A Polyakov formula for sectors

We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to a conformal deformation in the direction of a conformal factor with a logarithmic singularity at the origin. We compute explicitly all the contributions to this formula coming from the different parts of the sector. In the process, we obtain an explicit expression for the heat kernel on an infinite area sector using Carslaw-Sommerfeld's heat kernel. We also compute the zeta-regularized determinant of rectangular domains of unit area and prove that it is uniquely maximized by the square.Comment: 51 pages, 2 figures. Major modification of Lemma 4, it was revised and corrected. Other small misprints were corrected. Accepted for publication in The Journal of Geometric Analysi

Polyakov formulas for conical singularities in two dimensions

We investigate the zeta-regularized determinant and its variation in the presence of conical singularities, boundaries, and corners. For surfaces with isolated conical singularities which may also have one or more smooth boundary components, we demonstrate both a variational Polyakov formula as well as an integrated Polyakov formula for the conformal variation of the Riemannian metric with conformal factors which are smooth up to all singular points and boundary components. We demonstrate the analogous result for curvilinear polygonal domains in surfaces. We then specialize to finite circular sectors and cones and via two independent methods obtain variational Polyakov formulas for the dependence of the determinant on the opening angle. Notably, this requires the conformal factor to be logarithmically singular at the vertex. Although these formulas look quite different, we prove that they are indeed equal. We further obtain explicit formulas for the determinant for finite circular sectors and cones

Female Correctional Workers:Perceptions of Sexual Abuse Training

Offenders return to the community after having been sexually abused by those who have been entrusted with the responsibility to protect them. The phenomenon of staff-on-inmate sexual abuse has become problematic within the criminal justice system. Research on the topic of sexual abuse in penal institutions reveals a lack of information pertaining to staff-on-inmate sexual abuse, and how correctional workers are trained in that area. Female correctional staff have been implicated in more incidences of staff-on-inmate sexual abuse than their male counterparts. The purpose of this phenomenological study was to explore sexual abuse training received by female correctional staff who were employed in a Mid Atlantic pre-release center, and to examine their perceptions of that training. The study was centered around the Thomas Theorem adopted by William Isaac Thomas. That theory postulates that an individuals\u27 actions are based on how they perceive a situation. Two research questions were addressed relating to sexual abuse training and perceptions of training. Semi-structured interviews were conducted which provided participants with an opportunity to express and describe new ideas relating to the topic. Data were analyzed using the Interpretive Phenomenological Analysis system because of its ability to address subjectivity. This research has revealed that sexual abuse training is developed for correctional staff as a collective and does not differentiate with respect to gender. In addition, it was concluded that correctional staff sexual abuse training lacks intensity and depth in terms of information disseminated. The results of this research will provide criminal justice scholars with information that could prove useful in future studies on the topic of staff -on-inmate sexual abuse

Role of gamma-aminobutyric acid type A (GABAA) receptor subtypes in acute benzodiazepine physical dependence-like effects: evidence from squirrel monkeys responding under a schedule of food presentation.

RATIONALE: Assays of schedule-controlled responding can be used to characterize the pharmacology of benzodiazepines and other GABAA receptor modulators, and are sensitive to changes in drug effects that are related to physical dependence. OBJECTIVE: The present study used this approach to investigate the role of GABAA receptor subtypes in mediating dependence-like effects following benzodiazepine administration. METHODS: Squirrel monkeys (n = 6) were trained on a fixed-ratio schedule of food reinforcement. Initially, the response rate-decreasing effects of chlordiazepoxide (0.1-10 mg/kg; nonselective GABAA receptor agonist), zolpidem (0.032-1.0 mg/kg; α1 subunit-containing GABAA subtype-preferring agonist), and HZ-166 (0.1-10 mg/kg; functionally selective α2 and α3 subunit-containing GABAA receptor agonist) were assessed. Next, acute dependence-like effects following single injections of chlordiazepoxide, zolpidem, and HZ-166 were assessed with flumazenil (0.1-3.2 mg/kg; nonselective GABAA receptor antagonist). Finally, acute dependence-like effects following zolpidem administration were assessed with βCCt and 3-PBC (0.1-3.2 mg/kg and 0.32-10 mg/kg, respectively; α1 subunit-containing GABAA receptor antagonists). RESULTS: Chlordiazepoxide, zolpidem, and HZ-166 produced dose- and time-dependent decreases in response rates, whereas flumazenil, βCCT, and 3-PBC were ineffective. After the drug effects waned, flumazenil produced dose-dependent decreases in response rates following administration of 10 mg/kg chlordiazepoxide and 1.0 mg/kg zolpidem, but not following any dose of HZ-166. Further, both βCCT and 3-PBC produced dose-dependent decreases in response rates when administered after 1.0 mg/kg zolpidem. CONCLUSIONS: These data raise the possibility that α1 subunit-containing GABAA receptors play a major role in physical dependence-related behaviors following a single injection of a benzodiazepine

The fundamental gap of simplices

The fundamental gap conjecture was recently proven by Andrews and Clutterbuck: for any convex domain in $\R^n$ normalized to have unit diameter, the difference between the first two Dirichlet eigenvalues of the Laplacian is bounded below by that of the interval. In this work, we focus on the moduli spaces of simplices in all dimensions, and later specialize to the moduli space of Euclidean triangles. Our first theorem is a compactness result for the gap function on the moduli space of simplices in any dimension. Our second main result verifies a recent conjecture of Antunes-Freitas: for any Euclidean triangle normalized to have unit diameter, the fundamental gap is uniquely minimized by the equilateral triangle.Comment: Final version, Journal ref adde

Battery-Flywheel Hybrid Electric Power System for Near Term Application. Volume 2. System Design.

