Extended Abstracts Summer 2015

Trends in Mathematics

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This book is divided into two parts, the first of which seeks to connect the phase transitions of various disciplines, including game theory, and to explore the synergies between statistical physics and combinatorics. Phase Transitions has been an active multidisciplinary field of research, bringing together physicists, computer scientists and mathematicians. The main research theme explores how atomic agents that act locally and microscopically lead to discontinuous macroscopic changes. Adopting this perspective has proven to be especially useful in studying the evolution of random and usually complex or large combinatorial objects (like networks or logic formulas) with respect to discontinuous changes in global parameters like connectivity, satisfiability etc. There is, of course, an obvious strategic element in the formation of a transition: the atomic agents “selfishly” seek to optimize a local parameter. However, up to now this game-theoretic aspect of abrupt, locally triggered changes had not been extensively studied.

In turn, the book’s second part is devoted to mathematical and computational methods applied to the pricing of financial contracts and the measurement of financial risks. The tools and techniques used to tackle these problems cover a wide spectrum of fields, like stochastic calculus, numerical analysis, partial differential equations, statistics and econometrics. Quantitative Finance is a highly active field of research and is increasingly attracting the interest of academics and practitioners alike. The material presented addresses a wide variety of new challenges for this audience.
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Additional Information

Publisher
Birkhäuser
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Published on
Feb 24, 2017
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Pages
139
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ISBN
9783319517537
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Language
English
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Genres
Business & Economics / Insurance / General
Mathematics / Combinatorics
Mathematics / Differential Equations / General
Mathematics / General
Mathematics / Geometry / Algebraic
Mathematics / Geometry / Analytic
Mathematics / Linear & Nonlinear Programming
Mathematics / Mathematical Analysis
Mathematics / Probability & Statistics / General
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Content Protection
This content is DRM protected.
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This two-part volume gathers extended conference abstracts corresponding to selected talks from the "Biostatnet workshop on Biomedical (Big) Data" and from the "DoReMi LD-RadStats: Workshop for statisticians interested in contributing to EU low dose radiation research", which were held at the Centre de Recerca Matemàtica (CRM) in Barcelona from November 26th to 27th, 2015, and at the Institut de Salut Global ISGlobal (former CREAL) from October 26th to 28th, 2015, respectively. Most of the contributions are brief articles, presenting preliminary new results not yet published in regular research journals.

The first part is devoted to the challenges of analyzing so called "Biomedical Big Data", tremendous amounts of biomedical and health data that are generated every day due to the use of recent technological advances such as massive genomic sequencing, electronic health records or high-resolution medical imaging, among others. The analysis of this information poses significant challenges for researchers in the fields of biostatistics, bioinformatics, and signal processing. Furthermore, other relevant challenges in biostatistical research, not necessarily involving big data, are also discussed.

In turn, the second part is dedicated to low dose radiation research, where there is a need to fully understand and characterize potential sources of uncertainty before they can be reduced. Further, the book demonstrates why formal uncertainty analysis has the potential to provide a common platform for multidisciplinary research in this field.

This book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the "Intensive Research Program on Advances in Nonsmooth Dynamics 2016", held at the Centre de Recerca Matemàtica (CRM) in Barcelona from February 1st to April 29th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and outlines of prominent discussion sessions. The articles are all the result of direct collaborations initiated during the research program.

The topic is the theory and applications of Nonsmooth Dynamics. This includes systems involving elements of: impacting, switching, on/off control, hybrid discrete-continuous dynamics, jumps in physical properties, and many others. Applications include: electronics, climate modeling, life sciences, mechanics, ecology, and more. Numerous new results are reported concerning the dimensionality and robustness of nonsmooth models, shadowing variables, numbers of limit cycles, discontinuity-induced bifurcations and chaos, determinacy-breaking, stability criteria, and the classification of attractors and other singularities. This material offers a variety of new exciting problems to mathematicians, but also a diverse range of new tools and insights for scientists and engineers making use of mathematical modeling and analysis.

