Vacuum orbit and spontaneous symmetry breaking in hyperbolic sigma models

We present a detailed study of quantized noncompact, nonlinear SO(1,N) sigma-models in arbitrary space-time dimensions D \geq 2, with the focus on issues of spontaneous symmetry breaking of boost and rotation elements of the symmetry group. The models are defined on a lattice both in terms of a transfer matrix and by an appropriately gauge-fixed Euclidean functional integral. The main results in all dimensions \geq 2 are: (i) On a finite lattice the systems have infinitely many nonnormalizable ground states transforming irreducibly under a nontrivial representation of SO(1,N); (ii) the SO(1,N) symmetry is spontaneously broken. For D =2 this shows that the systems evade the Mermin-Wagner theorem. In this case in addition: (iii) Ward identities for the Noether currents are derived to verify numerically the absence of explicit symmetry breaking; (iv) numerical results are presented for the two-point functions of the spin field and the Noether current as well as a new order parameter; (v) in a large N saddle-point analysis the dynamically generated squared mass is found to be negative and of order 1/(V \ln V) in the volume, the 0-component of the spin field diverges as \sqrt{\ln V}, while SO(1,N) invariant quantities remain finite.Comment: 60 pages, 12 Figures, AMS-Latex; v2: results on vacuum orbit and spontaneous symmetry breaking extended to all dimension

Use of state sequence analysis in pharmacoepidemiology: A tutorial

none6noWhile state sequence analysis (SSA) has been long used in social sciences, its use in pharmacoepidemiology is still in its infancy. Indeed, this technique is relatively easy to use, and its intrinsic visual nature may help investigators to untangle the latent information within prescription data, facilitating the individuation of specific patterns and possible inappropriate use of medications. In this paper, we provide an educational primer of the most important learning concepts and methods of SSA, including measurement of dissimilarities between sequences, the application of clustering methods to identify sequence patterns, the use of complexity measures for sequence patterns, the graphical visualization of sequences, and the use of SSA in predictive models. As a worked example, we present an application of SSA to opioid prescription patterns in patients with non-cancer pain, using real-world data from Italy. We show how SSA allows the identification of patterns in prescriptions in these data that might not be evident using standard statistical approaches and how these patterns are associated with future discontinuation of opioid therapy.openVanoli J.; Nava C.R.; Airoldi C.; Ucciero A.; Salvi V.; Barone-Adesi F.Vanoli, J.; Nava, C. R.; Airoldi, C.; Ucciero, A.; Salvi, V.; Barone-Adesi, F

Parabolic maps with spin: Generic spectral statistics with non-mixing classical limit

We investigate quantised maps of the torus whose classical analogues are ergodic but not mixing. Their quantum spectral statistics shows non-generic behaviour, i.e.it does not follow random matrix theory (RMT). By coupling the map to a spin 1/2, which corresponds to changing the quantisation without altering the classical limit of the dynamics on the torus, we numerically observe a transition to RMT statistics. The results are interpreted in terms of semiclassical trace formulae for the maps with and without spin respectively. We thus have constructed quantum systems with non-mixing classical limit which show generic (i.e. RMT) spectral statistics. We also discuss the analogous situation for an almost integrable map, where we compare to Semi-Poissonian statistics.Comment: 29 pages, 20 figure

Novel Methods for the Computational Analysis of Codon Usage Bias

The genetic code encodes the same amino acid with multiple codon choices, but in a biased fashion. This phenomenon is called the codon usage bias (CUB). There have been significant research efforts trying to quantify codon usage bias and probe into its origins. Understanding CUB is important for at least two reasons. Firstly, it is connected with gene expression, and thus of fundamental importance for our understanding of life. Secondly it is important for the optimisation of heterologous gene expression in industrial bioproduction including the pharmaceutical industry. This thesis makes three main contributions to the understanding of CUB: (1) It proposes a novel measure of codon usage bias which does not require any context information other than the nature of the coding sequences themselves. The proposed measure is capable of quantifying codon usage bias at different levels of an individual sequence, a particular amino acid type, and a whole genome, and also capable to provide comprehensive and desired CUB information for the correlation study about specific CUB related factors by constructing high dimensional CUB feature spaces. (2) It derives a stochastic thermodynamic based model to investigate what the evolutionary drivers of codon usage bias are from a macroscopic perspective. (3) It applies the proposed methods to extensive genomic data. Our main conclusions derived from the applications to real organisms include (a) codon usage bias and gene lengths cooperate together to satisfy different protein requirements in the cells; (b) codon usage bias correlates with phylogenetic distances among remote groups of species; (c) codon usage bias cannot be explained solely by selection pressures that act on the genome-wide codon frequencies, but also includes pressures that act at the level of individual genes

Use of State Sequence Analysis in Pharmacoepidemiology: A Tutorial.

While state sequence analysis (SSA) has been long used in social sciences, its use in pharmacoepidemiology is still in its infancy. Indeed, this technique is relatively easy to use, and its intrinsic visual nature may help investigators to untangle the latent information within prescription data, facilitating the individuation of specific patterns and possible inappropriate use of medications. In this paper, we provide an educational primer of the most important learning concepts and methods of SSA, including measurement of dissimilarities between sequences, the application of clustering methods to identify sequence patterns, the use of complexity measures for sequence patterns, the graphical visualization of sequences, and the use of SSA in predictive models. As a worked example, we present an application of SSA to opioid prescription patterns in patients with non-cancer pain, using real-world data from Italy. We show how SSA allows the identification of patterns in prescriptions in these data that might not be evident using standard statistical approaches and how these patterns are associated with future discontinuation of opioid therapy

Positive-density ground states of the Gross-Pitaevskii equation

We consider the nonlinear Gross-Pitaevskii equation at positive density, that is, for a bounded solution not tending to 0 at infinity. We focus on infinite ground states, which are by definition minimizers of the energy under local perturbations. When the Fourier transform of the interaction potential takes negative values we prove the existence of a phase transition at high density, where the constant solution ceases to be a ground state. The analysis requires mixing techniques from elliptic PDE theory and statistical mechanics, in order to deal with a large class of interaction potentials.Comment: Added a short proof of the uniform bounds in the simpler case of positive interaction