26,339 research outputs found
-minimization method for link flow correction
A computational method, based on -minimization, is proposed for the
problem of link flow correction, when the available traffic flow data on many
links in a road network are inconsistent with respect to the flow conservation
law. Without extra information, the problem is generally ill-posed when a large
portion of the link sensors are unhealthy. It is possible, however, to correct
the corrupted link flows \textit{accurately} with the proposed method under a
recoverability condition if there are only a few bad sensors which are located
at certain links. We analytically identify the links that are robust to
miscounts and relate them to the geometric structure of the traffic network by
introducing the recoverability concept and an algorithm for computing it. The
recoverability condition for corrupted links is simply the associated
recoverability being greater than 1. In a more realistic setting, besides the
unhealthy link sensors, small measurement noises may be present at the other
sensors. Under the same recoverability condition, our method guarantees to give
an estimated traffic flow fairly close to the ground-truth data and leads to a
bound for the correction error. Both synthetic and real-world examples are
provided to demonstrate the effectiveness of the proposed method
A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems
In this paper, we propose a method for the approximation of the solution of
high-dimensional weakly coercive problems formulated in tensor spaces using
low-rank approximation formats. The method can be seen as a perturbation of a
minimal residual method with residual norm corresponding to the error in a
specified solution norm. We introduce and analyze an iterative algorithm that
is able to provide a controlled approximation of the optimal approximation of
the solution in a given low-rank subset, without any a priori information on
this solution. We also introduce a weak greedy algorithm which uses this
perturbed minimal residual method for the computation of successive greedy
corrections in small tensor subsets. We prove its convergence under some
conditions on the parameters of the algorithm. The residual norm can be
designed such that the resulting low-rank approximations are quasi-optimal with
respect to particular norms of interest, thus yielding to goal-oriented order
reduction strategies for the approximation of high-dimensional problems. The
proposed numerical method is applied to the solution of a stochastic partial
differential equation which is discretized using standard Galerkin methods in
tensor product spaces
Waveform Relaxation for the Computational Homogenization of Multiscale Magnetoquasistatic Problems
This paper proposes the application of the waveform relaxation method to the
homogenization of multiscale magnetoquasistatic problems. In the monolithic
heterogeneous multiscale method, the nonlinear macroscale problem is solved
using the Newton--Raphson scheme. The resolution of many mesoscale problems per
Gauss point allows to compute the homogenized constitutive law and its
derivative by finite differences. In the proposed approach, the macroscale
problem and the mesoscale problems are weakly coupled and solved separately
using the finite element method on time intervals for several waveform
relaxation iterations. The exchange of information between both problems is
still carried out using the heterogeneous multiscale method. However, the
partial derivatives can now be evaluated exactly by solving only one mesoscale
problem per Gauss point.Comment: submitted to JC
Some Applications of Coding Theory in Computational Complexity
Error-correcting codes and related combinatorial constructs play an important
role in several recent (and old) results in computational complexity theory. In
this paper we survey results on locally-testable and locally-decodable
error-correcting codes, and their applications to complexity theory and to
cryptography.
Locally decodable codes are error-correcting codes with sub-linear time
error-correcting algorithms. They are related to private information retrieval
(a type of cryptographic protocol), and they are used in average-case
complexity and to construct ``hard-core predicates'' for one-way permutations.
