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The tendency for cell fate to be robust to most perturbations, yet sensitive to certain perturbations raises intriguing questions about the existence of a key path within the underlying molecular network that critically determines distinct cell fates. Reprogramming and trans-differentiation clearly show examples of cell fate change by regulating only a few or even a single molecular switch. However, it is still unknown how to identify such a switch, called a master regulator, and how cell fate is determined by its regulation. Here, we present CAESAR, a computational framework that can systematically identify master regulators and unravel the resulting canalizing kernel, a key substructure of interconnected feedbacks that is critical for cell fate determination. We demonstrate that CAESAR can successfully predict reprogramming factors for de-differentiation into mouse embryonic stem cells and trans-differentiation of hematopoietic stem cells, while unveiling the underlying essential mechanism through the canalizing kernel. CAESAR provides a system-level understanding of how complex molecular networks determine cell fates. [ABSTRACT FROM AUTHOR]

Constructing gene regulatory networks is a widely adopted approach for investigating gene regulation, offering diverse applications in biology and medicine. A great deal of research focuses on using time series data or single-cell RNA-sequencing data to infer gene regulatory networks. However, such gene expression data lack either cellular or temporal information. Fortunately, the advent of time-lapse confocal laser microscopy enables biologists to obtain tree-shaped gene expression data of Caenorhabditis elegans , achieving both cellular and temporal resolution. Although such tree-shaped data provide abundant knowledge, they pose challenges like non-pairwise time series, laying the inaccuracy of downstream analysis. To address this issue, a comprehensive framework for data integration and a novel Bayesian approach based on Boolean network with time delay are proposed. The pre-screening process and Markov Chain Monte Carlo algorithm are applied to obtain the parameter estimates. Simulation studies show that our method outperforms existing Boolean network inference algorithms. Leveraging the proposed approach, gene regulatory networks for five subtrees are reconstructed based on the real tree-shaped datatsets of Caenorhabditis elegans , where some gene regulatory relationships confirmed in previous genetic studies are recovered. Also, heterogeneity of regulatory relationships in different cell lineage subtrees is detected. Furthermore, the exploration of potential gene regulatory relationships that bear importance in human diseases is undertaken. All source code is available at the GitHub repository https://github.com/edawu11/BBTD.git. [ABSTRACT FROM AUTHOR]

We study relationships between lower estimates for the energy complexity E(Σ), the switching complexity S(Σ) of a normalized Boolean network Σ, and the positive sensitivity ps(f) of the Boolean function f implemented by this circuit. The lower estimate E (Σ) ⩾ ⌊ ps (f) − 1 m ⌋ is proved for a sufficiently wide class of bases consisting of monotone Boolean functions of at most m variables, the negation gate, and the Boolean constants 0 and 1. For the switching complexity of circuits, we construct a counterexample which shows that, for the standard basis of elements of the disjunction, conjunction, and negation, there do not exist a linear (with respect to ps(f)) lower estimate for the switching complexity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics of Boolean networks by using their matrices of support. We derive properties about the transients, fixed points, and limit cycles. We also study the graph properties of the phase spaces of Boolean networks, and show how to use matrices of support to construct Boolean networks with prescribed dynamics. [ABSTRACT FROM AUTHOR]

Reconstructing the topology of gene regulatory network from gene expression data has been extensively studied. With the abundance functional transcriptomic data available, it is now feasible to systematically decipher regulatory interaction dynamics in a logic form such as a Boolean network (BN) framework, which qualitatively indicates how multiple regulators aggregated to affect a common target gene. However, inferring both the network topology and gene interaction dynamics simultaneously is still a challenging problem since gene expression data are typically noisy and data discretization is prone to information loss. We propose a new method for BN inference from time-series transcriptional profiles, called LogicGep. LogicGep formulates the identification of Boolean functions as a symbolic regression problem that learns the Boolean function expression and solve it efficiently through multi-objective optimization using an improved gene expression programming algorithm. To avoid overly emphasizing dynamic characteristics at the expense of topology structure ones, as traditional methods often do, a set of promising Boolean formulas for each target gene is evolved firstly, and a feed-forward neural network trained with continuous expression data is subsequently employed to pick out the final solution. We validated the efficacy of LogicGep using multiple datasets including both synthetic and real-world experimental data. The results elucidate that LogicGep adeptly infers accurate BN models, outperforming other representative BN inference algorithms in both network topology reconstruction and the identification of Boolean functions. Moreover, the execution of LogicGep is hundreds of times faster than other methods, especially in the case of large network inference. [ABSTRACT FROM AUTHOR]

