Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from gene regulation, neuroscience, phylogenetics, molecular networks, assembly and folding of biomolecular structures, and the use of clustering methods in biology. A number of these chapters are surveys of new topics that have not been previously compiled into one unified source. These topics were selected because they highlight the use of technique from algebra and combinatorics that are becoming mainstream in the life sciences.

Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community since its first publication in 1988, the book shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in the book are still important and informative. Shortly after its publication, the genomics revolution turned Mathematical Biology into a prominent area of interdisciplinary research. In this new millennium, biologists have discovered that mathematics is not only useful, but indispensable! As a result, there has been much resurgent interest in, and a huge expansion of, the fields collectively called mathematical biology. This book serves as a basic introduction to concepts in deterministic biological modeling.

In recent years, substantial efforts are being made in the development of reliability theory including fuzzy reliability theories and their applications to various real-life problems. Fuzzy set theory is widely used in decision making and multi criteria such as management and engineering, as well as other important domains in order to evaluate the uncertainty of real-life systems. Fuzzy reliability has proven to have effective tools and techniques based on real set theory for proposed models within various engineering fields, and current research focuses on these applications. Advancements in Fuzzy Reliability Theory introduces the concept of reliability fuzzy set theory including various methods, techniques, and algorithms. The chapters present the latest findings and research in fuzzy reliability theory applications in engineering areas. While examining the implementation of fuzzy reliability theory among various industries such as mining, construction, automobile, engineering, and more, this book is ideal for engineers, practitioners, researchers, academicians, and students interested in fuzzy reliability theory applications in engineering areas.

The book addresses optimization in the petroleum industry from a practical, large-scale-application-oriented point of view. The models and techniques presented help to optimize the limited resources in the industry in order to maximize economic benefits, ensure operational safety, and reduce environmental impact. The book discusses several important real-life applications of optimization in the petroleum industry, ranging from the scheduling of personnel time to the blending of gasoline. It covers a wide spectrum of relevant activities, including drilling, producing, maintenance, and distribution. The text begins with an introductory overview of the petroleum industry and then of optimization models and techniques. The main body of the book details a variety of applications of optimization models and techniques within the petroleum industry. Applied  Optimization in the Petroleum Industry helps readers to find effective optimization-based solutions to their own practical problems in a large and important industrial sector, still the main source of the world’s energy and the source of raw materials for a wide variety of industrial and consumer products.

This book uses art photography as a point of departure for learning about physics, while also using physics as a point of departure for asking fundamental questions about the nature of photography as an art. Although not a how-to manual, the topics center around hands-on applications, sometimes illustrated by photographic processes that are inexpensive and easily accessible to students (including a versatile new process developed by the author, and first described in print in this series). A central theme is the connection between the physical interaction of light and matter on the one hand, and the artistry of the photographic processes and their results on the other. This is the third volume in this three-part series that uses art photography as a point of departure for learning about physics, while also using physics as a point of departure for asking fundamental questions about the nature of photography as an art. It focuses on the physics and chemistry of photographic light-sensitive materials, as well as the human retina. It also considers the fundamental nature of digital photography and its relationship to the analog photography that preceded it.

Maple is a comprehensive symbolic mathematics application which is well suited for demonstrating physical science topics and solving associated problems. Because Maple is such a rich application, it has a somewhat steep learning curve. Most existing texts concentrate on mathematics; the Maple help facility is too detailed and lacks physical science examples, many Maple-related websites are out of date giving readers information on older Maple versions. This book records the author's journey of discovery; he was familiar with SMath but not with Maple and set out to learn the more advanced application. It leads readers through the basic Maple features with physical science worked examples, giving them a firm base on which to build if more complex features interest them.

The world of single-board computing puts powerful coding tools in the palm of your hand. The portable Raspberry Pi computing platform with the power of Linux yields an exciting exploratory tool for beginning scientific computing. Science and Computing with Raspberry Pi takes the enterprising researcher, student, or hobbyist through explorations in a variety of computing exercises with the physical sciences. The book has tutorials and exercises for a wide range of scientific computing problems while guiding the user through: Configuring your Raspberry Pi and Linux operating system Understanding the software requirements while using the Pi for scientific computing Computing exercises in physics, astronomy, chaos theory, and machine learning

