7,913 research outputs found
Fractional operators and special functions. II. Legendre functions
Most of the special functions of mathematical physics are connected with the
representation of Lie groups. The action of elements of the associated Lie
algebras as linear differential operators gives relations among the functions
in a class, for example, their differential recurrence relations. In this
paper, we apply the fractional generalizations of these operators
developed in an earlier paper in the context of Lie theory to the group SO(2,1)
and its conformal extension. The fractional relations give a variety of
interesting relations for the associated Legendre functions. We show that the
two-variable fractional operator relations lead directly to integral relations
among the Legendre functions and to one- and two-variable integral
representations for those functions. Some of the relations reduce to known
fractional integrals for the Legendre functions when reduced to one variable.
The results enlarge the understanding of many properties of the associated
Legendre functions on the basis of the underlying group structure.Comment: 26 pages, Latex2e, reference correcte
the role of shock waves in modulation of galactic cosmic rays
The understanding of modulation of the galactic cosmic rays has considerably progressed by the exploration by space probes of major heliospheric structures, such as the Corotating Interaction Regions, the neutral sheet, and the compression regions of intense heliospheric magnetic fields. Also relevant in this context were the detections in the outer heliosphere of long lasting Forbush type decreases of cosmic ray intensity. The results of recent theoretical studies on the changes in intensity and energy, at different location from the Sun, induced by the passage of shocks across the heliosphere are presented. In this version of the research, the simplest cases of modulation of uGV and 2GV particles by single or several shocks during periods of positive and negative solar field polarity are reviewed. The results of the theoretical aspects of the search is reported. The comparison of the theoretical predictions with space probe data allows conclusions to be drawn on the role of shocks on the modulation on both the 11 and 22 year galactic cosmic ray cycles in the outer heliosphere and on the plausibility of the models and parameters used
On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry
We construct a canonical irreducible representation for the orthofermion
algebra of arbitrary order, and show that every representation decomposes into
irreducible representations that are isomorphic to either the canonical
representation or the trivial representation. We use these results to show that
every orthosupersymmetric system of order has a parasupersymmetry of order
and a fractional supersymmetry of order .Comment: 13 pages, to appear in J. Phys. A: Math. Ge
Localizing the Latent Structure Canonical Uncertainty: Entropy Profiles for Hidden Markov Models
This report addresses state inference for hidden Markov models. These models
rely on unobserved states, which often have a meaningful interpretation. This
makes it necessary to develop diagnostic tools for quantification of state
uncertainty. The entropy of the state sequence that explains an observed
sequence for a given hidden Markov chain model can be considered as the
canonical measure of state sequence uncertainty. This canonical measure of
state sequence uncertainty is not reflected by the classic multivariate state
profiles computed by the smoothing algorithm, which summarizes the possible
state sequences. Here, we introduce a new type of profiles which have the
following properties: (i) these profiles of conditional entropies are a
decomposition of the canonical measure of state sequence uncertainty along the
sequence and makes it possible to localize this uncertainty, (ii) these
profiles are univariate and thus remain easily interpretable on tree
structures. We show how to extend the smoothing algorithms for hidden Markov
chain and tree models to compute these entropy profiles efficiently.Comment: Submitted to Journal of Machine Learning Research; No RR-7896 (2012
Deep Bilateral Learning for Real-Time Image Enhancement
Performance is a critical challenge in mobile image processing. Given a
reference imaging pipeline, or even human-adjusted pairs of images, we seek to
reproduce the enhancements and enable real-time evaluation. For this, we
introduce a new neural network architecture inspired by bilateral grid
processing and local affine color transforms. Using pairs of input/output
images, we train a convolutional neural network to predict the coefficients of
a locally-affine model in bilateral space. Our architecture learns to make
local, global, and content-dependent decisions to approximate the desired image
transformation. At runtime, the neural network consumes a low-resolution
version of the input image, produces a set of affine transformations in
bilateral space, upsamples those transformations in an edge-preserving fashion
using a new slicing node, and then applies those upsampled transformations to
the full-resolution image. Our algorithm processes high-resolution images on a
smartphone in milliseconds, provides a real-time viewfinder at 1080p
resolution, and matches the quality of state-of-the-art approximation
techniques on a large class of image operators. Unlike previous work, our model
is trained off-line from data and therefore does not require access to the
original operator at runtime. This allows our model to learn complex,
scene-dependent transformations for which no reference implementation is
available, such as the photographic edits of a human retoucher.Comment: 12 pages, 14 figures, Siggraph 201
Unusual Closed Traumatic Avulsion of Both Flexor Tendons in Zones 1 and 3 of the Little Finger.
Closed tendon avulsion of both flexor tendons in the same finger is an extremely rare condition. We encountered the case of a patient who presented a rupture of the flexor digitorum profundus in zone 1 and flexor digitorum superficialis in zone 3 in the little finger. This occurrence has not been reported previously. We hereby present our case, make a review of the literature of avulsion of both flexor tendons of the same finger, and propose a treatment according to the site of the ruptures
The Scattering Approach to the Casimir Force
We present the scattering approach which is nowadays the best tool for
describing the Casimir force in realistic experimental configurations. After
reminders on the simple geometries of 1d space and specular scatterers in 3d
space, we discuss the case of stationary arbitrarily shaped mirrors in
electromagnetic vacuum. We then review specific calculations based on the
scattering approach, dealing for example with the forces or torques between
nanostructured surfaces and with the force between a plane and a sphere. In
these various cases, we account for the material dependence of the forces, and
show that the geometry dependence goes beyond the trivial {\it Proximity Force
Approximation} often used for discussing experiments.Comment: Proceedings of the QFEXT'09 conference (Oklahoma, 2009
Remote Sensing of River Discharge: A Review and a Framing for the Discipline
Remote sensing of river discharge (RSQ) is a burgeoning field rife with innovation. This innovation has resulted in a highly non-cohesive subfield of hydrology advancing at a rapid pace, and as a result misconceptions, mis-citations, and confusion are apparent among authors, readers, editors, and reviewers. While the intellectually diverse subfield of RSQ practitioners can parse this confusion, the broader hydrology community views RSQ as a monolith and such confusion can be damaging. RSQ has not been comprehensively summarized over the past decade, and we believe that a summary of the recent literature has a potential to provide clarity to practitioners and general hydrologists alike. Therefore, we here summarize a broad swath of the literature, and find after our reading that the most appropriate way to summarize this literature is first by application area (into methods appropriate for gauged, semi-gauged, regionally gauged, politically ungauged, and totally ungauged basins) and next by methodology. We do not find categorizing by sensor useful, and everything from un-crewed aerial vehicles (UAVs) to satellites are considered here. Perhaps the most cogent theme to emerge from our reading is the need for context. All RSQ is employed in the service of furthering hydrologic understanding, and we argue that nearly all RSQ is useful in this pursuit provided it is properly contextualized. We argue that if authors place each new work into the correct application context, much confusion can be avoided, and we suggest a framework for such context here. Specifically, we define which RSQ techniques are and are not appropriate for ungauged basins, and further define what it means to be ‘ungauged’ in the context of RSQ. We also include political and economic realities of RSQ, as the objective of the field is sometimes to provide data purposefully cloistered by specific political decisions. This framing can enable RSQ to respond to hydrology at large with confidence and cohesion even in the face of methodological and application diversity evident within the literature. Finally, we embrace the intellectual diversity of RSQ and suggest the field is best served by a continuation of methodological proliferation rather than by a move toward orthodoxy and standardization
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