Numerical analysis of the master equation

Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme that remains stable with much larger time increments than can be used in standard methods. When only the stationary distribution is required, a direct iteration method is even more rapid; this method may be extended to construct the quasi-stationary distribution of a process with an absorbing state. Applications to birth-and-death processes reveal gains in efficiency of two or more orders of magnitude.Comment: 7 pages 3 figure

The SU(2) X U(1) Electroweak Model based on the Nonlinearly Realized Gauge Group

The electroweak model is formulated on the nonlinearly realized gauge group SU(2) X U(1). This implies that in perturbation theory no Higgs field is present. The paper provides the effective action at the tree level, the Slavnov Taylor identity (necessary for the proof of unitarity), the local functional equation (used for the control of the amplitudes involving the Goldstone bosons) and the subtraction procedure (nonstandard, since the theory is not power-counting renormalizable). Particular attention is devoted to the number of independent parameters relevant for the vector mesons; in fact there is the possibility of introducing two mass parameters. With this choice the relation between the ratio of the intermediate vector meson masses and the Weinberg angle depends on an extra free parameter. We briefly outline a method for dealing with \gamma_5 in dimensional regularization. The model is formulated in the Landau gauge for sake of simplicity and conciseness: the QED Ward identity has a simple and intriguing form.Comment: 19 pages, final version published by Int. J. Mod. Phys. A, some typos corrected in eqs.(1) and (41). The errors have a pure editing origin. Therefore they do not affect the content of the pape

TASEP hydrodynamics using microscopic characteristics

The convergence of the totally asymmetric simple exclusion process to the solution of the Burgers equation is a classical result. In his seminal 1981 paper, Herman Rost proved the convergence of the density fields and local equilibrium when the limiting solution of the equation is a rarefaction fan. An important tool of his proof is the subadditive ergodic theorem. We prove his results by showing how second class particles transport the rarefaction-fan solution, as characteristics do for the Burgers equation, avoiding subadditivity. In the way we show laws of large numbers for tagged particles, fluxes and second class particles, and simplify existing proofs in the shock cases. The presentation is self contained.Comment: 20 pages, 13 figures. This version is accepted for publication in Probability Surveys, February 20 201

Path-integral over non-linearly realized groups and Hierarchy solutions

The technical problem of deriving the full Green functions of the elementary pion fields of the nonlinear sigma model in terms of ancestor amplitudes involving only the flat connection and the nonlinear sigma model constraint is a very complex task. In this paper we solve this problem by integrating, order by order in the perturbative loop expansion, the local functional equation derived from the invariance of the SU(2) Haar measure under local left multiplication. This yields the perturbative definition of the path-integral over the non-linearly realized SU(2) group.Comment: 26 page

Learning Visual Attributes

We present a probabilistic generative model of visual attributes, together with an efficient learning algorithm. Attributes are visual qualities of objects, such as ‘red’, ‘striped’, or ‘spotted’. The model sees attributes as patterns of image segments, repeatedly sharing some characteristic properties. These can be any combination of appearance, shape, or the layout of segments within the pattern. Moreover, attributes with general appearance are taken into account, such as the pattern of alternation of any two colors which is characteristic for stripes. To enable learning from unsegmented training images, the model is learnt discriminatively, by optimizing a likelihood ratio. As demonstrated in the experimental evaluation, our model can learn in a weakly supervised setting and encompasses a broad range of attributes. We show that attributes can be learnt starting from a text query to Google image search, and can then be used to recognize the attribute and determine its spatial extent in novel real-world images.

Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure

In [arXiv:0804.3035] we studied an interacting particle system which can be also interpreted as a stochastic growth model. This model belongs to the anisotropic KPZ class in 2+1 dimensions. In this paper we present the results that are relevant from the perspective of stochastic growth models, in particular: (a) the surface fluctuations are asymptotically Gaussian on a sqrt(ln(t)) scale and (b) the correlation structure of the surface is asymptotically given by the massless field.Comment: 13 pages, 4 figure