We give an elementary proof that there are two topological generators for the full group of every aperiodic hyperfinite probability measure preserving Borel equivalence relation. Our proof explicitly constructs topological generators for the orbit equivalence relation of the irrational rotation of the circle, and then appeals to Dye’s theorem and a Baire category argument to conclude the genera...

The explicit solution to the spectral problem of quantum graphs found recently in [20], is used to produce the exact periodic orbit theory description for the probability distributions of spectral statistics, including the distribution for the nearest neighbor separations, s n = k n − k n−1 , and the distribution of the spectral oscillations around the average, δk n = k n − ¯ k n .

In the first part of this paper, inspired by the geometric method of Jean-Pierre Marec, we consider the two-impulse Hohmann transfer problem between two coplanar circular orbits as a constrained nonlinear programming problem. By using the Kuhn-Tucker theorem, we analytically prove the global optimality of the Hohmann transfer. Two sets of feasible solutions are found, one of which corresponding...

Aiming to provide a new class of game dynamics with good long-term rationality properties, we derive a second-order inertial system that builds on the widely studied “heavy ball with friction” optimization method. By exploiting a well-known link between the replicator dynamics and the Shahshahani geometry on the space of mixed strategies, the dynamics are stated in a Riemannian geometric framew...

With 10 years of high-resolution imaging data now available on the stellar cluster in the Galactic Center, we analyze the dynamics of the stars at projected distances ≤ 1.2 ′′ from the central black hole candidate Sagittarius A* (Sgr A*). We find evidence for radial anisotropy of the cluster of stars surrounding Sgr A*. We confirm/find accelerated motion for 6 stars, with 4 stars having passed ...

Prediction, tracking, and retrodiction for targets whose motion is constrained by external conditions (e.g., shipping lanes, roads) present many challenges to tracking systems. The targets are moving along a path, defined by way-points and segments. Measurements are obtained by sensors at low revisit rates (e.g., spaceborne). Existing tracking algorithms assume that the targets follow the same ...

Introduction: Diagnosis of orbital foreign body (FB) penetration is usually obvious when part of the FB is still attached at the entry wound (1). However, the depth and course of the FB in this case was not visible.   Case Report: A 5-year old female presented with a pencil penetrating the left orbit. A computed tomography (CT) scan showed that the pencil penetrated the left orbit (extraseptal)...

We prove that low-rank matrices can be recovered efficiently from a small number of measurements that are sampled from orbits of a certain matrix group. As a special case, our theory makes statements about the phase retrieval problem. Here, the task is to recover a vector given only the amplitudes of its inner product with a small number of vectors from an orbit. Variants of the group in questi...

This paper deals with the taking into account a given target set of realizations as constraints in Kullback–Leibler divergence minimum principle (KLDMP). We present novel probabilistic learning algorithm that makes it possible to use KLDMP when are not defined by statistical moments for quantity interest (QoI) an uncertain/stochastic computational model, but QoI which associated these or cannot...