Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit

Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained

On the Supersymplectic Homogeneous Superspace Underlying the OSp(1/2) Coherent States

In this work we extend Onofri and Perelomov's coherent states methods to the recently introduced $OSp(1/2)$ coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely the homogeneous superspace $OSp(1/2)/U(1)$, which is clearly identified with a supercoadjoint orbit of $OSp(1/2)$ by exhibiting the corresponding equivariant supermoment map. Moreover, this supermanifold is shown to be a nontrivial example of Rothstein's supersymplectic supermanifolds. More precisely, we show that its supersymplectic structure is completely determined in terms of $SU(1,1)$-invariant (but unrelated) K\"ahler $2$-form and K\"ahler metric on the unit disc. This result allows us to define the notions of a superK\"ahler supermanifold and a superK\"ahler superpotential, the geometric structure of the former being encoded into the latter.Comment: 19 pgs, PlainTeX, Preprint CRM-185

The Ubiquity of Large Graphs and Surprising Challenges of Graph Processing: Extended Survey

Graph processing is becoming increasingly prevalent across many application domains. In spite of this prevalence, there is little research about how graphs are actually used in practice. We performed an extensive study that consisted of an online survey of 89 users, a review of the mailing lists, source repositories, and whitepapers of a large suite of graph software products, and in-person interviews with 6 users and 2 developers of these products. Our online survey aimed at understanding: (i) the types of graphs users have; (ii) the graph computations users run; (iii) the types of graph software users use; and (iv) the major challenges users face when processing their graphs. We describe the participants' responses to our questions highlighting common patterns and challenges. Based on our interviews and survey of the rest of our sources, we were able to answer some new questions that were raised by participants' responses to our online survey and understand the specific applications that use graph data and software. Our study revealed surprising facts about graph processing in practice. In particular, real-world graphs represent a very diverse range of entities and are often very large, scalability and visualization are undeniably the most pressing challenges faced by participants, and data integration, recommendations, and fraud detection are very popular applications supported by existing graph software. We hope these findings can guide future research

Electroweak Phase Transition in the U(1)' MSSM

In this work, we have investigated the nature of the electroweak phase transition in the U(1) extended minimal supersymmetric standard model without introducing any exotic fields. The effective potential has been estimated exactly at finite temperature taking into account the whole particle spectrum. For reasonable values of the lightest Higgs and neutralino, we found that the electroweak phase transition could be strongly first order due to: (1) the interactions of the singlet with the doublets in the effective potential, and (2) the evolution of the wrong vacuum that delays the transition.Comment: substantial changes, references added, 18 pages, 4 figure

Unknown Health States Recognition With Collective Decision Based Deep Learning Networks In Predictive Maintenance Applications

At present, decision making solutions developed based on deep learning (DL) models have received extensive attention in predictive maintenance (PM) applications along with the rapid improvement of computing power. Relying on the superior properties of shared weights and spatial pooling, Convolutional Neural Network (CNN) can learn effective representations of health states from industrial data. Many developed CNN-based schemes, such as advanced CNNs that introduce residual learning and multi-scale learning, have shown good performance in health state recognition tasks under the assumption that all the classes are known. However, these schemes have no ability to deal with new abnormal samples that belong to state classes not part of the training set. In this paper, a collective decision framework for different CNNs is proposed. It is based on a One-vs-Rest network (OVRN) to simultaneously achieve classification of known and unknown health states. OVRN learn state-specific discriminative features and enhance the ability to reject new abnormal samples incorporated to different CNNs. According to the validation results on the public dataset of Tennessee Eastman Process (TEP), the proposed CNN-based decision schemes incorporating OVRN have outstanding recognition ability for samples of unknown heath states, while maintaining satisfactory accuracy on known states. The results show that the new DL framework outperforms conventional CNNs, and the one based on residual and multi-scale learning has the best overall performance