Convex relaxation of mixture regression with efficient algorithms

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data

Control of conditional pattern with polarization entanglement

Conditional interference patterns can be obtained with twin photons from spontaneous parametric down-conversion and the phase of the pattern can be controlled by the relative transverse position of the signal and idler detectors. Using a configuration that produces entangled photons in both polarization and transverse momentum we report on the control of the conditional patterns by acting on the polarization degree of freedom.Comment: Submitted for publication in Optics Communication

Image transfer through a chaotic channel by intensity correlations

The three-wave mixing processes in a second-order nonlinear medium can be used for imaging protocols, in which an object field is injected into the nonlinear medium together with a reference field and an image field is generated. When the reference field is chaotic, the image field is also chaotic and does not carry any information about the object. We show that a clear image of the object be extracted from the chaotic image field by measuring the spatial intensity correlations between this field and one Fourier component of the reference. We experimentally verify this imaging protocol in the case of frequency downconversion.Comment: 17 pages, 7 figure

Explaining ATLAS and CMS Results Within the Reduced Minimal 3-3-1 model

Recently the ATLAS and CMS collaborations announced the discovery of a higgs particle with a mass of $\sim 125$ GeV. The results are mildly consistent with the Standard Model Higgs boson. However, the combined data from these collaborations seem to point to an excess in the $h \rightarrow \gamma \gamma$ channel. In this work we analyze under which conditions this excess may be plausibly explained within the reduced minimal 3-3-1 model, while being consistent with bb, WW, ZZ and $\tau^+\tau^-$ channels. Moreover, we derive the properties of the heavy neutral and the doubly charged scalars predicted by the model. We then conclude that at a scale of a few TeV, this model provides a good fit to the ATLAS and CMS signal strength measurements, and therefore stands as an appealing alternative to the standard model.Comment: 23 pages, 9 figures. References adde

Structural fluctuations and quantum transport through DNA molecular wires: a combined molecular dynamics and model Hamiltonian approach

Charge transport through a short DNA oligomer (Dickerson dodecamer) in presence of structural fluctuations is investigated using a hybrid computational methodology based on a combination of quantum mechanical electronic structure calculations and classical molecular dynamics simulations with a model Hamiltonian approach. Based on a fragment orbital description, the DNA electronic structure can be coarse-grained in a very efficient way. The influence of dynamical fluctuations arising either from the solvent fluctuations or from base-pair vibrational modes can be taken into account in a straightforward way through time series of the effective DNA electronic parameters, evaluated at snapshots along the MD trajectory. We show that charge transport can be promoted through the coupling to solvent fluctuations, which gate the onsite energies along the DNA wire

Combining type I and type II seesaw mechanisms in the minimal 3-3-1 model

The minimal 3-3-1 model is perturbative until energies around 4-5TeV, posing a challenge to generate neutrino masses at eV scale, mainly if one aims to take advantage of the seesaw mechanism. As a means to circumvent this problem we propose a modification of the model such that it accommodates the type I and type II seesaw mechanisms altogether. We show that the conjunction of both mechanisms yield a neutrino mass expression suppressed by a high power of the cutoff scale, $M^5$, in its denominator. With such a suppression term we naturally obtain neutrino masses at eV scale when $M$ is around few TeV. We also investigate the size of lepton flavor violation through the process $\mu \rightarrow e\gamma$.Comment: about 15 pages, no figure