We
explore two different threading approaches on a graphics processing
unit (GPU) exploiting two different characteristics of the current GPU
architecture. The fat thread approach tries to minimise data access time
by relying on shared memory and registers potentially sacrificing
parallelism. The thin thread approach maximises parallelism and tries to
hide access latencies. We apply these two approaches to the parallel
stochastic simulation of chemical reaction systems using the stochastic
simulation algorithm (SSA) by Gillespie. In these cases, the proposed
thin thread approach shows comparable performance while eliminating the
limitation of the reaction system's size.
Link to paper:
Much effort has been devoted to the study of weak scale particles, e.g. supersymmetric neutralinos, which have a relic abundance from thermal equilibrium in the early universe of order what is inferred for dark matter. This does not however provide any connection to the comparable abundance of baryonic matter, which must have a non-thermal origin. However "dark baryons" of mass ~5 GeV from a new strongly interacting sector would naturally provide dark matter and are consistent with recent putative signals in experiments such as CoGeNT and DAMA. Such particles would accrete in the Sun and affect heat transport in the interior so as to affect low energy neutrino fluxes and can possibly resolve the current conflict between helioseismological data and the Standard Solar Model.
We develop a theory based on relative entropy to show stabilityand uniqueness of extremal entropic Rankine-Hugoniot discontinuities forsystems of conservation laws (typically 1-shocks, n-shocks, 1-contactdiscontinuities and n-contact discontinuities of big amplitude), amongbounded entropic weak solutions having an additional strong traceproperty. The existence of a convex entropy is needed. No BV estimateis needed on the weak solutions considered. The theory holds withoutsmallness condition. The assumptions are quite general. For instance, thestrict hyperbolicity is not needed globally. For fluid mechanics, thetheory handles solutions with vacuum.
Abstract: We will explain a certain natural way to project elements of
the mapping class to simple closed curves on subsurfaces. Generalizing
a coordinate system on hyperbolic space, we will use these projections
to describe a way to characterize elements of the mapping class group
in terms of these projections. This point of view is useful in several
applications; time permitting we shall discuss how we have used this
to prove the Rapid Decay property for the mapping class group. This
talk will include joint work with Kleiner, Minksy, and Mosher.
We consider a dilute stationary system of N particles uniformly distributed in space and interacting pairwise according to a compactly supported potential, which is repellent at short distances and attractive at moderate distances. We are interested in the large-N behaviour of the system. We show that at a certain scale there are phase transitions in the temperature parameter and describe the energy and ground states explicitly in terms of a variational problem
Rough path theory, invented by T. Lyons, is a successful and general method for solving ordinary or stochastic differential equations driven by irregular H\"older paths, relying on the definition of a finite number of substitutes of iterated integrals satisfying definite algebraic and regularity properties.
Although these are known to exist, many questions are still open, in
particular: (1) "how many" possible choices are there ? (2) how to construct one explicitly ? (3) what is the connection to "true" iterated integrals obtained by an approximation scheme ?
In a series of papers, we (1) showed that "formal" rough paths (leaving aside
regularity) were exactly determined by so-called "tree data"; (2) gave several explicit constructions, the most recent ones relying on quantum field renormalization methods; (3) obtained with J. Magnen (Laboratoire de Physique Theorique, Ecole Polytechnique) a L\'evy area for fractional Brownian motion with Hurst index <1/4 as the limit in law of iterated integrals of a non-Gaussian interacting process, thus calling for a redefinition of the process itself. The latter construction belongs to the field of high energy physics, and as such established by using constructive field theory and renormalization; it should extend to a general rough path (work in progress).
The new model is that the universal small scale structure of high Reynolds number turbulence is determined by the dynamics of thin evolving shear layers, with thickness of the order of the Taylor micro scale,within which there are the familiar elongated vortices .Local quasi-linear dynamics shows how the shear layers act as barriers to external eddies and a filter for the transfer of energy to their interiors. The model is consistent with direct numerical simulations by Ishihara and Kaneda analysed in terms of conditional statistics relative to the layers and also with recent 4D measurements of lab turbulence by Wirth and Nickels. The model explains how the transport of energy into the layers leads to the observed inertial range spectrum and to the generation of intense structures, on the scale of the Kolmogorov micro-scale.