Objectives. The problem of choosing the best methods and programs for circuit implementation as part of digital ASIC (Application-Specific Integrated Circuit) sparse systems of disjunctive normal forms (DNF) of completely defined Boolean functions is considered. For matrix forms of sparse DNF systems, the ternary matrix specifying elementary conjunctions contains a large proportion of undefined values corresponding to missing literals of Boolean input variables, and the Boolean matrix specifying the occurrences of conjunctions in DNF functions contains a large proportion of zero values.Methods. It is proposed to investigate various methods of technologically independent logical optimization performed at the first stage of logical synthesis: joint minimization of systems of functions in the DNF class, separate and joint minimization in classes of multilevel representations in the form of Boolean networks and BDD representations using mutually inverse cofactors, as well as the division of a system of functions into subsystems with a limited number of input variables and the method of block cover of DNF systems, focused on minimizing the total area of the blocks forming the cover.Results. When implementing sparse DNF systems of Boolean functions in ASIC, along with traditional methods of joint minimization of systems of functions in the DNF class, methods for optimizing multilevel representations of Boolean function systems based on Shannon expansions can be used for technologically independent optimization, while separate minimization and joint minimization of the entire system as a whole turn out to be less effective compared with block partitions and coatings of the DNF system and subsequent minimization of multilevel representations. Schemes obtained as a result of synthesis using minimized representations of Boolean networks often have a smaller area than schemes obtained using minimized BDD representations.Conclusion. For the design of digital ASIC, the effectiveness of combined approach is shown, when initially the block coverage programs of the DNF system is used, followed by the use of programs to minimize multilevel block representations in the form of Boolean networks minimized based on Shannon expansion.

A technology for automating structural-parametric synthesis of a Boolean network with a given periodic trajectory is proposed. This technology provides a constructive solution for the considered problem. The attraction region of such a trajectory must coincide with a given subset of the state space. An additional constraint sets the acceptable time for reaching this trajectory from its attraction region. As admissible structures for dynamical models of the synthesis, we consider the following systems: linear systems, systems with the disjunctive and conjunctive right sides. The proposed technology is based on the author's method of Boolean restrictions. According to this method, all conditions of the problem are written in the form of a quantified Boolean formula with subsequent verification of its truth using a specialized solver, which gives values of the required parameters of the dynamical model. A software implementation of the proposed technology using microserviceoriented tools is presented. All stages of the parametric synthesis of a Boolean network in accordance with the proposed technology are demonstrated in the example of a one-step linear system. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of optimal preview pinning control for Boolean networks. The primary objective is to design efficient control strategies that leverage future reference information for improved control performance. We propose a policy iteration algorithm specifically for Boolean networks based on an augmented error system, constructed using the state augmentation technique in combination with the Exclusive-Or operator approach. The algorithm effectively optimizes control policies using future information. Finally, an example is presented to illustrate the effectiveness of the proposed algorithm. • First study of optimal preview pinning control problem of BNs. • Transformation using the semi-tensor product and exclusive-OR operator. • Deduction of a policy iteration algorithm for BNs. [ABSTRACT FROM AUTHOR]

Models of gene regulatory networks (GRNs) capture the dynamics of the regulatory processes that occur within the cell as a means to understanding the variability observed in gene expression between different conditions. Arguably the simplest mathematical construct used for modeling is the Boolean network, which dictates a set of logical rules for transition between states described as Boolean vectors. Due to the complexity of gene regulation and the limitations of experimental technologies, in most cases knowledge about regulatory interactions and Boolean states is partial. In addition, the logical rules themselves are not known a priori. Our goal in this work is to create an algorithm that finds the network that fits the data optimally, and identify the network states that correspond to the noise-free data. We present a novel methodology for integrating experimental data and performing a search for the optimal consistent structure via optimization of a linear objective function under a set of linear constraints. In addition, we extend our methodology into a heuristic that alleviates the computational complexity of the problem for datasets that are generated by single-cell RNA-Sequencing (scRNA-Seq). We demonstrate the effectiveness of these tools using simulated data, and in addition a publicly available scRNA-Seq dataset and the GRN that is associated with it. Our methodology will enable researchers to obtain a better understanding of the dynamics of GRNs and their biological role. [ABSTRACT FROM AUTHOR]

