A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity

We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is \Phi_{p,q}(A_1,A_2,...,A_m) = (trace((\sum_{j=1}^m A_j^p)^{q/p}))^{1/q} for m positive definite operators A_j. In part I we only considered the case q=1 and proved the concavity of \Phi_{p,1} for 0 < p \leq 1 and the convexity for p=2. We conjectured the convexity of \Phi_{p,1} for 1< p < 2. Here we not only settle the unresolved case of joint convexity for 1 \leq p \leq 2, we are also able to include the parameter q\geq 1 and still retain the convexity. Among other things this leads to a definition of an L^q(L^p) norm for operators when 1 \leq p \leq 2 and a Minkowski inequality for operators on a tensor product of three Hilbert spaces -- which leads to another proof of strong subadditivity of entropy. We also prove convexity/concavity properties of some other, related functionals.Comment: Proof of a conjecture in math/0701352. Revised version replaces earlier draft. 18 pages, late

Relativistic MHD with Adaptive Mesh Refinement

This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO method (CENO) in 3+1 dimensions, and the AMR is Berger-Oliger. Hyperbolic divergence cleaning is used to control the $\nabla\cdot {\bf B}=0$ constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.Comment: 24 pages, 14 figures, 3 table

Multi-platform assessment of transcriptional profiling technologies utilizing a precise probe mapping methodology

BACKGROUND: The arrival of RNA-seq as a high-throughput method competitive to the established microarray technologies has necessarily driven a need for comparative evaluation. To date, cross-platform comparisons of these technologies have been relatively few in number of platforms analyzed and were typically gene name annotation oriented. Here, we present a more extensive and yet precise assessment to elucidate differences and similarities in performance of numerous aspects including dynamic range, fidelity of raw signal and fold-change with sample titration, and concordance with qRT-PCR (TaqMan). To ensure that these results were not confounded by incompatible comparisons, we introduce the concept of probe mapping directed “transcript pattern”. A transcript pattern identifies probe(set)s across platforms that target a common set of transcripts for a specific gene. Thus, three levels of data were examined: entire data sets, data derived from a subset of 15,442 RefSeq genes common across platforms, and data derived from the transcript pattern defined subset of 7,034 RefSeq genes. RESULTS: In general, there were substantial core similarities between all 6 platforms evaluated; but, to varying degrees, the two RNA-seq protocols outperformed three of the four microarray platforms in most categories. Notably, a fourth microarray platform, Agilent with a modified protocol, was comparable, or marginally superior, to the RNA-seq protocols within these same assessments, especially in regards to fold-change evaluation. Furthermore, these 3 platforms (Agilent and two RNA-seq methods) demonstrated over 80 % fold-change concordance with the gold standard qRT-PCR (TaqMan). CONCLUSIONS: This study suggests that microarrays can perform on nearly equal footing with RNA-seq, in certain key features, specifically when the dynamic range is comparable. Furthermore, the concept of a transcript pattern has been introduced that may minimize potential confounding factors of multi-platform comparison and may be useful for similar evaluations. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12864-015-1913-6) contains supplementary material, which is available to authorized users

The Ground States of Large Quantum Dots in Magnetic Fields

The quantum mechanical ground state of a 2D $N$-electron system in a confining potential $V(x)=Kv(x)$ ($K$ is a coupling constant) and a homogeneous magnetic field $B$ is studied in the high density limit $N\to\infty$, $K\to \infty$ with $K/N$ fixed. It is proved that the ground state energy and electronic density can be computed {\it exactly} in this limit by minimizing simple functionals of the density. There are three such functionals depending on the way $B/N$ varies as $N\to\infty$: A 2D Thomas-Fermi (TF) theory applies in the case $B/N\to 0$; if $B/N\to{\rm const.}\neq 0$ the correct limit theory is a modified $B$-dependent TF model, and the case $B/N\to\infty$ is described by a ``classical'' continuum electrostatic theory. For homogeneous potentials this last model describes also the weak coupling limit $K/N\to 0$ for arbitrary $B$. Important steps in the proof are the derivation of a new Lieb-Thirring inequality for the sum of eigenvalues of single particle Hamiltonians in 2D with magnetic fields, and an estimation of the exchange-correlation energy. For this last estimate we study a model of classical point charges with electrostatic interactions that provides a lower bound for the true quantum mechanical energy.Comment: 57 pages, Plain tex, 5 figures in separate uufil

