Cohomogeneity one manifolds and selfmaps of nontrivial degree

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).Comment: v2, v3: minor improvement

On the singularity formation and relaxation to equilibrium in 1D Fokker–Planck model with superlinear drift

We consider a class of Fokker–Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite critical mass above which the measure minimising the associated entropy functional displays a singular component. Our approach, which addresses the one-dimensional case, is based on a reformulation of the problem in terms of the pseudo-inverse distribution function. Motivated by the structure of the equation in the new variables, we establish a general framework for global-in-time existence, uniqueness and regularity of monotonic viscosity solutions to a class of nonlinear degenerate (resp. singular) parabolic equations, using as a key tool comparison principles and maximum arguments. We then focus on a specific equation and study in more detail the regularity and dynamics of solutions. In particular, blow-up behaviour, formation of condensates (i.e. Dirac measures at zero) and long-time asymptotics are investigated. As a consequence, in the mass-supercritical case, solutions will blow up in L∞ in finite time and—understood in a generalised, measure sense—they will eventually have condensate. We further show that the singular part of the measure solution does in general interact with the density and that condensates can be transient. The equations considered are motivated by a model for bosons introduced by Kaniadakis and Quarati (1994), which has a similar entropy structure and a critical mass if d ≥ 3

Advancing Workplace Diversity Through the Culturally Responsive Teamwork Framework.

Purpose Diversification of the profession is an important element of combating racism, bias, and prejudice in the speech-language pathology workforce at national and systemic levels. However, national and systemic change needs to be combined with equipping individual speech-language pathologists to adapt to the challenges that they face to engaging in culturally responsive practice. This paper presents four interacting levels of practice within the Culturally Responsive Teamwork Framework (CRTF): (a) intrapersonal practices, (b) interpersonal practices, (c) intraprofessional practices, and (d) the interprofessional practices. Conclusion CRTF is a practical, strengths-based framework that draws on international research and expertise to expand personal and professional practice and describe critical behaviors within the workplace that can be used to promote principles of evidence-based practice and social justice, especially when working with people from nondominant cultural or linguistic groups

Amino acid coevolution reveals three-dimensional structure and functional domains of insect odorant receptors.

Insect odorant receptors (ORs) comprise an enormous protein family that translates environmental chemical signals into neuronal electrical activity. These heptahelical receptors are proposed to function as ligand-gated ion channels and/or to act metabotropically as G protein-coupled receptors (GPCRs). Resolving their signalling mechanism has been hampered by the lack of tertiary structural information and primary sequence similarity to other proteins. We use amino acid evolutionary covariation across these ORs to define restraints on structural proximity of residue pairs, which permit de novo generation of three-dimensional models. The validity of our analysis is supported by the location of functionally important residues in highly constrained regions of the protein. Importantly, insect OR models exhibit a distinct transmembrane domain packing arrangement to that of canonical GPCRs, establishing the structural unrelatedness of these receptor families. The evolutionary couplings and models predict odour binding and ion conduction domains, and provide a template for rationale structure-activity dissection

Neural mechanisms of surround attenuation and distractor competition in visual search

Visual attention biases relevant processing in the visual system by amplifying relevant or attenuating irrelevant sensory input. A potential signature of the latter operation, referred to as surround attenuation, has recently been identified in the electromagnetic brain response of human observers performing visual search. It was found that a zone of attenuated cortical excitability surrounds the target when the search required increased spatial resolution for item discrimination. Here we address the obvious hypothesis that surround attenuation serves distractor suppression in the vicinity of the target where interference from irrelevant search items is maximal. To test this hypothesis, surround attenuation was assessed under conditions when the target was presented in isolation versus when it was surrounded by distractors. Surprisingly, substantial and indistinguishable surround attenuation was seen under both conditions, indicating that it reflects an attentional operation independent of the presence of distractors. Adding distractors in the target's surround, however, increased the amplitude of the N2pc-an evoked response known to index distractor competition in visual search. Moreover, adding distractors led to a topographical change of source activity underlying the N2pc toward earlier extrastriate areas. In contrast, the topography of reduced source activity due to surround attenuation remained unaltered with and without distractors in the target's surround. We conclude that surround attenuation is not a direct consequence of the attenuation of distractors in visual search and that it dissociates from attentional operations reflected by the N2pc. A theoretical framework is proposed that links both operations in a common model of top-down attentional selection in visual cortex

