The Local Group as a test of cosmological models

The dynamics of the Local Group and its environment provide a unique challenge to cosmological models. The velocity field within 5h-1 Mpc of the Local Group (LG) is extremely ``cold''. The deviation from a pure Hubble flow, characterized by the observed radial peculiar velocity dispersion, is measured to be about 60km/s. We compare the local velocity field with similarly defined regions extracted from N-body simulations of Universes dominated by cold dark matter (CDM). This test is able to strongly discriminate between models that have different mean mass densities. We find that neither the Omega=1 (SCDM) nor Omega=0.3 (OCDM) cold dark matter models can produce a single candidate Local Group that is embedded in a region with such small peculiar velocities. For these models, we measure velocity dispersions between 500-700km/s and 150-300km/s respectively, more than twice the observed value. Although both CDM models fail to produce environments similar to those of our Local Group on a scale of a few Mpc, they can give rise to many binary systems that have similar orbital properties as the Milky Way--Andromeda system. The local, gravitationally induced bias of halos in the CDM ``Local Group'' environment, if defined within a sphere of 10 Mpc around each Local Group is about 1.5, independent of Omega. No biasing scheme could reconcile the measured velocity dispersions around Local Groups with the observed one. Identification of binary systems using a halo finder (named Skid (http://www-hpcc.astro.washington.edu/tools/DENMAX for a public version)) based on local density maxima instead of a simple linking algorithm, gives a much more complete sample. We show that a standard ``friend of friends'' algorithm would miss 40% of the LG candidates present in the simulations.Comment: Latex file (19 pages) + 13 figures. Submitted to New Astronomy. Two MPEG movies were not included. Also available (this time with the movies) at http://www-hpcc.astro.washington.edu/faculty/fabio/index.htm

Dynamic Effective Resistances and Approximate Schur Complement on Separable Graphs

We consider the problem of dynamically maintaining (approximate) all-pairs effective resistances in separable graphs, which are those that admit an n^{c}-separator theorem for some c0, unless the Online Matrix Vector Multiplication (OMv) conjecture is false. We further show that for general graphs, no incremental or decremental algorithm can maintain the s-t effective resistance problem with worst-case update time O(n^{1-delta}) and query-time O(n^{2-delta}) for any delta >0, unless the OMv conjecture is false

Recent Advances in Fully Dynamic Graph Algorithms

In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms

Appearance Preserving Rendering of Out-of-Core Polygon and NURBS Models

In Computer Aided Design (CAD) trimmed NURBS surfaces are widely used due to their flexibility. For rendering and simulation however, piecewise linear representations of these objects are required. A relatively new field in CAD is the analysis of long-term strain tests. After such a test the object is scanned with a 3d laser scanner for further processing on a PC. In all these areas of CAD the number of primitives as well as their complexity has grown constantly in the recent years. This growth is exceeding the increase of processor speed and memory size by far and posing the need for fast out-of-core algorithms. This thesis describes a processing pipeline from the input data in the form of triangular or trimmed NURBS models until the interactive rendering of these models at high visual quality. After discussing the motivation for this work and introducing basic concepts on complex polygon and NURBS models, the second part of this thesis starts with a review of existing simplification and tessellation algorithms. Additionally, an improved stitching algorithm to generate a consistent model after tessellation of a trimmed NURBS model is presented. Since surfaces need to be modified interactively during the design phase, a novel trimmed NURBS rendering algorithm is presented. This algorithm removes the bottleneck of generating and transmitting a new tessellation to the graphics card after each modification of a surface by evaluating and trimming the surface on the GPU. To achieve high visual quality, the appearance of a surface can be preserved using texture mapping. Therefore, a texture mapping algorithm for trimmed NURBS surfaces is presented. To reduce the memory requirements for the textures, the algorithm is modified to generate compressed normal maps to preserve the shading of the original surface. Since texturing is only possible, when a parametric mapping of the surface - requiring additional memory - is available, a new simplification and tessellation error measure is introduced that preserves the appearance of the original surface by controlling the deviation of normal vectors. The preservation of normals and possibly other surface attributes allows interactive visualization for quality control applications (e.g. isophotes and reflection lines). In the last part out-of-core techniques for processing and rendering of gigabyte-sized polygonal and trimmed NURBS models are presented. Then the modifications necessary to support streaming of simplified geometry from a central server are discussed and finally and LOD selection algorithm to support interactive rendering of hard and soft shadows is described

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Undergraduate catalog 2006-08, revised

The Undergraduate Catalog for the University of Missouri Columbia has been organized to enhance readability. The initial sections are related to University-wide programs, policies and procedures. The second section provides the listing of academic offerings, organized by the academic units (also may be called colleges or schools) that offer the courses and/or the degrees (major, minor or certificate) that students seek to earn. In addition to the Table of Contents, the Faculty listing and Index at the back of the catalog are invaluable for locating a person or topic quickly. An electronic version is also on the MU web site. Graduate and professional programs (Law, Medicine and Veterinary Medicine) have separate catalogs. -- Page 11.Revised July 2007