Specular sets

We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract generalization of the natural codings of linear involutions. We prove several results concerning the subgroups generated by return words and by maximal bifix codes in these sets.Comment: arXiv admin note: substantial text overlap with arXiv:1405.352

New holomorphically closed subalgebras of C∗C^*-algebras of hyperbolic groups

We construct dense, unconditional subalgebras of the reduced group $C^*$-algebra of a word-hyperbolic group, which are closed under holomorphic functional calculus and possess many bounded traces. Applications to the cyclic cohomology of group $C^*$-algebras and to delocalized $L^2$-invariants of negatively curved manifolds are given

Polynomial growth of volume of balls for zero-entropy geodesic systems

The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{pol}$} and the {\em weak polynomial entropy $h_{pol}^*$}. Both are infinite when the topological entropy is positive and they satisfy $h_{pol}^*\leq h_{pol}$. We first prove that the growth rate of the volume of balls is bounded above by means of the strong polynomial entropy and we show that for the flat torus this inequality becomes an equality. We then study the explicit example of the torus of revolution for which we can give an exact asymptotic equivalent of the growth rate of volume of balls, which we relate to the weak polynomial entropy.Comment: 22 page

Property (RD) for Hecke pairs

As the first step towards developing noncommutative geometry over Hecke C*-algebras, we study property (RD) (Rapid Decay) for Hecke pairs. When the subgroup H in a Hecke pair (G,H) is finite, we show that the Hecke pair (G,H) has (RD) if and only if G has (RD). This provides us with a family of examples of Hecke pairs with property (RD). We also adapt Paul Jolissant's works in 1989 to the setting of Hecke C*-algebras and show that when a Hecke pair (G,H) has property (RD), the algebra of rapidly decreasing functions on the set of double cosets is closed under holomorphic functional calculus of the associated (reduced) Hecke C*-algebra. Hence they have the same K_0-groups.Comment: A short note added explaining other methods to prove that the subalgebra of rapidly decreasing functions is smooth. This is the final version as published. The published version is available at: springer.co

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

On the complexity of some birational transformations

Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions

C*-simplicity and the unique trace property for discrete groups

In this paper, we introduce new methods for working with group and crossed product C*-algebras that allow us to settle the longstanding open problem of characterizing groups with the unique trace property

Optimizing quantum process tomography with unitary 2-designs

We show that weighted unitary 2-designs define optimal measurements on the system-ancilla output state for ancilla-assisted process tomography of unital quantum channels. Examples include complete sets of mutually unbiased unitary-operator bases. Each of these specifies a minimal series of optimal orthogonal measurements. General quantum channels are also considered.Comment: 28 page

Testing for allergic disease: Parameters considered and test value

<p>Abstract</p> <p>Background</p> <p>Test results for allergic disease are especially valuable to allergists and family physicians for clinical evaluation, decisions to treat, and to determine needs for referral.</p> <p>Methods</p> <p>This study used a repeated measures design (conjoint analysis) to examine trade offs among clinical parameters that influence the decision of family physicians to use specific IgE blood testing as a diagnostic aid for patients suspected of having allergic rhinitis. Data were extracted from a random sample of 50 family physicians in the Southeastern United States. Physicians evaluated 11 patient profiles containing four clinical parameters: symptom severity (low, medium, high), symptom length (5, 10, 20 years), family history (both parents, mother, neither), and medication use (prescribed antihistamines, nasal spray, over-the-counter medications). Decision to recommend specific IgE testing was elicited as a "yes" or "no" response. Perceived value of specific IgE blood testing was evaluated according to usefulness as a diagnostic tool compared to skin testing, and not testing.</p> <p>Results</p> <p>The highest odds ratios (OR) associated with decisions to test for allergic rhinitis were obtained for symptom severity (OR, 12.11; 95%CI, 7.1–20.7) and length of symptoms (OR, 1.46; 95%CI, 0.96–2.2) with family history having significant influence in the decision. A moderately positive association between testing issues and testing value was revealed (β = 0.624, <it>t </it>= 5.296, <it>p </it>≤ 0.001) with 39% of the variance explained by the regression model.</p> <p>Conclusion</p> <p>The most important parameters considered when testing for allergic rhinitis relate to symptom severity, length of symptoms, and family history. Family physicians recognize that specific IgE blood testing is valuable to their practice.</p

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy