. In the first model, exaptation occurs through the exchange of artifacts and information between two agents. In the second model many agents are producers and consumers of thousands of artifacts and are able to introduce innovations. The latter model is explicitly designed to simulate the emergence of recurrent patterns of interactions, and their changes, as consequence of locally introduced innovations. Section 7 concludes the chapter.
2013
 Identification of Dynamical Structures in Artificial Brains: An Analysis of Boolean Network Controlled Robots
[Relazione in Atti di Convegno]
Andrea, Roli; Villani, Marco; Serra, Roberto; Lorenzo, Garattoni; Carlo, Pinciroli; Mauro, Birattari
abstract
Automatic techniques for the design of artificial computational systems, such as control programs for robots, are currently achieving increasing attention within the AI community. A prominent case is the design of artificial neural network systems by means of search techniques, such as genetic algorithms. Frequently, the search calibrates not only the system parameters, but also its structure. This procedure has the advantage of reducing the bias introduced by the designer and makes it possible to explore new, innovative solutions. The drawback, though, is that the analysis of the resulting system might be extremely difficult and limited to few coarsegrained characteristics. In this paper, we consider the case of robots controlled by Boolean networks that are automatically designed by means of a training process based on local search. We propose to analyse these systems by a method that detects mesolevel dynamical structures. These structures are emerging patterns composed of elements that behave in a coherent way and loosely interact with the rest of the system. In general, this method can be used to detect functional clusters and emerging structures in nonlinear discrete dynamical systems. It is based on an extension of the notion of cluster index, which has been previously proposed by Edelman and Tononi to analyse biological neural systems. Our results show that our approach makes it possible to identify the computational core of a Boolean network which controls a robot
2013
 Mechanism for the formation of density gradients through semipermeable membranes
[Articolo su rivista]
Serra, Roberto; Villani, Marco
abstract
We describe and theoretically analyze here a phenomenon which can take place in a system with two different
compartments, each containing the same chemicals, which undergo reactions on the surface of both sides of the
membrane which separates the two compartments, in the case where the membrane permeabilities to the various
chemicals are different and diffusion is fast. There are two main reasons of interest for this kind of system.
First, if the overall system is isolated, starting from the case where the initial concentrations of the chemicals are
the same in the two phases, one observes the formation of a transient concentration difference. This difference
eventually vanishes, although it might last for a long time, depending upon the value of the relevant parameters.
The second reason of interest is that, in the case of an open system, one can achieve a steadystate value of the
concentration of some chemicals in the smaller compartment which is higher than that in the external one. These
results may prove important, inter alia, to understand the behavior of lipid vesicles in water, a topic which is
important for studies on the origin of life as well as for possible future applications.
2013
 On the dynamical properties of a model of cell differentiation
[Articolo su rivista]
Villani, Marco; Serra, Roberto
abstract
One of the major challenges in complex systems biology is that of providing a general theoretical framework to
describe the phenomena involved in cell differentiation, i.e., the process whereby stem cells, which can develop
into different types, become progressively more specialized. The aim of this study is to briefly review a dynamical
model of cell differentiation which is able to cover a broad spectrum of experimentally observed phenomena and
to present some novel results.
2013
 Recent developments in research on catalytic reaction networks
[Relazione in Atti di Convegno]
Chiara, Damiani; Alessandro, Filisetti; Alex, Graudenzi; Villani, Marco; Serra, Roberto
abstract
Over the last years, analyses performed on a stochastic model of catalytic reaction networks have provided some indications about the reasons why wetlab experiments hardly ever comply with the phase transition typically predicted by theoretical models with regard to the emergence of collectively selfreplicating sets of molecule (also defined as autocatalytic sets, ACSs), a phenomenon that is often observed in nature and that is supposed to have played a major role in the emergence of the primitive
forms of life.
The model at issue has allowed to reveal that the emerging ACSs are characterized by a general dynamical fragility, which might explain the difficulty to observe them in wetlab experiments. In this work, the main results of the various analyses are reviewed, with particular regard to the
factors able to affect the generic properties of catalytic reactions networks, for what concerns not only the probability of ACSs to be observed, but also the overall activity of the system, in terms of
production of new species, reactions and matter.
2013
 The detection of intermediatelevel emergent structures and patterns
[Relazione in Atti di Convegno]
Villani, Marco; A., Filisetti; S., Benedettini; A., Roli; Lane, David Avra; Serra, Roberto
abstract
Artificial life is largely concerned with systems that exhibit
different emergent phenomena; yet, the identification of
emergent structures is frequently a difficult challenge. In this
paper we introduced a system to identify candidate emergent
mesolevel dynamical structures in dynamical networks. This
method is based on an extension of a measure introduced for
detecting clusters in biological neural networks; its main
novelty in comparison to previous application of similar
measures is that we used it to consider truly dynamical
networks, and not only fluctuations around stable asymptotic
states. The identified structures are clusters of elements that
behave in a coherent and coordinated way and that loosely
interact with the remainder of the system. We have evidence
that our approach is able to identify these “emerging things”
in some artificial network models and in more complex data
coming from catalytic reaction networks and biological gene
regulatory systems (A.thaliana). We think that this system
could suggest interesting new ways in dealing with artificial
and biological systems.
2013
 The role of backward reactions in a stochastic model of catalytic reaction networks
[Relazione in Atti di Convegno]
Alessandro, Filisetti; Alex, Graudenzi; Chiara, Damiani; Villani, Marco; Serra, Roberto
abstract
We investigate the role of backward reactions in a stochastic model of catalytic reaction network, with specific regard to the influence on the emergence of autocatalytic sets (ACSs), which are supposed to be one of the prerequisites in the transition between nonliving to living matter.
In particular, we analyse the impact that a variation in the kinetic rates of forward and backward reactions may have on the overall dynamics.
Significant effects are indeed observed, provided that the intensity of backward reactions is sufficiently high. In spite of an invariant activity of the system in terms of production of new species, as backward reactions are intensified, the emergence of ACSs becomes more likely and an increase in their number, as well as in the proportion of species belonging to them, is observed. Furthermore, ACSs appear to be more robust to fluctuations than in the usual settings with no backward reaction.
This outcome may rely not only on the higher average connectivity of the reaction graph, but also on the distinguishing property of backward reactions of recreating the substrates of the corresponding forward reactions.
2012
 A stochastic model of autocatalytic reaction networks
[Articolo su rivista]
Alessandro, Filisetti; Alex, Graudenzi; Serra, Roberto; Villani, Marco; Rudolf M., Füchslin; Norman, Packard; Stuart A., Kauffman; Irene, Poli
abstract
Autocatalytic cycles are rather widespread in nature and in several theoretical models of catalytic reaction networks their emergence is hypothesized to be inevitable when the network is or becomes sufficiently complex. Nevertheless, the emergence of autocatalytic cycles has been never observed in wet laboratory experiments. Here, we present a novel model of catalytic reaction networks with the explicit goal of filling the gap between theoretical predictions and experimental findings. The model is based on previous study of Kauffman, with new features in the introduction of a stochastic algorithm to describe the dynamics and in the possibility to increase the number of elements and reactions according to the dynamical evolution of the system. Furthermore, the introduction of a temporal threshold allows the detection of cycles even in our context of a stochastic model with asynchronous update. In this study, we describe the model and present results concerning the effect on the overall dynamics of varying (a) the average residence time of the elements in the reactor, (b) both the composition of the firing disk and the concentration of the molecules belonging to it, (c) the composition of the incoming flux.
2012
 NoiseInduced Emergent Hierarchies in a CA Model
[Relazione in Atti di Convegno]
Villani, Marco; Serra, Roberto; Stefano, Benedettini; Andrea, Roli; Lane, David Avra
abstract
This paper introduces the notion of noiseinduced emergent
hierarchies and analyses the influence of the topology of the underlying network on these hierarchies. By developing upon a previous model of cell differentiation based on noisy random Boolean networks, we show that the adoption of a regular topology such that of cellular automata can lead to interesting effects, the most remarkable one being that, ceteris paribus, the resulting hierarchies have a larger number of levels and could
therefore describe more “structured” complex systems.
2012
 WIVACE 2012  Workshop Italiano di Vita Artificiale e Computazione Evolutiva
[Esposizione]
Stefano, Cagnoni; Marco, Mirolli; Villani, Marco
abstract
WIVACE 2012 offre agli studiosi di Calcolo Evolutivo, Vita Artificiale e Sistemi Complessi l’occasione di presentare i propri risultati in un’ottica di collaborazione e confronto, al fine di condividere le proprie conoscenze in un approccio multidisciplinare allo studio e alla modellazione di processi biologici naturali e artificiali. Il workshop comprenderà sessioni orali, una sessione di poster, relazioni invitate e una tavola rotonda.
2011
 A Dynamical Model of Cell Differentiation
[Relazione in Atti di Convegno]
Villani, Marco; A., Barbieri; Serra, Roberto
abstract
One of the major challenges in complex systems biologyis that of providing a general theoretical framework todescribe the phenomena involved in cell differentiation,i.e. the process whereby stem cells, which can developinto different types, become progressively more specialized.The aim of this work is that of describing a dynamicalmodel of cell differentiation which is able to cover abroad spectrum of experimentally observed phenomena
2011
 A dynamical model of genetic networks for cell differentiation
[Articolo su rivista]
Villani, Marco; Barbieri, Alessia; Serra, Roberto
abstract
A mathematical model is proposed which is able to describe the most important features of cell diﬀer entiation, without requiring speciﬁc detailed assumptions concerning the interactions which drive the phenomenon. On the contrary, cell diﬀerentiation is described here as an emergent property of a generic model of the underlying gene regulatory network, and it can therefore be applied to a variety of diﬀerent organisms. The model points to a peculiar role of cellular noise in diﬀerentiation and leads to non trivial predictions which could be sub ject to experimental testing. Moreover, a single model proves able to describe several diﬀerent phenomena observed in various diﬀerentiation processes.
2011
 A stochastic model of the emergence of autocatalytic cycles
[Articolo su rivista]
Alessandro, Filisetti; Alex, Graudenzi; Serra, Roberto; Villani, Marco; Davide De, Lucrezia; Rudolf M., Füchslin; Stuart A., Kauffman; Norman, Packard; Irene, Poli
abstract
Autocatalytic cycles are rather common in biological systems and they might have played a major role in the transition from nonliving to living systems. Several theoretical models have been proposed to address the experimentalists during the investigation of this issue and most of them describe a phase transition depending upon the level of heterogeneity of the chemical soup. Nevertheless, it is well known that reproducing the emergence of autocatalytic sets in wet laboratories is a hard task. Understanding the rationale at the basis of such a mismatch between theoretical predictions and experimental observations is therefore of fundamental importance.We here introduce a novel stochastic model of catalytic reaction networks, in order to investigate the emergence of autocatalytic cycles, sensibly considering the importance of noise, of smallnumber effects and the possible growth of the number of different elements in the system.Furthermore, the introduction of a temporal threshold that defines how long a specific reaction is kept in the reaction graph allows to univocally define cycles also within an asynchronous framework.The foremost analyses have been focused on the study of the variation of the composition of the incoming flux. It was possible to show that the activity of the system is enhanced, with particular regard to the emergence of autocatalytic sets, if a larger number of different elements is present in the incoming flux, while the specific length of the species seems to entail minor effects on the overall dynamics.
