Related papers: Invariant Subspace Approach to Boolean (Control) N…

Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been…

The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However,…

A deep neural network (DNN) with piecewise linear activations can partition the input space into numerous small linear regions, where different linear functions are fitted. It is believed that the number of these regions represents the…

Network control theory has recently emerged as a promising approach for understanding brain function and dynamics. By operationalizing notions of control theory for brain networks, it offers a fundamental explanation for how brain dynamics…

Biological processes, including cell differentiation, organism development, and disease progression, can be interpreted as attractors (fixed points or limit cycles) of an underlying networked dynamical system. In this paper, we study the…

Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…

This review explains in a self-contained way the properties of random Boolean networks and their attractors, with a special focus on critical networks. Using small example networks, analytical calculations, phenomenological arguments, and…

We present a renormalization-grouplike method performed in the state space for detecting the dynamical behaviors of large scale-free Boolean networks, especially for the chaotic regime as well as the edge of chaos. Numerical simulations…

We show that the steady-state variance as a performance measure for a class of networked linear control systems is expressible as the summation of a rational function over the Laplacian eigenvalues of the network graph. Moreover, we…

The concept of a nested canalizing Boolean function has been studied over the course of the last decade in the context of understanding the regulatory logic of molecular interaction networks, such as gene regulatory networks. Such functions…

We present a smoothly broken power law functional form (that we refer to as a Broken Neural Scaling Law (BNSL)) that accurately models & extrapolates the scaling behaviors of deep neural networks (i.e. how the evaluation metric of interest…

This study introduces a new normalization layer termed Batch Layer Normalization (BLN) to reduce the problem of internal covariate shift in deep neural network layers. As a combined version of batch and layer normalization, BLN adaptively…

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. We here derive an expression for the number of attractors in…

Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of…

The rapid growth of the size and complexity in deep neural networks has sharply increased computational demands, challenging their efficient deployment in real-world scenarios. Boolean networks, constructed with logic gates, offer a…

We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…

In this work, we explore the state-space formulation of a network process to recover, from partial observations, the underlying network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system…

This paper describes and discusses Bayesian Neural Network (BNN). The paper showcases a few different applications of them for classification and regression problems. BNNs are comprised of a Probabilistic Model and a Neural Network. The…

This paper studies the controllability backbone problem in dynamical networks defined over graphs. The main idea of the controllability backbone is to identify a small subset of edges in a given network such that any subnetwork containing…

We investigate dynamical properties of a quantum generalization of classical reversible Boolean networks. The state of each node is encoded as a single qubit, and classical Boolean logic operations are supplemented by controlled bit-flip…