Energy and power are fundamental concepts in electromagnetism and circuit theory, as well as in optics, signal processing, power engineering, electrical machines, and power electronics. However, in crossing the disciplinary borders, we encounter understanding difficulties due to (1) the many possible mathematical representations of the same physical objects, and (2) the many possible physical interpretations of the same mathematical entities. The monograph proposes a quantum and a relativistic approach to electromagnetic power theory that is based on recent advances in physics and mathematics. The book takes a fresh look at old debates related to the significance of the Poynting theorem and the interpretation of reactive power. Reformulated in the mathematical language of geometric algebra, the new expression of electromagnetic power reflects the laws of conservation of energy-momentum in fields and circuits. The monograph offers a mathematically consistent and a physically coherent interpretation of the power concept and of the mechanism of power transmission at the subatomic (mesoscopic) level. The monograph proves (paraphrasing Heaviside) that there is no finality in the development of a vibrant discipline: power theory.

What do economic chaos and uncertainties mean in rational or irrational economic theories? How do simple deterministic interactions among a few variables lead to unpredictable complex phenomena? Why is complexity of economies causing so many conflicts and confusions worldwide?This book provides a comprehensive introduction to recent developments of complexity theory in economics. It presents different models based on well-accepted economic mechanisms such as the Solow model, Ramsey model, and Lucas model. It is focused on presenting complex behaviors, such as business cycles, aperiodic motion, bifurcations, catastrophes, chaos, and hidden attractors, in basic economic models with nonlinear behavior. It shows how complex nonlinear phenomena are identified from various economic mechanisms and theories. These models demonstrate that the traditional or dominant economic views on evolution of, for instance, capitalism market, free competition, or Keynesian economics, are not generally valid. Markets are unpredictable and nobody knows with certainty the consequences of policies or other external factors in economic systems with simple interactions.

Combining insights from academic research and practical examples, this book aims to better understand the link between financial markets and innovation management. First, we are back to the very definition of innovation and what it means for financial and non-financial companies. Then, we analyze if efficient innovation management by companies is recognized and valued by financial markets. Finally, we focus on innovation within the financial sector: does it really create value outside the financial sector itself. Are Financial innovations value ... or risk creators?

This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results. In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.

Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems.

The modelling of systems by differential equations usually requires that the parameters involved be completely known. Such models often originate from problems in physics or economics where we have insufficient information on parameter values. One important class of stochastic mathematical models is stochastic partial differential equations (SPDEs), which can be seen as deterministic partial differential equations (PDEs) with finite or infinite dimensional stochastic processes - either with colour noise or white noise. Though white noise is a purely mathematical construction, it can be a good model for rapid random fluctuations.This research monograph concerns analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes. The first chapter of the book provides a theoretical basis for working with SDEs and stochastic processes.This book has been written in a simple and clear mathematical logical language. The basic definitions and theorems on stochastic calculus have been provided initially. Each chapter contains illustrated examples via figures and tables. Problems are included which will help readers understand the theories better. Also, the reader can construct new wavelets by using the procedure presented in the book. It will certainly fill up the blank space that the lack of a comprehensive book has caused.

This book demonstrates Microsoft EXCEL-based Fourier transform of selected physics examples. Spectral density of the auto-regression process is also described in relation to Fourier transform. Rather than offering rigorous mathematics, readers will "try and feel" Fourier transform for themselves through the examples. Readers can also acquire and analyze their own data following the step-by-step procedure explained in this book. A hands-on acoustic spectral analysis can be one of the ideal long-term student projects.

Holographic dualities are at the forefront of contemporary physics research, peering into the fundamental nature of our universe and providing best attempt answers to humankind's bold questions about basic physical phenomena. Yet, the concepts, ideas and mathematical rigors associated with these dualities have long been reserved for the specific field researchers and experts. This book shatters this long held paradigm by bringing several aspects of holography research into the class room, starting at the college physics level and moving up from there.

Quartic anharmonic oscillator with potential V(x)= x(2) + g(2)x4 was the first non-exactly-solvable problem tackled by the newly-written Schroedinger equation in 1926. Since that time thousands of articles have been published on the subject, mostly about the domain of small g(2) (weak coupling regime), although physics corresponds to g(2) ~ 1, and they were mostly about energies.This book is focused on studying eigenfunctions as a primary object for any g(2). Perturbation theory in g(2) for the logarithm of the wavefunction is matched to the true semiclassical expansion in powers of : it leads to locally-highly-accurate, uniform approximation valid for any g(2) [0, ) for eigenfunctions and even more accurate results for eigenvalues. This method of matching can be easily extended to the general anharmonic oscillator as well as to the radial oscillators. Quartic, sextic and cubic (for radial case) oscillators are considered in detail as well as quartic double-well potential.