2011
 Analysis of attractor distances in random boolean networks
[Relazione in Atti di Convegno]
Roli, A.; Benedettini, S.; Serra, Roberto; Villani, Marco
abstract
We study the properties of the distance between attractors in RandomBoolean Networks, a prominent model of genetic regulatory networks. We definethree distance measures, upon which attractor distance matrices are constructed andtheir main statistic parameters are computed. The experimental analysis shows thatordered networks have a very clustered set of attractors, while chaotic networks’ attractorsare scattered; critical networks show, instead, a pattern with characteristicsof both ordered and chaotic networks.
2011
 Cell differentiation in noisy random boolean networks.
[Relazione in Atti di Convegno]
Barbieri, A.; Villani, Marco; Serra, Roberto; Kauffman, S. A.; Colacci,
abstract
The dynamics of genetic regulatory networks are often affected bystochastic noise, due to the small number of molecules involved in some reactions.The role of these fluctuations is analyzed in a discrete model of gene regulatorynetworks, i.e. that of noisy random Boolean networks. By relating the asymptoticstates of the noisy system to the different cell types, we show how the main featuresof the important process of cell differentiation can be described by assuming thatthe noise level changes as differentiation proceeds. Differentiation is seen as a seriesof transitions from an asymptotic state in which the system can wander amongmany states under the action of noise to other asymptotic states in which the systemcan reach fewer and fewer states. This model easily describes the fact that multipotentcells can stochastically differentiate along various routes.We show here thatthe process can also be controlled (as it happens in the embryo growth) so that it ispossible to determine the final fully differentiated state of the cell. This is achievedby forcing some genes, which are called here "swithces", to take constant values,in a way which mimicks the influence of external signals, and by simoultaneouslyvarying the noise level in the cell
2011
 Cellcell interaction and diversity of emergent behaviours
[Articolo su rivista]
Damiani, Chiara; Serra, Roberto; Villani, Marco; S. A., Kauffman; A., Colacci
abstract
Despite myriads of possible gene expression proﬁles, cells tend to be found a in a conﬁned number of expression patterns. The dynamics of Boolean models of gene regulatory networks has proven to be a likely candidate for the description of such selforganization phenomena. Since cells do not leave in iso lation, but they constantly shape their functions in order to adapt to signals from other cells, this raises the question of whether the cooperation among cells en tails en expansion or a reduction of their possible steady states. Multi Random Boolean Networks (MRBNs) are here introduced as a model for the interaction among cells suitable for the investigation of some generic properties regarding the inﬂuence of communication on the diversity of cell behaviours. In spite of its simplicity, the model exhibits a not obvious phenomenon according to which a moderate exchange of products among adjacent cells would foster the spectra of their possible behaviours, which on the other hand would be more similar to one another. On the contrary, a more invasive coupling would lead cells towards homogeneity.
2011
 Conditions for long lasting sustainable innovation in an agentbased model
[Relazione in Atti di Convegno]
Ansaloni, L.; Villani, Marco; Serra, Roberto; Lane, David Avra
abstract
contexts: in particular, a key problem is that of understanding its origins. Moreover, scientists are not able to evaluate the sustainability of innovation processes, and it is difficult to discover what sort of conditions might lead to their crisis and even collapse. In this paper we present a model where agents are able to create new artifacts and can develop and enact strategies able to sustain innovation for very long periods. We discuss some results and make observations useful for understanding the processes and the strategies that sustain the growth of diversity in social and technological organizations.
2011
 Dynamical properties of a Boolean model of gene regulatory network with memory
[Articolo su rivista]
Graudenzi, G.; Serra, Roberto; Villani, Marco; Damiani, C.; Colacci, A.; Kauffman, S. A.
abstract
Classical random Boolean networks (RBN) are not well suited to describe experimental data from timecourse microarray, mainly because of the strict assumptions about the synchronicity of the regulatory mechanisms. In order to overcome this setback, a generalization of the RBN model is described and analyzed. Gene products (e.g., regulatory proteins) are introduced, with each one characterized by a specific decay time, thereby introducing a form of memory in the system. The dynamics of these networks is analyzed, and it is shown that the distribution of the decay times has a strong effect that can be adequately described and understood. The implications for the dynamical criticality of the networks are also discussed.
2011
 Dynamical stability in random Boolean Networks
[Relazione in Atti di Convegno]
Davide, Campioli; Villani, Marco; Irene, Poli; Serra, Roberto
abstract
In this work we propose a new approach to the stability analysis ofRandom Boolean Networks (RBNs). In particular, we focus on two families ofRBNs with k=2, in which only two subsets of canalizing Boolean function areallowed, and we show that the usual measure of RBNs stability  sometimesknown as the Derrida parameter (DP)  is similar in the two cases, while theirdynamics (e.g. number of attractors, length of cycles, number of frozen nodes) aredifferent. For this reason we have introduced a new measure, that we have calledattractor sensitivity (AS), computed in a way similar to DP, but perturbing only theattractors of the networks. It is proven that AS turns out to be different in the twocases analyzed. Finally, we investigate Boolean networks with k=3, tailored tosolve the Density Classification Problem, and we show that also in this case theAS describes the system dynamical stability.
2011
 Robustness analysis of a model of gene regulatory network with memory
[Articolo su rivista]
Graudenzi, Alex; Serra, Roberto; Villani, Marco; Damiani, Chiara; A., Colacci; S. A., Kauffman
abstract
The response to different kinds of perturbations of a discrete model of gene regulatory network, which is a generalization of the random Boolean network model (RBN), is extensively discussed. The model includes memory effects and the analysis pays particular attention to the influence on the system stability of a parameter (i.e. the decay time of the gene products) that determines the duration of the memory effects. It is shown that this parameter deeply affects the overall behaviour of the system, with special regard to the dynamical regimes and the sensitivity. Furthermore, a noteworthy difference in the response of systems characterized by different memory lengths in presence of either temporary or permanent damages is highlighted, as well as a substantial difference, with respect to classical RBNs, concerning the relationship between the specific dynamical regime and the landscape of the attractors.
2011
 Stochastic Local Search to Automatically Design Boolean Networks with Maximally Distant Attractors
[Relazione in Atti di Convegno]
Stefano, Benedettini; Andrea, Roli; Serra, Roberto; Villani, Marco
abstract
In this work we address the issue of designing a Boolean network such that its attractors are maximally distant. The design objective is converted into an optimisation problem, that is solved via an iterated local search algorithm. This technique proves to be effective and enables us to design networks with size up to 200 nodes. We also show that the networks obtained through the optimisation technique exhibit a mixture of characteristics typical of networks in the critical and chaotic dynamical regime
2011
 The influence of the residence time on the dynamics of catalytic reaction networks
[Relazione in Atti di Convegno]
Filisetti, A.; Serra, Roberto; Villani, Marco; Graudenzi, A.; Fuechslin, R.; Poli, I.
abstract
Although autocatalytic networks are common in nature, it is very difficultto reproduce them in laboratory. Since there are several models in literaturedescribing a phase transition to an autocatalytic set once that a certain degree ofheterogeneity in the composition of the system is reached, it is interesting to understandwhy it is so difficult to observe such a phenomenon in the laboratory. Forthis reason, we here present a model designed for the study of that systems takinginto account the stochastic nature of the dynamics of interacting molecules. In particular,the analysis is focused on the emergence of autocatalytic sets in accordancewith different residence times and influx compositions
2011
 The role of energy in a stochastic model of the emergence of autocatalytic sets
[Relazione in Atti di Convegno]
Filisetti, A.; Graudenzi, A.; Serra, Roberto; Villani, Marco; De Lucrezia, D.; Poli, I.
abstract
In most theories concerning the origin of life autocatalytic sets are supposed to play an important role in the phase tran sition between nonliving and living matter. Although several theoretical models describe this phase transition, it is very hard to recreate the experimental conditions in wet lab. We here introduce a stochastic model of catalytic reaction net works with energy constraints, devoted to the study of the emergence of autocatalytic sets, in which some of the as sumptions of the already existing model are relaxed in order to explore the possible reasons which make the emergence of autocatalytic cycles difficult or which make them unstable. Moreover, since living systems operate with a continuous ex change of matter and energy with the environment, we inves tigate the effects on the model behavior of changes in the rate of the energy intake.
2010
 A stochastic model of catalytic reaction networks
[Relazione in Atti di Convegno]
Filisetti, A.; Serra, Roberto; Villani, Marco; Fuechslin, R.; Packard, N.; Kauffman, S. A.; Poli, I.
abstract
Autocatalytic networks are widespread in nature, but theyare diffcult to create or to reproduce in laboratory. There are however several models of coupled reactions which describe a phase transition to an autocatalytic cycle when a certain level of heterogeneity in the composition of the chemical soup is reached, so it is interesting to understand why these phenomena are not easily achieved in the laboratory. For this purpose we introduce here a model, inspired by a previous one by Kauffman, tailored for the study of such properties. In particular, we take intoaccount the stochastic nature of the dynamics of interacting molecules, in the case of a well stirred tank reactor. We describe the model and we analyse its behaviour under dierent circumstances. In particular, the onset of an autocatalytic set is studied as the feed is varied, and its stability is analysed
2010
 A theorybased dinamical model of exaptive innovation processes
[Capitolo/Saggio]
Villani, Marco; Ansaloni, Luca
abstract
A major problem in research on innovations is the understanding of invention, that is, the origin of innovations. In this paper we propose that radical innovations are created by a process of 'exaptation', and we introduce a dynamical model which describes how it may happen. In particular, our model is focussed on the interplay between artifact innovation and attributions of functionality. We propose that the explicit representation of artifacts and categories eases the understanding of the exaptation phenomenon, seen in this context as a shift in terms of “leading attributions”, and allows the identification of the elements favouring the emergence of innovations
2010
 Dynamical stability of autocatalytic sets
[Relazione in Atti di Convegno]
Fuechslin, R.; Filisetti, A.; Serra, Roberto; Villani, Marco; De Lucrezia, D.; Poli, I.
abstract
occurrence of selfsustaining sets of molecules to be a genericproperty of random reaction networks. This stands in somecontrast to the experimental difficulty to actually find suchsystems. In this work, we argue that the usual approach,which is based on the study of static properties of reactiongraphs has to be complemented with a dynamic perspectivein order to avoid overestimation of the probability of gettingautocatalytic sets. Especially under the, from the experimentalpoint of view, important flow reactor conditions, it is notsufficient just to have a pathway generating a given type ofmolecules. The respective process has also to happen with asufficient rate in order to compensate the outflow. Reactionrates are therefore of crucial importance. Furthermore, processessuch as cleavage are on one hand advantageous for thesystem, because they enhance the molecular variability andtherefore the potential for catalysis. On the other hand, cleavagemay also act in an inhibiting manner by the destructionof vital components: therefore, an optimal balance betweenligation and cleavage has to be found. If energy is included asa limiting resource, the concentration profiles of the componentsof autocatalytic sets are altered in a manner that rendersa certain range for the energy supply rate as optimal for therealization of robust autocatalytic sets.The results presented are based on a theoretical model and obtainedby numerical integration of systems of ODE. This limitsthe number of involved molecular species which impliesthat the quantitative findings of this work may have no directrelevance for experimental situations, whereas the qualitativeinsights in the dynamics of the systems under considerationmay generalize to systems of truly combinatorial size.
