Gap Probabilities for Edge Intervals in Finite Gaussian and Jacobi Unitary Matrix Ensembles

The probabilities for gaps in the eigenvalue spectrum of the finite dimension $N \times N$ random matrix Hermite and Jacobi unitary ensembles on some single and disconnected double intervals are found. These are cases where a reflection symmetry exists and the probability factors into two other related probabilities, defined on single intervals. Our investigation uses the system of partial differential equations arising from the Fredholm determinant expression for the gap probability and the differential-recurrence equations satisfied by Hermite and Jacobi orthogonal polynomials. In our study we find second and third order nonlinear ordinary differential equations defining the probabilities in the general $N$ case. For N=1 and N=2 the probabilities and thus the solution of the equations are given explicitly. An asymptotic expansion for large gap size is obtained from the equation in the Hermite case, and also studied is the scaling at the edge of the Hermite spectrum as $N \to \infty$, and the Jacobi to Hermite limit; these last two studies make correspondence to other cases reported here or known previously. Moreover, the differential equation arising in the Hermite ensemble is solved in terms of an explicit rational function of a {Painlev\'e-V} transcendent and its derivative, and an analogous solution is provided in the two Jacobi cases but this time involving a {Painlev\'e-VI} transcendent.Comment: 32 pages, Latex2

Watersheds dynamics following wildfires: Nonlinear feedbacks and implications on hydrologic responses

In recent years, wildfires in the western United States have occurred with increasing frequency and scale. Climate change scenarios in California predict prolonged periods of droughts with even greater potential for conditions amenable to wildfires. The Sierra Nevada Mountains provide 70% of water resources in California, yet how wildfires will impact watershed-scale hydrology is highly uncertain. In this work, we assess the impacts of wildfires perturbations on watershed hydrodynamics using a physically based integrated hydrologic model in a high-performance-computing framework. A representative Californian watershed, the Cosumnes River, is used to demonstrate how postwildfire conditions impact the water and energy balance. Results from the high-resolution model show counterintuitive feedbacks that occur following a wildfire and allow us to identify the regions most sensitive to wildfires conditions, as well as the hydrologic processes that are most affected. For example, whereas evapotranspiration generally decreases in the postfire simulations, some regions experience an increase due to changes in surface water run-off patterns in and near burn scars. Postfire conditions also yield greater winter snowpack and subsequently greater summer run-off as well as groundwater storage in the postfire simulations. Comparisons between dry and wet water years show that climate is the main factor controlling the timing at which some hydrologic processes occur (such as snow accumulation) whereas postwildfire changes to other metrics (such as streamflow) show seasonally dependent impacts primarily due to the timing of snowmelt, illustrative of the integrative nature of hydrologic processes across the Sierra Nevada-Central Valley interface

Localized cyclical variations in immunoproteins in the female genital tract and the implications on the design and assessment of mucosal infection and therapies.

PROBLEM: Fluctuating hormones regulate reproductive processes in the female genital tract. Consequent changes in the local immunological environment are likely to affect cellular interaction with infectious agents and the assessment of therapies that target mucosal infections. METHOD OF STUDY: We compared Softcup and Weck-Cel sampling protocols and assessed the changes in the concentrations of 39 soluble proteins with menstrual cycle progression in the mucosal and peripheral compartments. RESULTS: We demonstrate that the mucosal immunological profile is distinct from serum with inflammatory and migratory signatures that are localized throughout the cycle. The analytes highlighted in the mucosal compartment were generally highest at the follicular phase with a tendency to fall as the cycle progressed through ovulation to the luteal phase. CONCLUSION: Our results underscore the need to consider these localized cyclical differences in studies aimed at assessing the outcome of disease and the efficacy of mucosal vaccines and other therapies

General-relativistic Model of Magnetically Driven Jet

The general scheme for the construction of the general-relativistic model of the magnetically driven jet is suggested. The method is based on the usage of the 3+1 MHD formalism. It is shown that the critical points of the flow and the explicit radial behavior of the physical variables may be derived through the jet ``profile function."Comment: 12 pages, LaTex, no figure

Fully Electrified Neugebauer Spacetimes

Generalizing a method presented in an earlier paper, we express the complex potentials E and Phi of all stationary axisymmetric electrovac spacetimes that correspond to axis data of the form E(z,0) = (U-W)/(U+W) , Phi(z,0) = V/(U+W) , where U = z^{2} + U_{1} z + U_{2} , V = V_{1} z + V_{2} , W = W_{1} z + W_{2} , in terms of the complex parameters U_{1}, V_{1}, W_{1}, U_{2}, V_{2} and W_{2}, that are directly associated with the various multipole moments. (Revised to clarify certain subtle points.)Comment: 25 pages, REVTE

Determining parameters of the Neugebauer family of vacuum spacetimes in terms of data specified on the symmetry axis

We express the complex potential E and the metrical fields omega and gamma of all stationary axisymmetric vacuum spacetimes that result from the application of two successive quadruple-Neugebauer (or two double-Harrison) transformations to Minkowski space in terms of data specified on the symmetry axis, which are in turn easily expressed in terms of multipole moments. Moreover, we suggest how, in future papers, we shall apply our approach to do the same thing for those vacuum solutions that arise from the application of more than two successive transformations, and for those electrovac solutions that have axis data similar to that of the vacuum solutions of the Neugebauer family. (References revised following response from referee.)Comment: 18 pages (REVTEX