211,305 research outputs found
Regular and Estimable Inverse Demand Systems: A Distance Function Approach
To be useful for realistic policy simulation in an environment of rapid structural change, inverse demand systems must remain regular over substantial variations in quantities. The distance function is a convenient vehicle for generating such systems. While it directly yields Hicksian inverse demand functions, those functions will not usually have an explicit representation in terms of the observable variables. Note however that this problem need not hinder estimation and could be solved by using the numerical inversion estimation approach. This paper develops the formal theory for using distance functions in this context, and demonstrates the operational feasibility of the method.Inverse Demands; Distance Functions; Numerical Inversion Estimation Method; Separability.
Group-theoretic models of the inversion process in bacterial genomes
The variation in genome arrangements among bacterial taxa is largely due to
the process of inversion. Recent studies indicate that not all inversions are
equally probable, suggesting, for instance, that shorter inversions are more
frequent than longer, and those that move the terminus of replication are less
probable than those that do not. Current methods for establishing the inversion
distance between two bacterial genomes are unable to incorporate such
information. In this paper we suggest a group-theoretic framework that in
principle can take these constraints into account. In particular, we show that
by lifting the problem from circular permutations to the affine symmetric
group, the inversion distance can be found in polynomial time for a model in
which inversions are restricted to acting on two regions. This requires the
proof of new results in group theory, and suggests a vein of new combinatorial
problems concerning permutation groups on which group theorists will be needed
to collaborate with biologists. We apply the new method to inferring distances
and phylogenies for published Yersinia pestis data.Comment: 19 pages, 7 figures, in Press, Journal of Mathematical Biolog
Using phonetic constraints in acoustic-to-articulatory inversion
The goal of this work is to recover articulatory information from the speech
signal by acoustic-to-articulatory inversion. One of the main difficulties with
inversion is that the problem is underdetermined and inversion methods
generally offer no guarantee on the phonetical realism of the inverse
solutions. A way to adress this issue is to use additional phonetic
constraints. Knowledge of the phonetic caracteristics of French vowels enable
the derivation of reasonable articulatory domains in the space of Maeda
parameters: given the formants frequencies (F1,F2,F3) of a speech sample, and
thus the vowel identity, an "ideal" articulatory domain can be derived. The
space of formants frequencies is partitioned into vowels, using either
speaker-specific data or generic information on formants. Then, to each
articulatory vector can be associated a phonetic score varying with the
distance to the "ideal domain" associated with the corresponding vowel.
Inversion experiments were conducted on isolated vowels and vowel-to-vowel
transitions. Articulatory parameters were compared with those obtained without
using these constraints and those measured from X-ray data
On the Inversion-Indel Distance
Willing E, Zaccaria S, Dias Vieira Braga M, Stoye J. On the Inversion-Indel Distance. BMC Bioinformatics. 2013;14(Suppl 15: Proc. of RECOMB-CG 2013): S3.Background
The inversion distance, that is the distance between two unichromosomal genomes with the same content allowing only inversions of DNA segments, can be computed thanks to a pioneering approach of Hannenhalli and Pevzner in 1995. In 2000, El-Mabrouk extended the inversion model to allow the comparison of unichromosomal genomes with unequal contents, thus insertions and deletions of DNA segments besides inversions. However, an exact algorithm was presented only for the case in which we have insertions alone and no deletion (or vice versa), while a heuristic was provided for the symmetric case, that allows both insertions and deletions and is called the inversion-indel distance. In 2005, Yancopoulos, Attie and Friedberg started a new branch of research by introducing the generic double cut and join (DCJ) operation, that can represent several genome rearrangements (including inversions). Among others, the DCJ model gave rise to two important results. First, it has been shown that the inversion distance can be computed in a simpler way with the help of the DCJ operation. Second, the DCJ operation originated the DCJ-indel distance, that allows the comparison of genomes with unequal contents, considering DCJ, insertions and deletions, and can be computed in linear time.
Results
In the present work we put these two results together to solve an open problem, showing that, when the graph that represents the relation between the two compared genomes has no bad components, the inversion-indel distance is equal to the DCJ-indel distance. We also give a lower and an upper bound for the inversion-indel distance in the presence of bad components
Bayes and maximum likelihood for -Wasserstein deconvolution of Laplace mixtures
We consider the problem of recovering a distribution function on the real
line from observations additively contaminated with errors following the
standard Laplace distribution. Assuming that the latent distribution is
completely unknown leads to a nonparametric deconvolution problem. We begin by
studying the rates of convergence relative to the -norm and the Hellinger
metric for the direct problem of estimating the sampling density, which is a
mixture of Laplace densities with a possibly unbounded set of locations: the
rate of convergence for the Bayes' density estimator corresponding to a
Dirichlet process prior over the space of all mixing distributions on the real
line matches, up to a logarithmic factor, with the rate
for the maximum likelihood estimator. Then, appealing to an inversion
inequality translating the -norm and the Hellinger distance between
general kernel mixtures, with a kernel density having polynomially decaying
Fourier transform, into any -Wasserstein distance, , between the
corresponding mixing distributions, provided their Laplace transforms are
finite in some neighborhood of zero, we derive the rates of convergence in the
-Wasserstein metric for the Bayes' and maximum likelihood estimators of
the mixing distribution. Merging in the -Wasserstein distance between
Bayes and maximum likelihood follows as a by-product, along with an assessment
on the stochastic order of the discrepancy between the two estimation
procedures
The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry
The closest tensors of higher symmetry classes are derived in explicit form
for a given elasticity tensor of arbitrary symmetry. The mathematical problem
is to minimize the elastic length or distance between the given tensor and the
closest elasticity tensor of the specified symmetry. Solutions are presented
for three distance functions, with particular attention to the Riemannian and
log-Euclidean distances. These yield solutions that are invariant under
inversion, i.e., the same whether elastic stiffness or compliance are
considered. The Frobenius distance function, which corresponds to common
notions of Euclidean length, is not invariant although it is simple to apply
using projection operators. A complete description of the Euclidean projection
method is presented. The three metrics are considered at a level of detail far
greater than heretofore, as we develop the general framework to best fit a
given set of moduli onto higher elastic symmetries. The procedures for finding
the closest elasticity tensor are illustrated by application to a set of 21
moduli with no underlying symmetry.Comment: 48 pages, 1 figur
Velocity estimation via registration-guided least-squares inversion
This paper introduces an iterative scheme for acoustic model inversion where
the notion of proximity of two traces is not the usual least-squares distance,
but instead involves registration as in image processing. Observed data are
matched to predicted waveforms via piecewise-polynomial warpings, obtained by
solving a nonconvex optimization problem in a multiscale fashion from low to
high frequencies. This multiscale process requires defining low-frequency
augmented signals in order to seed the frequency sweep at zero frequency.
Custom adjoint sources are then defined from the warped waveforms. The proposed
velocity updates are obtained as the migration of these adjoint sources, and
cannot be interpreted as the negative gradient of any given objective function.
The new method, referred to as RGLS, is successfully applied to a few scenarios
of model velocity estimation in the transmission setting. We show that the new
method can converge to the correct model in situations where conventional
least-squares inversion suffers from cycle-skipping and converges to a spurious
model.Comment: 20 pages, 13 figures, 1 tabl
- …