2010
 Information transfer among coupled Random Boolean Networks
[Relazione in Atti di Convegno]
Chiara, Damiani; Stuart A., Kauffman; Serra, Roberto; Villani, Marco; Annamaria, Colacci
abstract
Information processing and information flow occur at many levels in the course of an organism’s development and throughout its lifespan. Biological networks inside cells transmit information from their inputs (e.g. the concentrations of proteins or other signaling molecules) to their outputs (e.g. the expression levels of various genes). Moreover, cells do not exist in isolation, but they constantly interact with one another. We study the information flow in a model of interacting genetic networks, which are represented as Boolean graphs. It is observed that the information transfer among the networks is not linearly dependent on the amount of nodes that are able to influence the state of genes in surrounding cells.
2010
 Noisy random boolean networks and cell differentiation
[Relazione in Atti di Convegno]
Villani, Marco; Serra, Roberto; Barbieri, A.; Roli, A.; Kauffman, S. A.; Colacci, A.
abstract
Autocatalytic networks are widespread in nature, but theyare difficult to create or to reproduce in laboratory. There are howeverseveral models of coupled reactions which describe a phase transition toan autocatalytic cycle when a certain level of heterogeneity in the compositionof the chemical soup is reached, so it is interesting to understandwhy these phenomena are not easily achieved in the laboratory. For thispurpose we introduce here a model, inspired by a previous one by Kauman, tailored for the study of such properties. In particular, we take intoaccount the stochastic nature of the dynamics of interacting molecules,in the case of a well stirred tank reactor. We describe the model andwe analyse its behaviour under dierent circumstances. In particular,the onset of an autocatalytic set is studied as the feed is varied, and itsstability is analysed.
2010
 Nonlinear protocell models: synchronization and chaos
[Articolo su rivista]
Filisetti, Alessandro; Serra, Roberto; T., Carletti; Villani, Marco; I., Poli
abstract
We consider generic protocells models allowing linear and nonlinear kinetics for the main in volved chemical reactions. We are interested in understanding if and how the protocell division and the metabolism do synchronize to give rise to sustainable evolution of the protocell.
2010
 On the dynamics of random Boolean networks subject to noise: attractors, ergodic sets and cell types
[Articolo su rivista]
Serra, Roberto; Villani, Marco; Barbieri, Alessia; S. A., Kauffman; A., Colacci
abstract
The asymptotic dynamics of random Boolean networks sub ject to ran dom ﬂuctuations is investigated. Under the inﬂuence of noise, the system can escape from the attractors of the deterministic model, and a thorough study of these transitions is presented. We show that the dynamics is more properly described by sets of attractors rather than single ones. We gener alize here a previous notion of ergodic sets, and we show that the Threshold Ergodic Sets so deﬁned are robust with respect to noise and, at the same time, that they do not suﬀer from a ma jor drawback of ergodic sets. The system jumps from one attractor to another of the same Threshold Ergodic Set under the inﬂuence of noise, never leaving it. By interpreting random Boolean networks as models of genetic regulatory networks, we also propose to associate cell types to Threshold Ergodic Sets rather than to deterministic attractors or to ergodic sets, as it had been previously suggested. We also propose to associate cell diﬀerentiation to the process whereby a Thresh old Ergodic Set composed by several attractors gives rise to another one composed by a smaller number of attractors. We show that this approach accounts for several interesting experimental facts about cell diﬀerentiation, including the possibility to obtain an induced pluripotent stem cell from a fully diﬀerentiated one by overexpressing some of its genes
2010
 WIRN 2010  SPECIAL SESSION on THE DYNAMICS OF BIOLOGICAL NETWORKS
[Esposizione]
Villani, Marco; Serra, Roberto; Carlo, Morabito
abstract
Networks have attracted considerable interests in recent years and it has become increasingly clear that many important biological and artificial processes are indeed supported by dedicated network structures. This is so not only for neural networks, which are the main topic of the WIRN workshop, but also for other relevant systems like e.g. genetic, metabolic and computer networks. The purpose of the special session is that of discussing recent advances in understanding the properties of these networks and in novel mathematical and computational techniques. The session is intended for a broad interdisciplinary audience and is also aimed at fostering a dialogue between neural network scholars and researchers in the dynamics of biological and artificial networks
2009
 Corrigendum to "Sufficient conditions for emergent synchronization in protocell models" [J. Theor. Biol. 254 (2008) 741751] (DOI:10.1016/j.jtbi.2008.07.008)
[Articolo su rivista]
Carletti, T.; Serra, R.; Poli, I.; Villani, M.; Filisetti, A.
abstract
2009
 Distributed processes in an agentbased model of innovation
[Relazione in Atti di Convegno]
Ansaloni, Luca; Villani, Marco; Lane, David Avra
abstract
In this work we investigate the conditions inuencing the creation of noveltiesand their diusion through networks composed by agents interacting via theexchange of artifacts. By means of simulation we veried that the presence ofstereotyped routines deeply inuences (negatively) the robustness properties ofthe system, whereas the impact of strong spatial limitations or of a particularkind of direct information exchange (a request system) have more complexconsequences, not all aligned to the same direction. None of these results isobvious, nor can it be simply deduced from the qualitative theory. Therefore,the simulations could make possible comparisons between the model behaviorsand the theory claims, indicating new ways of improvement and development
2009
 Dynamical critical systems for information processing: a preliminary study
[Relazione in Atti di Convegno]
Ansaloni, Luca; Villani, Marco; Serra, Roberto
abstract
A general and inspiring hypothesis states that organizationsand systems subject to evolutionary pressure tend to reach a particularstate, often called critical: in particular, in presence of changing environments the critical systems could have signicant advantages with respectto ordered or chaotic systems. From the previous consideration naturallyfollows the question if also articial systems could take advantage fromoperating in critical conditions, with respect to more ordered (and lessexible) structures. In order to study this topic some methodological issues have to be solved; this work shows the rst results of the proposedresearch approach.
2009
 Dynamics of Interconnected Boolean Networks with scalefree topology
[Relazione in Atti di Convegno]
Damiani, Chiara; Villani, Marco; Darabos, C.; Tomassini, M.
abstract
In this paper we investigate how the dynamics of a set of coupled RandomBoolean Netowrks is aected by the changes in their topology. The Multi Random Boolean Networks (MRBN) is a model for the interaction among RandomBoolean Networks (RBN). A single RBN may be regarded as an abstractionof gene regulatory networks, thus MRBNs might represent collections of communicating cells e.g. in tissues or in bacteria colonies. Past studies have shownhow the dynamics of classical RBNs in the critical regime is aected by suchan interaction. Here we compare the behaviour of RBNs with random topologyto that of RBNs with scalefree topology for dierent dynamical regimes
2009
 Exaptive processes: an agentbased model
[Capitolo/Saggio]
Villani, Marco; Bonacini, Stefano; Ferrari, Davide; Serra, Roberto
abstract
his chapter introduces an agentbased model designed to investigate the dynamics of some aspects of exaptation that have been discussed previously in this volume. It is strongly related to the model introduced in the previous chapter. Indeed, in the model described here, cognitive categories represent the main tools that the producers and users of artifacts employ in order to interpret their environment, as in the case discussed in Chapter 14. The main addition provided by the current model, however, is the explicit introduction of artifacts.
2009
 Extended notion of attractors in noisy random Boolean networks
[Relazione in Atti di Convegno]
Barbieri, Alessia; Villani, Marco; Serra, Roberto; S. A., Kauffman; A., Colacci
abstract
Since real networks are noisy systems, in this work we investigate thedynamics of the random Boolean networks affected by different size of smallrandom fluctuations. In this case jumps among different attractors are possible,thereby leading to an asymptotic dynamics different from that of the underlyingdeterministic model. The significance of the jumps among attractors is investigated.The notion of “ergodic set” is discussed and generalized in terms of“threshold ergodic set”, a concept that take into account the system lifetime. Inorder to evaluate possible differences due to the topology of the nets the experimentsare effectuated on ErdosRenyi and scalefree topologies, showing similarbehaviours
2009
 Genetic regulatory networks and neural networks
[Relazione in Atti di Convegno]
Serra, Roberto; Graudenzi, Alex; Villani, Marco
abstract
comparison between neural nets and random boolean networks with different constraints on the choice of boolean functions
2009
 How critical random boolean networks may be affected by the interaction with others
[Relazione in Atti di Convegno]
Damiani, Chiara; Graudenzi, Alex; Villani, Marco
abstract
In previous articles we have introduced Multi Random Boolean Networks (MRBNs) as a possible model for the interaction among cells within multi cellular organisms or within bacteria colonies. MRBNs are sets of Random Boolean Networks (RBNs), placed on a Cellular Automaton, whose gene ex pressions may be affected by the activation of some genes in neighbouring networks. In this paper we study the effects induced by interaction on the dy namics of those RBNs that  if isolated  lay in the critical region. It is shown that the influence of interaction is not univocal; nevertheless its possible to identify three classes of representative behaviours. RBNs belonging to each class seem to have different dynamical peculiarities even in isolation: although sharing the parameters proper of critical networks, they differ substantially in their typical response to perturbations
2009
 Investigating cell criticality
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco; Damiani, Chiara; Graudenzi, Alex; P., Ingrami; A., Colacci
abstract
random boolean networks for investigating cell criticality
2009
 L’influenza delle perturbazioni sul paesaggio degli attrattori di una rete booleana casuale
[Relazione in Atti di Convegno]
Barbieri, A.; Villani, Marco; Serra, Roberto
abstract
Le reti booleane casuali proposte più di 40 anni fa da Stuart Kauffman, rappresentano uno dei modelli più noti di sistemi complessi. Esse si sono rivelate particolarmente utili per descrivere diverse importanti proprietà delle reti di regolazione genica in cellule eucariote. In questo lavoro esaminiamo se e come il modello e la sua interpretazione possono cambiare una volta introdotta una dinamica stocastica
2009
 Modelling Innovation
[Capitolo/Saggio]
Serra, Roberto; Villani, Marco; Lane, David Avra
abstract
The innovation theory (briefly, IT), which has been developed in the ISCOM project and which is presented in this book (Chapters 9 and 10), is based on the analysis of different case studies, spanning different time periods and different kinds of products, from the introduction of printing in the Renaissance, to key new technologies introduced in the 19th and 20th centuries, up to presentday ongoing innovation efforts.
2009
 Non linear protocell models: Syncronisation and Chaos
[Relazione in Atti di Convegno]
Filisetti, Alessandro; Serra, Roberto; T., Carletti; Villani, Marco; I., Poli
abstract
Abstract We consider generic protocells models allowing linear and nonlinear kineticsfor the main involved chemical reactions.We are interested in understanding if and howthe protocell division and the metabolism do synchronize to give rise to sustainableevolution of the protocell.
