5,299 research outputs found
Geometric transformations in octrees using shears
Existent algorithms to perform geometric transformations on octrees
can be classified in two families: inverse transformation and address
computation ones. Those in the inverse transformation family
essentially resample the target octree from the source one, and are
able to cope with all the affine transformations. Those in the address
computation family only deal with translations, but are commonly
accepted as faster than the former ones for they do no intersection
tests, but directly calculate the transformed address of each black
node in the source tree. This work introduces a new translation
algorithm that shows to perform better than previous one when very
small displacements are involved. This property is particularly useful
in applications such as simulation, robotics or computer animation.Postprint (published version
Integrating OLAP and Ranking: The Ranking-Cube Methodology
Recent years have witnessed an enormous growth of data in business, industry, and Web applications. Database search often returns a large collection of results, which poses challenges to both efficient query processing and effective digest of the query results. To address this problem, ranked search has been introduced to database systems. We study the problem of On-Line Analytical Processing (OLAP) of ranked queries, where ranked queries are conducted in the arbitrary subset of data defined by multi-dimensional selections. While pre-computation and multi-dimensional aggregation is the standard solution for OLAP, materializing dynamic ranking results is unrealistic because the ranking criteria are not known until the query time. To overcome such difficulty, we develop a new ranking cube method that performs semi on-line materialization and semi online computation in this thesis. Its complete life cycle, including cube construction, incremental maintenance, and query processing, is also discussed. We further extend the ranking cube in three dimensions. First, how to answer queries in high-dimensional data. Second, how to answer queries which involves joins over multiple relations. Third, how to answer general preference queries (besides ranked queries, such as skyline queries). Our performance studies show that ranking-cube is orders of magnitude faster than previous approaches
The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
We present a compendium of numerical simulation techniques, based on tensor
network methods, aiming to address problems of many-body quantum mechanics on a
classical computer. The core setting of this anthology are lattice problems in
low spatial dimension at finite size, a physical scenario where tensor network
methods, both Density Matrix Renormalization Group and beyond, have long proven
to be winning strategies. Here we explore in detail the numerical frameworks
and methods employed to deal with low-dimension physical setups, from a
computational physics perspective. We focus on symmetries and closed-system
simulations in arbitrary boundary conditions, while discussing the numerical
data structures and linear algebra manipulation routines involved, which form
the core libraries of any tensor network code. At a higher level, we put the
spotlight on loop-free network geometries, discussing their advantages, and
presenting in detail algorithms to simulate low-energy equilibrium states.
Accompanied by discussions of data structures, numerical techniques and
performance, this anthology serves as a programmer's companion, as well as a
self-contained introduction and review of the basic and selected advanced
concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure
Fast, accurate, and transferable many-body interatomic potentials by symbolic regression
The length and time scales of atomistic simulations are limited by the
computational cost of the methods used to predict material properties. In
recent years there has been great progress in the use of machine learning
algorithms to develop fast and accurate interatomic potential models, but it
remains a challenge to develop models that generalize well and are fast enough
to be used at extreme time and length scales. To address this challenge, we
have developed a machine learning algorithm based on symbolic regression in the
form of genetic programming that is capable of discovering accurate,
computationally efficient manybody potential models. The key to our approach is
to explore a hypothesis space of models based on fundamental physical
principles and select models within this hypothesis space based on their
accuracy, speed, and simplicity. The focus on simplicity reduces the risk of
overfitting the training data and increases the chances of discovering a model
that generalizes well. Our algorithm was validated by rediscovering an exact
Lennard-Jones potential and a Sutton Chen embedded atom method potential from
training data generated using these models. By using training data generated
from density functional theory calculations, we found potential models for
elemental copper that are simple, as fast as embedded atom models, and capable
of accurately predicting properties outside of their training set. Our approach
requires relatively small sets of training data, making it possible to generate
training data using highly accurate methods at a reasonable computational cost.
We present our approach, the forms of the discovered models, and assessments of
their transferability, accuracy and speed
On the size of quadtrees generalized to d-dimensional binary pictures
AbstractSome results about the size of quadtrees and linear quadtrees, used to represent binary 2n × 2n digital pictures, are generalized to d-dimensional 2n × … × 2n pictures. Among these results are a comparison of the space-efficiency of linear vs regular trees, in terms of both the number of nodes of the tree and the number of bits needed to store each node, and an upper bound on the number of nodes as a function of n and the perimeter of the picture
Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation
We investigate an encoding scheme for lossy compression of a binary symmetric
source based on simple spatially coupled Low-Density Generator-Matrix codes.
The degree of the check nodes is regular and the one of code-bits is Poisson
distributed with an average depending on the compression rate. The performance
of a low complexity Belief Propagation Guided Decimation algorithm is
excellent. The algorithmic rate-distortion curve approaches the optimal curve
of the ensemble as the width of the coupling window grows. Moreover, as the
check degree grows both curves approach the ultimate Shannon rate-distortion
limit. The Belief Propagation Guided Decimation encoder is based on the
posterior measure of a binary symmetric test-channel. This measure can be
interpreted as a random Gibbs measure at a "temperature" directly related to
the "noise level of the test-channel". We investigate the links between the
algorithmic performance of the Belief Propagation Guided Decimation encoder and
the phase diagram of this Gibbs measure. The phase diagram is investigated
thanks to the cavity method of spin glass theory which predicts a number of
phase transition thresholds. In particular the dynamical and condensation
"phase transition temperatures" (equivalently test-channel noise thresholds)
are computed. We observe that: (i) the dynamical temperature of the spatially
coupled construction saturates towards the condensation temperature; (ii) for
large degrees the condensation temperature approaches the temperature (i.e.
noise level) related to the information theoretic Shannon test-channel noise
parameter of rate-distortion theory. This provides heuristic insight into the
excellent performance of the Belief Propagation Guided Decimation algorithm.
The paper contains an introduction to the cavity method
- …