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The Probability Integral: Its Origin, Its Importance, and Its Calculation
by Paul J. NahinThis book tells the story of the probability integral, the approaches to analyzing it throughout history, and the many areas of science where it arises. The so-called probability integral, the integral over the real line of a Gaussian function, occurs ubiquitously in mathematics, physics, engineering and probability theory. Stubbornly resistant to the undergraduate toolkit for handling integrals, calculating its value and investigating its properties occupied such mathematical luminaries as De Moivre, Laplace, Poisson, and Liouville. This book introduces the probability integral, puts it into a historical context, and describes the different approaches throughout history to evaluate and analyze it. The author also takes entertaining diversions into areas of math, science, and engineering where the probability integral arises: as well as being indispensable to probability theory and statistics, it also shows up naturally in thermodynamics and signal processing. Designed to be accessible to anyone at the undergraduate level and above, this book will appeal to anyone interested in integration techniques, as well as historians of math, science, and statistics.
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
by William J. StewartProbability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics.The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation.Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only).Numerous examples illuminate the mathematical theoriesCarefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approachEach chapter concludes with an extensive set of exercises
Probability Models in Operations Research (Operations Research Series)
by C. Richard Cassady Joel A. NachlasIndustrial engineering has expanded from its origins in manufacturing to transportation, health care, logistics, services, and more. A common denominator among all these industries, and one of the biggest challenges facing decision-makers, is the unpredictability of systems. Probability Models in Operations Research provides a comprehensive
Probability, Random Signals, and Statistics
by X. Rong LiWith this innovative text, the study-and teaching- of probability and random signals becomes simpler, more streamlined, and more effective. Its unique "textgraph" format makes it both student-friendly and instructor-friendly. Pages with a larger typeface form a concise text for basic topics and make ideal transparencies; pages with smaller type provide more detailed explanations and more advanced material.
Probability, Random Variables, and Data Analytics with Engineering Applications
by P. Mohana ShankarThis book bridges the gap between theory and applications that currently exist in undergraduate engineering probability textbooks. It offers examples and exercises using data (sets) in addition to traditional analytical and conceptual ones. Conceptual topics such as one and two random variables, transformations, etc. are presented with a focus on applications. Data analytics related portions of the book offer detailed coverage of receiver operating characteristics curves, parametric and nonparametric hypothesis testing, bootstrapping, performance analysis of machine vision and clinical diagnostic systems, and so on. With Excel spreadsheets of data provided, the book offers a balanced mix of traditional topics and data analytics expanding the scope, diversity, and applications of engineering probability. This makes the contents of the book relevant to current and future applications students are likely to encounter in their endeavors after completion of their studies. A full suite of classroom material is included. A solutions manual is available for instructors. Bridges the gap between conceptual topics and data analytics through appropriate examples and exercises; Features 100's of exercises comprising of traditional analytical ones and others based on data sets relevant to machine vision, machine learning and medical diagnostics;Intersperses analytical approaches with computational ones, providing two-level verifications of a majority of examples and exercises.
Probability, Statistics and Other Frightening Stuff (Working Guides to Estimating & Forecasting #2)
by Alan R. JonesProbability, Statistics and Other Frightening Stuff (Volume II of the Working Guides to Estimating & Forecasting series) considers many of the commonly used Descriptive Statistics in the world of estimating and forecasting. It considers values that are representative of the ‘middle ground’ (Measures of Central Tendency), and the degree of data scatter (Measures of Dispersion and Shape) around the ‘middle ground’ values. A number of Probability Distributions and where they might be used are discussed, along with some fascinating and useful ‘rules of thumb’ or short-cut properties that estimators and forecasters can exploit in plying their trade. With the help of a ‘Correlation Chicken’, the concept of partial correlation is explained, including how the estimator or forecaster can exploit this in reflecting varying levels of independence and imperfect dependence between an output or predicted value (such as cost) and an input or predictor variable such as size. Under the guise of ‘Tails of the unexpected’ the book concludes with two chapters devoted to Hypothesis Testing (or knowing when to accept or reject the validity of an assumed estimating relationship), and a number of statistically-based tests to help the estimator to decide whether to include or exclude a data point as an ‘outlier’, one that appears not to be representative of that which the estimator is tasked to produce. This is a valuable resource for estimators, engineers, accountants, project risk specialists as well as students of cost engineering.
