Applications In Computer Science Research Articles

Computational Adequacy for Substructural Lambda Calculi

Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum programming. We describe one linear and one affine type systems and we formulate abstract categorical models for both of them which are sound and computationally adequate. We also show, under basic assumptions, that interpreting lambda abstractions via a monoidal closed structure (a popular method for linear type systems) necessarily leads to degenerate and inadequate models for call-by-value affine type systems with recursion. In our categorical treatment, a solution to this problem is clearly presented. Our categorical models are more general than linear/non-linear models used to study linear logic and we present a homogeneous categorical account of both linear and affine type systems in a call-by-value setting. We also give examples with many concrete models, including classical and quantum ones.

On the Application of Computer Science and Technology in Computer Education

The computer has become an indispensable and important tool in people's daily life and work. It brings more convenience to people and provides important conditions for human survival and development. Therefore, the application of computer science and technology to computer education can enable students to have a correct understanding of computer application concepts and practical operations, thereby improving the level of computer education. This article mainly analyzes the advantages and significance of the application of computer science and technology in computer education, and proposes the measures to be used, hoping to provide certain references and suggestions for the cultivation of computer talents.

Efficient exponential time integration for simulating nonlinear coupled oscillators

In this paper, we propose an advanced time integration technique associated with explicit exponential Rosenbrock-based methods for the simulation of large stiff systems of nonlinear coupled oscillators. In particular, a novel reformulation of these systems is introduced and a general family of efficient exponential Rosenbrock schemes for simulating the reformulated system is derived. Moreover, we show the required regularity conditions and prove the convergence of these schemes for the system of coupled oscillators. We present an efficient implementation of this new approach and discuss several applications in scientific and visual computing. The accuracy and efficiency of our approach are demonstrated through a broad spectrum of numerical examples, including a nonlinear Fermi–Pasta–Ulam–Tsingou model, elastic and nonelastic deformations as well as collision scenarios focusing on relevant aspects such as stability and energy conservation, large numerical stiffness, high fidelity, and visual accuracy.

Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index

A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also an NP-complete problem. In this paper, we study the Hamilton-connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton-connected. An infinite family of non-Hamilton-connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton-connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index.

KSPHPDDM and PCHPDDM: Extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners

Contemporary applications in computational science and engineering often require the solution of linear systems which may be of different sizes, shapes, and structures. The goal of this paper is to explain how two libraries, PETSc and HPDDM, have been interfaced in order to offer end-users robust overlapping Schwarz preconditioners and advanced Krylov methods featuring recycling and the ability to deal with multiple right-hand sides. The flexibility of the implementation is showcased and explained with minimalist, easy-to-run, and reproducible examples, to ease the integration of these algorithms into more advanced frameworks. The examples provided cover applications from eigenanalysis, elasticity, combustion, and electromagnetism.

Verification and Reachability Analysis of Fractional-Order Differential Equations Using Interval Analysis

Interval approaches for the reachability analysis of initial value problems for sets of classical ordinary differential equations have been investigated and implemented by many researchers during the last decades. However, there exist numerous applications in computational science and engineering, where continuous-time system dynamics cannot be described adequately by integer-order differential equations. Especially in cases in which long-term memory effects are observed, fractional-order system representations are promising to describe the dynamics, on the one hand, with sufficient accuracy and, on the other hand, to limit the number of required state variables and parameters to a reasonable amount. Real-life applications for such fractional-order models can, among others, be found in the field of electrochemistry, where methods for impedance spectroscopy are typically used to identify fractional-order models for the charging/discharging behavior of batteries or for the dynamic relation between voltage and current in fuel cell systems if operated in a non-stationary state. This paper aims at presenting an iterative method for reachability analysis of fractional-order systems that is based on an interval arithmetic extension of Mittag-Leffler functions. An illustrating example, inspired by a low-order model of battery systems concludes this contribution.

The psychological aspects of paraconsistency

The creation of paraconsistent logics have expanded the boundaries of formal logic by introducing coherent systems that tolerate contradictions without triviality. Thanks to their novel approach and rigorous formalization they have already found many applications in computer science, linguistics and mathematics. As a natural next step, some philosophers have also tried to answer the question if human everyday reasoning could be accurately modelled with paraconsistent logics. The purpose of this article is to argue against the notion that human reasoning is paraconsistent. Numerous findings in the area of cognitive psychology and cognitive neuroscience go against the hypothesis that humans tolerate contradictions in their inferences. Humans experience severe stress and confusion when confronted with contradictions (i.e., the so-called cognitive dissonance). Experiments on the ways in which humans process contradictions point out that the first thing humans do is remove or modify one of the contradictory statements. From an evolutionary perspective, contradiction is useless and even more dangerous than lack of information because it takes up resources to process. Furthermore, it appears that when logicians, anthropologists or psychologists provide examples of contradictions in human culture and behaviour, their examples very rarely take the form of: $$(p \wedge \lnot p)$$ . Instead, they are often conditional statements, probabilistic judgments, metaphors or seemingly incompatible beliefs. At different points in time humans are definitely able to hold contradictory beliefs, but within one reasoning leading to a particular behaviour, contradiction is never tolerated.

