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This book includes papers in crossdisciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cuttingedge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a mustread for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods.
human behaviour  organisational risk  multicriteria decisionmaking  DEMATEL  bottling process  cellular automata  game of life  brain dynamics  random nonautonomous second order linear differential equation  mean square analytic solution  random power series  uncertainty quantification  systems of nonlinear equations  iterative methods  Newton’s method  order of convergence  computational efficiency  basin of attraction  F110 frigate  decisionmaking  ASW  antitorpedo decoy  AHP  uncertainty modelling  Chikungunya disease  mathematical modeling  nonlinear dynamical systems  numerical simulations  parameter estimation  Markov chain Monte Carlo  block preconditioner  generalized eigenvalue problem  neutron diffusion equation  modified block Newton method  bone repair  macrophages  immune system  cytokines  stem cells  exponential polynomial  discrete dynamical systems  convergence  Hidden Markov models  mathematical linguistics  Voynich Manuscript  IPV  violence index  independence index  model  ode
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Modern biology is rapidly becoming a study of large sets of data. Understanding these data sets is a major challenge for most life sciences, including the medical, environmental, and bioprocess fields. Computational biology approaches are essential for leveraging this ongoing revolution in omics data. A primary goal of this Special Issue, entitled “Methods in Computational Biology”, is the communication of computational biology methods, which can extract biological design principles from complex data sets, described in enough detail to permit the reproduction of the results. This issue integrates interdisciplinary researchers such as biologists, computer scientists, engineers, and mathematicians to advance biological systems analysis. The Special Issue contains the following sections:•Reviews of Computational Methods•Computational Analysis of Biological Dynamics: From Molecular to Cellular to Tissue/Consortia Levels•The Interface of Biotic and Abiotic Processes•Processing of Large Data Sets for Enhanced Analysis•Parameter Optimization and Measurement
biomass reaction  computational biology  macromolecular composition  metabolic model  methods  metabolic network visualization  metabolic modelling  elementary flux modes visualization  flux balance analysis  ADAR  breast  cancer  inosine  microRNA  microRNA targeting  RNA editing  computational model  explanatory model  hybrid model  mechanism  mechanistic model  modeling methods  provenance  workflow  systems modeling  simulation  bioreactor integrated modeling  CFD simulation  compartmental modeling  reducedorder model  bioreactor operation optimization  ordinary differential equation  SREBP2  nonlinear dynamics  multiple time scales  geometric singular perturbation theory  bifurcation analysis  canardinduced EADs  calcium current  multiscale systems biology  computational biology  quantitative systems pharmacology (QSP)  immunooncology  immunotherapy  immune checkpoint inhibitor  mathematical modeling  gut microbiota dysbiosis  Clostridium difficile infection  bacterial biofilms  metabolic modeling  parameter optimization  differential evolution  evolutionary algorithm  bistable switch  oscillator  turning point bifurcation  Hopf bifurcation  biological networks  massaction networks  BioModels Database  n/a
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In order to measure and quantify the complex behavior of realworld systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and nonuniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineeringoriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and antisynchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.
multitime scale fractional stochastic differential equations  fractional Brownian motion  fractional stochastic partial differential equation  analytical solution  nonautonomous (autonomous) dynamical system  topological entropy  (asymptotical) focal entropy point  disturbation  mdimensional manifold  geometric nonlinearity  Bernoulli–Euler beam  colored noise  noise induced transitions  true chaos  Lyapunov exponents  wavelets  Lyapunov exponents  Wolf method  Rosenstein method  Kantz method  neural network method  method of synchronization  Benettin method  Fourier spectrum  Gauss wavelets  fractional calculus  Adomian decomposition  Mittag–Leffler function  descriptor fractional linear systems  regular pencils  Schur factorization  hyperchaotic system  selfsynchronous stream cipher  permutation entropy  image encryption  wavelet transform  product MValgebra  partition  Tsallis entropy  conditional Tsallis entropy  dynamical system  discrete chaos  discrete fractional calculus  hidden attractors  approximate entropy  stabilization  Information transfer  continuous flow  discrete mapping  Lorenz system  Chua’s system  deterministic chaos  random number generator  unbounded chaos  bounded chaos  phaselocked loop  Gaussian white noise  n/a
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Developing techniques for assessing various risks and calculating probabilities of ruin and survival are exciting topics for mathematicallyinclined academics. For practicing actuaries and financial engineers, the resulting insights have provided enormous opportunities but also created serious challenges to overcome, thus facilitating closer cooperation between industries and academic institutions. In this book, several renown researchers with extensive interdisciplinary research experiences share their thoughts that, in one way or another, contribute to the betterment of practice and theory of decision making under uncertainty. Behavioral, cultural, mathematical, and statistical aspects of risk assessment and modelling have been explored, and have been often illustrated using real and simulated data. Topics range from financial and insurance risks to securitytype risks, from onedimensional to multi and even infinitedimensional risks.
