arXiv subjects

Sylvain Sené

Publications and source records attributed to Sylvain Sené.

At least 19 recordsLinked to original sources

arXiv2026

Parsimonious computational inference protocol for Boolean networks: Application to osteogenesis

Boolean networks are powerful mathematical tools for modeling the qualitative dynamics of genetic regulation. Yet inferred models often generate spurious attractors that lack biological viability. In this paper, we propose a parsimonious computational framework to systematically refine Boolean network models by eliminating these non-biological asymptotic behaviors while strictly preserving known, biologically relevant attractors. Through an exhaustive exploration of local function substitutions, we generate a comprehensive set of candidate models. To identify the most biologically consistent networks, we implement an incremental pruning protocol that filters candidates based on structural interaction digraph similarity, attraction basin topological organization, trajectorial isomorphism, and the minimization of dynamical instability and frustration. We apply this methodology to a 9-node genetic control model of the osteogenesis regulation network. Our protocol effectively evaluates a syntactic search space of 51,138 potential networks, ultimately narrowing them down to a robust family of 6 parsimonious models that are fully compatible with current biological knowledge.

q-bio.MN↗

arXiv2026

Robustness of Boolean networks to update modes: an application to hereditary angioedema

Many familial diseases are caused by genetic accidents, which affect both the genome and its epigenetic environment, expressed as an interaction graph between the genes as that involved in one familial disease we shall study, the hereditary angioedema. The update of the gene states at the vertices of this graph (1 if a gene is activated, 0 if it is inhibited) can be done in multiple ways, well studied over the last two decades: Parallel, sequential, block-sequential, block-parallel, random, etc. We will study a particular graph, related to the familial disease proposed as an example, which has subgraphs which activate in an intricate manner (\emph{i.e.}, in an alternating block-parallel mode, with one core constantly updated and two complementary subsets of genes alternating their updating), of which we will study the structural aspects, robust or unstable, in relation to some classical periodic update modes.

cs.DM↗

arXiv2026

On the Convergence of Elementary Cellular Automata under Sequential Update Modes

In this paper, we perform a theoretical analysis of the sequential convergence of elementary cellular automata that have at least one fixed point. Our aim is to establish which elementary rules always reach fixed points under sequential update modes, regardless of the initial configuration. In this context, we classify these rules according to whether all initial configurations converge under all, some, one or none sequential update modes, depending on if they have fixed points under synchronous (or parallel) update modes.

cs.DM↗

arXiv2025

Creation of fixed points in block-parallel Boolean automata networks

In the context of discrete dynamical systems and their applications, fixed points often have a clear interpretation. This is indeed a central topic of gene regulatory mechanisms modeled by Boolean automata networks (BANs), where a collection of Boolean entities (the automata) update their state depending on the states of others. Fixed points represent phenotypes such as differentiated cell types. The interaction graph of a BAN captures the architecture of dependencies among its automata. A first seminal result is that cycles of interactions (so called feedbacks) are the engines of dynamical complexity. A second seminal result is that fixed points are invariant under block-sequential update schedules, which update the automata following an ordered partition of the set of automata. In this article we study the ability of block-parallel update schedules (dual to the latter) to break this fixed point invariance property, with a focus on the simplest feedback mechanism: the canonical positive cycle. We quantify numerically the creation of new fixed points, and provide families of block-parallel update schedules generating exponentially many fixed points on this elementary structure of interaction.

cs.DM↗

arXiv2025

Foundations of block-parallel automata networks

We settle the theoretical ground for the study of automata networks under block-parallel update schedules, which are somehow dual to the block-sequential ones, but allow for repetitions of automaton updates. This gain in expressivity brings new challenges, and we analyse natural equivalence classes of update schedules: those leading to the same dynamics, and to the same limit dynamics, for any automata network. Countings and enumeration algorithms are provided, for their numerical study. We also prove computational complexity bounds for many classical problems, involving fixed points, limit cycles, the recognition of subdynamics, reachability, etc. The PSPACE-completeness of computing the image of a single configuration lifts the complexity of most problems, but the landscape keeps some relief, in particular for reversible computations.

cs.DM↗

arXiv2024

Dynamical Stability of Threshold Networks over Undirected Signed Graphs

This paper, we explore the dynamics of threshold networks on undirected signed graphs. Much attention has been dedicated to understanding the convergence and long-term behavior of this model. Yet, an open question persists: How does the underlying graph structure impact network dynamics? Similar studies have been carried out for threshold networks and other types of Boolean networks, but the latter primarily focus on unsigned networks. Here, we address this question in the context of signed threshold networks. We introduce the stability index of a signed graph, related to the concepts of antibalance in signed graphs. Our index establishes a connection between the structure and the dynamics of signed threshold networks. We show that signed graphs having a negative stability index on every induced subgraph exhibit stable dynamics, i.e., the dynamics converge to fixed points regardless of their threshold parameters. Conversely, if at least one induced subgraph has a non-negative stability index, oscillations in long-term behavior may appear. Furthermore, we generalize the analysis to network dynamics under periodic update schemes.

