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

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

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

Solid-state photochemistry of molecular photo-switchable species:the role of photocrystallographic techniques

Over the last 30 years, the single-crystal photocrystallographic technique has been developed to determine the three-dimensional crystal and mol­ecular structures of metastable species which have been generated in the crystal photochemically. Transition-metal complexes that have been investigated using this methodology include complexes that contain nitrosyl, di­nitro­gen, sulfur dioxide and nitrite ligands, all of which form new linkage isomers in the solid state when photoactivated by light of the appropriate wavelength. Both steric and electronic factors determine the level of the conversion from the ground-state structure to the metastable isomeric structure, and both the `reaction cavity' size and the nature of the inter­molecular inter­actions are shown to be among the key factors that influence the percentage conversion

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

Midcourse Corrections and Life Satisfaction in a Sample of Mid-Career Doctoral Students

The focus of this study was to examine motivations and reactions in context of a midlife decision to seek a doctoral degree. Participants were 116 non-traditional age, men and women graduate students and recent alumni from one of three geographically distributed and blended delivery model doctoral programs. Demographic information was collected, including career history and goals, age, gender, and ethnicity. The mean and median ages were between 41 and 50. The research questionnaire featured narrative questions regarding “midcourse corrections,” any experienced trauma, and life satisfactions. Autobiographical material was also analyzed thematically, providing further illustrative examples of the midlife experiences in the course of negotiating a doctoral education. Both the narrative responses and autobiographies were analyzed using content analysis (Ryan & Bernard, 2000). Forty-four percent of the sample reported seeking the doctoral degree as part of a career change plan, while 56% sought to achieve an advanced degree in their current fields. Despite a high rate of reported regret, surprise, and even trauma, considerable life satisfaction (91%) was reported as the result of seeking doctoral education in midlife, by definition a “midcourse correction.

Metabolic Energy Correlates of Heart Rate Variability Spectral Power Associated with a 900-Calorie Challenge

We studied healthy males challenged with a 900 Cal test beverage and correlated EE with the raw (ms2) and normalized units (nu) of total power (TP), low frequency/high frequency (LF/HF) and VLF spectral power of heart rate variability (HRV). The correlations were evaluated during 20 min of normal breathing (NB, control) and 20 min of paced breathing (PB) at 12 breaths·min−1 (0.2 Hz). EE was not significantly correlated with any of the HRV variables before the metabolic challenge. After the challenge, EE was positively correlated with LF/HF and with VLF; VLF was also positively correlated with LF/HF during both NB and PB. These findings suggest that EE may be a correlate of LF/HF and of VLF spectral power of HRV in healthy adolescent/young adult males. The association of lower resting energy expenditure with lower amounts of VLF spectral power may occur in individuals with predilections for obese phenotypes

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

Technical Note: Molecular characterization of aerosol-derived water soluble organic carbon using ultrahigh resolution electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry

Despite the acknowledged relevance of aerosol-derived water-soluble organic carbon (WSOC) to climate and biogeochemical cycling, characterization of aerosol WSOC has been limited. Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR MS) was utilized in this study to provide detailed molecular level characterization of the high molecular weight (HMW; m/z>223) component of aerosol-derived WSOC collected from rural sites in Virginia and New York, USA. More than 3000 peaks were detected by ESI FT-ICR MS within a m/z range of 223–600 for each sample. Approximately 86% (Virginia) and 78% (New York) of these peaks were assigned molecular formulas using only carbon (C), hydrogen (H), oxygen (O), nitrogen (N), and sulfur (S) as elemental constituents. H/C and O/C molar ratios were plotted on van Krevelen diagrams and indicated a strong contribution of lignin-like and lipid-like compounds to the aerosol-derived WSOC samples. Approximately 1–4% of the peaks in the aerosol-derived WSOC mass spectra were classified as black carbon (BC) on the basis of double bond equivalents calculated from the assigned molecular formulas. In addition, several high-magnitude peaks in the mass spectra of samples from both sites corresponded to molecular formulas proposed in previous secondary organic aerosol (SOA) laboratory investigations indicating that SOAs are important constituents of the WSOC. Overall, ESI FT-ICR MS provides a level of resolution adequate for detailed compositional and source information of the HMW constituents of aerosol-derived WSOC