Boolean functions and networks are commonly used in the modeling and analysis of complex biological systems, and this paradigm is highly relevant in other important areas in data science and decision making, such as in the medical field and in the finance industry. In a Boolean model, the truth state of a variable is either 0 or 1 at a given time. Despite its apparent simplicity, Boolean networks are surprisingly relevant in many areas of application such as in bioinformatics to model gene expressions and interactions. In the latter case, a gene is either ``on" or ``off" depending on its expression level. Despite the promising utility of Boolean modeling, in most practical applications the Boolean network is not known. Automated learning of a Boolean network and Boolean functions, from data, is a challenging task due in part to the large number of unknowns (including both the structure of the network and the functions) to be estimated, for which a brute force approach would be exponentially complex. In this paper we develop a new information theoretic methodology that we show to be significantly more efficient than previous approaches. Building on the recently developed optimal causation entropy principle (oCSE), that we proved can correctly infer networks distinguishing between direct versus indirect connections, we develop here an efficient algorithm that furthermore infers a Boolean network (including both its structure and function) based on data observed from the evolving states at nodes. We call this new inference method, Boolean optimal causation entropy (BoCSE), which we will show that our method is both computationally efficient and also resilient to noise. Furthermore, it allows for selection of a set of features that best explains the process, a statement that can be described as a networked Boolean function reduced order model. We highlight our method to the feature selection in several real-world examples: (1) diagnosis of urinary diseases, (2) Cardiac SPECT diagnosis, (3) informative positions in the game Tic-Tac-Toe, and (4) risk causality analysis of loans in default status. Our proposed method is effective and efficient in all examples.

The P versus NP problem is a fundamental question in computer science. It asks whether problems whose solutions can be quickly verified can also be quickly solved. Here, "quickly" refers to computational time that grows proportionally to the size of the input (polynomial time). While the problem's roots trace back to a 1955 letter from John Nash, its formalization is attributed to Stephen Cook and Leonid Levin. Despite extensive research, a definitive answer remains elusive. Closely tied to this is the concept of NP-completeness. If a single NP-complete problem could be solved efficiently, it would imply that all problems in NP can be solved efficiently, proving that P equals NP. This work posits that MONOTONE ONE-IN-THREE 3SAT, a notoriously difficult NP-complete problem, can be solved efficiently, thereby establishing the equivalence of P and NP.

In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. To do this, its randomness is estimated using three measures, of which Algorithmic Complexity is the only one capable of both a) revealing transitions towards the chaotic regime, and b) disclosing the algorithmic contribution of certain states to the transition diagram and their relationship with the order they occupy in the temporal evolution of the respective RBN. The results obtained from both types of analysis are useful for the introduction of both Algorithmic Complexity and Perturbation Analysis in the context of Boolean networks, and their potential applications in regulatory network models.

Abstract—In this paper, decidability of the structures of real, rational, integer and natural numbers will be studied in different languages. Decidability or undecidability of mathematical structures is one of the fundamental and sometimes very difficult problems of mathematical logic, where several examples of problems in this field are still open and unresolved even after decades. One of the goals of Mathematical Logic is the axiomatization of mathematical theoriesTarski has proved the decidability of the theory of real and complex numbers in the language of addition and multiplication, and it is proved that theories of natural, integer, and rational numbers, in the language of addition and multiplication, are undecidable (Theorems of Gödel and Robinson). We will review The following problemes: The Main Problem 1: ⟨Q; ⊑⟩ is decidable? Problem 2: an explicit axiomatization for ⟨Z; \times⟩? and we will study boolean algebras. Boolean algebras are famous mathematical structures.Tarski showed the decidability of the elementary theory of Boolean algebras.In this paper, we study the different kinds of Boolean algebras and their properties. And we present for the first-order theory of atomic Boolean algebras a quantifier elimination algorithm. The subset relation is a partial order and indeed a lattice order,And I will prove that the theory of atomic Boolean lattice orders is decidable, and furthermore admits elimination of quantifiers. So the theory of the subset relation is decidable. And we will study decidability of atomlss boolean algebra.

