2,004 research outputs found
k-d Darts: Sampling by k-Dimensional Flat Searches
We formalize the notion of sampling a function using k-d darts. A k-d dart is
a set of independent, mutually orthogonal, k-dimensional subspaces called k-d
flats. Each dart has d choose k flats, aligned with the coordinate axes for
efficiency. We show that k-d darts are useful for exploring a function's
properties, such as estimating its integral, or finding an exemplar above a
threshold. We describe a recipe for converting an algorithm from point sampling
to k-d dart sampling, assuming the function can be evaluated along a k-d flat.
We demonstrate that k-d darts are more efficient than point-wise samples in
high dimensions, depending on the characteristics of the sampling domain: e.g.
the subregion of interest has small volume and evaluating the function along a
flat is not too expensive. We present three concrete applications using line
darts (1-d darts): relaxed maximal Poisson-disk sampling, high-quality
rasterization of depth-of-field blur, and estimation of the probability of
failure from a response surface for uncertainty quantification. In these
applications, line darts achieve the same fidelity output as point darts in
less time. We also demonstrate the accuracy of higher dimensional darts for a
volume estimation problem. For Poisson-disk sampling, we use significantly less
memory, enabling the generation of larger point clouds in higher dimensions.Comment: 19 pages 16 figure
Performance Analysis of Wireless Systems with Doubly Selective Rayleigh Fading
Theoretical error performances of wireless communication systems suffering from both doubly selective (time varying and frequency selective) Rayleigh fading and sampler timing offset are analyzed in this paper. Single-input-single-output systems with doubly selective fading channels are equivalently represented as discrete-time single-input-multiple-output (SIMO) systems with correlated frequency-flat fading channels, with the correlation information being determined by the combined effects of sampler timing phase, maximum Doppler spread, and power delay profile of the physical fading. Based on the equivalent SIMO system representation, closed-form error-probability expressions are derived as tight lower bounds for linearly modulated systems with fractionally spaced equalizers. The information on the sampler timing offset and the statistical properties of the physical channel fading, along with the effects of the fractionally spaced equalizer, are incorporated in the error-probability expressions. Simulation results show that the new analytical results can accurately predict the error performances of maximum-likelihood sequence estimation and maximum a posteriori equalizers for practical wireless communication systems in a wide range of signal-to-noise ratio. Moreover, some interesting observations about receiver oversampling and system timing phase sensitivity are obtained based on the new analytical results
How to mesh up Ewald sums (II): An accurate error estimate for the P3M algorithm
We construct an accurate estimate for the root mean square force error of the
particle-particle-particle-mesh (P3M) algorithm by extending a single particle
pair error measure which has been given by Hockney and Eastwood. We also derive
an easy-to-use analytic approximation to the error formula. This allows a
straightforward and precise determination of the optimal splitting parameter
(as a function of system specifications and P3M parameters) and hence knowledge
of the force accuracy prior to the actual simulation. The high quality of the
estimate is demonstrated in several examples.Comment: 9 pages, 7 figures included, revtex styl
An exact general remeshing scheme applied to physically conservative voxelization
We present an exact general remeshing scheme to compute analytic integrals of
polynomial functions over the intersections between convex polyhedral cells of
old and new meshes. In physics applications this allows one to ensure global
mass, momentum, and energy conservation while applying higher-order polynomial
interpolation. We elaborate on applications of our algorithm arising in the
analysis of cosmological N-body data, computer graphics, and continuum
mechanics problems.
We focus on the particular case of remeshing tetrahedral cells onto a
Cartesian grid such that the volume integral of the polynomial density function
given on the input mesh is guaranteed to equal the corresponding integral over
the output mesh. We refer to this as "physically conservative voxelization".
At the core of our method is an algorithm for intersecting two convex
polyhedra by successively clipping one against the faces of the other. This
algorithm is an implementation of the ideas presented abstractly by Sugihara
(1994), who suggests using the planar graph representations of convex polyhedra
to ensure topological consistency of the output. This makes our implementation
robust to geometric degeneracy in the input. We employ a simplicial
decomposition to calculate moment integrals up to quadratic order over the
resulting intersection domain.
We also address practical issues arising in a software implementation,
including numerical stability in geometric calculations, management of
cancellation errors, and extension to two dimensions. In a comparison to recent
work, we show substantial performance gains. We provide a C implementation
intended to be a fast, accurate, and robust tool for geometric calculations on
polyhedral mesh elements.Comment: Code implementation available at https://github.com/devonmpowell/r3
Advanced signal processing methods in dynamic contrast enhanced magnetic resonance imaging
Tato dizertační práce představuje metodu zobrazování perfúze magnetickou rezonancí, jež je výkonným nástrojem v diagnostice, především v onkologii. Po ukončení sběru časové sekvence T1-váhovaných obrazů zaznamenávajících distribuci kontrastní látky v těle začíná fáze zpracování dat, která je předmětem této dizertace. Je zde představen teoretický základ fyziologických modelů a modelů akvizice pomocí magnetické rezonance a celý řetězec potřebný k vytvoření obrazů odhadu parametrů perfúze a mikrocirkulace v tkáni. Tato dizertační práce je souborem uveřejněných prací autora přispívajícím k rozvoji metodologie perfúzního zobrazování a zmíněného potřebného teoretického rozboru.This dissertation describes quantitative dynamic contrast enhanced magnetic resonance imaging (DCE-MRI), which is a powerful tool in diagnostics, mainly in oncology. After a time series of T1-weighted images recording contrast-agent distribution in the body has been acquired, data processing phase follows. It is presented step by step in this dissertation. The theoretical background in physiological and MRI-acquisition modeling is described together with the estimation process leading to parametric maps describing perfusion and microcirculation properties of the investigated tissue on a voxel-by-voxel basis. The dissertation is divided into this theoretical analysis and a set of publications representing particular contributions of the author to DCE-MRI.
Orthogonal or superimposed pilots? A rate-efficient channel estimation strategy for stationary MIMO fading channels
©IEEE, 2017This paper considers channel estimation for multiple-input multiple-output (MIMO) channels and revisits two competing concepts of including training data into the transmit signal, namely orthogonal pilot (OP) that periodically transmits alternating pilot-data symbols, and superimposed pilot (SP) that overlays pilot-data symbols over time. We investigate rates achievable by both schemes when the channel undergoes time-selective bandlimited fading and analyze their behaviors with respect to the MIMO dimension and fading speed. By incorporating the multiple-antenna factors, we demonstrate that the widely-known trend, in which the OP is superior to the SP in the regimes of high signal-to-noise ratio (SNR) and slow-fading, and vice-versa, does not hold in general. As the number of transmit antennas (nt) increases, the range of operable fading speeds for the OP is significantly narrowed due to limited time resources for channel estimation and insufficient fading samples, which results in the SP being competitive in wider speed and SNR ranges. For a sufficiently small nt, we demonstrate thatas the fading variation becomes slower, the estimation quality for the SP can be superior to that for the OP. In this case, the SP outperforms the OP in the slow-fading regime due to full utilization of time for data transmission
Attitude-referenced radiometer study. Volume 2 - Precision radiometric system
Attitude reference radiometer study for earth orbiting spacecraf
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