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Advanced Problems in Mathematics

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Book Series: OBP Series in Mathematics ISBN: 9781783741441 Year: Pages: 186 DOI: 10.11647/OBP.0075 Language: English
Publisher: Open Book Publishers
Subject: Mathematics
Added to DOAB on : 2017-08-22 11:01:03
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" This book is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge colleges as the basis for conditional offers. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics. "

Applications of Quantum Mechanical Techniques to Areas Outside of Quantum Mechanics

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Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889454273 Year: Pages: 162 DOI: 10.3389/978-2-88945-427-3 Language: English
Publisher: Frontiers Media SA
Subject: Science (General) --- Physics (General)
Added to DOAB on : 2018-11-16 17:17:57
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This book deals with applications of quantum mechanical techniques to areas outside of quantum mechanics, so-called quantum-like modeling. Research in this area has grown over the last 15 years. But even already more than 50 years ago, the interaction between Physics Nobelist Pauli and the psychologist Carl Jung in the 1950's on seeking to find analogous uses of the complementarity principle from quantum mechanics in psychology needs noting. This book does NOT want to advance that society is quantum mechanical! The macroscopic world is manifestly not quantum mechanical. But this rules not out that one can use concepts and the mathematical apparatus from quantum physics in a macroscopic environment. A mainstay ingredient of quantum mechanics, is 'quantum probability' and this tool has been proven to be useful in the mathematical modelling of decision making. In the most basic experiment of quantum physics, the double slit experiment, it is known (from the works of A. Khrennikov) that the law of total probability is violated. It is now well documented that several decision making paradoxes in psychology and economics (such as the Ellsberg paradox) do exhibit this violation of the law of total probability. When data is collected with experiments which test 'non-rational' decision making behaviour, one can observe that such data often exhibits a complex non-commutative structure, which may be even more complex than if one considers the structure allied to the basic two slit experiment. The community exploring quantum-like models has tried to address how quantum probability can help in better explaining those paradoxes. Research has now been published in very high standing journals on resolving some of the paradoxes with the mathematics of quantum physics. The aim of this book is to collect the contributions of world's leading experts in quantum like modeling in decision making, psychology, cognition, economics, and finance.

An Invitation to Statistics in Wasserstein Space

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Book Series: SpringerBriefs in Probability and Mathematical Statistics ISBN: 9783030384388 Year: Pages: 147 DOI: 10.1007/978-3-030-38438-8 Language: English
Publisher: Springer Nature
Subject: Mathematics
Added to DOAB on : 2020-05-14 09:30:34
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This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph. ; Gives a succinct introduction to necessary mathematical background, focusing on the results useful for statistics from an otherwise vast mathematical literature. Presents an up to date overview of the state of the art, including some original results, and discusses open problems. Suitable for self-study or to be used as a graduate level course text. Open access.

Improving Bayesian Reasoning: What Works and Why?

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Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889197453 Year: Pages: 207 DOI: 10.3389/978-2-88919-745-3 Language: English
Publisher: Frontiers Media SA
Subject: Psychology --- Science (General)
Added to DOAB on : 2016-04-07 11:22:02
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We confess that the first part of our title is somewhat of a misnomer. Bayesian reasoning is a normative approach to probabilistic belief revision and, as such, it is in need of no improvement. Rather, it is the typical individual whose reasoning and judgments often fall short of the Bayesian ideal who is the focus of improvement. What have we learnt from over a half-century of research and theory on this topic that could explain why people are often non-Bayesian? Can Bayesian reasoning be facilitated, and if so why? These are the questions that motivate this Frontiers in Psychology Research Topic. Bayes' theorem, named after English statistician, philosopher, and Presbyterian minister, Thomas Bayes, offers a method for updating one’s prior probability of an hypothesis H on the basis of new data D such that P(H|D) = P(D|H)P(H)/P(D). The first wave of psychological research, pioneered by Ward Edwards, revealed that people were overly conservative in updating their posterior probabilities (i.e., P(D|H)). A second wave, spearheaded by Daniel Kahneman and Amos Tversky, showed that people often ignored prior probabilities or base rates, where the priors had a frequentist interpretation, and hence were not Bayesians at all. In the 1990s, a third wave of research spurred by Leda Cosmides and John Tooby and by Gerd Gigerenzer and Ulrich Hoffrage showed that people can reason more like a Bayesian if only the information provided takes the form of (non-relativized) natural frequencies. Although Kahneman and Tversky had already noted the advantages of frequency representations, it was the third wave scholars who pushed the prescriptive agenda, arguing that there are feasible and effective methods for improving belief revision. Most scholars now agree that natural frequency representations do facilitate Bayesian reasoning. However, they do not agree on why this is so. The original third wave scholars favor an evolutionary account that posits human brain adaptation to natural frequency processing. But almost as soon as this view was proposed, other scholars challenged it, arguing that such evolutionary assumptions were not needed. The dominant opposing view has been that the benefit of natural frequencies is mainly due to the fact that such representations make the nested set relations perfectly transparent. Thus, people can more easily see what information they need to focus on and how to simply combine it. This Research Topic aims to take stock of where we are at present. Are we in a proto-fourth wave? If so, does it offer a synthesis of recent theoretical disagreements? The second part of the title orients the reader to the two main subtopics: what works and why? In terms of the first subtopic, we seek contributions that advance understanding of how to improve people’s abilities to revise their beliefs and to integrate probabilistic information effectively. The second subtopic centers on explaining why methods that improve non-Bayesian reasoning work as well as they do. In addressing that issue, we welcome both critical analyses of existing theories as well as fresh perspectives. For both subtopics, we welcome the full range of manuscript types.

