Boolean network

Boolean modelling of biological networks is a well-established technique for abstracting dynamical biomolecular regulation in cells. Specifically, decoding linkages between salient regulatory network states and corresponding cell fate outcomes can help uncover pathological foundations of diseases such as cancer. Attractor landscape analysis is one such methodology which converts complex network behavior into a landscape of network states wherein each state is represented by propensity of its occurrence. Towards undertaking attractor landscape analysis of Boolean networks, we propose an Attractor Landscape Analysis Toolbox (ATLANTIS) for cell fate discovery, from biomolecular networks, and reprogramming upon network perturbation. ATLANTIS can be employed to perform both deterministic and probabilistic analyses. It has been validated by successfully reconstructing attractor landscapes from several published case studies followed by reprogramming of cell fates upon therapeutic treatmen...

Abstract: The whole complex process to obtain a protein encoded by a gene is difficult to include in a mathematical model. There are many models for describing different aspects of a genetic network. Finding a better model is one of the most important and interesting ...

Background A gene network's capacity to process information, so as to bind past events to future actions, depends on its structure and logic. From previous and new microarray measurements in Saccharomyces cerevisiae following gene deletions and overexpressions, we identify a core gene regulatory network (GRN) of functional interactions between 328 genes and the transfer functions of each gene. Inferred connections are verified by gene enrichment. Results We find that this core network has a generalized clustering coefficient that is much higher than chance. The inferred Boolean transfer functions have a mean p-bias of 0.41, and thus similar amounts of activation and repression interactions. However, the distribution of p-biases differs significantly from what is expected by chance that, along with the high mean connectivity, is found to cause the core GRN of S. cerevisiae's to have an overall sensitivity similar to critical Boolean networks. In agreement, we find that the am...

We propose a quantum algorithm to estimate the Gowers U2 norm of a Boolean function, and extend it into a second algorithm to distinguish between linear Boolean functions and Boolean functions that are ǫ-far from the set of linear Boolean functions, which seems to perform better than the classical BLR algorithm. Finally, we outline an algorithm to estimate Gowers U3 norms of Boolean functions.

We propose a quantum algorithm to estimate the Gowers U2 norm of a Boolean function, and extend it into a second algorithm to distinguish between linear Boolean functions and Boolean functions that are ǫ-far from the set of linear Boolean functions, which seems to perform better than the classical BLR algorithm. Finally, we outline an algorithm to estimate Gowers U3 norms of Boolean functions.

In biological networks, the temporal evolution of gene or protein expressions constitutes a dynamical system. Modeling the coupled dynamics and characterization of the longrun behavior of such networks is perhaps the most important task in genomic signal processing. In the literature, long-run distribution has been conjectured to correspond

In this paper, we present a new Boolean resubstitution technique with permissible functions and ordered binary decision diagrams, abbreviated as OBDD . Boolean resubstitution is one technique for multi-level logic optimization. Permissible functions are special don't care sets. We represent the data structure of permissible functions and logic functions at each node in Boolean networks in terms of OBDD. Therefore, logic functions can be flexibly manipulated and rapidly executed. We have previously reported a multi-level logic optimization technique called transduction methods[l] using OBDD in ICCAD'89 . We have improved the OBDD operation techniques, so that now OBDD operations can be executed faster than we reported before. We also applied Boolean resubstitution to our multi-level logic synthesis. We present results of experiments employing the improved OBDD operation techniques and applying Boolean resubstitution to our multi-level logic synthesis.

Random Boolean networks have been used as simple models of gene regulatory networks, enabling the study of the dynamic behavior of complex biological systems. However, analytical treatment has been difficult because of the structural heterogeneity and the vast state space of these networks. Here we used mean field approximations to analyze the dynamics of a class of Boolean networks in which nodes have random degree (connectivity) distributions, characterized by the mean degree k and variance D. To achieve this we generalized the simple cellular automata rule 126 and used it as the Boolean function for all nodes. The equation for the evolution of the density of the network state is presented as a one-dimensional map for various input degree distributions, with k and D as the control parameters. The mean field dynamics is compared with the data obtained from the simulations of the Boolean network. Bifurcation diagrams and Lyapunov exponents for different parameter values were compute...

