Orbit Spaces of Gradient Vector Fields

We study orbit spaces of generalized gradient vector fields for Morse functions. Typically, these orbit spaces are non-Hausdorff. Nevertheless, they are quite structured topologically and are amenable to study. We show that these orbit spaces are locally contractible. We also show that the quotient map associated to each such orbit space is a weak homotopy equivalence and has the path lifting property.Comment: 16 pages, 4 figures; strengthened a main result (Corollary 3.5) and updated the introduction and the conclusio

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

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

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

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

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

Integrable theories and loop spaces: fundamentals, applications and new developments

We review our proposal to generalize the standard two-dimensional flatness construction of Lax-Zakharov-Shabat to relativistic field theories in d+1 dimensions. The fundamentals from the theory of connections on loop spaces are presented and clarified. These ideas are exposed using mathematical tools familiar to physicists. We exhibit recent and new results that relate the locality of the loop space curvature to the diffeomorphism invariance of the loop space holonomy. These result are used to show that the holonomy is abelian if the holonomy is diffeomorphism invariant. These results justify in part and set the limitations of the local implementations of the approach which has been worked out in the last decade. We highlight very interesting applications like the construction and the solution of an integrable four dimensional field theory with Hopf solitons, and new integrability conditions which generalize BPS equations to systems such as Skyrme theories. Applications of these ideas leading to new constructions are implemented in theories that admit volume preserving diffeomorphisms of the target space as symmetries. Applications to physically relevant systems like Yang Mills theories are summarized. We also discuss other possibilities that have not yet been explored.Comment: 64 pages, 8 figure