Fossil fuels are non-renewable sources of energy, used particularly in developing countries. There are insufficient fossil fuels and their availability is gradually declining. This leads to a steady increase in prices. Renewable energy is clean, cost-effective and limitless. The considerable population growth and industrial growth have made the construction of solar power plants essential in developing countries. The study used Boolean logical-AHP techniques to select a suitable site for solar power in Duhok Governorate. The result indicated that 68.5% of the area in the governorate of Duhok is available for solar power station construction, especially the most appropriate zone which has 132.2 sq. km and can provide more than 8000 megawatts of solar energy. Most of the appropriate areas are in the south and southwest regions of the governorate, located mostly in the districts of Bardarash, Shekhan and Semel, situated between the major cities of Mosul, Erbil and Duhok. These locations can supply a significant amount of clean, renewable energy for these areas.

The P versus NP problem is a cornerstone of theoretical computer science, asking whether problems that are easy to check are also easy to solve. "Easy" here means solvable in polynomial time, where the computation time grows proportionally to the input size. While this problem's origins can be traced to John Nash's 1955 letter, its formalization is credited to Stephen Cook and Leonid Levin. Despite decades of research, a definitive answer remains elusive. Central to this question is the concept of NP-completeness. If even one NP-complete problem could be solved efficiently, it would imply that all problems in NP could be solved efficiently, proving P equals NP. This research proposes that EXACT CLOSURE, a notoriously difficult NP-complete problem, can be solved efficiently, thereby potentially establishing the equivalence of P and NP. This work is an expansion and refinement of the article "Note for the P versus NP problem", published in IPI Letters.

P versus NP is considered as one of the most fundamental open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, a precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is NP-complete. It is well-known that P is equal to NP under the assumption of the existence of a polynomial time algorithm for some NP-complete. We show that the Monotone Weighted Xor 2-satisfiability problem (MWX2SAT) is NP-complete and P at the same time. Certainly, we make a polynomial time reduction from every directed graph and positive integer k in the K-CLOSURE problem to an instance of MWX2SAT. In this way, we show that MWX2SAT is also an NP-complete problem. Moreover, we create and implement a polynomial time algorithm which decides the instances of MWX2SAT. Consequently, we prove that P = NP.

In the realm of System Biology, it is a challenging endeavor to infer a gene regulatory network from time-series gene expression data. Numerous Boolean network inference techniques have emerged for reconstructing a gene regulatory network from a time series gene expression dataset. However, most of these techniques pose scalability concerns given their capability to consider only 2 to 3 regulatory genes over a specific target gene. To overcome this limitation, a novel inference method, LBF- MI, has been proposed in this research. This two-phase method utilizes limited Boolean functions and multivariate mutual information to reconstruct a Boolean gene regulatory network from time-series gene expression data. Initially, Boolean functions are applied to determine the optimum solutions. In case of failure, multivariate mutual information is applied to obtain the optimum solutions. This research conducted a performance-comparison experiment between LBF-MI and two other methods: Context Likelihood Relatedness, and Relevance Network. When examined on artificial as well as real time-series gene expression data, the outcomes exhibited that the proposed LBF-MI method outperformed Context Likelihood Relatedness and Relevance Network on artificial datasets, and two real Escherichia Coli datasets (E. coli gene regulatory network, and SOS response of E. coli regulatory network).

In this paper we provide some important and significant observations on invo-regular rings appeared in Ann. Univ. Mariae Curie-Sklodowska Sect. A Mathematica (2018). In addition we exhibit that strongly invo-regular rings, invo-regular rings and quasi invo-regular rings all coincide with the well known and well characterized tripotent rings and all these rings further coincide with the well known unit regular rings.

The dynamics of many complex systems can be classified as ordered, chaotic, or critical. Order offers stability and robustness, while chaos allows for change and adaptability. Criticality, then, is often seen as a balance required by living systems at different scales. In classical models, however, criticality is only found near phase transitions, restricting the parameter space (and thus the likelihood) of critical dynamics, as most parameters yield ``undesirable'' solutions. Here we show that this limitation is due to the homogeneity built-in these models, i.e., all elements sharing parameter values. By exploring heterogeneous versions of archetypal models in physics and computer science, we observe critical dynamics in a broader range of parameters, and thus could be more common than previously thought.