Locally testable codes are error-correcting codes with sub-linear time
error-detection algorithms, and they are the combinatorial core of
probabilistically checkable proofs
Quantum Error Correction beyond the Bounded Distance Decoding Limit
In this paper, we consider quantum error correction over depolarizing
channels with non-binary low-density parity-check codes defined over Galois
field of size . The proposed quantum error correcting codes are based on
the binary quasi-cyclic CSS (Calderbank, Shor and Steane) codes. The resulting
quantum codes outperform the best known quantum codes and surpass the
performance limit of the bounded distance decoder. By increasing the size of
the underlying Galois field, i.e., , the error floors are considerably
improved.Comment: To appear in IEEE Transactions on Information Theor
Efficient Quantum Transforms
Quantum mechanics requires the operation of quantum computers to be unitary,
and thus makes it important to have general techniques for developing fast
quantum algorithms for computing unitary transforms. A quantum routine for
computing a generalized Kronecker product is given. Applications include
re-development of the networks for computing the Walsh-Hadamard and the quantum
Fourier transform. New networks for two wavelet transforms are given. Quantum
computation of Fourier transforms for non-Abelian groups is defined. A slightly
relaxed definition is shown to simplify the analysis and the networks that
computes the transforms. Efficient networks for computing such transforms for a
class of metacyclic groups are introduced. A novel network for computing a
Fourier transform for a group used in quantum error-correction is also given.Comment: 30 pages, LaTeX2e, 7 figures include
Error Correction for Index Coding With Coded Side Information
Index coding is a source coding problem in which a broadcaster seeks to meet
the different demands of several users, each of whom is assumed to have some
prior information on the data held by the sender. If the sender knows its
clients' requests and their side-information sets, then the number of packet
transmissions required to satisfy all users' demands can be greatly reduced if
the data is encoded before sending. The collection of side-information indices
as well as the indices of the requested data is described as an instance of the
index coding with side-information (ICSI) problem. The encoding function is
called the index code of the instance, and the number of transmissions employed
by the code is referred to as its length. The main ICSI problem is to determine
the optimal length of an index code for and instance. As this number is hard to
compute, bounds approximating it are sought, as are algorithms to compute
efficient index codes. Two interesting generalizations of the problem that have
appeared in the literature are the subject of this work. The first of these is
the case of index coding with coded side information, in which linear
combinations of the source data are both requested by and held as users'
side-information. The second is the introduction of error-correction in the
problem, in which the broadcast channel is subject to noise.
In this paper we characterize the optimal length of a scalar or vector linear
index code with coded side information (ICCSI) over a finite field in terms of
a generalized min-rank and give bounds on this number based on constructions of
random codes for an arbitrary instance. We furthermore consider the length of
an optimal error correcting code for an instance of the ICCSI problem and
obtain bounds on this number, both for the Hamming metric and for rank-metric
errors. We describe decoding algorithms for both categories of errors
Exploring single-sample SNP and INDEL calling with whole-genome de novo assembly
Motivation: Eugene Myers in his string graph paper (Myers, 2005) suggested
that in a string graph or equivalently a unitig graph, any path spells a valid
assembly. As a string/unitig graph also encodes every valid assembly of reads,
such a graph, provided that it can be constructed correctly, is in fact a
lossless representation of reads. In principle, every analysis based on
whole-genome shotgun sequencing (WGS) data, such as SNP and insertion/deletion
(INDEL) calling, can also be achieved with unitigs.
Results: To explore the feasibility of using de novo assembly in the context
of resequencing, we developed a de novo assembler, fermi, that assembles
Illumina short reads into unitigs while preserving most of information of the
input reads. SNPs and INDELs can be called by mapping the unitigs against a
reference genome. By applying the method on 35-fold human resequencing data, we
showed that in comparison to the standard pipeline, our approach yields similar
accuracy for SNP calling and better results for INDEL calling. It has higher
sensitivity than other de novo assembly based methods for variant calling. Our
work suggests that variant calling with de novo assembly be a beneficial
complement to the standard variant calling pipeline for whole-genome
resequencing. In the methodological aspects, we proposed FMD-index for
forward-backward extension of DNA sequences, a fast algorithm for finding all
super-maximal exact matches and one-pass construction of unitigs from an
FMD-index.
Availability: http://github.com/lh3/fermi
Contact: [email protected]: Rev2: submitted version with minor improvements; 7 page
A multilevel algorithm for flow observables in gauge theories
We study the possibility of using multilevel algorithms for the computation
of correlation functions of gradient flow observables. For each point in the
correlation function an approximate flow is defined which depends only on links
in a subset of the lattice. Together with a local action this allows for
independent updates and consequently a convergence of the Monte Carlo process
faster than the inverse square root of the number of measurements. We
demonstrate the feasibility of this idea in the correlation functions of the
topological charge and the energy density.Comment: Minor modifications to the text. Version accepted to be published in
PRD. 18 pages, 5 figure
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