Boolean networks are used to model biological networks such as gene regulatory networks. Often Boolean networks show very chaotic behaviour which is sensitive to any small perturbations. In order to reduce the chaotic behaviour and to attain stability in the gene regulatory network, nested Canalizing Functions (NCFs) are best suited. NCFs and its variants have a wide range of applications in systems biology. Previously, many works were done on the application of canalizing functions, but there were fewer methods to check if any arbitrary Boolean function is canalizing or not. In this paper, by using Karnaugh Map this problem is solved and also it has been shown that when the canalizing functions of n variable is given, all the canalizing functions of 1  n variable could be generated by the method of concatenation. In this paper we have uniquely identified the number of NCFs having a particular Hamming Distance (H.D) generated by each variable i x as starting canalizing input. Partially NCFs of 4 variables has also been studied in this paper.

A notion of Integral Value Transformations (IVTs) is defined over $\mathbb{N} \times \mathbb{N}$ using pair of two variable Boolean functions. The dynamics of the IVTs over $\mathbb{N} \times \mathbb{N}$ is studied from algebraic perspective. It is seen that the dynamics of the IVTs solely depend on the dynamics (state transition diagram) of the pair of two variable Boolean functions. A set of sixteen Collatz-like IVTs are identified. Also, the dynamical system of IVTs having attractor with one (Non-Collatz-like) two, three and four cycles are studied.

We present an exact algorithm, based on techniques from the field of Model Checking, for finding control policies for Boolean networks (BN) with control nodes. Given a BN, a set of starting states, I, a set of goal states, F , and a target time, t, our algorithm automatically finds a sequence of control signals that deterministically drives the BN from I to F at, or before time t, or else guarantees that no such policy exists. Despite recent hardness-results for finding control policies for BNs, we show that, in practice, our algorithm runs in seconds to minutes on over 13,400 BNs of varying sizes and topologies, including a BN model of embryogenesis in D. melanogaster with 15,360 Boolean variables. We then extend our method to automatically identify a set of Boolean transfer functions that reproduce the qualitative behavior of gene regulatory networks. Specifically, we automatically (re)learn a BN model of D. melanogaster embryogenesis in 5.3 seconds, from a space containing 6.9 × 10 10 possible models.

We present algorithms for finding control strategies in Boolean Networks (BN). Our approach uses symbolic techniques from the field of model checking. We show that despite recent hardness-results for finding control policies, a model checking-based approach is often capable of scaling to extremely large and complex models. We demonstrate the effectiveness of our approach by applying it to a BN model of embryogenesis in D. melanogaster with 15,360 Boolean variables.

In this article, a model is presented of a network whose structure was inspired by the 'five elements law' of Chinese medicine. Computer simulations illustrate the dynamic behavior of this system, that can be set in different attractors of Boolean type and can be differentially modified by delays and perturbations. We suggest that this model may contribute to the understanding of the 'logic' of the regulation of biological systems by means of small and carefully selected perturbations, a major line of thought of complementary therapies.

We propose a new representation of quantum circuits that eliminates the projection steps traditionally associated with measurement, resulting in a fundamentally static depiction of the circuit without intrinsic time ordering. In this framework, the evolution of the quantum system is fully unitary and deterministic, with no irreversible processes. By decoupling physical evolution from subjective measurement outcomes, this approach offers a novel, time-symmetric view of quantum mechanics, free from traditional notions of causality and the directional flow of time.

