Computational Theory Research Articles

Vertex cover algorithm

Problem to solve P=NP, using the coverage problem of a graph that is NP and convert it to P. In the mathematical discipline of graph theory, a vertex cover, simply a graph cover, is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The problem of finding the smallest vertex coverage in a graph is called the vertex coverage problem. In computational complexity theory, it has been shown that this is an NP-complete problem. An NPcomplete problem is that it is not known if it has a Polynomial solution. I have found an algorithm that proves that it is Polynomial.

On the non-efficient PAC learnability of conjunctive queries

This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in much of the computational learning theory literature; (ii) we establish a strong negative PAC learnability result that applies to many restricted classes of conjunctive queries (CQs), including acyclic CQs for a wide range of notions of acyclicity; (iii) we show that CQs (and UCQs) are efficiently PAC learnable with membership queries.

Neural Activity and Information Processing Capacity of Neuronal Culture.

Whether artificial or living, neural networks perform tremendously diverse kinds of information processing, such as visual feature extraction, speech recognition, motor control, and so on. Some studies have evaluated the computational ability of living neural networks based on the performances of specific tasks, yet could not comprehensively grasp the versatile ability. In this study, we investigated dissociated culture of neurons as a physical reservoir, which generates diverse outputs through linear regression, or readout, of the dynamical states. Based on the theory of reservoir computing, the potential computational capabilities of neuronal culture were evaluated by the information processing capacity (IPC), which indicates how a target function can be achieved from the given dynamics. As a result, we found that the neuronal culture exhibited significant IPC and that IPC varied with the inter-step interval (ISI), the time step of reservoir computing. The cultures exhibited a memory capacity of 10 time steps for computation, and this memory capacity decayed at an ISI of 5 ms or shorter. In addition, the IPC had a significant positive correlation with the intensity of the evoked response relative to spontaneous activity. The multiple regression model with evoked response and ISI showed the positive effect of evoked response and 30 ms as the best ISI for IPC. These results suggest that the distinct evoked response and the optimal time step to interact with the neuronal culture are key factors to uncover computational resources from the neuronal system.

Biased Processing and Opinion Polarization: Experimental Refinement of Argument CommunicationTheory in the Context of the Energy Debate

We combine empirical experimental research on biased argument processing with a computational theory of group deliberation to overcome the micro–macro problem of sociology and to clarify the role of biased processing in debates around energy. We integrate biased processing into the framework of argument communication theory in which agents exchange arguments about a certain topic and adapt opinions accordingly. Our derived mathematical model fits significantly better to the experimentally observed attitude changes than the neutral argument processing assumption made in previous models. Our approach provides new insight into the relationship between biased processing and opinion polarization. Our analysis reveals a sharp qualitative transition from attitude moderation to polarization at the individual level. At the collective level, we find that weak biased processing significantly accelerates group decision processes, whereas strong biased processing leads to a meta-stable conflictual state of bi-polarization that becomes persistent as the bias increases.

A method for converting the existing mechanical zoom optical system to the focus tunable lens zoom optical system

The focus tunable lens (FTL), an emerging device, has brought a new development direction for the research of zoom optical systems, and the zoom lens designed with this lens has more advantages in response speed and mechanical vibration control than the conventional mechanical zoom system. However, there is a relative lack of design methods and computational theories for this type of system at present, and there is a lack of initial structure patents for reference. To solve this problem, this paper proposes a method that can convert the existing conventional mechanical zoom system into an FTL zoom system, and we first introduce the equivalent group element substitution theory for optical systems, then we design a computational screening algorithm for the equivalent FTL group element. We performed an example demonstration to illustrate the details of this method, and we finally obtain one FTL zoom optical system with an F/# of 4, a total length of 120 mm, and an 8 mm image plane. The whole design process is smooth, and the system structure is stable.

