856 research outputs found
Rearrangement on Lattices with Pick-n-Swaps: Optimality Structures and Efficient Algorithms
We propose and study a class of rearrangement problems under a novel
pick-n-swap prehensile manipulation model, in which a robotic manipulator,
capable of carrying an item and making item swaps, is tasked to sort items
stored in lattices of variable dimensions in a time-optimal manner. We
systematically analyze the intrinsic optimality structure, which is fairly rich
and intriguing, under different levels of item distinguishability (fully
labeled, where each item has a unique label, or partially labeled, where
multiple items may be of the same type) and different lattice dimensions.
Focusing on the most practical setting of one and two dimensions, we develop
low polynomial time cycle-following based algorithms that optimally perform
rearrangements on 1D lattices under both fully- and partially-labeled settings.
On the other hand, we show that rearrangement on 2D and higher dimensional
lattices becomes computationally intractable to optimally solve. Despite their
NP-hardness, we prove that efficient cycle-following based algorithms remain
asymptotically optimal for 2D fully- and partially-labeled settings, in
expectation, using the interesting fact that random permutations induce only a
small number of cycles. We further improve these algorithms to provide
1.x-optimality when the number of items is small. Simulation studies
corroborate the effectiveness of our algorithms.Comment: To appear in R:SS 202
Generalized Weiszfeld algorithms for Lq optimization
In many computer vision applications, a desired model of some type is computed by minimizing a cost function based on several measurements. Typically, one may compute the model that minimizes the L₂ cost, that is the sum of squares of measurement errors with respect to the model. However, the Lq solution which minimizes the sum of the qth power of errors usually gives more robust results in the presence of outliers for some values of q, for example, q = 1. The Weiszfeld algorithm is a classic algorithm for finding the geometric L1 mean of a set of points in Euclidean space. It is provably optimal and requires neither differentiation, nor line search. The Weiszfeld algorithm has also been generalized to find the L1 mean of a set of points on a Riemannian manifold of non-negative curvature. This paper shows that the Weiszfeld approach may be extended to a wide variety of problems to find an Lq mean for 1 ≤ q <; 2, while maintaining simplicity and provable convergence. We apply this problem to both single-rotation averaging (under which the algorithm provably finds the global Lq optimum) and multiple rotation averaging (for which no such proof exists). Experimental results of Lq optimization for rotations show the improved reliability and robustness compared to L₂ optimization.This research has been funded by National ICT Australia
A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows
In this article we set up a splitting variant of the JKO scheme in order to
handle gradient flows with respect to the Kantorovich-Fisher-Rao metric,
recently introduced and defined on the space of positive Radon measure with
varying masses. We perform successively a time step for the quadratic
Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao
distance. Exploiting some inf-convolution structure of the metric we show
convergence of the whole process for the standard class of energy functionals
under suitable compactness assumptions, and investigate in details the case of
internal energies. The interest is double: On the one hand we prove existence
of weak solutions for a certain class of reaction-advection-diffusion
equations, and on the other hand this process is constructive and well adapted
to available numerical solvers.Comment: Final version, to appear in SIAM SIM
Functional, randomized and smoothed multivariate quantile regions
A notion of multivariate depth, resp. quantile region, was introduced in [Chernozhukov et al., 2017], based on a mass transportation approach. In [Faugeras and Ruschendorf, 2017], this approach was generalized by dening quantiles as Markov morphisms carrying suitable algebraic, ordering and topological structures over probability measures. In addition, a copula step was added to the mass transportation step. Empirical versions of these depth areas do not give exact level depth regions. In this paper, we introduce randomized depth regions by means of a formulation by depth functions, resp. by randomized quantiles sets. These versions attain the exact level and also provide the corresponding consistency property. We also investigate in the case of continuous marginals a smoothed version of the empirical copula and compare its behavior with the unsmoothed version. Extensive simulations illustrate the resulting randomized depth areas and show that they give a valid representation of the central depth areas of a multivariate distribution, and thus are a valuable tool for their analysis
Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem
We present an adaptation of the MA-LBR scheme to the Monge-Amp{\`e}re
equation with second boundary value condition, provided the target is a convex
set. This yields a fast adaptive method to numerically solve the Optimal
Transport problem between two absolutely continuous measures, the second of
which has convex support. The proposed numerical method actually captures a
specific Brenier solution which is minimal in some sense. We prove the
convergence of the method as the grid stepsize vanishes and we show with
numerical experiments that it is able to reproduce subtle properties of the
Optimal Transport problem
Fully differential photo-electron spectra of hydrogen and helium atoms
The ability to probe and manipulate electron dynamics and correlations on their characteristic time scales would open up many technological
and scientific possibilities.
While modern laser technology already allows to
do that in principle, a lot of theoretical ground work is still missing.