We consider incomplete exponential sums in several variables of the form where m > 1 is odd and f is a polynomial of degree d with coefficients in Z/mZ. We investigate the conjecture, originating in a problem in computational complexity, that for each fixed d and m the maximum norm of S(f, n, m) converges exponentially fast to 0 as n tends to infinity; we also investigate the optimal bounds for these sums. Previous work has verified the conjecture when m = 3 and d = 2. In the present paper we develop three separate techniques for studying the problem in the case of quadratic f , each of which establishes a different special case. We show that a bound of the required sort holds for almost all quadratic polynomials, the conjecture holds for all quadratic polynomials with n ≤ 10 variables (and the conjectured bounds are sharp), and for arbitrarily many variables the conjecture is true for a class of quadratic polynomials having a special form.

This brief addresses the problem of implementing very large constant multiplications by a single variable under the shift-adds architecture using a minimum number of adders/subtractors. Due to the intrinsic complexity of the problem, we introduce an approximate algorithm, called TÕLL, which partitions the very large constants into smaller ones. To reduce the number of operations, TÕLL incorporates graph-based and common subexpression elimination methods proposed for the shift-adds design of constant multiplications. It can also consider the delay of a multiplierless design defined in terms of the maximum number of operations in series, i.e., the number of adder-steps, while reducing the number of operations. High-level experimental results show that the adder-steps of a shift-adds design can be reduced significantly with a little overhead in the number of operations. Gate-level experimental results indicate that while the shift-adds design can lead to a 36.6% reduction in gate-level area with respect to a design using a multiplier, the delay-aware optimization can yield a 48.3% reduction in minimum achievable delay of the shift-adds design when compared to the area-aware optimization.

This brief addresses the problem of implementing very large constant multiplications by a single variable under the shift-adds architecture using a minimum number of adders/subtractors. Due to the intrinsic complexity of the problem, we introduce an approximate algorithm, called TÕLL, which partitions the very large constants into smaller ones. To reduce the number of operations, TÕLL incorporates graph-based and common subexpression elimination methods proposed for the shift-adds design of constant multiplications. It can also consider the delay of a multiplierless design defined in terms of the maximum number of operations in series, i.e., the number of adder-steps, while reducing the number of operations. High-level experimental results show that the adder-steps of a shift-adds design can be reduced significantly with a little overhead in the number of operations. Gate-level experimental results indicate that while the shift-adds design can lead to a 36.6% reduction in gate-level area with respect to a design using a multiplier, the delay-aware optimization can yield a 48.3% reduction in minimum achievable delay of the shift-adds design when compared to the area-aware optimization.

The main contribution of this paper is an exact common subexpression elimination algorithm for the optimum sharing of partial terms in multiple constant multiplications (MCMs). We model this problem as a Boolean network that covers all possible partial terms that may be used to generate the set of coefficients in the MCM instance. We cast this problem into a 0-1 integer linear programming (ILP) problem by requiring that the single output of this network is asserted while minimizing the number of gates representing operations in the MCM implementation that evaluate to one. A satisfiability (SAT)-based 0-1 ILP solver is used to obtain the exact solution. We argue that for many real problems, the size of the problem is within the capabilities of current SAT solvers. Because performance is often a primary design parameter, we describe how this algorithm can be modified to target the minimum area solution under a user-specified delay constraint. Additionally, we propose an approximate algorithm based on the exact approach with extremely competitive results. We have applied these algorithms on the design of digital filters and present a comprehensive set of results that evaluate ours and existing approximation schemes against exact solutions under different number representations and using different SAT solvers.

Boolean Inference makes it possible to observe the congestion status of end-to-end paths and infer, from that, the congestion status of individual network links. In principle, this can be a powerful monitoring tool, in scenarios where we want to monitor a network without having direct access to its links. We consider one such real scenario: a Tier-1 ISP operator wants to monitor the congestion status of its peers. We show that, in this scenario, Boolean Inference cannot be solved with enough accuracy to be useful; we do not attribute this to the limitations of particular algorithms, but to the fundamental difficulty of the Inference problem. Instead, we argue that the "right" problem to solve, in this context, is compute the probability that each set of links is congested (as opposed to try to infer which particular links were congested when). Even though solving this problem yields less information than provided by Boolean Inference, we show that this information is more useful in practice, because it can be obtained accurately under weaker assumptions than typically required by Inference algorithms and more challenging network conditions (link correlations, nonstationary network dynamics, sparse topologies).

