3,724 research outputs found
Times series averaging from a probabilistic interpretation of time-elastic kernel
At the light of regularized dynamic time warping kernels, this paper
reconsider the concept of time elastic centroid (TEC) for a set of time series.
From this perspective, we show first how TEC can easily be addressed as a
preimage problem. Unfortunately this preimage problem is ill-posed, may suffer
from over-fitting especially for long time series and getting a sub-optimal
solution involves heavy computational costs. We then derive two new algorithms
based on a probabilistic interpretation of kernel alignment matrices that
expresses in terms of probabilistic distributions over sets of alignment paths.
The first algorithm is an iterative agglomerative heuristics inspired from the
state of the art DTW barycenter averaging (DBA) algorithm proposed specifically
for the Dynamic Time Warping measure. The second proposed algorithm achieves a
classical averaging of the aligned samples but also implements an averaging of
the time of occurrences of the aligned samples. It exploits a straightforward
progressive agglomerative heuristics. An experimentation that compares for 45
time series datasets classification error rates obtained by first near
neighbors classifiers exploiting a single medoid or centroid estimate to
represent each categories show that: i) centroids based approaches
significantly outperform medoids based approaches, ii) on the considered
experience, the two proposed algorithms outperform the state of the art DBA
algorithm, and iii) the second proposed algorithm that implements an averaging
jointly in the sample space and along the time axes emerges as the most
significantly robust time elastic averaging heuristic with an interesting noise
reduction capability. Index Terms-Time series averaging Time elastic kernel
Dynamic Time Warping Time series clustering and classification
Regularized brain reading with shrinkage and smoothing
Functional neuroimaging measures how the brain responds to complex stimuli.
However, sample sizes are modest, noise is substantial, and stimuli are high
dimensional. Hence, direct estimates are inherently imprecise and call for
regularization. We compare a suite of approaches which regularize via
shrinkage: ridge regression, the elastic net (a generalization of ridge
regression and the lasso), and a hierarchical Bayesian model based on small
area estimation (SAE). We contrast regularization with spatial smoothing and
combinations of smoothing and shrinkage. All methods are tested on functional
magnetic resonance imaging (fMRI) data from multiple subjects participating in
two different experiments related to reading, for both predicting neural
response to stimuli and decoding stimuli from responses. Interestingly, when
the regularization parameters are chosen by cross-validation independently for
every voxel, low/high regularization is chosen in voxels where the
classification accuracy is high/low, indicating that the regularization
intensity is a good tool for identification of relevant voxels for the
cognitive task. Surprisingly, all the regularization methods work about equally
well, suggesting that beating basic smoothing and shrinkage will take not only
clever methods, but also careful modeling.Comment: Published at http://dx.doi.org/10.1214/15-AOAS837 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Jet Structure in Heavy Ion Collisions
We review recent theoretical developments in the study of the structure of
jets that are produced in ultra relativistic heavy ion collisions. The core of
the review focusses on the dynamics of the parton cascade that is induced by
the interactions of a fast parton crossing a quark-gluon plasma. We recall the
basic mechanisms responsible for medium induced radiation, underline the rapid
disappearance of coherence effects, and the ensuing probabilistic nature of the
medium induced cascade. We discuss how large radiative corrections modify the
classical picture of the gluon cascade, and how these can be absorbed in a
renormalization of the jet quenching parameter . Then, we analyze the
(wave)-turbulent transport of energy along the medium induced cascade, and
point out the main characteristics of the angular structure of such a cascade.