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics, computer science, and engineering. This review presents a comprehensive study of works on Quaternion Algebra and GA applications in computer science and engineering from 1995 to 2020. After a brief introduction of GA, the applications of GA are reviewed across many fields. We discuss the characteristics of the applications of GA to various problems of computer science and engineering. In addition, the challenges and prospects of various applications proposed by many researchers are analyzed. We analyze the developments using GA in image processing, computer vision, neurocomputing, quantum computing, robot modeling, control, and tracking, as well as improvement of computer hardware performance. We believe that up to now GA has proven to be a powerful geometric language for a variety of applications. Furthermore, there is evidence that this is the appropriate geometric language to tackle a variety of existing problems and that consequently, step-by-step GA-based algorithms should continue to be further developed. We also believe that this extensive review will guide and encourage researchers to continue the advancement of geometric computing for intelligent machines.

A Nonmonotone Matrix-Free Algorithm for Nonlinear Equality-Constrained Least-Squares Problems

Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must account for nonlinear dynamics by incorporating constraints. In addition, these systems often incorporate a large number of variables, which increases the difficulty of the problem, and motivates the need for efficient algorithms amenable to large-scale implementations. In this paper, we propose and analyze a Levenberg-Marquardt algorithm for nonlinear least squares subject to nonlinear equality constraints. Our algorithm is based on inexact solves of linear least-squares problems, that only require Jacobian-vector products. Global convergence is guaranteed by the combination of a composite step approach and a nonmonotone step acceptance rule. We illustrate the performance of our method on several test cases from data assimilation and inverse problems: our algorithm is able to reach the vicinity of a solution from an arbitrary starting point, and can outperform the most natural alternatives for these classes of problems.

Polynomials and General Degree‐Based Topological Indices of Generalized Sierpinski Networks

Sierpinski networks are networks of fractal nature having several applications in computer science, music, chemistry, and mathematics. These networks are commonly used in chaos, fractals, recursive sequences, and complex systems. In this article, we compute various connectivity polynomials such as M‐polynomial, Zagreb polynomials, and forgotten polynomial of generalized Sierpinski networks and recover some well‐known degree‐based topological indices from these. We also compute the most general Zagreb index known as (α, β)‐Zagreb index and several other general indices of similar nature for this network. Our results are the natural generalizations of already available results for particular classes of such type of networks.

A linear algorithm for a minimax location of a path-shaped facility with a specific length in a weighted tree network

This paper considers the problem of locating a path-shaped facility of a specific size on a weighted tree network. The criterion for optimality used in this paper is the minimax criterion in which the weighted distance to the farthest vertex from the facility is minimised. The minimax criterion gives acceptable results from the point of view of the fast response for the clients who are located far away from the facility. This location problem usually has applications in computer science, information science, and operations research. An O(n) time algorithm is proposed for finding the optimal location of a path-shaped facility of a bounded length on a weighted tree network, where n is the number of vertices in the tree.

Generalized Relation between the Roots of Polynomial and Term of Recurrence Relation Sequence