It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it "generates" several stable 1 states (resp. a cyclic attractor). However, there are no definite mathematical frameworks translating the underlying meaning of "generates". Focusing on Boolean networks, we recall and propose some definitions concerning the notion of functionality along with associated mathematical results.

In this work, a perturbation analysis of stochastic boolean network with perturbation has been realized, by using power series expansions. More specifically, we have considered the sensitivity analysis of a SBNP with three genes, where we have perturbed the perturbation probability. keywords: Power series expansions; Stochastic boolean network; Markov chains. MSC2010: 30E; 37N; 65C.

We use probabilistic boolean networks to simulate the pathogenesis of Dengue Hemorraghic Fever (DHF). Based on Chaturvedi's work, the strength of cytokine influences are modeled stochastically as inducement probabilities. Two basins of attractors are observed with synchronous updating; the Null Infection cycle attractor shows an expected cross-regulation of Th1 and Th2 cytokines corresponding to the homeostasis of an uninfected person, while the DHF Infection attractor shows the onset of DHF. With asynchronous updating, our model remains valid with clinical comparisons against qualitative changes in signal durations. In order to find intervention points that could prevent DHF, we design a genetic algorithm to shift the DHF attractor to the DF attractor basin by using the DF final state as the fitness measure. Our simulation results identify TGF-β, IL-8 and IL-13 as the intervention points which are consistent with known clinical results to prevent DHF from occurring.

OPTIMIZING LARGE COMBINATIONAL NETWORKS FOR K-LUT BASED FPGA MAPPING Ion I. BUCUR, PhD Ioana FĂGĂRĂŞAN, PhD Cornel POPESCU, PhD University Politehnica of Bucharest George CULEA, PhD University of Bacǎu, Faculty of Electrical Engineering, ...

This paper describes the effects of perturbations, which simulate the knock-out of single genes, one at a time, in random Boolean models of genetic networks (RBN). The analysis concentrates on the probability distribution of so-called avalanches (defined in the text) in gene expression. The topology of the random Boolean networks considered here is of the scale-free type, with a power-law distribution of outgoing connectivities. The results for these scale-free random Boolean networks (SFRBN) are compared with those of classical RBNs, which had been previously analyzed, and with experimental 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.

The asymptotic dynamics of random Boolean networks subject to random 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 generalize 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 major 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 Threshold 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

Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are de ned by regulatory rules driving the dynamics that have certain so-called canalizing properties. In this paper, we investigate the dynamics of a random Boolean network with such properties using analytical methods and simulations. From our simulations, we observe that Boolean networks with higher canalizing depth have generally fewer attractors, the attractors are smaller, and the basins are larger, with implications for the stability and robustness of the models. ese properties are relevant to many biological applications. Moreover, our results show that, from the standpoint of the attractor structure, high canalizing depth, compared to relatively small positive canalizing depth, has a very modest impact on dynamics. Motivated by these observations, we conduct mathematical study of the attractor structure of a random Boolean network of canalizing depth one (i.e., the smallest positive depth). For every positive integer ℓ, we give an explicit formula for the limit of the expected number of attractors of length ℓ in an n-state random Boolean network as n goes to in nity.

Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by regulatory rules driving the dynamics that have certain so-called canalizing properties. In this paper, we investigate the dynamics of a random Boolean network with such properties using analytical methods and simulations. From our simulations, we observe that Boolean networks with higher canalizing depth have generally fewer attractors, the attractors are smaller, and the basins are larger, with implications for the stability and robustness of the models. These properties are relevant to many biological applications. Moreover, our results show that, from the standpoint of the attractor structure, high canalizing depth, compared to relatively small positive canalizing depth, has a very modest impact on dynamics. Motivated by these observations, we con...