We investigate the optimal preview control problem of Boolean Networks (BNs) in this paper. An augmented system, which can control BNs with a minimal cost function, is established through a model transformation based on the semi-tensor product of matrices and the Exclusive-Or operator. Then the optimal preview controller that is equipped with various features such as state feedback, integrator, and preview feedforward is given for BNs. Finally, we present a numerical example to illustrate the validity of the proposed optimal preview controller of BNs. [ABSTRACT FROM AUTHOR]

Asynchronous behavior is significant for real biological systems. This paper explores the impact of state‐dependent asynchronous updating rule (SDAUR) on the set reachability and set stability of Boolean networks (BNs). First, a set of state‐dependent control variables is introduced to describe the SDAUR. Second, a new asynchronous set reachablity matrix is constructed based on an auxiliary input and semi‐tensor product. Third, using the asynchronous set reachablity matrix, several necessary and sufficient conditions are obtained for the set reachablity and set stability of BNs with SDAUR. Finally, the new results proposed in this paper are verified through the immunomic network. [ABSTRACT FROM AUTHOR]

Deciphering gene regulatory networks' functioning is an essential step for better understanding of life, as these networks play a fundamental role in the control of cellular processes. Boolean networks have been widely used to represent gene regulatory networks. They allow to describe the dynamics of complex gene regulatory networks straightforwardly and efficiently. The attractors are essential in the analysis of the dynamics of a Boolean network. They explain that a particular cell can acquire specific phenotypes that may be transmitted over several generations. In this work, we consider a new representation of Boolean networks' dynamics based on a new semantics used in Answer Set Programming (ASP). We use logic programs and ASP to express and deal with gene regulatory networks seen as Boolean networks, and develop a method to detect all the attractors of such networks. We first show how to represent and deal with general Boolean networks for the synchronous and asynchronous updates modes, where the computation of attractors requires a simulation of these networks' dynamics. Then, we propose an approach for the particular case of circular networks where no simulation is needed. This last specific case plays an essential role in biological systems. We show several theoretical properties; in particular, simple attractors of the gene networks are represented by the stable models of the corresponding logic programs and cyclic attractors by its extra-stable models. These extra-stable models correspond to the extra-extensions of the new semantics that are not captured by the semantics of stable models. We then evaluate the proposed approach for general Boolean networks on real biological networks and the one dedicated to the case of circular networks on Boolean networks generated randomly. The obtained results for both approaches are encouraging. [ABSTRACT FROM AUTHOR]

Abstract Background Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis. Results We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance. Conclusions BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs.

The asynchronous automaton of a Boolean network f : { 0 , 1 } n → { 0 , 1 } n , considered in many applications, is the finite deterministic automaton where the set of states is { 0 , 1 } n , the alphabet is [ n ] , and the action of letter i on a state x consists in either switching the i th component if f i (x) ≠ x i or doing nothing otherwise. In this paper, we ask for the existence of synchronizing words for this automaton, and their minimal length, when f is the and-net over an arc-signed digraph G on [ n ] : for every i ∈ [ n ] , f i (x) = 1 if and only if x j = 1 (x j ≠ 0) for every positive (negative) arc from j to i. Our main result is that if G is strongly connected and has no positive cycles, then either there exists a synchronizing word of length at most 10 (5 + 1) n or G is a cycle and there are no synchronizing words. We also give complexity results showing that the situation is much more complex if one of the two hypothesis made on G is removed. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the following decision problem: given a conjunctive Boolean network defined by its interaction digraph, does it have a limit cycle of a given length k? We prove that this problem is NP-complete in general if k is a parameter of the problem and is in P if the interaction digraph is strongly connected. The case where k is fixed, but the interaction digraph is not strongly connected, remains open. Furthermore, we study some variations of the decision problem: given a conjunctive Boolean network, does there exist a block-sequential (resp. sequential) update schedule such that there is a limit cycle of length k? We prove that these problems are NP-complete for any fixed constant k ≥ 2 . [ABSTRACT FROM AUTHOR]

