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Table Of Integrals Series And Products

Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

Probability on Trees and Networks

Neurodegenerative diseases pose a substantial socioeconomic burden on society. Unfortunately, the aging world population and lack of effective cures foreshadow a negative outlook. Although a large amount of research has been dedicated to elucidating the pathologies of neurodegenerative diseases, their principal causes remain elusive. Metal ion dyshomeostasis, proteopathy, oxidative stress, and neurotransmitter deficiencies are pathological features shared across multiple neurodegenerative disorders. In addition, these factors are proposed to be interrelated upon disease progression. Thus, the development of multifunctional compounds capable of simultaneously interacting with several pathological components has been suggested as a solution to undertake the complex pathologies of neurodegenerative diseases. In this review, we outline and discuss possible therapeutic targets in Alzheimer’s disease, Parkinson’s disease, and amyotrophic lateral sclerosis and molecules, previously designed or discovered as pote...

Development of Multifunctional Molecules as Potential Therapeutic Candidates for Alzheimer’s Disease, Parkinson’s Disease, and Amyotrophic Lateral Sclerosis in the Last Decade

Three-dimensional geometry and topology. Volume 1, by William P. Thurston, (edited by Sylvio Levy). Princeton Mathematical Series, 35. £29.95. 1997. ISBN 0-691-08304-5 (Princeton University Press).

Chiral separation of β-blockers by high-performance capillary electrophoresis based on non-immobilized cellulase as enantioselective protein

We study integrable cocycles u.n; x/ over an ergodic measure preserving transformation that take values in a semigroup of nonexpanding maps of a nonpositively curved space Y , e.g. a Cartan-Hadamard space or a uniformly convex Banach space. It is proved that for any y 2 Y and almost all x; there exist A 0 and a unique geodesic ray .t; x/in Y starting at y such that lim n!1 1 n d. .An; x/; u.n; x/y/ D 0: In the case where Y is the symmetric space GLN.R/=ON.R/ and the cocycles take values in GLN.R/; this is equivalent to the multiplicative ergodic theorem of Oseledec. Two applications are also described. The first concerns the determination of Poisson boundaries and the second concerns Hilbert-Schmidt operators.

/pdf/a-multiplicative-ergodic-theorem-and-nonpositively-curved-jvzbzqp91v.pdf

A Multiplicative Ergodic Theorem and Nonpositively Curved Spaces

We give stronger versions and alternative simple proofs of some results of Beardon, [Be1] and [Be2]. These results concern contractions of locally compact metric spaces and generalize the theorems ...

/pdf/non-expanding-maps-and-busemann-functions-1ff5zgdap7.pdf

Non-expanding maps and Busemann functions

We prove a general noncommutative law of large numbers. This applies in particular to random walks on any locally finite homogeneous graph, as well as to Brownian motion on Riemannian manifolds whi ...

/pdf/on-laws-of-large-numbers-for-random-walks-197yz6fwdw.pdf

On Laws of Large Numbers for Random Walks

We prove that when a countable group admits a nontrivial Floyd-type boundary, then every nonelementary and metrically proper subgroup contains a noncommutative free subgroup. This generalizes the c ...

/pdf/free-subgroups-of-groups-with-nontrivial-floyd-boundary-56il05w823.pdf

Free Subgroups of Groups with Nontrivial Floyd Boundary

We consider a nondegenerate random walk on a locally compact group with finite first moment. Then, if there are no nonconstant bounded harmonic functions, all the linear drift comes from a real additive character on the group. As a corollary we obtain a generalization of Varopoulos’ theorem that in the case of symmetric random walks, positive linear drift implies the existence of nonconstant bounded harmonic functions. Another consequence is the phenomenon that for some groups (including certain Grigorchuk groups) the drift vanishes for any measure of finite first moment.

/pdf/linear-drift-and-poisson-boundary-for-random-walks-1o41d0uh7k.pdf

Anders Karlsson

Papers

A Multiplicative Ergodic Theorem and Nonpositively Curved Spaces

Non-expanding maps and Busemann functions

On Laws of Large Numbers for Random Walks

Free Subgroups of Groups with Nontrivial Floyd Boundary

Linear Drift and Poisson Boundary for Random Walks