Cost-effectiveness of ASHRAE Standard 90.1-2010 Compared to ASHRAE Standard 90.1-2007

Pacific Northwest National Laboratory (PNNL) completed this project for the U.S. Department of Energy’s (DOE’s) Building Energy Codes Program (BECP). DOE’s BECP supports upgrading building energy codes and standards, and the states’ adoption, implementation, and enforcement of upgraded codes and standards. Building energy codes and standards set minimum requirements for energy-efficient design and construction for new and renovated buildings, and impact energy use and greenhouse gas emissions for the life of buildings. Continuous improvement of building energy efficiency is achieved by periodically upgrading energy codes and standards. Ensuring that changes in the code that may alter costs (for building components, initial purchase and installation, replacement, maintenance and energy) are cost-effective encourages their acceptance and implementation. ANSI/ASHRAE/IESNA Standard 90.1 is the energy standard for commercial and multi-family residential buildings over three floors

Ernst Freund as Precursor of the Rational Study of Corporate Law

Gindis, David, Ernst Freund as Precursor of the Rational Study of Corporate Law (October 27, 2017). Journal of Institutional Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2905547, doi: https://dx.doi.org/10.2139/ssrn.2905547The rise of large business corporations in the late 19th century compelled many American observers to admit that the nature of the corporation had yet to be understood. Published in this context, Ernst Freund's little-known The Legal Nature of Corporations (1897) was an original attempt to come to terms with a new legal and economic reality. But it can also be described, to paraphrase Oliver Wendell Holmes, as the earliest example of the rational study of corporate law. The paper shows that Freund had the intuitions of an institutional economist, and engaged in what today would be called comparative institutional analysis. Remarkably, his argument that the corporate form secures property against insider defection and against outsiders anticipated recent work on entity shielding and capital lock-in, and can be read as an early contribution to what today would be called the theory of the firm.Peer reviewe

U1 small nuclear ribonucleoproteins (snRNPs) aggregate in Alzheimer’s disease due to autosomal dominant genetic mutations and trisomy 21

BACKGROUND: We recently identified U1 small nuclear ribonucleoprotein (snRNP) tangle-like aggregates and RNA splicing abnormalities in sporadic Alzheimer’s disease (AD). However little is known about snRNP biology in early onset AD due to autosomal dominant genetic mutations or trisomy 21 in Down syndrome. Therefore we investigated snRNP biochemical and pathologic features in these disorders. FINDINGS: We performed quantitative proteomics and immunohistochemistry in postmortem brain from genetic AD cases. Electron microscopy was used to characterize ultrastructural features of pathologic aggregates. U1-70k and other snRNPs were biochemically enriched in the insoluble fraction of human brain from subjects with presenilin 1 (PS1) mutations. Aggregates of U1 snRNP-immunoreactivity formed cytoplasmic tangle-like structures in cortex of AD subjects with PS1 and amyloid precursor protein (APP) mutations as well as trisomy 21. Ultrastructural analysis with electron microscopy in an APP mutation case demonstrated snRNP immunogold labeling of paired helical filaments (PHF). CONCLUSIONS: These studies identify U1 snRNP pathologic changes in brain of early onset genetic forms of AD. Since dominant genetic mutations and trisomy 21 result in dysfunctional amyloid processing, the findings suggest that aberrant β-amyloid processing may influence U1 snRNP aggregate formation

Protein-coding variants implicate novel genes related to lipid homeostasis contributing to body-fat distribution.

Body-fat distribution is a risk factor for adverse cardiovascular health consequences. We analyzed the association of body-fat distribution, assessed by waist-to-hip ratio adjusted for body mass index, with 228,985 predicted coding and splice site variants available on exome arrays in up to 344,369 individuals from five major ancestries (discovery) and 132,177 European-ancestry individuals (validation). We identified 15 common (minor allele frequency, MAF ≥5%) and nine low-frequency or rare (MAF &lt;5%) coding novel variants. Pathway/gene set enrichment analyses identified lipid particle, adiponectin, abnormal white adipose tissue physiology and bone development and morphology as important contributors to fat distribution, while cross-trait associations highlight cardiometabolic traits. In functional follow-up analyses, specifically in Drosophila RNAi-knockdowns, we observed a significant increase in the total body triglyceride levels for two genes (DNAH10 and PLXND1). We implicate novel genes in fat distribution, stressing the importance of interrogating low-frequency and protein-coding variants