Logahedra: A new weakly relational domain

Weakly relational numeric domains express restricted classes of linear inequalities that strike a balance between what can be described and what can be efficiently computed. Popular weakly relational domains such as bounded differences and octagons have found application in model checking and abstract interpretation. This paper introduces logahedra, which are more expressiveness than octagons, but less expressive than arbitrary systems of two variable per inequality constraints. Logahedra allow coefficients of inequalities to be powers of two whilst retaining many of the desirable algorithmic properties of octagons

Positive Lyapunov Exponents for Quasiperiodic Szego cocycles

In this paper we first obtain a formula of averaged Lyapunov exponents for ergodic Szego cocycles via the Herman-Avila-Bochi formula. Then using acceleration, we construct a class of analytic quasi-periodic Szego cocycles with uniformly positive Lyapunov exponents. Finally, a simple application of the main theorem in [Y] allows us to estimate the Lebesgue measure of support of the measure associated to certain class of C1 quasiperiodic 2- sided Verblunsky coefficients. Using the same method, we also recover the [S-S] results for Schrodinger cocycles with nonconstant real analytic potentials and obtain some nonuniform hyperbolicity results for arbitrarily fixed Brjuno frequency and for certain C1 potentials.Comment: 27 papge

Risk Factors for Hyperfunctional Voice Disorders Among Teachers

The aim of the study was to assess the prevalence of voice problems among teachers, and identify risk factors for developing voice pathology. In this study we evaluated 448 teachers (400 females and 48 males) between the age range of 25 to 55 years, from primary school as well as secondary school which were selected randomly. A questionnaire was given to them to find out how many of them had a voice problem. All the positive cases were further evaluated by an Otorhinolaryngologist, an Audiologist and a Speech Language Pathologist. Out of the 448 teachers, 39 of them(9%) had an indication of voice disorder based on the positive respose got from the questionnaire. Among the 39 cases identified 11 were males (28%) and 28 were females (71%). We tried to investigate on the factors that would have contributed to voice problem in the identified 9% of cases .Detailed history was taken and was examined by an otorhinolaryngologist, an audiologist and a Speech Language Pathologist.Out of the 39 cases identified 26% had history of recurrent allergic rhinitis and laryngitis, 18% had sinusitis and post nasal drip, 18% had asthma, 26% had gastoesophageal reflux disorder, (8%) had minimal sensori neural hearing loss and hypothyroidism was found in 8%. Interaction of multiple factors like hereditory, behavioral, lifestyle, medical and environmental can contribute to voice disorders in occupational voice users. Teachers need to be educated regarding vocal mechanism, vocal hygiene and effective voice use , dust free and noise free work environment, diet modification like drinking adequate water, avoiding spicy and deep fried food, regularizing meals and avoiding sleeping immediately after food. The underlying medical issues like allergy, sinusitis, laryngitis, hypothyroidism, gastroesophageal reflux, hearing loss etc also need to be addressed , since vocal hygiene alone will not help until and unless the underlying cause is taken care of

Critical Behavior of Coupled q-state Potts Models under Weak Disorder

We investigate the effect of weak disorder on different coupled $q$-state Potts models with $q\le 4$ using two loops renormalisation group. This study presents new examples of first order transitions driven by randomness. We found that weak disorder makes the models decouple. Therefore, it appears that no relations emerge, at a perturbation level, between the disordered $q_1\times q_2$-state Potts model and the two disordered $q_1$, $q_2$-state Potts models ($q_1\ne q_2$), despite their central charges are similar according to recent numerical investigations. Nevertheless, when two $q$-state Potts models are considered ($q>2$), the system remains always driven in a strong coupling regime, violating apparently the Imry-Wortis argument.Comment: 7 pages + 1 PS figure (Latex

Optimal and Robust Quantum Metrology Using Interaction-Based Readouts

Useful quantum metrology requires nonclassical states with a high particle number and (close to) the optimal exploitation of the state's quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cram{\'e}r-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. "Interaction-based readout" protocols have been shown to allow optimal interferometry \emph{or} to provide robustness against detection noise at the expense of optimality. In this Letter, we prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal \emph{and} robust quantum metrology is achievable in current spin-squeezing experiments.Comment: 7 pages, 3 figure

Discrimination and synthesis of recursive quantum states in high-dimensional Hilbert spaces

We propose an interferometric method for statistically discriminating between nonorthogonal states in high dimensional Hilbert spaces for use in quantum information processing. The method is illustrated for the case of photon orbital angular momentum (OAM) states. These states belong to pairs of bases that are mutually unbiased on a sequence of two-dimensional subspaces of the full Hilbert space, but the vectors within the same basis are not necessarily orthogonal to each other. Over multiple trials, this method allows distinguishing OAM eigenstates from superpositions of multiple such eigenstates. Variations of the same method are then shown to be capable of preparing and detecting arbitrary linear combinations of states in Hilbert space. One further variation allows the construction of chains of states obeying recurrence relations on the Hilbert space itself, opening a new range of possibilities for more abstract information-coding algorithms to be carried out experimentally in a simple manner. Among other applications, we show that this approach provides a simplified means of switching between pairs of high-dimensional mutually unbiased OAM bases

Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late