Hua\u27s Matrix Equality and Schur Complements

The purpose of this paper is to revisit Hua\u27s matrix equality (and inequality) through the Schur complement. We present Hua\u27s original proof and two new proofs with some extensions of Hua\u27s matrix equality and inequalities. The new proofs use a result concerning Shur complements and a generalization of Sylvester\u27s law of inertia, each of which is useful in its own right

Towards Healing the Blindness of Score Matching

Score-based divergences have been widely used in machine learning and statistics applications. Despite their empirical success, a blindness problem has been observed when using these for multi-modal distributions. In this work, we discuss the blindness problem and propose a new family of divergences that can mitigate the blindness problem. We illustrate our proposed divergence in the context of density estimation and report improved performance compared to traditional approaches

Peripheral Innate Immune Activation Correlates With Disease Severity in GRN Haploinsufficiency.

Objective: To investigate associations between peripheral innate immune activation and frontotemporal lobar degeneration (FTLD) in progranulin gene (GRN) haploinsufficiency. Methods: In this cross-sectional study, ELISA was used to measure six markers of innate immunity (sCD163, CCL18, LBP, sCD14, IL-18, and CRP) in plasma from 30 GRN mutation carriers (17 asymptomatic, 13 symptomatic) and 29 controls. Voxel based morphometry was used to model associations between marker levels and brain atrophy in mutation carriers relative to controls. Linear regression was used to model relationships between plasma marker levels with mean frontal white matter integrity [fractional anisotropy (FA)] and the FTLD modified Clinical Dementia Rating Scale sum of boxes score (FTLD-CDR SB). Results: Plasma sCD163 was higher in symptomatic GRN carriers [mean 321 ng/ml (SD 125)] compared to controls [mean 248 ng/ml (SD 58); p < 0.05]. Plasma CCL18 was higher in symptomatic GRN carriers [mean 56.9 pg/ml (SD 19)] compared to controls [mean 40.5 pg/ml (SD 14); p < 0.05]. Elevation of plasma LBP was associated with white matter atrophy in the right frontal pole and left inferior frontal gyrus (p FWE corrected <0.05) in all mutation carriers relative to controls. Plasma LBP levels inversely correlated with bilateral frontal white matter FA (R2 = 0.59, p = 0.009) in mutation carriers. Elevation in plasma was positively correlated with CDR-FTLD SB (b = 2.27 CDR units/μg LBP/ml plasma, R2 = 0.76, p = 0.003) in symptomatic carriers. Conclusion: FTLD-GRN is associated with elevations in peripheral biomarkers of macrophage-mediated innate immunity, including sCD163 and CCL18. Clinical disease severity and white matter integrity are correlated with blood LBP, suggesting a role for peripheral immune activation in FTLD-GRN

LSMR: An iterative algorithm for sparse least-squares problems

An iterative method LSMR is presented for solving linear systems $Ax=b$ and least-squares problem \min \norm{Ax-b}_2, with $A$ being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is analytically equivalent to the MINRES method applied to the normal equation A\T Ax = A\T b, so that the quantities \norm{A\T r_k} are monotonically decreasing (where $r_k = b - Ax_k$ is the residual for the current iterate $x_k$). In practice we observe that \norm{r_k} also decreases monotonically. Compared to LSQR, for which only \norm{r_k} is monotonic, it is safer to terminate LSMR early. Improvements for the new iterative method in the presence of extra available memory are also explored.Comment: 21 page

Linking Dynamical and Thermal Models of Ultrarelativistic Nuclear Scattering

To analyse ultrarelativistic nuclear interactions, usually either dynamical models like the string model are employed, or a thermal treatment based on hadrons or quarks is applied. String models encounter problems due to high string densities, thermal approaches are too simplistic considering only average distributions, ignoring fluctuations. We propose a completely new approach, providing a link between the two treatments, and avoiding their main shortcomings: based on the string model, connected regions of high energy density are identified for single events, such regions referred to as quark matter droplets. Each individual droplet hadronizes instantaneously according to the available n-body phase space. Due to the huge number of possible hadron configurations, special Monte Carlo techniques have been developed to calculate this disintegration.Comment: Complete paper enclosed as postscript file (uuencoded