Cutting the same fraction of several measures

We study some measure partition problems: Cut the same positive fraction of $d+1$ measures in $\mathbb R^d$ with a hyperplane or find a convex subset of $\mathbb R^d$ on which $d+1$ given measures have the same prescribed value. For both problems positive answers are given under some additional assumptions.Comment: 7 pages 2 figure

Minimal surfaces and particles in 3-manifolds

We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic, anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these manifolds admit ``nice'' foliations and explicit metrics, and whether the space of these metrics has a simple description in terms of Teichm\"uller theory. In the hyperbolic settings both questions have positive answers for a certain subset of the quasi-Fuchsian manifolds: those containing a closed surface with principal curvatures at most 1. We show that this subset is parameterized by an open domain of the cotangent bundle of Teichm\"uller space. These results are extended to ``quasi-Fuchsian'' manifolds with conical singularities along infinite lines, known in the physics literature as ``massive, spin-less particles''. Things work better for globally hyperbolic anti-de Sitter manifolds: the parameterization by the cotangent of Teichm\"uller space works for all manifolds. There is another description of this moduli space as the product two copies of Teichm\"uller space due to Mess. Using the maximal surface description, we propose a new parameterization by two copies of Teichm\"uller space, alternative to that of Mess, and extend all the results to manifolds with conical singularities along time-like lines. Similar results are obtained for de Sitter or Minkowski manifolds. Finally, for all four settings, we show that the symplectic form on the moduli space of 3-manifolds that comes from parameterization by the cotangent bundle of Teichm\"uller space is the same as the 3-dimensional gravity one.Comment: 53 pages, no figure. v2: typos corrected and refs adde

A Quantum Approach to Classical Statistical Mechanics

We present a new approach to study the thermodynamic properties of $d$-dimensional classical systems by reducing the problem to the computation of ground state properties of a $d$-dimensional quantum model. This classical-to-quantum mapping allows us to deal with standard optimization methods, such as simulated and quantum annealing, on an equal basis. Consequently, we extend the quantum annealing method to simulate classical systems at finite temperatures. Using the adiabatic theorem of quantum mechanics, we derive the rates to assure convergence to the optimal thermodynamic state. For simulated and quantum annealing, we obtain the asymptotic rates of $T(t) \approx (p N) /(k_B \log t)$ and $\gamma(t) \approx (Nt)^{-\bar{c}/N}$, for the temperature and magnetic field, respectively. Other annealing strategies, as well as their potential speed-up, are also discussed.Comment: 4 pages, no figure

Changes in temperature of heel skin under pressure in hip surgery patients

OBJECTIVE: The aim of the study was to examine the effect of external pressure of the bed surface on heel skin temperature in adults in the first 3 days after hip surgery. DESIGN: A quasi-experimental study in a prospective, within-subjects, repeated-measures design. SETTING: This study was performed at 2 acute-care hospitals. PARTICIPANTS: Eighteen subjects (9 men and 9 women) with a mean age of 58.3 (±16.1) years were recruited after hip surgery at the 2 hospitals. METHODS: Temperature sensors were placed on the plantar surface of each foot, close to the heels. Measures were taken when the heels were (1) suspended above the bed surface for 20 minutes (preload), (2) on the bed surface for 15 minutes (loading), and (3) suspended again above the bed surface for 15 minutes (unloading). MAIN OUTCOME MEASURES: Heel skin temperature and demographic data. RESULTS: Heel temperature increased during loading and unloading in both legs on postoperative days 1 (P = .003) and 3 (P = .04) but not on postoperative day 2. Heel temperature in the nonoperative leg decreased in the first 3 minutes of unloading on postoperative days 2 (P = .02) and 3 (P .01). CONCLUSION: Heel temperature increased with loading and unloading on postoperative days 1 and 3. Upon immediate unloading, hyperemic response was present only in the nonoperative leg. Keeping the heels off the bed surface at all times may avoid heel skin temperature changes and prevent tissue damage. Further research is needed to identify the mechanisms that explain the effect of external pressure on heel temperature