The effects of the finite size of the network on the evolutionary dynamics of a Boolean network are analyzed. In the model considered, Boolean networks evolve via a competition between nodes that punishes those in the majority. Previous studies of the model have found that large networks evolve to a statistical steady state that is both critical and highly canalized, and that the evolution of canalization, which is a form of robustness found in genetic regulatory networks, is associated with a particular symmetry of the evolutionary dynamics. Here it is found that finite size networks evolve in a fundamentally different way than infinitely large networks do. The symmetry of the evolutionary dynamics of infinitely large networks that selects for canalizing Boolean functions is broken in the evolutionary dynamics of finite size networks. In finite size networks there is an additional selection for input inverting Boolean functions that output a value opposite to the majority of input values. These results are revealed through an empirical study of the model that calculates the frequency of occurrence of the different possible Boolean functions. Classes of functions are found to occur with the same frequency. Those classes depend on the symmetry of the evolutionary dynamics and correspond to orbits of the relevant symmetry group. The empirical results match analytic results, determined by utilizing Pólya's theorem, for the number of orbits expected in both finite size and infinitely large networks. The reason for the symmetry breaking in the evolutionary dynamics is found to be due to the need for nodes in finite size networks to behave differently in order to cooperate so that the system collectively performs as well as possible. The results suggest that both finite size effects and symmetry are important for understanding the evolution of real-world complex networks, including genetic regulatory networks.

We study the dynamics of majority automata networks when the vertices are updated according to a block sequential updating scheme. In particular, we show that the complexity of the problem of predicting an eventual state change in some vertex, given an initial configuration, is PSPACE-complete.

We study the dynamics of majority automata networks when the vertices are updated according to a block sequential updating scheme. In particular, we show that the complexity of the problem of predicting an eventual state change in some vertex, given an initial configuration, is PSPACE-complete.

In this paper, we discuss the problem of optimizing a multi-level logic combinational Boolean network. Our techniques apply a sequence of local perturbations and modifications of the network which are guided by the automatic test pattern generation ATPG based reasoning. In particular, we propose several new ways in which one or more redundant gates or wires can be added to a network. We show how to identify gates which are good candidates for local functionality change. Furthermore, we discuss the problem of adding and removing two wires, none of which alone is redundant, but when jointly added/removed they do not affect functionality of the network. We also address the problem of efficient redundancy computation which allows to eliminate many unnecessary redundancy tests. We have performed experiments on MCNC benchmarks and compared the results to those of misII and RAMBO[6]. Experimental results are very encouraging.

Intestinal crypts are multicellular structures the properties of which have been partially characterized, both in the "normal" and in the "transformed" development. Only in the last years there has been an increasing interest in using mathematical and computational models to achieve new insights from a "systems point-of-view". However, the overall picture lacks of a general model covering all the key distinct processes and phenomena involved in the activity of the crypt. Here we propose a new multiscale model of crypt dynamics combining Gene Regulatory Networks at the intra-cellular level with a morphological model comprising spatial patterning, cell migration and crypt homeostasis at the inter-cellular level. The intra-cellular model is a Noisy Random Boolean Network ruling cell growth, division rate and lineage commitment in terms of emergent properties. The inter-cellular spatial dynamics is an extension of the Cellular Potts Model, a statistical mechanics model in which cells are represented as lattice sites in a 2D cellular automaton successfully used to model homeostasis in the crypts. The internal dynamics of each cell is modeled with a Noisy Random Boolean Network (NRBN) , a generalization of classical RBNs [18,, a highly abstract and general model of gene regulatory network, which was proven to reproduce several biological properties of real networks . As proposed by Villani et al. [30], NRBNs are particularly effective in describing some of the

Standard Random Boolean Networks display an order-disorder phase transition. We add to the standard Random Boolean Networks a disconnection rule which couples the control and order parameters. By this way, the system is driven to the critical line transition. Under the influence of perturbations the system point out self-organized critical behavior. Several numerical simulations have been done and compared with a proposed analytical treatment.

