Determination and Correlation of Anticardiolipin Antibody with High Sensitivity C- reactive Proteins and its Role in Predicting Short Term Outcome in Patients with Acute Coronary Syndrome

Anticardiolipin antibody (aCL) is considered to be an independent risk factor while high sensitivity C reactive protein (hsCRP) is an established marker for coronary artery disease. This study was conducted to determine levels of aCL antibodies and hsCRP, their correlation and role in predicting recurrence of events in patients presenting with Acute Coronary Syndrome (ACS). Sixty patients admitted with Acute Coronary Syndrome were followed up for 7 days or until discharge. Patients were classified into two groups as those having experienced an ischemic event needing intervention within 7 days (Group I) and other having an event free recovery (Group II). aCL antibody and hsCRP levels were estimated and compared in these two groups. Twenty age and sex matched disease free persons served as controls. The levels of aCL were significantly higher in patients with ACS as compared to the controls (p=0.020). However the levels of aCL in Group I (13.39±9.46 GPL-U/ml) and Group II (13.51±9.93 GPL-U/ml) were not significantly different (p =0.838). The mean hsCRP levels were higher in cases with an event (23.30±10.68 mg/dl) than in cases without an event (20.60±11.45mg/dl) though it was not significant statistically (p=0.389). aCL and CRP were not found to be significantly correlated in causing the recurrence of events(p=0.178). Therefore anticardiolipin antibody is an independent risk factor which could be implicated in the pathogenesis of ACS. However it is not significantly associated with recurrence of short-term events in patients with ACS. Also, aCL antibody does not have significant correlation with hSCRP in causing recurrence of events in the patients of acute coronary syndrome

Eigenfunctions of electrons in weakly disordered quantum dots: Crossover between orthogonal and unitary symmetries

A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained with recent results derived from first principles within the framework of supersymmetry technique allows to identify a transition parameter with real microscopic characteristics of the problem. The random-matrix model is applied to the statistics of the height of the resonance conductance of a quantum dot in the regime of the crossover between orthogonal and unitary symmetry classes.Comment: 6 pages (latex), 3 figures available upon request, to appear in Physical Review

Steinberg modules and Donkin pairs

We prove that in positive characteristic a module with good filtration for a group of type E6 restricts to a module with good filtration for a subgroup of type F4. (Recall that a filtration of a module for a semisimple algebraic group is called good if its layers are dual Weyl modules.) Our result confirms a conjecture of Brundan for one more case. The method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, in characteristic not 2, with a computer-aided variation on the old method of Donkin.Comment: 16 pages; proof of Brundan's conjecture adde

Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices

We compute exact asymptotic results for the probability of the occurrence of large deviations of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the probability that all the eigenvalues of an (NxN) random matrix are positive (negative) decreases for large N as ~\exp[-\beta \theta(0) N^2] where the Dyson index \beta characterizes the ensemble and the exponent \theta(0)=(\ln 3)/4=0.274653... is universal. We compute the probability that the eigenvalues lie in the interval [\zeta_1,\zeta_2] which allows us to calculate the joint probability distribution of the minimum and the maximum eigenvalue. As a byproduct, we also obtain exactly the average density of states in Gaussian ensembles whose eigenvalues are restricted to lie in the interval [\zeta_1,\zeta_2], thus generalizing the celebrated Wigner semi-circle law to these restricted ensembles. It is found that the density of states generically exhibits an inverse square-root singularity at the location of the barriers. These results are confirmed by numerical simulations.Comment: 17 pages Revtex, 5 .eps figures include

Generalised Separable Solution of Double Phase Flow through Homogeneous Porous Medium in Vertical Downward Direction Due to Difference in Viscosity

In this paper the instability (fingering) phenomenon in a double phase immiscible (oil and water) flow through the homogeneous porous medium with mean capillary pressure in the vertical downward direction is discussed. The mathematical formulation of this problem yields a nonlinear partial differential equation and the generalised separable solution is given in the exponential form. The numerical solution and graphical presentation is given using MAT LAB coding

Stretched exponentials and power laws in granular avalanching

We introduce a model for granular avalanching which exhibits both stretched exponential and power law avalanching over its parameter range. Two modes of transport are incorporated, a rolling layer consisting of individual particles and the overdamped, sliding motion of particle clusters. The crossover in behaviour observed in experiments on piles of rice is attributed to a change in the dominant mode of transport. We predict that power law avalanching will be observed whenever surface flow is dominated by clustered motion. Comment: 8 pages, more concise and some points clarified

Singular normal form for the Painlev\'e equation P1

We show that there exists a rational change of coordinates of Painlev\'e's P1 equation $y''=6y^2+x$ and of the elliptic equation $y''=6y^2$ after which these two equations become analytically equivalent in a region in the complex phase space where $y$ and $y'$ are unbounded. The region of equivalence comprises all singularities of solutions of P1 (i.e. outside the region of equivalence, solutions are analytic). The Painlev\'e property of P1 (that the only movable singularities are poles) follows as a corollary. Conversely, we argue that the Painlev\'e property is crucial in reducing P1, in a singular regime, to an equation integrable by quadratures