Related papers: Revealing the canalizing structure of Boolean func…
Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The…
This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory…
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…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…
The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…
Nowadays, Deep Neural Networks are among the main tools used in various sciences. Convolutional Neural Network is a special type of DNN consisting of several convolution layers, each followed by an activation function and a pooling layer.…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…
We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…
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…
Inferring dynamic biochemical networks is one of the main challenges in systems biology. Given experimental data, the objective is to identify the rules of interaction among the different entities of the network. However, the number of…
The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal…
We introduce combinatorial interpretability, a methodology for understanding neural computation by analyzing the combinatorial structures in the sign-based categorization of a network's weights and biases. We demonstrate its power through…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to…
Many researchers have studied symmetry properties of various Boolean functions. A class of Boolean functions, called nested canalyzing functions (NCFs), has been used to model certain biological phenomena. We identify some interesting…