We present set-theoretical solutions of the Yang-Baxter equation in BCK–algebras. Some solutions in BCK−algebras are not solutions in other structures (such as MV −algebras). Related to our investigations we also consider some new structures: Boolean coalgebras and a unified braid condition – quantum Yang-Baxter equation. Finally, we will see how poetry has accompanied the development / history of the Yang–Baxter equation.

An orthogonal pore ('orthopore') is conceptually based on an electrolytic cell with a standard pore (the main or 'longitudinal' pore) between cis and trans compartments filled with electrolyte and augmented by a secondary or 'transverse' pore in the form of a channel that is perpendicular to and intersects the main pore. Orthopores can be designed at different scales: macro through micro to nano. With nano-sized pores an analyte (polymer) can be threaded through the main pore and exposed at the junction to electrolyte flow through the secondary pore. Polymer translocation speeds are then independent of the current measured, which can be of an arbitrary magnitude even with the polymer stationary. Orthopores have a wide range of potential applications, including polymer (DNA and protein) sequencing, DNA unzipping, logic circuitry, and protein identification. The present report shows how orthopores can be used to implement boolean logic.

Human keratinocytes and melanoma can stick together to form clusters after eight days in co-culture. As in dynamic system concepts, one can consider cluster formation as the system attractor, cell seeding as the initial condition, and density change over time as a path within the basin of attraction. Herein, Cellular Automata, which is a class of Agent-Based Models, and Boolean Networks are discrete modeling methods used in population dynamics such that running the dynamics of cellular automata backward reveals an underlying network in terms of basin of attraction, also known as global dynamics. Thus, we hypothesize that one can estimate the local dynamic of an agent-based model from the basin of attraction of a boolean network. Here, we propose an approach to estimating these agent-based model rules, which consists of comparing the density states within each state transition and reaching a consensus among state transitions belonging to a basin of attraction of a boolean network. The objectives of this study are: (1) to infer a boolean network from the co-culture growth curve; (2) to estimate the rules of agent-based models; and (3) to implement spatial dynamics simulations. The binarization of the growth curve shows high population density after four days; the estimated agent-based model rules were compatible with cell proliferation and migration in agreement with literature, so we had to propose individual rules for survival and death. Spatial dynamics shows that (1) keratinocytes exhibit a higher density in neighborhoods where melanoma is present; (2) the chance of keratinocyte migration increases until the fourth day, then decreases, and the probability of survival increases substantially after four days; and (3) cells with low proliferation capacity die and free space for those with high ones. Our approach suggests that the attractor state of cell co-culture is induced mainly by an increase in keratinocyte migration and survival. Our approach has the potential to offer valuable clues about microenvironmental interactions or configurations that drive population dynamics.

Sub-Saharan social-ecological systems are undergoing changes in environmental conditions, including modifications in rainfall pattern and biodiversity loss. Consequences of such changes depend on complex causal chains which call for integrated management strategies whose efficiency could benefit from ecosystem dynamic modelling. However, ecosystem models often require lots of quantitative information for estimating parameters, which is often unavailable. Alternatively, qualitative modelling frameworks have proved useful for explaining ecosystem response to perturbations, while requiring fewer information and providing more general predictions. However, current qualitative methods have some shortcomings which may limit their utility for specific issues. In this paper, we propose the Ecological Discrete-Event Network (EDEN), an innovative qualitative dynamic modelling framework based on "if-then" rules which generates many alternative event sequences (trajectories). Based on expert knowledge, observations and literature, we use this framework to assess the effect of permanent changes in surface water and herbivores diversity on vegetation and socio-economic transitions in an East African savanna. Results show that water availability drives changes in vegetation and socio-economic transitions, while herbivore functional groups had highly contrasted effects depending on the group. This first use of EDEN in a savanna context is promising for bridging expert knowledge and ecosystem modelling.