This article studies an algebra‐logic mixed representation of gate networks and its application to stuck‐at fault diagnosis. First, the gate network is characterized through a logic expression of disjoint sum‐of‐products, and the system structure of the gate network is described based on 2‐to‐1 multiplexers. Then, by resorting to the semi‐tensor product of matrices, a novel algebra‐logic mixed representation is proposed for the gate network through its logic expression and system structure. Furthermore, a novel stuck‐at fault diagnosis algorithm for the gate network is presented, where the stuck‐at fault testability of the gate network is equivalent to the solution existence of the system of linear equations. Finally, the fault diagnosis of the 4‐bit carry look‐ahead adder is carried out to demonstrate the effectiveness and feasibility of the proposed theoretical approach and algorithms. [ABSTRACT FROM AUTHOR]

Boolean networks (BNs) are well-studied models of genomic regulation in biology where nodes are genes and their state transition is controlled by Boolean functions. We propose to learn Boolean functions as Boolean formulas in disjunctive normal form (DNFs) by an explainable neural network Mat_DNF and apply it to learning BNs. Directly expressing DNFs as a pair of binary matrices, we learn them using a single layer NN by minimizing a logically inspired non-negative cost function to zero. As a result, every parameter in the network has a clear meaning of representing a conjunction or literal in the learned DNF. Also we can prove that learning DNFs by the proposed approach is equivalent to inferring interpolants in logic between the positive and negative data. We applied our approach to learning three literature-curated BNs and confirmed its effectiveness. We also examine how generalization occurs when learning data is scarce. In doing so, we introduce two new operations that can improve accuracy, or equivalently generalizability for scarce data. The first one is to append a noise vector to the input learning vector. The second one is to continue learning even after learning error becomes zero. The first one is explainable by the second one. These two operations help us choose a learnable DNF, i.e., a root of the cost function, to achieve high generalizability. [ABSTRACT FROM AUTHOR]

This article concentrates on the function perturbation impact on robust stability and robust stabilization of Boolean networks with disturbance inputs (DBNs). First, using the semi-tensor product (STP) of matrices, the algebraic representation of DBNs with function perturbation is given. Second, a state set is determined to detect the robust stability of DBNs subject to function perturbation. The result shows that the robust stability of DBNs remains unchanged if and only if the perturbed point is not in the constructed state set. Third, DBNs with control inputs (DBCNs) are considered, and several criteria to verify whether DBCNs with function perturbation can still maintain robust stabilization under a given state feedback stabilizer are presented. Finally, two examples are provided to illustrate the validity of the theoretical results.

In this paper, we describe the orbital structure of homogeneous fuzzy parallel dynamical systems on Zadeh operators. In particular, we show that, when the (global) evolution operator is either the Zadeh conjunction operator AND or the Zadeh disjunction operator OR, all the points of the system are fixed points or eventually fixed points. Specifically, such systems present infinitely many fixed points. On the other hand, when the (global) evolution operator is either the Zadeh operator NOR or the Zadeh operator NAND, the orbital structure consists of an only fixed point and infinitely many 2‐periodic points. [ABSTRACT FROM AUTHOR]

Background: Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis. Results: We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance. Conclusions: BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs. [ABSTRACT FROM AUTHOR]

Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality—a balance between change and stability, order and chaos—is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks—a general model of discrete dynamical systems—we show that heterogeneity—in time, structure, and function—can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the "optimal" balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic. [ABSTRACT FROM AUTHOR]

Algebraic state space theory (ASST) of logical systems, developed based on the semi-tensor product (STP) which is a new matrix analysis tool built in recent ten years, provides an algebraic analysis approach for many fields of science, such as logical dynamical systems, finite-valued systems, discrete event dynamic systems, and networked game systems. This study focuses on comprehensively surveying the applications of the ASST method to the field of finite state machines (FSMs). Some necessary preliminaries on the method are first reviewed. Then the applications of the method in the FSM field are reviewed, including deterministic FSMs, nondeterministic FSMs, probabilistic FSMs, networked FSMs, and controlled and combined FSMs. In addition, other applications related to both STP and FSMs are surveyed, such as the application of FSM to Boolean control networks and the application of graph theory to FSMs. Finally, some potential research directions with respect to the ASST method in the FSM field are predicted. [ABSTRACT FROM AUTHOR]

