Mathematical and Statistical Applications in Life Sciences and Engineering

373 Pages·2017·7.339 MB·English

by  Avishek Adhikari,Mahima Ranjan Adhikari,Yogendra Prasad Chaubey (eds.)

Avishek Adhikari
Mahima Ranjan Adhikari
Yogendra Prasad Chaubey E ditors
Mathematical
and Statistical
Applications in
Life Sciences and
Engineering
Mathematical and Statistical Applications in Life
Sciences and Engineering
Avishek Adhikari Mahima Ranjan Adhikari
(cid:129)
Yogendra Prasad Chaubey
Editors
Mathematical and Statistical
Applications in Life Sciences
and Engineering
123
Editors
Avishek Adhikari Yogendra PrasadChaubey
Department ofPure Mathematics Department ofMathematics andStatistics
University of Calcutta Concordia University
Kolkata, West Bengal Montreal,QC
India Canada
Mahima RanjanAdhikari
IMBIC
Kolkata, West Bengal
India
ISBN978-981-10-5369-6 ISBN978-981-10-5370-2 (eBook)
https://doi.org/10.1007/978-981-10-5370-2
LibraryofCongressControlNumber:2017953827
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Preface
This is the commemoration volume celebrating the 10th foundation anniversary
of the Institute for Mathematics, Bioinformatics, Information Technology and
Computer Science (IMBIC), a research institute that was founded in India in 2006
withbranchesinSwedenandJapan,andisdedicatedtothescientificandtechnical
activities at the forefront of various areas across interdisciplinary Mathematics,
Statistics, and Computer Science.
To achieve its objectives, IMBIC organizes international interdisciplinary con-
ferences in every December in Kolkata on “Mathematical Sciences for
Advancement of Science and Technology (MSAST).” The conference MSAST
2016wasthe10thoftheseriesoftheseconferences.Prominentmathematiciansand
statisticians were invited to contribute articles to the celebration of this milestone.
The response was overwhelming. The present volume was conceived in order to
exhibitthebeautyofmathematicsandstatisticsandemphasizeapplicationsinallied
sciences. In order to achieve this goal, eminent scientists featuring such contribu-
tions were invited to contribute to the volume. As a culmination of this effort, the
present volume contains articles covering a wide range of topics of current
importance.
The articles on mathematical applications cover the topics of coloring problem,
control of stochastic structures, and information dynamics, whereas the articles on
statistical applications cover the areas on image denoising, life testing and relia-
bility, survival and frailty models, analysis of drought periods, prediction of
genomicprofiles,competingrisks,environmentalapplications,andchronicdisease
control.Thearticlescontainedinthisvolumepresentstate-of-the-artmaterialalong
with a detailed and lucid review of the relevant topics and issues concerned. This
volume reports on the newest developments in some of the interesting and
promising areas of mathematical and statistical research today, and is expected to
provideanimportantresourceforresearchersandpractitionersintherelevantareas
mentioned above. The key features of this volume such as
v
vi Preface
(cid:129) Focus on mathematical and statistical applications in a single volume,
(cid:129) Accessible and lucid presentation,
(cid:129) Detailed review of the cutting edge technologies,
(cid:129) Articles from the worldwide experts in the field, and
(cid:129) Wide range of topics on applications of modern relevance,
are expanded in 16 book chapters.
Mathematicalapplicationsspanthefirstthreechapters.Chapter1dealswiththe
problem of allocating radio frequencies to the base stations of the cellular network
suchthatinterference betweenstationsatadifferent distance canbeavoidedwhile
keepingtherangeofdistinctfrequenciestoaminimum.Chapter2discussestheuse
of vibration control techniques in order to control or suppress wild vibrations in
structures caused by resonance or flutter due to external sources along with a
numericalexamplewitharecordeddatasetfromaCaliforniaearthquake.Chapter3
discusses the solutions of Hamilton ODE’s and Hamilton–Jacobi PDE’s involving
single-time and multi-time higher-order Lagrangians, and is expected to be of
interest to engineers and applied mathematicians.