Many researchers have been working on recurrence relation which is an important topic not only in mathematics but also in physics, economics and various applications in computer science. There are many useful results on recurrence relation sequence but there main problem to find any term of recurrence relation sequence we need to find all previous terms of recurrence relation sequence. There were many important theorems obtained on recurrence relations. In this paper we have given special identity for generalized kth order recurrence relation. These identities are very useful for finding any term of any order of recurrence relation sequence. Authors define a special formula in this paper by this we can find direct any term of a recurrence relation sequence. In this recurrence relation sequence to find any terms we need to find all previous terms so this result is very important. There is important property of a relation between coefficients of recurrence relation terms and roots of a polynomial for second order relation but in this paper, we gave this same property of recurrence relation of all higher order recurrence relation. So finally, we can say that this theorem is valid all order of recurrence relation only condition that roots are distinct. So, we can say that this paper is generalization of property of a relation between coefficients of recurrence relation terms and roots of a polynomial. Theorem: - Let C₁ and C₂ are arbitrary real numbers and suppose the equation <img src=image/13422456_01.gif> (1) Has X₁ and X₂ are distinct roots. Then the sequence <img src=image/13422456_25.gif> is a solution of the recurrence relation <img src=image/13422456_02.gif> (2) <img src=image/13422456_03.gif>. For n= 0, 1, 2 …where β₁ and β₂ are arbitrary constants. Proof: - First suppose that <img src=image/13422456_25.gif> of type <img src=image/13422456_04.gif> we shall prove <img src=image/13422456_25.gif> is a solution of recurrence relation (2). Since X₁, X₂ and X₃ are roots of equation (1) so all are satisfied equation (1) so we have<img src=image/13422456_05.gif>, <img src=image/13422456_06.gif>. Consider <img src=image/13422456_07.gif><img src=image/13422456_08.gif>. This implies <img src=image/13422456_09.gif>. So the sequence <img src=image/13422456_25.gif> is a solution of the recurrence relation. Now we will prove the second part of theorem. Let <img src=image/13422456_10.gif> is a sequence with three <img src=image/13422456_11.gif>. Let <img src=image/13422456_12.gif>. So <img src=image/13422456_13.gif> (3). <img src=image/13422456_14.gif> (4). Multiply by X₁ to (3) and subtracts from (4). We have <img src=image/13422456_15.gif> similarly we can find <img src=image/13422456_16.gif>. So we can say that values of β₁ and β₂ are defined as roots are distinct. So non- trivial values ofβ₁ and β₂ can find and we can say that result is valid. Example: Let <img src=image/13422456_25.gif> be any sequence such that <img src=image/13422456_17.gif> n≥3 and a₀=0, a₁=1, a₂=2. Then find a₁₀ for above sequence. Solution: The polynomial of above sequence is <img src=image/13422456_18.gif>. Solving this equation we have roots are 1, 2, and 3 using above theorem we have <img src=image/13422456_19.gif> (7). Using a₀=0, a₁=1, a₂=2 in (7) we have β₁+β₂+β₃=0 (8). β₁+2β₂+3β₂=1 (9).β₁+4β₂+9β₃=2 (10) Solving (8), (9) and (10) we have <img src=image/13422456_20.gif>, <img src=image/13422456_21.gif>, <img src=image/13422456_22.gif>. This implies <img src=image/13422456_23.gif>. Now put n=10 we have a₁₀=-27478. Recurrence relation is a very useful topic of mathematics, many problems of real life may be solved by recurrence relations, but in recurrence relation there is a major difficulty in the recurrence relation. If we want to find 100th term of sequence, then we need to find all previous 99 terms of given sequence, then we can get 100th term of sequence but above theorem is very useful if coefficients of recurrence relation of given sequence satisfies the condition of the above theorem, then we can apply above theorem and we can find direct any term of sequence without finding all previous terms.

Computation of reverse degree-based topological indices of hex-derived networks

&lt;abstract&gt;&lt;p&gt;Network theory gives an approach to show huge and complex frameworks through a complete arrangement of logical devices. A network is made is made of vertices and edges, where the degree of a vertex refers to the number of joined edges. The degree appropriation of a network represents the likelihood of every vertex having a particular degree and shows significant worldwide network properties. Network theory has applications in many disciplines like basic sciences, computer science, engineering, medical, business, public health and sociology. There are some important networks like logistical networks, gene regulatory networks, metabolic networks, social networks, derived networks. Topological index is a numerical number assigned to the molecular structure/netwrok which is used for correlation analysis in physical, theoretical and environmental chemistry. The hex-derived networks are created by hexagonal networks of dimension $ t $, these networks have an assortment of valuable applications in computer science, medical science and engineering. In this paper we discuss the reverse degree-based topological for third type of hex-derived networks.&lt;/p&gt;&lt;/abstract&gt;

Computation of Vertex-Edge Degree Based Topological Descriptors for Hex-Derived Networks

A numeric number that represents the entire structure of a graph is defined to be a topological descriptor. Graph theory has been found to be a useful area of research in the direction of topological descriptors. The different physical and chemical properties of basic chemical compounds are related by main factors of topological descriptors. In the study of QSAR/QSPR, the vertex-edge topological descriptors are used to predict the bioactivity of chemical compound. The hex-derived networks are generated by hexagonal networks of dimension p, these networks have an assortment of valuable applications in computer science, medical science and engineering. Simonraj and George derived a new type of graphs, which is named a third type of hex-derived networks and this work carried out by Ali et al. with calculation of degree-based topological descriptors for these networks. In this paper, we compute the exact values of vertex-edge based topological descriptors for third type of hex-derived networks.

A Linear Algorithm for a Minimax Location of a Path-Shaped Facility with a Specific Length in a Weighted Tree Network

This paper considers the problem of locating a path-shaped facility of a specific size on a weighted tree network. The criterion for optimality used in this paper is the minimax criterion in which the weighted distance to the farthest vertex from the facility is minimised. The minimax criterion gives acceptable results from the point of view of the fast response for the clients who are located far away from the facility. This location problem usually has applications in computer science, information science, and operations research. An O(n) time algorithm is proposed for finding the optimal location of a path-shaped facility of a bounded length on a weighted tree network, where n is the number of vertices in the tree.

