324 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
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 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
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
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
Topological wave functions and heat equations
It is generally known that the holomorphic anomaly equations in topological
string theory reflect the quantum mechanical nature of the topological string
partition function. We present two new results which make this assertion more
precise: (i) we give a new, purely holomorphic version of the holomorphic
anomaly equations, clarifying their relation to the heat equation satisfied by
the Jacobi theta series; (ii) in cases where the moduli space is a Hermitian
symmetric tube domain , we show that the general solution of the anomaly
equations is a matrix element \IP{\Psi | g | \Omega} of the
Schr\"odinger-Weil representation of a Heisenberg extension of , between an
arbitrary state and a particular vacuum state .
Based on these results, we speculate on the existence of a one-parameter
generalization of the usual topological amplitude, which in symmetric cases
transforms in the smallest unitary representation of the duality group in
three dimensions, and on its relations to hypermultiplet couplings, nonabelian
Donaldson-Thomas theory and black hole degeneracies.Comment: 50 pages; v2: small typos fixed, references added; v3: cosmetic
changes, published version; v4: typos fixed, small clarification adde
Temporal Dissociation between Myeloperoxidase (MPO)-Modified LDL and MPO Elevations during Chronic Sleep Restriction and Recovery in Healthy Young Men
OBJECTIVES: Many studies have evaluated the ways in which sleep disturbances may influence inflammation and the possible links of this effect to cardiovascular risk. Our objective was to investigate the effects of chronic sleep restriction and recovery on several blood cardiovascular biomarkers. METHODS AND RESULTS: Nine healthy male non-smokers, aged 22-29 years, were admitted to the Sleep Laboratory for 11 days and nights under continuous electroencephalogram polysomnography. The study consisted of three baseline nights of 8 hours sleep (from 11 pm to 7 am), five sleep-restricted nights, during which sleep was allowed only between 1 am and 6 am, and three recovery nights of 8 hours sleep (11 pm to 7 am). Myeloperoxidase-modified low-density lipoprotein levels increased during the sleep-restricted period indicating an oxidative stress. A significant increase in the quantity of slow-wave sleep was measured during the first recovery night. After this first recovery night, insulin-like growth factor-1 levels increased and myeloperoxidase concentration peaked. CONCLUSIONS: We observed for the first time that sleep restriction and the recovery process are associated with differential changes in blood biomarkers of cardiovascular disease
Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
Higgs bundles and non-abelian Hodge theory provide holomorphic methods with
which to study the moduli spaces of surface group representations in a
reductive Lie group G. In this paper we survey the case in which G is the
isometry group of a classical Hermitian symmetric space of non-compact type.
Using Morse theory on the moduli spaces of Higgs bundles, we compute the number
of connected components of the moduli space of representations with maximal
Toledo invariant.Comment: v2: added due credits to the work of Burger, Iozzi and Wienhard. v3:
corrected count of connected components for G=SU(p,q) (p \neq q); added due
credits to the work of Xia and Markman-Xia; minor corrections and
clarifications. 31 page
Notes on Stein-Sahi representations and some problems of non harmonic analysis
We discuss one natural class of kernels on pseudo-Riemannian symmetric
spaces.Comment: 40p
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