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Books > Science & Mathematics > Mathematics
This volume considers resistance networks: large graphs which are
connected, undirected, and weighted. Such networks provide a
discrete model for physical processes in inhomogeneous media,
including heat flow through perforated or porous media. These
graphs also arise in data science, e.g., considering
geometrizations of datasets, statistical inference, or the
propagation of memes through social networks. Indeed, network
analysis plays a crucial role in many other areas of data science
and engineering. In these models, the weights on the edges may be
understood as conductances, or as a measure of similarity.
Resistance networks also arise in probability, as they correspond
to a broad class of Markov chains.The present volume takes the
nonstandard approach of analyzing resistance networks from the
point of view of Hilbert space theory, where the inner product is
defined in terms of Dirichlet energy. The resulting viewpoint
emphasizes orthogonality over convexity and provides new insights
into the connections between harmonic functions, operators, and
boundary theory. Novel applications to mathematical physics are
given, especially in regard to the question of self-adjointness of
unbounded operators.New topics are covered in a host of areas
accessible to multiple audiences, at both beginning and more
advanced levels. This is accomplished by directly linking diverse
applied questions to such key areas of mathematics as functional
analysis, operator theory, harmonic analysis, optimization,
approximation theory, and probability theory.
Data Science: Theory and Applications, Volume 44 in the Handbook of
Statistics series, highlights new advances in the field, with this
new volume presenting interesting chapters on a variety of
interesting topics, including Modeling extreme climatic events
using the generalized extreme value distribution, Bayesian Methods
in Data Science, Mathematical Modeling in Health Economic
Evaluations, Data Science in Cancer Genomics, Blockchain
Technology: Theory and Practice, Statistical outline of animal home
ranges, an application of set estimation, Application of Data
Handling Techniques to Predict Pavement Performance, Analysis of
individual treatment effects for enhanced inferences in medicine,
and more. Additional sections cover Nonparametric Data Science:
Testing Hypotheses in Large Complex Data, From Urban Mobility
Problems to Data Science Solutions, and Data Structures and
Artificial Intelligence Methods.
A recent development is the discovery that simple systems of
equations can have chaotic solutions in which small changes in
initial conditions have a large effect on the outcome, rendering
the corresponding experiments effectively irreproducible and
unpredictable. An earlier book in this sequence, Elegant Chaos:
Algebraically Simple Chaotic Flows provided several hundred
examples of such systems, nearly all of which are purely
mathematical without any obvious connection with actual physical
processes and with very limited discussion and analysis.In this
book, we focus on a much smaller subset of such models, chosen
because they simulate some common or important physical phenomenon,
usually involving the motion of a limited number of point-like
particles, and we discuss these models in much greater detail. As
with the earlier book, the chosen models are the mathematically
simplest formulations that exhibit the phenomena of interest, and
thus they are what we consider 'elegant.'Elegant models, stripped
of unnecessary detail while maximizing clarity, beauty, and
simplicity, occupy common ground bordering both real-world modeling
and aesthetic mathematical analyses. A computational search led one
of us (JCS) to the same set of differential equations previously
used by the other (WGH) to connect the classical dynamics of Newton
and Hamilton to macroscopic thermodynamics. This joint book
displays and explores dozens of such relatively simple models
meeting the criteria of elegance, taste, and beauty in structure,
style, and consequence.This book should be of interest to students
and researchers who enjoy simulating and studying complex particle
motions with unusual dynamical behaviors. The book assumes only an
elementary knowledge of calculus. The systems are initial-value
iterated maps and ordinary differential equations but they must be
solved numerically. Thus for readers a formal differential
equations course is not at all necessary, of little value and
limited use.
Classical Deformation Theory is used for determining the
completions of the local rings of an eventual moduli space. When a
moduli variety exists, a main result in the book is that the local
ring in a closed point can be explicitly computed as an
algebraization of the pro-representing hull (therefore, called the
local formal moduli) of the deformation functor for the
corresponding closed point.The book gives explicit computational
methods and includes the most necessary prerequisites. It focuses
on the meaning and the place of deformation theory, resulting in a
complete theory applicable to moduli theory. It answers the
question 'why moduli theory' and it give examples in mathematical
physics by looking at the universe as a moduli of molecules.