Detecting Programming Flaws in Student Submissions with Static Source Code Analysis

"Static code analyzer tools can detect several programming mistakes, that would lead to run-time errors. Such tools can also detect violations of the conventions and guidelines of the given programming language. Thus, the feedback provided by these tools can be valuable for both students and instructors in computer science education. In our paper, we evaluated over 5000 student submissions from the last two years written in C++ and C# programming languages at Eotvos Lorand University Faculty of Informatics (Budapest, Hungary), by executing various static code analyzers on them. From the findings of the analyzers, we highlight some of the most typical and serious issues. Based on these results, we argue to include static analysis of programming submissions in automated and assisted semi-automatic evaluating and grading systems at universities, as these could increase the quality of programming assignments and raise the attention of students on various otherwise missed bugs and other programming errors. 2010 Mathematics Subject Classification. 68U99, 68Q55, 97Q70. 1998 CR Categories and Descriptors. F.3.2 [Theory of Computation]: Logics and Meanings of Programs – Semantics of Programming Languages; D.3.4 [Software]: Programming Languages – Processors; K.3.2 [Computing Milieux]: Computers and Education – Computer and Information Science Education. Key words and phrases. static code analysis, C++, C#, student submission, computer science education, programming flaw."

Dynamic Effect of Fluid–Structure Interaction and Modal Analysis of Crude–Pipeline Interaction System Considering the Fluctuating Pressure of Medium

This work explored the fluid–structure interaction (FSI) effect of crude oil and pipeline and the vibration characteristics of the pipe–crude oil structural system. A finite element computational analysis theory and corresponding simulation method were proposed for crude oil pipelines considering the FSI effect. Meanwhile, the spring model of the FSI interface between crude oil and pipeline was proposed. The experimental simulation and neural network were adopted to obtain the flow-excited pulsation pressure (FEPP), and the kinetic equations of the pipe–crude oil FSI were analyzed. The finite element computation (FEC) model for pipe–crude oil bi-directional FSI dynamics was established, which was composed of five support span lengths and four pipe liquid levels and can provide five different crude oil fluid velocities. One hundred orthogonal simulation test conditions were designed. In addition, the displacement response and acceleration response under FSI of the pipe wall were calculated, and the first six orders of inherent frequencies and main vibration patterns of the FEC model were analyzed. The results revealed that the dynamic effect of FSI between the crude oil transport medium and pipeline was complex and was influenced by the length of the pipeline crossing section, medium flow velocity, difference of liquid surface height, and displacement response. The acceleration response possessed prominent vibration decay characteristics, and the response peak in the same condition was about 8.2 times larger than that of the steady-flow state response. Therefore, the effect changed the inherent frequency and vibration pattern of the pipeline, to which the engineering design should pay sufficient attention.

Information Theory: Applications to the Study of Mutation Dynamics

This study investigates the mutation dynamics of viral genomes using computational methods and information theory. The analysis focuses on Influenza-A virus genomes collected from Tianjin, China, between November 2009 and February 2011. The GENetic Information Entropy Spectra (GENIES) software is employed to calculate the information entropy (IE) of viral genomes and to compare them against a reference genome. The analysis reveals frequent mutation sites, with adenine (A) exhibiting the highest mutation frequency. The study provides valuable insights into the mutation patterns and dynamics of the analysed genomes, however, limitations in data size and the capabilities of the software are acknowledged, highlighting the need for further research and larger datasets to validate and expand upon these findings. Overall, this computational approach demonstrates the potential of using information theory and GENIES to enhance our understanding of viral mutation dynamics, with implications for vaccine design and preparedness for future viral strains.

Dual Copper- and Aldehyde-Catalyzed Transient C-H Sulfonylation of Benzylamines.

This study reports the first example of using a dual catalytic system with copper(II) acetate and 2-hydroxynicotinaldehyde to achieve transient C(sp2)-H sulfonylation of benzylamines with sulfinate salts via a dynamically formed imine directing group. Manganese(IV) oxide was identified as an effective oxidant and base. Computational density functional theory investigations suggest that the transient directing group lowers the energy barrier for an acetate-mediated, turnover-limiting C-H activation step and subsequent combination of the cupracycle with a RSO2 radical.