Multi-terminal switching lattices are typically exploited for modeling switching nano-crossbar arrays that lead to the design and construction of emerging nanocomputers. In this paper we propose a switching lattice optimization method for a special class of "regular" Boolean functions, called autosymmetric functions. Autosymmetry is a property that is frequent enough within Boolean functions to be interesting in the synthesis process. Each autosymmetric function can be synthesized through a new function (called restriction), depending on less variables and with a smaller on-set, which can be computed in polynomial time. In this paper we describe how to exploit the autosymmetry property of a Boolean function in oder to obtain a smaller lattice representation in a reduced minimization time. The original Boolean function can be constructed through a composition of the restriction with some EXORs of subsets of the input variables. Similarly, the lattice implementation of the function can be constructed using some external lattices for the EXORs, whose outputs will input the lattice implementing the restriction. Finally, the output of the restriction lattice corresponds to the output of the original function. Experimental results show that the total area of the obtained lattices is often significantly reduced. Moreover, in many cases, the computational time necessary to minimize the restriction is smaller than the time necessary to perform the lattice synthesis of the entire function.

Neural networks have been applied in various domain including science, commerce, medicine, and industry. However, The knowledge learned by a trained neural network is difficult to understand. This paper proposes a Boolean algebra based algorithm to extract comprehensible Boolean rules from supervised feed-forward neural networks to uncover the black-boxed knowledge. This algorithm is called the BAB-BB rule extraction algorithm, which stands for a Boolean algebra based rule extraction algorithm for neural networks with binary and bipolar inputs. Decomposition techniques and interval arithmetic are used in the algorithm. First, each neuron associated with its inputs is analyzed and a Boolean function, describing the activation rule from its inputs to the neuron, is derived. These Boolean functions are merged into an aggregated Boolean rule according to the network topology. The Boolean rule is then further simplified by Boolean algebra operations. During the rule extraction procedure, redundant hidden neurons can be detected and removed without affecting the original function of the neural network. Examples of unipolar and bipolar inputs are presented to demonstrate the use of our algorithm. Finally, the Exclusive OR problem is presented and solved by our algorithm. Results show that our BAB-BB algorithm is practicable and of high efficiency.

Tissue engineering protocols achieve building miniature hearts but mechanisms determining cell differentiation still need to be fully understood and optimized. In this study, we present a gene regulatory network (GRN) that describes the differentiation of committed cardiomyocytes towards ventricular or atrial cardiomyocytes. The GRN is coupled with Boolean dynamics and steady state analysis shows steady states which agree with the experimental expression of marker genes. Our Boolean model extends earlier work on a model describing the first and second heart field formation to include atrial and ventricular cardiomyocytes. Thus, our study paves the way for the generation of heart field-specific cardiomyocytes located in specific chambers of the fully developed heart. The Boolean model is validated through simulations and by its ability to reproduce known knockouts.

