Related papers: Partial Order on the set of Boolean Regulatory Fun…
Canalization of genetic regulatory networks has been argued to be favored by evolutionary processes due to the stability that it can confer to phenotype expression. We explore whether a significant amount of canalization and partial…
We study the dynamical properties of small regulatory networks treated as non autonomous dynamical systems called modules when working inside larger networks or, equivalently when subject to external signal inputs. Particular emphasis is…
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…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…
In problems such as variable selection and graph estimation, models are characterized by Boolean logical structure such as presence or absence of a variable or an edge. Consequently, false positive error or false negative error can be…
We present an exploration of the rich theoretical connections between several classes of regularized models, network flows, and recent results in submodular function theory. This work unifies key aspects of these problems under a common…
Dynamical systems theory and complexity science provide powerful tools for analysing artificial agents and robots. Furthermore, they have been recently proposed also as a source of design principles and guidelines. Boolean networks are a…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and…
We have considered a Boolean control network where the state evolution equations depend on past states, controls and first derivatives of a function with respect to controls. Total approach has been the efficient use of matrix semi tensor…
The determination and classification of fixed points of large Boolean networks is addressed in terms of constraint satisfaction problem. We develop a general simplification scheme that, removing all those variables and functions belonging…
Biological phenomena differ significantly from physical phenomena. At the heart of this distinction is the fact that biological entities have computational abilities and thus they are inherently difficult to predict. This is the reason why…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…
Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give…
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…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
Multi-valued logical models can be used to describe biological networks on a high level of abstraction based on the network structure and logical parameters capturing regulatory effects. Interestingly, the dynamics of two distinct models…
Partial orders may be used for modeling and summarising ranking data when the underlying order relations are less strict than a total order. They are a natural choice when the data are lists recording individuals' positions in queues in…