Applications In Computer Science Research Articles

Differentially private Choquet integral: extending mean, median, and order statistics

The Choquet integral is a well known aggregation function that generalizes several other well known functions. For example, appropriate parameterizations reduce a Choquet integral to the arithmetic mean, the weighted mean, order statistics, and linear combination of order statistics. This integral has been used extensively in data fusion. We find applications in computer science, economy, and decision making. Formally, Choquet integrals integrate a function (the data to be aggregated) with respect to a non-additive measure also called a fuzzy measure (which represents the background knowledge on the information sources that provide the data to be aggregated). In this paper we propose a privacy preserving Choquet integral which satisfies differential privacy. Then, we study the sensitivity of the Choquet integral with respect to different types of fuzzy measures. Our results generalize previous knowledge about the sensitivity of minimum, maximum, and the arithmetic mean.

Topological Analysis of Fractal Binary and Ternary Trees

Fractals are complex geometric objects that seem the same at different scales and have self-similarity. Because of this special characteristic, fractals can be used to simulate intricate biological processes. Fractal binary and ternary trees are novel data types that combine the productiveness of tree architectures with the ideas of fractal geometry. In addition to self-similarity and scalability, these trees have potential across a range of computer science and medical applications. The main goal of the study is to identify and analyze topological indices and graph entropy for fractal binary and fractal ternary trees. By examining indices such as the Randić index, Zagreb indices, and entropy measurements, the study aims to obtain a comprehensive knowledge of the structural complexity and information-theoretic properties of these fractal graphs. The study starts with the vertex and edge partitioning of fractal binary and ternary trees in order to distinguish different structural classes. Using these partitions, we obtained topological indices and graph entropy values for the fractal trees. Also, this study compares the topological indices for each fractal tree with the number of copies in the fractal dimension for a succession of graphs.

Optimizing Heap Sort for Repeated Values: A Modified Approach to Improve Efficiency in Duplicate-Heavy Data Sets

Sorting algorithms are critical to various computer science applications, including database management, big data analytics, and real-time systems. While Heap Sort is a widely used comparison-based sorting algorithm, its efficiency significantly diminishes when dealing with data sets containing a high volume of duplicate values. To address this limitation, this paper introduces a modified Heap Sort algorithm optimized for duplicate-heavy data. The proposed modification detects and handles duplicate values more efficiently by reducing unnecessary comparisons and swaps at the root of the heap and restructuring the heap more strategically. Experimental results demonstrate that the modified Heap Sort achieves up to a 15% reduction in sorting time, a 30% decrease in the number of swaps, and a 10% reduction in comparisons when tested on data sets with varying levels of duplication. These improvements highlight the enhanced computational efficiency and scalability of the modified algorithm in duplicate-heavy data scenarios. This advancement offers significant potential for improving sorting performance in practical domains such as big data analytics, database operations, and real-time data processing.

Markov processes: branching properties and asymptotic behavior applications in computer science

Markov processes: branching properties and asymptotic behavior applications in computer science

Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations

AbstractThe randomly pivoted Cholesky algorithm (RPCholesky) computes a factorized rank‐ approximation of an positive‐semidefinite (psd) matrix. RPCholesky requires only entry evaluations and additional arithmetic operations, and it can be implemented with just a few lines of code. The method is particularly useful for approximating a kernel matrix. This paper offers a thorough new investigation of the empirical and theoretical behavior of this fundamental algorithm. For matrix approximation problems that arise in scientific machine learning, experiments show that RPCholesky matches or beats the performance of alternative algorithms. Moreover, RPCholesky provably returns low‐rank approximations that are nearly optimal. The simplicity, effectiveness, and robustness of RPCholesky strongly support its use in scientific computing and machine learning applications.

A multiobjective evolutionary algorithm for optimizing the small-world property.

