A stochastic Fokker-Planck equation and double probabilistic representation for the stochastic porous media type equation

The purpose of the present paper consists in proposing and discussing a double probabilistic representation for a porous media equation in the whole space perturbed by a multiplicative colored noise. For almost all random realizations $\omega$, one associates a stochastic differential equation in law with random coefficients, driven by an independent Brownian motion. The key ingredient is a uniqueness lemma for a linear SPDE of Fokker-Planck type with measurable bounded (possibly degenerated) random coefficients

The stochastic porous media equation in Rd\R^d

Existence and uniqueness of solutions to the stochastic porous media equation dX-\D\psi(X) dt=XdW in \rr^d are studied. Here, $W$ is a Wiener process, $\psi$ is a maximal monotone graph in \rr\times\rr such that $\psi(r)\le C|r|^m$, \ff r\in\rr, $W$ is a coloured Wiener process. In this general case the dimension is restricted to $d\ge 3$, the main reason being the absence of a convenient multiplier result in the space \calh=\{\varphi\in\mathcal{S}'(\rr^d);\ |\xi|(\calf\varphi)(\xi)\in L^2(\rr^d)\}, for $d\le2$. When $\psi$ is Lipschitz, the well-posedness, however, holds for all dimensions on the classical Sobolev space H^{-1}(\rr^d). If $\psi(r)r\ge\rho|r|^{m+1}$ and $m=\frac{d-2}{d+2}$, we prove the finite time extinction with strictly positive probability

Cutting Red Tape in Health Care: How Streamlining Billing Can Reduce California's Health Care Costs

Examines inefficiencies in the state's administrative systems and proposes streamlining key processes and integrating health information networks to cut costs and add value. Offers case profiles of networks in Utah and New England as best practices

Eisenstein series for higher-rank groups and string theory amplitudes

Scattering amplitudes of superstring theory are strongly constrained by the requirement that they be invariant under dualities generated by discrete subgroups, E_n(Z), of simply-laced Lie groups in the E_n series (n<= 8). In particular, expanding the four-supergraviton amplitude at low energy gives a series of higher derivative corrections to Einstein's theory, with coefficients that are automorphic functions with a rich dependence on the moduli. Boundary conditions supplied by string and supergravity perturbation theory, together with a chain of relations between successive groups in the E_n series, constrain the constant terms of these coefficients in three distinct parabolic subgroups. Using this information we are able to determine the expressions for the first two higher derivative interactions (which are BPS-protected) in terms of specific Eisenstein series. Further, we determine key features of the coefficient of the third term in the low energy expansion of the four-supergraviton amplitude (which is also BPS-protected) in the E_8 case. This is an automorphic function that satisfies an inhomogeneous Laplace equation and has constant terms in certain parabolic subgroups that contain information about all the preceding terms.Comment: Latex. 38 pages. 1 figure. v2: minor changes and clarifications. v3: minor corrections, version to appear in Communications in Number Theory and Physics. v4: corrections to table

Modular properties of two-loop maximal supergravity and connections with string theory

The low-momentum expansion of the two-loop four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a circle and a two-torus is considered up to terms of order S^6R^4 (where S is a Mandelstam invariant and R is the linearized Weyl curvature). In the case of the toroidal compactification the coefficient of each term in the low energy expansion is generically a sum of a number of SL(2,Z)-invariant functions of the complex structure of the torus. Each such function satisfies a separate Poisson equation on moduli space with particular source terms that are bilinear in coefficients of lower order terms, consistent with qualitative arguments based on supersymmetry. Comparison is made with the low-energy expansion of type II string theories in ten and nine dimensions. Although the detailed behaviour of the string amplitude is not generally expected to be reproduced by supergravity perturbation theory to all orders, for the terms considered here we find agreement with direct results from string perturbation theory. These results point to a fascinating pattern of interrelated Poisson equations for the IIB coefficients at higher orders in the momentum expansion which may have a significance beyond the particular methods by which they were motivated.Comment: 79 pages, 4 figures. Latex format. v2: Small corrections made, version to appear in JHE

Insect Phylogenetics: A Guided Tour of Insect Evolution

Interview with Dr. Noah Whitema

A comprehensive study of infrared OH prompt emission in two comets. I. Observations and effective g-factors

We present high-dispersion infrared spectra of hydroxyl (OH) in comets C/2000 WM1 (LINEAR) and C/2004 Q2 (Machholz), acquired with the Near Infrared Echelle Spectrograph at the Keck Observatory atop Mauna Kea, Hawaii. Most of these rovibrational transitions result from photodissociative excitation of H_2O giving rise to OH "prompt" emission. We present calibrated emission efficiencies (equivalent g-factors, measured in OH photons s^(-1) [H_2O molecule]^(-1)) for more than 20 OH lines sampled in these two comets. The OH transitions analyzed cover a broad range of rotational excitation. This infrared database for OH can be used in two principal ways: (1) as an indirect tool for obtaining water production in comets simultaneously with the production of other parent volatiles, even when direct detections of H_2O are not available; and (2) as an observational constraint to models predicting the rotational distribution of rovibrationally excited OH produced by water photolysis

Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

50 pagesInternational audienceWe consider a possibly degenerate porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution

The Role of Toeholds and Capital Gains Taxes for Corporate Acquisition Strategies

Ownership takeovers often follow complex strategies where the control of the target firm is acquired through a sequence of independent contracts. Based on this observation, we develop a novel theoretical model wherein the acquiring firm decides on the number of steps towards the full ownership of the target (the acquisition structure) and on the combination of cash and stock used to finance the takeover (the method of payment). Within this framework, we analyze the effect of the capital gains tax on these two decision margins and test our theoretical prediction using a bivariate probit model on a sample of acquisition contracts between 2002 and 2014, collected from Bureau van Dijk's Zephyr database. Our estimates confirm the lock-in-effect and indicate a larger discouraging effect of rising capital gains taxes (+10%-points increase) on one-shot full acquisition (-6.0%-points) versus on sequential acquisitions (-5.2%-points). Further, we provide evidence that an increase in the capital gains tax (+10%-points) raises the probability of choosing one-shot full acquisition (+5.5%-points) instead of sequential acquisitions