Spatal Dynamics Models in the Life Sciences and the Role of Feedback in Robust Developments

Frederic Y M Wan University of California, Irvine, USA

Key Features

• Provides a comprehensive overview o histor and politcs in China since 949

• pplies a thematc approach revoluton, recover and re uvenaton encompassing a chronological breakdown o events

• E amines the rise and re uvenaton o China not ust within an economic and militar conte t but also within ramework o increasingl dominant Chinese discourses

• ddresses topical issues such as human rights, environment and natonalism

Descripton

Basic mathematcal techniques for partal diferental equatons (PDE) with applicatons to the life sciences form an integral part of the core curriculum for programs in mathematcal biology. et, students in such a program with an undergraduate training in biolog are t picall defcient in an e posure to P E. his volume starts with simple frst order P E and progresses through higher order e uatons and s stems but with interestng applicatons, even at the level o a single frst order P E with constant coe cients.

Similar to the two previous volumes b the author, another uni ue eature o the book is highlightng the scientfc theme(s) o interest or the biological phenomena being modelled and anal sed. n additon to temporal evoluton o a biological phenomenon, its limitng e uilibrium states and their stabilit , the possibilit o locatonal variatons leads to a stud o additonal themes such as (signal and wave) propagaton, spatal pa erning and robustness. he re uirement that biological developments are relatvel insensitve to sustained environmental changes provides an opportunit to e amine the issue o eedback and robustness not encountered in the previous two volumes o this series.

Author

Frederic Wan has been a Pro essor o athematcs at the Universit o Cali ornia, rvine (UC ) since 995 where he was also ice Chancellor or esearch and ean o Graduate Studies, 995 2000. Prior to UC , Pro essor Wan received S , S and Ph in athematcs at ( 955 965) and was on the acult o the athematcs epartment ( 965 974). He was appointed Pro essor o athematcs and the ounding irector o the nsttute o pplied athematcs and Statstcs at the Universit o ritsh Columbia ( 974 983). n 983, Pro essor Wan relocated to the Universit o Washington as Pro essor ( 983 995) and the ounding Chair o epartment o pplied athematcs ( 983 988), and later the ivisional ean o atural and athematcal Sciences ( 988 992). t the re uest o the atonal Science oundaton ( S ), Pro essor Wan was re assigned b the Universit to serve as the irector o the oundaton s ivision o athematcal Sciences ( 992 994). or his research contributons (supported b both S and the atonal nsttute o Health ( H)), Pro essor Wan was elected a ellow o S E, S, S and a oreign ember o the ussian cadem o atural Sciences among others.

January 2023

£100 | HARDCOVER 978 98 25 656

Imprint: World Scientfc Publishing Compan

Extent: 420pp

Type: e tbook

Main Subject: athematcs

Sub-Subjects: athematcal iolog athematcal odeling iomathematcs issue Engineering rdinar i erental E uatons Partal i erental E uatons

Keywords: athematcal iolog Spatal namics odels in Li e Sciences obust iological evelopments Partal i erental E uatons S stems iolog eedback in iological evelopments iological issue Pa erning ultple Concurrent eedback

Readership: eginning graduate students and upper division undergraduates in mathematcal biolog . lso accessible to researchers in the li e sciences interested in spatall nonuni orm models but with li le or no background in partal di erental e uatons

• enewal and Propagaton

• ethod o Characteristcs

• rownian oton and Heat Conducton

• Eigen uncton E pansions

• Well Posedness

• shore erritorial Sovereignt

• eacton i usion S stems

• raveling Waves

• raveling Waves in Higher rder onlinear odels

• n E tracellular ne i usive orphogen odel

• on receptors

• obust evelopment 29

• Earl eedback odels toward obust Signaling

• Spatall Uni orm Concurrent eedback

• Spatall onuni orm Concurrent eedback