Advanced Problems in Mathematics: Preparing for University

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Book Series: OBP Series in Mathematics ISSN: 2397-1126 / 2397-1134 ISBN: 9781783747764 9781783747771 Pages: 186 DOI: 10.11647/OBP.0181 Language: English
Publisher: Open Book Publishers
Subject: Mathematics
Added to DOAB on : 2019-10-29 12:26:38
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This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

DNA, statistics and the law: a cross-disciplinary approach to forensic inference

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Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889192502 Year: Pages: 39 DOI: 10.3389/978-2-88919-250-2 Language: English
Publisher: Frontiers Media SA
Subject: Science (General) --- Genetics
Added to DOAB on : 2015-11-16 15:44:59
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From ABO typing during the first half of the 20th century, to the use of enzymes and protein contained in blood serums and finally direct DNA typing, biology has been serving forensic purposes for many decades. Statistics, in turn, has been constantly underpinning the discussions of the probative value of results of biological analyses, in particular when defendants could not be considered as excluded as potential sources because of different genetic traits. The marriage between genetics and statistics has never been an easy one, though, as is illustrated by fierce arguments that peaked in the so-called "DNA wars" in some American courtrooms in the mid-1990s. This controversy has contributed to a lively production of research and publications on various interpretative topics, such as the collection of relevant data, foundations in population genetics as well as theoretical and practical considerations in probability and statistics. Both DNA profiling as a technique and the associated statistical considerations are now widely accepted as robust, but this does not yet guarantee or imply a neat transition to their application in court. Indeed, statistical principles applied to results of forensic DNA profiling analyses are a necessary, yet not a sufficient preliminary requirement for the contextually meaningful use of DNA in the law. Ultimately, the appropriate use of DNA in the forensic context relies on inference, i.e. reasoning reasonably in the face of uncertainty. This is all the more challenging that such thought processes need to be adopted by stakeholders from various backgrounds and holding diverse interests. Although several topics of the DNA controversy have been settled over time, some others are still debated (such as the question of how to deal with the probability of error), while yet others - purportedly settled topics - saw some recent revivals (e.g., the question of how to deal with database searches). In addition, new challenging topics have emerged over the last decade, such as the analysis and interpretation of traces containing only low quantities of DNA where artefacts of varying nature may affect results. Both technical and interpretative research involving statistics thus represent areas where ongoing research is necessary, and where scholars from the natural sciences and the law should collaborate. The articles in this Research Topic thus aim to investigate, from an interdisciplinary perspective, the current understanding of the strengths and limitations of DNA profiling results in legal applications. This Research Topic accepts contributions in all frontiers article type categories and places an emphasis on topics with a multidisciplinary perspective that explore (while not being limited to) statistical genetics for forensic scientists, case studies and reports, evaluation and interpretation of forensic findings, communication of expert findings to laypersons, quantitative legal reasoning and fact-finding using probability.

Innovations in Derivatives Markets: Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation

Authors: --- --- ---
Book Series: Springer Proceedings in Mathematics & Statistics ISSN: 2194-1009 ISBN: 9783319334455 9783319334462 Year: Volume: 165 Pages: 449 DOI: 10.1007/978-3-319-33446-2 Language: English
Publisher: Springer Nature
Subject: Mechanical Engineering --- Therapeutics --- Biotechnology --- Business and Management --- Chemical Technology
Added to DOAB on : 2017-03-08 12:08:06
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This book presents 20 peer-reviewed chapters on current aspects of derivatives markets and derivative pricing. The contributions, written by leading researchers in the field as well as experienced authors from the financial industry, present the state of the art in:• Modeling counterparty credit risk: credit valuation adjustment, debit valuation adjustment, funding valuation adjustment, and wrong way risk.• Pricing and hedging in fixed-income markets and multi-curve interest-rate modeling.• Recent developments concerning contingent convertible bonds, the measuring of basis spreads, and the modeling of implied correlations.The recent financial crisis has cast tremendous doubts on the classical view on derivative pricing. Now, counterparty credit risk and liquidity issues are integral aspects of a prudent valuation procedure and the reference interest rates are represented by a multitude of curves according to their different periods and maturities.A panel discussion included in the book (featuring Damiano Brigo, Christian Fries, John Hull, and Daniel Sommer) on the foundations of modeling and pricing in the presence of counterparty credit risk provides intriguing insights on the debate.