Anaerobic Porphyromonas gingivalis is a rod-shaped bacterium and is a primary agent of periodontal inflammation and thus periodontitis. This bacterium disturbs the normal flora of the oral cavity and causes dysbiosis. Databases including Google Scholar Scopus and PubMed were employed to find the evidence by using keywords like 'Porphyromonas gingivalis,' 'Boolean network,' 'inflammatory response and Porphyromonas gingivalis,' 'inflammation and Porphyromonas gingivalis. Only articles that reviewed the role of Porphyromonas gingivalis in oral inflammation were selected. Porphyromonas gingivalis promotes and reorganizes host immune systems against normal host flora, which causes a dysbiotic state. A reorganized immune system induces dysbiosis and periodontitis. Specifically, the role of the C5a receptor in the complement system is vital in this mechanism. P. gingivalis can change the metabolic pathways of phagocytic cells without impeding inflammation. Toll-like receptor and complement signaling are inverted by Porphyromonas gingivalis, which aids them in overcoming immunological responses. However, they sustain the inflammation process, which promotes dysbiosis. Instead of a subjective approach, a systems perspective is required to comprehend this intricate process. A Boolean network is a system approach that seems to be a better approach to understanding this complicated interaction process of Porphyromonas gingivalis with the immune system and inflammation. In short, attempts to understand the complex process using the Boolean network will ultimately help in the early detection of periodontitis, and immediate treatment can prevent soft tissue destruction and dentition loss. [ABSTRACT FROM AUTHOR]

Boolean networks have been used in a variety of settings, as models for general complex systems as well as models of specific systems in diverse fields, such as biology, engineering, and computer science. Traditionally, their properties as dynamical systems have been studied through simulation studies, due to a lack of mathematical structure. This paper uses a common mathematical technique to identify a class of Boolean networks with a "simple" structure and describes an algorithm to construct arbitrary extensions of a collection of simple Boolean networks. In this way, all Boolean networks can be obtained from a collection of simple Boolean networks as building blocks. The paper furthermore provides a formula for the number of extensions of given simple networks and, in some cases, provides a parametrization of those extensions. This has potential applications to the construction of networks with particular properties, for instance in synthetic biology, and can also be applied to develop efficient control algorithms for Boolean network models. • Network restrictions/extensions are defined for building Boolean networks modularly. • Parameterized all extensions of two Boolean networks represented by labeled graphs. • A combinatorial formula enumerates all extensions of two Boolean networks. • Extensions of Boolean networks with nested canalizing functions are enumerated. [ABSTRACT FROM AUTHOR]

The Boolean network (BN) is a mathematical model used to represent various biological processes such as gene regulatory networks. The state of a BN is determined from the previous state and eventually reaches a stable state called an attractor. Due to its significance for elucidating the whole system, extensive studies have been conducted on analysis of attractors. However, the problem of detecting an attractor from a given BN has been shown to be NP-hard, and for general BNs, the time complexity of most existing algorithms is not guaranteed to be less than O(2n). Therefore, the computational difficulty of attractor detection has been a big obstacle for analysis of BNs. This review highlights singleton/periodic attractor detection algorithms that have guaranteed computational complexities less than O(2n) time for particular classes of BNs under synchronous update in which the maximum indegree is limited to a constant, each Boolean function is AND or OR of literals, or each Boolean function is given as a nested canalyzing function. We also briefly review practically efficient algorithms for the problem.

Controlling phenotypical landscapes is of vital interest to modern biology. This task becomes highly demanding because cellular decisions involve complex networks engaging in crosstalk interactions. Previous work on control theory indicates that small sets of compounds can control single phenotypes. However, a dynamic approach is missing to determine the drivers of the whole network dynamics. By analyzing 35 biologically motivated Boolean networks, we developed a method to identify small sets of compounds sufficient to decide on the entire phenotypical landscape. These compounds do not strictly prefer highly related compounds and show a smaller impact on the stability of the attractor landscape. The dynamic driver sets include many intervention targets and cellular reprogramming drivers in human networks. Finally, by using a new comprehensive model of colorectal cancer, we provide a complete workflow on how to implement our approach to shift from in silico to in vitro guided experiments.

