We prove that the integrality gap of the Goemans-Linial semidefinite programming relaxation for the Sparsest Cut Problem is Ω(√logn) on inputs with n vertices, thus matching the previously best known upper bound (logn)1/2+o(1) up to lower-order factors. This statement is a consequence of the following new isoperimetric-type inequality. Consider the 8-regular graph whose vertex set is the 5-dimensional integer grid ℤ5 and where each vertex (a,b,c,d,e)∈ ℤ5 is connected to the 8 vertices (a± 1,b,c,d,e), (a,b± 1,c,d,e), (a,b,c± 1,d,e± a), (a,b,c,d± 1,e± b). This graph is known as the Cayley graph of the 5-dimensional discrete Heisenberg group. Given Ω⊆ ℤ5, denote the size of its edge boundary in this graph (a.k.a. the horizontal perimeter of Ω) by |∂hΩ|. For t ϵ ℕ, denote by |∂vtΩ| the number of (a,b,c,d,e)ϵ ℤ5 such that exactly one of the two vectors (a,b,c,d,e),(a,b,c,d,e+t) is in Ω. The vertical perimeter of Ω is defined to be |∂vΩ|= √Σt=1∞|∂vtΩ|2/t2. We show that every subset Ω⊆ ℤ5 satisfies |∂vΩ|=O(|∂hΩ|). This vertical-versus-horizontal isoperimetric inequality yields the above-stated integrality gap for Sparsest Cut and answers several geometric and analytic questions of independent interest.

Decision makers (humans or software agents alike) are faced with the challenge of examining large volumes of information originating from heterogeneous sources with the goal of ascertaining trust in various pieces of information. In this paper we argue (using examples) that traditional trust models are limited in their data model by assuming a pair-wise numeric rating between two entities (e.g., eBay recommendations, Netflix movie rating, etc). We present a novel trust computational model for rich, complex and uncertain information encoded using Bayesian Description Logics. We present security and scalability tradeoffs that arise in the new model, and the results of an evaluation of the first prototype implementation under a variety attack scenarios.

This paper describes the robust reading competitions for ICDAR 2003. With the rapid growth in research over the last few years on recognizing text in natural scenes, there is an urgent need to establish some common benchmark datasets, and gain a clear understanding of the current state of the art. We use the term robust reading to refer to text images that are beyond the capabilities of current commercial OCR packages. We chose to break down the robust reading problem into three sub-problems, and run competitions for each stage, and also a competition for the best overall system. The sub-problems we chose were text locating, character recognition and word recognition. By breaking down the problem in this way, we hope to gain a better understanding of the state of the art in each of the sub-problems. Furthermore, our methodology involves storing detailed results of applying each algorithm to each image in the data sets, allowing researchers to study in depth the strengths and weaknesses of each algorithm. The text locating contest was the only one to have any entries. We report the results of this contest, and show cases where the leading algorithms succeed and fail. 1.

A cascade of increasing scale, 1-D, recursive median filters produces a sieve, termed an R-sieve, has a number of properties important to image processing. In particular, it (1) Simplifies signals without introducing new extrema or edges, that is, it preserves scale-space. It shares this property with Gaussian filters, but has the advantage of being significantly more robust. (2) The differences between successive stages of the sieve yield a transform, to the granularity domain. Patterns and shapes can be recognized in this domain using idempotent matched sieves and the result transformed back to the spatial domain. The R-sieve is very fast to compute and has a close relationship to 1-D alternating sequential filters with flat structuring elements. They are useful for machine vision applications.

article Free Access Share on Report on Experiments in Approximating the Solution of a Differential Equation Author: Robert Young Wright-Patterson Air Force Base, Dayton, Ohio Wright-Patterson Air Force Base, Dayton, OhioView Profile Authors Info & Claims Journal of the ACMVolume 3Issue 1Jan. 1956 pp 26–28https://doi.org/10.1145/320815.320822Online:01 January 1956Publication History 0citation315DownloadsMetricsTotal Citations0Total Downloads315Last 12 Months2Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF