We provide an efficient data structure for dynamically maintaining a ham-sandwich cut of two nonoverlapping convex polygons in the plane. Given two non-overlapping convex polygons P1 and P2 in the plane, the ham-sandwich cut of P1 and P2 is a line that simultaneously bisects the area (or perimeter or vertex count) of both polygons. We provide a data structure that supports queries for the ham-s...

Typically, one approaches a supervised machine learning problem by writing down an objective function and finding a hypothesis that minimizes it. This is equivalent to finding the Maximum A Posteriori (MAP) hypothesis for a Boltzmann distribution. However, MAP is not a robust statistic. We present an alternative approach by defining a median of the distribution, which we show is both more robus...

What largeness and structural assumptions on A ⊆ [R]ω can guarantee the existence of a non-empty perfect set P ⊆ R such that [P ]ω ⊆ A? Such a set P is called A-homogeneous. We show that even if A is open, in general it is independent of ZFC whether for a cardinal κ, the existence of an A-homogeneous set H ∈ [R]κ implies the existence of a non-empty perfect A-homogeneous set. On the other hand,...

The non-biodegradable polymer occupying the world leads to many issues concerning global warming and other related problems. Due these issues, there is a need for biodegradable polymers overcome issues. This paper focussed on processing polyvinylalcohol (PVA) crosslinked with glutaraldehyde(GA) studying harness of polymer. from 0 40 volume percent glutaraldehyde than post cured immersed in 2 mo...

The aim of the given paper is the development of an approach for parametric identification of Wiener systems with piecewise linear nonlinearities, i.e., when the linear part with unknown parameters is followed by a saturation-like function with unknown slopes. It is shown here that by a simple data reordering and by a following data partition the problem of identification of a nonlinear Wiener ...

Pure and Applied Mathematics—Two Sides of a Coin In November of 1979 there appeared in the Bulletin of the AMS a paper by L. Auslander and R. Tolimieri [3] with the delightful title “Is Computing with the Finite Fourier Transform Pure or Applied Mathematics?” This rhetorical question was answered by showing that in fact the finite Fourier transform and the family of efficient algorithms used to...

In November of 1979, there appeared a paper in the Bulletin of the AMS by L. Auslander and R. Tolimieri with the delightful title of “Is Computing with the Finite Fourier Transform Pure or Applied Mathematics?” The question was of course rhetorical and one of the main goals of the paper was to show that the finite Fourier transform, and the family of efficient algorithms used to compute it, the...

Introduction: There has always been interest in speeding the acquisition of MRI data by acquiring fewer data in k-space. Recently there has been a significant interest in applying inverse problem techniques to reconstructing images from undersampled k-space MRI data [1-6]. One class of methods, from the nascent field of compressed sensing, is based on the sparse representation of images. As an ...