Statistical and Mathematical Foundations and R Scripts
Presents advanced techniques for the identifiability analysis, standard and
robust regression analysis of complex dynamical models
Illustrated with a wealth of real-world examples
Provides exercises and codes in R that are essential to statistical analysis
This richly illustrated book presents the objectives of, and the latest techniques for, the
identifiability analysis and standard and robust regression analysis of complex dynamical
models. The book first provides a definition of complexity in dynamic systems by introducing
readers to the concepts of system size, density of interactions, stiff dynamics, and hybrid nature
of determination. In turn, it presents the mathematical foundations of and algorithmic
procedures for model structural and practical identifiability analysis, multilinear and non-linear
regression analysis, and best predictor selection. Although the main fields of application
discussed in the book are biochemistry and systems biology, the methodologies described can
also be employed in other disciplines such as physics and the environmental sciences. Readers
will learn how to deal with problems such as determining the identifiability conditions,
searching for an identifiable model, and conducting their own regression analysis and
diagnostics without supervision. Featuring a wealth of real-world examples, exercises, and
codes in R, the book addresses the needs of doctoral students and researchers in
bioinformatics, bioengineering, systems biology, biophysics, biochemistry, the environmental
sciences and experimental physics. Readers should be familiar with the fundamentals of
probability and statistics (as provided in first-year university courses) and a basic grasp of R.
1st ed. 2020, X, 82 p. 13 illus., 8 illus. in color.
Softcover
ISBN 978-3-030-41254-8
Product category : Brief
Series : SpringerBriefs in Statistics
Offers an overview on optimization and control applied to real world problems
Addresses a wide range of subjects
Of interest to researchers as well as PhD students
This volume comprises high-quality works in pure and applied mathematics from the
mathematical communities in Spain and Brazil. A wide range of subjects are covered, ranging
from abstract algebra, including Lie algebras, commutative semigroups, and differential
geometry, to optimization and control in real world problems such as fluid mechanics, the
numerical simulation of cancer PDE models, and the stability of certain dynamical systems. The
book is based on contributions presented at the Second Joint Meeting Spain-Brazil in
Mathematics, held in Cádiz in December 2018, which brought together more than 330
delegates from around the world.All works were subjected to a blind peer review process. The
book offers an excellent summary of the recent activity of Spanish and Brazilian research
groups and will be of interest to researchers, PhD students, and graduate scholars seeking
upto-date knowledge on these pure and applied mathematics subjects
Due 2020-05-13
1st ed. 2020, X, 170 p. 40
illus., 25 illus. in color.
Hardcover
ISBN 978-3-030-41320-0
Product category : Contributed volume
Series : RSME Springer Series
Accurate parameter determination supported by rigorous existence,
regularity, uniqueness, and stability results
Three innovative mathematical modelling approaches to complex ice state
(sea ice) and composition (morainic ice)
Novel method for event screening categorization of carbon dioxide
concentration time series
This book presents important recent applied mathematics research on environmental problems
and impacts due to climate change. Although there are inherent difficulties in addressing
phenomena that are part of such a complex system, exploration of the subject using
mathematical modelling is especially suited to tackling poorly understood issues in the field. It
is in this spirit that the book was conceived. It is an outcome of the International INDAM
Workshop Mathematical Approach to Climate Change Impacts MAC2I held in
Rome in
March 2017. The workshop comprised four sessions, on Ecosystems, Hydrology, Glaciology, and
Monitoring. The book includes peer-reviewed contributions on research issues discussed during
each of these sessions or generated by collaborations among the specialists involved. Accurate
parameter determination techniques are explained and innovative mathematical modelling
approaches, presented. The book also provides useful material and mathematical problemsolving
tools for doctoral programs dealing with the complexities of climate change.
Due 2020-05-19
1st ed. 2020, XVI, 237 p. 58
illus., 40 illus. in color.
Hardcover
ISBN 978-3-030-38668-9
Product category : Contributed volume
Series : Springer INdAM Series
Serves as an introductory text to the basic concepts of infinite-dimensional
system theory
Contains detailed proofs of precise results with worked-out examples
throughout
Provides many exercises for each chapter
Supplements references with a large appendix for further reading
Infinite-dimensional systems is a well established area of research with an ever increasing
number of applications. Given this trend, there is a need for an introductory text treating
system and control theory for this class of systems in detail. This textbook is suitable for
courses focusing on the various aspects of infinite-dimensional state space theory. This book is
made accessible for mathematicians and post-graduate engineers with a minimal background
in infinite-dimensional system theory. To this end, all the system theoretic concepts introduced
throughout the text are illustrated by the same types of examples, namely, diffusion equations,
wave and beam equations, delay equations and the new class of platoon-type systems. Other
commonly met distributed and delay systems can be found in the exercise sections. Every
chapter ends with such a section, containing about 30 exercises testing the theoretical
concepts as well. An extensive account of the mathematical background assumed is contained
in the appendix
Due 2020-05-12
1st ed. 2020, XII, 754 p. 22 illus.