2009
 On the fate of perturbations in critical random Boolean networks
[Relazione in Atti di Convegno]
Damiani, Chiara; Graudenzi, Alex; Villani, Marco; Serra, Roberto; A., Colacci; Stuart A., Kauffman
abstract
Abstract Random Boolean models of genetic regulatory networks, when subject tosmall noise, may either forget past distinctions or yield divergence in state space trajectoriesprecluding reliable action. With a specic choice of the model parameters, suchnetworks are in a critical regime and optimize capacity to bind past and future. Anindepth study of the response to perturbation of critical random Boolean networks ishere presented. It is shown that networks built with critical values of the parametersmay, however, frequently show behaviours that are more typical of the ordered or of thedisordered regime. A further classication of critical networks is thus proposed withthe objective of isolating those networks that exhibit really critical dynamics
2009
 Quando un insieme di reazioni è autocatalitico
[Relazione in Atti di Convegno]
Filisetti, A.; Serra, Roberto; Villani, Marco; Carletti, T.; Füchslin, R. M.; Poli, I.
abstract
L’emergenza di uno o più cicli autocatalitici all’interno di una rete di molecole interagenti è una proprietà fondamentale sia nello sviluppo di possibili scenari legati all’origine della vita, sia nell’indirizzare la ricerca di laboratorio verso lo sviluppo di nuove molecole capaci di evolversi interagendo con i propri bersagli.Alcuni modelli teorici di reti catalitiche hanno dimostrato una certapredisposizione alla comparsa di cicli, fenomeno che al contrario difficilmente si riesce ad ottenere nei laboratori. UIl nostro studio prende spunto dai lavori di Stuart Kauffman eFarmer, nei quali è stato sviluppato un modello contenentedue tipi di reazioni (condensazione e cleavage) ed in cui tali reazioni vengono catalizzate dalle altre molecole presenti nel sistema.L’obiettivo del nostro lavoro è di migliorare il modello originale introducendo una dinamica stocastica delle molecole, basata sul noto algoritmo di Gillespie, in modo da poter trattare adeguatamente i problemi connessi alla numerosità degli esemplari delle varie specie molecolari, che in alcuni casi può essere anche molto bassa, e alla cinetica delle reazioni. Discutiamo il tipo di analisi di rete necessario per interpretare gli schemi di reazione stocastici
2009
 Separating internal and external fluctuation in distributed webbased services
[Relazione in Atti di Convegno]
Casolari, Sara; Villani, Marco; Colajanni, Michele; Serra, Roberto
abstract
The observable behavior of a complex system reflects the mechanisms governingthe internal interactions between the system’s components and the effect ofexternal perturbations. We investigate the behavior of a distributed system providingWebbased services and the effects of the impact of external request arrivals on theinternal system resources; the results of our study are of primary importance for takingseveral runtime decisions on load and resource management. Here we show that bycapturing the simultaneous activities of several performance indexes of the Webbasedsystem nodes we can separate the internal dynamics from the external fluctuations. Forevery internal performance index, we are able to determine the origin of fluctuations,finding that while all the considered performance indexes of the application server haverobust internal dynamics, the CPU utilization and the network throughput of the Weband database servers are mainly driven by external demand.
2009
 Studi preliminari per una rete booleana capace di apprendere da esempi
[Relazione in Atti di Convegno]
Ansaloni, L.; Villani, Marco; Serra, Roberto
abstract
Le reti booleane casuali (brevemente, RBN) sono uno dei modelli più noti di sistemi complessi, e si sono rivelate utili per descrivere diverse importanti proprietà delle reti di regolazione genica in cellule eucariote. Una caratteristica originale della proposta è quella di cercare di verificare se, in presenza di un ambiente mutevole, le prestazioni di una rete critica sono superiori a quelle di reti non critiche. A tal fine però è necessario affrontare alcuni problemi preliminare, cui è dedicato questo lavoro.
2009
 Synchronization phenomena in non linear protocell model
[Relazione in Atti di Convegno]
Filisetti, Alessandro; Serra, Roberto; Carletti, T.; Villani, Marco; Poli, I.
abstract
In this paper we study general protocell models aiming to understand the synchronization phenomenon of genetic material and containerproductions, a necessary condition to ensure sustainable growth in protocellsand eventually leading to Darwinian evolution when applied to a populationof protocells.Synchronization has been proved to be an emergent property in many relevant protocell models in the class of the so–called Surface Reaction Models,assuming both linear and nonlinear dynamics for the involved chemical reactions.
2009
 The influence of noise on the dynamics of random boolean networks
[Relazione in Atti di Convegno]
Barbieri, Alessia; Villani, Marco; Serra, Roberto; S. A., Kauffman; A., Colacci
abstract
noise induces transitions among attractor in random boolean networks
2009
 Timing of molecular processes in a synchronous Boolean model of genetic regulatory network
[Relazione in Atti di Convegno]
Graudenzi, Alex; Serra, Roberto; Villani, Marco; Damiani, Chiara; A., Colacci; Stuart A., Kauffman
abstract
A generalization of the model of random Boolean network (RBN) is presented, in whichthe concept of timing of regulatory processes is explicitly introduced, together with novel types ofentity and interaction, directly inspired to real genetic networks. Beyond the attempt ofapproaching a higher level of faithfulness to the natural world, at the base of the development ofthe model is the need for a sensible comparison with timeseries microarray datasets, inaccessibleto the original RBN model, because of the strict assumptions about the simultaneity of theregulation mechanisms. Preliminary analysis on networks typified by “critical” parameters showeda strong, even though not univocal, influence of a variation in the distribution of the time delaysthat characterize the entities of the system on the emerging dynamics: the larger the “memory” ofthe system about its dynamical evolution is, the more ordered the behaviour would tend to be.
2009
 WORKSHOP on COMPLEXITY, EVOLUTION AND EMERGENT INTELLIGENCE
[Esposizione]
Villani, Marco; Stefano, Cagnoni
abstract
The workshop aims at bringing together scientists who work from different perspectives, from basic science to applications, on the common theme of systems composed by many components that interact nonlinearly.
2008
 A CA MODEL OF SPONTANEOUS FORMATION OF CONCENTRATION GRADIENTS
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco
abstract
It is shown that a twocompartment isolated fluid system,where a chemical reaction takes place close to the surfaces of the semipermeableseparating membrane, can spontaneously develop a transient concentrationdifference across the membrane. If the system is open to theflow of chemicals, the difference can persist in the steady state. Thisallows concentrating chemicals in a single compartment, which may beuseful for chemical engineering purposes, and which is particular interestingin the study of the dynamics of vesicles and protocells. The phenomenonis investigated and demonstrated here with a CA model: it isalso shown that, in the limiting case of infinitely fast diffusion, the resultsare coherent with those of a homogeneous model.
2008
 ARTIFICIAL LIFE AND EVOLUTIONARY COMPUTATION
[Curatela]
Serra, Roberto; Villani, Marco; I., Poli
abstract
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE WIVACE 08, VENICE )ITALY) SEPTEMBER 810, 2008
2008
 COMUNICAZIONE CELLULARE, LIVELLI E STRUTTURE ORDINATE
[Articolo su rivista]
Serra, Roberto; Villani, Marco; Damiani, Chiara; Graudenzi, Alex; A., Colacci
abstract
Le cellule interagiscono per formare strutture di ordine superiore come colonie monoclonali o tessuti cellulari. Le Reti Booleane Casuali (RBN) possono essere considerate come modello di una cellula isolata ed è dunque di estrema importanza l’analisi della relazione tra la dinamica di una singola RBN e quella di un insieme di reti interagenti. Presentiamo un modello adatto allo scopo: un automa cellulare bidimensionale in cui ogni cella è occupata da una RBN. Il meccanismo di interazione tra le reti dell’automa è ispirato alla comunicazione intercellulare. L’analisi dello stato di ordine del modello può avvenire al livello dell’automa e a quello della singola rete costituente. Si osserva che l’influenza della forza di interazione sul grado di ordine delle RBN non è univoca, in alcuni casi l’ordine è accresciuto, mentre in altri è amplificato il disordine. Sono state individuate tre tipologie di comportamento, al crescere dell’intensità dell’interazione, che appaiono correlate alla dinamica della specifica RBN in assenza di interazione.
2008
 Global and local processes in a model of innovation
[Relazione in Atti di Convegno]
Villani, Marco; Serra, Roberto; Ansaloni, Luca; Lane, David Avra
abstract
In this work we present the introduction of spatial constraintsin a model of generation and diffusion of innovations. The presenceof spatial limitations introduces several feedbacks, whose main effectsare the decrease of global diversity in favour of a higher robustness,despite the apparent minor success of the individual agents. All thesefeatures hold contemporarily, but the individuated feedbacks are able toexplain their only apparently contradictory nature. None of these resultsis obvious, nor can it be simply deduced from the qualitative theory.Moreover, the simulations could make possible comparisons between themodel behaviours and the theory claims, indicating new ways of improvementand development
2008
 SUFFICIENT CONDITIONS FOR EMERGENT SYNCHRONIZATION IN PROTOCELL MODELS
[Articolo su rivista]
T., Carletti; Serra, Roberto; I., Poli; Villani, Marco; Filisetti, Alessandro
abstract
In this paper, we study general protocell models aiming to understand the synchronizationphenomenon of genetic material and container productions, a necessary condition to ensure sustainablegrowth in protocells and eventually leading to Darwinian evolution when applied to a population ofprotocells.Synchronization has been proved to be an emergent property in many relevant protocell models inthe class of the socalled surface reaction models, assuming both linear and nonlinear dynamics forthe involved chemical reactions. We here extend this analysis by introducing and studying a new classof models where the relevant chemical reactions are assumed to occur inside the protocell, in contrastwith the former model where the reaction site was the external surface.While in our previous studies, the replicators were assumed to compete for resources,without any direct interaction among them, we here improve both models by allowing linearinteraction between replicators: catalysis and/or inhibition. Extending some techniques previouslyintroduced, we are able to give a quite general analytical answer about the synchronizationphenomenon in this more general context. We also report on results of numerical simulations tosupport the theory, where applicable, and allow the investigation of cases which are not amenable toanalytical calculations.
2008
 SYNCHRONIZATION PHENOMENA IN PROTOCELL MODELS
[Relazione in Atti di Convegno]
Filisetti, Alessandro; Serra, Roberto; T., Carletti; I., Poli; Villani, Marco
abstract
A protocell comprises at least one kind of“container”(typically an amphiphile) and one kind of replicator molecule. There are therefore two kinds of reactions whichare crucial for the working of the protocell, which will be called here keyreactions: those which synthesize the container molecules and those whichsynthesize the replicators.The two key reactions may take place at different rates. However, toachieve sustained protocell growth and avoiding death by dilution it isnecessary that the two are proceed at equal rate, a condition referred to as synchronization. With our models we are able to prove that synchronization is an emergent property in contrast to earlier models, like the well–knownChemoton where synchronization was achieved by ad hoc hypothesesconcerning the form of kinetic equations.We consider here several protocells models both linear and non–linear inreplicators kinetic (the overall model is definitely non–linear because of thedivision event), moreover some models posses only autoreplicator moleculeswithout interaction between them while other models has either catalyticor inhibitory interaction between replicators.
2008
 THE DIFFUSION OF PERTURBATIONS IN A MODEL OF COUPLED RANDOM BOOLEAN NETWORKS
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco; Damiani, Chiara; Graudenzi, Alex; A., Colacci
abstract
Deciphering the influence of the interaction among the constituentsof a complex system on the overall behaviour is one of themain goals of complex systems science. The model we present in thiswork is a 2D square cellular automaton whose of each cell is occupiedby a complete random Boolean network. Random Boolean networks area wellknown simplified model of genetic regulatory networks and thismodel of interacting RBNs may be therefore regarded as a simplifiedmodel of a tissue or a monoclonal colony. The mechanism of celltocellinteraction is here simulated letting some nodes of a particular networkbeing influenced by the state of some nodes belonging to its neighbouringcells. One possible means to investigate the overall dynamics of acomplex system is studying its response to perturbations. Our analysesfollow this methodological approach. Even though the dynamics of thesystem is far from trivial we could show in a clear way how the interactionaffects the dynamics and the global degree of order.