Neural network-based analytical solver for Fokker–Planck equation

The Fokker–Planck equation has significant applications in dynamical systems. In recent years, some neural network methods have been used in combination with physical models to obtain its numerical solutions. However, it is also appealing if the analytical solution of the physical model can be obtained. This paper proposes a neural network-based method for the analytical solution of the FP equation. It relies on neural networks and uses their explicit model as the trial function for the FP equation. The trial function contains the weights and biases in the neural network. Therefore, the solving of the FP equation is converted into the calculation of the weights and biases. In the proposed method, the FP equations are first reduced to a set of easily solvable nonlinear algebraic equations using some trial functions, and then the corresponding weights and biases are determined using the method of pending coefficients. In this paper, linear and nonlinear numerical examples were used to verify the effectiveness of the proposed method. The results demonstrated that the proposed method can obtain the exact solution of the FP equations without data samples. Finally, the proposed method is compared in detail with physics-informed neural networks in terms of computational theory and computational effectiveness.

Learning from positive and negative examples: New proof for binary alphabets

One of the most fundamental problems in computational learning theory is the problem of learning a finite automaton A consistent with a finite set P of positive examples and with a finite set N of negative examples. By consistency, we mean that A accepts all strings in P and rejects all strings in N. It is well known that this problem is NP-complete. In the literature, it is stated that NP-hardness holds even in the case of a binary alphabet. As a standard reference for this theorem, the work of Gold from 1978 is either cited or adapted. Nevertheless, the results in Gold's work are stated in terms of Mealy machines, and not in terms of deterministic finite automata (DFAs) as most commonly defined. As Mealy machines are equipped with an output function, they can be more compact than DFAs which accept the same language. We show that the adaptations of Gold's construction for Mealy machines stated in the literature have some issues, and provide a correct proof for the fact that the DFA-consistency problem for binary alphabets is NP-complete.

A survey of intelligent optimization algorithms for solving satisfiability problems

Constraint satisfaction problems have a wide range of applications in areas such as basic computer theory research and artificial intelligence, and many major studies in industry are not solved directly, but converted into instances of satisfiability problems for solution. Therefore, the solution of the satisfiability problem is a central problem in many important areas in the future. A large number of solution algorithms for this problem are mainly based on completeness algorithms and heuristic algorithms. Intelligent optimization algorithms with heuristic policies run significantly more efficiently on large-scale instances compared to completeness algorithms. This paper compares the principles, implementation steps, and applications of several major intelligent optimization algorithms in satisfiability problems, analyzes the characteristics of these algorithms, and focuses on the performance in solving satisfiability problems under different constraints. In terms of algorithms, evolutionary algorithms and swarm intelligence algorithms are introduced; in terms of applications, the solution to the satisfiability problem is studied. At the same time, the performance of the listed intelligent optimization algorithms in applications is analyzed in detail in terms of the direction of improvement of the algorithms, advantages and disadvantages and comparison algorithms, respectively, and the future application of intelligent optimization algorithms in satisfiability problems is prospected.

Knowledge Representation and The Semantic Web: An Historical Overview of Influences on Emerging Tools

Abstract: suite of standards known as the Semantic Web is transforming the Internet into a semantic graph rather than a graph of hypertext links. This paper will describe how various ideas and initiatives in artificial intelligence knowledge representation influenced its design. We begin with the seminal work by Alan Turing and Alonzo Church that led to the definition of Turing Machines, enabled digital computing, and provided the mathematical theory of computation, which has been one of the determining factors for Artificial Intelligence knowledge representation. We then provide a brief history of artificial intelligence knowledge representation, starting with groundbreaking researchers, such as Newell and Simon, then to the first "AI boom" driven primarily by rule-based expert systems, followed by major initiatives such as Cyc and the DARPA Knowledge Sharing Initiative. We will discuss how innovations from these initiatives affected standards that, in turn, led to the suite of standards known as the Semantic Web. We conclude with a brief overview of the most important issues currently facing those who wish to see widespread adoption of Semantic Web technology in the industry.