Statistical applications span the next 13 chapters. Chapter 4 presents a com-
prehensive overview of the denoising problem and subsequent development in the
context of cDNA microarray images, in the context of genomic research, where
wavelet-based methods have been quite useful. Chapter 5 introduces a
transformation-baseddistributionfamilyappropriateforhazardmodelingwherethe
well-known Weibull model may fail, and Chap. 6 introduces yet another family
basedontheso-calledmode-centricGaussiandistributionasafraternaltwinofthe
Gaussian distribution appropriate for life-data models.
Chapter7considerstheuseofstochasticvolatilitymodelsforanalyzingdrought
periods with discussions of real examples. Chapter 8 gives a new estimator of the
meanresiduallifefunctionandcomparesitsperformancewithothernonparametric
estimatorsavailableintheliteraturewhileillustratingtherelevanceoftheresultson
a real dataset. Chapter 9 gives a detailed overview of techniques for predicting
outcomes such as colon cancer survival from diverse genomic profiles whereas
Chap. 10 discusses a bivariate frailty model with an application to competing risk
theory. Chapter 11 considers the estimation of the stress strength parameter under
the Bayesian paradigm with illustrations on a real dataset.
Chapter12reportsonthespatiotemporalanalysisofairpollutioneffectsonclinic
visitsusingthedatafromTaiwanthatisbasedonseveralBayesiantechniques,and
Chap. 13 gives a comprehensive review of statistical inference procedures in the
contextofcompetingriskswhenthecauseoffailuremaybemissingormaskedfor
someunits.Chapter14discussesandillustratesseveralenvironmentalapplications
based on the Birnbaum–Saunders model, and Chap. 15 considers multistate mod-
eling in the context of data on chronic conditions from individuals in disease reg-
istries.Thefinalchapter,Chap.16,presentsestimationforlifetimecharacteristicsin
connectionwitha time-constrained life-testing experiment.
We had invited more than 50 potential contributors, and 19 articles were sub-
mitted. After a careful review, 16 articles were selected that make the 16 chapters
Preface vii
of the present volume. We are thankful to all the contributors to this volume and
especiallytothecorrespondingauthorsfortheircooperationandtimelysubmission
of the articles and revisions. We have derived substantial help in reviewing these
articles from the following reviewers to whom we owe our immense gratitude:
Jorge A.Achcar (Brazil), Koby Asubonteng (USA), Saria Awadalla (USA), M.
L. Lakhal-Chaieb (Canada), Ashish K. Chattopadhyay (India), Propser Donovon
(Canada), Sujit K. Ghosh (USA), David Hanagal (India), Tamanna Howlader
(Bangladesh), Abdulkadir Hussein (Canada), Nachimuthu Manickam (USA),
Manoel Santos-Neto (Brazil), Partha Sarathi Roy (Japan), Satyajit Roy (India),
Helton Saulo (Brazil), and Jingjing Wu (Canada).
Weapologizeforanyomissions.WearealsogratefultoSpringerforpublishing
thisvolumeandtoallindividualswhohaveextendedtheirsupportandcooperation
in order to bring the project of IMBIC for publishing this commemorative volume
to fruition.
Kolkata, India Avishek Adhikari
Kolkata, India Mahima Ranjan Adhikari
Montreal, Canada Yogendra Prasad Chaubey
August, 2017
Contents
Part I Mathematics
1 Hole: An Emerging Character in the Story of Radio k-Coloring
Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Ushnish Sarkar and Avishek Adhikari
2 Robust Control of Stochastic Structures Using Minimum Norm
Quadratic Partial Eigenvalue Assignment Technique . . . . . . . . . . . 43
Kundan Goswami, Sonjoy Das and Biswa Nath Datta
3 Single-Time and Multi-Time Hamilton–Jacobi Theory Based on
Higher Order Lagrangians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Savin Treanţă and Constantin Udrişte
Part II Statistics
4 On Wavelet-Based Methods for Noise Reduction of cDNA
Microarray Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Tamanna Howlader, S. M. Mahbubur Rahman
and Yogendra Prasad Chaubey
5 A Transformation for the Analysis of Unimodal Hazard Rate
Lifetimes Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Kobby Asubonteng, Govind S. Mudholkar and Alan Hutson
6 The Power M-Gaussian Distribution: An R-Symmetric Analog
