The finite sample properties of sparse M-estimators with pseudo-observations

Annals of the Institute of Statistical Mathematics - We provide finite sample properties of general regularized statistical criteria in the presence of pseudo-observations. Under the restricted...     

A COMPACT UPWIND SECOND ORDER SCHEME FOR THE EIKONAL EQUATION

We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation. This new scheme is based on： 1. the numerical observation that classical first order monotone upwind schemes for the Eikonal equation yield numerical upwind gradient which is also first order accurate up to singularities; 2. a remark that partial information on the second derivatives of the solution is known and given in the structure of the Eikonal equation and can be used to reduce the size of the stencil. We implement the second order scheme as a correction to the well known sweeping method but it should be applicable to any first order monotone upwind scheme. Care is needed to choose the appropriate stencils to avoid instabilities.     

A non-stationary problem coupling PDEs and ODEs modelizing an automotive catalytic converter

In this article we prove the existence and uniqueness of the solution of a non-stationary problem that modelizes the behavior of the concentrations and the temperature of gases going through a cylindrical passage of an automotive catalytic converter. This problem couples parabolic partial differential equations (PDEs) in a domain with one parabolic partial differential equation and some ordinary differential equations (ODEs) on a part of its boundary.     

Second-Order Models for Optimal Transport and Cubic Splines on the Wasserstein Space

Foundations of Computational Mathematics - On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation....     

Source point discovery through high frequency asymptotic time reversal

Given local frequency domain wave data, the Numerical Micro-Local Analysis (NMLA) method (Benamou et al., 2004) [5] and its recent improved version (Benamou et al., 2011) [4] gives a pointwise numerical approximation of the number of rays, their slowness vectors and corresponding wavefront curvatures. With time domain wave data and assuming the source wavelet is given, the method also estimates the travel-time. The paper provides a non technical presentation of the improved NMLA algorithm and presents a numerical application which can be interpreted as a high frequency asymptotic version of the classical time reversal method (Borcea et al., 2003) [7]. A detailed technical presentation of the algorithm is available in Benamou et al. (2011) [4] and more numerical experiments can be found in Collino and Marmorat (2011) [15].     

Nonparametric estimation of competing risks models with covariates

In competing risks model, several failure times arise potentially. The smallest failure time and its index only are observed. Without specific assumptions, the joint or even the marginal distribution functions of the underlying failure times are not identifiable (A. Tsiatis, Proc. Natl. Acad. Sci. USA 72 (1975) 20). Nonetheless, if each individual is characterized by a “sufficiently informative” set of covariates, these distributions are identifiable under some conditions of regularity (J.J. Heckman and B. Honoré, Biometrika 76 (1989) 325). In this paper, nonparametric kernel estimators of the joint distribution function of failure times conditional on the covariates are proposed. Their weak and strong consistency are discussed.     

An empirical central limit theorem with applications to copulas under weak dependence

We state a multidimensional Functional Central Limit Theorem for weakly dependent random vectors. We apply this result to copulas. We get the weak convergence of the empirical copula process and of its smoothed version. The finite dimensional convergence of smoothed copula densities is also proved. A new definition and the theoretical analysis of conditional copulas and their empirical counterparts are provided.      

Tuning the Aggregates of Thiophene-based Trimers by Methyl Side-chain Engineering for Photocatalytic Hydrogen Evolution

Organic π-conjugated semiconductors (OCSs) have recently emerged as a promising alternative to traditional inorganic materials for photocatalysis. However, the aggregation of OCSs in photocatalytic aqueous solution caused by self-assembly, which closely relates to the photocatalytic activity, has not yet been studied. Here, the relationship between the aggregation of 4,7-Bis(thiophen-2-yl) benzothiadiazole (TBT) and the photocatalytic activity was systematically investigated by introducing and varying the position of methyl side chains on the two peripheral thiophene units. Experimental and theoretical results indicated that the introduction of -CH₃ group at the 3-position of TBT resulted in the smallest size and best crystallinity of aggregates compared to that of TBT, 4- and 5-positions. As a result, TBT-3 exhibited an excellent photocatalytic activity towards H₂ evolution, ascribed to the shorten charge carrier transport distance and solid long-range order. These results suggest the important role of aggregation behavior of OCSs for efficient photocatalysis.