This thesis focuses on the elementary effect of laser strong field ionization of the two
simplest systems: The Hydrogen and Helium atoms.
To that end, the time-dependent Schroedinger equation is solved numerically, and photo-electron spectra are extracted
using the highly efficient tSurff technique.
We implemented both the one and two particle versions of tSurff together with several other numerical techniques in a new
parallelizable C++ code. We provide details
on the employed methods and algorithms,
and study numerical efficiency properties of
various approaches.
We propose a description of the electric field interaction
in a mixture of length and velocity gauge
for the correct and most efficient
implementation of a coupled channels approach,
which can be used
to compute accurate single ionization photo-electron spectra
from true multi-electron systems,
even molecules.
We provide extensive numerical data for a detailed study
of the Hydrogen atom in an Attoclock experimental setup,
where it is found that
the involved strong field tunnel ionization processes
can be considered instantaneous.
In particular, there appear no tunneling delays, which
can be used as a calibration for experiments with
more complicated targets.
Similarly, it is investigated whether discrepancies
between theory and experimental
data for the longitudinal photo-electron momentum spread, resulting
from photo-ionization of Helium in
elliptically polarized laser pulses,
can be explained by non-adiabatic effects,
and a related consistency problem
in current laser intensity calibration
methods is pointed out.
We further show that Fano resonance line shapes
of doubly excited states in the Helium atom,
prominently appearing in single ionization spectra
generated by short wavelength laser pulses,
can be controlled by an external long wavelength streaking field.
The resulting line shapes are still characterized
by the general Fano situation, but with
a complex - rather than real - Fano parameter.
We provide a theoretical description of this two color process
and prove numerically that the entire doubly excited state series
exhibits synchronized
line shape modifications as the specifics of the
involved states are unimportant.
Finally, we compute fully differential double ionization spectra
and suggest a measure of correlation that is directly applicable
to experimental data.
We confirm literature results at short wavelengths,
and achieve to compute five-fold differential
double ionization photo-electron
spectra at infrared wavelengths from the Helium atom,
thereby reproducing a characteristic
several orders of magnitude
enhancement of double emission due to
correlation effects
High performance graph analysis on parallel architectures
PhD ThesisOver the last decade pharmacology has been developing computational
methods to enhance drug development and testing. A computational
method called network pharmacology uses graph analysis
tools to determine protein target sets that can lead on better targeted
drugs for diseases as Cancer. One promising area of network-based
pharmacology is the detection of protein groups that can produce
better e ects if they are targeted together by drugs. However, the
e cient prediction of such protein combinations is still a bottleneck
in the area of computational biology.
The computational burden of the algorithms used by such protein
prediction strategies to characterise the importance of such proteins
consists an additional challenge for the eld of network pharmacology.
Such computationally expensive graph algorithms as the all pairs
shortest path (APSP) computation can a ect the overall drug discovery
process as needed network analysis results cannot be given on
time. An ideal solution for these highly intensive computations could
be the use of super-computing. However, graph algorithms have datadriven
computation dictated by the structure of the graph and this
can lead to low compute capacity utilisation with execution times
dominated by memory latency.
Therefore, this thesis seeks optimised solutions for the real-world
graph problems of critical node detection and e ectiveness characterisation
emerged from the collaboration with a pioneer company in the
eld of network pharmacology as part of a Knowledge Transfer Partnership
(KTP) / Secondment (KTS). In particular, we examine how
genetic algorithms could bene t the prediction of protein complexes
where their removal could produce a more e ective 'druggable' impact.
Furthermore, we investigate how the problem of all pairs shortest
path (APSP) computation can be bene ted by the use of emerging
parallel hardware architectures as GPU- and FPGA- desktop-based
accelerators.
In particular, we address the problem of critical node detection with
the development of a heuristic search method. It is based on a genetic
algorithm that computes optimised node combinations where their removal
causes greater impact than common impact analysis strategies.
Furthermore, we design a general pattern for parallel network analysis
on multi-core architectures that considers graph's embedded properties.
It is a divide and conquer approach that decomposes a graph
into smaller subgraphs based on its strongly connected components
and computes the all pairs shortest paths concurrently on GPU. Furthermore,
we use linear algebra to design an APSP approach based
on the BFS algorithm. We use algebraic expressions to transform the
problem of path computation to multiple independent matrix-vector
multiplications that are executed concurrently on FPGA. Finally, we
analyse how the optimised solutions of perturbation analysis and parallel
graph processing provided in this thesis will impact the drug
discovery process.This research was part of a Knowledge Transfer Partnership (KTP)
and Knowledge Transfer Secondment (KTS) between e-therapeutics
PLC and Newcastle University. It was supported as a collaborative
project by e-therapeutics PLC and Technology Strategy boar
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