Related papers: An Algorithm for Detecting Fixed Points of Boolean…
A distributed algorithm is described for finding a common fixed point of a family of m>1 nonlinear maps M_i : R^n -> R^n assuming that each map is a paracontraction and that at least one such common fixed point exists. The common fixed…
The mutations of a complex systemic disease like cancer can be modeled as stuck-at faults in the Boolean system paradigm. For a class of multiple faults, the fault identification is exceptionally significant under the incomplete access of…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…
We propose a general approach for change-point detection in dynamic networks. The proposed method is model-free and covers a wide range of dynamic networks. The key idea behind our approach is to effectively utilize the network structure in…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
Interacting biological systems at all organizational levels display emergent behavior. Modeling these systems is made challenging by the number and variety of biological components and interactions (from molecules in gene regulatory…
Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to…
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…
Gene regulatory networks (GRNs) are increasingly used for explaining biological processes with complex transcriptional regulation. A GRN links the expression levels of a set of genes via regulatory controls that gene products exert on one…
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…
A change point problem occurs in many statistical applications. If there exist change points in a model, it is harmful to make a statistical analysis without any consideration of the existence of the change points and the results derived…
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…
Boolean equivalence allows Boolean networks with identical functionality to exhibit diverse graph structures. This gives more room for exploration in logic optimization, while also posing a challenge for tasks involving consistency between…
We prove that the fully asynchronous dynamics of a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$ without negative loop can be simulated, in a very specific way, by a monotone Boolean network with $2n$ components. We then use this result to…
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…
Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by…
Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…
Recent empirical studies have identified fixed point iteration phenomena in deep neural networks, where the hidden state tends to stabilize after several layers, showing minimal change in subsequent layers. This observation has spurred the…
Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by…
Using a graph-theoretic approach, we derive a new sufficient condition for observability of a Boolean control network (BCN). Based on this condition, we describe two algorithms: the first selects a set of nodes so that observing this set…