Bücher: „Stochastic second order methods“

1

Multidimensional second order stochastic processes. Singapore: World Scientific, 1997.

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2

Lan, Guanghui. First-order and Stochastic Optimization Methods for Machine Learning. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39568-1.

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3

Shepherd, Adrian J. Second-Order Methods for Neural Networks. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0953-2.

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4

Strassert, Günter. The balancing principle, strict superiority relations, and a transitive overall final order of options. Karlsruhe: Institut für Regionalwissenschaft der Universität Karlsruhe, 2000.

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5

Otmani, Zoulikha Zaidi ep. Numerical methods for second order parabolic partial differential equations. Uxbridge: Brunel University, 1986.

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6

Aamir, Shabbir, und United States. National Aeronautics and Space Administration., Hrsg. Methods of ensuring realizability for non-realizable second order closures. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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7

Shepherd, Adrian J. Second-order methods for neural networks: Fast and reliable training methods for multi-layer perceptrons. London: Springer, 1997.

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8

Krispin, J. Second-order Godunov methods and self-similar steady supersonic three-dimensional flowfields. Washington, D. C: American Institute of Aeronautics and Astronautics, 1991.

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9

Joost, Engelfriet, Hrsg. Graph structure and monadic second-order logic: A language-theoretic approach. Cambridge: Cambridge University Press, 2012.

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10

Heinrich, Bernd. Finite difference methods on irregular networks: A generalized approach to second order elliptic problems. Basel: Birkhäuser Verlag, 1987.

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11

Heinrich, Bernd. Finite difference methods on irregular networks: A generalized approach to second order elliptic problems. Berlin: Akademie-Verlag, 1987.

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12

International Conference on Spectral and High Order Methods (2nd 1992 Montpellier, France). ICOSAHOM'92: Selected papers from the second International Conference on Spectral and High Order Methods, Montpellier, France, 22-26 June 1992. Amsterdam: North-Holland, 1994.

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13

Fokker-Planck-Kolmogorov equations. Providence, Rhode Island: American Mathematical Society, 2015.

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14

Ammari, Habib. Imaging, multi-scale, and high-contrast partial differential equations: Seoul ICM 2014 Satellite Conference, August 7-9, 2014, Daejeon, Korea. Providence, Rhode Island: American Mathematical Society, 2016.

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15

1973-, Warzel Simone, Hrsg. Random operators: Disorder effects on quantum spectra and dynamics. Providence, Rhode Island: American Mathematical Society, 2015.

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16

1943-, Gossez J. P., und Bonheure Denis, Hrsg. Nonlinear elliptic partial differential equations: Workshop in celebration of Jean-Pierre Gossez's 65th birthday, September 2-4, 2009, Université libre de Bruxelles, Belgium. Providence, R.I: American Mathematical Society, 2011.

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17

1966-, Pérez Joaquín, und Galvez José A. 1972-, Hrsg. Geometric analysis: Partial differential equations and surfaces : UIMP-RSME Santaló Summer School geometric analysis, June 28-July 2, 2010, University of Granada, Granada, Spain. Providence, R.I: American Mathematical Society, 2012.

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18

Gesztesy, Fritz, Barry Simon, H. Holden und Gerald Teschl. Spectral analysis, differential equations, and mathematical physics: A festschrift in honor of Fritz Gesztesy's 60th birthday. Providence, Rhode Island: American Mathematical Society, 2013.

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19

Chemodurov, Vladimir, und Ella Litvinova. Physical and mathematical modeling of building systems. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1014191.

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Physical and mathematical modeling is widely used in scientific research. This is due to the fact that field experiments on real construction sites are often impossible to organize for various reasons. The material included in the textbook is a summary of the authors ' experience in the field of system analysis. In the first section, the regularities of physical modeling of the functioning of objects based on the similarity and dimension theorems are considered. The second section presents modern models and methods for choosing optimal solutions: linear, nonlinear, stochastic, and statistical. The third section deals with experimental methods of system optimization based on the theory of experimental planning. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of higher educational institutions studying in the direction of training 08.04.01 "Construction", and graduate students of higher educational institutions. It will be useful for specialists in the field of mathematical methods for the study of complex systems and their applications.

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20

Sequeira, A., H. Beirão da Veiga und V. A. Solonnikov. Recent advances in partial differential equations and applications: International conference in honor of Hugo Beirao de Veiga's 70th birthday, February 17-214, 2014, Levico Terme (Trento), Italy. Herausgegeben von Rădulescu, Vicenţiu D., 1958- editor. Providence, Rhode Island: American Mathematical Society, 2016.

