We characterize the invariant filtering measures resulting from Kalman filtering with intermittent observations ([1]), where the observation arrival is modeled as a Bernoulli process. In [2], it was shown that there exists a γsb > 0 such that for every observation packet arrival probability γ, γ > γsb > 0, the sequence of random conditional error covariance matrices converges in distribution to...

The μ(I)-rheology is a nonlinear viscous law, with a strain-rate invariant and pressure-dependent viscosity, that has proved to be effective at modelling dry granular flows in the intermediate range of the inertial number, I. This paper shows how to incorporate the rheology into depth-averaged granular avalanche models. To leading order, the rheology generates an effective basal friction, which...

We consider a Cauchy problem for a scalar conservation law in one space dimension with a compactly supported initial datum,

Laws of nature are universal in scope, hold with unfailing regularity, and receive support from a wide array of facts and observations. The Law of Conservation of Information (LCI) is such a law. LCI characterizes the information costs that searches incur in outperforming blind search. Searches that operate by Darwinian selection, for instance, often significantly outperform blind search. But w...

A power-law distribution of the length of perfectly conserved sequence from mouse/human whole-genome intersection and alignment is exhibited. Spatial correlations of these elements within the mouse genome are studied. It is argued that these power-law distributions and correlations are comprised in part by functional noncoding sequence and ought to be accounted for in estimating the statistical...

We consider the parabolic regularization of a scalar conservation law in which the Laplacian operator has been replaced by a fractional power of itself. Using a splitting method, we prove the existence of a solution to the problem and, thanks to the Banach fixed point theorem, its uniqueness and regularity. We also show that, as the regularization vanishes, the solution converge to the entropy ...

For the generalized Thomas–Fermi differential equation (|x|x) = q(t)|x|x, it is proved that if 1 6 α < β and q(t) is a regularly varying function of index μ with μ > −α − 1, then all positive solutions that tend to zero as t → ∞ are regularly varying functions of one and the same negative index ρ and their asymptotic behavior at infinity is governed by the unique definite decay law. Further, an...