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This book gathers selected high-quality research papers presented at the International Conference on Paradigms of Communication, Computing and Data Sciences (PCCDS 2021), held at the National Institute of Technology, Kurukshetra, India, during May 07–09, 2021. It discusses high-quality and cutting-edge research in the areas of advanced computing, communications, and data science techniques. The book is a collection of latest research articles in computation algorithm, communication, and data sciences, intertwined with each other for efficiency.
Mathematical morphology is a powerful methodology for the processing and analysis of geometric structure in signals and images. This book contains the proceedings of the fifth International Symposium on Mathematical Morphology and its Applications to Image and Signal Processing, held June 26-28, 2000, at Xerox PARC, Palo Alto, California. It provides a broad sampling of the most recent theoretical and practical developments of mathematical morphology and its applications to image and signal processing. Areas covered include: decomposition of structuring functions and morphological operators, morphological discretization, filtering, connectivity and connected operators, morphological shape analysis and interpolation, texture analysis, morphological segmentation, morphological multiresolution techniques and scale-spaces, and morphological algorithms and applications. Audience: The subject matter of this volume will be of interest to electrical engineers, computer scientists, and mathematicians whose research work is focused on the theoretical and practical aspects of nonlinear signal and image processing. It will also be of interest to those working in computer vision, applied mathematics, and computer graphics.
String art is a well-known and popular activity that uses string, a board, and nails to produce artistic images (although there are variations that use different modalities). This activity is beloved because simple counting rules are used to create beautiful images that can both adorn walls and excite young minds. The downside of this highly tactile activity is that it is quite time-consuming and rigid. By contrast, electronic string art offers much more flexibility to set up or change nail locations and counting rules, and the images created from those changes change instantaneously. Electronic String Art: Rhythmic Mathematics invites readers to use the author’s digital resources available on the ESA website to play with the parameters inherent in string art models while offering concise, accessible explanations of the underlying mathematical principles regarding how the images were created and how they change. Readers will have the opportunity to create visually beautiful works of art while learning concepts from geometry, number theory, and modular arithmetic from approximately 200 short-interdependent sections. Features Readers are able to drill-down on images in order to understand why they work using short (1 to 2 page) stand-alone sections Sections are lessons that were created so that they could be digested in a single sitting These sections are stand-alone in the sense that they need not be read sequentially but can be referred to based on images that the reader finds interesting An open-ended, inherently flexible teaching resource for elementary, middle, and high school-level mathematics The most mathematically challenging sections (or portions of a section) are designated MA and may not be accessible to elementary and middle school readers Will be appreciated by anyone interested in recreational mathematics or mathematical artworks even if the users are not interested in the underlying mathematics Includes exercises, solutions, and many online digital resources These QR codes take you to these digital resources. One takes you directly to the web version of the string art model (used as a starting point for teaching the parameters of the model in Section 25.5). The other takes you to the ESA web page with additional links to a variety of resources.
Calendars in the Making investigates the Roman and medieval origins of several calendars we are most familiar with today, including the Christian liturgical calendar, the Islamic calendar, and the week as a standard method of dating and time reckoning.
Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs. The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The author’s motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems. Features Approachable for students who have not yet studied mathematics beyond school Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof Draws attention to connections with other areas of mathematics Plenty of exercises for students, both straightforward problems and more in-depth investigations Introduces many concepts that are required in more advanced topics in mathematics.
This book focuses on numerous examples of tasks represented by c-e structure. Cause–effect (c-e) structures are dynamic objects devised for algebraic and graphic description of realistic tasks. They constitute a formal system providing means to specify or implement (depending on degree of description generality) the tasks. They can be transformed, thus come under simplification, in accordance with rules-axioms of their algebra. Also, their properties can be inferred from the axioms. One objective of this book is presentation, by many realistic examples, of computing capability of c-e structures, without entering into mathematical details of their algebra. In particular, how computing with natural numbers and in propositional calculus can be performed by c-e structures and how to specify behavior of data structures. But also demonstration of many other tasks taken from the area of parallel processing, specified as c-e structures. Another objective is modelling or simulation by means of c-e structures, of other descriptive systems, devised for tasks from various fields. Also without formalizing by usage of functions between the systems. This concerns formalisms such as reaction systems, rough sets, Petri nets and CSP-like languages. Also on such, where temporal interdependence between actions matters. The presentation of examples is prevalently graphic, in the form of peculiar nets, but accompanied by their algebraic and set-theoretic expressions. A fairly complete exposition of concepts and properties of the algebra of cause-effect structures is in the previous book appeared in the Lecture Notes in Networks and Systems series. But basic notions of c-e structures are here provided for understanding the examples.
There is a software gap between the hardware potential and the performance that can be attained using today's software parallel program development tools. The tools need manual intervention by the programmer to parallelize the code. Programming a parallel computer requires closely studying the target algorithm or application, more so than in the traditional sequential programming we have all learned. The programmer must be aware of the communication and data dependencies of the algorithm or application. This book provides the techniques to explore the possible ways to program a parallel computer for a given application.
Fractals, Visualization and J is a text that uses fractals as a motivational goal for the study of visualization. The language J is introduced as needed for the topics at hand. Included are chapters: Introduction to J and Graphics, Plots, Verbs and First Fractals, Time Series and Fractals, Iterated function systems and Raster Fractals, Color, Contours and Animations, Complex Dynamics, Cellular Automata.