Background: Structural analysis of cellular interaction networks contributes to a deeper understanding of network-wide interdependencies, causal relationships, and basic functional capabilities. While the structural analysis of metabolic networks is a well-established field, similar methodologies have been scarcely developed and applied to signaling and regulatory networks. We propose formalisms and methods, relying on adapted and partially newly introduced approaches, which facilitate a structural analysis of signaling and regulatory networks with focus on functional aspects. We use two different formalisms to represent and analyze interaction networks: interaction graphs and (logical) interaction hypergraphs. We show that, in interaction graphs, the determination of feedback cycles and of all the signaling paths between any pair of species is equivalent to the computation of elementary modes known from metabolic networks. Knowledge on the set of signaling paths and feedback loops facilitates the computation of intervention strategies and the classification of compounds into activators, inhibitors, ambivalent factors, and non-affecting factors with respect to a certain species. In some cases, qualitative effects induced by perturbations can be unambiguously predicted from the network scheme. Interaction graphs however, are not able to capture AND relationships which do frequently occur in interaction networks. The consequent logical concatenation of all the arcs pointing into a species leads to Boolean networks. For a Boolean representation of cellular interaction networks we propose a formalism based on logical (or signed) interaction hypergraphs, which facilitates in particular a logical steady state analysis (LSSA). LSSA enables studies on the logical processing of signals and the identification of optimal intervention points (targets) in cellular networks. LSSA also reveals network regions whose parametrization and initial states are crucial for the dynamic behavior. We have implemented these methods in our software tool CellNetAnalyzer (successor of FluxAnalyzer) and illustrate their applicability using a logical model of T-Cell receptor signaling providing non-intuitive results regarding feedback loops, essential elements, and (logical) signal processing upon different stimuli. The methods and formalisms we propose herein are another step towards the comprehensive functional analysis of cellular interaction networks. Their potential, shown on a realistic Tcell signaling model, makes them a promising tool.

There is considerable research relating the structure of Boolean networks to their state space dynamics. In this paper, we extend the standard model to include the effects of thermal noise, which has the potential to deflect the trajectory of a dynamical system within its state space, sending it from one stable attractor to another. We introduce a new "thermal robustness" measure, which quantifies a Boolean network's resilience to such deflections. In particular, we investigate the impact of structural homogeneity on two dynamical properties: thermal robustness and attractor density. Through computational experiments on cyclic Boolean networks, we ascertain that as a homogeneous Boolean network grows in size, it tends to underperform most of its heterogeneous counterparts with respect to at least one of these two dynamical properties. These results strongly suggest that during an organism's growth and morphogenesis, cellular differentiation is required if the organism seeks to exhibit both an increasing number of attractors and resilience to thermal noise.

With the advent of the integrated circuits, greater emphasis was given on performance and miniaturization. But with the increasing prominence of portable and battery operated appliances the key factor that requires attention is power consumption. The feature size is shrinking due to the advancement in fabrication technology which causes integration of more transistors in the integrated circuit. As a result, the magnitude of power per unit area is growing and the accompanying problem of heat removal and cooling is worsening. To maintain the chip temperature at an acceptable level the dissipated heat must be removed effectively, the cost of heat removal and cooling becomes a significant factor in these circuits. The reliability of the

Timing convergence problem arises when the estimations made during logic synthesis can not be met during physical design. In this paper, an efficient rewiring engine is proposed to explore maximal freedom after placement. The most important feature of this approach is that the existing placement solution is left intact throughout the optimization. A linear time algorithm is proposed to detect functional symmetries in the Boolean network and is used as the basis for rewiring. Integration with an existing gate sizing algorithm further proves the effectiveness of our technique. Experimental results are very promising.

ere exist general transforms that convert pseudo-Boolean functions into k-bounded pseudo-Boolean functions, for all k ≥ 2. In addition to these general transforms, there can also exist specialized transforms that can be applied in special cases. New results are presented examining what happens to the "bit ip" neighborhood when transforms are applied. Transforms condense variables in a particular order. We show that di erent variable orderings produce di erent results in terms of problem di culty. We also prove new results about the embedding of the original function in the new k-bounded function. Finally, this paper also looks at how parameter optimization problems can be expressed as high precision k-bounded pseudo-Boolean functions. is paper lays a foundation for the wider application of evolutionary algorithms to k-bounded pseudo-Boolean functions. CCS CONCEPTS •Mathematics of computing →Graph algorithms; Combinatorial algorithms; • eory of computation →Evolutionary algorithms;

In this paper, we address the formal characterization of targets triggering cellular trans-differentiation in the scope of Boolean networks with asynchronous dynamics. Given two fixed points of a Boolean network, we are interested in all the combinations of mutations which allow to switch from one fixed point to the other, either possibly, or inevitably. In the case of existential reachability, we prove that the set of nodes to (permanently) flip are only and necessarily in certain connected components of the interaction graph. In the case of inevitable reachability, we provide an algorithm to identify a subset of possible solutions.

