Domains in Infinite Jets: C-Spectral Sequence

Domains in infinite jets present the simplest class of diffieties with boundary. In this note some basic elements of geometry of these domains are introduced and an analogue of the C-spectral sequence in this context is studied. This, in particular, allows cohomological interpretation and analysis of initial data, boundary conditions, etc, for general partial differential equations and of transversality conditions in calculus of variations. This kind applications and extensions to arbitrary diffieties will be considered in subsequent publications.Comment: 7 pages; no proofs give

The 750 GeV Diphoton Excess as a First Light on Supersymmetry Breaking

One of the most exciting explanations advanced for the recent diphoton excess found by ATLAS and CMS is in terms of sgoldstino decays: a signal of low-energy supersymmetry-breaking scenarios. The sgoldstino, a scalar, couples directly to gluons and photons, with strength related to gaugino masses, that can be of the right magnitude to explain the excess. However, fitting the suggested resonance width, Gamma ~ 45 GeV, is not so easy. In this paper we explore efficient possibilities to enhance the sgoldstino width, via the decay into two Higgses, two Higgsinos and through mixing between the sgoldstino and the Higgs boson. In addition, we present an alternative and more efficient mechanism to generate a mass splitting between the scalar and pseudoscalar components of the sgoldstino, which has been suggested as an interesting alternative explanation to the apparent width of the resonance.Comment: 14 pages, 3 figure

Finite size scaling of the bayesian perceptron

We study numerically the properties of the bayesian perceptron through a gradient descent on the optimal cost function. The theoretical distribution of stabilities is deduced. It predicts that the optimal generalizer lies close to the boundary of the space of (error-free) solutions. The numerical simulations are in good agreement with the theoretical distribution. The extrapolation of the generalization error to infinite input space size agrees with the theoretical results. Finite size corrections are negative and exhibit two different scaling regimes, depending on the training set size. The variance of the generalization error vanishes for $N \rightarrow \infty$ confirming the property of self-averaging.Comment: RevTeX, 7 pages, 7 figures, submitted to Phys. Rev.

Predicting spinor condensate dynamics from simple principles

We study the spin dynamics of quasi-one-dimensional F=1 condensates both at zero and finite temperatures for arbitrary initial spin configurations. The rich dynamical evolution exhibited by these non-linear systems is explained by surprisingly simple principles: minimization of energy at zero temperature, and maximization of entropy at high temperature. Our analytical results for the homogeneous case are corroborated by numerical simulations for confined condensates in a wide variety of initial conditions. These predictions compare qualitatively well with recent experimental observations and can, therefore, serve as a guidance for on-going experiments.Comment: 4 pages, 2 figures. v3: matches version appeared in PR