3,922 research outputs found
Traffic Analysis in Random Delaunay Tessellations and Other Graphs
In this work we study the degree distribution, the maximum vertex and edge
flow in non-uniform random Delaunay triangulations when geodesic routing is
used. We also investigate the vertex and edge flow in Erd\"os-Renyi random
graphs, geometric random graphs, expanders and random -regular graphs.
Moreover we show that adding a random matching to the original graph can
considerably reduced the maximum vertex flow.Comment: Submitted to the Journal of Discrete Computational Geometr
The Emergence of Canalization and Evolvability in an Open-Ended, Interactive Evolutionary System
Natural evolution has produced a tremendous diversity of functional
organisms. Many believe an essential component of this process was the
evolution of evolvability, whereby evolution speeds up its ability to innovate
by generating a more adaptive pool of offspring. One hypothesized mechanism for
evolvability is developmental canalization, wherein certain dimensions of
variation become more likely to be traversed and others are prevented from
being explored (e.g. offspring tend to have similarly sized legs, and mutations
affect the length of both legs, not each leg individually). While ubiquitous in
nature, canalization almost never evolves in computational simulations of
evolution. Not only does that deprive us of in silico models in which to study
the evolution of evolvability, but it also raises the question of which
conditions give rise to this form of evolvability. Answering this question
would shed light on why such evolvability emerged naturally and could
accelerate engineering efforts to harness evolution to solve important
engineering challenges. In this paper we reveal a unique system in which
canalization did emerge in computational evolution. We document that genomes
entrench certain dimensions of variation that were frequently explored during
their evolutionary history. The genetic representation of these organisms also
evolved to be highly modular and hierarchical, and we show that these
organizational properties correlate with increased fitness. Interestingly, the
type of computational evolutionary experiment that produced this evolvability
was very different from traditional digital evolution in that there was no
objective, suggesting that open-ended, divergent evolutionary processes may be
necessary for the evolution of evolvability.Comment: SI can be found at: http://www.evolvingai.org/files/SI_0.zi
Line Patterns in Free Groups
We study line patterns in a free group by considering the topology of the
decomposition space, a quotient of the boundary at infinity of the free group
related to the line pattern. We show that the group of quasi-isometries
preserving a line pattern in a free group acts by isometries on a related space
if and only if there are no cut pairs in the decomposition space.Comment: 35 pages, 22 figures, PDFLatex; v2. finite index requires extra
hypothesis; v3. 37 pages, 24 figures: updated references and add example in
Section 6.3 of a rigid pattern for which the free group is not finite index
in the group of pattern preserving quasi-isometries; v4. 40 pages, 26
figures: improved exposition and add example in Section 6.4 of a rigid
pattern whose cube complex is not a tre
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
DeformNet: Free-Form Deformation Network for 3D Shape Reconstruction from a Single Image
3D reconstruction from a single image is a key problem in multiple
applications ranging from robotic manipulation to augmented reality. Prior
methods have tackled this problem through generative models which predict 3D
reconstructions as voxels or point clouds. However, these methods can be
computationally expensive and miss fine details. We introduce a new
differentiable layer for 3D data deformation and use it in DeformNet to learn a
model for 3D reconstruction-through-deformation. DeformNet takes an image
input, searches the nearest shape template from a database, and deforms the
template to match the query image. We evaluate our approach on the ShapeNet
dataset and show that - (a) the Free-Form Deformation layer is a powerful new
building block for Deep Learning models that manipulate 3D data (b) DeformNet
uses this FFD layer combined with shape retrieval for smooth and
detail-preserving 3D reconstruction of qualitatively plausible point clouds
with respect to a single query image (c) compared to other state-of-the-art 3D
reconstruction methods, DeformNet quantitatively matches or outperforms their
benchmarks by significant margins. For more information, visit:
https://deformnet-site.github.io/DeformNet-website/ .Comment: 11 pages, 9 figures, NIP
Homology-based Distributed Coverage Hole Detection in Wireless Sensor Networks
Homology theory provides new and powerful solutions to address the coverage
problems in wireless sensor networks (WSNs). They are based on algebraic
objects, such as Cech complex and Rips complex. Cech complex gives accurate
information about coverage quality but requires a precise knowledge of the
relative locations of nodes. This assumption is rather strong and hard to
implement in practical deployments. Rips complex provides an approximation of
Cech complex. It is easier to build and does not require any knowledge of nodes
location. This simplicity is at the expense of accuracy. Rips complex can not
always detect all coverage holes. It is then necessary to evaluate its
accuracy. This work proposes to use the proportion of the area of undiscovered
coverage holes as performance criteria. Investigations show that it depends on
the ratio between communication and sensing radii of a sensor. Closed-form
expressions for lower and upper bounds of the accuracy are also derived. For
those coverage holes which can be discovered by Rips complex, a homology-based
distributed algorithm is proposed to detect them. Simulation results are
consistent with the proposed analytical lower bound, with a maximum difference
of 0.5%. Upper bound performance depends on the ratio of communication and
sensing radii. Simulations also show that the algorithm can localize about 99%
coverage holes in about 99% cases
- …