This edited volume is a definitive text on adaptive clinical trial designs from creation and customization to utilization. As this book covers the full spectrum of topics involved in the adaptive designs arena, it will serve as a valuable reference for researchers working in industry, government and academia. The target audience is anyone involved in the planning and execution of clinical trials, in particular, statisticians, clinicians, pharmacometricians, clinical operation specialists, drug supply managers, and infrastructure providers. In spite of the increased efficiency of adaptive trials in saving costs and time, ultimately getting drugs to patients sooner, their adoption in clinical development is still relatively low. One of the chief reasons is the higher complexity of adaptive design trials as compared to traditional trials. Barriers to the use of clinical trials with adaptive features include the concerns about the integrity of study design and conduct, the risk of regulatory non-acceptance, the need for an advanced infrastructure for complex randomization and clinical supply scenarios, change management for process and behavior modifications, extensive resource requirements for the planning and design of adaptive trials and the potential to relegate key decision makings to outside entities. There have been limited publications that address these practical considerations and recommend best practices and solutions. This book fills this publication gap, providing guidance on practical considerations for adaptive trial design and implementation. The book comprises three parts: Part I focuses on practical considerations from a design perspective, whereas Part II delineates practical considerations related to the implementation of adaptive trials. Putting it all together, Part III presents four illustrative case studies ranging from description and discussion of specific adaptive trial design considerations to the logistic and regulatory issues faced in trial implementation.

Bringing together the expertise of leading key opinion leaders from pharmaceutical industry, academia, and regulatory agencies, this book provides a balanced and comprehensive coverage of practical considerations for adaptive trial design and implementation.

This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces. The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussion of the monograph, namely, Yosida approximations of SDEs, Yosida approximations of SDEs with Poisson jumps, and their applications. Most of the results considered in the main chapters appear for the first time in a book form, and contain illustrative examples on stochastic partial differential equations. The key steps are included in all proofs, especially the various estimates, which help the reader to get a true feel for the theory of Yosida approximations and their use. This work is intended for researchers and graduate students in mathematics specializing in probability theory and will appeal to numerical analysts, engineers, physicists and practitioners in finance who want to apply the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in stochastic processes.

This book introduces the basic fundamentals, models, emulators and analyses of mem-elements in the circuit theory with applications. The book starts reviewing the literature on mem-elements, models and their recent applications. It presents mathematical models, numerical results, circuit simulations, and experimental results for double-loop hysteresis behavior of mem-elements. The authors introduce a generalized memristor model in the fractional-order domain under different input and different designs for emulator-based mem-elements, with circuit and experimental results. The basic concept of memristive-based relaxation-oscillators in the circuit theory is also covered. The reader will moreover find in this book information on memristor-based multi-level digital circuits, memristor-based multi-level multiplier and memcapacitor-based oscillators and synaptic circuits.

The articles in this collection are a sampling of some of the research presented during the conference "Stochastic Analysis and Related Topics", held in May of 2015 at Purdue University in honor of the 60th birthday of Rodrigo Banuelos. A wide variety of topics in probability theory is covered in these proceedings, including heat kernel estimates, Malliavin calculus, rough paths differential equations, Levy processes, Brownian motion on manifolds, and spin glasses, among other topics.

During the last two decades, structural equation modelling (SEM) has emerged as a powerful multivariate data analysis tool in social science research settings, especially in the fields of sociology, psychology, and education. Social science researchers and students benefit greatly from acquiring knowledge and skills in SEM, since the methods can provide a bridge between the theoretical and empirical aspects of behavioural research. Ramlall explains in a rigorous, concise, and practical manner all the vital components embedded in structural equation modelling (SEM). Focusing on R and Stata to implement and perform various structural equation models, Ramlall examines the types, benefits, and drawbacks of SEM, delving into model specifications and identifications, fit evaluations, and path diagrams.

This volume is a unique combination of papers that cover critical topics in biostatistics from academic, government, and industry perspectives. The 6 sections cover Bayesian methods in biomedical research; Diagnostic medicine and classification; Innovative Clinical Trials Design; Modelling and Data Analysis; Personalized Medicine; and Statistical Genomics. The real world applications are in clinical trials, diagnostic medicine and genetics. The peer-reviewed contributions were solicited and selected from some 400 presentations at the annual meeting of the International Chinese Statistical Association (ICSA), held with the International Society for Biopharmaceutical Statistics (ISBS). The conference was held in Bethesda in June 2013, and the material has been subsequently edited and expanded to cover the most recent developments.