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21

Habib, Ammari, Capdeboscq Yves 1971- und Kang Hyeonbae, Hrsg. Multi-scale and high-contrast PDE: From modelling, to mathematical analysis, to inversion : Conference on Multi-scale and High-contrast PDE:from Modelling, to Mathematical Analysis, to Inversion, June 28-July 1, 2011, University of Oxford, United Kingdom. Providence, R.I: American Mathematical Society, 2010.

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22

Zhukova, Galina. Differential equations. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1072180.

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The textbook presents the theory of ordinary differential equations constituting the subject of the discipline "Differential equations". Studied topics: differential equations of first, second, arbitrary order; differential equations; integration of initial and boundary value problems; stability theory of solutions of differential equations and systems. Introduced the basic concepts, proven properties of differential equations and systems. The article presents methods of analysis and solutions. We consider the applications of the obtained results, which are illustrated on a large number of specific tasks. For independent quality control mastering the course material suggested test questions on the theory, exercises and tasks. It is recommended that teachers, postgraduates and students of higher educational institutions, studying differential equations and their applications.

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23

Lan, Guanghui. First-Order and Stochastic Optimization Methods for Machine Learning. Springer International Publishing AG, 2021.

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24

Lan, Guanghui. First-order and Stochastic Optimization Methods for Machine Learning. Springer, 2020.

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25

Second Order PDE's in Finite & Infinite Dimensions. Springer, 2001.

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26

Shepherd, Adrian J. Second-Order Methods for Neural Networks: Fast and Reliable Training Methods for Multi-Layer Perceptrons. Springer, 2014.

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27

Shepherd, Adrian J. Second-Order Methods for Neural Networks: Fast and Reliable Training Methods for Multi-Layer Perceptrons. Springer London, Limited, 2012.

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28

Mitchell, Andrew. Second-order Learning in Developmental Evaluation: New Methods for Complex Conditions. Palgrave Pivot, 2018.

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29

Mitchell, Andrew. Second-order Learning in Developmental Evaluation: New Methods for Complex Conditions. Palgrave Pivot, 2018.

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30

Chen, Nan. Stochastic Methods for Modeling and Predicting Complex Dynamical Systems: Uncertainty Quantification, State Estimation, and Reduced-Order Models. Springer International Publishing AG, 2023.

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31

Scan Statistics: Methods and Applications. Springer London, Limited, 2009.

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32

Wang, Junping. Asymptotic expansions and L [infinity symbol]-error estimates for mixed finite element methods for second order elliptic problems. 1988.

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33

Edmunds, D. E., und W. D. Evans. Second-Order Differential Operators on Arbitrary Open Sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0007.

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In this chapter, three different methods are described for obtaining nice operators generated in some L2 space by second-order differential expressions and either Dirichlet or Neumann boundary conditions. The first is based on sesquilinear forms and the determination of m-sectorial operators by Kato’s First Representation Theorem; the second produces an m-accretive realization by a technique due to Kato using his distributional inequality; the third has its roots in the work of Levinson and Titchmarsh and gives operators T that are such that iT is m-accretive. The class of such operators includes the self-adjoint operators, even ones that are not bounded below. The essential self-adjointness of Schrödinger operators whose potentials have strong local singularities are considered, and the quantum-mechanical interpretation of essential self-adjointness is discussed.

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34

Heinrich, Bernd. Finite Difference Methods on Irregular Networks: A Generalized Approach to Second Order Elliptic Problems (Intl Series Numerical Mathematic, Vol 82). Birkhauser, 1988.

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35

Implementing Families of Implicit Chebyshev Methods with Exact Coefficients for the Numerical Integration of First- and Second-Order Differential Equations. Storming Media, 2002.

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36

Advances in Distribution Theory, Order Statistics, and Inference (Statistics for Industry and Technology). Birkhäuser Boston, 2007.

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37

Krylov, Nicolai V., Michael Rockner, Vladimir I. Bogachev und Stanislav V. Shaposhnikov. Fokker-Planck-Kolmogorov Equations. American Mathematical Society, 2015.

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38

Ratner, Bruce. Statistical and Machine-Learning Data Mining: Techniques for Better Predictive Modeling and Analysis of Big Data, Second Edition. Taylor & Francis Group, 2013.

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39

Glaz, Joseph, Joseph Naus und Sylvan Wallenstein. Scan Statistics. Springer London, Limited, 2013.

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40

Scan Statistics (Springer Series in Statistics). Springer, 2001.

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41

author, Mazʹi︠a︡ V. G., Hrsg. Maximum principles and sharp constants for solutions of elliptic and parabolic systems. 2012.

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42

Kubek, Maria M., und Zhong Li, Hrsg. Autonomous Systems 2018. VDI Verlag, 2018. http://dx.doi.org/10.51202/9783186862105.

