Related papers: Collectively canalizing Boolean functions
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…
A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a Boolean function, depending on a selected subset of variables. Boolean networks have been widely…
Nested canalization (NC) is a property of Boolean functions which has been recently extended to multivalued functions. We study the effect of the Van Ham mapping (from multivalued to Boolean functions) on this property. We introduce the…
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…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
Methods for learning Bayesian network structure can discover dependency structure between observed variables, and have been shown to be useful in many applications. However, in domains that involve a large number of variables, the space of…
Living systems operate in a critical dynamical regime -- between order and chaos -- where they are both resilient to perturbation, and flexible enough to evolve. To characterize such critical dynamics, the established 'structural theory' of…
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…
Consider a point-to-point communication system in which the transmitter holds a binary message of length $m$ and transmits a corresponding codeword of length $n$. The receiver's goal is to recover a Boolean function of that message, where…
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 study the class of cooperative Boolean networks whose only regulatory functions are COPY, binary AND, and binary OR. We prove that for all sufficiently large N and c < 2 there exist Boolean networks in this class that have an attractor…
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determine the states of most other nodes in the network? To answer…
Estimating dependence relationships between variables is a crucial issue in many applied domains, such as medicine, social sciences and psychology. When several variables are entertained, these can be organized into a network which encodes…
This survey provides a comprehensive overview of the study of the binary and Boolean rank from both a mathematical and a computational perspective, with particular emphasis on their relationship to the real rank. We review the basic…
This paper surveys mathematical models, structural results and algorithms in controlled sensing with social learning in social networks. Part 1, namely Bayesian Social Learning with Controlled Sensing addresses the following questions: How…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
We investigate the dynamical properties of the transcriptional regulation of gene expression in the yeast Saccharomyces Cerevisiae within the framework of a synchronously and deterministically updated Boolean network model. By means of a…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Correlation-immune (CI) multi-output Boolean functions have the property of keeping the same output distribution when some input variables are fixed. Recently, a new application of CI functions has appeared in the system of resisting…