A Local Extended Algorithm Combined with Degree and Clustering Coefficient to Optimize Overlapping Community Detection

Community structure is one of the most important characteristics of complex networks, which has important applications in sociology, biology, and computer science. The community detection method based on local expansion is one of the most adaptable overlapping community detection algorithms. However, due to the lack of effective seed selection and community optimization methods, the algorithm often gets community results with lower accuracy. In order to solve these problems, we propose a seed selection algorithm of fusion degree and clustering coefficient. The method calculates the weight value corresponding to degree and clustering coefficient by entropy weight method and then calculates the weight factor of nodes as the seed node selection order. Based on the seed selection algorithm, we design a local expansion strategy, which uses the strategy of optimizing adaptive function to expand the community. Finally, community merging and isolated node adjustment strategies are adopted to obtain the final community. Experimental results show that the proposed algorithm can achieve better community partitioning results than other state‐of‐the‐art algorithms.

Matrix representation of operations of soft partial orderings on a generalized soft poset

A soft set is a parametrized family of subsets of an initial universal set. Soft set theory is a generalization of fuzzy set theory and is a mathematical tool for dealing with uncertainty and vagueness. Posets are used in many applications of Mathematics and Computer Science. Matrix representations are more applicable for handling data in computer programs. In this paper, we introduce the ordinary matrix representation of a soft relation, soft matrix representation of soft partial ordering and operations of soft partial orderings on a generalized soft poset.

A Systematic Literature Review of Lexical Analyzer Implementation Techniques in Compiler Design

The term “lexical” in lexical analysis process of the compilation is derived from the word “lexeme”, which is the basic conceptual unit of the linguistic morphological study. In computer science, lexical analysis, also referred to as lexing, scanning or tokenization, is the process of transforming the string of characters in source program to a stream of tokens, where the token is a string with a designated and identified meaning. It is the first phase of a two-step compilation processing model known as the analysis stage of compilation process used by compiler to understand the input source program. The objective is to convert character streams into words and recognize its token type. The generated stream of tokens is then used by the parser to determine the syntax of the source program. A program in compilation phase that performs a lexical analysis process is termed as lexical analyzer, lexer, scanner or tokenizer. Lexical analyzer is used in various computer science applications, such as word processing,information retrieval systems, pattern recognition systems and language-processing systems. However, the scope of our review study is related to language processing. Various tools are used for automatic generation of tokens and are more suitable for sequential execution of the process. Recent advances in multi-core architecture systems have led to the need to re-engineer the compilation process to integrate the multi-core architecture. By parallelization in the recognition of tokens in multiple cores, multi cores can be used optimally, thus reducing compilation time. To attain parallelism in tokenizationon multi-core machines, the lexical analyzer phase of compilation needs to be restructured to accommodate the multi-core architecture and by exploiting the language constructs which can run parallel and the concept of processor affinity. This paper provides a systematic analysis of literature to discuss emerging approaches and issues related to lexical analyzer implementation and the adoption of improved methodologies. This has been achieved by reviewing 30 published articles on the implementation of lexical analyzers. The results of this review indicate various techniques, latest developments, and current approaches for implementing auto generated scanners and hand-crafted scanners. Based on the findings, we draw on the efficacy of lexical analyzer implementation techniques from the results discussed in the selected review studies and the paper provides future research challenges and needs to explore the previously under-researched areas for scanner implementation processes.

Efficient Computation of the Large Inductive Dimension Using Order- and Graph-theoretic Means

Finite topological spaces and their dimensions have many applications in computer science, e.g., in digital topology, computer graphics and the analysis and synthesis of digital images. Georgiou et. al. [11] provided a polynomial algorithm for computing the covering dimension dim(X; 𝒯) of a finite topological space (X; 𝒯). In addition, they asked whether algorithms of the same complexity for computing the small inductive dimension ind(X; 𝒯) and the large inductive dimension Ind(X; 𝒯) can be developed. The first problem was solved in a previous paper [4]. Using results of the that paper, we also solve the second problem in this paper. We present a polynomial algorithm for Ind(X; 𝒯), so that there are now efficient algorithms for the three most important notions of a dimension in topology. Our solution reduces the computation of Ind(X; 𝒯), where the specialisation pre-order of (X; 𝒯) is taken as input, to the computation of the maximal height of a specific class of directed binary trees within the partially ordered set. For the latter an efficient algorithm is presented that is based on order- and graph-theoretic ideas. Also refinements and variants of the algorithm are discussed.

'Anti-blackness is no glitch'

The conversation around and application of computer science often reinforces neoliberal ideals of what pathways students should take. Computer science education is said to be the great equalizer for marginalized youth. We grapple with how this can never be true in an educational system grounded in anti-Blackness.