improved accuracy of the data processing software and reliable accuracy measures to reduce the need for human involvement in error correction and make human review more efficient. Here, we describe one step toward that goal: a base-calling program for automated sequencer traces, phred, with improved

. From the perspective of the user, the verification is highly automated: the only input required is the BMC bound. The tool is integrated into a graphical user interface. This is essential for presenting long counterexample traces: the tool allows stepping through the trace in the same way a debugger

on large Internet access traces and find that it performs quite well. However, the success of the algorithm is tempered by the discovery that large sites have many users who routinely traverse stepping stones for a variety of legitimate reasons. Hence, stepping-stone detection also requires a significant

-gineering measurements and the relationship between error and uncertainty. Then the path of an uncertainty analysis is traced from its first step, identify-ing the intended true value of a measurement, through the quantitative estima-tion of the individual errors, to the end objective--the interpretation a d re

(photons) from the light sources and storing these as they hit surfaces within the scene. We use one high resolution caustics photon map to render caustics that are visualized directly and one low resolution photon map that is used during the rendering step. The scene is rendered using a distribution ray

We examine various simple algorithms that exploit homogeneity and accumulated opacity for tracing rays through shaded volumes. Most of these methods have error criteria which allow them to trade quality for speed. The time vs. quality tradeoff for these adaptive methods is compared to fixed step

tracing which takes a first step toward alleviating this deficiency. The problem addressed

toward its first intersection in steps guaranteed not to penetrate the implicit surface. Sphere tracing is particularly adept at rendering pathological surfaces. Creased and rough implicit surfaces are defined by functions with discontinuous or undefined derivatives. Current root finding techniques

. In this work, an efficient iterative procedure is presented to directly solve the Trace Ratio problem. In each step, a Trace Difference problem argmaxW Tr[WT (Sp−λSl)W] is solved with λ being the trace ratio value computed from the previous step. Con-vergence of the projection matrix W, as well as the global

Abstract. Alternating transition systems are a general model for composite systems which allow the study of collaborative as well as adversarial relationships between individual system components. Unlike in labeled transition systems, where each transition corresponds to a possible step