1,625 research outputs found
A Gaussian approximation of the distributed computing process
The authors propose a refinement of the stochastic model describing the dynamics of the Desktop Grid (DG) project with many hosts and many workunits to be performed, originally proposed by Morozov et al. in 2017. The target performance measure is the mean duration of the runtime of the project. To this end, the authors derive an asymptotic expression for the amount of the accumulated work to be done by means of limit theorems for superposed on-off sources that lead to a Gaussian approximation. In more detail, depending on the distribution of active and idle periods, Brownian or fractional Brownian processes are obtained. The authors present the analytic results related to the hitting time of the considered processes (including the case in which the overall amount of work is only known in a probabilistic way), and highlight how the runtime tail distribution could be estimated by simulation. Taking advantage of the properties of Gaussian processes and the Conditional Monte-Carlo (CMC) approach, the authors present a theoretical framework for evaluating the runtime tail distribution
Doctor of Philosophy
dissertationHigh-order finite element methods, using either the continuous or discontinuous Galerkin formulation, are becoming more popular in fields such as fluid mechanics, solid mechanics and computational electromagnetics. While the use of these methods is becoming increasingly common, there has not been a corresponding increase in the availability and use of visualization methods and software that are capable of displaying visualizations of these volumes both accurately and interactively. A fundamental problem with the majority of existing visualization techniques is that they do not understand nor respect the structure of a high-order field, leading to visualization error. Visualizations of high-order fields are generally created by first approximating the field with low-order primitives and then generating the visualization using traditional methods based on linear interpolation. The approximation step introduces error into the visualization pipeline, which requires the user to balance the competing goals of image quality, interactivity and resource consumption. In practice, visualizations performed this way are often either undersampled, leading to visualization error, or oversampled, leading to unnecessary computational effort and resource consumption. Without an understanding of the sources of error, the simulation scientist is unable to determine if artifacts in the image are due to visualization error, insufficient mesh resolution, or a failure in the underlying simulation. This uncertainty makes it difficult for the scientists to make judgments based on the visualization, as judgments made on the assumption that artifacts are a result of visualization error when they are actually a more fundamental problem can lead to poor decision-making. This dissertation presents new visualization algorithms that use the high-order data in its native state, using the knowledge of the structure and mathematical properties of these fields to create accurate images interactively, while avoiding the error introduced by representing the fields with low-order approximations. First, a new algorithm for cut-surfaces is presented, specifically the accurate depiction of colormaps and contour lines on arbitrarily complex cut-surfaces. Second, a mathematical analysis of the evaluation of the volume rendering integral through a high-order field is presented, as well as an algorithm that uses this analysis to create accurate volume renderings. Finally, a new software system, the Element Visualizer (ElVis), is presented, which combines the ideas and algorithms created in this dissertation in a single software package that can be used by simulation scientists to create accurate visualizations. This system was developed and tested with the assistance of the ProjectX simulation team. The utility of our algorithms and visualization system are then demonstrated with examples from several high-order fluid flow simulations
Optimal Rates for Estimation of Two-Dimensional Totally Positive Distributions
We study minimax estimation of two-dimensional totally positive
distributions. Such distributions pertain to pairs of strongly positively
dependent random variables and appear frequently in statistics and probability.
In particular, for distributions with -H\"older smooth densities where
, we observe polynomially faster minimax rates of estimation
when, additionally, the total positivity condition is imposed. Moreover, we
demonstrate fast algorithms to compute the proposed estimators and corroborate
the theoretical rates of estimation by simulation studies.Comment: 41 pages, 6 figures; accepted for publication in the Electronic
Journal of Statistic
Real-time Visual Flow Algorithms for Robotic Applications
Vision offers important sensor cues to modern robotic platforms.
Applications such as control of aerial vehicles, visual servoing,
simultaneous localization and mapping, navigation and more
recently, learning, are examples where visual information is
fundamental to accomplish tasks. However, the use of computer
vision algorithms carries the computational cost of extracting
useful information from the stream of raw pixel data. The most
sophisticated algorithms use complex mathematical formulations
leading typically to computationally expensive, and consequently,
slow implementations. Even with modern computing resources,
high-speed and high-resolution video feed can only be used for
basic image processing operations. For a vision algorithm to be
integrated on a robotic system, the output of the algorithm
should be provided in real time, that is, at least at the same
frequency as the control logic of the robot. With robotic
vehicles becoming more dynamic and ubiquitous, this places higher
requirements to the vision processing pipeline.
This thesis addresses the problem of estimating dense visual flow
information in real time. The contributions of this work are
threefold. First, it introduces a new filtering algorithm for the
estimation of dense optical flow at frame rates as fast as 800 Hz
for 640x480 image resolution. The algorithm follows a
update-prediction architecture to estimate dense optical flow
fields incrementally over time. A fundamental component of the
algorithm is the modeling of the spatio-temporal evolution of the
optical flow field by means of partial differential equations.
Numerical predictors can implement such PDEs to propagate current
estimation of flow forward in time. Experimental validation of
the algorithm is provided using high-speed ground truth image
dataset as well as real-life video data at 300 Hz.
The second contribution is a new type of visual flow named
structure flow. Mathematically, structure flow is the
three-dimensional scene flow scaled by the inverse depth at each
pixel in the image. Intuitively, it is the complete velocity
field associated with image motion, including both optical flow
and scale-change or apparent divergence of the image. Analogously
to optic flow, structure flow provides a robotic vehicle with
perception of the motion of the environment as seen by the
camera. However, structure flow encodes the full 3D image motion
of the scene whereas optic flow only encodes the component on the
image plane. An algorithm to estimate structure flow from image
and depth measurements is proposed based on the same filtering
idea used to estimate optical flow.
The final contribution is the spherepix data structure for
processing spherical images. This data structure is the numerical
back-end used for the real-time implementation of the structure
flow filter. It consists of a set of overlapping patches covering
the surface of the sphere. Each individual patch approximately
holds properties such as orthogonality and equidistance of
points, thus allowing efficient implementations of low-level
classical 2D convolution based image processing routines such as
Gaussian filters and numerical derivatives.
These algorithms are implemented on GPU hardware and can be
integrated to future Robotic Embedded Vision systems to provide
fast visual information to robotic vehicles
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