Symmetric Laplacians, Quantum Density Matrices and their Von-Neumann Entropy

We show that the (normalized) symmetric Laplacian of a simple graph can be obtained from the partial trace over a pure bipartite quantum state that resides in a bipartite Hilbert space (one part corresponding to the vertices, the other corresponding to the edges). This suggests an interpretation of the symmetric Laplacian's Von Neumann entropy as a measure of bipartite entanglement present between the two parts of the state. We then study extreme values for a connected graph's generalized R\'enyi-$p$ entropy. Specifically, we show that (1) the complete graph achieves maximum entropy, (2) the $2$-regular graph: a) achieves minimum R\'enyi-$2$ entropy among all $k$-regular graphs, b) is within $\log 4/3$ of the minimum R\'enyi-$2$ entropy and $\log4\sqrt{2}/3$ of the minimum Von Neumann entropy among all connected graphs, c) achieves a Von Neumann entropy less than the star graph. Point $(2)$ contrasts sharply with similar work applied to (normalized) combinatorial Laplacians, where it has been shown that the star graph almost always achieves minimum Von Neumann entropy. In this work we find that the star graph achieves maximum entropy in the limit as the number of vertices grows without bound. Keywords: Symmetric; Laplacian; Quantum; Entropy; Bounds; R\'enyi

Outage Performance Analysis of Multicarrier Relay Selection for Cooperative Networks

In this paper, we analyze the outage performance of two multicarrier relay selection schemes, i.e. bulk and per-subcarrier selections, for two-hop orthogonal frequency-division multiplexing (OFDM) systems. To provide a comprehensive analysis, three forwarding protocols: decode-and-forward (DF), fixed-gain (FG) amplify-and-forward (AF) and variable-gain (VG) AF relay systems are considered. We obtain closed-form approximations for the outage probability and closed-form expressions for the asymptotic outage probability in the high signal-to-noise ratio (SNR) region for all cases. Our analysis is verified by Monte Carlo simulations, and provides an analytical framework for multicarrier systems with relay selection

The von Neumann Theil index : characterizing graph centralization using the von Neumann index

We show that the von Neumann entropy (from herein referred to as the von Neumann index) of a graph’s trace normalized combinatorial Laplacian provides structural information about the level of centralization across a graph. This is done by considering the Theil index, which is an established statistical measure used to determine levels of inequality across a system of ‘agents’, for example, income levels across a population. Here, we establish a Theil index for graphs, which provides us with a macroscopic measure of graph centralization. Concretely, we show that the von Neumann index can be used to bound the graph’s Theil index, and thus we provide a direct characterization of graph centralization via the von Neumann index. Because of the algebraic similarities between the bound and the Theil index, we call the bound the von Neumann Theil index. We elucidate our ideas by providing examples and a discussion of different n=7 vertex graphs. We also discuss how the von Neumann Theil index provides a more comprehensive measure of centralization when compared to traditional centralization measures, and when compared to the graph’s classical Theil index. This is because it more accurately accounts for macro-structural changes that occur from micro-structural changes in the graph (e.g. the removal of a vertex). Finally, we provide future direction, showing that the von Neumann Theil index can be generalized by considering the Rényi entropy. We then show that this generalization can be used to bound the negative logarithm of the graph’s Jain fairness index

Do women with diabetes need more intensive action for cardiovascular reduction than men with diabetes?

Purpose of Review: This narrative review makes the case for greater efforts to reduce cardiovascular disease (CVD) risk in women with diabetes. Recent Findings: In a recent meta-analysis including five CVOTs of diabetes medications with 46,606 subjects, women (vs men) with type 2 diabetes had a higher relative risk for stroke (RR 1.28; 95% CI 1.09, 1.50) and heart failure (1.30; 1.21, 1.40). Prior studies found higher “within-gender” RR for CVD mortality in women with diabetes although men have an absolute higher risk. Women with prior gestational diabetes mellitus (GDM) have a 2-fold higher CVD risk than the background population. Worse CVD and CVD risk factor management in women, as well as lower female therapy adherence, contribute further to these disparities. Summary: The mechanism behind this excess risk includes biological, hormonal, socioeconomic, clinical, and behavioral factors that still require further investigation. The need for more intensive CVD reduction in women now includes more attention to screening for both incident diabetes and CVD risk factors among high-risk women

Comparisons Between Spectral Quality Metrics and Analyst Performance in Hyperspectral Target Detection

Quantitative methods to assess or predict the quality of a spectral image continue to be the subject of a number of current research activities. An accepted methodology would be highly desirable for use in data collection tasking or data archive searching in ways analogous to the current prediction of panchromatic image quality through the National Imagery Interpretation Rating Scale (NIIRS) using the General Image Quality Equation (GIQE). A number of approaches to the estimation of quality of a spectral image have been published, but most capture only the performance of automated algorithms applied to the spectral data. One recently introduced metric, however, the General Spectral Utility Metric (GSUM), provides for a framework to combine the performance from the spectral aspects together with the spatial aspects. In particular, this framework allows the metric to capture the utility of a spectral image resulting when the human analyst is included in the process. This is important since nearly all hyperspectral imagery analysis procedures include an analyst. To investigate the relationships between candidate spectral metrics and task performance from volunteer human analysts in conjunction with the automated results, simulated images are generated and processed in a blind test. The performance achieved by the analysts is then compared to predictions made from various spectral quality metrics to determine how well the metrics function. The task selected is one of finding a specific vehicle in a cluttered environment using a detection map produced from the hyperspectral image along with a panchromatic rendition of the image. Various combinations of spatial resolution, number of spectral bands, and signal-to-noise ratios are investigated as part of the effort

Review of Top Quark Physics

We present an overview of Top Quark Physics - from what has been learned so far at the Tevatron, to the searches that lie ahead at present and future colliders. We summarize the richness of the measurements and discuss their possible impact on our understanding of the Standard Model by pointing out their key elements and limitations. When possible, we discuss how the top quark may provide a connection to new or unexpected physics.Comment: 84 pp. With permission from the Annual Review of Nuclear & Particle Science. Final version of this material is scheduled to appear in the Annual Review of Nuclear & Particle Science Vol. 53, to be published in December 2003 by Annual Reviews (http://www.annualreviews.org

Quantum authentication with unitary coding sets

A general class of authentication schemes for arbitrary quantum messages is proposed. The class is based on the use of sets of unitary quantum operations in both transmission and reception, and on appending a quantum tag to the quantum message used in transmission. The previous secret between partners required for any authentication is a classical key. We obtain the minimal requirements on the unitary operations that lead to a probability of failure of the scheme less than one. This failure may be caused by someone performing a unitary operation on the message in the channel between the communicating partners, or by a potential forger impersonating the transmitter.Comment: RevTeX4, 10 page