In the third part of the thesis, the data-driven input model generation strategies coupled with the sparse grid collocation strategies are utilized to analyze systems characterized by multi-length scale uncertainties. A stochastic variational multiscale formulation is developed to incorporate uncertain multiscale features. The framework is applied to analyze flow through random heterogeneous media when only limited statistics about the permeability variation are given.

The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from: · statistics, · time-frequency analysis, and · low-dimensional reductions The blend of these ideas provides meaningful insight into the data sets one is faced with in every scientific subject today, including those generated from complex dynamical systems. This is a particularly exciting field and much of the final part of the book is driven by intuitive examples from it, showing how the three areas can be used in combination to give critical insight into the fundamental workings of various problems. Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences. An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

An integrated treatment of models and computational methods for stochastic design and stochastic optimization problems. Through many realistic examples, stochastic models and algorithmic solution methods are explored in a wide variety of application areas. These include inventory/production control, reliability, maintenance, queueing, and computer and communication systems. Includes many problems, a significant number of which require the writing of a computer program.

The Handbook of Dynamic Data Driven Applications Systems establishes an authoritative reference of DDDAS, pioneered by Dr. Darema and the co-authors for researchers and practitioners developing DDDAS technologies. Beginning with general concepts and history of the paradigm, the text provides 32 chapters by leading experts in ten application areas to enable an accurate understanding, analysis, and control of complex systems; be they natural, engineered, or societal: The authors explain how DDDAS unifies the computational and instrumentation aspects of an application system, extends the notion of Smart Computing to span from the high-end to the real-time data acquisition and control, and manages Big Data exploitation with high-dimensional model coordination. The Dynamically Data Driven Applications Systems (DDDAS) paradigm inspired research regarding the prediction of severe storms. Specifically, the DDDAS concept allows atmospheric observing systems, computer forecast models, and cyberinfrastructure to dynamically configure themselves in optimal ways in direct response to current or anticipated weather conditions. In so doing, all resources are used in an optimal manner to maximize the quality and timeliness of information they provide. Kelvin Droegemeier, Regents’ Professor of Meteorology at the University of Oklahoma; former Director of the White House Office of Science and Technology Policy We may well be entering the golden age of data science, as society in general has come to appreciate the possibilities for organizational strategies that harness massive streams of data. The challenges and opportunities are even greater when the data or the underlying system are dynamic - and DDDAS is the time-tested paradigm for realizing this potential. Sangtae Kim, Distinguished Professor of Mechanical Engineering and Distinguished Professor of Chemical Engineering at Purdue University

Stable, predictive biomarkers and interpretable disease signatures are seen as a significant step towards personalized medicine. In this perspective, integration of multi-omic data coming from genomics, transcriptomics, glycomics, proteomics, metabolomics is a powerful strategy to reconstruct and analyse complex multi-dimensional interactions, enabling deeper mechanistic and medical insight. At the same time, there is a rising concern that much of such different omic data –although often publicly and freely available- lie in databases and repositories underutilised or not used at all. Issues coming from lack of standardisation and shared biological identities are also well-known. From these considerations, a novel, pressing request arises from the life sciences to design methodologies and approaches that allow for these data to be interpreted as a whole, i.e. as intertwined molecular signatures containing genes, proteins, mRNAs and miRNAs, able to capture inter-layers connections and complexity. Papers discuss data integration approaches and methods of several types and extents, their application in understanding the pathogenesis of specific diseases or in identifying candidate biomarkers to exploit the full benefit of multi-omic datasets and their intrinsic information content. Topics of interest include, but are not limited to: • Methods for the integration of layered data, including, but not limited to, genomics, transcriptomics, glycomics, proteomics, metabolomics; • Application of multi-omic data integration approaches for diagnostic biomarker discovery in any field of the life sciences; • Innovative approaches for the analysis and the visualization of multi-omic datasets; • Methods and applications for systematic measurements from single/undivided samples (comprising genomic, transcriptomic, proteomic, metabolomic measurements, among others); • Multi-scale approaches for integrated dynamic modelling and simulation; • Implementation of applications, computational resources and repositories devoted to data integration including, but not limited to, data warehousing, database federation, semantic integration, service-oriented and/or wiki integration; • Issues related to the definition and implementation of standards, shared identities and semantics, with particular focus on the integration problem. Research papers, reviews and short communications on all topics related to the above issues were welcomed.

Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edition: a new chapter on diffusion processes that gives an accessible and non-measure-theoretic treatment with applications to finance; a more streamlined, application-oriented approach to renewal, regenerative, and Markov regenerative processes; and, two appendices that collect relevant results from analysis and differential and difference equations. Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, students will be well-equipped to build and analyze useful stochastic models for various situations. A collection of MATLAB[registered]-based programs can be downloaded from the author's website and a solutions manual is available for qualifying instructors.

This lecture presents research on a general framework for perceptual organization that was conducted mainly at the Institute for Robotics and Intelligent Systems of the University of Southern California. It is not written as a historical recount of the work, since the sequence of the presentation is not in chronological order. It aims at presenting an approach to a wide range of problems in computer vision and machine learning that is data-driven, local and requires a minimal number of assumptions. The tensor voting framework combines these properties and provides a unified perceptual organization methodology applicable in situations that may seem heterogeneous initially. We show how several problems can be posed as the organization of the inputs into salient perceptual structures, which are inferred via tensor voting. The work presented here extends the original tensor voting framework with the addition of boundary inference capabilities; a novel re-formulation of the framework applicable to high-dimensional spaces and the development of algorithms for computer vision and machine learning problems. We show complete analysis for some problems, while we briefly outline our approach for other applications and provide pointers to relevant sources.

"Constructive Computation in Stochastic Models with Applications: The RG-Factorizations" provides a unified, constructive and algorithmic framework for numerical computation of many practical stochastic systems. It summarizes recent important advances in computational study of stochastic models from several crucial directions, such as stationary computation, transient solution, asymptotic analysis, reward processes, decision processes, sensitivity analysis as well as game theory. Graduate students, researchers and practicing engineers in the field of operations research, management sciences, applied probability, computer networks, manufacturing systems, transportation systems, insurance and finance, risk management and biological sciences will find this book valuable. Dr. Quan-Lin Li is an Associate Professor at the Department of Industrial Engineering of Tsinghua University, China.

This practical and accessible text enables readers from engineering, business, operations research, public policy and computer science to analyze stochastic systems. Emphasizing the modeling of real-life situations with stochastic elements and analyzing the resulting stochastic model, it presents the major cases of useful stochastic processes-discrete and continuous time Markov chains, renewal processes, regenerative processes, and Markov regenerative processes. The author provides reader-friendly yet rigorous coverage. He follows a set pattern of development for each class of stochastic processes and introduces Markov chains before renewal processes, so that readers can begin modeling systems early. He demonstrates both numerical and analytical solution methods in detail and dedicates a separate chapter to queueing applications. Modeling and Analysis of Stochastic Systems includes numerous worked examples and exercises, conveniently categorized as modeling, computational, or conceptual and making difficult concepts easy to grasp. Taking a practical approach to working with stochastic models, this book helps readers to model and analyze the increasingly complex and interdependent systems made possible by recent advances.