Probability, Statistics, and Stochastic Processes for Engineers and Scientists (Mathematical Engineering, Manufacturing, and Management Sciences)
by Aliakbar Montazer Haghighi Indika WickramasingheFeaturing recent advances in the field, this new textbook presents probability and statistics, and their applications in stochastic processes. This book presents key information for understanding the essential aspects of basic probability theory and concepts of reliability as an application. The purpose of this book is to provide an option in this field that combines these areas in one book, balances both theory and practical applications, and also keeps the practitioners in mind. Features Includes numerous examples using current technologies with applications in various fields of study Offers many practical applications of probability in queueing models, all of which are related to the appropriate stochastic processes (continuous time such as waiting time, and fuzzy and discrete time like the classic Gambler’s Ruin Problem) Presents different current topics like probability distributions used in real-world applications of statistics such as climate control and pollution Different types of computer software such as MATLAB®, Minitab, MS Excel, and R as options for illustration, programing and calculation purposes and data analysis Covers reliability and its application in network queues
Probability Theory: A Comprehensive Course (Universitext)
by Achim KlenkeThis popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory.Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as: limit theorems for sums of random variables martingales percolation Markov chains and electrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integrals and stochastic differential equations. The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts.This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.
Probability Theory and Mathematical Statistics for Engineers
by Paolo L. GattiProbability Theory and Statistical Methods for Engineers brings together probability theory with the more practical applications of statistics, bridging theory and practice. It gives a series of methods or recipes which can be applied to specific problems.This book is essential reading for practicing engineers who need a sound background knowledge
Probing Popular Culture: On and Off the Internet
by Marshall Fishwick"When it comes to seeing depth and lateral connections in the development of popular culture, nobody exceeds Marshall Fishwick." -Canadian Psychology In Probing Popular Culture: On and Off the Internet, one of the leading authorities in American and popular culture studies presents an eye-opening examination o
Probing the Response of Two-Dimensional Crystals by Optical Spectroscopy
by Yilei LiThis thesis focuses on the study of the optical response of new atomically thin two-dimensional crystals, principally the family of transition metal dichalcogenides like MoS2. One central theme of the thesis is the precise treatment of the linear and second-order nonlinear optical susceptibilities of atomically thin transition metal dichalcogenides. In addition to their significant scientific interest as fundamental material responses, these studies provide essential knowledge and convenient characterization tools for the application of these 2D materials in opto-electronic devices. Another important theme of the thesis is the valley physics of atomically thin transition metal dichalcogenides. It is shown that the degeneracy in the valley degree of freedom can be lifted and a valley polarization can be created using a magnetic field, which breaks time reversal symmetry in these materials. These findings enhance our basic understanding of the valley electronic states and open up new opportunities for valleytronic applications using two-dimensional materials.
Probing Two-Dimensional Quantum Fluids with Cavity Optomechanics (Springer Theses)
by Yauhen SachkouSuperfluid helium is a quantum liquid that exhibits a range of counter-intuitive phenomena such as frictionless flow. Quantized vortices are a particularly important feature of superfluid helium, and all superfluids, characterized by a circulation that can only take prescribed integer values. However, the strong interactions between atoms in superfluid helium prohibit quantitative theory of vortex behaviour. Experiments have similarly not been able to observe coherent vortex dynamics.This thesis resolves this challenge, bringing microphotonic techniques to bear on two-dimensional superfluid helium, observing coherent vortex dynamics for the first time, and achieving this on a silicon chip. This represents a major scientific contribution, as it opens the door not only to providing a better understanding of this esoteric quantum state of matter, but also to building new quantum technologies based upon it, and to understanding the dynamics of astrophysical superfluids such as those thought to exist in the core of neutron stars.