Placental adaptations in growth restriction

The placenta is the primary interface between the fetus and mother and plays an important role in maintaining fetal development and growth by facilitating the transfer of substrates and participating in modulating the maternal immune response to prevent immunological rejection of the conceptus. The major substrates required for fetal growth include oxygen, glucose, amino acids and fatty acids, and their transport processes depend on morphological characteristics of the placenta, such as placental size, morphology, blood flow and vascularity. Other factors including insulin-like growth factors, apoptosis, autophagy and glucocorticoid exposure also affect placental growth and substrate transport capacity. Intrauterine growth restriction (IUGR) is often a consequence of insufficiency, and is associated with a high incidence of perinatal morbidity and mortality, as well as increased risk of cardiovascular and metabolic diseases in later life. Several different experimental methods have been used to induce placental insufficiency and IUGR in animal models and a range of factors that regulate placental growth and substrate transport capacity have been demonstrated. While no model system completely recapitulates human IUGR, these animal models allow us to carefully dissect cellular and molecular mechanisms to improve our understanding and facilitate development of therapeutic interventions

Supersymmetry and the LHC Inverse Problem

Given experimental evidence at the LHC for physics beyond the standard model, how can we determine the nature of the underlying theory? We initiate an approach to studying the "inverse map" from the space of LHC signatures to the parameter space of theoretical models within the context of low-energy supersymmetry, using 1808 LHC observables including essentially all those suggested in the literature and a 15 dimensional parametrization of the supersymmetric standard model. We show that the inverse map of a point in signature space consists of a number of isolated islands in parameter space, indicating the existence of "degeneracies"--qualitatively different models with the same LHC signatures. The degeneracies have simple physical characterizations, largely reflecting discrete ambiguities in electroweak-ino spectrum, accompanied by small adjustments for the remaining soft parameters. The number of degeneracies falls in the range 1<d<100, depending on whether or not sleptons are copiously produced in cascade decays. This number is large enough to represent a clear challenge but small enough to encourage looking for new observables that can further break the degeneracies and determine at the LHC most of the SUSY physics we care about. Degeneracies occur because signatures are not independent, and our approach allows testing of any new signature for its independence. Our methods can also be applied to any other theory of physics beyond the standard model, allowing one to study how model footprints differ in signature space and to test ways of distinguishing qualitatively different possibilities for new physics at the LHC.Comment: 55 pages, 30 figure

Detection of small-molecule enzyme inhibitors with peptides isolated from phage-displayed combinatorial peptide libraries

AbstractBackground: The rapidly expanding list of pharmacologically important targets has highlighted the need for ways to discover new inhibitors that are independent of functional assays. We have utilized peptides to detect inhibitors of protein function. We hypothesized that most peptide ligands identified by phage display would bind to regions of biological interaction in target proteins and that these peptides could be used as sensitive probes for detecting low molecular weight inhibitors that bind to these sites.Results: We selected a broad range of enzymes as targets for phage display and isolated a series of peptides that bound specifically to each target. Peptide ligands for each target contained similar amino acid sequences and competition analysis indicated that they bound one or two sites per target. Of 17 peptides tested, 13 were found to be specific inhibitors of enzyme function. Finally, we used two peptides specific for Haemophilus influenzae tyrosyl-tRNA synthetase to show that a simple binding assay can be used to detect small-molecule inhibitors with potencies in the micromolar to nanomolar range.Conclusions: Peptidic surrogate ligands identified using phage display are preferentially targeted to a limited number of sites that inhibit enzyme function. These peptides can be utilized in a binding assay as a rapid and sensitive method to detect small-molecule inhibitors of target protein function. The binding assay can be used with a variety of detection systems and is readily adaptable to automation, making this platform ideal for high-throughput screening of compound libraries for drug discovery