The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

This volume contains extended abstracts outlining selected presentations given by participants of the joint international multidisciplinary workshop MURPHYS-HSFS-2016 (MUltiRate Processes and HYSteresis; Hysteresis and Slow-Fast Systems), which was dedicated to the mathematical theory and applications of multiple scale systems and systems with hysteresis, and held at the Centre de Recerca Matemàtica (CRM) in Barcelona from June 13th to 17th, 2016. The collection includes brief research articles on new results, preliminary work, open problems, and the outcomes of group work initiated during the workshop.

The book addresses multiple scale phenomena, singular perturbations, phase transitions, and hysteresis phenomena occurring in mathematical, physical, economic, engineering and information systems. Its scope includes both new results in the theory of hysteresis, singularly perturbed systems and dynamical systems in general; and applications to the physical, chemical, biological, microbiological, economic, and engineering sciences, such as: elasto-plasticity and mechanical structures, damage processes, magnetic materials, photonics and optoelectronics, energy storage systems, hydrology, biology, semiconductor lasers, and shock phenomena in economic modeling. Given its breadth of coverage, the book offers a valuable resource for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active research areas.


The main goal of the two authors is to help undergraduate students understand the concepts and ideas of combinatorics, an important realm of mathematics, and to enable them to ultimately achieve excellence in this field. This goal is accomplished by familiariz ing students with typical examples illustrating central mathematical facts, and by challenging students with a number of carefully selected problems. It is essential that the student works through the exercises in order to build a bridge between ordinary high school permutation and combination exercises and more sophisticated, intricate, and abstract concepts and problems in undergraduate combinatorics. The extensive discussions of the solutions are a key part of the learning process. The concepts are not stacked at the beginning of each section in a blue box, as in many undergraduate textbooks. Instead, the key mathematical ideas are carefully worked into organized, challenging, and instructive examples. The authors are proud of their strength, their collection of beautiful problems, which they have accumulated through years of work preparing students for the International Math ematics Olympiads and other competitions. A good foundation in combinatorics is provided in the first six chapters of this book. While most of the problems in the first six chapters are real counting problems, it is in chapters seven and eight where readers are introduced to essay-type proofs. This is the place to develop significant problem-solving experience, and to learn when and how to use available skills to complete the proofs.
This two-part volume gathers extended conference abstracts corresponding to selected talks from the "Biostatnet workshop on Biomedical (Big) Data" and from the "DoReMi LD-RadStats: Workshop for statisticians interested in contributing to EU low dose radiation research", which were held at the Centre de Recerca Matemàtica (CRM) in Barcelona from November 26th to 27th, 2015, and at the Institut de Salut Global ISGlobal (former CREAL) from October 26th to 28th, 2015, respectively. Most of the contributions are brief articles, presenting preliminary new results not yet published in regular research journals.

The first part is devoted to the challenges of analyzing so called "Biomedical Big Data", tremendous amounts of biomedical and health data that are generated every day due to the use of recent technological advances such as massive genomic sequencing, electronic health records or high-resolution medical imaging, among others. The analysis of this information poses significant challenges for researchers in the fields of biostatistics, bioinformatics, and signal processing. Furthermore, other relevant challenges in biostatistical research, not necessarily involving big data, are also discussed.

In turn, the second part is dedicated to low dose radiation research, where there is a need to fully understand and characterize potential sources of uncertainty before they can be reduced. Further, the book demonstrates why formal uncertainty analysis has the potential to provide a common platform for multidisciplinary research in this field.

This book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

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This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the "Intensive Research Program on Advances in Nonsmooth Dynamics 2016", held at the Centre de Recerca Matemàtica (CRM) in Barcelona from February 1st to April 29th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and outlines of prominent discussion sessions. The articles are all the result of direct collaborations initiated during the research program.

The topic is the theory and applications of Nonsmooth Dynamics. This includes systems involving elements of: impacting, switching, on/off control, hybrid discrete-continuous dynamics, jumps in physical properties, and many others. Applications include: electronics, climate modeling, life sciences, mechanics, ecology, and more. Numerous new results are reported concerning the dimensionality and robustness of nonsmooth models, shadowing variables, numbers of limit cycles, discontinuity-induced bifurcations and chaos, determinacy-breaking, stability criteria, and the classification of attractors and other singularities. This material offers a variety of new exciting problems to mathematicians, but also a diverse range of new tools and insights for scientists and engineers making use of mathematical modeling and analysis.

The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

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