Evidence in Civil Law - Latvia

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Book Series: Law & Society ISBN: 9789616842532 Year: Pages: 94 DOI: 10.4335/978-961-6842-53-2 Language: English
Publisher: Institute for Local Self-Government and Public Procurement Maribor
Subject: Political Science
Added to DOAB on : 2015-11-09 21:56:58
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The national report of civil procedure in Latvia is based on review of the Latvian Civil Procedure Law, court practice, feedback by the Ministry of Justice on cooperation with the EU states as well as with third countries in various matters of jurisdiction as well as on legal science. Civil procedure includes all legal principles like disposition, right to be present and to be heard, competition of parties in gaining all necessary evidence and similar concepts to be found in almost every modern civil procedure system. However, there are certain specific features due to which Latvian process stands out. For instance, there is still a system of legal presumptions which apparently is inherited from Roman law, yet still prescribed by the Latvian Civil law (Civil code). Also certain degree of formal attitude remains as a characteristic feature of the Latvian civil procedure.

Computer and Information Sciences: 31st International Symposium, ISCIS 2016, Kraków, Poland, October 27–28, 2016, Proceedings

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Book Series: Communications in Computer and Information Science ISSN: 1865-0929 ISBN: 9783319472164 9783319472171 Year: Volume: 659 Pages: 278 DOI: 10.1007/978-3-319-47217-1 Language: English
Publisher: Springer Nature
Subject: Business and Management --- Transportation --- Manufactures --- Biotechnology --- Therapeutics --- Electrical and Nuclear Engineering
Added to DOAB on : 2017-03-08 12:46:55
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This book constitutes the refereed proceedings of the 31st International Symposium on Computer and Information Sciences, ISCIS 2016, held in Krakow, Poland, in October 2016.The 29 revised full papers presented were carefully reviewed and selected from 65 submissions. The papers are organized in topical sections on smart algorithms; data classification and processing; stochastic modelling; performance evaluation; queuing systems; wireless networks and security; image processing and computer vision.

Multilevel Modelling for Public Health and Health Services Research

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ISBN: 9783030348014 Year: Pages: 286 DOI: 10.1007/978-3-030-34801-4 Language: English
Publisher: Springer Nature
Subject: Public Health --- Medicine (General) --- Sociology --- Internal medicine --- Mathematics
Added to DOAB on : 2020-06-16 23:58:40
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This open access book is a practical introduction to multilevel modelling or multilevel analysis (MLA) – a statistical technique being increasingly used in public health and health services research. The authors begin with a compelling argument for the importance of researchers in these fields having an understanding of MLA to be able to judge not only the growing body of research that uses it, but also to recognise the limitations of research that did not use it. The volume also guides the analysis of real-life data sets by introducing and discussing the use of the multilevel modelling software MLwiN, the statistical package that is used with the example data sets. Importantly, the book also makes the training material accessible for download – not only the datasets analysed within the book, but also a freeware version of MLwiN to allow readers to work with these datasets. The book’s practical review of MLA comprises: Theoretical, conceptual, and methodological background Statistical background The modelling process and presentation of research Tutorials with example datasets Multilevel Modelling for Public Health and Health Services Research: Health in Context is a practical and timely resource for public health and health services researchers, statisticians interested in the relationships between contexts and behaviour, graduate students across these disciplines, and anyone interested in utilising multilevel modelling or multilevel analysis. “Leyland and Groenewegen’s wealth of teaching experience makes this book and its accompanying tutorials especially useful for a practical introduction to multilevel analysis.” ̶ Juan Merlo, Professor of Social Epidemiology, Lund University “Comprehensive and insightful. A must for anyone interested in the applications of multilevel modelling to population health”. ̶ S. (Subu) V. Subramanian, Professor of Population Health and Geography, Harvard University ; For researchers and students with a basic mastery of ordinary least squares and logistic regression Discusses multilevel analysis in context of public health, health services research, and epidemiology Includes an online component where users can download the datasets analyzed in the book, and also a freeware version of the multilevel modelling software MLwiN ​​​​​​​Can be used as part of a course on multilevel modelling, or as a self-training text

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