Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

* Measure Theory-Basic Notions * Measure Theory-Key Results * Processes, Distributions, and Independence * Random Sequences, Series, and Averages * Characteristic Functions and Classical Limit Theorems * Conditioning and Disintegration * Martingales and Optional Times * Markov Processes and Discrete-Time Chains * Random Walks and Renewal Theory * Stationary Processes and Ergodic Theory * Special Notions of Symmetry and Invariance * Poisson and Pure Jump-Type Markov Processes * Gaussian Processes and Brownian Motion * Skorohod Embedding and Invariance Principles * Independent Increments and Infinite Divisibility * Convergence of Random Processes, Measures, and Sets * Stochastic Integrals and Quadratic Variation * Continuous Martingales and Brownian Motion * Feller Processes and Semigroups * Ergodic Properties of Markov Processes * Stochastic Differential Equations and Martingale Problems * Local Time, Excursions, and Additive Functionals * One-Dimensional SDEs and Diffusions * Connections with PDEs and Potential Theory * Predictability, Compensation, and Excessive Functions * Semimartingales and General Stochastic Integration * Large Deviations * Appendix 1: Advanced Measure Theory * Appendix 2: Some Special Spaces * Historical and Bibliographical Notes * Bibliography * Indices

http://cyber.sibsutis.ru:82/Monarev/docs/nauka/PROBABILITY/Kallenberg%20O.%20Foundations%20of%20Modern%20Probability%20(Springer,1997)(ISBN%200387949577)(535s).pdf

Foundations of modern probability

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

Levy processes form a wide and rich class of random process, and have many applications ranging from physics to finance Stochastic calculus is the mathematics of systems interacting with random noise Here, the author ties these two subjects together, beginning with an introduction to the general theory of Levy processes, then leading on to develop the stochastic calculus for Levy processes in a direct and accessible way This fully revised edition now features a number of new topics These include: regular variation and subexponential distributions; necessary and sufficient conditions for Levy processes to have finite moments; characterisation of Levy processes with finite variation; Kunita's estimates for moments of Levy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Levy processes; multiple Wiener-Levy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Levy-driven SDEs

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Lévy Processes and Stochastic Calculus

A method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described. The particles may also be subject to the usual interparticle or external forces (e.g., electrostatic) which have been included in previous methods for simulating Brownian dynamics of particles in the absence of hydrodynamic interactions. The present method is derived from the Langevin equations for the N particle assembly, and the results are shown to be consistent with the corresponding Fokker–Planck results. Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulations. The method should be useful for simulation studies of diffusion limited reactions, polymer dynamics, protein folding, particle coagulation, and other phenomena in solution.

Brownian dynamics with hydrodynamic interactions

The definition of the solvation Gibbs energy of a solute A in any solvent is repeated in exactly the same way as was done almost 20 years ago. Some recent publications that challenged this definiti...

Size Dependence of Solvation Gibbs Energies: A Critique and a Rebuttal of Some Recent Publications

An equation of evolution for a heavy particle immersed in a solvent of lighter particles is derived for the case when the system suffers gradients of temperature composition, or velocity. The derivation unifies the theory by applying the same methods which have proved useful in the uniform case. The final equation contains some new terms due to concentration gradients in the solvent, and is applicable to the case when the heavy particles are present at finite concentration and interact with each other.

On the theory of Brownian motion. II. Nonuniform systems

Etude de l'ecoulement d'un fluide parallelement aux couches d'un systeme stratifie. Les particules suspendues dans le fluide sont entrainees par l'ecoulement et font egalement des sauts aleatoires vers les strates voisines ou la vitesse du fluide est differente. Applications possibles a la chromatographie, a la diffusion de Taylor et aux marches aleatoires

Exact results for the asymptotic dispersion of particles in n-layer systems

The general theory of the irreversible thermodynamics of chemically reacting systems interacting with radiation is developed. From this, a limit to the efficiency of photochemical processes is derived, and this is compared with approximate experimental efficiencies of published researches. The computed efficiencies are appreciably lower than the theoretical limit; reasons for this are discussed.

Irreversible Thermodynamics of Systems Containing Radiation. Application to Photochemical Reactions

An analysis of the salting-out, or Sechenow, effect is given in terms of Kirkwood−Buff, or fluctuation, integrals. The analysis is formally exact but cannot easily be applied in its original form. When the solute that is being salted out is sparingly soluble, simplifications arise and the theory can be used to compute one of the Kirkwood−Buff integrals which is otherwise difficult to obtain.

Robert M. Mazo

Papers

Size Dependence of Solvation Gibbs Energies: A Critique and a Rebuttal of Some Recent Publications

On the theory of Brownian motion. II. Nonuniform systems

Exact results for the asymptotic dispersion of particles in n-layer systems

Irreversible Thermodynamics of Systems Containing Radiation. Application to Photochemical Reactions

A fluctuation theory analysis of the salting-out effect.