相关论文: On the Robustness of NK-Kauffman Networks Against …

Boolean variables are such that they take only values on $ \mathbb{Z}_2 \cong \left\{0, 1 \right\} $. \textit{NK}-Kauffman networks are dynamical deterministic systems of $ N $ Boolean functions that depend only on $ K \leq N $ Boolean…

We develop further the consequences of the irreducible-Boolean classification established in Ref. [9]; which have the advantage of allowing strong statistical calculations in disordered Boolean function models, such as the…

We determine the average number $ \vartheta (N, K) $, of \textit{NK}-Kauffman networks that give rise to the same binary function. We show that, for $ N \gg 1 $, there exists a connectivity critical value $ K_c $ such that $ \vartheta(N,K)…

In this work we consider random Boolean networks that provide a general model for genetic regulatory networks. We extend the analysis of James Lynch who was able to proof Kauffman's conjecture that in the ordered phase of random networks,…

We investigate Threshold Random Boolean Networks with $K = 2$ inputs per node, which are equivalent to Kauffman networks, with only part of the canalyzing functions as update functions. According to the simplest consideration these networks…

This paper proposes a new parameter for studying Boolean networks: the independence number. We establish that a Boolean network is $k$-independent if, for any set of $k$ variables and any combination of binary values assigned to them, there…

Boolean networks are used to model biological networks such as gene regulatory networks. Often Boolean networks show very chaotic behaviour which is sensitive to any small perturbations. In order to reduce the chaotic behaviour and to…

We consider Boolean functions f:{-1,1}^n->{-1,1} that are close to a sum of independent functions on mutually exclusive subsets of the variables. We prove that any such function is close to just a single function on a single subset. We also…

This paper revisits the problem of learning a k-CNF Boolean function from examples in the context of online learning under the logarithmic loss. In doing so, we give a Bayesian interpretation to one of Valiant's celebrated PAC learning…

The dynamics of Boolean networks (the N-K model) with scale-free topology are studied here. The existence of a phase transition governed by the value of the scale-free exponent of the network is shown analytically by analyzing the overlap…

A model of cellular metabolism due to S. Kauffman is analyzed. It consists of a network of Boolean gates randomly assembled according to a probability distribution. It is shown that the behavior of the network depends very critically on…

Boolean networks are used to model biological networks such as gene regulatory networks. Often Boolean networks show very chaotic behavior which is sensitive to any small perturbations.In order to reduce the chaotic behavior and to attain…

Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of…

It has been shown \citep{broeck90:physicalreview,patarnello87:europhys} that feedforward Boolean networks can learn to perform specific simple tasks and generalize well if only a subset of the learning examples is provided for learning.…

Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…

We consider the Stochastic Boolean Function Evaluation (SBFE) problem in the well-studied case of $k$-of-$n$ functions: There are independent Boolean random variables $x_1,\dots,x_n$ where each variable $i$ has a known probability $p_i$ of…

In this work we analyze scale-free networks with different power law spectra $N(k) \sim k^{-\gamma}$ under a boolean dynamic, where the boolean rule that each node obeys is a function of its connectivity $k$. This is done by using only two…

Approximate Bayesian inference is NP-hard. Dagum and Luby defined the Local Variance Bound (LVB) to measure the approximation hardness of Bayesian inference on Bayesian networks, assuming the networks model strictly positive joint…

Deep neural networks are renowned for their ability to generalise well across diverse tasks, even when heavily overparameterized. Existing works offer only partial explanations (for example, the NTK-based task-model alignment explanation…

A Boolean network (BN) with $n$ components is a discrete dynamical system described by the successive iterations of a function $f:\{0,1\}^n \to \{0,1\}^n$. This model finds applications in biology, where fixed points play a central role.…