15,712 research outputs found
Deformations of Toric Singularities and Fractional Branes
Fractional branes added to a large stack of D3-branes at the singularity of a
Calabi-Yau cone modify the quiver gauge theory breaking conformal invariance
and leading to different kinds of IR behaviors. For toric singularities
admitting complex deformations we propose a simple method that allows to
compute the anomaly free rank distributions in the gauge theory corresponding
to the fractional deformation branes. This algorithm fits Altmann's rule of
decomposition of the toric diagram into a Minkowski sum of polytopes. More
generally we suggest how different IR behaviors triggered by fractional branes
can be classified by looking at suitable weights associated with the external
legs of the (p,q) web. We check the proposal on many examples and match in some
interesting cases the moduli space of the gauge theory with the deformed
geometry.Comment: 40 pages, 23 figures; typos correcte
QED Corrections to Hadronic Observables
When aiming at the percent precision in hadronic quantities calculated by
means of lattice simulations, isospin breaking effects become relevant. These
are of two kinds: up/down mass splitting and electromagnetic corrections. In
order to account properly for the latter, a consistent formulation of
electrically-charged states in finite volume is needed. In fact on a periodic
torus Gauss law and large gauge transformations forbid the propagation of
electrically-charged states. In this talk I will review methods that have been
used or proposed so far in order to circumvent this problem, while highlighting
practical as well as conceptual pros and cons. I will also review and discuss
various methods to calculate electromagnetic corrections to hadron masses and
decay rates in numerical simulations.Comment: 31 pages, Proceedings of Lattice 2017, extended version (the official
PoS has only 20 pages
Exotic PDE's
In the framework of the PDE's algebraic topology, previously introduced by A.
Pr\'astaro, are considered {\em exotic differential equations}, i.e.,
differential equations admitting Cauchy manifolds identifiable with exotic
spheres, or such that their boundaries are exotic spheres. For
such equations are obtained local and global existence theorems and stability
theorems. In particular the smooth (-dimensional) Poincar\'e conjecture is
proved. This allows to complete the previous Theorem 4.59 in \cite{PRA17} also
for the case .Comment: 51 pages, 1 figur
Complete analytic solution to Brownian unicycle dynamics
This paper derives a complete analytical solution for the probability
distribution of the configuration of a non-holonomic vehicle that moves in two
spatial dimensions by satisfying the unicycle kinematic constraints and in
presence of Brownian noises. In contrast to previous solutions, the one here
derived holds even in the case of arbitrary linear and angular speed. This
solution is obtained by deriving the analytical expression of any-order moment
of the probability distribution. To the best of our knowledge, an analytical
expression for any-order moment that holds even in the case of arbitrary linear
and angular speed, has never been derived before. To compute these moments, a
direct integration of the Langevin equation is carried out and each moment is
expressed as a multiple integral of the deterministic motion (i.e., the known
motion that would result in absence of noise). For the special case when the
ratio between the linear and angular speed is constant, the multiple integrals
can be easily solved and expressed as the real or the imaginary part of
suitable analytic functions. As an application of the derived analytical
results, the paper investigates the diffusivity of the considered Brownian
motion for constant and for arbitrary time-dependent linear and angular speed.Comment: 22 pages, 6 figures, 2 table
On the posterior distribution of the number of components in a finite mixture
The posterior distribution of the number of components k in a finite mixture
satisfies a set of inequality constraints. The result holds irrespective of the
parametric form of the mixture components and under assumptions on the prior
distribution weaker than those routinely made in the literature on Bayesian
analysis of finite mixtures. The inequality constraints can be used to perform
an ``internal'' consistency check of MCMC estimates of the posterior
distribution of k and to provide improved estimates which are required to
satisfy the constraints. Bounds on the posterior probability of k components
are derived using the constraints. Implications on prior distribution
specification and on the adequacy of the posterior distribution of k as a tool
for selecting an adequate number of components in the mixture are also
explored.Comment: Published at http://dx.doi.org/10.1214/009053604000000788 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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