Self-accelerating universe in Galileon cosmology

We present a cosmological model with a solution that self-accelerates at late times without signs of ghost instabilities on small scales. The model is a natural extension of the Brans-Dicke (BD) theory including a nonlinear derivative interaction, which appears in a theory with the Galilean shift symmetry. The existence of the self-accelerating universe requires a negative BD parameter but, thanks to the nonlinear term, small fluctuations around the solution are stable on small scales. General relativity is recovered at early times and on small scales by this nonlinear interaction via the Vainshtein mechanism. At late time, gravity is strongly modified and the background cosmology shows a phantomlike behavior and the growth rate of structure formation is enhanced. Thus this model leaves distinct signatures in cosmological observations and it can be distinguished from standard LCDM cosmology

A hyperbolic system and the cost of null controllability for the Stokes system

This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method we show that the cost of driving the Stokes system to rest at time T is of order e^C/T when T -->0^+,i.e., the same order as for the heat equation. For this to be possible, we are led to study the exact controllability of one hyperbolic system with a resistance term, which will be done under assumptions on the control region.Comment: 17 page

A spatial scan statistic for zero-inflated Poisson process

The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. However, real data may present substantial departure from the underlying Poisson process. One of the possible departures has to do with zero excess. Some studies point out that when applied to data with excess zeros, the spatial scan statistic may produce biased inferences. In this work, we develop a closed-form scan statistic for cluster detection of spatial zero-inflated count data. We apply our methodology to simulated and real data. Our simulations revealed that the Scan-Poisson statistic steadily deteriorates as the number of zeros increases, producing biased inferences. On the other hand, our proposed Scan-ZIP and Scan-ZIP+EM statistics are, most of the time, either superior or comparable to the Scan-Poisson statistic

Categorical Aspects of the Double Structure of a Module

In this work we develop some categorical aspects of the double structure of a module

High harmonic generation in crystals using Maximally Localized Wannier functions

In this work, the nonlinear optical response, and in particular, the high harmonic generation of semiconductors is addressed by using the Wannier gauge. One of the main problems in the time evolution of the Semiconductor Bloch equations resides in the fact that the dipole couplings between different bands can diverge and have a random phase along the reciprocal space and this leads to numerical instability. To address this problem, we propose the use of the Maximally Localized Wannier functions that provide a framework to map ab-initio calculations to an effective tight-binding Hamiltonian with great accuracy. We show that working in the Wannier gauge, the basis set in which the Bloch functions are constructed directly from the Wannier functions, the dipole couplings become smooth along the reciprocal space thus avoiding the problem of random phases. High harmonic generation spectrum is computed for a 2D monolayer of hBN as a numerical demonstration

Acquisition and processing of data from the SL-2 mission (EREP pass no. 7) over the Lake Monroe, Indiana test site

There are no author-identified significant results in this report

A fully-discrete Semi-Lagrangian scheme for a first order mean field game problem

In this work we propose a fully-discrete Semi-Lagrangian scheme for a {\it first order mean field game system}. We prove that the resulting discretization admits at least one solution and, in the scalar case, we prove a convergence result for the scheme. Numerical simulations and examples are also discussed.Comment: 28 pages,16 figure