Probing Unconventional Transport Regimes in Delafossite Metals (Springer Theses)
by Philippa H. McGuinnessThis thesis describes in-depth studies of the remarkable electronic transport within the ultrahigh conductivity delafossite metals PtCoO_2 and PdCoO_2 using the tool of focused ion beam (FIB) microstucturing. Despite being first synthesised over 50 years ago, important questions remain regarding both the origin of the unusually high conductivity of these compounds and the consequences of their unique properties for unconventional electronic transport, such as that within the ballistic regime. The thesis explores both these areas.High-energy electron irradiation is used to examine the effects of deliberately introducing point defects into PdCoO_2 and PtCoO_2, demonstrating that the extremely low resistivity of these materials stems from an extreme purity as high as 1 defect in 120,000 atoms, rather than a novel scattering suppression mechanism. In addition, studies of the electronic transport in micron-scale squares of these metals show that their broadly hexagonal Fermi surfaces lead not only to long range ballistic behaviour but novel ballistic regime phenomena which cannot be observed in materials with a higher-symmetry Fermi surface.
Probiotic Bacteria and Enteric Infections
by J.F.J.G. Koninkx R. Marinsek-Logar J. J. MalagoEvery day many people suffer from intestinal diseases. These disorders can result from pathogens like bacteria, fungi, parasites and viruses, but the causes of non-infectious intestinal disorders and colorectal cancers remain to be elucidated. Disturbances to the normal gut flora (the microbiota) are central to the development of many, if not all, of these disorders. Disturbed gut microbiota is a prelude to public health issues like traveller's-, antibiotic- and Clostridium difficile-associated diarrhoea, irritable bowel syndrome, inflammatory bowel disease, and colorectal cancers. This book discusses the way intestinal disorders affect the microbiota, how the disturbed microbiotal balance leads to enteric disorders and the ways to prevent these disorders. Further his book explores the potential of probiotics (live microorganisms that when ingested bring a health benefit) in treating enteric disorders by analysing the probiotic genome through proteomics, metabolomics and functional assays. Discussed is how the ingestion of specific microorganisms repairs the disturbed microbiota and subsequently ameliorates enteric disorders. Finally this book addresses how genetic engineering and biotechnology will contribute to the development of effective and safe designer probiotics.
Probiotic Bacteria and Postbiotic Metabolites: Role in Animal and Human Health (Microorganisms for Sustainability #2)
by Naheed Mojgani Maryam DadarThis book covers all aspects of probiotic bacteria and their metabolites, as well as their role and significance in human and animal health. Given the role of probiotic bacterial strains in the production of short chain fatty acids, butyrate etc probiotics may be considered as an alternative approach for the prevention or treatment of intestinal dysbiosis, cancers, cardiovascular diseases, hypertensions. Additionally, the significance of probiotics added in aquaculture systems for improving health, performance and growth of aquatic organisms has been highlighted. In this book, the multi-functional role of probiotics and their post-biotic metabolites in improving overall health status of man and animals, is discussed. It is a comprehensive compilation useful for researchers, academics, veterinarians and students in the field of microbiology, food technology and biotechnology.
Probiotic Cities (Bio Design)
by Richard BeckettProbiotic Cities covers a body of work that is at the forefront of emerging knowledge within architecture, towards designing informed indoor and built environment microbiomes. Sited within the broader field of Bio Design, the book presents highly experimental design research at the intersection of architecture, engineering and microbiology. The book describes work which explores novel strategies towards directly (re)introducing beneficial microbes into buildings and cities. Through discussion of both the work and the processes and methodologies used, it provides a framework to enable designers and practitioners to begin to engage with contemporary human–microbe relationships towards the design of healthy and resilient cities. The book defines a new microbial paradigm for architecture that engages with broader emerging ecological or ‘more than human’ philosophies for design within the age of the Anthropocene.