But the modelling also explains the important discrepancies between data and the Kolmogorov-Richardson cascade concept ,eg larger amplitudes of the smallest scale motions and of the higher moments ,and why the latter are generally less isotropic than lower order moments, eg in thermal convection. Ref JCRHunt , I Eames, P Davidson,J.Westerweel, J Fernando, S Voropayev, M Braza J Hyd Env Res 2010
Let C be a smooth plane cubic curve over the rationals. The Mordell--Weil Theorem can be restated as follows: there is a finite subset B of rational points such that all rational points can be obtained from this subset by successive tangent and secant constructions. It is conjectured that a minimal such B can be arbitrarily large; this is indeed the well-known conjecture that there are elliptic curves with arbitrarily large ranks. This talk is concerned with the corresponding problem for cubic surfaces.
We extend for the first time the linear discretization theory of Schaback, developed for meshfree methods, to nonlinear operator equations, relying heavily on methods of Böhmer, Vol I. There is no restriction to elliptic problems or to symmetric numerical methods like Galerkin techniques.
Trial spaces can be arbitrary, but have to approximate the solution well, and testing can be weak or strong. We present Galerkin techniques as an example. On the downside, stability is not easy to prove for special applications, and numerical methods have to be formulated as optimization problems. Results of this discretization theory cover error bounds and convergence rates. These results remain valid for the general case of fully nonlinear elliptic differential equations of second order. Some numerical examples are added for illustration.
The theory of C*-algebras provides a good realisation of noncommutative topology. There is a dictionary relating commutative C*-algebras with locally compact spaces, which can be used to import topological concepts into the C*-world. This philosophy fails in the case of homotopy, where a more sophisticated definition has to be given, leading to the notion of asymptotic morphisms.
As a by-product one obtains a generalisation of Borsuk's shape theory and a universal boundary map for cohomology theories of C*-algebras.
In this talk we will survey some aspects of social choice theory: in particular, various impossibility theorems about voting systems and strategies. We begin with the famous Arrow's impossibility theorem -- proving the non-existence of a 'fair' voting system -- before moving on to later developments, such as the Gibbard–Satterthwaite theorem, which states that all 'reasonable' voting systems are subject to tactical voting.
Given time, we will study extensions of impossibility theorems to micro-economic situations, and common strategies in game theory given the non-existence of optimal solutions.
Recently Frenkel and Hernandez introduced a kind of "Langlands duality" for characters of semisimple Lie algebras. We will discuss a representation-theoretic interpretation of their duality using quantum analogues of exceptional isogenies. Time permitting we will also discuss a branching rule and relations to Littelmann paths.
This talk introduces the topic of random walks on a finitely generated group and asks what properties of such a group can be detected through knowledge of such walks.
Both parts will deal with spherical objects in the bounded derived
category of coherent sheaves on K3 surfaces. In the first talk I will
focus on cycle theoretic aspects. For this we think of the Grothendieck
group of the derived category as the Chow group of the K3 surface (which
over the complex numbers is infinite-dimensional due to a result of
Mumford). The Bloch-Beilinson conjecture predicts that over number
fields the Chow group is small and I will show that this is equivalent to
the derived category being generated by spherical objects (which
I do not know how to prove). In the second talk I will turn to stability
conditions and show that a stability condition is determined by its
behavior with respect to the discrete collections of spherical objects.
The problem of checking existence for an Euler tour of a graph is trivial (are all vertex degrees even?). The problem of counting (or even approximate counting) Euler tours seems to be very difficult. I will describe two simple classes of graphs where the problem can be
solved exactly in polynomial time. And also talk about the many many classes of graphs where no positive results are known.
We introduce and study ergodic multidimensional diffusion processes interacting through their ranks; these interactions lead to invariant measures which are in broad agreement with stability properties of large equity markets over long time-periods.
The models we develop assign growth rates and variances that depend on both the name (identity) and the rank (according to capitalization) of each individual asset.
Such models are able realistically to capture critical features of the observed stability of capital distribution over the past century, all the while being simple enough to allow for rather detailed analytical study.
The methodologies used in this study touch upon the question of triple points for systems of interacting diffusions; in particular, some choices of parameters may permit triple (or higher-order) collisions to occur. We show, however, that such multiple collisions have no effect on any of the stability properties of the resulting system. This is accomplished through a detailed analysis of intersection local times.
The theory we develop has connections with the analysis of Queueing Networks in heavy traffic, as well as with models of competing particle systems in Statistical Mechanics, such as the Sherrington-Kirkpatrick model for spin-glasses.
"We present a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for subgame perfect Nash equilibrium points.
For a general controlled Markov process and a fairly general objective functional we derive an extension of the standard Hamilton-Jacobi-Bellman equation, in the form of a system of non-linear equations. We give some concrete examples, and in particular we study the case of mean variance optimal portfolios with wealth dependent risk aversion"