Class preserving automorphisms of unitriangular groups

Let $\textrm{UT}_n (K)$ be a unitriangular group over a field $K$ and $\Gamma_{n,k} := \textrm{UT}_n (K)/ \gamma_k(\textrm{UT}_n (K))$, where $\gamma_k (\mathrm{UT}_n(K))$ denotes the $k$-th term of the lower central series of $\mathrm{UT}_n (K)$, $2 \le k \le n$. We prove that the group of all class preserving automorphisms of $\Gamma_{n,k}$ is equal to \Inn(\Gamma_{n,k}) if and only if $K$ is a prime field. Let $G_n^{(m)} := \mathrm{UT}_n (\mathbb{F}_{p^m}) / \gamma_3 (\mathrm{UT}_n(\mathbb{F}_{p^m}))$. We calculate the group of all class preserving automorphisms and class preserving outer automorphisms of $G_n^{(m)}$.Comment: 19 pages, accepted for publication in International Journal of Algebra and Computatio

Large Deviation Approach to the Randomly Forced Navier-Stokes Equation

The random forced Navier-Stokes equation can be obtained as a variational problem of a proper action. By virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large deviation functional. Since the hydrodynamic operator is nonlinear, the functional integral yielding the statistics of fluctuations can be practically computed by linearizing around a physical solution of the hydrodynamic equation. We show that this procedure yields the dimensional scaling predicted by K41 theory at the lowest perturbative order, where the perturbation parameter is the inverse Reynolds number. Moreover, an explicit expression of the prefactor of the scaling law is obtained.Comment: 24 page

Classical and Quantum Gravitational Collapse in d-dim AdS Spacetime I. Classical Solutions

We study the collapse of a spherically symmetric dust distribution in $d$-dimensional AdS spacetime. We investigate the role of dimensionality, and the presence of a negative cosmological constant, in determining the formation of trapped surfaces and the end state of gravitational collapse. We obtain the self-similar solution for the case of zero cosmological constant, and show that one cannot construct a self-similar solution when a cosmological constant is included.Comment: 19 pages, sections on surface gravity removed, section on self similar solution expanded, appendix removed, references added. To appear in Phys. Rev.

An active vesicle priming machinery suppresses axon regeneration upon adult CNS injury

Axons in the adult mammalian central nervous system fail to regenerate after spinal cord injury. Neurons lose their capacity to regenerate during development, but the intracellular processes underlying this loss are unclear. We found that critical components of the presynaptic active zone prevent axon regeneration in adult mice. Transcriptomic analysis combined with live-cell imaging revealed that adult primary sensory neurons downregulate molecular constituents of the synapse as they acquire the ability to rapidly grow their axons. Pharmacogenetic reduction of neuronal excitability stimulated axon regeneration after adult spinal cord injury. Genetic gain- and loss-of-function experiments uncovered that essential synaptic vesicle priming proteins of the presynaptic active zone, but not clostridial-toxin-sensitive VAMP-family SNARE proteins, inhibit axon regeneration. Systemic administration of Baclofen reduced voltage-dependent Ca2+ influx in primary sensory neurons and promoted their regeneration after spinal cord injury. These findings indicate that functional presynaptic active zones constitute a major barrier to axon regeneration

Effects of habitat and livestock on nest productivity of the Asian houbara Chlamydotis macqueenii in Bukhara Province, Uzbekistan

To inform population support measures for the unsustainably hunted Asian houbara Chlamydotis macqueenii (IUCN Vulnerable) we examined potential habitat and land-use effects on nest productivity in the Kyzylkum Desert, Uzbekistan. We monitored 177 nests across different semi-arid shrub assemblages (clay-sand and salinity gradients) and a range of livestock densities (0–80 km-2). Nest success (mean 51.4%, 95% CI 42.4–60.4%) was similar across four years; predation caused 85% of those failures for which the cause was known, and only three nests were trampled by livestock. Nesting begins within a few weeks of arrival when food appears scarce, but later nests were more likely to fail owing to the emergence of a key predator, suggesting foraging conditions on wintering and passage sites may be important for nest productivity. Nest success was similar across three shrub assemblages and was unrelated to landscape rugosity, shrub frequency or livestock density, but was greater with taller mean shrub height (range 13–67 cm) within 50 m. Clutch size (mean = 3.2 eggs) and per-egg hatchability in successful nests (87.5%) did not differ with laying date, shrub assemblage or livestock density. We therefore found no evidence that livestock density reduced nest productivity across the range examined, while differing shrub assemblages appeared to offer similar habitat quality. Asian houbara appear well-adapted to a range of semi-desert habitats and tolerate moderate disturbance by pastoralism. No obvious in situ mitigation measures arise from these findings, leaving regulation and control as the key requirement to render hunting sustainable

A Feasibility Study of Quantifying Longitudinal Brain Changes in Herpes Simplex Virus (HSV) Encephalitis Using Magnetic Resonance Imaging (MRI) and Stereology.

