Number of Spin II States of Identical Particles

In this paper we study the enumeration of number (denoted as ${D_I}$) of spin $I$ states for fermions in a single-$j$ shell and bosons with spin $l$. We show that $D_I$ can be enumerated by the reduction from SU$(n+1)$ to SO(3). New regularities of $D_I$ are discerned.Comment: 3 pages, no figures. to be publishe

JJ-pairing interaction, number of states, and nine-jj sum rules of four identical particles

In this paper we study $J$-pairing Hamiltonian and find that the sum of eigenvalues of spin $I$ states equals sum of norm matrix elements within the pair basis for four identical particles such as four fermions in a single-$j$ shell or four bosons with spin $l$. We relate number of states to sum rules of nine-$j$ coefficients. We obtained sum rules for nine-$j$ coefficients $$and$$ summing over (1) even $J$ and $K$, (2) even $J$ and odd $K$, (3) odd $J$ and odd $K$, and (4) both even and odd $J,K$, where $j$ is a half integer and $l$ is an integer.Comment: 6 pages, no figure, updated version, to be published. Physical Review C, in pres

Shell-model description of monopole shift in neutron-rich Cu

Variations in the nuclear mean-field, in neutron-rich nuclei, are investigated within the framework of the nuclear shell model. The change is identified to originate mainly from the monopole part of the effective two-body proton-neutron interaction. Applications for the low-lying states in odd-$A$ Cu nuclei are presented. We compare the results using both schematic and realistic forces. We also compare the monopole shifts with the results obtained from large-scale shell-model calculations, using the same realistic interaction, in order to study two-body correlations beyond the proton mean-field variations.Comment: Phys. Rev. C (in press

Three-body correlations and finite-size effects in the Moore--Read states on a sphere

Two- and three-body correlations in partially filled degenerate fermion shells are studied numerically for various interactions between the particles. Three distinct correlation regimes are defined, depending on the short-range behavior of the pair pseudopotential. For pseudopotentials similar to those of electrons in the first excited Landau level, correlations at half-filling have a simple three-body form consisting of the maximum avoidance of the triplet state with the smallest relative angular momentum R_3=3. In analogy to the superharmonic criterion for Laughlin two-body correlations, their occurrence is related to the form of the three-body pseudopotential at short range. The spectra of a model three-body repulsion are calculated, and the zero-energy Moore--Read ground state, its +-e/4-charged quasiparticles, and the magnetoroton and pair-breaking bands are all identified. The quasiparticles are correctly described by a composite fermion model appropriate for Halperin's p-type pairing with Laughlin correlations between the pairs. However, the Moore--Read ground state, and specially its excitations, have small overlaps with the corresponding Coulomb eigenstates when calculated on a sphere. The reason lies in surface curvature which affects the form of pair pseudopotential for which the "R_3>3" three-body correlations occur. In finite systems, such pseudopotential must be slightly superharmonic at short range (different from Coulomb pseudopotential). However, the connection with the three-body pseudopotential is less size-dependent, suggesting that the Moore--Read state and its excitations are a more accurate description for experimental nu=5/2 states than could be expected from previous calculations.Comment: 12 pages, 12 figures, submitted to PR

Number of states with fixed angular momentum for identical fermions and bosons

We present in this paper empirical formulas for the number of angular momentum I states for three and four identical fermions or bosons. In the cases with large I we prove that the number of states with the same ${\cal M}$ and n but different J is identical if $I \ge (n-2)J - {1/2} (n-1)(n-2)$ for fermions and $I \ge (n-2)J$ for bosons, and that the number of states is also identical for the same ${\cal M}$ but different n and J if ${\cal M} \le$min(n, 2J+1 - n) for fermions and for ${\cal M} \le$min(n, 2J) for bosons. Here ${\cal M} =I_{max}-I$, n is the particle number, and J refers to the angular momentum of a single-particle orbit for fermions, or the spin L carried by bosons.Comment: 9 pages, no figure

Beta decay of 71,73Co; probing single particle states approaching doubly magic 78Ni

Low-energy excited states in 71,73Ni populated via the {\beta} decay of 71,73Co were investigated in an experiment performed at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University (MSU). Detailed analysis led to the construction of level schemes of 71,73Ni, which are interpreted using systematics and analyzed using shell model calculations. The 5/2- states attributed to the the f5/2 orbital and positive parity 5/2+ and 7/2+ states from the g9/2 orbital have been identified in both 71,73Ni. In 71Ni the location of a 1/2- {\beta}-decaying isomer is proposed and limits are suggested as to the location of the isomer in 73Ni. The location of positive parity cluster states are also identified in 71,73Ni. Beta-delayed neutron branching ratios obtained from this data are given for both 71,73Co.Comment: Accepted for publication in PR

