相关论文: Finite size corrections to random Boolean networks

The point estimates of ReLU classification networks---arguably the most widely used neural network architecture---have been shown to yield arbitrarily high confidence far away from the training data. This architecture, in conjunction with a…

This paper addresses the problem of distributed learning of average belief with sequential observations, in which a network of $n>1$ agents aim to reach a consensus on the average value of their beliefs, by exchanging information only with…

Boolean Networks (BNs) are established models to qualitatively describe biological systems. The analysis of BNs might be infeasible for medium to large BNs due to the state-space explosion problem. We propose a novel reduction technique…

In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…

An important part of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov Random Field. The belief propagation algorithm, which is an exact procedure to compute…

Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…

This paper investigates the approximation power of three types of random neural networks: (a) infinite width networks, with weights following an arbitrary distribution; (b) finite width networks obtained by subsampling the preceding…

Belief propagation is a well-studied algorithm for approximating local marginals of multivariate probability distribution over complex networks, while tensor network states are powerful tools for quantum and classical many-body problems.…

Boolean networks have been used successfully in modeling biological networks and provide a good framework for theoretical analysis. However, the analysis of large networks is not trivial. In order to simplify the analysis of such networks,…

Due to the scarcity of quantitative details about biological phenomena, quantitative modeling in systems biology can be compromised, especially at the subcellular scale. One way to get around this is qualitative modeling because it requires…

In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows to prune simple logical cascades and under-determined variables, returning thereby…

We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the…

Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive…

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…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

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…

It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…

Belief Propagation algorithms are instruments used broadly to solve graphical model optimization and statistical inference problems. In the general case of a loopy Graphical Model, Belief Propagation is a heuristic which is quite successful…

Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by…

Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a…