Localization of Multi-Dimensional Wigner Distributions

A well known result of P. Flandrin states that a Gaussian uniquely maximizes the integral of the Wigner distribution over every centered disc in the phase plane. While there is no difficulty in generalizing this result to higher-dimensional poly-discs, the generalization to balls is less obvious. In this note we provide such a generalization.Comment: Minor corrections, to appear in the Journal of Mathematical Physic

A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces

Entanglement witnesses (EWs) constitute one of the most important entanglement detectors in quantum systems. Nevertheless, their complete characterization, in particular with respect to the notion of optimality, is still missing, even in the decomposable case. Here we show that for any qubit-qunit decomposable EW (DEW) W the three statements are equivalent: (i) the set of product vectors obeying \bra{e,f}W\ket{e,f}=0 spans the corresponding Hilbert space, (ii) W is optimal, (iii) W=Q^{\Gamma} with Q denoting a positive operator supported on a completely entangled subspace (CES) and \Gamma standing for the partial transposition. While, implications $(i)\Rightarrow(ii)$ and $(ii)\Rightarrow(iii)$ are known, here we prove that (iii) implies (i). This is a consequence of a more general fact saying that product vectors orthogonal to any CES in C^{2}\otimes C^{n} span after partial conjugation the whole space. On the other hand, already in the case of C^{3}\otimes C^{3} Hilbert space, there exist DEWs for which (iii) does not imply (i). Consequently, either (i) does not imply (ii), or (ii) does not imply (iii), and the above transparent characterization obeyed by qubit-qunit DEWs, does not hold in general.Comment: 13 pages, proof of lemma 4 corrected, theorem 3 removed, some parts improve

Transfer of K-types on local theta lifts of characters and unitary lowest weight modules

In this paper we study representations of the indefinite orthogonal group O(n,m) which are local theta lifts of one dimensional characters or unitary lowest weight modules of the double covers of the symplectic groups. We apply the transfer of K-types on these representations of O(n,m), and we study their effects on the dual pair correspondences. These results provide examples that the theta lifting is compatible with the transfer of K-types. Finally we will use these results to study subquotients of some cohomologically induced modules

The impact of luteal phase support on endometrial estrogen and progesterone receptor expression: a randomized control trial

<p>Abstract</p> <p>Background</p> <p>To assess the impact of luteal phase support on the expression of estrogen receptor (ER) alpha and progesterone receptors B (PR-B) on the endometrium of oocyte donors undergoing controlled ovarian hyperstimulation (COH).</p> <p>Methods</p> <p>A prospective, randomized study was conducted in women undergoing controlled ovarian hyperstimulation for oocyte donation. Participants were randomized to receive no luteal support, vaginal progesterone alone, or vaginal progesterone plus orally administered 17 Beta estradiol. Endometrial biopsies were obtained at 4 time points in the luteal phase and evaluated by tissue microarray for expression of ER alpha and PR-B.</p> <p>Results</p> <p>One-hundred and eight endometrial tissue samples were obtained from 12 patients. No differences were found in expression of ER alpha and PR-B among all the specimens with the exception of one sample value.</p> <p>Conclusions</p> <p>The administration of progesterone during the luteal phase of COH for oocyte donor cycles, either with or without estrogen, does not significantly affect the endometrial expression of ER alpha and PR.</p

Forms on Vector Bundles Over Hyperbolic Manifolds and the Conformal Anomaly

We study gauge theories based on abelian $p-$forms on real compact hyperbolic manifolds. An explicit formula for the conformal anomaly corresponding to skew--symmetric tensor fields is obtained, by using zeta--function regularization and the trace tensor kernel formula. Explicit exact and numerical values of the anomaly for $p-$forms of order up to $p=4$ in spaces of dimension up to $n=10$ are then calculated.Comment: 13 pages, 2 table

Locality-oblivious cache organization leveraging single-cycle multi-hop NoCs

Locality has always been a critical factor in on-chip data placement on CMPs as accessing further-away caches has in the past been more costly than accessing nearby ones. Substantial research on locality-aware designs have thus focused on keeping a copy of the data private. However, this complicatesthe problem of data tracking and search/invalidation; tracking the state of a line at all on-chip caches at a directory or performing full-chip broadcasts are both non-scalable and extremely expensive solutions. In this paper, we make the case for Locality-Oblivious Cache Organization (LOCO), a CMP cache organization that leverages the on-chip network to create virtual single-cycle paths between distant caches, thus redefining the notion of locality. LOCO is a clustered cache organization, supporting both homogeneous and heterogeneous cluster sizes, and provides near single-cycle accesses to data anywhere within the cluster, just like a private cache. Globally, LOCO dynamically creates a virtual mesh connecting all the clusters, and performs an efficient global data search and migration over this virtual mesh, without having to resort to full-chip broadcasts or perform expensive directory lookups. Trace-driven and full system simulations running SPLASH-2 and PARSEC benchmarks show that LOCO improves application run time by up to 44.5% over baseline private and shared cache.Semiconductor Research CorporationUnited States. Defense Advanced Research Projects Agency (Semiconductor Technology Advanced Research Network