Elements of the Theory of Computation

Abstract: On the undergraduate level, this book is an introduction to the Theory of Computation. A public purpose of terminology must protect a combination of different classifications. Natural languages, programming languages, mathematical languages, etc. The notation of a natural language is like English, Hindi, etc. Informal language can be defined as a system suitable for expressing specific ideas, facts, or concepts, including symbols and rules to manipulate these. The language we consider for our discussion is an abstraction of natural languages. The theory of Computation is based on Logic, Algorithms, and Theorem-proving. A machine is used to perform the user's essential tasks (requirements). So, it is equally important to know the computing models that compare the study. The model tells us how the machine will work together to do Computation. The theory of Computation abstractly provides computational models.

Urgent Call for Astronomer's Validation of “G-D’s Physics” Unique UNCIARE-JRH Critical Prediction!

Twenty-First Century Theoretical Physics has undergone a major “Paradigmatic-Shift” from the Old “Material-Causal” Paradigm underlying General Relativity Theory (GRT) and Quantum Mechanics (QM) to the New “G-D’s Physics” (“Computational Unified Field Theory”, CUFT) [1-47]. This “ParadigmaticShift” inevitably followed the appearance of a fundamental “Paradigmatic-Crisis” of the Old “Material-Causal” Paradigm signified by a basic “theoretical-inconsistency” between its (abovementioned) constituting Models (e.g., GRT & QM), as well as its principle inability to explain the accelerated rate of the universe’s expansion, e.g., assumed to be “caused” by purely hypothetical “dark-matter” and “dark-energy” concepts, but could not be detected experimentally (despite over twenty years of intensive experimental efforts to do so)?! Instead, the New “G-D’s Physics” (CUFT) has been shown capable of resolving this (apparent) “theoretical-inconsistency” between GRT & QM based on its discovery of a singular (higher-ordered) UCP which simultaneously computes the four basic physical features (e.g., of “space”, “energy”, ”mass” and “time”) of every exhaustive spatial pixel in the universe – in the incredible rate of “c2 /h” = 1.36-50 sec’(!) thereby producing an extremely rapid series of UF’s frames comprising the entire physical universe at every “minimal time-point”!

On primitivity and regularity of wreath product groups of degree 5p that are not p- groups using numerical approach

Let p be an odd prime number. This work applies some group concepts to construct the Wreath Product of two permutation groups of prime degrees. We used numerical approach to investigate and determine the primitive and regular nature of the constructed Wreath Product Group of degree 5p. We apply Computational Group Theory (GAP) to facilitate as well as validate our results.

Suicide prevention and ketamine: insights from computational modeling.

Suicide is a pressing public health issue, with over 700,000 individuals dying each year. Ketamine has emerged as a promising treatment for suicidal thoughts and behaviors (STBs), yet the complex mechanisms underlying ketamine's anti-suicidal effect are not fully understood. Computational psychiatry provides a promising framework for exploring the dynamic interactions underlying suicidality and ketamine's therapeutic action, offering insight into potential biomarkers, treatment targets, and the underlying mechanisms of both. This paper provides an overview of current computational theories of suicidality and ketamine's mechanism of action, and discusses various computational modeling approaches that attempt to explain ketamine's anti-suicidal effect. More specifically, the therapeutic potential of ketamine is explored in the context of the mismatch negativity and the predictive coding framework, by considering neurocircuits involved in learning and decision-making, and investigating altered connectivity strengths and receptor densities targeted by ketamine. Theory-driven computational models offer a promising approach to integrate existing knowledge of suicidality and ketamine, and for the extraction of model-derived mechanistic parameters that can be used to identify patient subgroups and personalized treatment approaches. Future computational studies on ketamine's mechanism of action should optimize task design and modeling approaches to ensure parameter reliability, and external factors such as set and setting, as well as psychedelic-assisted therapy should be evaluated for their additional therapeutic value.