2008
 THE SIMULATION OF GENE KNOCKOUT IN SCALEFREE RANDOM BOOLEAN MODELS OF GENETIC NETWORKS
[Articolo su rivista]
Serra, Roberto; Villani, Marco; Graudenzi, Alex; A., Colacci; S. A., Kauffman
abstract
This paper describes the effects of perturbations, which simulatethe knockout of single genes, one at a time, in random Boolean models ofgenetic networks (RBN). The analysis concentrates on the probability distributionof socalled avalanches (defined in the text) in gene expression. Thetopology of the random Boolean networks considered here is of the scalefreetype, with a powerlaw distribution of outgoing connectivities. The results forthese scalefree random Boolean networks (SFRBN) are compared with thoseof classical RBNs, which had been previously analyzed, and with experimentaldata on S. cerevisiae. It is shown that, while both models approximatethe main features of the distribution of experimental data, SFRBNs tend tooverestimate the number of large avalanches.
2007
 An agentbased model of exaptive processes
[Articolo su rivista]
Villani, Marco; S., Bonacini; Ferrari, Davide; Serra, Roberto; Lane, David Avra
abstract
A key problem in research on innovations is that of understanding their origins. In thispaper, we propose that radical innovations are created by a process of ’exaptation’, andwe introduce a dynamical model that describes how it may happen. In particular, ourmodel is focussed on the interplay between artefact innovation and attributions offunctionality. We propose that the explicit representation of artefacts and categories easesthe understanding of the exaptation phenomenon, seen in this context as a shift in termsof ‘leading attributions’ and allows the identification of the elements favouring theemergence of innovations.
2007
 Complexity course design
[Capitolo/Saggio]
Mancinelli, E; Moretti, M; Villani, Marco
abstract
The “Science of Complex Systems” represents, for the Europeanvocational training systems, an innovative approach because it shallintroduce within educational studies a concrete multidisciplinaryapproach.The project CETRA, as underlined by the “European Foundationfor the Improvement of Living and working conditions”, hasidentified, among the guiding principles, the emphasis on anintegrated view of issues across systems. The 21st century isbeginning with changes, for enterprises, employees and the society asa whole, the extent of which is difficult to assess at present.Furthermore, EU reports31 have outlined the global dimension and thecontinuous trends of changes within the relationship betweeneconomy, knowhow and technology.The traditional approach to disciplinary knowledge, which stillinfluences education and training systems, is no more fitting the needsof the new organisation of culture, science and training32. The lifelonglearning approach, requires integration among the different educationand training opportunities.General aim of the course on Complex systems is the transmissionof the contents, of the approach and over all of the new visions thisrecent field of science is able to offer.
2007
 Comunicazione cellulare, livelli e strutture ordinate.
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco; Damiani, C.; Graudenzi, A.; Colacci, A.
abstract
Le cellule interagiscono per formare strutture di ordine superiorecome colonie monoclonali o tessuti cellulari. Le Reti Booleane Casuali (RBN)possono essere considerate come modello di una cellula isolata ed è dunque diestrema importanza l’analisi della relazione tra la dinamica di una singola RBNe quella di un insieme di reti interagenti. Presentiamo un modello adatto alloscopo: un automa cellulare bidimensionale in cui ogni cella è occupata da unaRBN. Il meccanismo di interazione tra le reti dell’automa è ispirato allacomunicazione intercellulare. L’analisi dello stato di ordine del modello puòavvenire al livello dell’automa e a quello della singola rete costituente. Siosserva che l’influenza della forza di interazione sul grado di ordine delle RBNnon è univoca, in alcuni casi l’ordine è accresciuto, mentre in altri è amplificatoil disordine. Sono state individuate tre tipologie di comportamento, al cresceredell’intensità dell’interazione, che appaiono correlate alla dinamica dellaspecifica RBN in assenza di interazione.
2007
 Conditions for emergent synchronization in protocells.
[Relazione in Atti di Convegno]
Serra, Roberto; Carletti, T.; Poli, I.; Villani, Marco; Filisetti, Alessandro
abstract
In this paper we study general protocell models, called Surface Reactions Models, aiming to understand the synchronization of genetic material and container productions, a necessary condition to assure sustainable growth in protocells.Synchronization has been proved to be an emergent property in many relevant protocell models , assuming both linear and nonlinear law for the replications rates. While in those previous studies the replicators were assumed to compete forresources, without any direct interaction among them, here we improve the model by allowing linear interaction between replicators: catalysis and/or inhibition.Extending some techniques introduced in, we are able to give a quite general analytical answer about the synchronization phenomenon in this more general context.We also report on the results of numerical simulations to support the theory, where applicable, and allow to investigate cases which are not amenable to analytical calculations . A short comment on preliminary results concerning fully nonlinearmodels is presented in the conclusions
2007
 Educating managers in Complexity
[Curatela]
Villani, Marco
abstract
The science of complex systems can change, and it is changing, our vision of the world. This new knowledge allows new interpretations and new points of view, thereby allowing a deeper understanding of the behaviour of natural, social, and technical systems. In particular, it promises to offer effective concepts and methods in order to foster innovation, the key process in any company or organisation. Therefore, complexity constitutes a new challenge for trainers and teachers which have to develop an effective educational process able to provide the necessary competencies. This book is one of the outcomes of the European Project CETRA, funded by the Leonardo da Vinci Programme, that aims to provide a theoretical framework and concrete supports for vocational trainers, to help them (and their students) to understand change and the relationship between different levels of change. By learning about complexity the learners should be enabled to understand the dynamics of the internal and external processes in which organisations engage and in which knowledge, innovation and emerging technologies are created. Successful management of innovative organisations lies in the capability of capture the structure and the dynamics of the recurring patterns of interactions among the involved entities, and in the adequate exploitation of this knowledge. This book is not limited to the illustration of the project results but is presenting the dense interrelations that the science, the management and the formation are developing in order to interpret and to face the challenge of innovation.
2007
 Interacting random boolean networks
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco; Damiani, Chiara; Graudenzi, Alex; A., Colacci; S. A., Kauffamn
abstract
Random Boolean networks (RBN) have been extensively studied asmodels of genetic regulatory networks. While many studies have been devoted tothe dynamics of isolated random Boolean networks, which may considered asmodels of isolated cells, in this paper we consider a set of interacting RBNs,which may be regarded as a simplified model of a tissue or a monoclonal colony.In order to do so, we introduce a cellular automata (CA) model, where each cellsite is occupied by a RBN. The mutual influence among cells is modelled byletting the activation of some genes in a RBN be affected by that of some genes inneighbouring RBNs. It is shown that the dynamics of the CA is far from trivial.Different measures are introduced to provide indications about the overallbehaviour. In a sense which is made precise in the text, it is shown that the degreeof order of the CA is affected by the interaction strength, and that markedlydifferent behaviours are observed. We propose a classification of these behavioursinto four classes, based upon the way in which the various measures of order areaffected by the interaction strength. It is shown that the dynamical properties ofisolated RBNs affect the probability that a CA composed by those RBNs belongsto one of the four classes, and therefore also affects the probability that a higherinteraction strength leads to a greater, or a smaller, degree of order.
2007
 Learning about complexity.
[Capitolo/Saggio]
Mancinelli, E; Moretti, M; Villani, Marco
abstract
In the framework of the CETRA project the potential of elearningfor providing specific training on complexity theory and itsapplications and implications in the work of managers and trainers hasbeen examined. This contribution presents the key methodological andpedagogical principles that have been developed and adapted so tomeet the needs of the addressed target groups.The objective pursued has consisted in supporting trainingpractitioners and those in charge of training in the process ofeffectively integrating elearning within the existing and availabletraining and learning opportunities.This Chapter presents a possible model for an elearning systemwhich capitalises the work that the transnational partnership hascarried out in the CETRA project. It also proposes a flexible andscalable approach which is consistent with the project objectives andthe needs of the addressed target groups.In this respect, the present chapter “Learning about complexity”provides design criteria and solutions to design an effective elearningpath to be used in different contexts, such as higher education andcontinuing professional development. The following chapter“Complexity course design” represents an example of a coursedesigned on the basis of the proposed guidelines.
2007
 Modelli di protocellule e sincronizzazione
[Relazione in Atti di Convegno]
Serra, Roberto; Carletti, T.; Poli, I.; Villani, Marco; Filisetti, A.
abstract
L'articolo tratta delle condizioni che permettono l'emergere di sincronizzazione fra la velocità di replica delle specie chimiche interne ad una cellula e la velocità di accrescimento delle membrana cellulare
2007
 Networks and complex systems
[Capitolo/Saggio]
Villani, Marco
abstract
For over a century, modelling of physical as well as nonphysicalsystems and processes has been performed under an implicitassumption that the interaction patterns among the individuals of theunderlying system or process can be embedded onto a regular andperhaps universal structure such as a Euclidean lattice. Anotherwidespread hypothesis assumes that all the entities composing asystem can freely interact with each other, without any particularrestriction.In late 1950s, two mathematicians, Erdös and Rényi, made a stepforward in the classical mathematical graph theory: they described anetwork with complex topology by a random graph. Their workinitiated a cascade of innovations in network theory, followed byintensive studies in the next 40 years and even today. Althoughintuition clearly indicates that many reallife complex networks areneither completely regular nor completely random, the random graphmodel was the only sensible and rigorous approach that dominatedscientists’ thinking about complex networks for nearly half of acentury. This fact is due essentially to:• the absence of supercomputational power• the absence of detailed topological information about verylargescale realworld networksIn the past few years, the computerisation of data acquisition andthe availability of high computing power have led to the emergence ofhuge databases on various real networks of complex topology. Thepublic access to the huge amount of real data has in turn stimulatedgreat interest in trying to uncover the generic properties of differentkinds of networks. In this endeavour, two significant recentdiscoveries are the smallworld effect and the scalefree feature ofmost complex networks.The discovery of these effects has led to dramatic advances in thefield of complex networks theory. In particular, it has led to theconviction that in order to correctly analyse a real system scientistsìhave to take into consideration not only the feature they areaccustomed to (the dynamics), but also a new aspect: the systemunderlying topology.
2007
 Novelties and structural changes in a dynamical model of innovation processes
[Relazione in Atti di Convegno]
Villani, Marco; Ansaloni, Luca; D., Bagatti; Lane, David Avra; Serra, Roberto
abstract
We discuss the emergence of non linear behaviours andthe genesis of structures within an agentbased model of innovationprocesses based upon a theory of innovation introduced by Lane andMaxfield. This work focuses on how the innovation strategies of theagents and stable relationships among them affect systemperformance. In addition, it describes a social network analysis of theemergence of collective structures in artifact space
2007
 Synchronization phenomena in protocell models
[Relazione in Atti di Convegno]
Filisetti, Alessandro; Serra, Roberto; Carletti, T.; Poli, I.; Villani, Marco
abstract
Almost all life forms known today, are composed by cells, fundamental constituting units able to self–replicate and evolve through changes in genetic information; it is generally believed that this was not the case when first life–forms emerged on Earth almost 4 billion years ago. These protocells were much simpler, probably exhibiting only few simplified functionalities, that required a primitive embodiment structure, a protometabolism and a rudimentary genetics, so to guarantee that offsprings were similar to their parents. Artificial protocells have not yet been reproduced and intense research programs are being established aiming at developing reference models to capture the essence of the first protocells appeared on earth and enableto monitor their subsequent evolution. The interest for these researches is motivated either by the quest to understand which are the minimal requirements for a life form to exist and evolve, or by the search for indications about the way in which primitive life might have developed on earth. Moreover besides from their interest for the origin–of–life problem, protocells may be of practical interest in applications: obtain populations ofprotocells that grow and reproduce, specialized for useful tasks, like drug synthesis and reduce pollution.Because protocells didn’t yet exist, in order to study how they can develop researchers have considered simplified models able to capture general behaviors, without carefully adding complicating details.
