arXiv subjects

Eric Goles

Publications and source records attributed to Eric Goles.

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

Complexity of Fungal Automaton Prediction

Fungal automata are a nature-inspired computational model, where a rule is alternatively applied verticaly and horizontaly. In this work we study the computational complexity of predicting the dynamics of all fungal freezing totalistic one-dimentional rules of radius $1$, exhibiting various behaviors. Despite efficiently predictable in most cases (with non-deterministic logspace algorithms), a non-linear rule is left open to characterize. We further explore the freezing majority rule (which is totalistic), and prove that at radius $1.5$ it becomes $\mathbf{P}$-complete to predict.

cs.CC↗

arXiv2026

Embedding arbitrary Boolean circuits into fungal automata with arbitrary update sequences

The sandpile automata of Bak, Tang, and Wiesenfeld (Phys. Rev. Lett., 1987) are a simple model for the diffusion of particles in space. A fundamental problem related to the complexity of the model is predicting its evolution in the parallel setting. Despite decades of effort, a classification of this problem for two-dimensional sandpile automata remains outstanding. Fungal automata were recently proposed by Goles et al. (Phys. Lett. A, 2020) as a spin-off of the model in which diffusion occurs either in horizontal $(H)$ or vertical $(V)$ directions according to a so-called update scheme. Goles et al. proved that the prediction problem for this model with the update scheme $H^4V^4$ is $\textbf{P}$-complete. This result was subsequently improved by Modanese and Worsch (Algorithmica, 2024), who showed the problem is $\textbf{P}$-complete also for the simpler updatenscheme $HV$. In this work, we fill in the gaps and prove that the prediction problem is $\textbf{P}$-complete for any update scheme that contains both $H$ and $V$ at least once.

cs.CC↗

arXiv2025

On the complexity of freezing automata networks of bounded pathwidth

An automata network is a graph of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on the states such that the state evolution of any node is non-decreasing in any orbit. They are commonly used to model epidemic propagation, diffusion phenomena like bootstrap percolation or cristal growth. Previous works have established that, under the hypothesis that the network graph is of bounded treewidth, many problems that can be captured by trace specifications at individual nodes admit efficient algorithms. In this paper we study the even more restricted case of a network of bounded pathwidth and show two hardness results that somehow illustrate the complexity of freezing dynamics under such a strong graph constraint. First, we show that the trace specification checking problem is NL-complete. Second, we show that deciding first order properties of the orbits augmented with a reachability predicate is NP-hard.

cs.CC↗

arXiv2025

Solving decision problems by distributed consensus with one-dimensional, binary, radius-$2$ cellular automata over cyclic configurations

Probing the ability of automata networks to solve decision problems has received a continuous attention in the literature, and specially with the automata reaching the answer by distributed consensus, i.e., their all taking on a same state, out of two. In the case of binary automata networks, regardless of the kind of update employed, the networks should display only two possible attractors, the fixed points $0^L$ and $1^L$, for all cyclic configurations of size $L$. A previous investigation into the space of one-dimensional, binary, radius-2 cellular automata identified a restricted subset of rules as potential solvers of decision problems, but the reported results were incomplete and lacked sufficient detail for replication. To address this gap, we conducted a comprehensive reevaluation of the entire radius-2 rule space, by filtering it with all configuration sizes from 5 to 20, according to their basins of attraction being formed by only the two expected fixed points. A set of over fifty-four thousand potential decision problem solvers were then obtained. Among these, more than forty-five thousand were associated with 3 well-defined decision problems, and precise formal explanations were provided for over forty thousand of them. The remaining candidate rules suggest additional problem classes yet to be fully characterised. Overall, this work substantially extends the understanding of radius-2 cellular automata, offering a more complete picture of their capacity to solve decision problems by consensus.

cs.DM↗

arXiv2025

Complexity of the Freezing Majority Rule with L-shaped Neighborhoods

In this article we investigate the computational complexity of predicting two dimensional freezing majority cellular automata with states $\{-1,+1\}$, where the local interactions are based on an L-shaped neighborhood structure. In these automata, once a cell reaches state $+1$, it remains fixed in that state forever, while cells in state $-1$ update to the most represented state among their neighborhoods. We consider L-shaped neighborhoods, which mean that the vicinity of a given cell $c$ consists in a subset of cells in the north and east of $c$. We focus on the prediction problem, a decision problem that involves determining the state of a given cell after a given number of time-steps. We prove that when restricted to the simplest L-shaped neighborhood, consisting of the central cell and its nearest north and east neighbors, the prediction problem belongs to $\mathsf{NC}$, meaning it can be solved efficiently in parallel. We generalize this result for any L-shaped neighborhood of size two. On the other hand, for other L-shaped neighborhoods, the problem becomes $\mathsf{P}$-complete, indicating that the problem might be inherently sequential.

cs.CC↗

arXiv2025

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

Boolean-network simplification and rule fitting to unravel chemotherapy resistance in non-small cell lung cancer

Boolean networks are powerful frameworks for capturing the logic of gene-regulatory circuits, yet their combinatorial explosion hampers exhaustive analyses. Here, we present a systematic reduction of a 31-node Boolean model that describes cisplatin- and pemetrexed-resistance in non-small-cell lung cancer to a compact 9-node core that exactly reproduces the original attractor landscape. The streamlined network shrinks the state space by four orders of magnitude, enabling rapid exploration of critical control points, rules fitting and candidate therapeutic targets. Extensive synchronous and asynchronous simulations confirm that the three clinically relevant steady states and their basins of attraction are conserved and reflect resistance frequencies close to those reported in clinical studies. The reduced model provides an accessible scaffold for future mechanistic and drug-discovery studies.

