Schrijver graphs and projective quadrangulations

In a recent paper [J. Combin. Theory Ser. B}, 113 (2015), pp. 1-17], the authors have extended the concept of quadrangulation of a surface to higher dimension, and showed that every quadrangulation of the $n$-dimensional projective space $P^n$ is at least $(n+2)$-chromatic, unless it is bipartite. They conjectured that for any integers $k\geq 1$ and $n\geq 2k+1$, the Schrijver graph $SG(n,k)$ contains a spanning subgraph which is a quadrangulation of $P^{n-2k}$. The purpose of this paper is to prove the conjecture

Analyzing Morton's Typology of Service Paradigms and Integrity

Research on college students found limited support for Morton’s (1995) hypothesis that students have a preference for one distinct type of service orientation (i.e., charity, project, social change). The findings did replicate previous findings that college students prefer the charity paradigm. A measure of integrity was developed and two dimensions were identified that possessed distinct correlates. As Morton predicted, as the degree of integrity increased the preference for a distinct type of service became blurred, suggesting that developing integrity should be an intentional educational goal and it might be aided by exposing students to all three approaches to community service. Implications for service-learning educators are discussed

Quantized Response and Topology of Insulators with Inversion Symmetry

We study three dimensional insulators with inversion symmetry, in which other point group symmetries, such as time reversal, are generically absent. Their band topology is found to be classified by the parities of occupied states at time reversal invariant momenta (TRIM parities), and by three Chern numbers. The TRIM parities of any insulator must satisfy a constraint: their product must be +1. The TRIM parities also constrain the Chern numbers modulo two. When the Chern numbers vanish, a magneto-electric response parameterized by "theta" is defined and is quantized to theta= 0, 2pi. Its value is entirely determined by the TRIM parities. These results may be useful in the search for magnetic topological insulators with large theta. A classification of inversion symmetric insulators is also given for general dimensions. An alternate geometrical derivation of our results is obtained by using the entanglement spectrum of the ground state wave-function.Comment: 12 pages main text; 12 pages appendices; 11 figures. Added new refs. in 2nd versio

Quantum statistics on graphs

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of abelian statistics for two particles. In spite of the fact that graphs are locally one-dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs -- equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molecular physics.Comment: 21 pages, 6 figure

An infinite genus mapping class group and stable cohomology

We exhibit a finitely generated group \M whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface \su of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus $g$ with $n$ boundary components, for any $g\geq 0$ and $n>0$. We construct a representation of \M into the restricted symplectic group ${\rm Sp_{res}}({\cal H}_r)$ of the real Hilbert space generated by the homology classes of non-separating circles on \su, which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first universal Chern class in H^2(\M,\Z) is the pull-back of the Pressley-Segal class on the restricted linear group ${\rm GL_{res}}({\cal H})$ via the inclusion ${\rm Sp_{res}}({\cal H}_r)\subset {\rm GL_{res}}({\cal H})$.Comment: 14p., 8 figures, to appear in Commun.Math.Phy

What is the value of short? Exploring the benefits of episodic volunteer experiences for college students

This exploratory study is designed to understand the civic outcomes (e.g., civic-mindedness, intentions to volunteer in the future, and intentions to donate money in the future) for college students who participate in a “Day of Service”. Understanding civic outcomes for college student episodic volunteers helps to justify the investment of staff time devoted to planning and implementing short-term volunteer events by both campus and community-based organizations

Inverse monoids and immersions of 2-complexes

It is well known that under mild conditions on a connected topological space $\mathcal X$, connected covers of $\mathcal X$ may be classified via conjugacy classes of subgroups of the fundamental group of $\mathcal X$. In this paper, we extend these results to the study of immersions into 2-dimensional CW-complexes. An immersion $f : {\mathcal D} \rightarrow \mathcal C$ between CW-complexes is a cellular map such that each point $y \in {\mathcal D}$ has a neighborhood $U$ that is mapped homeomorphically onto $f(U)$ by $f$. In order to classify immersions into a 2-dimensional CW-complex $\mathcal C$, we need to replace the fundamental group of $\mathcal C$ by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex

S-duality in N=1 orientifold SCFTs

We present a general solution to the problem of determining all S-dual descriptions for a specific (but very rich) class of urn:x-wiley:00158208:media:prop201700013:prop201700013-math-0003 SCFTs. These SCFTs are indexed by decorated toric diagrams, and can be engineered in string theory by probing orientifolds of isolated toric singularities with D3 branes. The S-dual phases are described by quiver gauge theories coupled to specific types of conformal matter which we describe explicitly. We illustrate our construction with many examples, including S-dualities in previously unknown SCFTs

Explicit expressions for the topological defects of spinor Bose-Einstein condensates

In this paper we first derive a general method which enables one to create expressions for vortices and monopoles. By using this method we construct several order-parameters describing the vortices and monopoles of Bose-Einstein condensates with hyperfine spin F=1 and F=2. We concentrate on defects which are topologically stable in the absence of an external magnetic field. In particular we show that in a ferromagnetic condensate there can be a vortex which does not produce any superfluid flow. We also point out that the order-parameter space of the cyclic phase of F=2 condensate consists of two disconnected sets. Finally we examine the effect of an external magnetic field on the vortices of a ferromagnetic F=1 condensate and discuss the experimental preparation of a vortex in this system.Comment: 17 pages, partly rewritten to improve clarity, conclusions unchange

Differences in client and therapist views of the working alliance in drug treatment

Background - There is growing evidence that the therapeutic alliance is one of the most consistent predictors of retention and outcomes in drug treatment. Recent psychotherapy research has indicated that there is a lack of agreement between client, therapist and observer ratings of the therapeutic alliance; however, the clinical implications of this lack of consensus have not been explored. Aims - The aims of the study are to (1) explore the extent to which, in drug treatment, clients and counsellors agree in their perceptions of their alliance, and (2) investigate whether the degree of disagreement between clients and counsellors is related to retention in treatment. Methods - The study recruited 187 clients starting residential rehabilitation treatment for drug misuse in three UK services. Client and counsellor ratings of the therapeutic alliance (using the WAI-S) were obtained during weeks 1-12. Retention was in this study defined as remaining in treatment for at least 12 weeks. Results - Client and counsellor ratings of the alliance were only weakly related (correlations ranging from r = 0.07 to 0.42) and tended to become more dissimilar over the first 12 weeks in treatment. However, whether or not clients and counsellors agreed on the quality of their relationship did not influence whether clients were retained in treatment. Conclusions - The low consensus between client and counsellor views of the alliance found in this and other studies highlights the need for drug counsellors to attend closely to their clients' perceptions of the alliance and to seek regular feedback from clients regarding their feelings about their therapeutic relationship