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This book celebrates the 50th anniversary of the Institute of
Mathematics, Statistics and Scientific Computing (IMECC) of the
University of Campinas, Brazil, by offering reviews of selected
research developed at one of the most prestigious mathematics
institutes in Latin America. Written by senior professors at the
IMECC, it covers topics in pure and applied mathematics and
statistics ranging from differential geometry, dynamical systems,
Lie groups, and partial differential equations to computational
optimization, mathematical physics, stochastic process, time
series, and more. A report on the challenges and opportunities of
research in applied mathematics - a highly active field of research
in the country - and highlights of the Institute since its
foundation in 1968 completes this historical volume, which is
unveiled in the same year that the International Mathematical Union
(IMU) names Brazil as a member of the Group V of countries with the
most relevant contributions in mathematics.
This volume is a collection of research surveys on the Distance
Geometry Problem (DGP) and its applications. It will be divided
into three parts: Theory, Methods and Applications. Each part will
contain at least one survey and several research papers. The first
part, Theory, will deal with theoretical aspects of the DGP,
including a new class of problems and the study of its complexities
as well as the relation between DGP and other related topics, such
as: distance matrix theory, Euclidean distance matrix completion
problem, multispherical structure of distance matrices, distance
geometry and geometric algebra, algebraic distance geometry theory,
visualization of K-dimensional structures in the plane, graph
rigidity, and theory of discretizable DGP: symmetry and complexity.
The second part, Methods, will discuss mathematical and
computational properties of methods developed to the problems
considered in the first chapter including continuous methods (based
on Gaussian and hyperbolic smoothing, difference of convex
functions, semidefinite programming, branch-and-bound), discrete
methods (based on branch-and-prune, geometric build-up, graph
rigidity), and also heuristics methods (based on simulated
annealing, genetic algorithms, tabu search, variable neighborhood
search). Applications will comprise the third part and will
consider applications of DGP to NMR structure calculation, rational
drug design, molecular dynamics simulations, graph drawing and
sensor network localization. This volume will be the first edited
book on distance geometry and applications. The editors are in
correspondence with the major contributors to the field of distance
geometry, including important research centers in molecular biology
such as Institut Pasteur in Paris.
This book is about quantum computing and quantum algorithms. The
book starts with a chapter introducing the basic rules of quantum
mechanics and how they can be used to build quantum circuits and
perform computations. Further, Grover's algorithm is presented for
unstructured search discussing its consequences and applications.
Next, important techniques are discussed such as Quantum Fourier
Transform and quantum phase estimation. Finally, Shor's algorithm
for integer factorization is explained. At last, quantum walks are
explained in detail covering both the discrete and continuous time
models,and applications of this techniques are described for the
design and analyses of quantum algorithms.
This book celebrates the 50th anniversary of the Institute of
Mathematics, Statistics and Scientific Computing (IMECC) of the
University of Campinas, Brazil, by offering reviews of selected
research developed at one of the most prestigious mathematics
institutes in Latin America. Written by senior professors at the
IMECC, it covers topics in pure and applied mathematics and
statistics ranging from differential geometry, dynamical systems,
Lie groups, and partial differential equations to computational
optimization, mathematical physics, stochastic process, time
series, and more. A report on the challenges and opportunities of
research in applied mathematics - a highly active field of research
in the country - and highlights of the Institute since its
foundation in 1968 completes this historical volume, which is
unveiled in the same year that the International Mathematical Union
(IMU) names Brazil as a member of the Group V of countries with the
most relevant contributions in mathematics.
This book is a pedagogical presentation aimed at advanced
undergraduate students, beginning graduate students and
professionals who are looking for an introductory text to the field
of Distance Geometry, and some of its applications. This versions
profits from feedback acquired at undergraduate/graduate courses in
seminars and a number of workshops.
This volume is a collection of research surveys on the Distance
Geometry Problem (DGP) and its applications. It will be divided
into three parts: Theory, Methods and Applications. Each part will
contain at least one survey and several research papers. The first
part, Theory, will deal with theoretical aspects of the DGP,
including a new class of problems and the study of its complexities
as well as the relation between DGP and other related topics, such
as: distance matrix theory, Euclidean distance matrix completion
problem, multispherical structure of distance matrices, distance
geometry and geometric algebra, algebraic distance geometry theory,
visualization of K-dimensional structures in the plane, graph
rigidity, and theory of discretizable DGP: symmetry and complexity.
The second part, Methods, will discuss mathematical and
computational properties of methods developed to the problems
considered in the first chapter including continuous methods (based
on Gaussian and hyperbolic smoothing, difference of convex
functions, semidefinite programming, branch-and-bound), discrete
methods (based on branch-and-prune, geometric build-up, graph
rigidity), and also heuristics methods (based on simulated
annealing, genetic algorithms, tabu search, variable neighborhood
search). Applications will comprise the third part and will
consider applications of DGP to NMR structure calculation, rational
drug design, molecular dynamics simulations, graph drawing and
sensor network localization. This volume will be the first edited
book on distance geometry and applications. The editors are in
correspondence with the major contributors to the field of distance
geometry, including important research centers in molecular biology
such as Institut Pasteur in Paris.
This book offers a gentle introduction to key elements of Geometric
Algebra, along with their applications in Physics, Robotics and
Molecular Geometry. Major applications covered are the physics of
space-time, including Maxwell electromagnetism and the Dirac
equation; robotics, including formulations for the forward and
inverse kinematics and an overview of the singularity problem for
serial robots; and molecular geometry, with 3D-protein structure
calculations using NMR data. The book is primarily intended for
graduate students and advanced undergraduates in related fields,
but can also benefit professionals in search of a pedagogical
presentation of these subjects.
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