Thereby giving a meaning to most noncommutative theories.The book
contains the first explicit definition of a noncommutative scheme,
covered by not necessarily commutative rings. This definition does
not contradict any of the previous abstract definitions of
noncommutative algebraic geometry, but rather gives interesting
relations to other theories which is left for further
investigation.
The Blockchain Technology for Secure and Smart Applications across
Industry Verticals, Volume 121, presents the latest information on
a type of distributed ledger used for maintaining a permanent and
tamper-proof record of transactional data. The book presents a
novel compendium of existing and budding Blockchain technologies
for various smart applications. Chapters in this new release
include the Basics of Blockchain, The Blockchain History,
Architecture of Blockchain, Core components of Blockchain,
Blockchain 2.0: Smart Contracts, Empowering Digital Twins with
Blockchain, Industrial Use Cases at the Cusp of the IoT and
Blockchain Paradigms, Blockchain Components and Concepts, Digital
Signatures, Accumulators, Financial Systems, and more. This book is
a unique effort to illuminate various techniques to represent,
improve and authorize multi-institutional and multidisciplinary
research in a different type of smart applications, like the
financial system, smart grid, transportation system, etc. Readers
in identity-privacy, traceability, immutability, transparency,
auditability, and security will find it to be a valuable resource.
Besides their intrinsic mathematical interest, geometric partial
differential equations (PDEs) are ubiquitous in many scientific,
engineering and industrial applications. They represent an
intellectual challenge and have received a great deal of attention
recently. The purpose of this volume is to provide a missing
reference consisting of self-contained and comprehensive
presentations. It includes basic ideas, analysis and applications
of state-of-the-art fundamental algorithms for the approximation of
geometric PDEs together with their impacts in a variety of fields
within mathematics, science, and engineering.
The Handbook of Reliability, Maintenance, and System Safety through
Mathematical Modeling discusses the many factors affect reliability
and performance, including engineering design, materials,
manufacturing, operations, maintenance, and many more. Reliability
is one of the fundamental criteria in engineering systems design,
with maintenance serving as a way to support reliability throughout
a system's life. Addressing these issues requires information,
modeling, analysis and testing. Different techniques are proposed
and implemented to help readers analyze various behavior measures
(in terms of the functioning and performance) of systems.
The modelling of systems by differential equations usually requires
that the parameters involved be completely known. Such models often
originate from problems in physics or economics where we have
insufficient information on parameter values. One important class
of stochastic mathematical models is stochastic partial
differential equations (SPDEs), which can be seen as deterministic
partial differential equations (PDEs) with finite or infinite
dimensional stochastic processes - either with colour noise or
white noise. Though white noise is a purely mathematical
construction, it can be a good model for rapid random
fluctuations.This research monograph concerns analysis of
discrete-time approximations for stochastic differential equations
(SDEs) driven by Wiener processes. The first chapter of the book
provides a theoretical basis for working with SDEs and stochastic
processes.This book has been written in a simple and clear
mathematical logical language. The basic definitions and theorems
on stochastic calculus have been provided initially. Each chapter
contains illustrated examples via figures and tables. Problems are
included which will help readers understand the theories better.
Also, the reader can construct new wavelets by using the procedure
presented in the book. It will certainly fill up the blank space
that the lack of a comprehensive book has caused.
AI and Cloud Computing, Volume 120 in the Advances in Computers
series, highlights new advances in the field, with this updated
volume presenting interesting chapters on topics including A
Deep-forest based Approach for Detecting Fraudulent Online
Transaction, Design of Cyber-Physical-Social Systems with
Forensic-awareness Based on Deep Learning, Review on
Privacy-preserving Data Comparison Protocols in Cloud Computing,
Fingerprint Liveness Detection Using an Improved CNN with the
Spatial Pyramid Pooling Structure, Protecting Personal Sensitive
Data Security in the Cloud with Blockchain, and more.
This is a book for the second course in linear algebra whereby
students are assumed to be familiar with calculations using real
matrices. To facilitate a smooth transition into rigorous proofs,
it combines abstract theory with matrix calculations.This book
presents numerous examples and proofs of particular cases of
important results before the general versions are formulated and
proved. The knowledge gained from a particular case, that
encapsulates the main idea of a general theorem, can be easily
extended to prove another particular case or a general case. For
some theorems, there are two or even three proofs provided. In this
way, students stand to gain and study important results from
different angles and, at the same time, see connections between
different results presented in the book.
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