1,695 research outputs found

    Powers of the Vandermonde determinant, Schur Functions, and recursive formulas

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    Since every even power of the Vandermonde determinant is a symmetric polynomial, we want to understand its decomposition in terms of the basis of Schur functions. We investigate several combinatorial properties of the coefficients in the decomposition. In particular, we give recursive formulas for the coefficient of the Schur function s_{\m} in the decomposition of an even power of the Vandermonde determinant in n+1n + 1 variables in terms of the coefficient of the Schur function s_{\l} in the decomposition of the same even power of the Vandermonde determinant in nn variables if the Young diagram of \m is obtained from the Young diagram of \l by adding a tetris type shape to the top or to the left. An extended abstract containing the statement of the results presented here appeared in the Proceedings of FPSAC11Comment: 23 pages; extended abstract appeared in the Proceedings of FPSAC1

    Targeted Neuronal Death Affects Neuronal Replacement and Vocal Behavior in Adult Songbirds

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    AbstractIn the high vocal center (HVC) of adult songbirds, increases in spontaneous neuronal replacement correlate with song changes and with cell death. We experimentally induced death of specific HVC neuron types in adult male zebra finches using targeted photolysis. Induced death of a projection neuron type that normally turns over resulted in compensatory replacement of the same type. Induced death of the normally nonreplaced type did not stimulate their replacement. In juveniles, death of the latter type increased recruitment of the replaceable kind. We infer that neuronal death regulates the recruitment of replaceable neurons. Song deteriorated in some birds only after elimination of replaceable neurons. Behavioral deficits were transient and followed by variable degrees of recovery. This raises the possibility that induced neuronal replacement can restore a learned behavior

    Long-Distance Retinoid Signaling in the Zebra Finch Brain

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    All-trans retinoic acid (ATRA), the main active metabolite of vitamin A, is a powerful signaling molecule that regulates large-scale morphogenetic processes during vertebrate embryonic development, but is also involved post-natally in regulating neural plasticity and cognition. In songbirds, it plays an important role in the maturation of learned song. The distribution of the ATRA-synthesizing enzyme, zRalDH, and of ATRA receptors (RARs) have been described, but information on the distribution of other components of the retinoid signaling pathway is still lacking. To address this gap, we have determined the expression patterns of two obligatory RAR co-receptors, the retinoid X receptors (RXR) α and γ, and of the three ATRA-degrading cytochromes CYP26A1, CYP26B1, and CYP26C1. We have also studied the distribution of zRalDH protein using immunohistochemistry, and generated a refined map of ATRA localization, using a modified reporter cell assay to examine entire brain sections. Our results show that (1) ATRA is more broadly distributed in the brain than previously predicted by the spatially restricted distribution of zRalDH transcripts. This could be due to long-range transport of zRalDH enzyme between different nuclei of the song system: Experimental lesions of putative zRalDH peptide source regions diminish ATRA-induced transcription in target regions. (2) Four telencephalic song nuclei express different and specific subsets of retinoid-related receptors and could be targets of retinoid regulation; in the case of the lateral magnocellular nucleus of the anterior nidopallium (lMAN), receptor expression is dynamically regulated in a circadian and age-dependent manner. (3) High-order auditory areas exhibit a complex distribution of transcripts representing ATRA synthesizing and degrading enzymes and could also be a target of retinoid signaling. Together, our survey across multiple connected song nuclei and auditory brain regions underscores the prominent role of retinoid signaling in modulating the circuitry that underlies the acquisition and production of learned vocalizations

    Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry

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    To obtain the one-loop corrections to the mass of a kink by mode regularization, one may take one-half the result for the mass of a widely separated kink-antikink (or sphaleron) system, where the two bosonic zero modes count as two degrees of freedom, but the two fermionic zero modes as only one degree of freedom in the sums over modes. For a single kink, there is one bosonic zero mode degree of freedom, but it is necessary to average over four sets of fermionic boundary conditions in order (i) to preserve the fermionic Z2_2 gauge invariance ψψ\psi \to -\psi, (ii) to satisfy the basic principle of mode regularization that the boundary conditions in the trivial and the kink sector should be the same, (iii) in order that the energy stored at the boundaries cancels and (iv) to avoid obtaining a finite, uniformly distributed energy which would violate cluster decomposition. The average number of fermionic zero-energy degrees of freedom in the presence of the kink is then indeed 1/2. For boundary conditions leading to only one fermionic zero-energy solution, the Z2_2 gauge invariance identifies two seemingly distinct `vacua' as the same physical ground state, and the single fermionic zero-energy solution does not correspond to a degree of freedom. Other boundary conditions lead to two spatially separated ω0\omega \sim 0 solutions, corresponding to one (spatially delocalized) degree of freedom. This nonlocality is consistent with the principle of cluster decomposition for correlators of observables.Comment: 32 pages, 5 figure

