Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators

Let B=A+K where A is a bounded selfadjoint operator and K is an element of the von Neumann-Schatten ideal S_p with p>1. Let {\lambda_n} denote an enumeration of the discrete spectrum of B. We show that \sum_n \dist(\lambda_n, \sigma(A))^p is bounded from above by a constant multiple of |K|_p^p. We also derive a unitary analog of this estimate and apply it to obtain new estimates on zero-sets of Cauchy transforms.Comment: Differences to previous version: Extended Introduction, new Section 5, additional references. To appear in Int. Eq. Op. Theor

Quantum Correlations in Large-Dimensional States of High Symmetry

In this article, we investigate how quantum correlations behave for the so-called Werner and pseudo-pure families of states. The latter refers to states formed by mixing any pure state with the totally mixed state. We derive closed expressions for the Quantum Discord (QD) and the Relative Entropy of Quantumness (REQ) for these families of states. For Werner states, the classical correlations are seen to vanish in high dimensions while the amount of quantum correlations remain bounded and become independent of whether or not the the state is entangled. For pseudo-pure states, nearly the opposite effect is observed with both the quantum and classical correlations growing without bound as the dimension increases and only as the system becomes more entangled. Finally, we verify that pseudo-pure states satisfy the conjecture of [\textit{Phys. Rev. A} \textbf{84}, 052110 (2011)] which says that the Geometric Measure of Discord (GD) always upper bounds the squared Negativity of the state

Generating qudits with d=3,4 encoded on two-photon states

We present an experimental method to engineer arbitrary pure states of qudits with d=3,4 using linear optics and a single nonlinear crystal.Comment: 4 pages, 1 eps figure. Minor changes. The title has been changed for publication on Physical Review

Extensions of Lieb's concavity theorem

The operator function (A,B)\to\tr f(A,B)(K^*)K, defined on pairs of bounded self-adjoint operators in the domain of a function f of two real variables, is convex for every Hilbert Schmidt operator K, if and only if f is operator convex. As a special case we obtain a new proof of Lieb's concavity theorem for the function (A,B)\to\tr A^pK^*B^{q}K, where p and q are non-negative numbers with sum p+q\le 1. In addition, we prove concavity of the operator function (A,B)\to \tr(A(A+\mu_1)^{-1}K^* B(B+\mu_2)^{-1}K) on its natural domain D_2(\mu_1,\mu_2), cf. Definition 4.1Comment: The format of one reference is changed such that CiteBase can identify i

Impaired glucose tolerance or newly diagnosed diabetes mellitus diagnosed during admission adversely affects prognosis after myocardial infarction: An observational study

Objective To investigate the prognostic effect of newly diagnosed diabetes mellitus (NDM) and impaired glucose tolerance (IGT) post myocardial infarction (MI). Research Design and Methods Retrospective cohort study of 768 patients without preexisting diabetes mellitus post-MI at one centre in Yorkshire between November 2005 and October 2008. Patients were categorised as normal glucose tolerance (NGT n = 337), IGT (n = 279) and NDM (n = 152) on predischarge oral glucose tolerance test (OGTT). Primary end-point was the first occurrence of major adverse cardiovascular events (MACE) including cardiovascular death, non-fatal MI, severe heart failure (HF) or non-haemorrhagic stroke. Secondary end-points were all cause mortality and individual components of MACE. Results Prevalence of NGT, impaired fasting glucose (IFG), IGT and NDM changed from 90%, 6%, 0% and 4% on fasting plasma glucose (FPG) to 43%, 1%, 36% and 20% respectively after OGTT. 102 deaths from all causes (79 as first events of which 46 were cardiovascular), 95 non fatal MI, 18 HF and 9 non haemorrhagic strokes occurred during 47.2 ± 9.4 months follow up. Event free survival was lower in IGT and NDM groups. IGT (HR 1.54, 95% CI: 1.06–2.24, p = 0.024) and NDM (HR 2.15, 95% CI: 1.42–3.24, p = 0.003) independently predicted MACE free survival. IGT and NDM also independently predicted incidence of MACE. NDM but not IGT increased the risk of secondary end-points. Conclusion Presence of IGT and NDM in patients presenting post-MI, identified using OGTT, is associated with increased incidence of MACE and is associated with adverse outcomes despite adequate secondary prevention

Second-order Democratic Aggregation

Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization after aggregation can significantly improve the generalization of second-order representations. We show that matrix power normalization implicitly equalizes contributions during aggregation thus establishing a connection between matrix normalization techniques and prior work on minimizing interference. Based on the analysis we present {\gamma}-democratic aggregators that interpolate between sum ({\gamma}=1) and democratic pooling ({\gamma}=0) outperforming both on several classification tasks. Moreover, unlike power normalization, the {\gamma}-democratic aggregations can be computed in a low dimensional space by sketching that allows the use of very high-dimensional second-order features. This results in a state-of-the-art performance on several datasets

UV and X-ray Spectral Lines of FeXXIII Ion for Plasma Diagnostics

We have calculated X-ray and UV spectra of Be-like Fe (FeXXIII) ion in collisional-radiative model including all fine-structure transitions among the 2s^2, 2s2p, 2p^2, 2snl, and 2pnl levels where n=3 and 4, adopting data for the collision strengths by Zhang & Sampson (1992) and by Sampson, Goett, & Clark (1984). Some line intensity ratios can be used for the temperature diagnostics. We show 5 ratios in UV region and 9 ratios in X-ray region as a function of electron temperature and density at 0.3keV < T_e < 10keV and $n_e = 1 - 10^{25} cm^{-3}$. The effect of cascade in these line ratios and in the level population densities are discussed.Comment: LaTeX, 18 pages, 10 Postscript figures. To appear in Physica Script

How did the discussion go: Discourse act classification in social media conversations

We propose a novel attention based hierarchical LSTM model to classify discourse act sequences in social media conversations, aimed at mining data from online discussion using textual meanings beyond sentence level. The very uniqueness of the task is the complete categorization of possible pragmatic roles in informal textual discussions, contrary to extraction of question-answers, stance detection or sarcasm identification which are very much role specific tasks. Early attempt was made on a Reddit discussion dataset. We train our model on the same data, and present test results on two different datasets, one from Reddit and one from Facebook. Our proposed model outperformed the previous one in terms of domain independence; without using platform-dependent structural features, our hierarchical LSTM with word relevance attention mechanism achieved F1-scores of 71\% and 66\% respectively to predict discourse roles of comments in Reddit and Facebook discussions. Efficiency of recurrent and convolutional architectures in order to learn discursive representation on the same task has been presented and analyzed, with different word and comment embedding schemes. Our attention mechanism enables us to inquire into relevance ordering of text segments according to their roles in discourse. We present a human annotator experiment to unveil important observations about modeling and data annotation. Equipped with our text-based discourse identification model, we inquire into how heterogeneous non-textual features like location, time, leaning of information etc. play their roles in charaterizing online discussions on Facebook