**Author**: François Charest

**Publisher:**American Mathematical Society

**ISBN:**147045310X

**Category :**Mathematics

**Languages :**en

**Pages :**178

**Book Description**

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A collection of twenty-one real-life probability puzzles and shows how to get numerical answers without having to solve complicated mathematical equations.

Probability and Conditional Expectations bridges the gap between books on probability theory and statistics by providing the probabilistic concepts estimated and tested in analysis of variance, regression analysis, factor analysis, structural equation modeling, hierarchical linear models and analysis of qualitative data. The authors emphasize the theory of conditional expectations that is also fundamental to conditional independence and conditional distributions. Probability and Conditional Expectations Presents a rigorous and detailed mathematical treatment of probability theory focusing on concepts that are fundamental to understand what we are estimating in applied statistics. Explores the basics of random variables along with extensive coverage of measurable functions and integration. Extensively treats conditional expectations also with respect to a conditional probability measure and the concept of conditional effect functions, which are crucial in the analysis of causal effects. Is illustrated throughout with simple examples, numerous exercises and detailed solutions. Provides website links to further resources including videos of courses delivered by the authors as well as R code exercises to help illustrate the theory presented throughout the book.

Illustrates by example the typical steps necessary in computer science to build a mathematical model of any programming paradigm . Presents results of a large and integrated body of research in the area of 'quantitative' program logics.

This volume is based on the 2008 Clifford Lectures on Information Flow in Physics, Geometry and Logic and Computation, held March 12-15, 2008, at Tulane University in New Orleans, Louisiana. The varying perspectives of the researchers are evident in the topics represented in the volume, including mathematics, computer science, quantum physics and classical and quantum information. A number of the articles address fundamental questions in quantum information and related topics in quantum physics, using abstract categorical and domain-theoretic models for quantum physics to reason about such systems and to model spacetime. Readers can expect to gain added insight into the notion of information flow and how it can be understood in many settings. They also can learn about new approaches to modeling quantum mechanics that provide simpler and more accessible explanations of quantum phenomena, which don't require the arcane aspects of Hilbert spaces and the cumbersome notation of bras and kets.

The continued digitalization of our society means that more and more things are getting connected electronically. Since currently used inorganic electronics are not well suited for these new applications because of costs and environmental issues, organic electronics can play an important role here. These essentially plastic materials are cheap to produce and relatively easy to recycle. Unfortunately, their poor performance has so far hindered widespread application beyond displays. One key component of any electronic device is the memory. For organic electronics several technologies are being investigated that could serve as memories. One of these are the ferroelectrics, materials that have a spontaneous electrical polarization that can be reversed with an electric field. This bistable polarization which shows hysteresis makes these materials excellent candidates for use as memories. This thesis focuses on a specific type of organic ferroelectric, the supramolecular discotics. These materials consist of disk?like molecules that form columns in which all dipolar groups are aligned, giving a macroscopic ferroelectric polarization. Of particular interest are the benzenetricarboxamides (BTA), which are used as a model system for the whole class of discotic ferroelectrics. BTA uses a core?shell architecture which allows for easy modification of the molecular structure and thereby the ferroelectric properties. To gain a deeper understanding of the switching processes in this organic ferroelectric BTA, both microscopic and analytical modeling are used. This is supported by experimental data obtained through electrical characterization. The microscopic model reduces the material to a collection of dipoles and uses electrostatics to calculate the probability that these dipoles flip. These flipping rates are the input for a kinetic Monte Carlo simulation (kMC), which simulates the behavior of the dipoles over time. With this model we simulated three different switching processes on experimental time and length scales: hysteresis loops, spontaneous depolarization, and switching transients. The results of these simulations showed a good agreement with experiments and we can rationalize the obtained parameter dependencies in the framework of thermally activated nucleation limited switching (TA?NLS). The microscopic character of the model allows for a unique insight into the nucleation process of the polarization switching. We found that nucleation happens at different locations for field driven polarization switching as compared to spontaneous polarization switching. Field?driven nucleation happens at the contacts, whereas spontaneous depolarization starts at defects. This means that retention times in disordered ferroelectrics could be improved by reducing the disorder, without affecting the coercive field. Detailed analysis of the nucleation process also revealed a critical nucleation volume that decreases with applied field, which explains the Merz?like field?dependence of the switching time observed in experiments. In parallel to these microscopic simulations we developed an analytical framework based on the theory of TA?NLS. This framework is mainly focused on describing the switching transients of disordered ferroelectrics. It can be combined with concepts of the Preisach model, which considers a non?ideal ferroelectric as a collection of ideal hysterons. We were able to relate these hysterons and the distribution in their up? and down?switching fields to the microscopic structure of the material and use the combined models to explain experimentally observed dispersive switching kinetics. Whereas ferroelectrics on their own could potentially serve as memories, the readout of ferroelectric memories becomes easier if they are combined with semiconductors. We have introduced several molecular materials following the same design principle of a core?shell structure, which uniquely combine ferroelectricity and semiconductivity in one material. The experimental IV?curves of these materials could be described using an asymmetric Marcus hopping model and show their potential as memories. The combination of modeling and experimental work in this thesis thereby provides an increased understanding of organic ferroelectrics, which is crucial for their application as memories.

Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

This book constitutes the refereed proceedings of the Cryptographer's Track at the RSA Conference 2014, CT-RSA 2014, held in San Francisco, CA, USA, in February 2014. The 25 papers presented in this volume were carefully reviewed and selected from 66 submissions. They are organized in topical sections on non-integral asymmetric functions, public-key encryption, hardware implementations, side-channel attacks, symmetric encryption and cryptanalysis, digital signatures, protocols, hash function cryptanalysis, and applications of cryptographic primitives.

This book discusses physical design and mask synthesis of directed self-assembly lithography (DSAL). It covers the basic background of DSAL technology, physical design optimizations such as placement and redundant via insertion, and DSAL mask synthesis as well as its verification. Directed self-assembly lithography (DSAL) is a highly promising patterning solution in sub-7nm technology.

This book presents contributions of international and local experts from the African Institute for Mathematical Sciences (AIMS-Cameroon) and also from other local universities in the domain of orthogonal polynomials and applications. The topics addressed range from univariate to multivariate orthogonal polynomials, from multiple orthogonal polynomials and random matrices to orthogonal polynomials and Painlevé equations. The contributions are based on lectures given at the AIMS-Volkswagen Stiftung Workshop on Introduction of Orthogonal Polynomials and Applications held on October 5–12, 2018 in Douala, Cameroon. This workshop, funded within the framework of the Volkswagen Foundation Initiative "Symposia and Summer Schools", was aimed globally at promoting capacity building in terms of research and training in orthogonal polynomials and applications, discussions and development of new ideas as well as development and enhancement of networking including south-south cooperation.