As a class of state estimation issues, detectability is widely used in fault diagnosis, circuit design, and disease status detection. This brief analyzes the robust weak detectability of Boolean networks (BNs) under function perturbation. A simplified parallel system is constructed for BNs. Based on the transition of state pairs in the simplified parallel system, a new criterion is proposed for the weak detectability of BNs. Using the reachability from perturbed state pairs to attractors in indistinguishable pairs, the robust weak detectability of BNs subject to function perturbation is analyzed. A practical example of p53-MDM2 negative feedback regulatory loop is used to illustrate the obtained criteria. [ABSTRACT FROM AUTHOR]

We introduce a discrete-time dynamical system method, the Boolean network method, that may be useful for modeling, studying, and controlling nonlinear dynamics in multivariate systems, particularly when binary time-series are available. We introduce the method in three steps: inference of the temporal relations as Boolean functions, extraction of attractors and assignment of desirability based on domain knowledge, and design of network control to direct a psychological system toward a desired attractor. To demonstrate how the Boolean network can describe and prescribe control for emotion regulation dynamics, we applied this method to data from a study of how children use bidding to an adult and/or distraction to regulate their anger during a frustrating task (N = 120, T = 480 seconds). Network control strategies were designed to move the child into attractors where anger is OFF. The sample shows heterogeneous emotion regulation dynamics across children in 22 distinct Boolean networks, and heterogeneous control strategies regarding which behavior to perturb and how to perturb it. The Boolean network method provides a novel method to describe nonlinear dynamics in multivariate psychological systems and is a method with potential to eventually inform the design of interventions that can guide those systems toward desired goals. [ABSTRACT FROM AUTHOR]

Nonlinear feedback shift registers (NFSRs) have been used in many recent stream ciphers. They are generally classified into Fibonacci NFSRs and Galois NFSRs according to their implementation configurations. An NFSR is observable if any two distinct initial states can be distinguished from their corresponding output sequences. From the security perspective, NFSR-based stream ciphers should select observable NFSRs; otherwise, they will be subject to weak key attacks. Any Fibonacci NFSR is observable as the first n bits of its output sequence is just its initial state, where n is the stage number of the Fibonacci NFSR. This paper considers the observability of Galois NFSRs. Some necessary and/or sufficient conditions are presented, using the semi-tensor product-based Boolean network theory. In particular, a new observability matrix is proposed to facilitate the observability determination. [ABSTRACT FROM AUTHOR]

Recent developments in Omics-technologies revolutionized the investigation of biology by producing molecular data in multiple dimensions and scale. This breakthrough in biology raises the crucial issue of their interpretation based on modeling. In this undertaking, the network provides a suitable framework for modeling the interactions between molecules. A biological network comprises nodes referring to the components such as genes or proteins, and the edges/arcs formalizing interactions between them. The evolution of the interactions is then modeled by the definition of a dynamical system. Among the different network categories, the Boolean network offers a reliable qualitative framework for modeling the biological systems. Automatically synthesizing a Boolean network from experimental data, therefore, remains a necessary but challenging issue. This study, presents taboon, an original work-flow for synthesizing Boolean Networks from biological data. The methodology uses the data in the form of Boolean profiles for inferring all the potential local formula inference. They combine to form the model space from which the most truthful model regarding biological knowledge and experiments must be found. In the taboon work-flow, the selection of the fittest model is achieved by a Tabu-search algorithm. taboon is an automated method for Boolean Network inference from experimental data that helps biologists synthesize a reliable model faster and assist in evaluating and optimizing the biological networks’ dynamic behavior, further modeling and predictions. [ABSTRACT FROM AUTHOR]

The study of the dynamical behavior of Boolean networks with different update schedules has so far focused primarily on the possible dynamics and equivalent networks that can be obtained. However, few studies have been done about which networks can be obtained from another network with a non-parallel schedule. In this article, we define the problem of finding a Boolean network that is dynamically equivalent to another network. For the general case, it is shown that the problem is NP-Hard. However, if the problem is restricted to disjunctive Boolean networks, it can be solved in polynomial time. [ABSTRACT FROM AUTHOR]

