On certain Toeplitz operators and associated completely positive maps

We study Toeplitz operators with respect to a commuting $n$-tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a particular such tuple on a function space. The algebra of Toeplitz operators with respect to that particular tuple becomes naturally homeomorphic to $L^\infty$ of a certain compact subset of $\mathbb C^n$. Dual Toeplitz operators are characterized. En route, we prove an extension type theorem which is not only important for studying Toeplitz operators, but also has an independent interest because dilation theorems do not hold in general for $n>2$.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1706.0346

Deep Model Compression: Distilling Knowledge from Noisy Teachers

The remarkable successes of deep learning models across various applications have resulted in the design of deeper networks that can solve complex problems. How- ever, the increasing depth of such models also results in a higher storage and runtime complexity, which restricts the deployability of such very deep models on mobile and portable devices, which have limited storage and battery capacity. While many methods have been proposed for deep model compression in recent years, almost all of them have focused on reducing storage complexity. In this work, we extend the teacher-student framework for deep model com- pression, since it has the potential to address runtime and train time complexity too. We propose a simple method- ology to include a noise-based regularizer while training the student from the teacher, which provides a healthy im- provement in the performance of the student network. Our experiments on the CIFAR-10, SVHN and MNIST datasets show promising improvement, with the best performance on the CIFAR-10 dataset. We also conduct a comprehensive empirical evaluation of the proposed method under related settings on the CIFAR-10 dataset to show the promise of the proposed approach

Search for Higgs Bosons Decay H→γγH\to \gamma\gamma Using Vector Boson Fusion

The sensitivity of the ATLAS experiment to low mass SM Higgs produced via Vector Boson Fusion mechanism with $H\to \gamma\gamma$ is invest igated. A cut based event selection has been chosen to optimize the expected signal significance with this decay mode. A signal significance of 2. 2$\sigma$ may be achieved for M_H=130 \gev with 30 fb$^{-1}$ of accumulated luminosity

A number conserving theory for topologically protected degeneracy in one-dimensional fermions

Semiconducting nanowires in proximity to superconductors are among promising candidates to search for Majorana fermions and topologically protected degeneracies which may ultimately be used as building blocks for topological quantum computers. The prediction of neutral Majorana fermions in the proximity-induced superconducting systems ignores number-conservation and thus leaves open the conceptual question of how a topological degeneracy that is robust to all local perturbations arises in a number-conserving system. In this work, we study how local attractive interactions generate a topological ground-state near-degeneracy in a quasi one-dimensional superfluid using bosonization of the fermions. The local attractive interactions opens a topological quasiparticle gap in the odd channel wires (with more than one channel) with end Majorana modes associated with a topological near-degeneracy. We explicitly study the robustness of the topological degeneracy to local perturbations and find that such local perturbations result in quantum phase slips which split of the topological degeneracy by an amount that does not decrease exponentially with the length of the wire, but still decreases rapidly if the number of channels is large. Therefore a bulk superconductor with a large number of channels is crucial for true topological degeneracy.Comment: 11 pages, 2 figure

Productividad de la rotación anual raigrás- maíz en galicia: evaluación durante cinco años en regadío y secano y bajo dos sistemas de siembra

Es un estudio sobre la productividad de la rotación anual raigrás- maíz en galicia: evaluación durante cinco años en regadío y secano y bajo dos sistemas de siembr

Diamagnetic susceptibility obtained from the six-vertex model and its implications for the high-temperature diamagnetic state of cuprate superconductors

We study the diamagnetism of the 6-vertex model with the arrows as directed bond currents. To our knowledge, this is the first study of the diamagnetism of this model. A special version of this model, called F model, describes the thermal disordering transition of an orbital antiferromagnet, known as d-density wave (DDW), a proposed state for the pseudogap phase of the high-Tc cuprates. We find that the F model is strongly diamagnetic and the susceptibility may diverge in the high temperature critical phase with power law arrow correlations. These results may explain the surprising recent observation of a diverging low-field diamagnetic susceptibility seen in some optimally doped cuprates within the DDW model of the pseudogap phase.Comment: 4.5 pages, 2 figures, revised version accepted in Phys. Rev. Let