Zero-Shot Linear Combinations of Grounded Social Interactions with Linear Social MDPs

Humans and animals engage in rich social interactions. It is often theorized that a relatively small number of basic social interactions give rise to the full range of behavior observed. But no computational theory explaining how social interactions combine together has been proposed before. We do so here. We take a model, the Social MDP, which is able to express a range of social interactions, and extend it to represent linear combinations of social interactions. Practically for robotics applications, such models are now able to not just express that an agent should help another agent, but to express goal-centric social interactions. Perhaps an agent is helping someone get dressed, but preventing them from falling, and is happy to exchange stories in the meantime. How an agent responds socially, should depend on what it thinks the other agent is doing at that point in time. To encode this notion, we take linear combinations of social interactions as defined in Social MDPs, and compute the weights on those combinations on the fly depending on the estimated goals of other agents. This new model, the Linear Social MDP, enables zero-shot reasoning about complex social interactions, provides a mathematical basis for the long-standing intuition that social interactions should compose, and leads to interesting new behaviors that we validate using human observers. Complex social interactions are part of the future of intelligent agents, and having principled mathematical models built on a foundation like MDPs will make it possible to bring social interactions to every robotic application.

Experimental and computational exploration of synergistic effect of Laurus nobilis extract:Zinc cation on mild steel corrosion inhibition in saline solution

According to the literature, the effectiveness of green corrosion inhibitors in chloride-containing solutions is not acceptable. To improve the anti-corrosion efficiency, a mixture of metal cations and green corrosion inhibitors can be used. In the current study, the synergistic corrosion mitigation effect of Laurus nobilis (LN) extract: Zn mixture on the mild steel (MS) in 3.5% NaCl solution was comprehensively studied by aiding various electrochemical and morphological techniques, as well as molecular-electronic scale modeling approaches (Molecular Dynamics coupled with Monte Carlo, and DFT). The observations from the EIS and polarization methods confirmed 90% inhibition degree using 200–600 ppm LN:Zn mixture along with mixed protection mechanism. Also, EIS results displayed maximum corrosion resistance achievement in the presence of 200–600 ppm LN:Zn mixture (about 10,000 Ω cm2 at 24 h of immersion). The MS surface characterizations via FE-SEM (equipped with EDS) technique disclosed the production of a smooth protective film composed of the LN molecules, Zn oxide/hydroxide species as well as LN/Zn chelation. Additionally, the outcome of the contact angle (CA) analysis clarified the hydrophilic nature of the sample surface protected by LN:Zn mixtures. FT-IR and UV–Visible analyses illustrated the successful LN molecules and Zn cations adsorption over the metal surface. The detailed findings proposed by computational studies (Molecular Dynamics (MD), Monte Carlo (MC), and Density Functional Theory (DFT)) revealed that the LN:Zn+2 complexes interfacially adsorbed onto the metal-based adsorbents through local/global atomic regions, further affirming their strong anti-corrosion propensity.

Is the mind in the brain in contemporary computational neuroscience?

According to contemporary computational neuroscience the mental is associated with computations implemented in the brain. We analyze in physical terms based on recent results in the foundations of statistical mechanics two well-known (independent) problems that arise for this approach: the problem of multiple-computations and the problem of multiple-realization. We show that within the computational theory of the mind the two problems are insoluble by the physics of the brain. We further show that attempts to solve the problems by the interactions of the systems implementing the computations with an environment (in or outside the brain) must introduce non-physical factors, and therefore fail on physical grounds. We also show that the problems are endemic and pertain to other forms of functional theories of the mind, most notably, causal functionalism. Finally, we propose a physicalist reductive identity theory, which is a generalization of statistical mechanics for all the special sciences, and show that only a theory of this kind can provide physical solutions to the above two problems in computational neuroscience. We conclude that functionalism in the theory of mind must be replaced with a reductive identity theory. This result has far-reaching implications with respect to the research programs in brain science.