Due to advances in computing power and internet technology, various industrial sectors are adopting IT infrastructure and artificial intelligence (AI) technologies. Recently, data-driven predictions have attracted interest in high-stakes decision-making. Despite this, advanced AI methods are less often used for such tasks. This is because AI technology is a black box for the social systems it is meant to support; trustworthiness and fairness have not yet been established. Meanwhile in the field of marketing, strategic decision-making is a high-stakes problem that has a significant impact on business trends. For global marketing, with its diverse cultures and market environments, future decision-making is likely to focus on building consensus on the formulation of the problem itself rather than on solutions for achieving the goal. There are two important and conflicting facts: the fact that the core of domestic strategic decision-making comes down to the formulation of the problem itself, and the fact that it is difficult to realize AI technology that can achieve problem formulation. How can we resolve this difficulty with current technology? This is the main challenge for the realization of high-level human-AI systems in the marketing field. Thus, we propose customer journey mapping (CJM) automation through model-level data fusion, a process for the practical problem formulation known as explainable alignment. Using domain-specific requirements and observations as inputs, the system automatically outputs a CJM. Explainable alignment corresponds with both human and AI perspectives and in formulating the problem, thereby improving strategic decision-making in marketing. Following preprocessing to make latent variables and their dynamics transparent with latent Dirichlet allocation and a variational autoencoder, a post-hoc explanation is implemented in which a hidden Markov model and learning from an interpretation transition are combined with a long short-term memory architecture that learns sequential data between touchpoints for extracting attitude rules for CJM. Finally, we realize the application of human-AI systems to strategic decision-making in marketing with actual logs in over-the-top media services, in which the dynamic behavior of customers for CJM can be automatically extracted.

Understanding control mechanisms in biological systems plays a crucial role in important applications, for instance in cell reprogramming. Boolean modeling allows the identification of possible efficient strategies, helping to reduce the usually high and time-consuming experimental efforts. Available approaches to control strategy identification usually focus either on attractor or phenotype control, and are unable to deal with more complex control problems, for instance phenotype avoidance. They also fail to capture, in many situations, all possible minimal strategies, finding instead only sub-optimal solutions. In order to fill these gaps, we present a novel approach to control strategy identification in Boolean networks based on model checking. The method is guaranteed to identify all minimal control strategies, and provides maximal flexibility in the definition of the control target. We investigate the applicability of the approach by considering a range of control problems for different biological systems, comparing the results, where possible, to those obtained by alternative control methods.

Adaptability, heterogeneity, and plasticity are the hallmarks of macrophages. How these complex properties emerge from the molecular interactions is an open question. Thus, in this study we propose an actualized regulatory network of cytokines, signaling pathways, and transcription factors to survey the differentiation, heterogeneity, and plasticity of macrophages. The network recovers attractors, which in regulatory networks correspond to cell types, that correspond to M0, M1, M2a, M2b, M2c, M2d, M2-like, and IL-6 producing cells, including multiple cyclic attractors that are stable to perturbations. These cyclic attractors reproduce experimental observations and show that oscillations result from the structure of the network. We also study the effect of the environment in the differentiation and plasticity of macrophages, showing that the observed heterogeneity in macrophage populations is a result of the regulatory network and its interaction with the micro-environment. The macrophage regulatory network gives a mechanistic explanation to the heterogeneity and plasticity of macrophages seen in vivo and in vitro, and offers insights into the mechanism that allows the immune system to react to a complex dynamic environment.

Background: A novel data-driven Boolean model, namely, the fundamental Boolean model (FBM), has been proposed to draw genetic regulatory insights into gene activation, inhibition, and protein decay, published in 2018. This novel Boolean model facilitates the analysis of the activation and inhibition pathways. However, the novel model does not handle the situation well, where genetic regulation might require more time steps to complete. Methods: Here, we propose extending the fundamental Boolean modelling to address the issue that some gene regulations might require more time steps to complete than others. We denoted this extension model as the temporal fundamental Boolean model (TFBM) and related networks as the temporal fundamental Boolean networks (TFBNs). The leukaemia microarray datasets downloaded from the National Centre for Biotechnology Information have been adopted to demonstrate the utility of the proposed TFBM and TFBNs. Results: We developed the TFBNs that contain 285 components and 2775 Boolean rules based on TFBM on the leukaemia microarray datasets, which are in the form of short-time series. The data contain gene expression measurements for 13 GC-sensitive children under therapy for acute lymphoblastic leukaemia, and each sample has three time points: 0 hour (before GC treatment), 6/8 hours (after GC treatment) and 24 hours (after GC treatment). Conclusion: We conclude that the proposed TFBM unlocks their predecessor's limitation, i.e., FBM, that could help pharmaceutical agents identify any side effects on clinic-related data. New hypotheses could be identified by analysing the extracted fundamental Boolean networks and analysing their up-regulatory and down-regulatory pathways. [ABSTRACT FROM AUTHOR]