``Fermi Liquid'' Shell Model Approach to Composite Fermion Excitation Spectra in Fractional Quantum Hall States

Numerical results for the energy spectra of $N$ electrons on a spherical surface are used as input data to determine the quasiparticle energies and the pairwise ``Fermi liquid'' interactions of composite Fermion (CF) excitations in fractional quantum Hall systems. The quasiparticle energies and their interactions are then used to determine the energy spectra, $E$ vs total angular momentum $L$, of states containing more than two quasiparticles. The qualitative agreement with the numerical results gives a remarkable new confirmation of the CF picture.Comment: LaTex, 4 pages, including 4 .eps-figures, to be appear in pr

DeepBrain: Functional Representation of Neural In-Situ Hybridization Images for Gene Ontology Classification Using Deep Convolutional Autoencoders

This paper presents a novel deep learning-based method for learning a functional representation of mammalian neural images. The method uses a deep convolutional denoising autoencoder (CDAE) for generating an invariant, compact representation of in situ hybridization (ISH) images. While most existing methods for bio-imaging analysis were not developed to handle images with highly complex anatomical structures, the results presented in this paper show that functional representation extracted by CDAE can help learn features of functional gene ontology categories for their classification in a highly accurate manner. Using this CDAE representation, our method outperforms the previous state-of-the-art classification rate, by improving the average AUC from 0.92 to 0.98, i.e., achieving 75% reduction in error. The method operates on input images that were downsampled significantly with respect to the original ones to make it computationally feasible

Functional characterization of a melon alcohol acyl-transferase gene family involved in the biosynthesis of ester volatiles. Identification of the crucial role of a threonine residue for enzyme activity

Volatile esters, a major class of compounds contributing to the aroma of many fruit, are synthesized by alcohol acyl-transferases (AAT). We demonstrate here that, in Charentais melon (Cucumis melo var. cantalupensis), AAT are encoded by a gene family of at least four members with amino acid identity ranging from 84% (Cm-AAT1/Cm-AAT2) and 58% (Cm-AAT1/Cm-AAT3) to only 22% (Cm-AAT1/Cm-AAT4). All encoded proteins, except Cm-AAT2, were enzymatically active upon expression in yeast and show differential substrate preferences. Cm-AAT1 protein produces a wide range of short and long-chain acyl esters but has strong preference for the formation of E-2-hexenyl acetate and hexyl hexanoate. Cm-AAT3 also accepts a wide range of substrates but with very strong preference for producing benzyl acetate. Cm-AAT4 is almost exclusively devoted to the formation of acetates, with strong preference for cinnamoyl acetate. Site directed mutagenesis demonstrated that the failure of Cm-AAT2 to produce volatile esters is related to the presence of a 268-alanine residue instead of threonine as in all active AAT proteins. Mutating 268-A into 268-T of Cm-AAT2 restored enzyme activity, while mutating 268-T into 268-A abolished activity of Cm-AAT1. Activities of all three proteins measured with the prefered substrates sharply increase during fruit ripening. The expression of all Cm-AAT genes is up-regulated during ripening and inhibited in antisense ACC oxidase melons and in fruit treated with the ethylene antagonist 1-methylcyclopropene (1-MCP), indicating a positive regulation by ethylene. The data presented in this work suggest that the multiplicity of AAT genes accounts for the great diversity of esters formed in melon

Shape resonance for the anisotropic superconducting gaps near a Lifshitz transition: the effect of electron hopping between layers

The multigap superconductivity modulated by quantum confinement effects in a superlattice of quantum wells is presented. Our theoretical BCS approach captures the low-energy physics of a shape resonance in the superconducting gaps when the chemical potential is tuned near a Lifshitz transition. We focus on the case of weak Cooper-pairing coupling channels and strong pair exchange interaction driven by repulsive Coulomb interaction that allows to use the BCS theory in the weak-coupling regime neglecting retardation effects like in quantum condensates of ultracold gases. The calculated matrix element effects in the pairing interaction are shown to yield a complex physics near the particular quantum critical points due to Lifshitz transitions in multigap superconductivity. Strong deviations of the ratio $2\Delta/T_c$ from the standard BCS value as a function of the position of the chemical potential relative to the Lifshitz transition point measured by the Lifshitz parameter are found. The response of the condensate phase to the tuning of the Lifshitz parameter is compared with the response of ultracold gases in the BCS-BEC crossover tuned by an external magnetic field. The results provide the description of the condensates in this regime where matrix element effects play a key role.Comment: 12 pages, 6 figure