**Author**: George A. Anastassiou

**Publisher:** Springer Science & Business Media

**ISBN:** 9783642170980

**Category:** Computers

**Page:** 802

**View:** 3881

Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. The strongly related to that Computational Analysis is a very large area with lots of applications. This monograph includes a great variety of topics of Computational Analysis. We present: probabilistic wavelet approximations, constrained abstract approximation theory, shape preserving weighted approximation, non positive approximations to definite integrals, discrete best approximation, approximation theory of general Picard singular operators including global smoothness preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators. We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals. We further deal with semi group operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations. We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities. We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities. We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation \ in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers.

In this short monograph Newton-like and other similar numerical methods with applications to solving multivariate equations are developed, which involve Caputo type fractional mixed partial derivatives and multivariate fractional Riemann-Liouville integral operators. These are studied for the first time in the literature. The chapters are self-contained and can be read independently. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this short monograph is suitable for researchers, graduate students, to be used in graduate classes and seminars of the above subjects, also to be in all science and engineering libraries.

In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.

Information granules are fundamental conceptual entities facilitating perception of complex phenomena and contributing to the enhancement of human centricity in intelligent systems. The formal frameworks of information granules and information granulation comprise fuzzy sets, interval analysis, probability, rough sets, and shadowed sets, to name only a few representatives. Among current developments of Granular Computing, interesting options concern information granules of higher order and of higher type. The higher order information granularity is concerned with an effective formation of information granules over the space being originally constructed by information granules of lower order. This construct is directly associated with the concept of hierarchy of systems composed of successive processing layers characterized by the increasing levels of abstraction. This idea of layered, hierarchical realization of models of complex systems has gained a significant level of visibility in fuzzy modeling with the well-established concept of hierarchical fuzzy models where one strives to achieve a sound tradeoff between accuracy and a level of detail captured by the model and its level of interpretability. Higher type information granules emerge when the information granules themselves cannot be fully characterized in a purely numerical fashion but instead it becomes convenient to exploit their realization in the form of other types of information granules such as type-2 fuzzy sets, interval-valued fuzzy sets, or probabilistic fuzzy sets. Higher order and higher type of information granules constitute the focus of the studies on Granular Computing presented in this study. The book elaborates on sound methodologies of Granular Computing, algorithmic pursuits and an array of diverse applications and case studies in environmental studies, option price forecasting, and power engineering.

The analysis of experimental data is at heart of science from its beginnings. But it was the advent of digital computers that allowed the execution of highly non-linear and increasingly complex data analysis procedures - methods that were completely unfeasible before. Non-linear curve fitting, clustering and machine learning belong to these modern techniques which are a further step towards computational intelligence. The goal of this book is to provide an interactive and illustrative guide to these topics. It concentrates on the road from two dimensional curve fitting to multidimensional clustering and machine learning with neural networks or support vector machines. Along the way topics like mathematical optimization or evolutionary algorithms are touched. All concepts and ideas are outlined in a clear cut manner with graphically depicted plausibility arguments and a little elementary mathematics. The major topics are extensively outlined with exploratory examples and applications. The primary goal is to be as illustrative as possible without hiding problems and pitfalls but to address them. The character of an illustrative cookbook is complemented with specific sections that address more fundamental questions like the relation between machine learning and human intelligence. These sections may be skipped without affecting the main road but they will open up possibly interesting insights beyond the mere data massage. All topics are completely demonstrated with the aid of the commercial computing platform Mathematica and the Computational Intelligence Packages (CIP), a high-level function library developed with Mathematica's programming language on top of Mathematica's algorithms. CIP is open-source so the detailed code of every method is freely accessible. All examples and applications shown throughout the book may be used and customized by the reader without any restrictions. The target readerships are students of (computer) science and engineering as well as scientific practitioners in industry and academia who deserve an illustrative introduction to these topics. Readers with programming skills may easily port and customize the provided code.

This volume contains the papers, updated in some cases, presented at the first AISMC (Artificial Intelligence and Symbolic Mathematical Computations)conference, held in Karlsruhe, August 3-6, 1992. This was the first conference to be devoted to such a topic after a long period when SMC made no appearance in AI conferences, though it used to be welcome in the early days of AI. Some conferences were held recently on mathematics and AI, but none was directly comparable in scope to this conference. Because of the novelty of the domain, authors were given longer allocations of time than usual in which to present their work. As a result, extended and fruitful discussions followed each paper. The introductory chapter in this book, which was not presented during the conference, reflects in many ways the flavor of these discussions and aims to set out the framework for future activities in this domain of research. In addition to the introduction, the volume contains 20 papers.