    The ATPase activity of MLH1 is required to orchestrate DNA double-strand breaks and end processing during class switch recombination.

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    PublishedJournal ArticleResearch Support, N.I.H., ExtramuralResearch Support, Non-U.S. Gov'tAntibody diversification through somatic hypermutation (SHM) and class switch recombination (CSR) are similarly initiated in B cells with the generation of U:G mismatches by activation-induced cytidine deaminase but differ in their subsequent mutagenic consequences. Although SHM relies on the generation of nondeleterious point mutations, CSR depends on the production of DNA double-strand breaks (DSBs) and their adequate recombination through nonhomologous end joining (NHEJ). MLH1, an ATPase member of the mismatch repair (MMR) machinery, is emerging as a likely regulator of whether a U:G mismatch progresses toward mutation or DSB formation. We conducted experiments on cancer modeled ATPase-deficient MLH1G67R knockin mice to determine the function that the ATPase domain of MLH1 mediates in SHM and CSR. Mlh1(GR/GR) mice displayed a significant decrease in CSR, mainly attributed to a reduction in the generation of DSBs and diminished accumulation of 53BP1 at the immunoglobulin switch regions. However, SHM was normal in these mice, which distinguishes MLH1 from upstream members of the MMR pathway and suggests a very specific role of its ATPase-dependent functions during CSR. In addition, we show that the residual switching events still taking place in Mlh1(GR/GR) mice display unique features, suggesting a role for the ATPase activity of MLH1 beyond the activation of the endonuclease functions of its MMR partner PMS2. A preference for switch junctions with longer microhomologies in Mlh1(GR/GR) mice suggests that through its ATPase activity, MLH1 also has an impact in DNA end processing, favoring canonical NHEJ downstream of the DSB. Collectively, our study shows that the ATPase domain of MLH1 is important to transmit the CSR signaling cascade both upstream and downstream of the generation of DSBs.Spanish Ministry of Education and ScienceNIHNational Women’s Division of the Albert Einstein College of Medicin

    Effect of Hadron Dynamics on the Proton Lifetime

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    A detailed, quantitative re-examination of the effect of hadron dynamics on baryon decay, modeled in terms of Skyrme-field tunneling, indicates that any hadronic suppression should be quite mild. This appears to be another illustration of the `Cheshire-cat' phenomenon, that variation of the apportionment between description of the nucleon as a bag of quarks and description as a Skyrme field configuration has little influence on many nucleon properties. Perhaps the largest remaining uncertainty in evaluating the decay rate has to do with the overlap between a specified quark-antiquark configuration and a final meson state.Comment: minor corrections, 19 pages, 9 figure

    Local Casimir Energy For Solitons

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    Direct calculation of the one-loop contributions to the energy density of bosonic and supersymmetric phi-to-the-fourth kinks exhibits: (1) Local mode regularization. Requiring the mode density in the kink and the trivial sectors to be equal at each point in space yields the anomalous part of the energy density. (2) Phase space factorization. A striking position-momentum factorization for reflectionless potentials gives the non-anomalous energy density a simple relation to that for the bound state. For the supersymmetric kink, our expression for the energy density (both the anomalous and non-anomalous parts) agrees with the published central charge density, whose anomalous part we also compute directly by point-splitting regularization. Finally we show that, for a scalar field with arbitrary scalar background potential in one space dimension, point-splitting regularization implies local mode regularization of the Casimir energy density.Comment: 18 pages. Numerous new clarifications and additions, of which the most important may be the direct derivation of local mode regularization from point-splitting regularization for the bosonic kink in 1+1 dimension
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