Real Analysis, Harmonic Analysis, and Applications

This chapter describes four interdisciplinary fields originated and defined by Ashu M. G. Solo in 2011 called political engineering, public policy engineering, computational politics, and computational public policy. Political engineering is the application of engineering, computer science, mathematics, or natural science to solving problems in politics. Computational politics is the application of computer science or mathematics to solving problems in politics. Political engineering and computational politics include, but are not limited to, principles and methods for political decision-making, analysis, modeling, optimization, forecasting, simulation, and expression. Public policy engineering is the application of engineering, computer science, mathematics, or natural science to solving problems in public policy. Computational public policy is the application of computer science or mathematics to solving problems in public policy. Public policy engineering and computational public policy include, but are not limited to, principles and methods for public policy formulation, decision-making, analysis, modeling, optimization, forecasting, and simulation. The chapter describes the scope of research and development in these fields, provides examples of research and development in these fields, and provides possible university curricula for academic programs in these fields.

The purpose of the study is to assess the application of Computer science in the fractional distillation of petroleum. The study sought to: Determine the merit of using Computer science in fractional distillation of petroleum. Evaluate the cost effectiveness to the application of Computer science in fractional distillation of petroleum to the welfare of citizens. Determine if Computer science can help in controlling the natural effects of fractional distillation of petroleum on the environment. Computer science has gained wider application in so many areas of human endeavor ranging from the homes to more scientific and industrial applications, hence its application of Computer science in fractional distillation of petroleum cannot be overemphasized. Irrespective of the benefits of the application of Computer science in fractional distillation of petroleum as a whole, it has become pertinent to ask how effective and efficient its application of Computer science in fractional distillation of petroleum has been. This research work tries to investigate how effective the application of Computer science in fractional distillation of petroleum. The project exertion covered statement of the problem, purpose of the study, research questions/hypotheses were formulated to enable the researcher find out facts about the study, highlighted in division one. Subdivision two was based on the literature review of this study. The study covers the research methodology which guided the study, the next stage was based on the presentation of data and its’ analysis as well as the discussion of findings. The final stage of the research was concerned with the conclusion as well as recommendations and suggestions for further studies

Additive combinatorics is the branch of combinatorics where the objects of study are subsets of the integers or of other abelian groups, and one is interested in properties and patterns that can be expressed in terms of linear equations. More generally, arithmetic combinatorics deals with properties and patterns that can be expressed via additions and multiplications. In the past ten years, it has been an extremely successful area of mathematics, featuring a convergence of techniques from graph theory, analysis and ergodic theory. It has helped prove long-standing open questions in additive number theory, and it offers much promise of future progress. Arithmetic combinatorics has found several applications in computer science, to property testing, PCP constructions, lower bounds, and extractor constructions. Typically, whenever a technique from arithmetic combinatorics becomes understood by computer scientists, it finds some application. Considering that there is still a lot of additive and arithmetic combinatorics that computer scientists do not understand (and, the field being very active, even more will be developed in the near future), there seems to be much potential for future connections and applications.

The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which established sharp local smoothing estimates for a natural class of Fourier integral operators. We also show how local smoothing estimates imply oscillatory integral estimates and obtain a maximal variant of an oscillatory integral estimate of Stein. Together with an oscillatory integral counterexample of Bourgain, this shows that our local smoothing estimates are sharp in odd spatial dimensions. Motivated by related counterexamples, we formulate local smoothing conjectures which take into account natural geometric assumptions arising from the structure of the Fourier integrals.

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.

We show some new local smoothing estimates of the fractional Schrödinger equations with initial data in $$\alpha $$ -modulation spaces via decoupling inequalities. Furthermore, our necessary conditions show that the local smoothing estimates are sharp in some cases. As applications, the local smoothing estimates could show some new local well-posedness on modulation spaces of the fourth-order nonlinear Schrödinger equations on the line.

Oscillatory integral operators with 1-homogeneous phase functions satisfying a convexity condition are considered. For these we show the Lp–Lp-estimates for the Fourier extension operator of the cone due to Ou–Wang via polynomial partitioning. For this purpose, we combine the arguments of Ou–Wang with the analysis of Guth–Hickman–Iliopoulou, who previously showed sharp Lp–Lp-estimates for non-homogeneous phase functions with variable coefficients under a convexity assumption. Furthermore, we provide examples exhibiting Kakeya compression, which shows a more restrictive range than dictated by the Knapp example in higher dimensions. We apply the oscillatory integral estimates to show new local smoothing estimates for wave equations on compact Riemannian manifolds (M, g) with dim M ≥ 3. This generalizes the argument for the Euclidean wave equation due to Gao–Liu–Miao–Xi.

The study of the Least Common Multiple (LCM) and the Greatest Common Divisor (GCD) explores the fundamental field of number theory. In addition to being essential to theoretical number theory, these mathematical ideas have extensive applications in computer science, algebra, and real-world settings like network routing and scheduling. Using techniques like the Euclidean algorithm for GCD calculation and prime factorization for LCM, the study starts by examining the fundamental concepts and notations of GCD and LCM. Then the author goes further into the detail about how these ideas are used to polynomial equations, highlighting how they may be used to solve challenging issues and simplify algebraic expressions. The studys practical applications, which demonstrate how GCD and LCM optimize scheduling tasks and boost network routing efficiency, are presented in the conclusion. The results of this study highlight the broad impact and adaptability of LCM and GCD in theoretical and applied mathematics, providing valuable insights for further research in these domains.

