Abstra t Most lassi ation algorithms experien e diÆ ulties when the input-output distribution is irregular (i.e., neighbor examples in the input spa e have di erent values in the output spa e), and sparse. We hara terize the diÆ ulty of a lassi ation problem using a limited number of examples by re-de ning a measure of lass variation to a ount for irregular distributions, and by introdu ing a n...

Subadditive time discounting means that discounting over a delay is greater when the delay is divided into subintervals than when it is left undivided. This may produce the most important result usually attributed to hyperbolic discounting: declining impatience, or the inverse relationship between the discount rate and the magnitude of the delay. Three choice experiments were conducted to test ...

We introduce a new variant of tight closure and give an interpretation of adjoint ideals via this tight closure. As a corollary, we prove that a log pair (X,∆) is plt if and only if the modulo p reduction of (X,∆) is divisorially F-regular for all large p ≫ 0. Here, divisorially F-regular pairs are a class of singularities in positive characteristic introduced by Hara and Watanabe [HW] in terms...

This paper reviews the trajectory of three information visualization innovations: treemaps, conetrees, and hyperbolic trees. These three ideas were first published in the early 1990s, so we are able to track academic publications, patents, trade press articles over almost two decades. We describe the early history of each approach, problems with data collection from differing sources, appropria...

__________ "[...] Agents are here to stay, not least because of their diversity, their wide range of applicability and the broad spectrum of companies investing in them. As we move further and further into the information age, any information-based organisation which does not invest in agent technology may be committing commercial hara-kiri."

It is shown how one can draw graphs on surfaces of negative Euler characteristic by using hyperbolic geometry and hyperbolic circle packing representations. The same approach applies to drawings of hyperbolic tessellations.

Let (Xi, di), i = 1, 2, be proper geodesic hyperbolic metric spaces. We give a general construction for a " hyperbolic product " X1× h X2 which is itself a proper geodesic hyperbolic metric space and examine its boundary at infinity.

We show that for certain hyperbolic manifolds all boundary slopes are slopes of π1-injective immersed surfaces, covered by incompressible embeddings in some finite cover. The manifolds include hyperbolic punctured torus bundles and hyperbolic two-bridge knots.

We show that for any non–elementary hyperbolic group H and any finitely presented group Q, there exists a short exact sequence 1 → N → G → Q → 1, where G is a hyperbolic group and N is a quotient group of H . As an application we construct a representation rigid but not superrigid hyperbolic group, show that adding relations of the form xn = 1 to a presentation of a hyperbolic group may drastic...

We prove global rigidity for compact hyperbolic and spherical cone-3-manifolds with cone-angles ≤ π (which are not Seifert fibered in the spherical case), furthermore for a class of hyperbolic cone-3-manifolds of finite volume with cone-angles ≤ π, possibly with boundary consisting of totally geodesic hyperbolic turnovers. To that end we first generalize the local rigidity result contained in [...