aggregate discounted claims  Markovian arrival process  partial integrodifferential equation  covariance  multivariate gamma distribution  multiplicative background risk model  aggregate risk  individual risk model  collective risk model  risk measure  cumulative Parisian ruin  stochastic orders  surplus process  renewal process  discounted aggregate claims  copulas  archimedean copulas  background risk  systematic risk  transfer function  information processing  order statistic  concomitant  ruin probability  dual risk model  constant interest rate  integral equation  Laplace transform  numerical approximation  maximal tail dependence  clustering  financial time series  weighted cuts  copula  national culture  survival analysis  hazard model  rating migrations  advanced measurement approach  confidence interval  Monte Carlo  operational risk  valueatrisk  central limit theorem  insurance  maxstable random fields  rate of spatial diversification  reinsurance  risk management  risk theory  spatial dependence  spatial risk measures and corresponding axiomatic approach  n/a
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.
highly oscillatory  convolution quadrature rule  volterra integral equation  Bessel kernel  convergence  higher order Schwarzian derivatives  Janowski starlike function  Janowski convex function  bound on derivatives  tangent numbers  tangent polynomials  Carlitztype qtangent numbers  Carlitztype qtangent polynomials  (p,q)analogue of tangent numbers and polynomials  (p,q)analogue of tangent zeta function  symmetric identities  zeros  Lommel functions  univalent functions  starlike functions  convex functions  inclusion relationships  analytic function  Hankel determinant  exponential function  upper bound  nonlinear boundary value problems  fractionalorder differential equations  RiemannStieltjes functional integral  LiouvilleCaputo fractional derivative  infinitepoint boundary conditions  advanced and deviated arguments  existence of at least one solution  Fredholm integral equation  Schauder fixed point theorem  Hölder condition  generalized Kuramoto–Sivashinsky equation  modified Kudryashov method  exact solutions  Maple graphs  analytic function  Hadamard product (convolution)  partial sum  Srivastava–Tomovski generalization of Mittag–Leffler function  subordination  differential equation  differential inclusion  Liouville–Caputotype fractional derivative  fractional integral  existence  fixed point  Bernoulli spiral  Grandi curves  Chebyshev polynomials  pseudoChebyshev polynomials  orthogonality property  symmetric  encryption  password  hash  cryptography  PBKDF  q–Bleimann–Butzer–Hahn operators  (p,q)integers  (p,q)Bernstein operators  (p,q)Bleimann–Butzer–Hahn operators  modulus of continuity  rate of approximation  Kfunctional  HurwitzLerch zeta function  generalized functions  analytic number theory  ?generalized HurwitzLerch zeta functions  derivative properties  series representation  basic hypergeometric functions  generating functions  qpolynomials  analytic functions  Mittag–Leffler functions  starlike functions  convex functions  Hardy space  vibrating string equation  initial conditions  spectral decomposition  regular solution  the uniqueness of the solution  the existence of a solution  analytic  ?convex function  starlike function  stronglystarlike function  subordination  q Sheffer–Appell polynomials  generating relations  determinant definition  recurrence relation  q Hermite–Bernoulli polynomials  q Hermite–Euler polynomials  q Hermite–Genocchi polynomials  Volterra integral equations  highly oscillatory Bessel kernel  Hermite interpolation  direct Hermite collocation method  piecewise Hermite collocation method  differential operator  qhypergeometric functions  meromorphic function  Mittag–Leffler function  Hadamard product  differential subordination  starlike functions  Bell numbers  radius estimate  (p, q)integers  Dunkl analogue  generating functions  generalization of exponential function  Szász operator  modulus of continuity  function spaces and their duals  distributions  tempered distributions  Schwartz testing function space  generalized functions  distribution space  wavelet transform of generalized functions  Fourier transform  analytic function  subordination  Dziok–Srivastava operator  nonlinear boundary value problem  nonlocal  multipoint  multistrip  existence  Ulam stability  functions of bounded boundary and bounded radius rotations  subordination  functions with positive real part  uniformly starlike and convex functions  analytic functions  univalent functions  starlike and qstarlike functions  qderivative (or qdifference) operator  sufficient conditions  distortion theorems  Janowski functions  analytic number theory  ?generalized Hurwitz–Lerch zeta functions  derivative properties  recurrence relations  integral representations  Mellin transform  natural transform  Adomian decomposition method  Caputo fractional derivative  generalized mittagleffler function  analytic functions  Hadamard product  starlike functions  qderivative (or qdifference) operator  Hankel determinant  qstarlike functions  fuzzy volterra integrodifferential equations  fuzzy general linear method  fuzzy differential equations  generalized Hukuhara differentiability  spectrum symmetry  DCT  MFCC  audio features  anuran calls  analytic functions  convex functions  starlike functions  strongly convex functions  strongly starlike functions  uniformly convex functions  Struve functions  truncatedexponential polynomials  monomiality principle  generating functions  Apostoltype polynomials and Apostoltype numbers  Bernoulli, Euler and Genocchi polynomials  Bernoulli, Euler, and Genocchi numbers  operational methods  summation formulas  symmetric identities  Euler numbers and polynomials  qEuler numbers and polynomials  HurwitzEuler eta function  multiple HurwitzEuler eta function  higher order qEuler numbers and polynomials  (p, q)Euler numbers and polynomials of higher order  symmetric identities  symmetry of the zero
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