Steam Generator Level Control System (SGLCS) is one of the key instrumentations and control subsystems to ensure the safe operation of nuclear power plants. It is highly recommended to perform reliability analysis for SGLCS for making better maintenance strategy. SGLCS is a digital control system with complex redundant configuration and failure\self-diagnosis\repair action, traditional fault tree is not applicable due to its static property, Markov model is not a good choice too because of heavy burden of creating state transition graph for even medium-size system. Boolean Logic Driven Markov Process (BDMP) can describe complex failure-repair state transition via ‘trigger link’ and three kinds of leaf nodes, as well as keep compact and easy-read struct like fault tree. So BDMP is adopted to analysis reliability of SGLCS. Graphical BDMP modeling environment KB3 and Monte Carlo simulator YAMS is used for BDMP modeling and quantitative analysis respectively, and unavailability of SGLCS is obtained. The contribution of three parts of SGLCS to the unavailability of the system is also evaluated, and it is found that the water supply flow control part contributes the most to the failure of SGLCS.

This research presents a comprehensive bibliometric and sentiment analysis of nanocomposite literature from 1990 to 2024. Employing cutting-edge computational methods, the study delves deep into the progression of microstructural characterization, electrical properties, and mechanical behaviors of nanocomposites. The analysis utilizes advanced Boolean search strategies from the Scopus database, ensuring a thorough extraction of thematic content. The results explore various themes and insights, shedding light on trends evident in the Scopus database, particularly the prominence of research on nanocomposite microstructure, electrical attributes, and mechanical performance. The paper also offers textual analytics and bibliometric data, showcasing critical collaborative efforts and influential studies. Significant discoveries encompass the evolution of research language, shifts in thematic focus, and global contributions, providing a comprehensive perspective on the current landscape of nanocomposite research and its dynamic evolution. Moving forward, the "State-of-the-Art and Gaps Extracted from Results and Discussions" section of the paper delves into the most recent advancements in nanocomposite research. It delves into various types of nanocomposites, with a particular emphasis on their microstructural characteristics, electrical properties, mechanical dynamics, and the application of nanocomposite films. This section identifies key research themes, traces historical progress, and highlights emerging trends while underscoring the significance of collaboration and the influence of pivotal studies that have shaped the field. Lastly, in the "Literature Review Guided by Artificial Intelligence" section, the paper introduces a revised approach for researching nanocomposites through AI-guided techniques. This approach prioritizes articles published in 2023 based on citation frequency. Here, the focus is on exploring the relationship between nanocomposites and their electrical properties, emphasizing their fundamental interactions and impact on electrical characteristics. Various nanocomposite systems are covered, highlighting their composition, structure, and functionality. Findings from recent studies are integrated to provide a comprehensive overview of the current state of knowledge in this area. Notably, the sentiment analysis, anchored by an average sentiment score of 0.638771, underscores a positive trajectory in academic discourse, emphasizing the growing recognition of the potential of nanocomposites. The bibliometric exploration maps the intellectual domain, emphasizing pivotal research themes and the influence of crosslinking time on nanocomposite attributes. While this study is thorough, it acknowledges its limitations and advocates for broader database inclusion in future research endeavors. This work elucidates the prevailing trends in nanocomposite research, emphasizing the indispensable role of computational tools in comprehending this vast wealth of information.

Microbiomes, comprised of diverse microbial species and viruses, play pivotal roles in human health, environmental processes, and biotechnological applications and interact with themselves, their environment, and hosts via metabolites and signaling molecules. Our understanding of microbiomes is still limited and hampered by their complexity. A concept improving this understanding is systems biology, which focuses on the holistic description of biological systems utilizing experimental and computational methods. An important set of such experimental methods are metaomics methods which analyze microbiomes and output lists of molecular features. These lists of data are integrated, interpreted, and compiled into computational microbiome models, to predict, optimize, and control microbiome behavior. There exists a gap in understanding between microbiologists and modelers/bioinformaticians, stemming from a lack of interdisciplinary knowledge. This knowledge gap hinders the establishment of computational models in microbiome analysis. This review aims to bridge this gap and is tailored for microbiologists, researchers new to microbiome modeling, and bioinformaticians. To achieve this goal, it provides an interdisciplinary overview of microbiome modeling, starting with fundamental knowledge of microbiomes, metagenomics methods, and modeling formalisms. Furthermore, the review explains model building, examples of microbiome model applications for prediction, optimization, and control. It concludes with guidelines, software, and repositories for modeling. Each section provides entry-level information, serving as a valuable resource for comprehending and navigating the complex landscape of microbiome research and modeling.