Hardcover
ISBN 978-1-0716-0588-2
Product category : Graduate/advanced undergraduate textbook
Series : Texts in Applied Mathematics
Commemorates the life and mathematical work of Jonathan M. Borwein
Provides in depth discussions on 5 prominent fields of mathematics
Accessible to students and researchers from a broad swath of mathematics
Students and researchers from all fields of mathematics are invited to read and treasure this
special Proceedings. A conference was held 25 -9 September 2017 at Noah
On the Beach,
Newcastle, Australia, to commemorate the life and work of Jonathan M. Borwein, a
mathematician extraordinaire whose untimely passing in August 2016 was a sorry loss to
mathematics and to so many members of its community, a loss that continues to be keenly
felt. A polymath, Jonathan Borwein ranks among the most wide ranging and influential
mathematicians of the last 50 years, making significant contributions to an exceptional diversity
of areas and substantially expanding the use of the computer as a tool of the research
mathematician. The contributions in this commemorative volume probe Dr. Borwein's ongoing
legacy in areas where he did some of his most outstanding work: Applied Analysis,
Optimization and Convex Functions; Mathematics Education; Financial Mathematics; plus
Number Theory, Special Functions and Pi, all tinged by the double prisms of Experimental
Mathematics and Visualization, methodologies he championed.
Due 2020-04-30
1st ed. 2020, XXIII, 439 p.71 illus., 32 illus. in color.
Hardcover
ISBN 978-3-030-36567-7
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistics
Shows the advantages of operational risk data analysis
Introduces an impartial method for identifying the risk classes for operational
risk losses
Uses the R software to implement the proposed procedures
This concise book for practitioners presents the statistical analysis of operational risk, which is
considered the most relevant source of bank risk, after market and credit risk. The book shows
that a careful statistical analysis can improve the results of the popular loss distribution
approach. The authors identify the risk classes by applying a pooling rule based on statistical
tests of goodness-of-fit, use the theory of the mixture of distributions to analyze the loss
severities, and apply copula functions for risk class aggregation. Lastly, they assess operational
risk data in order to estimate the so-called capital-at-risk that represents the minimum capital
requirement that a bank has to hold. The book is primarily intended for quantitative analysts
and risk managers, but also appeals to graduate students and researchers interested in bank
risks.
1st ed. 2020, IX, 84 p. 68 illus., 44 illus. in color.
Softcover
ISBN 978-3-030-42579-1
Product category : Brief
Series : SpringerBriefs in Statistics
Is the first introductory textbook for the Iitaka conjecture
Gives a simple new proof of Viehweg's conjecture for fiber spaces whose
geometric generic fiber is of general type
Provides a very accessible account for Viehweg's theory of weakly positive
sheaves and big sheaves
The ambitious program for the birational classification of higher-dimensional complex algebraic
varieties initiated by Shigeru Iitaka around 1970 is usually called the Iitaka program. Now it is
known that the heart of the Iitaka program is the Iitaka conjecture, which claims the
subadditivity of the Kodaira dimension for fiber spaces. The main purpose of this book is to
make the Iitaka conjecture more accessible. First, Viehweg's theory of weakly positive sheaves
and big sheaves is described, and it is shown that the Iitaka conjecture follows from the
Viehweg conjecture. Then, the Iitaka conjecture is proved in some special and interesting cases.
A relatively simple new proof of Viehweg's conjecture is given for fiber spaces whose geometric
generic fiber is of general type based on the weak semistable reduction theorem due to
Abramovickaru and the existence theorem of relative canonical models by
Birkaascin
HaconcKernan. No deep results of the theory of variations of Hodge structure
are needed.
The Iitaka conjecture for fiber spaces whose base space is of general type is also proved as an
easy application of Viehweg's weak positivity theorem, and the Viehweg conjecture for fiber
spaces whose general fibers are elliptic curves is explained. Finally, the subadditivity of the
logarithmic Kodaira dimension for morphisms of relative dimension one is proved. In this book,
for the reader's convenience, known arguments as well as some results are simplified and
generalized with the aid of relatively new techniques
Due 2020-05-31
1st ed. 2020, XI, 112 p. 52 illus.
Softcover
ISBN 978-981-15-3346-4
Product category : Brief
Series : SpringerBriefs in Mathematics