The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text.

This text presents a wide-ranging and rigorous overview of nearest neighbor methods, one of the most important paradigms in machine learning. Now in one self-contained volume, this book systematically covers key statistical, probabilistic, combinatorial and geometric ideas for understanding, analyzing and developing nearest neighbor methods. Gerard Biau is a professor at Universite Pierre et Marie Curie (Paris). Luc Devroye is a professor at the School of Computer Science at McGill University (Montreal).

This book is a comprehensive introduction of the reader into the simulation and modelling techniques and their application in the management of organisations. The book is rooted in the thorough understanding of systems theory applied to organisations and focuses on how this theory can apply to econometric models used in the management of organisations. The econometric models in this book employ linear and dynamic programming, graph theory, queuing theory, game theory, etc. and are presented and analysed in various fields of application, such as investment management, stock management, strategic decision making, management of production costs and the lifecycle costs of quality and non-quality products, production quality Management, etc.

This volume collects selected, peer-reviewed contributions from the 2nd Conference of the International Society for Nonparametric Statistics (ISNPS), held in Cadiz (Spain) between June 11-16 2014, and sponsored by the American Statistical Association, the Institute of Mathematical Statistics, the Bernoulli Society for Mathematical Statistics and Probability, the Journal of Nonparametric Statistics and Universidad Carlos III de Madrid. The 15 articles are a representative sample of the 336 contributed papers presented at the conference. They cover topics such as high-dimensional data modelling, inference for stochastic processes and for dependent data, nonparametric and goodness-of-fit testing, nonparametric curve estimation, object-oriented data analysis, and semiparametric inference. The aim of the ISNPS 2014 conference was to bring together recent advances and trends in several areas of nonparametric statistics in order to facilitate the exchange of research ideas, promote collaboration among researchers from around the globe, and contribute to the further development of the field.

This book fills an important gap in studies on D. D. Kosambi. For the first time, the mathematical work of Kosambi is described, collected and presented in a manner that is accessible to non-mathematicians as well. A number of his papers that are difficult to obtain in these areas are made available here. In addition, there are essays by Kosambi that have not been published earlier as well as some of his lesser known works. Each of the twenty four papers is prefaced by a commentary on the significance of the work, and where possible, extracts from technical reviews by other mathematicians.

A comprehensive guide to everything scientists need to know about data management, this book is essential for researchers who need to learn how to organize, document and take care of their own data. Researchers in all disciplines are faced with the challenge of managing the growing amounts of digital data that are the foundation of their research. Kristin Briney offers practical advice and clearly explains policies and principles, in an accessible and in-depth text that will allow researchers to understand and achieve the goal of better research data management. Data Management for Researchers includes sections on: * The data problem - an introduction to the growing importance and challenges of using digital data in research. Covers both the inherent problems with managing digital information, as well as how the research landscape is changing to give more value to research datasets and code. * The data lifecycle - a framework for data's place within the research process and how data's role is changing. Greater emphasis on data sharing and data reuse will not only change the way we conduct research but also how we manage research data. * Planning for data management - covers the many aspects of data management and how to put them together in a data management plan. This section also includes sample data management plans. * Documenting your data - an often overlooked part of the data management process, but one that is critical to good management; data without documentation are frequently unusable. * Organizing your data - explains how to keep your data in order using organizational systems and file naming conventions. This section also covers using a database to organize and analyze content. * Improving data analysis - covers managing information through the analysis process. This section starts by comparing the management of raw and analyzed data and then describes ways to make analysis easier, such as spreadsheet best practices. It also examines practices for research code, including version control systems. * Managing secure and private data - many researchers are dealing with data that require extra security. This section outlines what data falls into this category and some of the policies that apply, before addressing the best practices for keeping data secure. * Short-term storage - deals with the practical matters of storage and backup and covers the many options available. This section also goes through the best practices to insure that data are not lost. * Preserving and archiving your data - digital data can have a long life if properly cared for. This section covers managing data in the long term including choosing good file formats and media, as well as determining who will manage the data after the end of the project. * Sharing/publishing your data - addresses how to make data sharing across research groups easier, as well as how and why to publicly share data. This section covers intellectual property and licenses for datasets, before ending with the altmetrics that measure the impact of publicly shared data. * Reusing data - as more data are shared, it becomes possible to use outside data in your research. This chapter discusses strategies for finding datasets and lays out how to cite data once you have found it. This book is designed for active scientific researchers but it is useful for anyone who wants to get more from their data: academics, educators, professionals or anyone who teaches data management, sharing and preservation. "An excellent practical treatise on the art and practice of data management, this book is essential to any researcher, regardless of subject or discipline." -Robert Buntrock, Chemical Information Bulletin