Probiotic Dairy Products
by Adnan Y. Tamime Linda V. ThomasProbiotic Dairy Products, 2nd Edition The updated guide to the most current research and developments in probiotic dairy products The thoroughly revised and updated second edition of Probiotic Dairy Products reviews the recent advancements in the dairy industry and includes the latest scientific developments in regard to the 'functional' aspects of dairy and fermented milk products and their ingredients. Since the publication of the first edition of this text, there have been incredible advances in the knowledge and understanding of the human microbiota, mainly due to the development and use of new molecular analysis techniques. This new edition includes information on the newest developments in the field. It offers information on the new ‘omic’ technologies that have been used to detect and analyse all the genes, proteins and metabolites of individuals’ gut microbiota. The text also includes a description of the history of probiotics and explores the origins of probiotic products and the early pioneers in this field. Other chapters in this resource provide valuable updates on genomic analysis of probiotic strains and aspects of probiotic products’ production and quality control. This important resource: Offers a completely revised and updated edition to the text that covers the topic of probiotic dairy products Contains 4 brand new chapters on the following topics: the history of probiotics, prebiotic components, probiotic research, and the production of vitamins, exopolysaccharides (EPS), and bacteriocins Features a new co-editor and a host of new contributors, that offer the latest research findings and expertise Is the latest title in Wiley's Society of Dairy Technology Technical Series Probiotic Dairy Products is an essential resource for dairy scientists, dairy technologists and nutritionists. The text includes the results of the most reliable research in field and offers informed views on the future of, and barriers to, the progress for probiotic dairy products.
Probiotic Foods and Beverages: Technologies and Protocols (Methods and Protocols in Food Science)
by Adriano Gomes da Cruz Marcia Cristina Silva Tatiana Colombo Pimentel Erick Almeida Esmerino Silvani VerruckThis volume details state-of-the-art protocols on manufacturing functional probiotic foods and beverages. Chapters guide readers through processing procedures, probiotic strains, probiotic cheese, probiotic fermented milk, probiotic ice cream manufacturing, probiotic butter, plant-based beverages, probiotic plant-based cheeses, probiotic-fermented vegetables, Kombucha, probiotic beer, Friolano-type sausage, delivery of probiotics through bakery goods, synbiotic chocolate, methods on encapsulation of probiotics, paraprobiotics, and protocols for food products with psychobiotic potential. Written in the format of the Methods and Protocols in Food Science series, chapters list necessary materials and methods for readily reproducible protocols. Authoritative and cutting-edge, Probiotic Foods and Beverages: Technologies and Protocols aims to be a comprehensibly guide with well-established protocols and procedures.
Probiotic Ice Cream: Science and Technology
by Aziz Homayouni-RadComprehensive resource on probiotics as applied to ice cream and frozen desserts, covering fundamentals, development, technology, and quality control Probiotic Ice Cream is the first book to look at probiotics as applied to ice cream and frozen desserts, covering the whole product development process, from essential fundamentals to formulation and characterization of the final product. Written by a highly qualified specialist with significant research experience in this unique field, Probiotic Ice Cream includes information on: Science of probiotic ice cream, covering principles of probiotics and how to select appropriate probiotic strains for use in ice creamPhysical protection of probiotics in ice cream conditions, as well as nutritional value of functional ice cream for humansTechnology of probiotic ice cream, covering the definition, formulation, and characterization of prebiotic, probiotic, synbiotic and postbiotic ice creamsQuality control, with information on the physico-chemical and rheological properties, sensory properties, and shelf-life evaluation and packaging of probiotic ice cream Probiotic Ice Cream is an authoritative, comprehensive, and one-of-a-kind reference on the subject, ideal for dairy scientists, frozen desserts manufacturers, supermarkets, and food product developers, as well as students in related programs of study.
Probiotic Research in Therapeutics: Volume 1: Applications in Cancers and Immunological Diseases
by Indu Pal KaurThe volume sheds new light on role of gut dysbiosis in cancer and immunological diseases and their clinical manifestations. Contributions in the volume discuss about the gut microbiota as a therapeutic target and the role of probiotics in its management. The volume explores application of probiotics in the treatment of various cancers viz. colorectal, gastric, lung, and breast cancer and immunological diseases. The volume comprises of chapters from expert contributors organized into various important themes which include, introduction, relationship between gut microbiota and disease condition, mechanisms involved, clinical and in vivo status, conclusion and future directions. This is a highly informative and carefully presented book, providing recent and innovative insight for scholars and researchers with an interest in probiotics and its applications in cancer and immunological diseases.