Small-world effect plays an important role in the field of network science, and optimizing the small-world property has been a focus, which has many applications in computational social science. In the present study, we model the problem of optimizing small-world property as a multiobjective optimization, where the average clustering coefficient and average path length are optimized separately and simultaneously. A novel method for optimizing small-world property is then proposed based on the multiobjective evolutionary algorithm with decomposition. Experimental results have proved that the presented method is capable of solving this problem efficiently, where a uniform distribution of solutions on the Pareto-optional front can be generated. The optimization results are further discussed to find specific paths for optimizing different objective functions. In general, adding edges within the same community is helpful for promoting ACC, while adding edges between different communities is beneficial for reducing APL. The optimization on networks with the feature of community structure is more remarkable, but community structure has less impact on the optimization when the internal community is triangles-saturated.

LVGG-IE: A Novel Lightweight VGG-Based Image Encryption Scheme.

Image security faces increasing challenges with the widespread application of computer science and artificial intelligence. Although chaotic systems are employed to encrypt images and prevent unauthorized access or tampering, the degradation that occurs during the binarization process in chaotic systems reduces security. The chaos- and DNA-based image encryption schemes increases its complexity, while the integration of deep learning with image encryption is still in its infancy and has several shortcomings. An image encryption scheme with high security and efficiency is required for the protection of the image. To address these problems, we propose a novel image encryption scheme based on the lightweight VGG (LVGG), referred to as LVGG-IE. In this work, we design an LVGG network with fewer layers while maintaining a high capacity for feature capture. This network is used to generate a key seed, which is then employed to transform the plaintext image into part of the initial value of a chaotic system, ensuring that the chaos-based key generator correlates with the plaintext image. A dynamic substitution box (S-box) is also designed and used to scramble the randomly shuffled plaintext image. Additionally, a single-connected (SC) layer is combined with a convolution layer from VGG to encrypt the image, where the SC layer is dynamically constructed by the secret key and the convolution kernel is set to 1×2. The encryption efficiency is simulated, and the security is analyzed. The results show that the correlation coefficient between adjacent pixels in the proposed scheme achieves 10-4. The NPCR exceeds 0.9958, and the UACI falls within the theoretical value with a significance level of 0.05. The encryption quality, the security of the dynamic S-box and the SC layer, and the efficiency are tested. The result shows that the proposed image encryption scheme demonstrates high security, efficiency, and robustness, making it effective for image security in various applications.

An Innovative Hybrid Approach Producing Trial Solutions for Global Optimization

Global optimization is critical in engineering, computer science, and various industrial applications as it aims to find optimal solutions for complex problems. The development of efficient algorithms has emerged from the need for optimization, with each algorithm offering specific advantages and disadvantages. An effective approach to solving complex problems is the hybrid method, which combines established global optimization algorithms. This paper presents a hybrid global optimization method, which produces trial solutions for an objective problem utilizing a genetic algorithm’s genetic operators and solutions obtained through a linear search process. Then, the generated solutions are used to form new test solutions, by applying differential evolution techniques. These operations are based on samples derived either from internal line searches or genetically modified samples in specific subsets of Euclidean space. Additionally, other relevant approaches are explored to enhance the method’s efficiency. The new method was applied on a wide series of benchmark problems from recent studies and comparison was made against other established methods of global optimization.

The Logic and Application of Greedy Algorithms

Abstract. Being easy to implement and offering faster solutions, the greedy algorithms have widely been used in solving combinatorial optimization problems in computer science and many practical applications, such as resource allocation and data compression. This paper aims at analyzing the definitions, theory, and application of greedy algorithms in computer science as well as their logic and efficacy in numerous situations. In this analysis, concepts such as the greedy choice property and optimal substructure are examined as essential to understanding how greedy algorithms operate. The provided analysis mainly assumes prior knowledge of concepts and problems like the Fractional Knapsack problem and the Shortest Path problem solution as well as some practical problems, for example, resource allocation and the exact coin change problem. Analytical data and real applications are used to analyze the performance of greedy algorithms vis-a-vis other categories, such as the dynamic programming paradigm. The results reveal that greedy algorithms have the potential for great efficiency while also being restricted by certain parameters. They are ideal in the following aspects pertaining to computational aspects, that is, speed, ease of implementation, and applicability to large datasets. But they do not necessarily promise strong optimality in certain situations. The conclusion notes that greedy algorithms deserve further applications when the specified conditions are met and states that the effectiveness of these conditions needs to be studied.

