A holographic proof of the strong subadditivity of entanglement entropy

When a quantum system is divided into subsystems, their entanglement entropies are subject to an inequality known as "strong subadditivity". For a field theory this inequality can be stated as follows: given any two regions of space $A$ and $B$, $S(A) + S(B) \ge S(A \cup B) + S(A \cap B)$. Recently, a method has been found for computing entanglement entropies in any field theory for which there is a holographically dual gravity theory. In this note we give a simple geometrical proof of strong subadditivity employing this holographic prescription.Comment: 9 pages, 3 figure

Epidemiology of Prostate and Testicular Cancer

Prostate and testicular cancers account for a large percentage of cancer morbidity in men in the United States and worldwide due to high prevalence rates that continue to grow. Patterns of incidence and mortality vary greatly in both cancers among men of different age groups, ethnicities, and geographic locations. This article summarizes the incidence, prognosis, and risk factors of both prostate and testicular cancers, globally and in the United States

Aging and cancer mortality: Dynamics of change and sex differences

Age-related changes in cancer mortality risk are important for understanding the processes of disease and aging interaction. The extent to which these age changes differ by sex further contributes to this understanding but has not been well studied to date. We conducted a systematic examination of dynamics and heterogeneity of age changes in cancer mortality rates for the top 14 cancer sites using vital statistics from the NCHS and SEER between 1969 and 2007. We assessed patterns of age changes in site-specific mortality rates in terms of both increase (age slope) and acceleration (change in age slope) as measured by the log-log acceleration rate (LLA). We assessed sex differences in mortality rates through sex mortality rate ratios and sex differences in age changes through comparisons of the LLA by sex. The logged male-to-female mortality ratios are positive but vary substantially with age in magnitude. And the age patterns of sex ratios also vary across sites. The LLA values show similar declines and hence slowdowns of mortality increment into or during old age for both sexes for most sites and periods. Post-reproductive changes in sex differences in cancer mortality are not entirely consistent with the estrogenic hypothesis about the anticarcinogenic effects of sex hormones and suggest the utility of the multistage model of disease progression for some tumor sites. Analysis of age dynamics and sex differences in cancer mortality may modify extant aging-related theories of carcinogenesis and frame future searches for specific explanatory factors

Rhodium Bis(quinolinyl)benzene Complexes for Methane Activation and Functionalization

A series of rhodium(III) bis(quinolinyl)benzene (bisq^x) complexes was studied as candidates for the homogeneous partial oxidation of methane. Density functional theory (DFT) (M06 with Poisson continuum solvation) was used to investigate a variety of (bisq^x) ligand candidates involving different functional groups to determine the impact on Rh^(III)(bisq^x)-catalyzed methane functionalization. The free energy activation barriers for methane C H activation and Rh–methyl functionalization at 298 K and 498 K were determined. DFT studies predict that the best candidate for catalytic methane functionalization is Rh^(III) coordinated to unsubstituted bis(quinolinyl)benzene (bisq). Support is also found for the prediction that the η^2-benzene coordination mode of (bisq^x) ligands on Rh encourages methyl group functionalization by serving as an effective leaving group for S_N2 and S_R2 attack

Long-Range C–H Bond Activation by Rh^(III)-Carboxylates

Traditional C–H bond activation by a concerted metalation–deprotonation (CMD) mechanism involves precoordination of the C–H bond followed by deprotonation from an internal base. Reported herein is a “through-arene” activation of an uncoordinated benzylic C–H bond that is 6 bonds away from a Rh^(III) ion. The mechanism, which was investigated by experimental and DFT studies, proceeds through a dearomatized xylene intermediate. This intermediate was observed spectroscopically upon addition of a pyridine base to provide a thermodynamic trap

The Uniqueness Theorem for Entanglement Measures

We explore and develop the mathematics of the theory of entanglement measures. After a careful review and analysis of definitions, of preliminary results, and of connections between conditions on entanglement measures, we prove a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure to coincide with the reduced von Neumann entropy on pure states. We also prove several versions of a theorem on extreme entanglement measures in the case of mixed states. We analyse properties of the asymptotic regularization of entanglement measures proving, for example, convexity for the entanglement cost and for the regularized relative entropy of entanglement.Comment: 22 pages, LaTeX, version accepted by J. Math. Phy

T-infinity: The Dependency Inversion Principle for Rapid and Sustainable Multidisciplinary Software Development

The CFD Vision 2030 Study recommends that, NASA should develop and maintain an integrated simulation and software development infrastructure to enable rapid CFD technology maturation.... [S]oftware standards and interfaces must be emphasized and supported whenever possible, and open source models for noncritical technology components should be adopted. The current paper presents an approach to an open source development architecture, named T-infinity, for accelerated research in CFD leveraging the Dependency Inversion Principle to realize plugins that communicate through collections of functions without exposing internal data structures. Steady state flow visualization, mesh adaptation, fluid-structure interaction, and overset domain capabilities are demonstrated through compositions of plugins via standardized abstract interfaces without the need for source code dependencies between disciplines. Plugins interact through abstract interfaces thereby avoiding N 2 direct code-to-code data structure coupling where N is the number of codes. This plugin architecture enhances sustainable development by controlling the interaction between components to limit software complexity growth. The use of T-infinity abstract interfaces enables multidisciplinary application developers to leverage legacy applications alongside newly-developed capabilities. While rein, a description of interface details is deferred until the are more thoroughly tested and can be closed to modification

Reappraising the Evolutionary History of the Largest Known Gecko, the Presumably Extinct \u3cem\u3eHoplodactylus delcourti\u3c/em\u3e, via High-Throughput Sequencing of Archival DNA

Hoplodactylus delcourti is a presumably extinct species of diplodactylid gecko known only from a single specimen of unknown provenance. It is by far the largest known gekkotan, approximately 50% longer than the next largest-known species. It has been considered a member of the New Zealand endemic genus Hoplodactylus based on external morphological features including shared toe pad structure. We obtained DNA from a bone sample of the only known specimen to generate high-throughput sequence data suitable for phylogenetic analysis of its evolutionary history. Complementary sequence data were obtained from a broad sample of diplodactylid geckos. Our results indicate that the species is not most closely related to extant Hoplodactylus or any other New Zealand gecko. Instead, it is a member of a clade whose living species are endemic to New Caledonia. Phylogenetic comparative analyses indicate that the New Caledonian diplodactylid clade has evolved significantly more disparate body sizes than either the Australian or New Zealand clades. Toe pad structure has changed repeatedly across diplodactylids, including multiple times in the New Caledonia clade, partially explaining the convergence in form between H. delcourti and New Zealand Hoplodactylus. Based on the phylogenetic results, we place H. delcourti in a new genus

Exploring the Burden of Inpatient Readmissions After Major Cancer Surgery

Travel distances to care have increased substantially with centralization of complex cancer procedures at high-volume centers. We hypothesize that longer travel distances are associated with higher rates of postoperative readmission and poorer outcomes