The planar spectrum in U(N)-invariant quantum mechanics by Fock space methods: I. The bosonic case

Prompted by recent results on Susy-U(N)-invariant quantum mechanics in the large N limit by Veneziano and Wosiek, we have examined the planar spectrum in the full Hilbert space of U(N)-invariant states built on the Fock vacuum by applying any U(N)-invariant combinations of creation-operators. We present results about 1) the supersymmetric model in the bosonic sector, 2) the standard quartic Hamiltonian. This latter is useful to check our techniques against the exact result of Brezin et al. The SuSy case is where Fock space methods prove to be the most efficient: it turns out that the problem is separable and the exact planar spectrum can be expressed in terms of the single-trace spectrum. In the case of the anharmonic oscillator, on the other hand, the Fock space analysis is quite cumbersome due to the presence of large off-diagonal O(N) terms coupling subspaces with different number of traces; these terms should be absorbed before taking the planar limit and recovering the known planar spectrum. We give analytical and numerical evidence that good qualitative information on the spectrum can be obtained this way.Comment: 17 pages, 4 figures, uses youngtab.sty. Final versio

Understanding the determinants of stability and folding of small globular proteins from their energetics

The results of minimal model calculations suggest that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By mean of molecular dynamics simulations around the native conformation, which simulate the protein and the surrounding solvent at full--atom level, we generate an energetic map of the equilibrium state of the protein and simplify it with an Eigenvalue decomposition. The components of the Eigenvector associated with the lowest Eigenvalue indicate which are the "hot" sites responsible for the stability and for the fast folding of the protein. Comparison of these predictions with the results of mutatgenesis experiments, performed for five small proteins, provide an excellent agreement

Correlated Binomial Models and Correlation Structures

We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional probabilities. The beta-binomial distribution is derived by a strong symmetric assumption on the conditional correlations. Our derivation clarifies the 'correlation' structure of the beta-binomial distribution. It is also possible to study the correlation structures of other probability distributions of exchangeable (homogeneous) correlated Bernoulli random variables. We study some distribution functions and discuss their behaviors in terms of their correlation structures.Comment: 12 pages, 7 figure

The Effect of a Single Supernova Explosion on the Cuspy Density Profile of a Small-Mass Dark Matter Halo

Some observations of galaxies, and in particular dwarf galaxies, indicate a presence of cored density profiles in apparent contradiction with cusp profiles predicted by dark matter N-body simulations. We constructed an analytical model, using particle distribution functions (DFs), to show how a supernova (SN) explosion can transform a cusp density profile in a small-mass dark matter halo into a cored one. Considering the fact that a SN efficiently removes matter from the centre of the first haloes, we study the effect of mass removal through a SN perturbation in the DFs. We found that the transformation from a cusp into a cored profile is present even for changes as small as 0.5% of the total energy of the halo, that can be produced by the expulsion of matter caused by a single SN explosion.Comment: 6 pages, 4 figures, accepted for publication in MNRA

Label-Dependencies Aware Recurrent Neural Networks

In the last few years, Recurrent Neural Networks (RNNs) have proved effective on several NLP tasks. Despite such great success, their ability to model \emph{sequence labeling} is still limited. This lead research toward solutions where RNNs are combined with models which already proved effective in this domain, such as CRFs. In this work we propose a solution far simpler but very effective: an evolution of the simple Jordan RNN, where labels are re-injected as input into the network, and converted into embeddings, in the same way as words. We compare this RNN variant to all the other RNN models, Elman and Jordan RNN, LSTM and GRU, on two well-known tasks of Spoken Language Understanding (SLU). Thanks to label embeddings and their combination at the hidden layer, the proposed variant, which uses more parameters than Elman and Jordan RNNs, but far fewer than LSTM and GRU, is more effective than other RNNs, but also outperforms sophisticated CRF models.Comment: 22 pages, 3 figures. Accepted at CICling 2017 conference. Best Verifiability, Reproducibility, and Working Description awar

Adaptation of Hybrid ANN/HMM Models using Linear Hidden Transformations and Conservative Training

International audienceA technique is proposed for the adaptation of automatic speech recognition systems using Hybrid models combining Artificial Neural Networks with Hidden Markov Models. The application of linear transformations not only to the input features, but also to the outputs of the internal layers is investigated. The motivation is that the outputs of an internal layer represent a projection of the input pattern into a space where it should be easier to learn the classification or transformation expected at the output of the network. A new solution, called Conservative Training, is proposed that compensates for the lack of adaptation samples in certain classes. Supervised adaptation experiments with different corpora and for different adaptation types are described. The results show that the proposed approach always outperforms the use of transformations in the feature space and yields even better results when combined with linear input transformations

Influence of conformational fluctuations on enzymatic activity: modelling the functional motion of beta-secretase

Considerable insight into the functional activity of proteins and enzymes can be obtained by studying the low-energy conformational distortions that the biopolymer can sustain. We carry out the characterization of these large scale structural changes for a protein of considerable pharmaceutical interest, the human $\beta$-secretase. Starting from the crystallographic structure of the protein, we use the recently introduced beta-Gaussian model to identify, with negligible computational expenditure, the most significant distortion occurring in thermal equilibrium and the associated time scales. The application of this strategy allows to gain considerable insight into the putative functional movements and, furthermore, helps to identify a handful of key regions in the protein which have an important mechanical influence on the enzymatic activity despite being spatially distant from the active site. The results obtained within the Gaussian model are validated through an extensive comparison against an all-atom Molecular Dynamics simulation.Comment: To be published in a special issue of J. Phys.: Cond. Mat. (Bedlewo Workshop

Pyramiding resistance genes and widening the genetic base of the apple (Malus 7 domestica Borkh.) crop

Apple breeding is active worldwide and yet the apple crop is in a precarious state as it relies on few dominant cultivars and only the Rvi6 (formerly Vf) gene, that confers resistance to scab, has been extensively exploited in the cultivars entered the market in recent years. However, there are some 20 disease resistance genes described in apple and the apple germplasm includes thousands of accessions in the repositories. In this paper, a breeding programme is described, whereby 36 genotypes, including ancient and contemporary apple cultivars, were crossed to produce a new set of selections that combine extensive genetic resources with pyramided resistance genes to several apple diseases, such as scab and powdery mildew. The 110 cross combinations carried out successfully, of the 260 initially planned, produced 7,876 offsprings, reduced to 2,969 after screening with molecular markers associated with five resistance genes. Selections with three or two resistance genes and good agronomic characteristics were kept for further field observations with the aims of creating new cultivars for the market and new parents for future breeding projects