The Spectrum of a Certain Large Block Matrix

Large matrices appear in many applications in computer science, physics, chemistry and many other disciplines. This is because such matrices have the ability to hold huge amounts of memory. On of the main properties that researchers are interested is studying the spectral theory of these matrices. In this paper, we compute the spectrum of a certain large matrix that can serve as an adjacency matrix of a certain clean graph. In particular, we give a full characterization of the eigenvalues and eigenvectors of the intended matrix.

New Methods Based on the Calculation of Specific Decimal Fractions for Decomposing an Integer into a Product of Prime Factors

This article presents for the first time two methods for decomposing integers in products of prime factors which are based on the calculation of decimal fractions. Its originality lies in the fact that the divisors used are decimals and not prime divisors and in addition the decimal part is manipulated in such a way that two decimal digits are fixed and the others are variable. In the first method, the divisors are of type 2n and which have a very interesting particularity which is that they always have two same digits at the end of their decimal parts (25 or 75). And it is this particularity which is exploited to develop these methods. The other method introduces a new notion that of the decomposition key which is a product of prime factors used to decompose all numbers having the same number of digits. It is similar to the first method because it also uses decimal fractions for the calculation and the denominator is the square root. This article paves the way for new applications in computer science.

The number of spanning trees in K n -chain and ring graphs

The problem of counting spanning trees of graphs or networks is a fundamental and crucial area of research in combinatorics, while has numerous important applications in statistical physics, network theory and theoretical computer science. Very recently, Kosar, Zaman, Ali and Ullah obtained a nice formula on the number of spanning trees of a K 5-chain network K5ℓ constructed by connecting ℓcopys of complete graphs K 5. They made extensive use of matrix theory and spectral graph theory, especially the normalized Laplacian of graphs. In this paper, by using a rather simple and more physical treatment (the mesh-star transformation in electrical network) without any linear algebra, we generalize their result to K n -chain graphs and K n -ring graphs. The results show that there is a simple relation between the number of spanning trees of the K n -chain graph Lnℓ and the K n -ring graph Cnℓ . We also calculate the corresponding tree entropy (or so called ‘the asymptotic growth constant’) and find that the tree entropy of the corresponding K n -chain graphs and K n -ring graphs are totally the same.

A Comprehensive Survey on the Role of Law in Different Applications in Computer Science

One significant tool for addressing the concerns associated with the use of one of the applications in computer science is the law. Numerous laws and rules governing the use of computer science are designed to safeguard users, customers, and society at large. Law uses norms created by governmental and social institutions to control behavior. Programming is used to explore digital information in computer science. Computers got more potent and smaller as they evolved through generations, utilizing various technologies such as integrated circuits. Cyber law regulates online behavior and deals with matters pertaining to intellectual property, privacy, domain names, and other legal concerns. A few of the many concerns that the law must address in order to mitigate the electronic crimes are protecting privacy and security, upholding justice, limiting civil and criminal liability, ensuring safety, and controlling the application of AI in the workplace. Guidelines that people and organizations have to follow when utilizing computer science applications, making sure that these requirements are met in full. Additionally, as companies must commit to recording AI usage procedures and making clear the use of data and algorithms, the regulation fosters accountability and openness. By doing this, the possibility of prejudice and mistakes when utilizing AI is decreased. This survey provides a self-contained introduction to cybercrimes and types of cybercrimes. We also present ways to combat cybercrime and limit its spread.

Ai] Explore!: An Educational Game for Developing Programming Skills and Algorithmic Thinking

The game [ai] explore! was developed to introduce the algorithm behind the popular science exhibition. The idea behind the [ai] explore! exhibition was to show the application of mathematics and computer science in solving real engineering problems by creating the exhibit using the mathematical algorithm Heat Equation Driven Area Coverage (HEDAC). The algorithm is based on scientific research and has many applications: exploration and search in unknown space, painting, planning agricultural spraying, scanning 3D objects, etc. The exhibits show the process by which the algorithm paints objects with a virtual brush and explores their shape. By surveying the high school students, it was shown that new mathematical and engineering results can be explained and turned into a playable game. After playing the game, students respond positively to the game presented and state that they have a good understanding of the HEDAC algorithm presented and how it works. This motivated us to investigate [ai] explore! as an educational game for teaching mathematics and computer science. The aim of the research described in this paper is to investigate the potential of the developed game as an educational game. The game-based learning (GBL) approach is increasingly used to increase student motivation and engagement in STEM lessons. The main research question is: How do primary school teachers and students perceive the usefulness of the game [ai] explore! in supporting teaching and learning of computer science concepts? We have developed and implemented teaching scenarios on how the game [ai] explore! can be used as an educational game in computer science lessons. We show that the game has great potential to teach primary school students programming. In addition, the game promotes algorithmic thinking and computational thinking skills in general, which are valuable not only in computer science but also in other fields such as mathematics, where a systematic and analytical approach to problem-solving is required.

On separability of semigroups: application to models of physics and discrete optimization

Nilpotent semigroups are used in various fields of physics to model processes like system decay in quantum mechanics, state transitions in statistical mechanics, and simplifying dynamical systems. They also assist in optimizing control processes. The set of nilpotent matrices forms a semigroup and plays a key role in Jordan decomposition, which has many physical applications. In quantum mechanics, the Jordan form helps analyze linear operators on Hilbert spaces, especially with systems involving eigenvalue multiplicities. In vibration analysis, it aids in studying normal modes of mechanical systems with degenerate frequencies. Additionally, Jordan decomposition simplifies control theory for linear time-invariant systems, stability analysis in dynamical systems, and the behavior of coupled oscillators, as well as solving systems of linear differential equations. Certainly, the semigroup theory has even more applications in theoretical computer science: suffice it to say, for example, that some authors identify semigroups and finite automata. In this paper, we address the problem of P-separability of semigroups with respect to three key predicates: equality-separability, divisibility-separability, and subsemigroup-separability, achieved through homomorphisms into a nilpotent semigroup. We present some significant results that advance the understanding of these concepts.

Development and applications of computer science in Poland during the communist rule

Development and applications of computer science in Poland during the communist rule

A survey of deep causal models and their industrial applications

The notion of causality assumes a paramount position within the realm of human cognition. Over the past few decades, there has been significant advancement in the domain of causal effect estimation across various disciplines, including but not limited to computer science, medicine, economics, and industrial applications. Given the continous advancements in deep learning methodologies, there has been a notable surge in its utilization for the estimation of causal effects using counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective functions to estimate counterfactual data unbiasedly. Different from the existing surveys on causal models in machine learning, this review mainly focuses on the overview of the deep causal models based on neural networks, and its core contributions are as follows: (1) we cast insight on a comprehensive overview of deep causal models from both timeline of development and method classification perspectives; (2) we outline some typical applications of causal effect estimation to industry; (3) we also endeavor to present a detailed categorization and analysis on relevant datasets, source codes and experiments.

Pompeiu-Hausdorff Fuzzy <i>b</i>-metric Spaces Are Associated with a Common Fixed Point and Multivalued Mappings

