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 $\Gamma_{\rm hol}(\mathcal{L}^{\lambda})$ be the reproducing kernel Hilbert space of holomorphic sections of the homogeneous line bundle $\mathcal{L}^{\lambda}$ over $G/T$ associated with the highest weight $\lambda$ of the irreducible representation $\pi_{\lambda}$ of $G$. The multiplicity of a weight $m$ in $\pi_{\lambda}$ is computed from functional analytical structure of the Berezin symbol of the projector in $\Gamma_{\rm hol}(\mathcal{L}^{\lambda})$ 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

Comments on the Morphology of Nouns in Mishnaic Hebrew: Nouns attested and unattested in Biblical Hebrew

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The Cortical Underpinnings of Context-based Memory Distortion

Everyday contextual settings create associations that later afford generating predictions about what objects to expect in our environment. The cortical network that takes advantage of such contextual information is proposed to connect the representation of associated objects such that seeing one object (bed) will activate the visual representations of other objects sharing the same context (pillow). Given this proposal, we hypothesized that the cortical activity elicited by seeing a strong contextual object would predict the occurrence of false memories whereby one erroneously "remembers'' having seen a new object that is related to a previously presented object. To test this hypothesis, we used functional magnetic resonance imaging during encoding of contextually related objects, and later tested recognition memory. New objects that were contextually related to previously presented objects were more often falsely judged as "old'' compared with new objects that were contextually unrelated to old objects. This phenomenon was reflected by activity in the cortical network mediating contextual processing, which provides a better understanding of how the brain represents and processes context.Psycholog

Famous Faces Activate Contextual Associations in the Parahippocampal Cortex

The parahippocampal cortex (PHC) has been traditionally implicated both in place processing and in episodic memory. How could the same cortical region mediate these cognitive functions that seem quite different? We have recently proposed that the PHC should be seen as more generally mediating contextual associative processing, which is required for both navigation and memory. We therefore predicted that any associative objects should activate the PHC. To test this generalization, we investigated the extent to which common stimuli that are nonspatial by nature, namely faces, activate the PHC, although their perception is typically associated with other cortical structures. Specifically, we compared the activation elicited by famous faces, which are highly associated with rich pictorial and contextual information (e.g., Tom Cruise) and are not associated with a specific place, with activation elicited by unfamiliar faces. Consistent with our prediction, contrasting famous with unfamiliar faces revealed significant activation within the PHC. Taken collectively, these findings indicate that the PHC should be regarded as mediating contextual associations in general and not necessarily spatial or episodic informatio

Empathy: The Role of Expectations

To what extent can we feel what someone else feels? Data from neuroscience suggest that empathy is supported by a simulation process, namely the neural activation of the same or similar regions that subserve the representation of specific states in the observer. However, expectations significantly modulate sensory input, including affective information. For example, expecting painful stimulation can decrease the neural signal and the subjective experience thereof. For an accurate representation of the other person's state, such top-down processes would have to be simulated as well. However, this is only partly possible, because expectations are usually acquired by learning. Therefore, it is important to be aware of possible misleading simulations that lead to misinterpretations of someone's state

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

Geometric charges and nonlinear elasticity of soft metamaterials

Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and conceptual frameworks are largely lacking. Using an analogy with electrostatics, and building on recent developments in a nonlinear geometric formulation of elasticity, we develop a formalism that maps the elastic problem into that of nonlinear interaction of elastic charges. This approach offers an intuitive conceptual framework, qualitatively explaining the linear response, the onset of mechanical instability and aspects of the post-instability state. Apart from intuition, the formalism also quantitatively reproduces full numeric simulations of several prototypical structures. Possible applications of the tools developed in this work for the study of ordered and disordered porous mechanical metamaterials are discussed.Comment: 12 pages, 5 figure

Defective RNAs of Citrus tristeza virus analogous to Crinivirus genomic RNAs

AbstractThe family Closteroviridae includes the genera Closterovirus and Ampelovirus with monopartite genomes and the genus Crinivirus with bipartite genomes. Plants infected with the Closterovirus, Citrus tristeza virus (CTV), often contain one or more populations of defective RNAs (dRNAs). Although most dRNAs are comparatively small (2–5 kb) consisting of the genomic RNA termini with large internal deletions, we recently characterized large dRNAs of ∼12 kb that retained the open reading frames (ORFs) 1a plus 1b. These were self-replicating RNAs and appeared to be analogous to the genomic RNA 1 of the bipartite criniviruses. The present report describes the finding of an additional group of large dRNAs (LdRNAs) that retained all or most of the 10 3′ ORFs and appeared to be analogous to genomic RNA 2 of criniviruses. Isolates associated with LdRNAs were found associated with double-recombinant dRNAs (DR-dRNAs) of various sizes (1.7 to 5.1 kb) that comprised the two termini and a noncontiguous internal sequence from ORF2. The genetic and epidemiological implications of the architectural identities of LdRNAs and DR dRNAs and their apparent analogy with the genomic RNA 2 of criniviruses are discussed