We study simple closed geodesics on a hyperbolic surface of genus g with b geodesic boundary components and c cusps. We show that the number of such geodesics of length at most L is of order L 6g+2b+2c−6. This answers a long-standing open question.

Global uniqueness of inverse problem for a hyperbolic PDE with the unknown potential and a single incident plane wave is a well known long standing open question. This question is addressed for the case when derivatives with respect to variables orthogonal to this plane wave are expressed via

Abstract Many concepts have stereotypes. This leaves open the question of whether concepts are stereotypes. It has been argued elsewhere that theories that identify concepts with their stereotypes or with stereotypical properties of their instances (e.g.,

We give a linear-time algorithm for computing the medial axis of a simple polygon P, This answers a long-standing open question -- previously, the best deterministic algorithm ran in O(n log n) time. We decompose P into pseudo-normal histograms, then influence histograms and xy monotone histograms

cryptographic unrealistic to expect initial business contacts to be postponed problems of long standing. long enough for keys to be transmitted by some physical means. The cost and delay imposed by this key distribution problem is a major barrier to the transfer of business communications

function. Our results settle an open question about representability in the class of single bidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any

quantum gravity may provide predictions for their outcomes. Finally, we provide answers to frequently asked questions and a list of key open problems.

This is a visionary book written by a man on a mission. It articulates one possible answer to the question of what might come after the proprietary-based knowledge-based economy that currently exists in advanced countries. Benkler is professor of law at Yale Law School and one of the most ardent

and metric assumptions are open to question. It has been argued by many authors that dimensional representations are appropriate for certain stimuli (e.g., colors, tones) but not for others. It seems more appropriate to represent faces, countries, or personalities in terms of many qualitative features than

This paper shows that neural networks which use continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles a long-standing open question, namely whether the well-known O(w log w) bound, known for hard-threshold nets, also held