242,078 research outputs found
Regularity of conjugacies of linearizable generalized interval exchange transformations
We consider generalized interval exchange transformations (GIETs) of d
intervals () which are linearizable, i.e. differentiably conjugated to
standard interval exchange maps (IETs) via a diffeomorphism h of [0, 1] and
study the regularity of the conjugacy h. Using a renormalisation operator
obtained accelerating Rauzy-Veech induction, we show that, under a full measure
condition on the IET obtained by linearization, if the orbit of the GIET under
renormalisation converges exponentially fast in a distance to the
subspace of IETs, there exists an exponent such that h is
. Combined with the results proved by the authors in [4], this
implies in particular the following improvement of the rigidity result in genus
two proved in previous work by the same authors (from to
rigidity): for almost every irreducible IET with d = 4 or d = 5, for any
GIET which is topologically conjugate to via a homeomorphism h and has
vanishing boundary, the topological conjugacy h is actually a
diffeomorphism, i.e. a diffeomorphism h with derivative Dh which is
-H\"older continuous.Comment: 28 pages, 4 figure
De Novo Assembly of Nucleotide Sequences in a Compressed Feature Space
Sequencing technologies allow for an in-depth analysis
of biological species but the size of the generated datasets
introduce a number of analytical challenges. Recently, we
demonstrated the application of numerical sequence representations
and data transformations for the alignment of short
reads to a reference genome. Here, we expand out approach
for de novo assembly of short reads. Our results demonstrate
that highly compressed data can encapsulate the signal suffi-
ciently to accurately assemble reads to big contigs or complete
genomes
Manitest: Are classifiers really invariant?
Invariance to geometric transformations is a highly desirable property of
automatic classifiers in many image recognition tasks. Nevertheless, it is
unclear to which extent state-of-the-art classifiers are invariant to basic
transformations such as rotations and translations. This is mainly due to the
lack of general methods that properly measure such an invariance. In this
paper, we propose a rigorous and systematic approach for quantifying the
invariance to geometric transformations of any classifier. Our key idea is to
cast the problem of assessing a classifier's invariance as the computation of
geodesics along the manifold of transformed images. We propose the Manitest
method, built on the efficient Fast Marching algorithm to compute the
invariance of classifiers. Our new method quantifies in particular the
importance of data augmentation for learning invariance from data, and the
increased invariance of convolutional neural networks with depth. We foresee
that the proposed generic tool for measuring invariance to a large class of
geometric transformations and arbitrary classifiers will have many applications
for evaluating and comparing classifiers based on their invariance, and help
improving the invariance of existing classifiers.Comment: BMVC 201
Affine Subspace Representation for Feature Description
This paper proposes a novel Affine Subspace Representation (ASR) descriptor
to deal with affine distortions induced by viewpoint changes. Unlike the
traditional local descriptors such as SIFT, ASR inherently encodes local
information of multi-view patches, making it robust to affine distortions while
maintaining a high discriminative ability. To this end, PCA is used to
represent affine-warped patches as PCA-patch vectors for its compactness and
efficiency. Then according to the subspace assumption, which implies that the
PCA-patch vectors of various affine-warped patches of the same keypoint can be
represented by a low-dimensional linear subspace, the ASR descriptor is
obtained by using a simple subspace-to-point mapping. Such a linear subspace
representation could accurately capture the underlying information of a
keypoint (local structure) under multiple views without sacrificing its
distinctiveness. To accelerate the computation of ASR descriptor, a fast
approximate algorithm is proposed by moving the most computational part (ie,
warp patch under various affine transformations) to an offline training stage.
Experimental results show that ASR is not only better than the state-of-the-art
descriptors under various image transformations, but also performs well without
a dedicated affine invariant detector when dealing with viewpoint changes.Comment: To Appear in the 2014 European Conference on Computer Visio
Benchmarking integrated photonic architectures
Photonic platforms represent a promising technology for the realization of
several quantum communication protocols and for experiments of quantum
simulation. Moreover, large-scale integrated interferometers have recently
gained a relevant role for restricted models of quantum computing, specifically
with Boson Sampling devices. Indeed, various linear optical schemes have been
proposed for the implementation of unitary transformations, each one suitable
for a specific task. Notwithstanding, so far a comprehensive analysis of the
state of the art under broader and realistic conditions is still lacking. In
the present work we address this gap, providing in a unified framework a
quantitative comparison of the three main photonic architectures, namely the
ones with triangular and square designs and the so-called fast transformations.
All layouts have been analyzed in presence of losses and imperfect control over
the reflectivities and phases of the inner structure. Our results represent a
further step ahead towards the implementation of quantum information protocols
on large-scale integrated photonic devices.Comment: 10 pages, 6 figures + 2 pages Supplementary Informatio
Fast Color Space Transformations Using Minimax Approximations
Color space transformations are frequently used in image processing,
graphics, and visualization applications. In many cases, these transformations
are complex nonlinear functions, which prohibits their use in time-critical
applications. In this paper, we present a new approach called Minimax
Approximations for Color-space Transformations (MACT).We demonstrate MACT on
three commonly used color space transformations. Extensive experiments on a
large and diverse image set and comparisons with well-known multidimensional
lookup table interpolation methods show that MACT achieves an excellent balance
among four criteria: ease of implementation, memory usage, accuracy, and
computational speed
Minimizing Communication for Eigenproblems and the Singular Value Decomposition
Algorithms have two costs: arithmetic and communication. The latter
represents the cost of moving data, either between levels of a memory
hierarchy, or between processors over a network. Communication often dominates
arithmetic and represents a rapidly increasing proportion of the total cost, so
we seek algorithms that minimize communication. In \cite{BDHS10} lower bounds
were presented on the amount of communication required for essentially all
-like algorithms for linear algebra, including eigenvalue problems and
the SVD. Conventional algorithms, including those currently implemented in
(Sca)LAPACK, perform asymptotically more communication than these lower bounds
require. In this paper we present parallel and sequential eigenvalue algorithms
(for pencils, nonsymmetric matrices, and symmetric matrices) and SVD algorithms
that do attain these lower bounds, and analyze their convergence and
communication costs.Comment: 43 pages, 11 figure
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