With the proliferation of computing technologies and an ongoing trend of introducing digital and blended learning aspects into higher education, innovative approaches to teaching complex topics like artificial intelligence (AI) have emerged. Of particular interest is the use of game-based learning approaches. According to problem-based learning theory, providing students with an interactive problem and encouraging them to independently find solutions promotes deeper understanding and skill acquisition. Thus, game-based approaches offer an engaging way for students to explore challenging concepts. However, despite the growing use of game-based methods in fields like economics, their application in computer science - especially in teaching game AI - remains under-explored.Understanding AI is increasingly critical for game development, as modern games emulate human-like behaviour in areas such as decision-making, character routines, and adaptive strategies. While many mechanisms and approaches of agent-level decision-making and planning are well understood, their application in video games poses unique challenges, such as accommodating unpredictable player interactions and ensuring performance efficiency without degrading the player experience. While strategy games like StarCraft or multiplayer online battle arenas like DotA 2 have been of interest as proving grounds for advanced AI training methods, their use in education has been limited due to their high complexity and associated learning curve.This work proposes the development of a novel interactive application to fill this niche. Taking inspiration from city building and management games, the application simulates the campus of the University of Applied Sciences Mittweida, where students are given control of agents acting as archetypal roles of students. The agents' goal is the acquisition of knowledge, an abstract resource gained by participating in courses, requiring the agent to navigate the campus. Students interact with the system through an API that provides information on the state of the simulation and allows issuing commands to specific agents. For example, agents who continuously acquire knowledge over a prolonged period do so at decreasing efficiency. To remedy this, a student implements a routine checking the learning efficiency of all agents, commanding "tired" agents to take a break. Alternatively, the student could train a machine learning algorithm to do the same task, albeit more adaptive. Additionally, the application enables dynamic changes to the environment at runtime, such as adding or removing courses or buildings, simulating player-driven alterations to the game world. By designing decision-making algorithms for these agents, students gain hands-on experience with fundamental AI concepts, i.e. decision trees, bridging the gap between theoretical knowledge and practical application.To evaluate the effectiveness of the application, a comparative study with undergraduate students is planned. Over the course of two semesters, two groups of students will be taught the basics of game AI - one using traditional teaching methods (primarily lectures), the other using a game-based method incorporating the new application. The learning progress of both groups will be monitored using assignments, with students being given a sample project and tasked to develop a game AI solution, i.e. for a non-player character in a first-person shooter.

This paper reviews applications in computer science that decision theorists have addressed for years, discusses the requirements posed by these applications that place great strain on decision theory/social science methods, and explores applications in the social and decision sciences of newer decision-theoretic methods developed with computer science applications in mind. The paper deals with the relation between computer science and decision-theoretic methods of consensus, with the relation between computer science and game theory and decisions, and with “algorithmic decision theory.”

It is generally accepted that a course in discrete structures such as Course B3 in Curriculum 68 recommendations [1] is an important part of a Computer Science program. In many institutions a Discrete Structures course is offered in the Computer Science Department although it overlaps courses in the Mathematics Department [2,3,4]. In smaller schools the size of the student body and staff limitations make such a solution impractical. At Augusta College we have met the objective of early exposure to discrete mathematics with applications in computer science by offering a two-hour computer science course as a co-requisite to a three-hour mathematics course. While this approach is a compromise it does appear to have some merit.

Games provide mathematical models for interaction. Numerous tasks in computer science can be formulated in game-theoretic terms. This fresh and intuitive way of thinking through complex issues reveals underlying algorithmic questions and clarifies the relationships between different domains. This collection of lectures, by specialists in the field, provides an excellent introduction to various aspects of game theory relevant for applications in computer science that concern program design, synthesis, verification, testing and design of multi-agent or distributed systems. Originally devised for a Spring School organised by the GAMES Networking Programme in 2009, these lectures have since been revised and expanded, and range from tutorials concerning fundamental notions and methods to more advanced presentations of current research topics. This volume is a valuable guide to current research on game-based methods in computer science for undergraduate and graduate students. It will also interest researchers working in mathematical logic, computer science and game theory.

Artificial intelligence (AI) is a rapidly evolving field that has seen tremendous growth in recent years. In this chapter, the authors provide an overview of current trends in AI and their applications in computer science. They also discuss the future directions of AI research and their potential impact on the field of computer science. They start by introducing the basic concepts of AI and its various subfields. Then, they present an overview of current trends in AI research, including machine learning, natural language processing, computer vision, and robotics. The authors discuss how these trends are applied in computer science, such as autonomous vehicles, fraud detection, and personalized medicine. Finally, they discuss the future directions of AI research, including the development of more explainable AI systems, the integration of AI with other emerging technologies, and the ethical considerations of AI.

It is generally accepted that a course in discrete structures such as Course B3 in Curriculum 68 recommendations [1] is an important part of a Computer Science program. In many institutions a Discrete Structures course is offered in the Computer Science Department although it overlaps courses in the Mathematics Department [2,3,4]. In smaller schools the size of the student body and staff limitations make such a solution impractical. At Augusta College we have met the objective of early exposure to discrete mathematics with applications in computer science by offering a two-hour computer science course as a co-requisite to a three-hour mathematics course. While this approach is a compromise it does appear to have some merit.

Emerging Grid infrastructures present unprecedented opportunities for computational science and engineering, with the potential for fundamental insights into complex phenomenon. However, it also presents unprecedented challenges in terms of its scale, heterogeneity, dynamism and overall complexity that must be addressed before this potential can be realized. Autonomic computing concepts have been effectively used to address similar challenges in enterprise systems and applications; in this paper, we explore the role of autonomic computing to Grid-based computational science applications. Specifically, we use three representative computational applications to motivate Autonomic Computational Science (ACS). Using these applications, we develop a conceptual framework for ACS, consisting of mechanisms, strategies and objectives, and demonstrate how these concepts can be used to express autonomic behaviors. Finally we explore a research agenda towards realizing ACS behaviors and developing self-* patterns for large scale autonomic computational science application.