375 research outputs found
Berezin Kernels and Analysis on Makarevich Spaces
Following ideas of van Dijk and Hille we study the link which exists between
maximal degenerate representations and Berezin kernels. We consider the
conformal group of a simple real Jordan algebra . The
maximal degenerate representations () we shall study
are induced by a character of a maximal parabolic subgroup of . These representations can be realized on a space of
smooth functions on . There is an invariant bilinear form
on the space . The problem we consider is to diagonalize this bilinear
form , with respect to the action of a symmetric subgroup
of the conformal group . This bilinear form can be written as an
integral involving the Berezin kernel , an invariant kernel on the
Riemannian symmetric space , which is a Makarevich symmetric space in the
sense of Bertram. Then we can use results by van Dijk and Pevzner who computed
the spherical Fourier transform of . From these, one deduces that the
Berezin kernel satisfies a remarkable Bernstein identity : where is an invariant differential operator on
and is a polynomial. By using this identity we compute a Hua
type integral which gives the normalizing factor for an intertwining operator
from to . Furthermore we obtain the diagonalization of the
invariant bilinear form with respect to the action of the maximal compact group
of the conformal group
Weighted Bergman kernels and virtual Bergman kernels
We introduce the notion of "virtual Bergman kernel" and apply it to the
computation of the Bergman kernel of "domains inflated by Hermitian balls", in
particular when the base domain is a bounded symmetric domain.Comment: 12 pages. One-hour lecture for graduate students, SCV 2004, August
2004, Beijing, P.R. China. V2: typo correcte
The volume of Gaussian states by information geometry
We formulate the problem of determining the volume of the set of Gaussian
physical states in the framework of information geometry. That is, by
considering phase space probability distributions parametrized by the
covariances and supplying this resulting statistical manifold with the
Fisher-Rao metric. We then evaluate the volume of classical, quantum and
quantum entangled states for two-mode systems showing chains of strict
inclusion
Isometry theorem for the Segal-Bargmann transform on noncompact symmetric spaces of the complex type
We consider the Segal-Bargmann transform for a noncompact symmetric space of
the complex type. We establish isometry and surjectivity theorems for the
transform, in a form as parallel as possible to the results in the compact
case. The isometry theorem involves integration over a tube of radius R in the
complexification, followed by analytic continuation with respect to R. A
cancellation of singularities allows the relevant integral to have a
nonsingular extension to large R, even though the function being integrated has
singularities.Comment: Final version. To appear in Journal of Functional Analysis. Minor
revision
Balanced metrics on Cartan and Cartan-Hartogs domains
This paper consists of two results dealing with balanced metrics (in S.
Donaldson terminology) on nonconpact complex manifolds. In the first one we
describe all balanced metrics on Cartan domains. In the second one we show that
the only Cartan-Hartogs domain which admits a balanced metric is the complex
hyperbolic space. By combining these results with those obtained in [13]
(Kaehler-Einstein submanifolds of the infinite dimensional projective space, to
appear in Mathematische Annalen) we also provide the first example of complete,
Kaehler-Einstein and projectively induced metric g such that is not
balanced for all .Comment: 11 page
A second order cone formulation of continuous CTA model
The final publication is available at link.springer.comIn this paper we consider a minimum distance Controlled Tabular Adjustment (CTA) model for statistical disclosure limitation (control) of tabular data. The goal of the CTA model is to find the closest safe table to some original tabular data set that contains sensitive information. The measure of closeness is usually measured using l1 or l2 norm; with each measure having its advantages and disadvantages. Recently, in [4] a regularization of the l1 -CTA using Pseudo-Huber func- tion was introduced in an attempt to combine positive characteristics of both l1 -CTA and l2 -CTA. All three models can be solved using appro- priate versions of Interior-Point Methods (IPM). It is known that IPM in general works better on well structured problems such as conic op- timization problems, thus, reformulation of these CTA models as conic optimization problem may be advantageous. We present reformulation of Pseudo-Huber-CTA, and l1 -CTA as Second-Order Cone (SOC) op- timization problems and test the validity of the approach on the small example of two-dimensional tabular data set.Peer ReviewedPostprint (author's final draft
A hidden symmetry of a branching law
We consider branching laws for the restriction of some irreducible unitary
representations of to its subgroup . In Kobayashi
(arXiv:1907.07994), the irreducible subrepresentations of in the
restriction of the unitary are determined. By considering
the restriction of packets of irreducible representations we obtain another
very simple branching law, which was conjectured in Orsted-Speh
(arXiv:1907.07544).Comment: 16 page
Frequency of Drug Resistance Gene Amplification in Clinical Leishmania Strains
Experimental studies about Leishmania resistance to metal and antifolates have pointed out that gene amplification is one of the main mechanisms of drug detoxification. Amplified genes code for adenosine triphosphate-dependent transporters (multidrug resistance and P-glycoproteins P), enzymes involved in trypanothione pathway, particularly gamma glutamyl cysteine synthase, and others involved in folates metabolism, such as dihydrofolate reductase and pterine reductase. The aim of this study was to detect and quantify the amplification of these genes in clinical strains of visceral leishmaniasis agents: Leishmania infantum, L. donovani, and L. archibaldi. Relative quantification experiments by means of real-time polymerase chain reaction showed that multidrug resistance gene amplification is the more frequent event. For P-glycoproteins P and dihydrofolate reductase genes, level of amplification was comparable to the level observed after in vitro selection of resistant clones. Gene amplification is therefore a common phenomenon in wild strains concurring to Leishmania genomic plasticity. This finding, which corroborates results of experimental studies, supports a better understanding of metal resistance selection and spreading in endemic areas
A NWB-based dataset and processing pipeline of human single-neuron activity during a declarative memory task
A challenge for data sharing in systems neuroscience is the multitude of different data formats used. Neurodata Without Borders: Neurophysiology 2.0 (NWB:N) has emerged as a standardized data format for the storage of cellular-level data together with meta-data, stimulus information, and behavior. A key next step to facilitate NWB:N adoption is to provide easy to use processing pipelines to import/export data from/to NWB:N. Here, we present a NWB-formatted dataset of 1863 single neurons recorded from the medial temporal lobes of 59 human subjects undergoing intracranial monitoring while they performed a recognition memory task. We provide code to analyze and export/import stimuli, behavior, and electrophysiological recordings to/from NWB in both MATLAB and Python. The data files are NWB:N compliant, which affords interoperability between programming languages and operating systems. This combined data and code release is a case study for how to utilize NWB:N for human single-neuron recordings and enables easy re-use of this hard-to-obtain data for both teaching and research on the mechanisms of human memory
Metric trees of generalized roundness one
Every finite metric tree has generalized roundness strictly greater than one.
On the other hand, some countable metric trees have generalized roundness
precisely one. The purpose of this paper is to identify some large classes of
countable metric trees that have generalized roundness precisely one.
At the outset we consider spherically symmetric trees endowed with the usual
combinatorial metric (SSTs). Using a simple geometric argument we show how to
determine decent upper bounds on the generalized roundness of finite SSTs that
depend only on the downward degree sequence of the tree in question. By
considering limits it follows that if the downward degree sequence of a SST satisfies , then has generalized roundness one. Included among the
trees that satisfy this condition are all complete -ary trees of depth
(), all -regular trees () and inductive limits
of Cantor trees.
The remainder of the paper deals with two classes of countable metric trees
of generalized roundness one whose members are not, in general, spherically
symmetric. The first such class of trees are merely required to spread out at a
sufficient rate (with a restriction on the number of leaves) and the second
such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table
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