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Nowadays, forecast applications are receiving unprecedent attention thanks to their capability to improve the decision-making processes by providing useful indications. A large number of forecast approaches related to different forecast horizons and to the specific problem that have to be predicted have been proposed in recent scientific literature, from physical models to data-driven statistic and machine learning approaches. In this Special Issue, the most recent and high-quality researches about forecast are collected. A total of nine papers have been selected to represent a wide range of applications, from weather and environmental predictions to economic and management forecasts. Finally, some applications related to the forecasting of the different phases of COVID in Spain and the photovoltaic power production have been presented.

Research & information: general --- Direct Normal Irradiance (DNI) --- IFS/ECMWF --- forecast --- evaluation --- DNI attenuation Index (DAI) --- bias correction --- nowcast --- meteorological radar data --- optical flow --- deep learning --- Bates–Granger weights --- uniform weights --- (REG) ARIMA --- ETS --- Hodrick–Prescott trend --- Google Trends indices --- Himalayan region --- streamflow forecast verification --- persistence --- snow-fed rivers --- intermittent rivers --- costumer relation management --- business to business sales prediction --- machine learning --- predictive modeling --- microsoft azure machine-learning service --- travel time forecasting --- time series --- bus service --- transit systems --- sustainable urban mobility plan --- bus travel time --- learning curve --- forecasting --- production cost --- cost estimating --- semi-empirical model --- logistic map --- COVID-19 --- SARS-CoV-2 --- PV output power estimation --- PV-load decoupling --- behind-the-meter PV --- baseline prediction --- n/a --- Bates-Granger weights --- Hodrick-Prescott trend

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The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.

Differentiable dynamical systems. --- Chaotic behavior in systems. --- Stochastic systems. --- Systems, Stochastic --- Stochastic processes --- System analysis --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Affine transformation. --- Amplitude. --- Arbitrarily large. --- Attractor. --- Autocovariance. --- Big O notation. --- Central limit theorem. --- Change of variables. --- Chaos theory. --- Coefficient of variation. --- Compound Probability. --- Computational problem. --- Control theory. --- Convolution. --- Coriolis force. --- Correlation coefficient. --- Covariance function. --- Cross-covariance. --- Cumulative distribution function. --- Cutoff frequency. --- Deformation (mechanics). --- Derivative. --- Deterministic system. --- Diagram (category theory). --- Diffeomorphism. --- Differential equation. --- Dirac delta function. --- Discriminant. --- Dissipation. --- Dissipative system. --- Dynamical system. --- Eigenvalues and eigenvectors. --- Equations of motion. --- Even and odd functions. --- Excitation (magnetic). --- Exponential decay. --- Extreme value theory. --- Flow velocity. --- Fluid dynamics. --- Forcing (recursion theory). --- Fourier series. --- Fourier transform. --- Fractal dimension. --- Frequency domain. --- Gaussian noise. --- Gaussian process. --- Harmonic analysis. --- Harmonic function. --- Heteroclinic orbit. --- Homeomorphism. --- Homoclinic orbit. --- Hyperbolic point. --- Inference. --- Initial condition. --- Instability. --- Integrable system. --- Invariant manifold. --- Iteration. --- Joint probability distribution. --- LTI system theory. --- Limit cycle. --- Linear differential equation. --- Logistic map. --- Marginal distribution. --- Moduli (physics). --- Multiplicative noise. --- Noise (electronics). --- Nonlinear control. --- Nonlinear system. --- Ornstein–Uhlenbeck process. --- Oscillation. --- Parameter space. --- Parameter. --- Partial differential equation. --- Perturbation function. --- Phase plane. --- Phase space. --- Poisson distribution. --- Probability density function. --- Probability distribution. --- Probability theory. --- Probability. --- Production–possibility frontier. --- Relative velocity. --- Scale factor. --- Shear stress. --- Spectral density. --- Spectral gap. --- Standard deviation. --- Stochastic process. --- Stochastic resonance. --- Stochastic. --- Stream function. --- Surface stress. --- Symbolic dynamics. --- The Signal and the Noise. --- Topological conjugacy. --- Transfer function. --- Variance. --- Vorticity.