Related papers: Creation of fixed points in block-parallel Boolean…
The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean…
We consider Hodgkin-Huxley-type model that is a stiff ODE system with two fast and one slow variables. For the parameter ranges under consideration the original version of the model has unstable fixed point and the oscillating attractor…
The aim of this paper is to analyze a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks formed by agents with first-order dynamics. In particular, in the analyzed class a single evaluation of a…
We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants…
This paper considers a linear panel model with interactive fixed effects and unobserved individual and time heterogeneities that are captured by some latent group structures and an unknown structural break, respectively. To enhance realism…
We consider the problem of analyzing timestamped relational events between a set of entities, such as messages between users of an on-line social network. Such data are often analyzed using static or discrete-time network models, which…
We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent…
The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In the autonomous version, such a system is a set of functions x:R{\to}{0,1}^{n} called states (R is the time…
This paper presents a gate-level Boolean evolutionary geometric attention neural network that models images as Boolean fields governed by logic gates. Each pixel is a Boolean variable (0 or 1) embedded on a two-dimensional geometric…
Boolean networks are one of the most studied discrete models in the context of the study of gene expression. In order to define the dynamics associated to a Boolean network, there are several \emph{update schemes} that range from parallel…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
Non-stationary sequences arise naturally in control, forecasting, and decision-making. The data-generating process shifts at unknown times, and models must detect the change, discard or downweight obsolete evidence, and adapt to new…
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…
We propose a novel formalism for describing Structural Causal Models (SCMs) as fixed-point problems on causally ordered variables, eliminating the need for Directed Acyclic Graphs (DAGs), and establish the weakest known conditions for their…
Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or…
Feedback loops in a dynamic network play an important role in determining the dynamics of that network. Through a computational study, in this paper we show that networks with fewer independent negative feedback loops tend to exhibit more…
Many discrete models of biological networks rely exclusively on Boolean variables and many tools and theorems are available for analysis of strictly Boolean models. However, multilevel variables are often required to account for threshold…
The understanding of Boolean automata networks dynamics takes an important place in various domains of computer science such as computability, complexity and discrete dynamical systems. In this paper, we make a step further in this…
This paper establishes (set) identification results in a dynamic dyadic network formation model with time-varying observed covariates, lagged local network statistics, and unobserved heterogeneity in the form of fixed effects. Our framework…