Skin melanoma presents increasing prevalence and poor outcomes. Progression to aggressive stages is characterized by overexpression of the transcription factor E2F1 and activation of downstream prometastatic gene regulatory networks (GRNs). Appropriate therapeutic manipulation of the E2F1-governed GRNs holds the potential to prevent metastasis however, these networks entail complex feedback and feedforward regulatory motifs among various regulatory layers, which make it difficult to identify druggable components. To this end, computational approaches such as mathematical modeling and virtual screening are important tools to unveil the dynamics of these signaling networks and identify critical components that could be further explored as therapeutic targets. Herein, we integrated a well-established E2F1-mediated epithelial-mesenchymal transition (EMT) map with transcriptomics data from E2F1-expressing melanoma cells to reconstruct a core regulatory network underlying aggressive melanoma. Using logic-based in silico perturbation experiments of a core regulatory network, we identified that simultaneous perturbation of Protein kinase B (AKT1) and oncoprotein murine double minute 2 (MDM2) drastically reduces EMT in melanoma. Using the structures of the two protein signatures, virtual screening strategies were performed with the FDA-approved drug library. Thus, by combining drug repurposing and computer-aided drug design techniques, followed by molecular dynamics simulation analysis identified two potent drugs (Cialis and Finasteride) that can efficiently inhibit AKT1 and MDM2 protein signatures respectively, and with better therapeutic properties. We proposed that these two drugs could be considered for the development of therapeutic strategies for the management of aggressive melanoma.

Reservoir computers (RCs) are a biology inspired computational framework for signal processing typically implemented using recurrent neural networks. Recent work has shown that Boolean networks (BN) can also be used as reservoirs. We analyze the performance of BN RCs, measuring their flexibility and identifying factors that determine effective approximation of Boolean functions that are applied in a sliding-window fashion over a binary signal, either non-recursively or recursively. We train and test BN RCs of different sizes, signal connectivity, and in-degree to approximate 3-bit, 5-bit and 3-bit recursive binary functions. We analyze how BN RC parameters and function average sensitivity, a measure of function smoothness, affect approximation accuracy as well as the spread of accuracies for a single reservoir. We found that approximation accuracy and reservoir flexibility are highly dependent on RC parameters. Overall, our results indicate that not all reservoirs are equally flexible and RC instantiation and training can be more efficient if this is taken into account. The optimum range of RC parameters opens up an angle of exploration for understanding how biological systems might be tuned to balance system restraints with processing capacity.

The literature on substance use usually extracts conclusions from data with correlational methods. Our study shows the usefulness of complementing ordered logistic regression (OLR) and fuzzy set qualitative comparative analysis (fsQCA) to assess factors inducing cannabis consumption in a sample of 1,935 teenagers. OLR showed a significant influence of gender (odd ratio (OR) =0.383, p<0.0001), parental monitoring (OR=0.587, p=0.0201); religiousness (OR=0.476, p=0.006); parental tolerance to substance use (OR=42.01, p<0.0001) and having close peers that consume substances (OR=5.60, p<0.0001). FsQCA has allowed fitting linkages between factors from a complementary perspective. (1) Coverage (cov) and consistency (cons) attained by solutions explaining use (cons=0.808, cov=0.357) are clearly lower than by recipes of non-use (cons=0.952, cov=0.869) (2) The interaction of gender, a tolerant family to use and the attitude toward substances by peers is very consistent to explain cannabis use. (3) The most important recipe explaining resistance to cannabis is simply parental disagreement with substance consumption (cons=0.956, cov=0.861) (4) Factors as gender, religiosity, parental monitoring and age show also a relevant impact on attitude toward cannabis use. However, whereas some of them impact symmetrically on use and non-use this does not follow in factors such as parental monitoring or age.

