We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show that as the forcing and dissipation are removed a unique limit of the deterministic system is selected. The exact structure of the limiting measure depends on...

Abstract: We provide a Hamiltonian analysis of the Mixmaster Universe dynamics showing the covariant nature of its chaotic behavior with respect to any choice of time variable. We construct the appropriate invariant measure for the system (which relies on the existence of an “energy-like” constant of motion) without fixing the time gauge, i.e. the corresponding lapse function. The key point in ...

CP violation is expected in the standard model of particle physics with three or more families [1], [2]. Therefore it is an important problem that what is the measure of CP violation with such families which is invariant under the action of phase factors. To construct invariants for matrix action, the determinant is a useful tool. In the previous paper [3], C. Jarlskog succeeded to define invar...

The numerical approximation of Perron–Frobenius operators allows efficient determination of the physical invariant measure of chaotic dynamical systems as a fixed point of the operator. Eigenfunctions of the Perron–Frobenius operator corresponding to large subunit eigenvalues have been shown to describe “almost-invariant” dynamics in one-dimensional expanding maps. We extend these ideas to hype...

Critical circle homeomorphisms have an invariant measure totally singular with respect to the Lebesgue measure. We prove that singularities of the invariant measure are of Hőlder type. The Hausdorff dimension of the invariant measure is less than 1 but greater than 0.

This paper shows that the common task of interest region matching using local descriptors can be improved using a new similarity measure. The similarity measure is motivated by the information theoretic image alignment that maximize mutual information between images. A property of the mutual information metric is that it does not only depend on how similar the signals are but also how complex t...

In this work we analyze the concept of swap-invariance, which is a weaker variant of exchangeability. An integrable random vector ξ in R is called swap-invariant if E ∣∣∑ j ujξj ∣∣ is invariant under all permutations of the components of ξ for each u ∈ R. Further a random sequence is swap-invariant if its finite-dimensional distributions are swap-invariant. Two characterizations of large classe...

The purpose of this article was to assess the overall health behaviors of African American emerging adults who live in a Midwestern city. Two hundred participants, ages 18-25, completed a 129-item survey. Results indicate that African American emerging adults are engaged in relatively healthy behaviors (i.e., physical activity, low substance use). The results also showed that within the emergin...