This work illustrates research conducted over a ten-year timespan and addresses a fundamental issue in reliability theory. This still appears to be an empirically disorganized field and the book suggests employing a deductive base in order to evolve reliability as a science. The study is in line with the fundamental work by Gnedenko. Boris Vladimirovich Gnedenko (1912 - 1995) was a Soviet mathematician who made significant contributions in various scientific areas. His name is especially associated with studies of dependability, for which he is often recognized as the 'father' of reliability theory. In the last few decades, this area has expanded in new directions such as safety, security, risk analysis and other fields, yet the book 'Mathematical Methods in Reliability Theory' written by Gnedenko with Alexander Soloviev and Yuri Belyaev still towers as a pillar of the reliability sector's configuration and identity. The present book proceeds in the direction opened by the cultural project of the Russian authors; in particular it identifies different trends in the hazard rate functions by means of deductive logic and demonstrations. Further, it arrives at multiple results by means of the entropy function, an original mathematical tool in the reliability domain. As such, it will greatly benefit all specialists in the field who are interested in unconventional solutions.

Hardbound. This volume covers an area of statistics dealing with complex problems in the production of goods and services, maintenance and repair, and management and operations. The opening chapter is by W. Edwards Deming, pioneer in statistical quality control, who was involved in the quality control movement in Japan and helped the country in its rapid industrial development. He gives a program to keep a country in an ascending path of industrial development.Areas covered in the further 23 chapters of the work include: - reliability of hardware and process control software;- the concepts and theory of reliability and the statistical inference problems arising therein;- the aspects of Quality Control of manufactured goods.

This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail.
The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.

1. Lossless Coding.- 2.Universal Coding on Finite Alphabets.- 3.Universal Coding on Infinite Alphabets.- 4.Model Order Estimation.- Notation.- Index.

Articles from many of the main contributors to recent progress in stochastic analysis are included in this volume, which provides a snapshot of the current state of the area and its ongoing developments. It constitutes the proceedings of the conference on "Stochastic Analysis and Applications" held at the University of Oxford and the Oxford-Man Institute during 23-27 September, 2013. The conference honored the 60th birthday of Professor Terry Lyons FLSW FRSE FRS, Wallis Professor of Mathematics, University of Oxford. Terry Lyons is one of the leaders in the field of stochastic analysis. His introduction of the notion of rough paths has revolutionized the field, both in theory and in practice. Stochastic Analysis is the branch of mathematics that deals with the analysis of dynamical systems affected by noise. It emerged as a core area of mathematics in the late 20th century and has subsequently developed into an important theory with a wide range of powerful and novel tools, and with impressive applications within and beyond mathematics. Many systems are profoundly affected by stochastic fluctuations and it is not surprising that the array of applications of Stochastic Analysis is vast and touches on many aspects of life. The present volume is intended for researchers and Ph.D. students in stochastic analysis and its applications, stochastic optimization and financial mathematics, as well as financial engineers and quantitative analysts.

This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener-E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful. Furthermore we have added a new chapter on triangular representation, which is closely connected with previous results and includes a new important class of operators with non-trivial invariant subspaces. Numerous formulations and proofs have now been improved, and the bibliography has been updated to reflect more recent additions to the body of literature.

This book provides a snapshot of representative modeling analyses of coastal hypoxia and its effects. Hypoxia refers to conditions in the water column where dissolved oxygen falls below levels that can support most metazoan marine life (i.e., 2 mg O2 l-1). The number of hypoxic zones has been increasing at an exponential rate since the 1960s; there are currently more than 600 documented hypoxic zones in the estuarine and coastal waters worldwide. Hypoxia develops as a synergistic product of many physical and biological factors that affect the balance of dissolved oxygen in seawater, including temperature, solar radiation, wind, freshwater discharge, nutrient supply, and the production and decay of organic matter. A number of modeling approaches have been increasingly used in hypoxia research, along with the more traditional observational and experimental studies. Modeling is necessary because of rapidly changing coastal circulation and stratification patterns that affect hypoxia, the large spatial extent over which hypoxia develops, and limitations on our capabilities to directly measure hypoxia over large spatial and temporal scales. This book consists of 15 chapters that are broadly organized around three main topics: (1) Modeling of the physical controls on hypoxia, (2) Modeling of biogeochemical controls and feedbacks, and, (3) Modeling of the ecological effects of hypoxia. The final chapter is a synthesis chapter that draws generalities from the earlier chapters, highlights strengths and weaknesses of the current state-of-the-art modeling, and offers recommendations on future directions.

Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to multidimensional data visualization, regression, survey calibration, inventory management, timetabling, chemical engineering, energy systems, and competitive facility location. Graduate students, researchers, and scientists in computer science, numerical analysis, optimization, and applied mathematics will be fascinated by the theoretical, computational, and application-oriented aspects of stochastic and deterministic global optimization explored in this book. This volume is dedicated to the 70th birthday of Antanas Zilinskas who is a leading world expert in global optimization. Professor Zilinskas's research has concentrated on studying models for the objective function, the development and implementation of efficient algorithms for global optimization with single and multiple objectives, and application of algorithms for solving real-world practical problems.

In this book the dynamics of the non-ideal oscillatory system, in which the excitation is influenced by the response of the oscillator, is presented. Linear and nonlinear oscillators with one or more degrees of freedom interacting with one or more energy sources are treated. This concerns for example oscillating systems excited by a deformed elastic connection, systems excited by an unbalanced rotating mass, systems of parametrically excited oscillator and an energy source, frictionally self-excited oscillator and an energy source, energy harvesting system, portal frame - non-ideal source system, non-ideal rotor system, planar mechanism - non-ideal source interaction. For the systems the regular and irregular motions are tested. The effect of self-synchronization, chaos and methods for suppressing chaos in non-ideal systems are considered. In the book various types of motion control are suggested. The most important property of the non-ideal system connected with the jump-like transition from a resonant state to a non-resonant one is discussed. The so called 'Sommerfeld effect', resonant unstable state and jumping of the system into a new stable state of motion above the resonant region is explained. A mathematical model of the system is solved analytically and numerically. Approximate analytical solving procedures are developed. Besides, simulation of the motion of the non-ideal system is presented. The obtained results are compared with those for the ideal case. A significant difference is evident. The book aims to present the established results and to expand the literature in non-ideal vibrating systems. A further intention of the book is to give predictions of the effects for a system where the interaction between an oscillator and the energy source exist. The book is targeted at engineers and technicians dealing with the problem of source-machine system, but is also written for PhD students and researchers interested in non-linear and non-ideal problems.

The book includes articles from eminent international scientists discussing a wide spectrum of topics of current importance in mathematics and statistics and their applications. It presents state-of-the-art material along with a clear and detailed review of the relevant topics and issues concerned. The topics discussed include message transmission, colouring problem, control of stochastic structures and information dynamics, image denoising, life testing and reliability, survival and frailty models, analysis of drought periods, prediction of genomic profiles, competing risks, environmental applications and chronic disease control. It is a valuable resource for researchers and practitioners in the relevant areas of mathematics and statistics.

Nature didn't design human beings to be statisticians, and in fact our minds are more naturally attuned to spotting the saber-toothed tiger than seeing the jungle he springs from. Yet scienti?c discovery in practice is often more jungle than tiger. Those of us who devote our scienti?c lives to the deep and satisfying subject of statistical inference usually do so in the face of a certain under-appreciation from the public, and also (though less so these days) from the wider scienti?c world. With this in mind, it feels very nice to be over-appreciated for a while, even at the expense of weathering a 70th birthday. (Are we certain that some terrible chronological error hasn't been made?) Carl Morris and Rob Tibshirani, the two colleagues I've worked most closely with, both 't my ideal pro?le of the statistician as a mathematical scientist working seamlessly across wide areas of theory and application. They seem to have chosen the papers here in the same catholic spirit, and then cajoled an all-star cast of statistical savants to comment on them.

Theory and application of a variety of mathematical techniques in economics are presented in this volume. Topics discussed include: martingale methods, stochastic processes, optimal stopping, the modeling of uncertainty using a Wiener process, Ito's Lemma as a tool of stochastic calculus, and basic facts about stochastic differential equations. The notion of stochastic ability and the methods of stochastic control are discussed, and their use in economic theory and finance is illustrated with numerous applications.
The applications covered include: futures, pricing, job search, stochastic capital theory, stochastic economic growth, the rational expectations hypothesis, a stochastic macroeconomic model, competitive firm under price uncertainty, the Black-Scholes option pricing theory, optimum consumption and portfolio rules, demand for index bonds, term structure of interest rates, the market risk adjustment in project valuation, demand for cash balances and an asset pricing model.