Discrete, logic-based models are increasingly used to describe biological mechanisms. Initially introduced to study gene regulation, these models evolved to cover various molecular mechanisms, such as signalling, transcription factor cooperativity, and even metabolic processes. The abstract nature and amenability of discrete models to robust mathematical analyses make them appropriate for addressing a wide range of complex biological problems. Recent technological breakthroughs have generated a wealth of high throughput data. Novel, literature-based representations of biological processes and emerging algorithms offer new opportunities for model construction. Here, we review up-to-date efforts to address challenging biological questions by incorporating omic data into logic-based models, and discuss critical difficulties in constructing and analysing integrative, large-scale, logic-based models of biological mechanisms.

Bio-inspired gyroid triply periodic minimum surface (TPMS) lattice structures have been the focus of research in automotive engineering because they can absorb a lot of energy and have wider plateau ranges. The main challenge is determining the optimal energy absorption capacity and accurately capturing plastic plateau areas using finite element analysis (FEA). Using nTop's Boolean subtraction method, this study combined walled TPMS gyroid structures with normal TPMS gyroid lattice. This made a composite TPMS-gyroid lattice with relative densities ranging from 14% to 54%. Using the ideaMaker software and the fused deposition modeling (FDM) Raise3D Pro 2 3D printer to print polylactic acid (PLA) bioplastics in 1.75 mm filament made it possible to slice computer aided design (CAD) models and fabricate 36 lattices samples precisely layer by layer technique. Shimadzu 100kN testing equipment was utilized for the mechanical compression experiments. And the validation using finite element analysis (FEA). Further, CTG was examined using a field emission scanning electron microscope (FE-SEM) before and after compression testing. The composite TPMS gyroid lattice showed potential as shock absorbers for vehicles with relative densities of 33%, 38%, and 54%. The Gibson-Ashby model showed that the composite TPMS gyroid lattice deformed mainly by bending, and the size effect was seen when the relative densities were less than 15%. The lattice's relative density had a significant impact on its ability to absorb energy. The research also explored the use of these innovative foam-like composite TPMS-gyroid lattices in high-speed crash box scenarios, potentially enhancing vehicle safety and performance.

We find at least 4 quantum properties that are indeed universal in some number systems; and we can use them for quantum consciousness. Using the sets B={0,1}, N, Z, or Q has the +4 quantum properties that one can trust, as archetypes of easy communication to friends and foes, to ignoranti or cognoscenti, and for quantum computing. This paper proposes the use of Bayesian geometry to reduce the space of possible results, reducing or increasing initial beliefs by successive experimentation. This is exemplified in biology and mathematics, and can be applied to physics and other sciences. The conclusion is that an experimental fact can be absolutely verified. Any mathematical choice (as verified by computers) militating against R=Q, is under an absolutely low chance to succeed. Infinitesimals are denied based on 3^16 independent factors. This is not a probabilistic result, but based on reduction of the Bayes geometry for updating beliefs. This work applies to non-probabilistic and unknown phenomena, such as those found in oscillations (neutrino, health), evolution, and quantum computing, denies Gödel's uncertainty, and solves the liar's paradox by reflection. This connects different scientific fields with one another, in an internet, i.e., in a network of connections of multiple open networks, using the set Q, resembling a hologram, and includes entanglement.

This paper aims to outline the effectiveness of modern universal gate quantum computers when utilizing different configurations to solve the B-SAT(Boolean Satisfiability) problem. The quantum computing experiments are performed using Grover’s Search algorithm to find a valid solution. The experiments are performed under different variations to demonstrate their effects on the results. Changing the number of shots, qubit mapping, and using a different quantum processor are all among the experimental variables. The study also branches into a dedicated experiment highlighting a peculiar behavior that IBM quantum processors exhibit when running circuits with a certain number of shots.