Computational Analysis of Terrorist Groups: Lashkar-e-Taiba provides an in-depth look at Web intelligence, and how advanced mathematics and modern computing technology can influence the insights we have on terrorist groups. This book primarily focuses on one famous terrorist group known as Lashkar-e-Taiba (or LeT), and how it operates. After 10 years of counter Al Qaeda operations, LeT is considered by many in the counter-terrorism community to be an even greater threat to the US and world peace than Al Qaeda. Computational Analysis of Terrorist Groups: Lashkar-e-Taiba is the first book that demonstrates how to use modern computational analysis techniques including methods for “big data” analysis. This book presents how to quantify both the environment in which LeT operate, and the actions it took over a 20-year period, and represent it as a relational database table. This table is then mined using sophisticated data mining algorithms in order to gain detailed, mathematical, computational and statistical insights into LeT and its operations. This book also provides a detailed history of Lashkar-e-Taiba based on extensive analysis conducted by using open source information and public statements. Each chapter includes a case study, as well as a slide describing the key results which are available on the authors’ web sites. Computational Analysis of Terrorist Groups: Lashkar-e-Taiba is designed for a professional market composed of government or military workers, researchers and computer scientists working in the web intelligence field. Advanced-level students in computer science will also find this valuable as a reference book.

This book presents recent research in the field of interaction between computational intelligence and mathematics, ranging from theory to applications. Computational intelligence, or soft computing consists of various bio-inspired methods, especially fuzzy systems, artificial neural networks, evolutionary and memetic algorithms. These research areas were initiated by professionals in various applied fields, such as engineers, economists, and financial and medical experts. Although computational intelligence offered solutions (at least quasi-optimal solutions) for problems with high complexity, vague and undeterministic features, initially little attention was paid to the mathematical models and analysis of the methods successfully applied. A typical example is the extremely successful Mamdani-algorithm, and its modifications and extensions, applied since the mid-1970s, where the first analysis of the simplest cases, showing why this algorithm was so efficient and stable, was not given until the early 1990s. Since the mid-2000s, the authors have organized international conferences annually to focus on the mathematical methodological issues in connection with computational intelligence approaches. These conferences have attracted a large number of submissions with a wide scope of topics and quality. The editors selected several high-quality papers and approached the authors to submit an essentially extended and improved book chapter based on the lectures.This volume is the first contributed book on the subject.

Spine title: AISMC-3 : artificial intelligence and symbolic mathematical computation.

*Second International Conference, AISMC-2, Cambridge, United Kingdom, August 3-5, 1994. Selected Papers*

**Author**: Jacques Calmet,AISMC-2,International Conference on Integrating Symbolic Mathematical Computation and Artificial Intelligence

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540601562

**Category:** Computers

**Page:** 275

**View:** 7599

The book discusses real-world problems and exploratory research in computational intelligence and mathematical models. It brings new approaches and methods to real-world problems and exploratory research that describes novel approaches in the mathematical methods, computational intelligence methods and software engineering in the scope of the intelligent systems. This book constitutes the refereed proceedings of the Computational Methods in Systems and Software 2017, a conference that provided an international forum for the discussion of the latest high-quality research results in all areas related to computational methods, statistics, cybernetics and software engineering.

This book gathers selected papers presented at the conference of the Forum for Interdisciplinary Mathematics (FIM), held at Palau Macaya, Barcelona, on 18 to 20 November, 2015. The event was co-organized by the University of Barcelona (Spain), the Spanish Royal Academy of Economic and Financial Sciences (Spain) and the Forum for Interdisciplinary Mathematics (India). This instalment of the conference was presented with the title “Applied Mathematics and Computational Intelligence” and particularly focused on the use of Mathematics and Computational Intelligence techniques in a diverse range of scientific disciplines, as well as their applications in real-world problems. The book presents thirty peer-reviewed research papers, organised into four topical sections: on Mathematical Foundations; Computational Intelligence and Optimization Techniques; Modelling and Simulation Techniques; and Applications in Business and Engineering. This book will be of great interest to anyone working in the area of applied mathematics and computational intelligence and will be especially useful for scientists and graduate students pursuing research in these fields.

