On the permanent of random Bernoulli matrices

We show that the permanent of an $n \times n$ matrix with iid Bernoulli entries $\pm 1$ is of magnitude $n^{({1/2}+o(1))n}$ with probability $1-o(1)$. In particular, it is almost surely non-zero

Zooming in on local level statistics by supersymmetric extension of free probability

We consider unitary ensembles of Hermitian NxN matrices H with a confining potential NV where V is analytic and uniformly convex. From work by Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit of the characteristic function for a finite-rank Fourier variable K is determined by the Voiculescu R-transform, a key object in free probability theory. Going beyond these results, we argue that the same holds true when the finite-rank operator K has the form that is required by the Wegner-Efetov supersymmetry method of integration over commuting and anti-commuting variables. This insight leads to a potent new technique for the study of local statistics, e.g., level correlations. We illustrate the new technique by demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section

Smooth analysis of the condition number and the least singular value

Let \a be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of \a and $M$ be a fixed matrix of the same size. The goal of this paper is to give a general estimate for the condition number and least singular value of the matrix $M + N_{n}$, generalizing an earlier result of Spielman and Teng for the case when \a is gaussian. Our investigation reveals an interesting fact that the "core" matrix $M$ does play a role on tail bounds for the least singular value of $M+N_{n}$. This does not occur in Spielman-Teng studies when \a is gaussian. Consequently, our general estimate involves the norm $\|M\|$. In the special case when $\|M\|$ is relatively small, this estimate is nearly optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde

Universal microscopic correlation functions for products of independent Ginibre matrices

We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of the product matrix is found to be given by a determinantal point process as in the case of a single Ginibre matrix, but with a more complicated weight given by a Meijer G-function depending on n. Using the method of orthogonal polynomials we compute all eigenvalue density correlation functions exactly for finite N and fixed n. They are given by the determinant of the corresponding kernel which we construct explicitly. In the large-N limit at fixed n we first determine the microscopic correlation functions in the bulk and at the edge of the spectrum. After unfolding they are identical to that of the Ginibre ensemble with n=1 and thus universal. In contrast the microscopic correlations we find at the origin differ for each n>1 and generalise the known Bessel-law in the complex plane for n=2 to a new hypergeometric kernel 0_F_n-1.Comment: 20 pages, v2 published version: typos corrected and references adde

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment

ERBB2 in Cat Mammary Neoplasias Disclosed a Positive Correlation between RNA and Protein Low Expression Levels: A Model for erbB-2 Negative Human Breast Cancer

Human ERBB2 is a proto-oncogene that codes for the erbB-2 epithelial growth factor receptor. In human breast cancer (HBC), erbB-2 protein overexpression has been repeatedly correlated with poor prognosis. In more recent works, underexpression of this gene has been described in HBC. Moreover, it is also recognised that oncogenes that are commonly amplified or deleted encompass point mutations, and some of these are associated with HBC. In cat mammary lesions (CMLs), the overexpression of ERBB2 (27%–59.6%) has also been described, mostly at the protein level and although cat mammary neoplasias are considered to be a natural model of HBC, molecular information is still scarce. In the present work, a cat ERBB2 fragment, comprising exons 10 to 15 (ERBB2_10–15) was achieved for the first time. Allelic variants and genomic haplotype analyses were also performed, and differences between normal and CML populations were observed. Three amino acid changes, corresponding to 3 non-synonymous genomic sequence variants that were only detected in CMLs, were proposed to damage the 3D structure of the protein. We analysed the cat ERBB2 gene at the DNA (copy number determination), mRNA (expression levels assessment) and protein levels (in extra- and intra protein domains) in CML samples and correlated the last two evaluations with clinicopathological features. We found a positive correlation between the expression levels of the ERBB2 RNA and erbB-2 protein, corresponding to the intracellular region. Additionally, we detected a positive correlation between higher mRNA expression and better clinical outcome. Our results suggest that the ERBB2 gene is post-transcriptionally regulated and that proteins with truncations and single point mutations are present in cat mammary neoplastic lesions. We would like to emphasise that the recurrent occurrence of low erbB-2 expression levels in cat mammary tumours, suggests the cat mammary neoplasias as a valuable model for erbB-2 negative HBC.POCI/CVT/62940/2004 and by the PhD grants (SFRH/BD/23406/2005 and SFRH/BD/31754/2006, of the Science and Technology Foundation (FCT) from Portugal

Measurement of the energy asymmetry in tt¯ j production at 13 TeV with the ATLAS experiment and interpretation in the SMEFT framework

A measurement of the energy asymmetry in jet-associated top-quark pair production is presented using 139fb-1 of data collected by the ATLAS detector at the Large Hadron Collider during pp collisions at s=13TeV. The observable measures the different probability of top and antitop quarks to have the higher energy as a function of the jet scattering angle with respect to the beam axis. The energy asymmetry is measured in the semileptonic tt¯ decay channel, and the hadronically decaying top quark must have transverse momentum above 350GeV. The results are corrected for detector effects to particle level in three bins of the scattering angle of the associated jet. The measurement agrees with the SM prediction at next-to-leading-order accuracy in quantum chromodynamics in all three bins. In the bin with the largest expected asymmetry, where the jet is emitted perpendicular to the beam, the energy asymmetry is measured to be - 0.043 ± 0.020 , in agreement with the SM prediction of - 0.037 ± 0.003. Interpreting this result in the framework of the Standard Model effective field theory (SMEFT), it is shown that the energy asymmetry is sensitive to the top-quark chirality in four-quark operators and is therefore a valuable new observable in global SMEFT fits

Measurement of the energy response of the ATLAS calorimeter to charged pions from W±→ τ±(→ π±ντ) ντ events in Run 2 data

The energy response of the ATLAS calorimeter is measured for single charged pions with transverse momentum in the range 10 < pT< 300 GeV. The measurement is performed using 139 fb - 1 of LHC proton–proton collision data at s=13 TeV taken in Run 2 by the ATLAS detector. Charged pions originating from τ-lepton decays are used to provide a sample of high-pT isolated particles, where the composition is known, to test an energy regime that has not previously been probed by in situ single-particle measurements. The calorimeter response to single-pions is observed to be overestimated by ∼ 2 % across a large part of the pT spectrum in the central region and underestimated by ∼ 4 % in the endcaps in the ATLAS simulation. The uncertainties in the measurements are ≲ 1 % for 15 < pT< 185 GeV in the central region. To investigate the source of the discrepancies, the width of the distribution of the ratio of calorimeter energy to track momentum, the energies per layer and response in the hadronic calorimeter are also compared between data and simulation