Variational characterization of the regularity of Monge-Brenier maps

On an abstract Wiener space, assume that T is the solution of the quadratic Monge problem associated to the Wiener measure and a second one with a Radon-Nikodym derivative of exponential type. Under the finite information hypothesis, using a variational method, we prove that T minimizes a certain functional originating from the large deviations theory. Applying a variational method a la Euler, we obtain the Sobolev regularity of the backward Monge-Brenier map. A similar result also holds for the forward Monge-Brenier map.Comment: arXiv admin note: text overlap with arXiv:math/0403497, arXiv:math/040710

Chemical vapor deposition modeling: An assessment of current status

The shortcomings of earlier approaches that assumed thermochemical equilibrium and used chemical vapor deposition (CVD) phase diagrams are pointed out. Significant advancements in predictive capabilities due to recent computational developments, especially those for deposition rates controlled by gas phase mass transport, are demonstrated. The importance of using the proper boundary conditions is stressed, and the availability and reliability of gas phase and surface chemical kinetic information are emphasized as the most limiting factors. Future directions for CVD are proposed on the basis of current needs for efficient and effective progress in CVD process design and optimization

Log-concave measures

We study the log-concave measures, their characterization via the Pr\'ekopa-Leindler property and also define a subset of it whose elements are called super log-concave measures which have the property of satisfying a logarithmic Sobolev inequality. We give some results about their stability. Certain relations with measure transportation of Monge-Kantorovitch and the Monge-Amp\'ere equation are also indicated with applications

Compressive Diffusion Strategies Over Distributed Networks for Reduced Communication Load

We study the compressive diffusion strategies over distributed networks based on the diffusion implementation and adaptive extraction of the information from the compressed diffusion data. We demonstrate that one can achieve a comparable performance with the full information exchange configurations, even if the diffused information is compressed into a scalar or a single bit. To this end, we provide a complete performance analysis for the compressive diffusion strategies. We analyze the transient, steady-state and tracking performance of the configurations in which the diffused data is compressed into a scalar or a single-bit. We propose a new adaptive combination method improving the convergence performance of the compressive diffusion strategies further. In the new method, we introduce one more freedom-of-dimension in the combination matrix and adapt it by using the conventional mixture approach in order to enhance the convergence performance for any possible combination rule used for the full diffusion configuration. We demonstrate that our theoretical analysis closely follow the ensemble averaged results in our simulations. We provide numerical examples showing the improved convergence performance with the new adaptive combination method.Comment: Submitted to IEEE Transactions on Signal Processin