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To meet the expectations raised by the terms Industry 4.0, Industrial Internet and Internet of Things, real innovations are necessary, which can be brought about by information processing systems working autonomously. Owing to their growing complexity and their embedding in ever-changing environments, their design becomes increasingly critical. Thus, the many topics addressed in this book range from data integration on hardware level to methods for security and safety of data and to stochastic methods, data interferences as well as machine learning and search in decentralised systems. Their validity is proven by extensive simulation results. Also, applications for methods from deep learning and neurocomputing are presented. The sustainable management of energy systems using intelligent methods of self-organisation and learning is dealt with in the second major part of this book. As in these particular settings, the assessment of network vulnerabilities plays a crucial role, respective ...

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43

Nitzan, Abraham. Chemical Dynamics in Condensed Phases. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198529798.001.0001.

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This text provides a uniform and consistent approach to diversified problems encountered in the study of dynamical processes in condensed phase molecular systems. Given the broad interdisciplinary aspect of this subject, the book focuses on three themes: coverage of needed background material, in-depth introduction of methodologies, and analysis of several key applications. The uniform approach and common language used in all discussions help to develop general understanding and insight on condensed phases chemical dynamics. The applications discussed are among the most fundamental processes that underlie physical, chemical and biological phenomena in complex systems. The first part of the book starts with a general review of basic mathematical and physical methods (Chapter 1) and a few introductory chapters on quantum dynamics (Chapter 2), interaction of radiation and matter (Chapter 3) and basic properties of solids (chapter 4) and liquids (Chapter 5). In the second part the text embarks on a broad coverage of the main methodological approaches. The central role of classical and quantum time correlation functions is emphasized in Chapter 6. The presentation of dynamical phenomena in complex systems as stochastic processes is discussed in Chapters 7 and 8. The basic theory of quantum relaxation phenomena is developed in Chapter 9, and carried on in Chapter 10 which introduces the density operator, its quantum evolution in Liouville space, and the concept of reduced equation of motions. The methodological part concludes with a discussion of linear response theory in Chapter 11, and of the spin-boson model in chapter 12. The third part of the book applies the methodologies introduced earlier to several fundamental processes that underlie much of the dynamical behaviour of condensed phase molecular systems. Vibrational relaxation and vibrational energy transfer (Chapter 13), Barrier crossing and diffusion controlled reactions (Chapter 14), solvation dynamics (Chapter 15), electron transfer in bulk solvents (Chapter 16) and at electrodes/electrolyte and metal/molecule/metal junctions (Chapter 17), and several processes pertaining to molecular spectroscopy in condensed phases (Chapter 18) are the main subjects discussed in this part.

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44

Henriksen, Niels E., und Flemming Y. Hansen. Theories of Molecular Reaction Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805014.001.0001.

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This book deals with a central topic at the interface of chemistry and physics—the understanding of how the transformation of matter takes place at the atomic level. Building on the laws of physics, the book focuses on the theoretical framework for predicting the outcome of chemical reactions. The style is highly systematic with attention to basic concepts and clarity of presentation. Molecular reaction dynamics is about the detailed atomic-level description of chemical reactions. Based on quantum mechanics and statistical mechanics or, as an approximation, classical mechanics, the dynamics of uni- and bimolecular elementary reactions are described. The first part of the book is on gas-phase dynamics and it features a detailed presentation of reaction cross-sections and their relation to a quasi-classical as well as a quantum mechanical description of the reaction dynamics on a potential energy surface. Direct approaches to the calculation of the rate constant that bypasses the detailed state-to-state reaction cross-sections are presented, including transition-state theory, which plays an important role in practice. The second part gives a comprehensive discussion of basic theories of reaction dynamics in condensed phases, including Kramers and Grote–Hynes theory for dynamical solvent effects. Examples and end-of-chapter problems are included in order to illustrate the theory and its connection to chemical problems. The book has ten appendices with useful details, for example, on adiabatic and non-adiabatic electron-nuclear dynamics, statistical mechanics including the Boltzmann distribution, quantum mechanics, stochastic dynamics and various coordinate transformations including normal-mode and Jacobi coordinates.

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45

Lopes, Dominic McIver. Aesthetics in Three Dimensions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198796657.003.0002.

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This chapter begins with a historical overview of aesthetics and the philosophy of art before turning to a discussion of how the philosophy of art bears upon human culture. It then considers the methods used in attacking problems in aesthetics and the philosophy of art by highlighting the distinctions between pure and applied philosophy, between internal and external perspectives on aesthetic and artistic phenomena, and between first-order and second-order methods. It also examines how aesthetics and the philosophy of art are affected as the arts evolve and as empirical studies of aesthetic and artistic phenomena become well established in the social and behavioural sciences as well as the humanities.

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46

Lopes, Dominic McIver. Aesthetics and Philosophy of Art. Herausgegeben von Herman Cappelen, Tamar Szabó Gendler und John Hawthorne. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199668779.013.11.

