Singular Boolean Networks Research Articles

Identification of a class of singular Boolean control networks

System identification, recognized as an inverse control problem, is a significant aspect of modern control theory. This study focuses on addressing the identification problem related to a specific category of singular Boolean networks (SBNs) and singular Boolean control networks (SBCNs). The introduction of two novel concepts, namely the admissibility and solvability matrices, enables the establishment of conditions for determining the existence and uniqueness of solutions for SBNs and SBCNs. Then criteria are deduced to identify the number of dynamic equations. Based on observability, controllability and detectability, several conditions are presented to characterize identification. Among them, two crucial results show: When the solution to an SBN or SBCN is unique, the SBN is identifiable if and only if it is observable, and the SBCN is identifiable if and only if it is O1-observable, which is the most general type of observability. Besides, effective algorithms are devised to implement identification. Furthermore, the study delves into the normalization issue using the admissibility matrix, which provides a possibility to reduce the identified SBN or SBCN to a lower-order BN or BCN.

Original Disturbance Decoupling of Singular Boolean Networks: A Reduced State Transition Matrix-Based Method

Original Disturbance Decoupling of Singular Boolean Networks: A Reduced State Transition Matrix-Based Method

The Boolean constraint method application for qualitative analysis of the dynamical properties of singular Boolean networks

Qualitative study problems of trajectories behaviour for singular Boolean networks functioning on a finite time interval are solved using the method of Boolean constraints. In the form of Boolean constraints, models are built for local dynamical properties, the periodicity property of trajectories, and the property of the reachability of the tar- get state set from the initial state set. Depending on the property, the verification of Boolean models is reduced to the Boolean satisfiability problem or the problem of verifying the truth of a quantified Boolean formula. Several examples demonstrate the technology of qualitative analysis of dynamic properties in a microservice het- erogeneous computing environment. The applied software modules for constructing a Boolean model of the dynamical property of singular Boolean networks and verifying the feasibility of the model are implemented in the form of computational microser- vices. The use of this approach provides independence, reproducibility, autonomy, and scalability of modules. The developed microservices are integrated into the applied microservices package. This package is intended for the qualitative study of binary dynamic systems. The rights to launch microservices are delegated to the managing agents of this package installed in the nodes of the distributed environment. The de- veloped automation tools allow a specialist in automaton dynamics to formulate the problem statement on a computational model of the subject area in meaningful terms. С использованием метода булевых ограничений решены задачи качественного исследования динамики поведения траекторий на конечном интервале времени сингулярных булевых сетей. Получены в виде булевых ограничений модели локальных динамических свойств, свойства периодичности траекторий и свойства достижимости целевого множества состояний из множества начальных состояний. В зависимости от свойств проверка булевых ограничений сводится к задаче булевой выполнимости или задаче проверки истинности квантифицированной булевой формулы. Приведен ряд примеров, на которых продемонстрирована технология качественного исследования динамических свойств в микросервисной гетерогенной вычисли- тельной среде. Прикладные программные модули для построения булевой модели динамического свойства сингулярной булевой сети и проверки выполнимости модели реализованы в виде вычислительных микросервисов. Применение такого подхода обеспечивает независимость, воспроизводимость, автономность и масштабируемость модулей. Разработанные микросервисы расширили репозиторий пакета прикладных микросервисов для качественного исследования двоичных динамических систем. Права на запуск микросервисов делегированы управляющим агентам этого пакета, установленным в узлах распределенной среды. Разработанные средства автоматизации позволяют специалисту по автоматной динамике формулировать постановку задач на вычислительной модели предметной области в содержательных терминах.

Synchronization of drive–response singular Boolean networks

Network synchronization, explicating typical collective behaviors of coupled systems, plays a crucial role in social production and life. This paper addresses the synchronization problem of drive–response singular Boolean networks (SBNs). The solvability of drive–response SBNs is investigated based on the matrix representation. In view of the existence and uniqueness of the solutions to drive–response SBNs, three types of concepts, synchronization, strong synchronization and weak synchronization, are put forward for the first time. By two new systems, a restricted BN and a switched restricted BN, which are constructed from the considered systems, several synchronization conditions are provided to deal with the circumstances of unique solutions and multiple solutions, respectively. Besides, the synchronous ratio is defined to characterize the synchronization capability of drive–response SBNs for the case of multiple solutions. Finally, several examples are given to illustrate the effectiveness of the obtained results.

Dynamics and control of singular boolean networks

AbstractConsider a class of singular Boolean networks, which consist of two parts: difference part and algebraic part. Using the truth matrix of the algebraic part, the trajectories of the networks are obtained and certain properties are investigated. Then the results are extended to Boolean control networks and the controllability of singular Boolean control systems is investigated. Necessary and sufficient conditions are obtained.

Function perturbations on singular Boolean networks

This paper is devoted to studying function perturbations on the transition matrix and topological structure of a singular Boolean network (SBN) via the semi-tensor product of matrices. First, the algebraic form of an SBN is given, and we discuss how the transition matrix of the SBN changes under function perturbations. Then the local uniqueness of solutions to the SBN is studied, under which the impacts of function perturbations on the topological structure are investigated. Finally, examples are given to show the effectiveness of the obtained results.

Topological structure and the disturbance decoupling problem of singular Boolean networks

The general singular Boolean networks are proposed in this study, motivated by the algebraic form of dynamic-algebraic Boolean networks via the semi-tensor product of matrices. First, one of the most important problems for this kind of networks, solvability problem, is discussed. Then, in order to calculate the fixed points and cycles, the transition matrix of a singular Boolean network is defined, which contains all the state transferring information. At last, the general singular Boolean control networks are considered with their solvability and the disturbance decoupling problem is presented and solved by a constant control. Illustrative examples are given to show the feasibility of the results.

Singular Boolean networks: Semi-tensor product approach

Singular Boolean networks are introduced in this paper. Via semi-tensor product of matrices and the matrix expression of logical functions, two kinds of the condensed algebraic expressions of singular Boolean networks are obtained. The normalization problem of singular Boolean networks is addressed; that is, under what condition singular Boolean networks can be converted into normal Boolean networks with algebraic restrictions. Then one sufficient condition and one necessary and sufficient condition are derived for the normalization problem. Furthermore, the solvability of singular Boolean networks is discussed and the concept of admissible initial values of singular Boolean networks is presented. Finally, fixed points and cycles of singular Boolean networks are also investigated.