2007
 The influence of the topology of regulatory networks on the distribution of avalanches in gene expression data.
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco; Graudenzi, Alex; Colacci, A.; Kauffamn, S. A.
abstract
This paper describes the effects of perturbations, whichsimulate the knockout of single genes, one at a time, in randomBoolean models of genetic networks (RBNs). The analysis concentrates on the probability distribution of socalled avalanches (defined in the text) in gene expression. The topology of the random Boolean networks considered here is of the scalefree type, with a powerlaw distribution of outgoing connectivities. The results for these scalefree randomBoolean networks (SFRBNs) are firstly compared with those ofclassical RBNs, which had been previously analyzed, secondly withexperimental data on S. cerevisiae. It is shown that, while both models approximate the main features of the distribution of experimental data, SFRBNs tend to overestimate the number of large avalanches
2007
 The management of complexity, the complexity of management
[Esposizione]
Villani, Marco
abstract
The new science of complex systems can change, and is changing, the business world. And it promises to provide concepts and methods which are effective in handling the problems raised by globalization and local development.Complexity science is new, and is rapidly growing, so education and training must develop adequate programs to help managers and technicians to understand its main features. At this aim the CETRA project has been completed by a European consortium, headed by the Modena and Reggio Emilia University.In the workshop “The complexity of management, the management of complexity”, which takes place at the end of the CETRA project, not only will its main results be presented, but it will also be shown how science, education and management are developing a new web of ideas and methods to deal with the challenges of innovation. Particular care will be devoted to the ways in which complexity can be applied in real industrial settings.
2007
 Valanghe in reti booleane a topologia scalefree
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco; Graudenzi, A.; Colacci, A.
abstract
L'articolo tratta della simulazione di eventi di knockout tramite reti booleane con topologia scalefree, e del confronto dei risultati con dati reali (eventi in Saccaromicies Cerevisiae)
2007
 Why a simple model of genetic regulatory networks describes the distribution of avalanches in gene expression data
[Articolo su rivista]
Serra, Roberto; Villani, Marco; Graudenzi, Alex; S. A., Kauffman
abstract
In a previous study it was shown that a simple random Boolean network model, with two input connections per node, can describewith a good approximation (with the exception of the smallest avalanches) the distribution of perturbations in gene expression levelsinduced by the knockout of single genes in Saccharomyces cerevisiae. Here we address the reason why such a simple model actuallyworks: we present a theoretical study of the distribution of avalanches and show that, in the case of a Poissonian distribution of outgoinglinks, their distribution is determined by the value of the Derrida exponent. This explains why the simulations based on the simple modelhave been effective, in spite of the unrealistic hypothesis about the number of input connections per node. Moreover, we consider herethe problem of the choice of an optimal threshold for binarizing continuous data, and we show that tuning its value provides an evenbetter agreement between model and data, valuable also in the important case of the smallest avalanches. Finally, we also discuss thechoice of an optimal value of the Derrida parameter in order to match the experimental distributions: our results indicate a value slightlybelow the critical value 1.
2006
 A NEW MODEL FOR POLLUTED SOIL RISK ASSESSMENT
[Articolo su rivista]
M., Andretta; Serra, Roberto; Villani, Marco
abstract
In this paper, we discuss the most important theoretical aspects of polluted soil Risk Assessment Methodologies, whichhave been developed in order to evaluate the risk, for the exposed people, connected with the residual contaminantconcentration in polluted soil, and we make a short presentation of the major different kinds of risk assessmentmethodologies. We also underline the relevant role played, in this kind of analysis, by the pollutant transport models. Wealso describe a new and innovative model, based on the general framework of the socalled Cellular Automata (CA),initially developed in the UEEsprit Project COLOMBO for the simulation of bioremediation processes. These kinds ofmodels, for their intrinsic ‘‘finite and discrete’’ characteristics, seem to be very well suited for a detailed analysis of theshape of the pollutant sources, the contaminant fates and the evaluation of target in the risk assessment evaluation.In particular, we will describe the future research activities we are going to develop in the area of a strict integrationbetween pollutant fate and transport models and Risk Analysis Methodologies.
2006
 Agents, equations and all that: on the role of agents in understanding complex systems
[Capitolo/Saggio]
Serra, R; Villani, Marco
abstract
Differential equations and agentbased models are different formalisms which can be applied to describe the evolution of complex systems. In this paper, it is shown how differential equations can describe interactions among agents: it is pointed out that their capabilities are broader than is often assumed, and it is argued that such an approach should be preferred whenever applicable. Also discussed are the circumstances in which it is necessary to resort to agentbased models, and a rigorous approach is advocated in these cases. In particular, the relationship between the model and a theory of the processes under consideration provides both stimuli and constraints for the model. This relationship is discussed both in general terms and with reference to a specific example, which concerns a model of innovation processes.
2006
 Coupled random boolean network forming an artificial tissue
[Relazione in Atti di Convegno]
Villani, Marco; Serra, Roberto; Ingrami, P; Kauffman, Sa
abstract
Random boolean networks (shortly, RBN) have proven useful in describing complex phenomena occurring at the unicellular level. It is therefore interesting to investigate how their dynamical behavior is affected by cellcell interactions, which mimics those occurring in tissues in multicellular organisms. It has also been suggested that evolution may tend to adjust the parameters of the genetic network so that it operates close to a critical state, which should provide evolutionary advantage; this hypothesis has received intriguing, although not definitive support from recent findings. It is therefore particularly interesting to consider how the tissuelike organization alters the dynamical behavior of the networks close to a critical state. In this paper we define a model tissue, which is a cellular automaton each of whose cells hosts a full RBN, and we report preliminary studies of the way in which the dynamics is affected.
2006
 On the distribution of small avalanches in random boolean networks
[Relazione in Atti di Convegno]
Villani, Marco; Serra, Roberto; Graudenzi, Alex; Kauffman, S. A.
abstract
The distribution of small avalanches of gene perturbationsis analytically studied in the quenched model ofrandom Boolean networks, providing formulae whichhold at a very good approximation for networks wherethe number of connections per node is much smaller thanthe number of nodes. The expressions are particularlysimple and elegant in the case of a Poissonian distributionof outgoing connectivities. Comparisons with simulationsof a large network, with 6000 nodes, show verygood agreement.
2005
 A theory based dynamical model of innovation processes
[Articolo su rivista]
Lane, David Avra; Serra, Roberto; Villani, Marco; Ansaloni, Luca
abstract
We present an agentbased model of innovation processes, based upon a theory of innovation by Lane and Maxfield. The theory inspires and constrains the features of the model, thus reducing the embarasse de richesse that is one of the major methodological problems of agentbased modeling. Artifacts are produced by agents using recipes; the basic dynamics, absent innovation, is one of production and sales, where the external world supplies “raw materials” and external demand. Depending upon the initial conditions, selfsustaining cycles of production and exchange can emerge among the agents. Innovation – that is, the generation of new recipes, in particular desired directions, called “goals” – results in substantial modification of the system dynamics. Two innovation regimes are introduced: a “lonely” mode, in which each agent tries to introduce new products by itself, and a “relational” mode, in which two agents can improve their reciprocal knowledge and can decide to try to jointly develop a new artifact.
2005
 A theory based dynamical model of innovation processes
[Relazione in Atti di Convegno]
Lane, David Avra; Serra, Roberto; Villani, Marco
abstract
We present an agentbased model of innovation processes, based upon a theory of innovationby Lane and Maxfield. The theory inspires and constrains the features of the model,thus reducing the embarasse de richesse that is one of the major methodological problems ofagentbased modeling. Artefacts are produced by agents using recipes; the basic dynamics,absent innovation, is one of production and sales, where the external world supplies "rawmaterials" and external demand. Depending upon the initial conditions, selfsustainingcycles of production and exchange can emerge among the agents. Innovation – that is,the generation of new recipes, in particular desired directions, called "goals" – results insubstantial modification of the system dynamics. Two innovation regimes are introduced:a "lonely" mode, in which each agent tries to introduce new products by itself, and a"relational" mode, in which two agents can improve their reciprocal knowledge and candecide to try to jointly develop a new artifact.
2005
 RECENT RESULTS ON RANDOM BOOLEAN NETWORKS
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco
abstract
MISSING
2004
 A smallworld network where all nodes have the same connectivity, with application to the dynamics of boolean interacting automata
[Articolo su rivista]
Serra, Roberto; Villani, Marco; L., Agostini
abstract
In this paper a new algorithm (called ENL) is introduced, which generates a smallworld network starting from a regular lattice, by randomly rewiring some connections. The approach is similar to the wellknown WattsStrogatz model, but the present method is different as it leaves the number of connections k of each node unchanged, while the WS algorithm gives rise to a Poisson distribution of connectivities. The motivation for the ENL algorithm stems from the interest in studying the dynamics of interacting oscillators or automata (associated to the nodes of the network): indeed, leaving k unaltered allows one to study how the dynamics of these networks is affected by rewiring only (which gives rise to smallworld properties) disentangling its effects from those related to the modification of the connectivity of some nodes. The new algorithm is compared with that of Watts and Strogatz, by studying the topological properties of the network as a function of the number of rewirings. The effects on the dynamics are tested in the case of the majority rule, and it is shown that key dynamical properties (i.e. number of attractors, size of basins attraction, transient duration) are modified by rewiring. The quantitative differences between the dynamics on a ENL network and a WS one are discussed in detail. A comparison with scalefree networks of the BarabasiAlbert type and with completely random networks is also given.
2004
 Genetic network models and statistical properties of gene expression data in knockout experiments
[Articolo su rivista]
Serra, Roberto; Villani, Marco; A., Semeria
abstract
It is shown here how gene knockout experiments can be simulatedin Random Boolean Networks (RBN), which are wellknownsimplifiedmod els of genetic networks. The results of the simulations are presentedandcomparedwith those of actual experiments inS. cerevisiae. RBN with two incoming links per node have been considered, and the Boolean functions have been chosen at randomamong the set of socalledcanalizing functions.Genes are knockedout (i.e. silenced) one at a time, and the variations in the expression levels of the other genes, with respect tothe unperturbed case, are considered. Two important variables are defined: (i) avalanches, which measure the size of theperturbation generatedby knocking out a single gene, and(ii) susceptibilities, which measure how often the expression of a givengene is modified in these experiments.A remarkable observation is that the distributions of avalanches and susceptibilities are very robust, i.e. they are very similar indifferent random networks; this should be contrasted with the distribution of other variables that show a high variance in RBN.Moreover, the distribution of avalanches and susceptibilities of the RBN models are close to those observed in actual experimentsperformedwith S. cerevisiae, where the changes in gene expression levels have been recorded with DNA microarrays.These findings suggest that these distributions might be ‘‘generic’’ properties, common to a wide range of genetic models and realgenetic networks. The importance of such generic properties is discussed.
2004
 ON THE DYNAMICS OF RANDOM BOOLEAN NETWORKS WITH SCALEFREE OUTGOING CONNECTIONS
[Articolo su rivista]
Serra, Roberto; Villani, Marco; L., Agostini
abstract
In the classical model of Random Boolean Networks (RBN) the number of incoming connectionsis the same for every node, while the distribution of outgoing links is Poissonian. TheseRBN are known to display two major dynamical behaviours, depending upon the value of somemodel parameters: an “ordered” and a “chaotic” regime. We introduce a modi7cation of theclassical way of building a RBN, which maintains the property that all the nodes have the samenumber of incoming links, but which gives rise to a scalefree distribution of outgoing connections.Because of this modi7cation, the dynamical properties are deeply modi7ed: the number ofattractors is much smaller than in classical RBN, their length and the duration of the transientsare shorter. Moreover, the number of di8erent attractors is almost independent of the networksize, over almost three orders of magnitudes (while in classical RBN this number grows with thesize of the network). These results are based upon a detailed study of networks where each nodehas two input connections. A limited study of networks with three input connections per nodeshows that also in this case the number of attractors is almost independent of the network size.
