Harmonic Labeling of Graphs

Which graphs admit an integer value harmonic function which is injective and surjective onto $\Z$? Such a function, which we call harmonic labeling, is constructed when the graph is the $\Z^2$ square grid. It is shown that for any finite graph $G$ containing at least one edge, there is no harmonic labeling of $G \times \Z$

Monopoles and Solitons in Fuzzy Physics

Monopoles and solitons have important topological aspects like quantized fluxes, winding numbers and curved target spaces. Naive discretizations which substitute a lattice of points for the underlying manifolds are incapable of retaining these features in a precise way. We study these problems of discrete physics and matrix models and discuss mathematically coherent discretizations of monopoles and solitons using fuzzy physics and noncommutative geometry. A fuzzy sigma-model action for the two-sphere fulfilling a fuzzy Belavin-Polyakov bound is also put forth.Comment: 17 pages, Latex. Uses amstex, amssymb.Spelling of the name of one Author corrected. To appear in Commun.Math.Phy

The suppression of electron correlations in the collapsed tetragonal phase of CaFe2As2 under ambient pressure demonstrated by 75As NMR-NQR measurements

The static and the dynamic spin correlations in the low temperature collapsed tetragonal and the high temperature tetragonal phase in CaFe2As2 have been investigated by 75As nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements. Through the temperature (T) dependence of the nuclear spin lattice relaxation rates (1/T1) and the Knight shifts, although stripe-type antiferromagnetic (AFM) spin correlations are realized in the high temperature tetragonal phase, no trace of the AFM spin correlations can be found in the non-superconducting, low temperature, collapsed tetragonal (cT) phase. Given that there is no magnetic broadening in 75As NMR spectra, together with the T-independent behavior of magnetic susceptibility (x) and the T dependence of 1/T1Tx, we conclude that Fe spin correlations are completely quenched statically and dynamically in the non-superconducting cT phase in CaFe2As2.Comment: 5 pages, 4 figures, submitted to PR

Trisecant Lemma for Non Equidimensional Varieties

The classic trisecant lemma states that if $X$ is an integral curve of \PP^3 then the variety of trisecants has dimension one, unless the curve is planar and has degree at least 3, in which case the variety of trisecants has dimension 2. In this paper, our purpose is first to present another derivation of this result and then to introduce a generalization to non-equidimensional varities. For the sake of clarity, we shall reformulate our first problem as follows. Let $Z$ be an equidimensional variety (maybe singular and/or reducible) of dimension $n$, other than a linear space, embedded into \PP^r, $r \geq n+1$. The variety of trisecant lines of $Z$, say $V_{1,3}(Z)$, has dimension strictly less than $2n$, unless $Z$ is included in a $(n+1)-$dimensional linear space and has degree at least 3, in which case $\dim(V_{1,3}(Z)) = 2n$. Then we inquire the more general case, where $Z$ is not required to be equidimensional. In that case, let $Z$ be a possibly singular variety of dimension $n$, that may be neither irreducible nor equidimensional, embedded into \PP^r, where $r \geq n+1$, and $Y$ a proper subvariety of dimension $k \geq 1$. Consider now $S$ being a component of maximal dimension of the closure of \{l \in \G(1,r) \vtl \exists p \in Y, q_1, q_2 \in Z \backslash Y, q_1,q_2,p \in l\}. We show that $S$ has dimension strictly less than $n+k$, unless the union of lines in $S$ has dimension $n+1$, in which case $dim(S) = n+k$. In the latter case, if the dimension of the space is stricly greater then $n+1$, the union of lines in $S$ cannot cover the whole space. This is the main result of our work. We also introduce some examples showing than our bound is strict

A deep photometric survey of the eta Chamaeleontis cluster down to the brown dwarf - planet boundary

We report the outcome of the deep optical/infrared photometric survey of the central region (33 X 33 arcmin or 0.9 pc^2) of the eta Chamaeleontis pre-main sequence star cluster. The completeness limits of the photometry are I = 19.1, J = 18.2 and H = 17.6; faint enough to reveal low mass members down to the brown dwarf and planet boundary of ~ 13 M_Jup. We found no such low mass members in this region. Our result combined with a previous shallower (I = 17) but larger area survey indicates that low mass objects (0.013 < M/M(solar mass) < 0.075) either were not created in the eta Cha cluster or were lost due to the early dynamical history of the cluster and ejected to outside the surveyed areas.Comment: 5 pages with 4 figures, accepted by MNRA

Pilot Open Case Series of Voice over Internet Protocol-Delivered Assessment and Behavior Therapy for Chronic Tic Disorders

Comprehensive Behavioral Intervention for Tics (CBIT) is an efficacious treatment for children with chronic tic disorders (CTDs). Nevertheless, many families of children with CTDs are unable to access CBIT due to a lack of adequately trained treatment providers, time commitment, and travel distance. This study established the interrater reliability between in-person and Voice over Internet Protocol (VoIP) administrations of the Yale Global Tic Severity Scale (YGTSS), and examined the preliminary efficacy, feasibility, and acceptability of VoIP-delivered CBIT for reducing tics in children with CTDs in an open case series. Across in-person and VoIP administrations of the YGTSS, results showed mean agreement of 91%, 96%, and 95% for motor, phonic, and total tic severity subscales. In the pilot feasibility study, 4 children received 8 weekly sessions of CBIT via VoIP and were assessed at pre- and posttreatment by an independent evaluator. Results showed a 29.44% decrease in clinician-rated tic severity from pre- to posttreatment on the YGTSS. Two of the 4 patients were considered treatment responders at posttreatment, using Clinical Global Impressions–Improvement ratings. Therapeutic alliance, parent and child treatment satisfaction, and videoconferencing satisfaction ratings were high. CBIT was considered feasible to implement via VoIP, although further testing is recommended