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Although nonlinear dynamics have been mastered by physicists and mathematicians for a long time (as most physical systems are inherently nonlinear in nature), the recent successful application of nonlinear methods to modeling and predicting several evolutionary, ecological, physiological, and biochemical processes has generated great interest and enthusiasm among researchers in computational neuroscience and cognitive psychology. Additionally, in the last years it has been demonstrated that nonlinear analysis can be successfully used to model not only basic cellular and molecular data but also complex cognitive processes and behavioral interactions. The theoretical features of nonlinear systems (such unstable periodic orbits, period-doubling bifurcations and phase space dynamics) have already been successfully applied by several research groups to analyze the behavior of a variety of neuronal and cognitive processes. Additionally the concept of strange attractors has lead to a new understanding of information processing which considers higher cognitive functions (such as language, attention, memory and decision making) as complex systems emerging from the dynamic interaction between parallel streams of information flowing between highly interconnected neuronal clusters organized in a widely distributed circuit and modulated by key central nodes. Furthermore, the paradigm of self-organization derived from the nonlinear dynamics theory has offered an interesting account of the phenomenon of emergence of new complex cognitive structures from random and non-deterministic patterns, similarly to what has been previously observed in nonlinear studies of fluid dynamics. Finally, the challenges of coupling massive amount of data related to brain function generated from new research fields in experimental neuroscience (such as magnetoencephalography, optogenetics and single-cell intra-operative recordings of neuronal activity) have generated the necessity of new research strategies which incorporate complex pattern analysis as an important feature of their algorithms. Up to now nonlinear dynamics has already been successfully employed to model both basic single and multiple neurons activity (such as single-cell firing patterns, neural networks synchronization, autonomic activity, electroencephalographic measurements, and noise modulation in the cerebellum), as well as higher cognitive functions and complex psychiatric disorders. Similarly, previous experimental studies have suggested that several cognitive functions can be successfully modeled with basis on the transient activity of large-scale brain networks in the presence of noise. Such studies have demonstrated that it is possible to represent typical decision-making paradigms of neuroeconomics by dynamic models governed by ordinary differential equations with a finite number of possibilities at the decision points and basic heuristic rules which incorporate variable degrees of uncertainty. This e-book has include frontline research in computational neuroscience and cognitive psychology involving applications of nonlinear analysis, especially regarding the representation and modeling of complex neural and cognitive systems. Several experts teams around the world have provided frontline theoretical and experimental contributions (as well as reviews, perspectives and commentaries) in the fields of nonlinear modeling of cognitive systems, chaotic dynamics in computational neuroscience, fractal analysis of biological brain data, nonlinear dynamics in neural networks research, nonlinear and fuzzy logics in complex neural systems, nonlinear analysis of psychiatric disorders and dynamic modeling of sensorimotor coordination.

fMRI --- fractal analysis --- Cognitive neuroscience --- EEG --- Experimental neuroscience --- non-linear dynamics --- Neuropsychology --- applied neuroscience

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Over the last decades, assessment of heart rate variability (HRV) has increased in various fields of research. HRV describes changes in heartbeat intervals, which are caused by autonomic neural regulation, i.e. by the interplay of the sympathetic and the parasympathetic nervous systems. The most frequent application of HRV is connected to cardiological issues, most importantly to the monitoring of post-myocardial infarction patients and the prediction of sudden cardiac death. Analysis of HRV is also frequently applied in relation to diabetes, renal failure, neurological and psychiatric conditions, sleep disorders, psychological phenomena such as stress, as well as drug and addiction research including alcohol and smoking. The widespread application of HRV measurements is based on the fact that they are noninvasive, easy to perform, and in general reproducible – if carried out under standardized conditions. However, the amount of parameters to be analysed is still rising. Well-established time domain and frequency domain parameters are discussed controversially when it comes to their physiological interpretation and their psychometric properties like reliability and validity, and the sensitivity to cardiovascular properties of the variety of parameters seems to be a topic for further research. Recently introduced parameters like pNNxx and new dynamic methods such as approximate entropy and detrended fluctuation analysis offer new potentials and warrant standardization. However, HRV is significantly associated with average heart rate (HR) and one can conclude that HRV actually provides information on two quantities, i.e. on HR and its variability. It is hard to determine which of these two plays a principal role in the clinical value of HRV. The association between HRV and HR is not only a physiological phenomenon but also a mathematical one which is due to non-linear (mathematical) relationship between RR interval and HR. If one normalizes HRV to its average RR interval, one may get ‘pure’ variability free from the mathematical bias. Recently, a new modification method of the association between HRV and HR has been developed which enables us to completely remove the HRV dependence on HR (even the physiological one), or conversely enhance this dependence. Such an approach allows us to explore the HR contribution to the clinical significance of HRV, i.e. whether HR or its variability plays a main role in the HRV clinical value. This Research Topic covers recent advances in the application of HRV, methodological issues, basic underlying mechanisms as well as all aspects of the interaction between HRV and HR.

Heart Rate --- Autonomic Function --- sympathetic and vagal control --- baroreflex mechanisms --- heart rate turbulence --- spectral analysis --- Sudden cardiac death --- Heart rate variability --- non-linear methods

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This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension. The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.

Agricultural science --- Life sciences: general issues --- Botany & plant sciences --- Animal reproduction --- Probability & statistics --- open access --- Statistical learning --- Bayesian regression --- Deep learning --- Non linear regression --- Plant breeding --- Crop management --- multi-trait multi-environments models

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Differential equations --- Classical mechanics. Field theory --- Differential equations, Nonlinear --- Nonlinear mechanics --- Équations différentielles non linéaires. --- Mécanique non linéaire. --- Differential equations, Nonlinear. --- Nonlinear mechanics. --- Mathematical Sciences --- Applied Mathematics --- Complex Analysis --- General and Others --- non-linear phenomena --- computational techniques --- differential equations --- Mechanics, Nonlinear --- Mechanics, Analytic --- Nonlinear differential equations --- Nonlinear theories --- Équations différentielles non linéaires. --- Mécanique non linéaire. --- Chaos Theory. --- Differential Equations. --- Mathematics --- Calculus --- Équations différentielles non linéaires --- Mécanique non linéaire

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This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connection rule determines the graph topology. When the edges can be assigned a length and the wave functions on the edges are defined in metric spaces, the graph is called a metric graph. Evolution equations on metric graphs have attracted much attention as effective tools for the modeling of particle and wave dynamics in branched structures and networks. Since branched structures and networks appear in different areas of contemporary physics with many applications in electronics, biology, material science, and nanotechnology, the development of effective modeling tools is important for the many practical problems arising in these areas. The list of important problems includes searches for standing waves, exploring of their properties (e.g., stability and asymptotic behavior), and scattering dynamics. This Special Issue is a representative sample of the works devoted to the solutions of these and other problems.

quantum graphs --- ground states --- open sets converging to metric graphs --- norm convergence of operators --- NLD --- scaling limit --- standing waves --- bound states --- networks --- localized nonlinearity --- nonlinear Schrödinger equation --- metric graphs --- convergence of spectra --- sine-Gordon equation --- NLS --- star graph --- point interactions --- Laplacians --- nonrelativistic limit --- nonlinear wave equations --- quantum graph --- soliton --- nonlinear shallow water equations --- Kre?n formula --- breather --- non-linear Schrödinger equation --- Schrödinger equation --- nodal structure