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Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicine

predator-prey model --- n/a --- uncertainty quantification --- identification of DNA-binding proteins --- chemostat --- numerical characterization --- differential equations --- uniform persistence --- spotting --- 2-combination --- wildfire --- chronic myeloid leukemia --- combination therapy --- liquid-solid-porous media seepage coupling --- dynamic model --- obesity --- epidermis --- articular cartilage --- androgen deprivation therapy --- quorum sensing --- mechano-electrochemical model --- bifurcations --- bacterial competition --- global stability --- cartilage degeneration --- flocculation --- dynamical system --- transport equations --- bootstrapping --- stationary distribution --- algae growth models --- hemodynamic model --- delay --- Raphidocelis subcapitata --- cartilage loading --- Daphnia magna --- cell-based vector --- switched harvest --- hepatitis B --- rich dynamics --- spotting distribution --- asymptotic theory --- tyrosine kinase inhibitors --- phylogenetic analysis --- immune response --- microcirculation load --- graphical representation --- intraguild predation --- numerical simulation --- bacterial inflammation --- data fitting --- immunomodulatory therapies --- drug therapy --- delay differential equations (DDE) --- global asymptotic stability --- model comparison tests --- optimal control --- generalized pseudo amino acid composition --- random perturbations --- limit cycle --- prostate cancer --- mathematical model --- mathematical modeling --- persistence --- equilibrium points

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This book collects selected high-quality papers published in 2018–2020 to inaugurate the “Natural Hazards” Section of the Geosciences journal. The topics encompass: trends in publications at international level in the field of natural hazards research; the role of Big Data in natural disaster management; assessment of seismic risk through the understanding and quantification of its different components; climatic/hydro-meteorological hazards; and finally, the scientific analysis and disaster forensics of recent natural hazard events. The target audience includes not only specialists, but also graduate students who wish to approach the challenging, but also fascinating

big data --- disaster management --- review --- natural hazards --- disaster --- scientometrics --- bibliometrics --- citation analysis --- NatCatSERVICE --- Sigma Explorer --- Oroville Dam --- spillway --- incident --- flood control --- flood-frequency analysis --- dam operation --- drought --- impacts --- exposure --- vulnerability --- risk --- policy --- risk assessment --- earthquake risk --- energy security --- reliability of power supply --- Eurasian Economic Union (EAEU) --- integration process --- common electricity market --- masonry aggregates --- vulnerability assessment --- vulnerability curves --- damage scenarios --- local hazard effect --- psychological representation of earthquakes --- open-ended and closed-questions surveys --- children --- seismic hazard assessment --- emotions --- emotional prevention --- African easterly wave --- attractor coexistence --- chaos --- hurricane --- limit cycle --- Lorenz model --- predictability --- recurrence --- extended range weather prediction --- Jakarta basin --- site effects --- shear-wave velocity --- urban fabrics --- seismic vulnerability --- critic analysis --- cost modelling --- urban preservation programming --- building works programming --- natural hazard --- earthquake --- dam spillway --- psychology --- cyber-infrastructure

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This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.

Partial differential equations --- Differential equations, Partial. --- Probabilities. --- Integration, Functional. --- Functional integration --- Functional analysis --- Integrals, Generalized --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- A priori estimate. --- Absolute continuity. --- Almost surely. --- Analytic continuation. --- Axiom. --- Big O notation. --- Boundary (topology). --- Boundary value problem. --- Bounded function. --- Calculation. --- Cauchy problem. --- Central limit theorem. --- Characteristic function (probability theory). --- Chebyshev's inequality. --- Coefficient. --- Comparison theorem. --- Continuous function (set theory). --- Continuous function. --- Convergence of random variables. --- Cylinder set. --- Degeneracy (mathematics). --- Derivative. --- Differential equation. --- Differential operator. --- Diffusion equation. --- Diffusion process. --- Dimension (vector space). --- Direct method in the calculus of variations. --- Dirichlet boundary condition. --- Dirichlet problem. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Elliptic operator. --- Elliptic partial differential equation. --- Equation. --- Existence theorem. --- Exponential function. --- Feynman–Kac formula. --- Fokker–Planck equation. --- Function space. --- Functional analysis. --- Fundamental solution. --- Gaussian measure. --- Girsanov theorem. --- Hessian matrix. --- Hölder condition. --- Independence (probability theory). --- Integral curve. --- Integral equation. --- Invariant measure. --- Iterated logarithm. --- Itô's lemma. --- Joint probability distribution. --- Laplace operator. --- Laplace's equation. --- Lebesgue measure. --- Limit (mathematics). --- Limit cycle. --- Limit point. --- Linear differential equation. --- Linear map. --- Lipschitz continuity. --- Markov chain. --- Markov process. --- Markov property. --- Maximum principle. --- Mean value theorem. --- Measure (mathematics). --- Modulus of continuity. --- Moment (mathematics). --- Monotonic function. --- Navier–Stokes equations. --- Nonlinear system. --- Ordinary differential equation. --- Parameter. --- Partial differential equation. --- Periodic function. --- Poisson kernel. --- Probabilistic method. --- Probability space. --- Probability theory. --- Probability. --- Random function. --- Regularization (mathematics). --- Schrödinger equation. --- Self-adjoint operator. --- Sign (mathematics). --- Simultaneous equations. --- Smoothness. --- State-space representation. --- Stochastic calculus. --- Stochastic differential equation. --- Stochastic. --- Support (mathematics). --- Theorem. --- Theory. --- Uniqueness theorem. --- Variable (mathematics). --- Weak convergence (Hilbert space). --- Wiener process.

