On Pólya’s Orchard Problem

Pólya’s Recurrence Theorem

Pólya’s recurrence theorem states: a simple random walk on a d-dimensional lattice is recurrent for d = 1, 2 and transient for d > 2. In this paper we discuss proof for this theorem by formulating the problem as an electric circuit problem and using Rayleigh’s short-cut method from classical theory of electricity.

Abstract: A Quantitative Pólya’s Theorem with Zeros

A Quantitative Pólya’s Theorem with Zeros Mari Castle ∗ Victoria Powers † Bruce Reznick ‡

Non-Euclidean visibility problems

Consider in R2 the standard lattice L = Z×Z and the origin (0,0). A point (m,n) ∈ L−{(0,0)} is said to be visible if the segment connecting the origin and (m,n) does not contain any other lattice points. Visibility problems have been studied since a century. Perhaps the most celebrated problems are the visible version of Gauss circle problem and the so-called orchard problem (see other problems...

Identification and initial evaluation of superior genotypes almond of traditional orchard from Qazvin based on some quantitative traits

Combined Registration and Activation Detection for fMRI: Solving Both Problems Simultaneously

J. Orchard, C. Greif, G. H. Golub, B. Bjornson, M. S. Atkins Simon Fraser University, Burnaby, BC, Canada, University of British Columbia, Vancouver, BC, Canada, Stanford University, Stanford, CA, United States, British Columbia's Children's Hospital, Vancouver, BC, Canada Synopsis The large blood oxygenation level dependent (BOLD) signal present in high-field (3T or higher) fMRI datasets can i...