We consider the random walks killed at the boundary of the quarter plane, with homogeneous non-zero jump probabilities to the eight nearest neighbors and drift zero in the interior, and which admit a positive harmonic polynomial of degree three. For these processes, we find the asymptotic of the Green functions along all infinite paths of states, and from this we deduce that the Martin compacti...

We present a natural restriction of Hindman’s Finite Sums Theorem that admits a simple combinatorial proof (one that does not also prove the full Finite Sums Theorem) and low computability-theoretic and proof-theoretic upper bounds, yet implies the existence of the Turing Jump, thus realizing the only known lower bound for the full Finite Sums Theorem. This is the first example of this kind. In...

This report describes an experimental still image coder that grew out of a project in the graduate course “Advanced Video Coding” in spring 2000. The project has investigated the idea to use local orientation histograms in fractal coding. Instead of performing a correlation-like grey-level matching of image regions, the block search is made by matching feature histograms of the block contents. ...

We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds for positive harmonic functions in arbitrary open sets. It applies, e.g., to many subordinate Brownian motions, Lévy processes with and without continuous p...

the purpose of this study was to determine the intensity influence of perform one set half squat on vertical jump performance and muscle electrical activity in adolescent athletes. the subjects were 12 adolescent boys athletes. the subjects performed one set of dynamic half-squat using low and high intensities (li= low intensity with 40% 1rm, hi= high intensity with 80% 1rm), and a control (c) ...