A Method for Weight Multiplicity Computation Based on Berezin Quantization

Let G be a compact semisimple Lie group and T be a maximal torus of G. We describe a method for weight multiplicity computation in unitary irreducible representations of G, based on the theory of Berezin quantization on G/T. Let Γhol(Lλ) be the reproducing kernel Hilbert space of holomorphic sections of the homogeneous line bundle Lλ over G/T associated with the highest weight λ of the irreducible representation πλ of G. The multiplicity of a weight m in πλ is computed from functional analytical structure of the Berezin symbol of the projector in Γhol(Lλ) onto subspace of weight m. We describe a method of the construction of this symbol and the evaluation of the weight multiplicity as a rank of a Hermitian form. The application of this method is described in a number of examples

Realization of compact Lie algebras in K\"ahler manifolds

The Berezin quantization on a simply connected homogeneous K\"{a}hler manifold, which is considered as a phase space for a dynamical system, enables a description of the quantal system in a (finite-dimensional) Hilbert space of holomorphic functions corresponding to generalized coherent states. The Lie algebra associated with the manifold symmetry group is given in terms of first-order differential operators. In the classical theory, the Lie algebra is represented by the momentum maps which are functions on the manifold, and the Lie product is the Poisson bracket given by the K\"{a}hler structure. The K\"{a}hler potentials are constructed for the manifolds related to all compact semi-simple Lie groups. The complex coordinates are introduced by means of the Borel method. The K\"{a}hler structure is obtained explicitly for any unitary group representation. The cocycle functions for the Lie algebra and the Killing vector fields on the manifold are also obtained

Cortical Mechanisms Specific to Explicit Visual Object Recognition

AbstractThe cortical mechanisms associated with conscious object recognition were studied using functional magnetic resonance imaging (fMRI). Participants were required to recognize pictures of masked objects that were presented very briefly, randomly and repeatedly. This design yielded a gradual accomplishment of successful recognition. Cortical activity in a ventrotemporal visual region was linearly correlated with perception of object identity. Therefore, although object recognition is rapid, awareness of an object's identity is not a discrete phenomenon but rather associated with gradually increasing cortical activity. Furthermore, the focus of the activity in the temporal cortex shifted anteriorly as subjects reported an increased knowledge regarding identity. The results presented here provide new insights into the processes underlying explicit object recognition, as well as the analysis that takes place immediately before and after recognition is possible

Analytic representations based on SU(1,1) coherent states and their applications

We consider two analytic representations of the SU(1,1) Lie group: the representation in the unit disk based on the SU(1,1) Perelomov coherent states and the Barut-Girardello representation based on the eigenstates of the SU(1,1) lowering generator. We show that these representations are related through a Laplace transform. A ``weak'' resolution of the identity in terms of the Perelomov SU(1,1) coherent states is presented which is valid even when the Bargmann index $k$ is smaller than one half. Various applications of these results in the context of the two-photon realization of SU(1,1) in quantum optics are also discussed.Comment: LaTeX, 15 pages, no figures, to appear in J. Phys. A. More information on http://www.technion.ac.il/~brif/science.htm

Predominance of null mutations in ataxia-telangiectasia

Ataxia-telangiectasia (A-T) is an autosomal recessive disorder involving cerebellar degeneration, immunodeficiency, chromosomal instability, radiosensitivity and cancer predisposition. The responsible gene, ATM, was recently identified by positional cloning and found to encode a putative 350 kDa protein with a PI 3-kinase-like domain, presumably involved in mediating cell cycle arrest in response to radiation-induced DNA damage. The nature and location of A-T mutations should provide insight into the function of the ATM protein and the molecular basis of this pleiotropic disease. Of 44 A-T mutations identified by us to date, 39 (89%) are expected to inactivate the ATM protein by truncating it, by abolishing correct initiation or termination of translation, or by deleting large segments. Additional mutations are four smaller in-frame deletions and insertions, and one substitution of a highly conserved amino acid at the PI 3-kinase domain. The emerging profile of mutations causing A-T is thus dominated by those expected to completely inactivate the ATM protein. ATM mutations with milder effects may result in phenotypes related, but not identical, to A-T

Impact of COVID-19 on cardiovascular testing in the United States versus the rest of the world

Objectives: This study sought to quantify and compare the decline in volumes of cardiovascular procedures between the United States and non-US institutions during the early phase of the coronavirus disease-2019 (COVID-19) pandemic. Background: The COVID-19 pandemic has disrupted the care of many non-COVID-19 illnesses. Reductions in diagnostic cardiovascular testing around the world have led to concerns over the implications of reduced testing for cardiovascular disease (CVD) morbidity and mortality. Methods: Data were submitted to the INCAPS-COVID (International Atomic Energy Agency Non-Invasive Cardiology Protocols Study of COVID-19), a multinational registry comprising 909 institutions in 108 countries (including 155 facilities in 40 U.S. states), assessing the impact of the COVID-19 pandemic on volumes of diagnostic cardiovascular procedures. Data were obtained for April 2020 and compared with volumes of baseline procedures from March 2019. We compared laboratory characteristics, practices, and procedure volumes between U.S. and non-U.S. facilities and between U.S. geographic regions and identified factors associated with volume reduction in the United States. Results: Reductions in the volumes of procedures in the United States were similar to those in non-U.S. facilities (68% vs. 63%, respectively; p = 0.237), although U.S. facilities reported greater reductions in invasive coronary angiography (69% vs. 53%, respectively; p < 0.001). Significantly more U.S. facilities reported increased use of telehealth and patient screening measures than non-U.S. facilities, such as temperature checks, symptom screenings, and COVID-19 testing. Reductions in volumes of procedures differed between U.S. regions, with larger declines observed in the Northeast (76%) and Midwest (74%) than in the South (62%) and West (44%). Prevalence of COVID-19, staff redeployments, outpatient centers, and urban centers were associated with greater reductions in volume in U.S. facilities in a multivariable analysis. Conclusions: We observed marked reductions in U.S. cardiovascular testing in the early phase of the pandemic and significant variability between U.S. regions. The association between reductions of volumes and COVID-19 prevalence in the United States highlighted the need for proactive efforts to maintain access to cardiovascular testing in areas most affected by outbreaks of COVID-19 infection

Prediction is Production:The missing link between language production and comprehension

Published online: 18 January 2018Language comprehension often involves the generation of predictions. It has been hypothesized that such prediction-for-comprehension entails actual language production. Recent studies provided evidence that the production system is recruited during language comprehension, but the link between production and prediction during comprehension remains hypothetical. Here, we tested this hypothesis by comparing prediction during sentence comprehension (primary task) in participants having the production system either available or not (non-verbal versus verbal secondary task). In the primary task, sentences containing an expected or unexpected target noun-phrase were presented during electroencephalography recording. Prediction, measured as the magnitude of the N400 effect elicited by the article (expected versus unexpected), was hindered only when the production system was taxed during sentence context reading. The present study provides the first direct evidence that the availability of the speech production system is necessary for generating lexical prediction during sentence comprehension. Furthermore, these important results provide an explanation for the recruitment of language production during comprehension.This work was supported by the State Agency for Investigation (AEI), the European Regional Development Fund (FEDER) and the Spanish Ministry of Economy and Competitiveness (PSI2014-54500; SEV-2015-490); and the Basque Government (PI_2015_1_25). FMB was supported by a postdoctoral Marie Sklodowska-Curie fellowship (658341). MB was supported by the ICORE grant No 51/11 and by an Israel Science Foundation (ISF) grant # 673/17