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This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

Economics, finance, business & management --- mathematical economics --- economic theory --- fractional calculus --- fractional dynamics --- long memory --- non-locality --- fractional generalization --- econometric modelling --- identification --- Phillips curve --- Mittag-Leffler function --- generalized fractional derivatives --- growth equation --- Mittag-Leffler function --- Caputo fractional derivative --- economic growth model --- least squares method --- fractional diffusion equation --- fundamental solution --- option pricing --- risk sensitivities --- portfolio hedging --- business cycle model --- stability --- time delay --- time-fractional-order --- Hopf bifurcation --- Einstein's evolution equation --- Kolmogorov-Feller equation --- diffusion equation --- self-affine stochastic fields --- random market hypothesis --- efficient market hypothesis --- fractal market hypothesis --- financial time series analysis --- evolutionary computing --- modelling --- economic growth --- prediction --- Group of Twenty --- pseudo-phase space --- economy --- system modeling --- deep assessment --- least squares --- modeling --- GDP per capita --- LSTM --- econophysics --- continuous-time random walk (CTRW) --- Mittag-Leffler functions --- Laplace transform --- Fourier transform --- mathematical economics --- economic theory --- fractional calculus --- fractional dynamics --- long memory --- non-locality --- fractional generalization --- econometric modelling --- identification --- Phillips curve --- Mittag-Leffler function --- generalized fractional derivatives --- growth equation --- Mittag-Leffler function --- Caputo fractional derivative --- economic growth model --- least squares method --- fractional diffusion equation --- fundamental solution --- option pricing --- risk sensitivities --- portfolio hedging --- business cycle model --- stability --- time delay --- time-fractional-order --- Hopf bifurcation --- Einstein's evolution equation --- Kolmogorov-Feller equation --- diffusion equation --- self-affine stochastic fields --- random market hypothesis --- efficient market hypothesis --- fractal market hypothesis --- financial time series analysis --- evolutionary computing --- modelling --- economic growth --- prediction --- Group of Twenty --- pseudo-phase space --- economy --- system modeling --- deep assessment --- least squares --- modeling --- GDP per capita --- LSTM --- econophysics --- continuous-time random walk (CTRW) --- Mittag-Leffler functions --- Laplace transform --- Fourier transform

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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

n/a --- inosine --- immune checkpoint inhibitor --- geometric singular perturbation theory --- simulation --- BioModels Database --- ADAR --- calcium current --- bifurcation analysis --- bacterial biofilms --- nonlinear dynamics --- explanatory model --- turning point bifurcation --- oscillator --- workflow --- bioreactor integrated modeling --- modeling methods --- elementary flux modes visualization --- multiscale systems biology --- evolutionary algorithm --- metabolic model --- differential evolution --- reduced-order model --- computational model --- gut microbiota dysbiosis --- canard-induced EADs --- computational biology --- metabolic modelling --- methods --- SREBP-2 --- mechanistic model --- systems modeling --- biological networks --- macromolecular composition --- provenance --- flux balance analysis --- immunotherapy --- compartmental modeling --- immuno-oncology --- metabolic network visualization --- mechanism --- bistable switch --- Clostridium difficile infection --- bioreactor operation optimization --- microRNA targeting --- CFD simulation --- biomass reaction --- RNA editing --- ordinary differential equation --- metabolic modeling --- mass-action networks --- hybrid model --- multiple time scales --- quantitative systems pharmacology (QSP) --- mathematical modeling --- microRNA --- cancer --- parameter optimization --- Hopf bifurcation --- breast

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The transition to 100% renewable energy in the future is one of the most important ways of achieving "carbon peaking and carbon neutrality" and of reducing the adverse effects of climate change. In this process, the safe, stable and economical operation of renewable energy generation systems, represented by hydro-, wind and solar power, is particularly important, and has naturally become a key concern for researchers and engineers. Therefore, this book focuses on the fundamental and applied research on the modeling, control, monitoring and diagnosis of renewable energy generation systems, especially hydropower energy systems, and aims to provide some theoretical reference for researchers, power generation departments or government agencies.

Research & information: general --- Physics --- doubly-fed variable-speed pumped storage --- Hopf bifurcation --- stability analysis --- parameter sensitivity --- pumped storage unit --- degradation trend prediction --- maximal information coefficient --- light gradient boosting machine --- variational mode decomposition --- gated recurrent unit --- high proportional renewable power system --- active power --- change point detection --- maximum information coefficient --- cosine similarity --- anomaly detection --- thermal-hydraulic characteristics --- hydraulic oil viscosity --- hydraulic PTO --- wave energy converter --- pumped storage units --- pressure pulsation --- noise reduction --- sparrow search algorithm --- hybrid system --- facility agriculture --- chaotic particle swarms method --- operation strategy --- stochastic dynamic programming (SDP) --- power yield --- seasonal price --- reliability --- cascaded reservoirs --- doubly-fed variable speed pumped storage power station --- nonlinear modeling --- nonlinear pump turbine characteristics --- pumped storage units (PSUs) --- successive start-up --- ‘S’ characteristics --- low water head conditions --- multi-objective optimization --- fractional order PID controller (FOPID) --- hydropower units --- comprehensive deterioration index --- long and short-term neural network --- ensemble empirical mode decomposition --- approximate entropy --- 1D–3D coupling model --- transition stability --- sensitivity analysis --- hydro power

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Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

Research & information: general --- Mathematics & science --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal

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This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

mathematical economics --- economic theory --- fractional calculus --- fractional dynamics --- long memory --- non-locality --- fractional generalization --- econometric modelling --- identification --- Phillips curve --- Mittag-Leffler function --- generalized fractional derivatives --- growth equation --- Mittag–Leffler function --- Caputo fractional derivative --- economic growth model --- least squares method --- fractional diffusion equation --- fundamental solution --- option pricing --- risk sensitivities --- portfolio hedging --- business cycle model --- stability --- time delay --- time-fractional-order --- Hopf bifurcation --- Einstein’s evolution equation --- Kolmogorov–Feller equation --- diffusion equation --- self-affine stochastic fields --- random market hypothesis --- efficient market hypothesis --- fractal market hypothesis --- financial time series analysis --- evolutionary computing --- modelling --- economic growth --- prediction --- Group of Twenty --- pseudo-phase space --- economy --- system modeling --- deep assessment --- least squares --- modeling --- GDP per capita --- LSTM --- econophysics --- continuous-time random walk (CTRW) --- Mittag–Leffler functions --- Laplace transform --- Fourier transform --- n/a --- Einstein's evolution equation --- Kolmogorov-Feller equation --- Mittag-Leffler functions