2004
 On the dynamics of scalefree boolean networks
[Capitolo/Saggio]
Serra, Roberto; Villani, Marco; L., Agostini
abstract
The dynamical features of Random Boolean Networks (RBN) are examined, in the case where a scalefree distribution of outgoing connectivities is introduced. RBN are known to display two major dynamical behaviours, depending upon the value of some model parameters, In the ordered regime the number of attractors is a growing polynomial function of the number of nodes N, while in the chaotic regime the growth is exponential. We present here a modification of the classical way of building a RBN, which maintains the property that all the nodes have the same number of incoming links, but which gives rise to a scalefree distribution of outgoing connectivities. Because of this modification, the dynamical properties are deeply modified: the number of attractors is much smaller than in classical RBN, their length and the duration of the transients are shorter. Perhaps more surprising, the number of different attractors is almost independent of the network size, over almost three order of magnitudes. Besides pertaining to the study of the dynamics of nonlinear networks, these results may have interesting biological implications.
2004
 Perturbation in genetic regulatory networks: simulation and experiments
[Capitolo/Saggio]
Serra, Roberto; Villani, Marco; A., Semeria; S. A., Kauffman
abstract
Random boolean networks (RBN) have been proposed more thanthirty years ago as models of genetic regulatory networks. Recent studies on theperturbation in gene expression levels induced by the knockout (i.e. silencing)of single genes have shown that simple RBN models give rise to a distributionof the size of the perturbations which is very similar in different model networkrealizations, and is also very similar to the one actually found in experimentaldata concerning a unicellular organism (S.cerevisiae). In this paper we presentfurther results, based upon the same set of experiments, concerning thecorrelation between different perturbations. We compare actual data from S.cerevisiae with the results of simulations concerning RBN models with morethan 6000 nodes, and comment on the usefulness and limitations of RBNmodels.
2003
 DESCRIBING INVITRO CELL PROLIFERATION AND TRANSFORMATION WITH CELLULAR AUTOMATA
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco
abstract
The importance of invitro carcinogenesis tests is growing, either for health risk assessments or for screening candidate drugs. Although these systems are simpler than their invivo counterparts, their outcomes are nonetheless the result of the interaction of several nonlinear processes. Therefore modelling their behaviour may significantly improve our understanding of these tests. A dynamical model is introduced, which describes the growth of cell cultures (coupling metabolism with proliferation) and the birth of "transformed" cells (which give rise to malignant cell clusters) under the action of a carcinogen. By averaging over the space variable, a simpler (ordinary differential equation) model is obtained, and its behaviour is compared with that of a cellular automata model which preserves space dependence and locality of interactions. It is shown that the latter may describe important phenomena which are hidden by averaging over the whole space. Experimental data are interpreted on the basis of the model, pointing to the role of a previously overlooked experimental variable. These results provide a further indication of the usefulness of cellular automata in modelling complex biological systems.
2003
 ROBUSTNESS TO DAMAGE OF BIOLOGICAL AND SYNTHETIC NETWORKS
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco; A., Semeria
abstract
We analyze the perturbation of the expression levels of thousandsof genes when one of them is knockedout, by measuring avalanches, the numberof genes whose expression is affected in a knockout experiment, and genesusceptibilities, which measure how often the expression of a given gene ismodified. Experimental data concerning the yeast S. cerevisiae are available.Knockout is simulated, using random boolean network models of gene regulation,in several experiments, using different sets of boolean functions. The majorresults (when only canalizing functions are allowed) are that the distributionsof avalanches and susceptibilities are very similar in different syntheticnetworks, with very small variance, and that these two distributions closely resemblethe experimental ones (a result which is even more surprising since noparameter optimization has been performed). These results strongly suggestthat the distribution of avalanches and susceptibilities may be generic properties,common to many different genetic networks
2002
 PERTURBING THE REGULAR TOPOLOGY OF CELLULAR AUTOMATA: IMPLICATIONS FOR THE DYNAMICS
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco
abstract
The topology of Cellular Automata (CA) is that of regular graphs with high clustering coefficients and long characteristic path lengths. The introduction of some long range connections modifies the topology, and it may give rise to small world networks, with high clustering and short path lengths, modifying also the system dynamical properties (attractors, basins of attraction, transient duration). In order to investigate the effects on the dynamics of the introduction of long range connections it is appropriate to keep the number of connections per node constant, while the existing algorithms give rise to nodes with different connectivities. Here we present an algorithm able to redirect the links without changing the connectivity degree of the nodes. We then analyze the effects of small topological perturbations of a regular lattice upon the system dynamical properties in the case where the transition function is the majority rule; we show that these effects are indeed important and discuss their characteristics.
2001
 Bioremediation modelling: from the pilot plant to the field
[Relazione in Atti di Convegno]
Villani, Marco; M., Padovani; M., Andretta; Serra, Roberto; B., Muller; H. P., Ratzke; R., Rongo; W., Spataro; S., Di Gregorio
abstract
We report recent results achieved by applying in the field a dynamical model of in situ bioremediation that has been developed within the Colombo project, one of the major european endeavours in bioremediation modelling.Our approach relies upon the CabCol methodology, which is based upon the use of adaptive models, which are tailored to the case at hand in the pilot plant phase. The model is then used to forecast the results of real field interventions. A further original feature is that the model is based upon the cellular automata framework, instead of relying upon partial differential equations. A software environment for these models has been developed, which can make use of parallel as well as sequential hardware. Further discussion of the methodology and of the CA model can be found in the literature and in the 1999 Battelle Conference Proceedings, alongside with comparisons with experimental results on the pilot scale.We discuss here the results which have been achieved in the first two applications of the methodology to real cases, referring to two sites in Germany: one (site A) was contaminated mainly by TPH, the other (site B) by PAH. Pilot scale studies have been performed in both cases, where the indigenous bacteria were stimulated by the flow of an aqueous solution of nutrients and hydrogen peroxide. The pilot plants were composed by a series of three cylinders filled with contaminated soil coming from the site. The model has been adapted to the two different cases, in order to match both the overall degradation rate and its spacetime profile. After adaptation, the model has been applied in the field without any further change. The major results are as follows: in site A, the overall degradation rate is predicted with reasonable accuracy, while the detailed spatial distribution on its boundaries is not satisfactory. This is likely to be due to the fact that site A is actually a part of a larger site, and the boundaries are affected by operations taking place outside the monitored area and not considered in the model. In site B, both the overall degradation rate and the spatial distribution are correctly forecasted.What is particularly worth noticing is that the overall pilotplant degradation rate is similar in the two cases, while the kinetics in the field differ by about an order of magnitude. The model correctly forecasts this difference, and it also allows one to understand the reason of the difference. So, while a naive approach would have predicted similar rate constants in the two cases, the use of CabCol allows to forecast the different rates in the field. The importance of such a forecast for determining the duration and the cost of the remediation is obvious.Since two cases have been so far fully worked out, we cannot claim a general validity of the methodology; however, these first real field applications show very promising and potentially useful results in the scaleup from the lab to the field.
2001
 Continuous genetic networks
[Articolo su rivista]
Serra, Roberto; Villani, Marco; A., Salvemini
abstract
The dynamics of a continuous model of genetic networks, which generalizes the random boolean network one, is described
2001
 Differential equations and cellular automata models of the growth of cell cultures and transformation foci
[Articolo su rivista]
Serra, Roberto; Villani, Marco; A., Colacci
abstract
missing
2001
 MODELLING THE BIRTH OF TRANSFORMATION FOCI IN CELL CULTURES
[Articolo su rivista]
Serra, Roberto; Villani, Marco; A., Colacci
abstract
missing
2000
 A cellular automata model for the simulation of in vitro carcinogenesis tests
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco; A., Colacci
abstract
In vitro tests are very powerful methods to assess the carcinogenic effects of different substances and to study the initial phases of tumor development. A CA model of the formation of transformation foci in cell cultures which are exposed to a carcinogen is presented here, based on known facts about carcinogenesis and about reasonable assumptions, which gives rise to a cell growth dynamics similar to the one experimentally observed. The model can be used to test formal hypotheses about different interfering phenomena and about their relative strength
2000
 A new dynamical model of biodegradation
[Relazione in Atti di Convegno]
Villani, Marco; M., Mazzanti; M., Padovani; M., Andretta; Serra, Roberto; S., Di Gregorio; R., Rongo; W., Spataro
abstract
A new cellular automata model of the complex set of interacting phenomena which take place in bioremediation is described, which allows to treat a wider set of cases. The model has proven able to accurately describe several experimental data on a pilot plant. The general theory and the C.A. transition function are shown, and an example of the whole framework (fluid dynamics, chemical and biological layer) is analyzed and compared with experimental results
2000
 Cellular automata model for parallel simulation of contamination processes by oil in porous soils
[Relazione in Atti di Convegno]
M., Andretta; M. A., Mazzanti; Serra, Roberto; Villani, Marco; S., Di Gregorio; R., Rongo; W., Spataro
abstract
Cellular automata (CA) can be applied for modeling the dynamics of spatially extended physical systems, representing an alternative to the classical PDE approach. Furthermore, CA implementation on large parallel computer is straightforward because of their characteristics of parallelism and acentrism. In this paper, a CA model for simulating the fluiddynamics of contaminated porous soils is introduced. It is based on an empirical method for modeling complex phenomena from a macroscopic viewpoint; such a choice is motivated by the aim of simulating large scale systems. We report here first significant applications of this model concerning case studies and experiments in pilot plants. The results of the applications and a comparison between case studies and simulations are presented and commented on.
1999
 Applying cellular automata to complex environmental problems: the simulation of the bioremediation of contaminated soils
[Articolo su rivista]
S., DI GREGORIO; Serra, Roberto; Villani, Marco
abstract
Cellular automata can be applied to modelling the dynamics of spatially extended physicalsystems, and represent an alternative to the classical PDE approach. In this paper a macroscopiccellular automata model for simulating the bioremediation of contaminated soils is introduced.The choice of macroscopic automata is motivated by the aim to simulate largescale systems.It is suggested that in some cases, where the basic laws of continuum mechanics cannot bedirectly applied without adding phenomenological assumptions, and where the equation systemis not amenable to analytical solution, direct discrete modelling may represent a convenientalternative to the use of continuum models, followed by numerical discretization. This hypothesisis empirically tested in the bioremediation case.The model describes the bioremediation of contaminated soils, which relies upon the use ofindigeneous microorganisms to degrade the contaminant: bioremediation models pose particularchallenges as several physical, chemical and biological phenomena interact in a disordered andpartially unknown matrix (the soil). The model is hierarchical, and is composed by a fluiddynamical layer, a solute description layer and a biological layer. The model has been testedin a pilot plant, in the case of contamination by phenol. The values of the phenomenologicalparameters have been determined by the use of genetic algorithms. The model has proven capableto carefully describe experimental results in a wide range of experimental conditions. It has alsobeen run on a MIMD parallel architecture, achieving a high speedup. It therefore representsan example of application of cellular automata to a realworld problem which has a very highsocial and economic importance, and where progresses in modelling may greatly improve theeffectiveness of the decontamination interventions.