Going beyond performing simple analyses, researchers involved in the highly dynamic field of computational intelligent data analysis design algorithms that solve increasingly complex data problems in changing environments, including economic, environmental, and social data. Computational Intelligent Data Analysis for Sustainable Development presents novel methodologies for automatically processing these types of data to support rational decision making for sustainable development. Through numerous case studies and applications, it illustrates important data analysis methods, including mathematical optimization, machine learning, signal processing, and temporal and spatial analysis, for quantifying and describing sustainable development problems. With a focus on integrated sustainability analysis, the book presents a large-scale quadratic programming algorithm to expand high-resolution input-output tables from the national scale to the multinational scale to measure the carbon footprint of the entire trade supply chain. It also quantifies the error or dispersion between different reclassification and aggregation schemas, revealing that aggregation errors have a high concentration over specific regions and sectors. The book summarizes the latest contributions of the data analysis community to climate change research. A profuse amount of climate data of various types is available, providing a rich and fertile playground for future data mining and machine learning research. The book also pays special attention to several critical challenges in the science of climate extremes that are not handled by the current generation of climate models. It discusses potential conceptual and methodological directions to build a close integration between physical understanding, or physics-based modeling, and data-driven insights. The book then covers the conservation of species and ecologically valuable land. A case study on the Pennsylvania Dirt and Gravel Roads Program demonstrates that multiple-objective linear programming is a more versatile and efficient approach than the widely used benefit targeting selection process. Moving on to renewable energy and the need for smart grids, the book explores how the ongoing transformation to a sustainable energy system of renewable sources leads to a paradigm shift from demand-driven generation to generation-driven demand. It shows how to maximize renewable energy as electricity by building a supergrid or mixing renewable sources with demand management and storage. It also presents intelligent data analysis for real-time detection of disruptive events from power system frequency data collected using an existing Internet-based frequency monitoring network as well as evaluates a set of computationally intelligent techniques for long-term wind resource assessment. In addition, the book gives an example of how temporal and spatial data analysis tools are used to gather knowledge about behavioral data and address important social problems such as criminal offenses. It also applies constraint logic programming to a planning problem: the environmental and social impact assessment of the regional energy plan of the Emilia-Romagna region of Italy. Sustainable development problems, such as global warming, resource shortages, global species loss, and pollution, push researchers to create powerful data analysis approaches that analysts can then use to gain insight into these issues to support rational decision making. This volume shows both the data analysis and sustainable development communities how to use intelligent data analysis tools to address practical problems and encourages researchers to develop better methods.

This inaugural volume is devoted to computer systems research with an emphasis on core computational science issues faced by researchers and industries today, and focusing on the development of novel computational techniques that are versatile and verifiable in a wide range of applications. The volume is divided into two parts. The five papers in Part 1 focus on the theme of information system design, and the four papers in Part 2 are concerned with specific computational science problems in the area of data processing.

This two-volume set (CCIS 134 and CCIS 135) constitutes the refereed proceedings of the International Conference on Intelligent Computing and Information Science, ICICIS2011, held in Chongqing, China, in January 2011. The 226 revised full papers presented in both volumes, CCIS 134 and CCIS 135, were carefully reviewed and selected from over 600 initial submissions. The papers provide the reader with a broad overview of the latest advances in the field of intelligent computing and information science.

This book comprises a selection of papers on new methods for analysis and design of hybrid intelligent systems using soft computing techniques from the IFSA 2007 World Congress, held in Cancun, Mexico, June 2007.

This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and Computational Mathematics and Engineering practitioners, also for related graduate students and researchers. Furthermore it will be a useful resource for all science and engineering libraries. This book includes 29 self-contained and well-edited chapters that can be among others useful for seminars in applied and computational mathematics, as well as in engineering.

In recent years there has been a growing interest to extend classical methods for data analysis. The aim is to allow a more flexible modeling of phenomena such as uncertainty, imprecision or ignorance. Such extensions of classical probability theory and statistics are useful in many real-life situations, since uncertainties in data are not only present in the form of randomness --- various types of incomplete or subjective information have to be handled. About twelve years ago the idea of strengthening the dialogue between the various research communities in the field of data analysis was born and resulted in the International Conference Series on Soft Methods in Probability and Statistics (SMPS). This book gathers contributions presented at the SMPS'2012 held in Konstanz, Germany. Its aim is to present recent results illustrating new trends in intelligent data analysis. It gives a comprehensive overview of current research into the fusion of soft computing methods with probability and statistics. Synergies of both fields might improve intelligent data analysis methods in terms of robustness to noise and applicability to larger datasets, while being able to efficiently obtain understandable solutions of real-world problems.

An invaluable tool in Bioinformatics, this unique volume providesboth theoretical and experimental results, and describes basicprinciples of computational intelligence and pattern analysis whiledeepening the reader's understanding of the ways in which theseprinciples can be used for analyzing biological data in anefficient manner. This book synthesizes current research in the integration ofcomputational intelligence and pattern analysis techniques, eitherindividually or in a hybridized manner. The purpose is to analyzebiological data and enable extraction of more meaningfulinformation and insight from it. Biological data for analysisinclude sequence data, secondary and tertiary structure data, andmicroarray data. These data types are complex and advanced methodsare required, including the use of domain-specific knowledge forreducing search space, dealing with uncertainty, partial truth andimprecision, efficient linear and/or sub-linear scalability,incremental approaches to knowledge discovery, and increased leveland intelligence of interactivity with human experts and decisionmakers Chapters authored by leading researchers in CI in biologyinformatics. Covers highly relevant topics: rational drug design; analysisof microRNAs and their involvement in human diseases. Supplementary material included: program code and relevant datasets correspond to chapters.