Physics of Neutron Star Crusts

The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.Comment: 182 pages, published version available at <http://www.livingreviews.org/lrr-2008-10

The Existence and Uniqueness of Nash Equilibrium Point in an m-player Game “Shoot Later, Shoot First!”

Duel of m players, Nash equilibrium,

Stochastic scheduling:a short history of index policies and new approaches to index generation for dynamic resource allocation

In the 1970’s John Gittins discovered that multi-armed bandits, an important class of models for the dynamic allocation of a single key resource among a set of competing projects, have optimal solutions of index form. At each decision epoch such policies allocate the resource to whichever project has the largest Gittins index. Since the 1970’s, Gittins’ index result together with a range of developments and reformulations of it have constituted an influential stream of ideas and results contributing to research into the scheduling of stochastic objects. We give a brief account of many of the most important contributions to this work and proceed to describe how index theory has recently been developed to produce strongly performing heuristic policies for the dynamic allocation of a divisible resource to a collection of stochastic projects (or bandits). A limitation on this work concerns the need for the structural requirement of indexability which is notoriously difficult to establish. We introduce a general framework for the development of index policies for dynamic resource allocation which circumvents this difficulty. We utilise this framework to generate index policies for two model classes of independent interest. Their performance is evaluated in an extensive numerical study

Harnack inequalities and Bounds for Densities of Stochastic Processes

We consider possibly degenerate parabolic operators in the form of "sum of squares of vector fields plus a drif term" that are naturally associated to a suitable family of stochastic differential equations, and satisfying the H\uf6rmander condition. Note that, under this assumption, the operators considered have a smooth fundamental solution that agrees with the density of the corresponding stochastic process. We describe a method based on Harnack inequalities and on the construction of Harnack chains to prove lower bounds for the fundamental solution. We also briefly discuss PDE and SDE methods to prove analogous upper bounds. We eventually give a list of meaningful examples of operators to which the method applies

Harnack inequalities and Bounds for Densities of Stochastic Processes

We consider possibly degenerate parabolic operators in the form of "sum of squares of vector fields plus a drif term" that are naturally associated to a suitable family of stochastic differential equations, and satisfying the Hörmander condition. Note that, under this assumption, the operators considered have a smooth fundamental solution that agrees with the density of the corresponding stochastic process. We describe a method based on Harnack inequalities and on the construction of Harnack chains to prove lower bounds for the fundamental solution. We also briefly discuss PDE and SDE methods to prove analogous upper bounds. We eventually give a list of meaningful examples of operators to which the method applies

Linear and nonlinear ultraparabolic equations of Kolmogorov type arising in diffusion theory and in finance

This paper contains a survey on a series of papers by the authors, dealing with linear and non linear Kolmogorov-type operators, arising in diffusion theory, probability and finance. Some new results, about existence for Cauchy problems, regularity propertiesand pointwise estimates of solutions, are also announced

The Fock-Infeld Dispute: An Illustration of the Renaissance of General Relativity in the Soviet Union

International audienc