1999
 Biorisanamento insitu di terreni contaminati
[Relazione in Atti di Convegno]
Serra, Roberto; Mazzanti, M.; Villani, Marco; Andretta, M.; Di Gregorio, S.; Rongo, R.; Spataro, W.
abstract
Descrizione di un modello ad automi cellulari per la simulazione dei flussi di falda, del trasporto di inquinanti, e di azioni di bioremediation
1999
 Colombo: a new model for the simulation of soil remediation
[Relazione in Atti di Convegno]
Serra, Roberto; M., Andretta; M., Mazzanti; Villani, Marco; S., Di Gregorio
abstract
A main goal in order to face problems concerning polluted soil is the capability of computing the multiphase flows (gas, water, oils) in the soil matrix . In this paper, a CA model for simulating the fluiddynamics of contaminated porous soils is introduced. The choice of macroscopic automata is motivated by the aim of simulating large scale systems.
1999
 Progetto Colombo: realizzazione di impianti pilota per la taratura e la verifica sperimentale del modello
[Relazione in Atti di Convegno]
Andretta, M.; Campisi, T.; Mingozzi, L.; Villani, Marco; Serra, Roberto
abstract
L'articolo tratta la costruzione di impianti pilota per la validazione sperimentale di un modello ad automi cellulari, simulante eventi di biorisanamento
1999
 Progetto Colombo: un nuovo modello di simulazione di fenomeni di biorisanamento Insitu
[Relazione in Atti di Convegno]
Andretta, M.; Mazzanti, M.; Villani, Marco; Serra, Roberto; Di Gregorio, S.
abstract
L'articolo tratta di un modello ad automi cellulari per la simulazione di eventi di biorisanamento, nato all'interno del progetto europeo COLOMBO
1998
 Bioremediation simulation models
[Relazione in Atti di Convegno]
Serra, Roberto; Di Gregorio, S.; Villani, Marco; Andretta, M.
abstract
The remediation of contaminated soils is one of today's major environmental problems in industrial countries. Among the different techniques which can be applied, in situ bioremediation, which relies upon the use of indigeneous microorganisms to degrade the contaminant, is one of the most attractive, both from an environmental and an economic viewpoint.A (macroscopic) cellular automata model is presented here, which describes the major phenomena which take place in bioremediation. The reasons why macroscopic cellular automata have been used are discussed. The model is hierarchical, and is composed by i) a fluid dynamical layer, which describes multiphase flow through the soil, ii) a solute description layer, which deals with solute transport, adsorption/desorption, chemical reactions and iii) a biological layer, which describes biomass growth and its interaction with the different chemicals.The model has been tested in a pilot plant, in the case of contamination by phenol.
1998
 Environmental applications of genetic algorithms
[Relazione in Atti di Convegno]
Di Gregorio, S.; Serra, Roberto; Villani, Marco
abstract
An application of genetic algorithms to a problem of environmental restoration is presented. The application concerns the insitu bioremediation of contaminated soils, where indigeneous bacteria are stimulated to degrade the contaminant, by introducing a suitable nutrient solution directly in the soil. Forecasting the results of field operations from laboratory and pilot plant data is very important, and it requires the use of simulation models, which describe the interaction between different physical, chemical and biological phenomena. The main features are briefly summarized of a bioremediation model based on the paradigm of cellular automata, which successfully describes data obtained at a pilot plant scale. Genetic algorithms have been used in order to tailor the model to a specific case, namely contamination by phenol.
1998
 Genetic network models of biodegradation
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco; Salvemini, A.
abstract
The dynamical model of bacterial degradation of organic compounds which is discussed here provides a description of the degrading behaviour in terms of interacting genes which may switch from active to inactive state, thus providing a generalization of the well known Kauffman model of random boolean networks, which is well suited for single cells, to the multicell case. This generalization requires that the variables describing gene activation be real, instead of boolean. Moreover, the vast majority of the cell’s genes, which provide the standard metabolic machinery of the cell, are treated in a way different from the relatively few genes which are directly involved in the biodegradation : the latter ones are carefully described, while the effects of the former ones are described by an aggregate variable.Two different examples of specific models, which are both consistent with the overall framework, are introduced, and their dynamical behaviour is studied, in the particular case where all the genes are arranged on a 2D regular square topology, with connections among neighbouring sites. Thus, the model is an example of a cellularautomata like model, and a continuum generalization of random boolean networks.
1998
 MODELLING THE INTERACTION OF PHYSICAL, CHEMICAL AND BIOLOGICAL PHENOMENA IN POROUS SOILS: A SUMMARY OF RESULTS
[Articolo su rivista]
S., DI GREGORIO; Serra, Roberto; Villani, Marco
abstract
missing
1998
 Recent advances in dynamical models of bioremediation
[Relazione in Atti di Convegno]
Serra, Roberto; Villani, Marco; Oricchio, D.; Di Gregorio, S.
abstract
A cellular automata model of the complex set of interacting phenomena which take place in bioremediation has proven able to accurately describe several experimental data on a pilot plant. There are some parameters in the model which are chosen in such a way as to match experimental data. In this paper it is shown that the model has interesting generalization capabilities, i.e. that it can lead to accurate predictions also in some cases which have not been used for parameter adaptation.Moreover, some possible variants are examined : the first one amounts to a model simplification by resorting to a local equilibrium assumption for the adsorption/desorption process, while in the second one a cellular automata with time variable step is introduced, in order to avoid some nonphysical situations which might arise in the original model. Both variants are tested and discussed, and it is shown that they do not lead to improved performance, at least on the available set of experimental data.
1997
 A CELLULAR AUTOMATA MODEL OF SOIL BIOREMEDIATION
[Articolo su rivista]
S., DI GREGORIO; Serra, Roberto; Villani, Marco
abstract
The remediation of contaminated soils is one of the major environmental problems in industrial countries today. Among the different techniques that can be applied, in situ bioremediation, which relies upon the use of indigeneous microorganisms to degrade the contaminant, is one of the most attractive, both from an environmental and an economic viewpoint.A fullscale bioremediation process requires a number of laboratory and pilotscale tests in order to assess the feasibility of the remediation, to define potential health threats, and to find optimal operating conditions.Scaling up from the laboratory to the field can greatly benefit from the development of reliable mathematical models, which need to deal with several interacting physical, chemical, and biological phenomena.A macroscopic cellular automata (CA) model is presented here, which describes the major phenomena that take place in bioremediation. The reasons for using macroscopic CA are discussed. The model is composed of three layers, each layer depending on the others.The model has been tested in a pilot plant in the case of contamination by phenol. The values of the phenomenological parameters have been determined by the use of genetic algorithms (GAs). The model has provencapable of carefully describing experimental results for a wide range of experimental conditions. It is therefore an application of CA models to a realworld problem of high social and economic relevance.
1997
 MODELLING BACTERIAL DEGRADATION OF ORGANIC COMPOUNDS WITH GENETIC NETWORKS
[Articolo su rivista]
Serra, Roberto; Villani, Marco
abstract
The bacterial degradation of organic compounds plays a crucial role in the biogeochemical cycles ofthe earth and in the clean!up of contaminated soils[ The processes are carried out by bacterial consortia\rather than isolated strains\ which are usually modelled by phenomenological kinetic equations whichdescribe a _ctitious\ homogeneous bacterial species which mimics the behaviour of the consortium[An alternative modelling framework is presented here\ where the bacterial consortia are consideredas networks of genes interacting with other genes as well as with chemicals\ which may be eitherintroduced from outside or produced by bacterial metabolism[ The model is based on an extension ofthe random Boolean network model of genetic networks\ which makes use of continuous dynamicalvariables[ Three di}erent models are introduced\ which di}er in the way how they account for theexistence of di}erent species] "i# a single supercell model\ where all the genes can interact strongly witheach other^ "ii# a graded interaction model\ where genes interact strongly within a species\ and weaklyamong di}erent species^ and "iii# a separate subsets model\ where genes interact only within species[It is shown how this modelling framework is sound\ as it is able to reproduce some of the genericbehaviours of bacterial consortia\ describing experimentally observed phenomena like populationchanges induced by contamination\ and preypredator dynamics[
1996
 Combining cellular automata and genetic search in complex environmental modelling
[Relazione in Atti di Convegno]
Di Gregorio, S.; Serra, Roberto; Villani, Marco
abstract
Soil bioremediation is a highly complex phenomenon and involves several disciplines at the same time, including fluid dynamics, chemistry and biology. In this paper the fluid dynamical aspects of a cellular automata based model are discussed, and some comparisons with experimental data are presented. Genetic algorithms have been applied in order to tune the model to a specific case.
1996
 Mathematical models for bioremediation of contaminated soils
[Relazione in Atti di Convegno]
Andretta, M.; Di Gegorio, S.; Serra, Roberto; Villani, Marco
abstract
L'articolo tratta di un modello ad automi cellulari di eventi di biorisanamento, simulante flusso di acqua e trasporto di inquinanti
1996
 Parallel simulation of soil contamination by cellular automata
[Relazione in Atti di Convegno]
Di Gregorio, S.; Rongo, R.; Serra, Roberto; Spataro, W.; Spezzano, G.; Talia, D.; Villani, Marco
abstract
A new cellular automata model of the complex set of interacting phenomena which take place in bioremediation is described. The model allows the scaling between pilot plant situations and field operations, and  because its structure  shows interesting speedup capabilities
1996
 Simulation of water flow through a porous soil by a Cellular Automaton model
[Relazione in Atti di Convegno]
Di Gregorio, S.; Rongo, R.; Serra, Roberto; Spataro, W.; Villani, Marco
abstract
Soil bioremediation is a highly complex phenomenon and involves several disciplines at the same time, including fluid dynamics, chemistry and biology. A cellular automata model is currently under development, which deals with all these kinds of phenomena. In this paper the fluid dynamical aspects of this model are discussed, and some comparisons with experimental data are presented. Genetic algorithms have been applied in order to tune the model to a specific case.
1995
 LGANN: a parallel system combining a local genetic algorithm and neural networks for the prediction of secondary structure of proteins
[Articolo su rivista]
F., Vivarelli; G., Giusti; Villani, Marco; R., Campanini; P., Fariselli; M., Compiani; R., Casadio
abstract
In this work we describe a parallel system consisting of feedforward neural networks supervised by a local genetic algorithm. The system is implemented in a transputer architecture and is used to predict the secondary structures of globular proteins. This method allows a wide search in the parameter space of the neural networks and the determination of their optimal topology for the predictive task. Different neural network topologies are selected by the genetic algorithm on the basis of minimal values of mean square errors on the testing set. When the helix, ßstrand and random coil motifs of secondary structures are discriminated, the maximal efficiency obtained is 0.62, with correlation coefficients of 0.35, 0.31 and 0.37 respectively. This level of accuracy is similar to that previously attained by means of neural networks without hidden layers and using single protein sequences as input. The results validate the neural network topologies used for the prediction of protein secondary structures and highlight the relevance of the input information in determining the limit of their performance.
1994
 Parallel Architectures and intrinsically Parallel Algorithms: Genetics Algorithms
[Articolo su rivista]
R., Campanini; G., DI CARO; Villani, Marco; I., D'Antone; G., Giusti
abstract
Genetic algorithms are search or classification algorithms based on natural models. They present a high degree of internal parallelism. We developed two versions, differing in the way the population is organized and we studied and compared their characteristics and performances when applied to the optimization of multidimensional function problems. All the implementations are realized on transputer networks.