In high-dimensional Bayesian applications, choosing a prior such that the corresponding posterior distribution has optimal asymptotic concentration properties can be restrictive in the sense that the priors supported by theory may not be computationally convenient, and vice versa. This paper develops a general strategy for constructing empirical or data-dependent priors whose corresponding post...

Methods of topological analysis are inherently related to singular perturbations. For topology variation, a trial geometric object put in a test domain is examined by reducing the object size from a finite to an infinitesimal one. Based on the singular perturbation of the forward Helmholtz problem, a topology optimization approach, which is a direct one, is described for the inverse problem of ...

Self-adjoint extensions of elliptic operators are used to model the solution of a partial differential equation defined in a singularly perturbed domain. The asymptotic expansion of the solution of a Laplacian with respect to a small parameter ε is first performed in a domain perturbed by the creation of a small hole. The resulting singular perturbation is approximated by choosing an appropriat...

This paper presents a fixed-end two-mass system (TMS) with end constraints that permits uncoupled solutions for different masses. The coupled nonlinear models for the present fixed-end TMS were solved using the continuous piecewise linearization method (CPLM) and detailed investigation on the effect of mass-ratio on the TMS response was conducted. The investigations showed that increased mass-r...

The formation of a shock wave in one-dimensional granular gases is considered, for both the dry and the wet cases, and the results are compared with the analytical shock wave solution in a sticky gas. Numerical simulations show that the behavior of the shock wave in both cases tends asymptotically to the sticky limit. In the inelastic gas (dry case) there is a very close correspondence to the s...

This paper is concerned with the asymptotic behavior of solutions to an outflow problem for one-dimensional bipolar quantum Navier-Stokes-Poisson equations in half space. First, by means manifold theory and center theorem, we show existence spatial decay rate stationary solution provided boundary strength small enough. Next, based on elaborate energy estimates, prove that asymptotically stable ...

We develop a model of information exchange through communication and investigate its implications for information aggregation in large societies. An underlying state determines payoffs from different actions. Agents decide which others to form a costly communication link with incurring the associated cost. After receiving a private signal correlated with the underlying state, they exchange info...

We study the vortex location for minimizers of a Ginzburg-Landau energy with a discontinuous constraint. The discontinuous constraint appears in the potential (a − |u|). The function a is piecewise constant: it takes the value 0 < b < 1 in small disjoint domains (called inclusions) and 1 otherwise. It is proved, under some assumptions on the smallness of the inclusions and on their interdistanc...