Regularization is a principled way to control model complexity, prevent overfitting, and incorporate ancillary information into the learning process. As a convex relaxation of l0norm, l1-norm regularization is popular for learning in high-dimensional spaces, where a fundamental assumption is the sparsity of model parameters. However, model sparsity can be restrictive and not necessarily the mos...

A finite deterministic automaton A = (Q,Σ, δ) is k-compressible if there is a word w ∈ Σ such that the image of the state set Q under the natural action of w is reduced by at least k states. In such case w is called a k-compressing word for A. It is known that, for any alphabet Σ and any k ≥ 2, there exist words that are k-compressing for each k-compressible automaton with the input alphabet Σ....

Decay of the Kinetic and the Thermal Energy of Compressible Micropolar Fluids. We consider a heat conducting compressible micropolar fluid at rest and filling a closed stationary rigid container. We show that tim energy of arbitrary disturbances of the fluid eventually decays. Abnahme der kinetischcn und der thermischen Energie kompressibler mikropolarcr Fliissigkeiten. Betrachtet wird eine ruh...

Recently, a critical test of the Navier-Stokes-Fourier equations for compressible fluid continua was proposed [H. Brenner, Phys. Rev. E 87, 013014 (2013)]. It was shown that the equations of bivelocity hydrodynamics imply that a compressible fluid in an isolated rotating circular cylinder attains a nonequilibrium steady state with a nonuniform temperature increasing radially with distance from ...

In this paper, we prove the existence of global weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins entropy conservation [2]. The main contribution of this paper is to derive the Mellet-Vasseur type inequality [32] for the weak solutions, even if it is not verified by the first level of approximation. This provid...

We present a non-diffusive and contact discontinuity capturing scheme for linear advection and compressible Euler system. In the case of advection, this scheme is equivalent to the Ultra-Bee limiter of [20], [24]. We prove for the Ultra-Bee scheme a property of exact advection for a large set of piecewise constant functions. We prove that the numerical error is uniformly bounded in time for suc...

Bidimensional incompressible viscous flows with well-localised vorticity are well-known to develop vortex structures. The purpose of the present paper is to recover the asymptotic profiles describing these phenomena for homogeneous finite-energy flows as asymptotic profiles for near-equilibrium isentropic compressible flows. This task is performed by extending the sharp description of the asymp...