Cellular reprogramming, a technique that opens huge opportunities in modern and regenerative medicine, heavily relies on identifying key genes to perturb. Most of computational methods focus on finding mutations to apply to the initial state in order to control which attractor the cell will reach. However, it has been shown, and is proved in this article, that waiting between the perturbations and using the transient dynamics of the system allow new reprogramming strategies. To identify these temporal perturbations, we consider a qualitative model of regulatory networks, and rely on Petri nets to model their dynamics and the putative perturbations. Our method establishes a complete characterization of temporal perturbations, whether permanent (mutations) or only temporary, to achieve the existential or inevitable reachability of an arbitrary state of the system. We apply a prototype implementation on small models from the literature and show that we are able to derive temporal perturbations to achieve trans-differentiation.

Cellular reprogramming, a technique that opens huge opportunities in modern and regenerative medicine, heavily relies on identifying key genes to perturb. Most of the existing computational methods for controlling which attractor (steady state) the cell will reach focus on finding mutations to apply to the initial state. However, it has been shown, and is proved in this article, that waiting between perturbations so that the update dynamics of the system prepares the ground, allows for new reprogramming strategies. To identify such sequential perturbations, we consider a qualitative model of regulatory networks, and rely on Binary Decision Diagrams to model their dynamics and the putative perturbations. Our method establishes a set identification of sequential perturbations, whether permanent (mutations) or only temporary, to achieve the existential or inevitable reachability of an arbitrary state of the system. We apply an implementation for temporary perturbations on models from the literature, illustrating that we are able to derive sequential perturbations to achieve trans-differentiation.

Attractors of network dynamics represent the long-term behaviours of the modelled system. Their characterization is therefore crucial for understanding the response and differentiation capabilities of a dynamical system. In the scope of qualitative models of interaction networks, the computation of attractors reachable from a given state of the network faces combinatorial issues due to the state space explosion. In this paper, we present a new algorithm that exploits the concurrency between transitions of parallel acting components in order to reduce the search space. The algorithm relies on Petri net unfoldings that can be used to compute a compact representation of the dynamics. We illustrate the applicability of the algorithm with Petri net models of cell signalling and regulation networks, Boolean and multi-valued. The proposed approach aims at being complementary to existing methods for deriving the attractors of Boolean models, while being generic since it applies to any safe Petri net.

Boolean networks are commonly used in systems biology to model dynamics of biochemical networks by abstracting away many (and often unknown) parameters related to speed and species activity thresholds. It is then expected that Boolean networks produce an overapproximation of behaviours (reachable configurations), and that subsequent refinements would only prune some impossible transitions. However, we show that even generalized asynchronous updating of Boolean networks, which subsumes the usual updating modes including synchronous and fully asynchronous, does not capture all transitions doable in a multi-valued or timed refinement. We define a structural model transformation which takes a Boolean network as input and outputs a new Boolean network whose asynchronous updating simulates both synchronous and asynchronous updating of the original network, and exhibits even more behaviours than the generalized asynchronous updating. We argue that these new behaviours should not be ignored when analyzing Boolean networks, unless some knowledge about the characteristics of the system explicitly allows one to restrict its behaviour.

In this paper, we present a new type of neuron, called Boolean neuron. Further, we suggest the general structure of a neural network that includes only Boolean neurons and may realize several sets of Boolean functions. The advantages of these neural networks consist in the reduction of memory space and computation time in comparison to the representation of Boolean functions by usual neural networks. The Boolean neural network may be mapped to a FPGA so that our new training algorithms substitute classical design methods of these circuits. In the example, we show the decomposition of a set of Boolean functions into common basic functions and their mapping to the general Boolean neural network. Key-Words: Boolean neuron, BNN, data representation, FTFS, functions set