Finally, color decoherence of the in-cone jet structure is discussed. Modest
contact with phenomenology is presented towards the end of the review.Comment: Review to appear in QGP 5, 55 pages, 15 figure
A -uniform quantitative Tanaka's theorem for the conservative Kac's -particle system with Maxwell molecules
This paper considers the space homogenous Boltzmann equation with Maxwell
molecules and arbitrary angular distribution. Following Kac's program, emphasis
is laid on the the associated conservative Kac's stochastic -particle
system, a Markov process with binary collisions conserving energy and total
momentum. An explicit Markov coupling (a probabilistic, Markovian coupling of
two copies of the process) is constructed, using simultaneous collisions, and
parallel coupling of each binary random collision on the sphere of collisional
directions. The euclidean distance between the two coupled systems is almost
surely decreasing with respect to time, and the associated quadratic coupling
creation (the time variation of the averaged squared coupling distance) is
computed explicitly. Then, a family (indexed by ) of -uniform
''weak'' coupling / coupling creation inequalities are proven, that leads to a
-uniform power law trend to equilibrium of order , with constants depending on moments of the velocity
distributions strictly greater than . The case of order
moment is treated explicitly, achieving Kac's program without any chaos
propagation analysis. Finally, two counter-examples are suggested indicating
that the method: (i) requires the dependance on -moments, and (ii) cannot
provide contractivity in quadratic Wasserstein distance in any case.Comment: arXiv admin note: text overlap with arXiv:1312.225
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Entrainment, motion and deposition of coarse particles transported by water over a sloping mobile bed
In gravel-bed rivers, bedload transport exhibits considerable variability in
time and space. Recently, stochastic bedload transport theories have been
developed to address the mechanisms and effects of bedload transport
fluctuations. Stochastic models involve parameters such as particle
diffusivity, entrainment and deposition rates. The lack of hard information on
how these parameters vary with flow conditions is a clear impediment to their
application to real-world scenarios. In this paper, we determined the closure
equations for the above parameters from laboratory experiments. We focused on
shallow supercritical flow on a sloping mobile bed in straight channels, a
setting that was representative of flow conditions in mountain rivers.
Experiments were run at low sediment transport rates under steady nonuniform
flow conditions (i.e., the water discharge was kept constant, but bedforms
developed and migrated upstream, making flow nonuniform). Using image
processing, we reconstructed particle paths to deduce the particle velocity and
its probability distribution, particle diffusivity, and rates of deposition and
entrainment. We found that on average, particle acceleration, velocity and
deposition rate were responsive to local flow conditions, whereas entrainment
rate depended strongly on local bed activity. Particle diffusivity varied
linearly with the depth-averaged flow velocity. The empirical probability
distribution of particle velocity was well approximated by a Gaussian
distribution when all particle positions were considered together. In contrast,
the particles located in close vicinity to the bed had exponentially
distributed velocities. Our experimental results provide closure equations for
stochastic or deterministic bedload transport models.Comment: Submitted to Journal of Geophysical Researc
A Few Applications of Seismic Waves: Anisotropy Tomography and All That
Seismic anisotropy, the variation of seismic wave speed with direction, is an extremely important physical phenomena. When a certain type of seismic wave (shear wave) propagates in an anisotropic medium, the component polarized parallel to the fast direction (along which the speed is higher) begins to lead and the component polarized to the slow direction lags behind (analogous to the optical birefringence). This observation of seismic anisotropy may be used to infer several physical properties of the medium through which these waves are propagating. Fortunately, Earth\u27s upper mantle shows significant seismic anisotropy due to preferred crystallographic orientation of the constituent minerals. Therefore, it can provide crucial information regarding the convective flow and stress patterns in the upper mantle. To be more precise, seismic anisotropy can shed light on detail inner working of several geodynamic processes which are inherently anisotropic in nature and therefore insensitive to isotropic seismology. \\Owing to its simplicity, the classical ray theory based formulation is widely used to infer anisotropic structures of the upper mantle. However, due to the lack of vertical resolution of infinite frequency ray theory based methods and its numerous other shortcomings even in the simplified studies assuming isotropy, it is undesirable to use a ray theory based method in a fully anisotropic framework. The major portion of this thesis is devoted to developing anisotropy tomography method in a perturbative framework where the `finite-frequency\u27 or the full `wave\u27 feature is taken into account. Such technique is proven to be a substantial improvement in terms of localization of the anisotropy of upper mantle. After benchmarking, it is applied to infer the anisotropic structures beneath the High Lava Plains of Oregon and as such was able to provide an avenue for reconciling apparently contradictory constraints on anisotropic structures from different measurements. \\ In the last part of the thesis, we briefly discuss a technique (slightly tangential to the main theme of anisotropy however seems to enjoy a connection at a more fundamental level) we develop to obtain an effective description of the physical properties of a general heterogeneous medium (including pure randomness). This is motivated by the fact that when propagating through small heterogeneities, seismic waves naturally average the elastic properties of the medium and therefore only an effective physics is realized
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