cs.DM↗

arXiv2024

On elementary cellular automata asymptotic (a)synchronism sensitivity and complexity

Among the fundamental questions in computer science is that of the impact of synchronism/asynchronism on computations, which has been addressed in various fields of the discipline: in programming, in networking, in concurrence theory, in artificial learning, etc. In this paper, we tackle this question from a standpoint which mixes discrete dynamical system theory and computational complexity, by highlighting that the chosen way of making local computations can have a drastic influence on the performed global computation itself. To do so, we study how distinct update schedules may fundamentally change the asymptotic behaviors of finite dynamical systems, by analyzing in particular their limit cycle maximal period. For the message itself to be general and impacting enough, we choose to focus on a ``simple'' computational model which prevents underlying systems from having too many intrinsic degrees of freedom, namely elementary cellular automata. More precisely, for elementary cellular automata rules which are neither too simple nor too complex (the problem should be meaningless for both), we show that update schedule changes can lead to significant computational complexity jumps (from constant to superpolynomial ones) in terms of their temporal asymptotes.

nlin.CG↗

arXiv2024

Complexity of Boolean automata networks under block-parallel update modes

Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their 0-1 states according to local rules. The dynamics of the network is highly sensitive to update modes, i.e., to the schedule according to which the automata apply their local rule. A new family of update modes appeared recently, called block-parallel, which is dual to the well studied block-sequential. Although basic, it embeds the rich feature of update repetitions among a temporal updating period, allowing for atypical asymptotic behaviors. In this paper, we prove that it is able to breed complex computations, squashing almost all decision problems on the dynamics to the traditionally highest (for reachability questions) class PSPACE. Despite obtaining these complexity bounds for a broad set of local and global properties, we also highlight a surprising gap: bijectivity is still coNP.

cs.DM↗

arXiv2023

Turning block-sequential automata networks into smaller parallel networks with isomorphic limit dynamics

We state an algorithm that, given an automata network and a block-sequential update schedule, produces an automata network of the same size or smaller with the same limit dynamics under the parallel update schedule. Then, we focus on the family of automata cycles which share a unique path of automata, called tangential cycles, and show that a restriction of our algorithm allows to reduce any instance of these networks under a block-sequential update schedule into a smaller parallel network of the family and to characterize the number of reductions operated while conserving their limit dynamics. We also show that any tangential cycles reduced by our main algorithm are transformed into a network whose size is that of the largest cycle of the initial network. We end by showing that the restricted algorithm allows the direct characterization of block-sequential double cycles as parallel ones.

cs.DM↗

arXiv2023

On countings and enumerations of block-parallel automata networks

When we focus on finite dynamical systems from both the computability/complexity and the modelling standpoints, automata networks seem to be a particularly appropriate mathematical model on which theory shall be developed. In this paper, automata networks are finite collections of entities (the automata), each automaton having its own set of possible states, which interact with each other over discrete time, interactions being defined as local functions allowing the automata to change their state according to the states of their neighbourhoods. The studies on this model of computation have underlined the very importance of the way (i.e. the schedule) according to which the automata update their states, namely the update modes which can be deterministic, periodic, fair, or not. Indeed, a given network may admit numerous underlying dynamics, these latter depending highly on the update modes under which we let the former evolve. In this paper, we pay attention to a new kind of deterministic, periodic and fair update mode family introduced recently in a modelling framework, called the block-parallel update modes by duality with the well-known and studied block-sequential update modes. More precisely, in the general context of automata networks, this work aims at presenting what distinguish block-parallel update modes from block-sequential ones, and at counting and enumerating them: in absolute terms, by keeping only representatives leading to distinct dynamics, and by keeping only representatives giving rise to distinct isomorphic limit dynamics. Put together, this paper constitutes a first theoretical analysis of these update modes and their impact on automata networks dynamics.

cs.DM↗

arXiv2022

Boolean automata isolated cycles and tangential double-cycles dynamics

Our daily social and political life is more and more impacted by social networks. The functioning of our living bodies is deeply dependent on biological regulation networks such as neural, genetic, and protein networks. And the physical world in which we evolve, is also structured by systems of interacting particles. Interaction networks can be seen in all spheres of existence that concern us, and yet, our understanding of interaction networks remains severely limited by our present lack of both theoretical and applied insight into their clockworks. In the past, efforts at understanding interaction networks have mostly been directed towards applications. This has happened at the expense of developing understanding of the generic and fundamental aspects of interaction networks. Intrinsic properties of interaction networks (eg the ways in which they transmit information along entities, their ability to produce this or that kind of global dynamical behaviour depending on local interactions) are thus still not well understood. Lack of fundamental knowledge tends to limit the innovating power of applications. Without more theoretical fundamental knowledge, applications cannot evolve deeply and become more impacting. Hence, it is necessary to better apprehend and comprehend the intrinsic properties of interaction networks, notably the relations between their architecture and their dynamics and how they are affected by and set in time. In this chapter, we use the elementary mathematical model of Boolean automata networks as a formal archetype of interaction networks. We survey results concerning the role of feedback cycles and the role of intersections between feedback cycles, in shaping the asymptotic dynamical behaviours of interaction networks.