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This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. Such a framework is imperative for modern complex engineering systems that involve interacting continuous-time and discrete-time dynamics with multiple modes of operation that place stringent demands on controller design and require implementation of increasing complexity--whether advanced high-performance tactical fighter aircraft and space vehicles, variable-cycle gas turbine engines, or air and ground transportation systems. Impulsive and Hybrid Dynamical Systems goes beyond similar treatments by developing invariant set stability theorems, partial stability, Lagrange stability, boundedness, ultimate boundedness, dissipativity theory, vector dissipativity theory, energy-based hybrid control, optimal control, disturbance rejection control, and robust control for nonlinear impulsive and hybrid dynamical systems. A major contribution to mathematical system theory and control system theory, this book is written from a system-theoretic point of view with the highest standards of exposition and rigor. It is intended for graduate students, researchers, and practitioners of engineering and applied mathematics as well as computer scientists, physicists, and other scientists who seek a fundamental understanding of the rich dynamical behavior of impulsive and hybrid dynamical systems.

Automatic control. --- Control theory. --- Dynamics. --- Discrete-time systems. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Dynamics --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems --- Actuator. --- Adaptive control. --- Algorithm. --- Amplitude. --- Analog computer. --- Arbitrarily large. --- Asymptote. --- Asymptotic analysis. --- Axiom. --- Balance equation. --- Bode plot. --- Boundedness. --- Calculation. --- Center of mass (relativistic). --- Coefficient of restitution. --- Continuous function. --- Convex set. --- Differentiable function. --- Differential equation. --- Dissipation. --- Dissipative system. --- Dynamical system. --- Dynamical systems theory. --- Energy. --- Equations of motion. --- Equilibrium point. --- Escapement. --- Euler–Lagrange equation. --- Exponential stability. --- Forms of energy. --- Hamiltonian mechanics. --- Hamiltonian system. --- Hermitian matrix. --- Hooke's law. --- Hybrid system. --- Identity matrix. --- Inequality (mathematics). --- Infimum and supremum. --- Initial condition. --- Instability. --- Interconnection. --- Invariance theorem. --- Isolated system. --- Iterative method. --- Jacobian matrix and determinant. --- Lagrangian (field theory). --- Lagrangian system. --- Lagrangian. --- Likelihood-ratio test. --- Limit cycle. --- Limit set. --- Linear function. --- Linearization. --- Lipschitz continuity. --- Lyapunov function. --- Lyapunov stability. --- Mass balance. --- Mathematical optimization. --- Melting. --- Mixture. --- Moment of inertia. --- Momentum. --- Monotonic function. --- Negative feedback. --- Nonlinear programming. --- Nonlinear system. --- Nonnegative matrix. --- Optimal control. --- Ordinary differential equation. --- Orthant. --- Parameter. --- Partial differential equation. --- Passive dynamics. --- Poincaré conjecture. --- Potential energy. --- Proof mass. --- Quantity. --- Rate function. --- Requirement. --- Robust control. --- Second law of thermodynamics. --- Semi-infinite. --- Small-gain theorem. --- Special case. --- Spectral radius. --- Stability theory. --- State space. --- Stiffness. --- Supply (economics). --- Telecommunication. --- Theorem. --- Transpose. --- Uncertainty. --- Uniform boundedness. --- Uniqueness. --- Vector field. --- Vibration. --- Zeroth (software). --- Zeroth law of thermodynamics.

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Fluid–structure interactions (FSIs) play a crucial role in the design, construction, service and maintenance of many engineering applications, e.g., aircraft, towers, pipes, offshore platforms and long-span bridges. The old Tacoma Narrows Bridge (1940) is probably one of the most infamous examples of serious accidents due to the action of FSIs. Aircraft wings and wind-turbine blades can be broken because of FSI-induced oscillations. To alleviate or eliminate these unfavorable effects, FSIs must be dealt with in ocean, coastal, offshore and marine engineering to design safe and sustainable engineering structures. In addition, the wind effects on plants and the resultant wind-induced motions are examples of FSIs in nature. To meet the objectives of progress and innovation in FSIs in various scenarios of engineering applications and control schemes, this book includes 15 research studies and collects the most recent and cutting-edge developments on these relevant issues. The topics cover different areas associated with FSIs, including wind loads, flow control, energy harvesting, buffeting and flutter, complex flow characteristics, train–bridge interactions and the application of neural networks in related fields. In summary, these complementary contributions in this publication provide a volume of recent knowledge in the growing field of FSIs.

aerodynamic forces --- pressure distribution --- turbulence intensity --- twin-box girder --- trailing-edge reattachment --- trailing edge --- trailing-edge-changeable streamlined section mode --- limit cycle flutter --- hard flutter --- flutter stability --- wind engineering --- wind tunnel test --- wind-train-bridge system --- flow visualization --- flapping fringe --- CFD simulation --- vortex attenuation --- aerodynamics enhancement --- unsteady aerodynamic force --- single box girder --- Strouhal number --- linear stability analysis --- high-speed train --- enclosed housing for sound emission alleviation --- pressure wave --- unsteady aerodynamic pressure --- load patterns --- wake control --- drag reduction --- MSBC --- square cylinder --- numerical simulation --- wind characteristics --- wind tunnel testing --- complex terrain --- model truncation --- transition section --- deep learning --- prediction --- aerostatic performance --- shape --- convolutional neural networks --- long-span bridge --- buffeting response --- sectional model --- aerodynamic admittance --- integrated transfer function --- flow control --- traveling wave wall --- circular cylinder --- CFD --- wind turbines --- aerodynamic characteristics --- vortex shedding --- time domain method --- frequency domain method --- background and resonance coupled components --- wind induced dynamic responses --- equivalent static wind load --- aerodynamic shape optimization --- surrogate model --- wind energy harvester --- galloping --- passive jet control --- tower wake characteristics --- cobra probe --- n/a