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This article focuses on aesthetics and the philosophy of art as branches of so-called analytic philosophy. It begins with a historical overview of aesthetics and the philosophy of art before turning to a discussion of how the philosophy of art bears upon human culture. It then considers the methods used in attacking problems in aesthetics and the philosophy of art by highlighting the distinctions between pure and applied philosophy, between internal and external perspectives on aesthetic and artistic phenomena, and between first-order and second-order methods. It also examines how aesthetics and the philosophy of art are affected as the arts evolve and as empirical studies of aesthetic and artistic phenomena become well established in the social and behavioural sciences as well as the humanities.

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47

Ross, John, Igor Schreiber und Marcel O. Vlad. Determination of Complex Reaction Mechanisms. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780195178685.001.0001.

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In a chemical system with many chemical species several questions can be asked: what species react with other species: in what temporal order: and with what results? These questions have been asked for over one hundred years about simple and complex chemical systems, and the answers constitute the macroscopic reaction mechanism. In Determination of Complex Reaction Mechanisms authors John Ross, Igor Schreiber, and Marcel Vlad present several systematic approaches for obtaining information on the causal connectivity of chemical species, on correlations of chemical species, on the reaction pathway, and on the reaction mechanism. Basic pulse theory is demonstrated and tested in an experiment on glycolysis. In a second approach, measurements on time series of concentrations are used to construct correlation functions and a theory is developed which shows that from these functions information may be inferred on the reaction pathway, the reaction mechanism, and the centers of control in that mechanism. A third approach is based on application of genetic algorithm methods to the study of the evolutionary development of a reaction mechanism, to the attainment given goals in a mechanism, and to the determination of a reaction mechanism and rate coefficients by comparison with experiment. Responses of non-linear systems to pulses or other perturbations are analyzed, and mechanisms of oscillatory reactions are presented in detail. The concluding chapters give an introduction to bioinformatics and statistical methods for determining reaction mechanisms.

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48

Boudreau, Joseph F., und Eric S. Swanson. Classical spin systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0020.

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The thermodynamic properties of spin systems are evaluated with Monte Carlo methods. A review of classical thermodynamics is followed by a discussion of critical exponents. The Monte Carlo method is then applied to the two-dimensional Ising model with the goal of determining the phase diagram for magnetization. Boundary conditions, the reweighting method, autocorrelation, and critical slowing down are all explored. Cluster algorithms for overcoming critical slowing down are developed next and shown to dramatically reduce autocorrelation. A variety of spin systems that illustrate first, second, and infinite order (topological) phase transitions are explored. Finally, applications to random systems called spin glasses and to neural networks are briefly reviewed.

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49

Hugh, Beale, Bridge Michael, Gullifer Louise und Lomnicka Eva. Part III Registration and Other Perfection Requirements, 9 Registration and Other Perfection Requirements. Oxford University Press, 2018. http://dx.doi.org/10.1093/law/9780198795568.003.0009.

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This chapter looks at how the expression ‘perfection’ is a useful way to describe steps that a secured creditor has to take in order to be able to make the security effective against other secured creditors, trustees in bankruptcy, and company liquidators or administrators. The methods of perfection set out in Revised Article 9 of the Uniform Commercial Code consist of possession, control, and registration. Care must be taken, however, in applying the concept of perfection to English law. First, Article 9 requires that every security interest be perfected, although for some types of security interest no extra step is needed beyond the security being agreed and attaching to the collateral. Second, the steps needed to be taken to register, as well as those needed to obtain control, are different to those required in English law.

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50

Maquet, Pierre, und Julien Fanielle. Neuroimaging in normal sleep and sleep disorders. Herausgegeben von Sudhansu Chokroverty, Luigi Ferini-Strambi und Christopher Kennard. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780199682003.003.0011.

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Functional neuroimaging techniques include methods that probe various aspects of brain function and help derive models of brain organization in health and disease. These techniques can be grouped in two categories. Some are mainly based on electromagnetic signals (electroencephalography, magnetoencephalography), recording brain activity using a large number of sensors with exquisite temporal resolution (usually of the order of a kilohertz) but allowing only indirect characterization of three-dimensional brain activity by resorting to mathematical models. The second type includes different techniques (PET scan, SPECT, MRI, optical imaging) that typically assess metabolic or hemodynamic parameters, with millimeter spatial resolution and usually from the entire brain volume. However, temporal resolution is usually low because it is primarily driven by metabolic processes that unfold in several seconds or minutes. This chapter focuses on this second type, covering the contribution of brain imaging to understanding NREM sleep and REM sleep and also sleep disorders.

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Bücher zum Thema „Stochastic second order methods“

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