cs.DM↗

arXiv2025

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↗

arXiv2025

Impact of (a)Synchronism on ECA: Towards a New Classification

In this paper, we study the effect of (a)synchronism on the dynamics of elementary cellular automata. Within the framework of our study, we choose five distinct update schemes, selected from the family of periodic update modes: parallel, sequential, block-sequential, block-parallel, and local clocks. Our main measure of complexity is the maximum period of the limit cycles in the dynamics of each rule. In this context, we present a classification of the ECA rule landscape. We classified most elementary rules into three distinct regimes: constant, linear, and superpolynomial. Surprisingly, while some rules exhibit more complex behavior under a broader class of update schemes, others show similar behavior across all the considered update schemes. Although we are able to derive upper and lower bounds for the maximum period of the limit cycles in most cases, the analysis of some rules remains open. To complement the study of the 88 elementary rules, we introduce a numerical simulation framework based on two main measurements: the energy and density of the configurations. In this context, we observe that some rules exhibit significant variability depending on the update scheme, while others remain stable, confirming what was observed as a result of the classification obtained in the theoretical analysis.

cs.DM↗

arXiv2023

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↗

arXiv2023

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↗

arXiv2022

Exploring the Dynamics of Fungal Cellular Automata

Cells in a fungal hyphae are separated by internal walls (septa). The septa have tiny pores that allow cytoplasm flowing between cells. Cells can close their septa blocking the flow if they are injured, preventing fluid loss from the rest of filament. This action is achieved by special organelles called Woronin bodies. Using the controllable pores as an inspiration we advance one and two-dimensional cellular automata into Elementary fungal cellular automata (EFCA) and Majority fungal automata (MFA) by adding a concept of Woronin bodies to the cell state transition rules. EFCA is a cellular automaton where the communications between neighboring cells can be blocked by the activation of the Woronin bodies (Wb), allowing or blocking the flow of information (represented by a cytoplasm and chemical elements it carries) between them. We explore a novel version of the fungal automata where the evolution of the system is only affected by the activation of the Wb. We explore two case studies: the Elementary Fungal Cellular Automata (EFCA), which is a direct application of this variant for elementary cellular automata rules, and the Majority Fungal Automata (MFA), which correspond to an application of the Wb to two dimensional automaton with majority rule with Von Neumann neighborhood. By studying the EFCA model, we analyze how the 256 elementary cellular automata rules are affected by the activation of Wb in different modes, increasing the complexity on applied rule in some cases. Also we explore how a consensus over MFA is affected when the continuous flow of information is interrupted due to the activation of Woronin bodies.

nlin.CG↗

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 $\lambda$-phage and that of the genetic control of the floral morphogenesis of the plant \emph{Arabidopsis thaliana}.

cs.DM↗

arXiv2021

On the complexity of the generalized Q2R automaton

We study the dynamic and complexity of the generalized Q2R automaton. We show the existence of non-polynomial cycles as well as its capability to simulate with the synchronous update the classical version of the automaton updated under a block sequential update scheme. Furthermore, we show that the decision problem consisting in determine if a given node in the network changes its state is \textbf{P}-Hard.

cs.DM↗

arXiv2021

Generating Boolean Functions on Totalistic Automata Networks

We consider the problem of studying the simulation capabilities of the dynamics of arbitrary networks of finite states machines. In these models, each node of the network takes two states 0 (passive) and 1 (active). The states of the nodes are updated in parallel following a local totalistic rule, i.e., depending only on the sum of active states. Four families of totalistic rules are considered: linear or matrix defined rules (a node takes state 1 if each of its neighbours is in state 1), threshold rules (a node takes state 1 if the sum of its neighbours exceed a threshold), isolated rules (a node takes state 1 if the sum of its neighbours equals to some single number) and interval rule (a node takes state 1 if the sum of its neighbours belong to some discrete interval). We focus in studying the simulation capabilities of the dynamics of each of the latter classes. In particular, we show that totalistic automata networks governed by matrix defined rules can only implement constant functions and other matrix defined functions. In addition, we show that t by threshold rules can generate any monotone Boolean functions. Finally, we show that networks driven by isolated and the interval rules exhibit a very rich spectrum of boolean functions as they can, in fact, implement any arbitrary Boolean functions. We complement this results by studying experimentally the set of different Boolean functions generated by totalistic rules on random graphs.

cs.CC↗

arXiv2021

Phase transitions in a conservative Game of Life

We investigate the dynamics of a conservative version of Conway's Game of Life, in which a pair consisting of a dead and a living cell can switch their states following Conway's rules but only by swapping their positions, irrespective of their mutual distance. Our study is based on square-lattice simulations as well as a mean-field calculation. As the density of dead cells is increased, we identify a discontinuous phase transition between an inactive phase, in which the dynamics freezes after a finite time, and an active phase, in which the dynamics persists indefinitely in the thermodynamic limit. Further increasing the density of dead cells leads the system back to an inactive phase via a second transition, which is continuous on the square lattice but discontinuous in the mean-field limit.

cond-mat.stat-mech↗

arXiv2021

Freezing sandpiles and Boolean threshold networks: equivalence and complexity

The NC versus P-hard classification of the prediction problem for sandpiles on the two dimensional grid with von Neumann neighborhood is a famous open problem. In this paper we make two kinds of progresses, by studying its freezing variant. First, it enables to establish strong connections with other well known prediction problems on networks of threshold Boolean functions such as majority. Second, we can highlight some necessary and sufficient elements to the dynamical complexity of sandpiles, with a surprisingly crucial role of cells with two grains.

cs.DM↗