This is the second of two volumes which document the result of an investigation of Battery-Flywheel Power Systems

Biogeography of the Intestinal Mucosal and Lumenal Microbiome in the Rhesus Macaque

SummaryThe gut microbiome is widely studied by fecal sampling, but the extent to which stool reflects the commensal composition at intestinal sites is poorly understood. We investigated this relationship in rhesus macaques by 16S sequencing feces and paired lumenal and mucosal samples from ten sites distal to the jejunum. Stool composition correlated highly with the colonic lumen and mucosa and moderately with the distal small intestine. The mucosal microbiota varied most based on location and was enriched in oxygen-tolerant taxa (e.g., Helicobacter and Treponema), while the lumenal microbiota showed inter-individual variation and obligate anaerobe enrichment (e.g., Firmicutes). This mucosal and lumenal community variability corresponded to functional differences, such as nutrient availability. Additionally, Helicobacter, Faecalibacterium, and Lactobacillus levels in stool were highly predictive of their abundance at most other gut sites. These results quantify the composition and biogeographic relationships between gut microbial communities in macaques and support fecal sampling for translational studies

Hydrochloride Salt of the GABAkine KRM-II-81

Imidazodiazepine (5-(8-ethynyl-6-(pyridin-2-yl)-4H-benzo[f]imidazole[1,5-α][1,4]diazepin-3-yl) oxazole or KRM-II-81) is a potentiator of GABAA receptors (a GABAkine) undergoing preparation for clinical development. KRM-II-81 is active against many seizure and pain models in rodents, where it exhibits improved pharmacological properties over standard-of-care agents. Since salts can be utilized to create opportunities for increased solubility, enhanced absorption, and distribution, as well as for efficient methods of bulk synthesis, a hydrochloride salt of KRM-II-81 was prepared. KRM-II-81·HCl was produced from the free base with anhydrous hydrochloric acid. The formation of the monohydrochloride salt was confirmed by X-ray crystallography, as well as 1H NMR and 13C NMR analyses. High water solubility and a lower partition coefficient (octanol/water) were exhibited by KRM-II-81·HCl as compared to the free base. Oral administration of either KRM-II-81·HCl or the free base resulted in high concentrations in the brain and plasma of rats. Oral dosing in mice significantly increased the latency to both clonic and tonic convulsions and decreased pentylenetetrazol-induced lethality. The increased water solubility of the HCl salt enables intravenous dosing and the potential for higher concentration formulations compared with the free base without impacting anticonvulsant potency. Thus, KRM-II-81·HCl adds an important new compound to facilitate the development of these imidazodiazepines for clinical evaluation

Search for α3β2/3γ2 subtype selective ligands that are stable on human liver microsomes

Selective modulation of specific benzodiazepine receptor (BzR) gamma amino butyric acid-A (GABAA) receptor ion channels has been identified as an important method for separating out the variety of pharmacological effects elicited by BzR-related drugs. Importantly, it has been demonstrated that both α2β(2/3)γ2 (α2BzR) and α3BzR (and/or α2/α3) BzR subtype selective ligands exhibit anxiolytic effects with little or no sedation. Previously we have identified several such ligands; however, three of our parent ligands exhibited significant metabolic liability in rodents in the form of a labile ester group. Here eight analogs are reported which were designed to circumvent this liability by utilizing a rational replacement of the ester moiety based on medicinal chemistry precedents. In a metabolic stability study using human liver microsomes, four compounds were found to undergo slower metabolic transformation, as compared to their corresponding ester analogs. These compounds were also evaluated in in vitro binding as well as efficacy assays. Additionally, bioisostere 11 was evaluated in a rodent model of anxiety. It exhibited anxiolytic activity at doses of 10 and 100 mg/kg and was devoid of sedative properties

Anxiolytic-like effects of 8-acetylene imidazobenzodiazepines in a rhesus monkey conflict procedure

Conflict procedures can be used to study the receptor mechanisms underlying the anxiolytic effects of benzodiazepines and other GABAA receptor modulators. In the present study, we first determined the efficacy and binding affinity of the benzodiazepine diazepam and recently synthesized GABAA receptor modulators JY-XHe-053, XHe-II-053, HZ-166, SH-053-2'F-S-CH3 and SH-053-2'F-R-CH3 at GABAA receptors containing α1, α2, α3 and α5 subunits. Results from these studies suggest that each compound displayed lower efficacy at GABAA receptors containing α1 subunits and varying degrees of efficacy and affinity at GABAA receptors containing α2, α3 and α5 subunits. Next, we assessed their anxiolytic effects using a rhesus monkey conflict procedure in which behavior was maintained under a fixed-ratio schedule of food delivery in the absence (non-suppressed responding) and presence (suppressed responding) of response-contingent electric shock. Relatively non-selective compounds, such as diazepam and JY-XHe-053 produced characteristic increases in rates of suppressed responding at low to intermediate doses and decreased the average rates of non-suppressed responding at higher doses. XHe-II-053 and HZ-166 also produced increases in suppressed responding at low to intermediate doses, but were ineffective at decreasing rates of non-suppressed responding, consistent with their relatively low efficacy at GABAA receptors containing α1 and α5 subunits. In contrast, SH-053-2’F-S-CH3 and SH-053-2’F-R-CH3 produced only partial increases in suppressed responding and were ineffective on non-suppressed responding, consistent with their profiles as partial agonists at GABAA receptors containing α2, α3 and α5 subunits. These behavioral effects suggest that the anxiolytic and rate-reducing effects of GABAA receptor positive modulators are dependent on their relative efficacy and affinity at different GABAA receptor subtypes