of the Exponential-Power Distribution . . . . . . . . . . . . . . . . . . . . . . 141
Saria Salah Awadalla, Govind S. Mudholkar and Ziji Yu
7 Stochastic Volatility Models (SVM) in the Analysis of Drought
Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Jorge Alberto Achcar, Roberto Molina de Souza
and Emílio Augusto Coelho-Barros
ix
x Contents
8 NonparametricEstimationofMeanResidualLifeFunctionUsing
Scale Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Sujit K. Ghosh and Shufang Liu
9 Something Borrowed, Something New: Precise Prediction of
Outcomes from Diverse Genomic Profiles. . . . . . . . . . . . . . . . . . . . 193
J. Sunil Rao, Jie Fan, Erin Kobetz and Daniel Sussman
10 Bivariate Frailty Model and Association Measure. . . . . . . . . . . . . . 209
Ramesh C. Gupta
11 On Bayesian Inference of R = P(Y < X)
for Weibull Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Debasis Kundu
12 AirPollutionEffectsonClinicVisitsinSmallAreasofTaiwan:A
Review of Bayesian Spatio-Temporal Analysis . . . . . . . . . . . . . . . . 247
Atanu Biswas and Jean-Francois Angers
13 On Competing Risks with Masked Failures . . . . . . . . . . . . . . . . . . 257
Isha Dewan and Uttara Naik-Nimbalkar
14 Environmental Applications Based on Birnbaum–Saunders
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
Víctor Leiva and Helton Saulo
15 Analysis of Chronic Disease Processes Based on Cohort and
Registry Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
Richard J. Cook and Jerald F. Lawless
16 Exact Likelihood-Based Point and Interval Estimation for
Lifetime Characteristics of Laplace Distribution Based on a
Time-Constrained Life-Testing Experiment . . . . . . . . . . . . . . . . . . 327
Xiaojun Zhu and N. Balakrishnan
Editors and Contributors
About the Editors
Avishek Adhikari, Ph.D. is Assistant Professor of Pure Mathematics at the University of
Calcutta.HeisarecipientofthePresidentofIndiaMedalandYoungScientistAward.Hewasa
post-doctorate fellow at the Research Institute INRIA, Rocquencourt, France. He was a visiting
scientist at Indian Statistical Institute, Kolkata, and Linkoping University, Sweden. He visited
many institutions in India, Japan, Sweden, France, England, Switzerland, and South Korea on
invitation.Hismaininterestliesinalgebra,cryptology,discretemathematics,theoreticalcomputer
science, and their applications. He has published four textbooks on mathematics including one
bookBasicModernAlgebrawithApplications(Springer)andeditedoneresearchmonograph.He
haspublished several papers inforeign journals of international repute, conference proceedings,
andbookchapters.FourstudentshavealreadybeenawardedPh.D.degreeunderhisguidance.He
successfullycompletedseveralprojectsfundedbytheGovernmentofIndiaandisamemberofthe
research teams from India for collaborative Indo-Japan (DST-JST and DST-JSPS) research pro-
jects. He is a member on editorial board of several journals and Founder Secretary (honorary)
oftheResearchInstituteIMBICandTreasurer(honorary)oftheCryptologyResearchSocietyof
India(CRSI).
Mahima Ranjan Adhikari, Ph.D. is the Founder President of the Institute for Mathematics,
Bioinformatics, Information Technology and Computer Science (IMBIC), Kolkata, and former
ProfessorofPureMathematicsattheUniversityofCalcutta.Hehaspublishedanumberofpapers
in several Indian and foreign journals including Proceedings of American Mathematical Society
and eight textbooks including Basic Modern Algebra with Applications (Springer) and Basic
AlgebraicTopologyanditsApplications(Springer).Twelvestudentshavealreadybeenawarded
Ph.D.degreeunderhisguidanceonvarioustopicssuchasalgebra,algebraictopology,category
theory,geometry,analysis,graphtheory,knottheory,andhistoryofmathematics.Heisamember
of American Mathematical Society and on the editorial board of several Indian and foreign
journalsandresearchmonographs.HewaselectedasthepresidentoftheMathematicalScience
Section (including Statistics) of the 95th Indian Science Congress, 2008. He visited several
institutions in India, USA, UK, China, Japan, France, Greece, Sweden, Switzerland, Italy, and
manyothercountriesoninvitation.
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