Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\lambda$ is obtained for all $\lambda \in \mathfrak a^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\lambda$ away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The $L^p$-theory for the hypergeometric Fourier transform is developed for $0<p<2$. In particular, an inversion formula is proved when $1\leq p <2$

Disordered social media use and risky drinking in young adults:Differential associations with addiction-linked traits

Background Excessive or compulsive use of social media has been likened to an addiction, similar to other behavioural addictions such as pathological gambling or Internet addiction. This investigation sought to determine the degree to which personality traits associated with such disordered social media use overlap with those known to predict problematic substance use, with use of the most commonly abused legal substance alcohol as an example of the latter. Method Well‐known indices of disordered social media use, risky or problematic alcohol use, and the personality traits alexithymia, reward sensitivity, narcissism, and impulsivity were administered online to 143 men and women aged 18–35-years who were regular users of social media. The traits examined had previously been linked to substance misuse for a variety of substances, including alcohol, as presumed predisposing factors. Results After controlling for age, gender, and social desirability in hierarchical regressions, disordered social media use was predicted by narcissism, reward sensitivity, and impulsivity, whereas risky alcohol use was predicted by narcissism, alexithymia, and impulsivity. The ability of narcissism to predict disordered social media use was mediated by reward sensitivity, which was not the case for risky drinking. Conclusions Present results point to similarities and differences in addiction‐linked traits when comparing disordered social media use to risky or problematic substance use

struc2vec: Learning Node Representations from Structural Identity

Structural identity is a concept of symmetry in which network nodes are identified according to the network structure and their relationship to other nodes. Structural identity has been studied in theory and practice over the past decades, but only recently has it been addressed with representational learning techniques. This work presents struc2vec, a novel and flexible framework for learning latent representations for the structural identity of nodes. struc2vec uses a hierarchy to measure node similarity at different scales, and constructs a multilayer graph to encode structural similarities and generate structural context for nodes. Numerical experiments indicate that state-of-the-art techniques for learning node representations fail in capturing stronger notions of structural identity, while struc2vec exhibits much superior performance in this task, as it overcomes limitations of prior approaches. As a consequence, numerical experiments indicate that struc2vec improves performance on classification tasks that depend more on structural identity.Comment: 10 pages, KDD2017, Research Trac

Numerical computation of the beta function of large N SU(N) gauge theory coupled to an adjoint Dirac fermion

We use a single site lattice in four dimensions to study the scaling of large N Yang-Mills field coupled to a single massless Dirac fermion in the adjoint representation. We use the location of the strong to weak coupling transition defined through the eigenvalues of the folded Wilson loop operator to set a scale. We do not observe perturbative scaling in the region studied in this paper. Instead, we observe that the scale changes very slowly with the bare coupling. The lowest eigenvalue of the overlap Dirac operator is another scale that shows similar behavior as a function of the lattice coupling. We speculate that this behavior is due to the beta function appoaching close to a zero.Comment: 16 pages, 9 figures, revised version DOES NOT match the published version in Physical Review

Two dimensional fermions in three dimensional YM

Dirac fermions in the fundamental representation of SU(N) live on the surface of a cylinder embedded in $R^3$ and interact with a three dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the circumference of the cylinder is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit at a typical bulk scale. Replacing three dimensional YM by four dimensional YM introduces non-trivial renormalization effects.Comment: 21 pages, 7 figures, 5 table

Effect of Apex Locator and Electronic Pulp Tester on Pacemaker Function: An In Vitro study

This study evaluated the potential for interference of electronic pulp tester, electronic apex locators and diathermy with pacemaker function. Dental Instruments used. Apex locators: 1. Root ZX (J Morita Corp., Japan), 2. Propex (Dentsply Maillefer, Ballaigues, Switzerland), 3. Mini Apex locator (SybronEndo, Anaheim, CA, USA). Pulp tester: 1. Parkell pulp vitality tester (Farmingdale, NY, USA). Diathermy: 1. Neomed 250 B Pacing system used: 1. Medtronic (KVDD901. The study design consisted of directly connecting the pacemaker lead, EAL, and oscilloscope across a 150-ohm resistor. With the electronic apex locator/ electronic pulp tester/diathermy operating on a flat bench top, the telemetry wand was held directly over the pacemaker to monitor the pacing pattern for a period of 30 s. A negative control was conducted with the pacemaker alone. Pacemaker activity was continuously recorded on the EGM printout of the telemetric programmer. These recordings were then examined for pacer inhibition, noise reversion or inappropriate pacemaker pulses. CONCLUSION: From the results of the present study, it may be concluded, 1. The tested Electronic Apex Locators Root ZX (J Morita Corp., Japan), Propex (Dentsply Maillefer, Ballaigues, Switzerland), Sybron Endo mini (SybronEndo, Anaheim, CA, USA) do not interfere with cardiac pacemaker function. 2. The tested Electric pulp tester, Parkell pulp vitality tester (Farmingdale, NY, USA) does not interfere with cardiac pacemaker function. 3. The results show that the use of Diathermy (Neomed 250 B) interfered with the normal pacing, leading to complete inhibition of the pacing system. Manufacturers of EALs continue to warn against the use of their devices in patients with cardiac pacemakers despite the absence of evidence to support such claims. Although they may possess bench test data similar to those shown above, the lack of clinical data would make it difficult to obtain FDA approval for the devices without such warnings. Human trials are needed to clarify this issue

Chiral Symmetry Restoration in the Schwinger Model with Domain Wall Fermions

Domain Wall Fermions utilize an extra space time dimension to provide a method for restoring the regularization induced chiral symmetry breaking in lattice vector gauge theories even at finite lattice spacing. The breaking is restored at an exponential rate as the size of the extra dimension increases. Before this method can be used in dynamical simulations of lattice QCD, the dependence of the restoration rate to the other parameters of the theory and, in particular, the lattice spacing must be investigated. In this paper such an investigation is carried out in the context of the two flavor lattice Schwinger model.Comment: LaTeX, 37 pages including 18 figures. Added comments regarding power law fitting in sect 7. Also, few changes were made to elucidate the content in sect. 5.1 and 5.3. To appear in Phys. Rev.

X-ray Near Field Speckle: Implementation and Critical Analysis

We have implemented the newly-introduced, coherence-based technique of x-ray near-field speckle (XNFS) at 8-ID-I at the Advanced Photon Source. In the near field regime of high-brilliance synchrotron x-rays scattered from a sample of interest, it turns out, that, when the scattered radiation and the main beam both impinge upon an x-ray area detector, the measured intensity shows low-contrast speckles, resulting from interference between the incident and scattered beams. We built a micrometer-resolution XNFS detector with a high numerical aperture microscope objective and demonstrate its capability for studying static structures and dynamics at longer length scales than traditional far field x-ray scattering techniques. Specifically, we characterized the structure and dynamics of dilute silica and polystyrene colloidal samples. Our study reveals certain limitations of the XNFS technique, which we discuss.Comment: 53 pages, 16 figure