The notion of fuzzy logic was introduced by Zadeh. Unlike traditional logic theory, where an element either belongs to the set or does not, in fuzzy logic, the affiliation of the element to the set is expressed as a number from the interval [0, 1]. The study of the theory of fuzzy sets was prompted by the presence of uncertainty as an essential part of real-world problems, leading Zadeh to address the problem of indeterminacy. The theory of a fixed point in fuzzy metric spaces can be viewed in different ways, one of which involves the use of fuzzy logic. Fuzzy metric spaces, which are specific types of topological spaces with pleasing ”geometric” characteristics, possess a number of appealing properties and are commonly used in both pure and applied sciences. Metric spaces and their various generalizations frequently occur in computer science applications. For this reason, a new space called a Pompeiu-Hausdorff fuzzy <i>b</i>-metric space is constructed in this paper. In this space, some new fixed point results are also formulated and proven. Additionally, a general common fixed point theorem for a pair of multi-valued mappings in Pompeiu-Hausdorff fuzzy <i>b</i>-metric spaces is investigated. The findings obtained in fuzzy metric spaces, such as those discussed in Remark 3.1, are generalized by the results in this paper, and additional specific findings are produced and supported by examples. The study of denotational semantics and their applications in control theory using fuzzy <i>b</i>-metric spaces and Pompeiu-Hausdorff fuzzy <i>b</i>-metric spaces will be an important next step.

The ultrametric backbone is the union of all minimum spanning forests

Minimum spanning trees and forests are powerful sparsification techniques that remove cycles from weighted graphs to minimize total edge weight while preserving node reachability, with applications in computer science, network science, and graph theory. Despite their utility and ubiquity, they have several limitations, including that they are only defined for undirected networks, they significantly alter dynamics on networks, and they do not generally preserve important network features such as shortest distances, shortest path distribution, and community structure. In contrast, distance backbones, which are subgraphs formed by all edges that obey a generalized triangle inequality, are well defined in directed and undirected graphs and preserve those and other important network features. The backbone of a graph is defined with respect to a specified path-length operator that aggregates weights along a path to define its length, thereby associating a cost to indirect connections. The backbone is the union of all shortest paths between each pair of nodes according to the specified operator. One such operator, the max function, computes the length of a path as the largest weight of the edges that compose it (a weakest link criterion). It is the only operator that yields an algebraic structure for computing shortest paths that is consistent with De Morgan's laws. Applying this operator yields the ultrametric backbone of a graph in that (semi-triangular) edges whose weights are larger than the length of an indirect path connecting the same nodes (i.e. those that break the generalized triangle inequality based on max as a path-length operator) are removed. We show that the ultrametric backbone is the union of minimum spanning forests in undirected graphs and provides a new generalization of minimum spanning trees to directed graphs that, unlike minimum equivalent graphs and minimum spanning arborescences, preserves all shortest paths and De Morgan's law consistency.

Fast Algorithms for \(\ell_p\)-Regression

The ℓ p -norm regression problem is a classic problem in optimization with wide ranging applications in machine learning and theoretical computer science. The goal is to compute \(\boldsymbol {\mathit {x}}^{\star } =\arg \min _{\boldsymbol {\mathit {A}}\boldsymbol {\mathit {x}}=\boldsymbol {\mathit {b}}}\Vert \boldsymbol {\mathit {x}}\Vert _p^p \) , where \(\boldsymbol {\mathit {x}}^{\star }\in \mathbb {R}^n,\boldsymbol {\mathit {A}}\in \mathbb {R}^{d\times n},\boldsymbol {\mathit {b}} \in \mathbb {R}^d \) and d ≤ n . Efficient high-accuracy algorithms for the problem have been challenging both in theory and practice and the state-of-the-art algorithms require \(poly(p)\cdot n^{\frac{1}{2}-\frac{1}{p}} \) linear system solves for p ≥ 2. In this paper, we provide new algorithms for ℓ p -regression (and a more general formulation of the problem) that obtain a high-accuracy solution in O ( pn ( p − 2)/(3 p − 2) ) linear system solves. We further propose a new inverse maintenance procedure that speeds-up our algorithm to \(\widetilde{O}(n^{\omega }) \) total runtime, where O ( n ω ) denotes the running time for multiplying n × n matrices. Additionally, we give the first Iteratively Reweighted Least Squares (IRLS) algorithm that is guaranteed to converge to an optimum in a few iterations. Our IRLS algorithm has shown exceptional practical performance, beating the currently available implementations in MATLAB/CVX by 10-50x.