OBJECTIVES: To assess whether it is feasible to quantify acute change in temporal lobe volume and total oedema volumes in herpes simplex virus (HSV) encephalitis as a preliminary to a trial of corticosteroid therapy. METHODS: The study analysed serially acquired magnetic resonance images (MRI), of patients with acute HSV encephalitis who had neuroimaging repeated within four weeks of the first scan. We performed volumetric measurements of the left and right temporal lobes and of cerebral oedema visible on T2 weighted Fluid Attenuated Inversion Recovery (FLAIR) images using stereology in conjunction with point counting. RESULTS: Temporal lobe volumes increased on average by 1.6% (standard deviation (SD 11%) in five patients who had not received corticosteroid therapy and decreased in two patients who had received corticosteroids by 8.5%. FLAIR hyperintensity volumes increased by 9% in patients not receiving treatment with corticosteroids and decreased by 29% in the two patients that had received corticosteroids. CONCLUSIONS: This study has shown it is feasible to quantify acute change in temporal lobe and total oedema volumes in HSV encephalitis and suggests a potential resolution of swelling in response to corticosteroid therapy. These techniques could be used as part of a randomized control trial to investigate the efficacy of corticosteroids for treating HSV encephalitis in conjunction with assessing clinical outcomes and could be of potential value in helping to predict the clinical outcomes of patients with HSV encephalitis

On the trace of the antipode and higher indicators

We introduce two kinds of gauge invariants for any finite-dimensional Hopf algebra H. When H is semisimple over C, these invariants are respectively, the trace of the map induced by the antipode on the endomorphism ring of a self-dual simple module, and the higher Frobenius-Schur indicators of the regular representation. We further study the values of these higher indicators in the context of complex semisimple quasi-Hopf algebras H. We prove that these indicators are non-negative provided the module category over H is modular, and that for a prime p, the p-th indicator is equal to 1 if, and only if, p is a factor of dim H. As an application, we show the existence of a non-trivial self-dual simple H-module with bounded dimension which is determined by the value of the second indicator.Comment: additional references, fixed some typos, minor additions including a questions and some remark

Leonard Euler: addition theorems and superintegrable systems

We consider the Euler approach to construction and to investigation of the superintegrable systems related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel systems.Comment: The text of the talk at International Conference Geometry, Dynamics, Integrable Systems, September 2-7, 2008, Belgrade, Serbia, LaTeX, 18 page

Water from abandoned mines as a heat source: practical experiences of open- and closed-loop strategies, United Kingdom

Pilot heat pump systems have been installed at two former collieries in Yorkshire/Derbyshire, England, to extract heat from mine water. The installations represent three fundamental configurations of heat exchanger. At Caphouse Colliery, mine water is pumped through a heat exchanger coupled to a heat pump and then discharged to waste (an open-loop heat exchange system). The system performs with high thermal efficiency, but the drawbacks are: (1) it can only be operated when mine water is being actively pumped from the colliery shaft for the purposes of regional water-level management, and (2) the fact that the water is partially oxygenated means that iron oxyhydroxide precipitation occurs, necessitating regular removal of filters for cleaning. At Markham Colliery, near Bolsover, a small amount of mine water is pumped from depth in a flooded shaft, circulated through a heat exchanger coupled to a heat pump and then returned to the same mine shaft at a slightly different depth (a standing column arrangement). This system’s fundamental thermal efficiency is negatively impacted by the electrical power required to run the shaft submersible pump, but clogging issues are not significant. In the third system, at Caphouse, a heat exchanger is submerged in a mine water treatment pond (a closed-loop system). This can be run at any time, irrespective of mine pumping regime, and being a closed-loop system, is not susceptible to clogging issues