Probiotic Research in Therapeutics: Volume 2: Modulation of Gut Flora: Management of Inflammation and Infection Related Gut Etiology
by Indu Pal KaurIn a normal physiological state, several bacteria are present in the human gut that is essential to maintain the normal to healthy gastrointestinal function. Disturbances in this “normal flora” lead to gut inflammation and infection. This volume explores the potential of probiotics, the healthy bacteria, to manage gut-related diseases including gastrointestinal cancers, ulcerative colitis, H. pylori infections, and diarrhea; vaginosis; oral health; airway inflammation; and atopic dermatitis. The concept of designer probiotics, edible vaccines and future scope of research in the field is also presented. The animal models used for studying the benefits of probiotics in gut inflammation are described for beginners.
Probiotic Research in Therapeutics: Volume 3: Probiotics and Gut Skin Axis–Inside Out and Outside In
by Indu Pal KaurRecent research in science establishes a direct relation between human gut and skin. Several species of live microbes inhabit the human skin and intestines which far outnumbers the mammalian cells in the human body. Research interest of Nextgen scientists is focused on beneficially harnessing this microbial population to address skin disorders like acne, rosacea, eczema, premature aging, and skin cancer which are established to be a result of skin-microbiome dysbiosis. This volume highlights evidence-based endeavours of the scientific community in this sector. Currently there is no concrete literature which gives a detailed vision on the relationship between gut microbiota and skin related disorders. This volume is an attempt to put together available data in the area and demonstrate usefulness of probiotics as a new therapeutic option for management of these skin diseases which currently show poor prognosis, high cost of treatment and compromised quality of life of the patient.
Probiotic Research in Therapeutics: Volume 4: Probiotics in Neurodegenerative Disorders
by Indu Pal KaurHumans have numerous microorganisms residing in the body, especially in the gut, far exceeding the human body's normal mammalian cells. Recent research links the gut microbiome, the population of microorganisms living in the gastrointestinal tract, with brain diseases. This volume explores the concept and possibility of its extension to manage a galaxy of CNS diseases, including Parkinson's, Alzheimer's, Autism spectrum disorders, depression, insomnia, and chronic fatigue syndrome. This volume elaborates about communication channels between gut and brain via the vagus nerve, short-chain fatty acids including omega acids, and other inflammasomes.In contrast to the available books on the topic, this title is more versatile and endeavors to bring together scientific pre-clinical, and clinical claims on the probable psychobiotic implication of probiotic therapy. The book will appeal similar to the general public, students, experienced researchers, and academicians. It is endeavored to address an aspect of probiotic usage beyond gut disorders. We hope that it would be helpful to people studying the human nervous system and related conditions with their treatments.
Probiotics
by Min-Tze LiongProbiotic microorganisms have a long history of use, and their health benefits for hosts are well documented. This Microbiology Monographs volume provides an overview of the current knowledge and applications of probiotics. Reviews cover the biology and probiotic potential of the thoroughly studied prokaryotic genera Lactobacillus and Bifidobacterium, several eukaryotic microorganisms, probiotic strain characterization, and the analytical methods (such as FISH, microarray, and high throughput sequencing) required for their study. Further chapters describe the positive effects of probiotics on malabsorption disorders such as diarrhea and lactose intolerance, and document the clinical evidence of benefits in treating allergies and lung emphysema, and in dermatological applications. Also addresses are topics such as genetically engineered strains, new carriers for probiotics, protection techniques, challenges of health claims, safety aspects, and future market trends.
Probiotics and Health Claims
by Wolfgang Kneifel Seppo SalminenThis book examines the international picture regarding probiotic food applications, placing a particular emphasis on the legal context and assessment procedures of probiotic health claims in the major markets for these products. Health claim legislation is described and the ways in which manufacturers can ensure compliance are discussed. The book also covers the use of meta-analysis to assess available data, and case examples from various regulatory cultures and traditions are included. It will be of interest to food industry scientists, executives and R&D personnel; international regulatory advisers and administrators; researchers, educators and students on food science courses. Key Features: Focuses on health claim legislation for this commercially important food sector Includes chapters on the current situation in all the major world markets including Europe, the USA, Japan, India and China Covers food, feed and pharmaceutical applications of probiotics