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In order to measure and quantify the complex behavior of real-world 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 non-uniform 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 engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.

n/a --- nonautonomous (autonomous) dynamical system --- stabilization --- multi-time scale fractional stochastic differential equations --- conditional Tsallis entropy --- wavelet transform --- hyperchaotic system --- Chua’s system --- permutation entropy --- neural network method --- Information transfer --- self-synchronous stream cipher --- colored noise --- Benettin method --- method of synchronization --- topological entropy --- geometric nonlinearity --- Kantz method --- dynamical system --- Gaussian white noise --- phase-locked loop --- wavelets --- Rosenstein method --- m-dimensional manifold --- deterministic chaos --- disturbation --- Mittag–Leffler function --- approximate entropy --- bounded chaos --- Adomian decomposition --- fractional calculus --- product MV-algebra --- Tsallis entropy --- descriptor fractional linear systems --- analytical solution --- fractional Brownian motion --- true chaos --- discrete mapping --- partition --- unbounded chaos --- fractional stochastic partial differential equation --- noise induced transitions --- random number generator --- Fourier spectrum --- hidden attractors --- (asymptotical) focal entropy point --- regular pencils --- continuous flow --- Bernoulli–Euler beam --- image encryption --- Gauss wavelets --- Lyapunov exponents --- discrete fractional calculus --- Lorenz system --- Schur factorization --- discrete chaos --- Wolf method

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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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Following the tremendous reception of our first volume on topological groups called ""Topological Groups: Yesterday, Today, and Tomorrow"", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.

coarse structure --- descriptive set theory --- group representation --- thick set --- free topological group --- character --- selectively sequentially pseudocompact --- separable topological group --- quotient group --- Chabauty topology --- pseudo-?-bounded --- topological group --- free precompact Boolean group --- right-angled Artin groups --- Neretin’s group --- coarse space --- ultrafilter space --- endomorphism --- separable --- absolutely closed topological group --- tree --- strongly pseudocompact --- Gromov’s compactification --- dynamical system --- semigroup compactification --- tame function --- compact topological semigroup --- vast set --- space of closed subgroups --- reflexive group --- Lie group --- matrix coefficient --- maximal ideal --- topological semigroup --- ballean --- continuous inverse algebra --- extension --- subgroup --- Thompson’s group --- scale --- isomorphic embedding --- arrow ultrafilter --- H-space --- paratopological group --- pseudocompact --- Ramsey ultrafilter --- fibre bundle --- locally compact group --- product --- large set in a group --- Vietoris topology --- topological group of compact exponent --- Bourbaki uniformity --- p-compact --- mapping cylinder --- syndetic set --- p-adic Lie group --- Boolean topological group --- non-trivial convergent sequence --- fixed point algebra --- polish group topologies --- varieties of coarse spaces --- piecewise syndetic set --- maximal space