cs.DM↗

arXiv2022

About block-parallel Boolean networks: a position paper

In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or less asymptotic dynamical behaviours such as fixed points or limit cycles. Since such mathematical models have been used in the framework of biological networks modelling, the question of choosing appropriate update schedules has arised soon. In this note, focusing on Boolean networks, our aim is to emphasise that the adequate way of thinking regulations and genetic expression over time is certainly not to consider a wall segregating synchronicity from asynchronicity because they actually complement rather well. In particular, we highlight that specific update schedules, namely block-parallel update schedules, whose intrinsic features are still not known from a theoretical point of view, admit realistic and pertinent properties in the context of biological modelling and deserve certainly more attention from the community.

cs.DM↗

arXiv2022

Attractor landscapes in Boolean networks with firing memory

In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains at its firing state a finite number of steps. We prove in particular that these networks have the same computational power than the classical ones, ie any Boolean network with firing memory composed of $m$ vertices can be simulated by a Boolean network by adding vertices. We also prove general results on specific classes of networks. For instance, we show that the existence of at least one delay greater than 1 in disjunctive networks makes such networks have only fixed points as attractors. Moreover, for arbitrary networks composed of two vertices, we characterize the delay phase space, \ie the delay values such that networks admits limit cycles or fixed points. Finally, we analyze two classical biological models by introducing delays: the model of the immune control of the $λ$-phage and that of the genetic control of the floral morphogenesis of the plant \emph{Arabidopsis thaliana}.

cs.DM↗

arXiv2021

Non-deterministic updates of Boolean networks

Boolean networks are discrete dynamical systems where each automaton has its own Boolean function for computing its state according to the configuration of the network. The updating mode then determines how the configuration of the network evolves over time. Many of updating modes from the literature, including synchronous and asynchronous modes, can be defined as the composition of elementary deterministic configuration updates, i.e., by functions mapping configurations of the network. Nevertheless, alternative dynamics have been introduced using ad-hoc auxiliary objects, such as that resulting from binary projections of Memory Boolean networks, or that resulting from additional pseudo-states for Most Permissive Boolean networks. One may wonder whether these latter dynamics can still be classified as updating modes of finite Boolean networks, or belong to a different class of dynamical systems. In this paper, we study the extension of updating modes to the composition of non-deterministic updates, i.e., mapping sets of finite configurations. We show that the above dynamics can be expressed in this framework, enabling a better understanding of them as updating modes of Boolean networks. More generally, we argue that non-deterministic updates pave the way to a unifying framework for expressing complex updating modes, some of them enabling transitions that cannot be computed with elementary and non-elementary deterministic updates.

math.DS↗

arXiv2020

Optimising attractor computation in Boolean automata networks

This paper details a method for optimising the size of Boolean automata networks in order to compute their attractors under the parallel update schedule. This method relies on the formalism of modules introduced recently that allows for (de)composing such networks. We discuss the practicality of this method by exploring examples. We also propose results that nail the complexity of most parts of the process, while the complexity of one part of the problem is left open.

cs.LO↗

arXiv2020

#P-completeness of counting update digraphs, cacti, and a series-parallel decomposition method

Automata networks are a very general model of interacting entities, with applications to biological phenomena such as gene regulation. In many contexts, the order in which entities update their state is unknown, and the dynamics may be very sensitive to changes in this schedule of updates. Since the works of Aracena et. al, it is known that update digraphs are pertinent objects to study non-equivalent block-sequential update schedules. We prove that counting the number of equivalence classes, that is a tight upper bound on the synchronism sensitivity of a given network, is #P-complete. The problem is nevertheless computable in quasi-quadratic time for oriented cacti, and for oriented series-parallel graphs thanks to a decomposition method.

cs.DM↗

arXiv2020

On the complexity of acyclic modules in automata networks

Modules were introduced as an extension of Boolean automata networks. They have inputs which are used in the computation said modules perform, and can be used to wire modules with each other. In the present paper we extend this new formalism and study the specific case of acyclic modules. These modules prove to be well described in their limit behavior by functions called output functions. We provide other results that offer an upper bound on the number of attractors in an acyclic module when wired recursively into an automata network, alongside a diversity of complexity results around the difficulty of deciding the existence of cycles depending on the number of inputs and the size of said cycle.

cs.DM↗

arXiv2020

Complexity of limit-cycle problems in Boolean networks

Boolean networks are a general model of interacting entities, with applications to biological phenomena such as gene regulation. Attractors play a central role, and the schedule of entities update is a priori unknown. This article presents results on the computational complexity of problems related to the existence of update schedules such that some limit-cycle lengths are possible or not. We first prove that given a Boolean network updated in parallel, knowing whether it has at least one limit-cycle of length $k$ is $\text{NP}$-complete. Adding an existential quantification on the block-sequential update schedule does not change the complexity class of the problem, but the following alternation brings us one level above in the polynomial hierarchy: given a Boolean network, knowing whether there exists a block-sequential update schedule such that it has no limit-cycle of length $k$ is $Σ_2^\text{P}$-complete.

cs.DM↗