Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

The Response of River-Resident Fish to Reservoir Freshet Releases of Varying Profiles Intended to Facilitate a Spawning Migration

Natural hydrological regimes encompass varying seasonal flow characteristics that provide fish with cues and opportunities for upstream spawning migrations, but these flows are often modified/absent in regulated rivers. Compensatory artificial flows (freshets) can be released from reservoirs to replicate these characteristics, but studies testing their effectiveness are limited. To address this, river‐resident brown trout, a species known to undertake spawning migrations, were manually tracked using radio telemetry in a regulated upland river in northern England in response to 11 freshet releases of differing timing, magnitude and duration. Spawning migrations were not observed because extent of movement during freshets was generally small and the pattern of movement (i.e. directionality and relocation indices) was comparable between impact/control reaches. Movements during freshets were comparable with those observed the days immediately before/after and were small relative to the entire tracking period. In conclusion, freshets characteristic of those recommended to produce “naturalized” autumn/winter flow elevations did not stimulate/facilitate spawning migrations of river‐resident brown trout under the given seasonal conditions. Outside freshets, longer unidirectional movements occurred during low flow periods and elevated river level due to rainfall, including during periods of reservoir overtopping. Notwithstanding, fish in experimental reaches were significantly more active (total distance moved) and occupied a larger extent of river (range during freshet) than those in control reaches during short‐duration freshets. Therefore, during dry years/when (autumn/winter) reservoir overtopping events are unlikely, small‐magnitude freshets providing flows that allow fish short opportunities to search for/find superior local habitat whilst minimising total water released are recommended

A New Obesity Model Reveals the Hypophagic Properties of PACAP Involve the Regulation of Homeostatic Feeding in the Ventromedial Hypothalamic Nucleus and Hedonic Feeding in the Nucleus Accumbens

Binge eating in humans is a complex disorder that often involves discrete, compulsive feeding sessions of highly palatable foods even in the absence of a deprivation state or hunger. Binging can be effectively modeled in rodents by providing subjects with limited access to a palatable food source (Western Diet; WD) as an adjunct to ad lib access to normal chow (Standard Chow; SC). Although this design recapitulates several fundamental characteristics observed in binge eating disorder, the binge eating observed in this paradigm is likely a product of both hedonic and homeostatic drives with the need to balance energy stores still present. To isolate these feeding drives, we have developed a novel feeding regimen that modifies the classic limited access binge model to effectively delineate and separate homeostatic feeding from motivational feeding. This is achieved by entraining male Sprague-Dawley rats to a restricted feeding schedule (two hours per day) of SC followed by a short 15 minute limited access meal of either SC or WD (Restrict Fed-Limited Access; RFLA). The RFLA paradigm allows for the examination of pituitary adenylate-cyclase activating polypeptide (PACAP) on palatable food consumption in a fully satiated subject. PACAP has previously been shown to suppress feeding behavior when injected into the hypothalamus. In the current study, PACAP injected into the ventromedial hypothalamic nuclei (VMN) suppressed the two hour homeostatic SC meal, but not the subsequent 15 minute limited access meal of WD. By contrast, PACAP bilaterally administered into the nucleus accumbens (NAc) produced the opposite effect with PACAP suppressing the consumption of WD but not SC. Thus, PACAP mediated signaling in the VMN appears to be involved in homeostatic regulation of energy stores, whereas PACAP signaling in the NAc regulates feeding driven by palatability or hedonic qualities

The Atacama Cosmology Telescope: the stellar content of galaxy clusters selected using the Sunyaev-Zel'dovich effect

We present a first measurement of the stellar mass component of galaxy clusters selected via the Sunyaev-Zel'dovich (SZ) effect, using 3.6 um and 4.5 um photometry from the Spitzer Space Telescope. Our sample consists of 14 clusters detected by the Atacama Cosmology Telescope (ACT), which span the redshift range 0.27 < z < 1.07 (median z = 0.50), and have dynamical mass measurements, accurate to about 30 per cent, with median M500 = 6.9 x 10^{14} MSun. We measure the 3.6 um and 4.5 um galaxy luminosity functions, finding the characteristic magnitude (m*) and faint-end slope (alpha) to be similar to those for IR-selected cluster samples. We perform the first measurements of the scaling of SZ-observables (Y500 and y0) with both brightest cluster galaxy (BCG) stellar mass and total cluster stellar mass (M500star). We find a significant correlation between BCG stellar mass and Y500 (E(z)^{-2/3} DA^2 Y500 ~ M*^{1.2 +/- 0.6}), although we are not able to obtain a strong constraint on the slope of the relation due to the small sample size. Additionally, we obtain E(z)^{-2/3} DA^2 Y500 ~ M500star^{1.0 +/- 0.6} for the scaling with total stellar mass. The mass fraction in stars spans the range 0.006-0.034, with the second ranked cluster in terms of dynamical mass (ACT-CL J0237-4939) having an unusually low total stellar mass and the lowest stellar mass fraction. For the five clusters with gas mass measurements available in the literature, we see no evidence for a shortfall of baryons relative to the cosmic mean value.Comment: Accepted for publication in MNRAS; 12 pages, 10 figure

Behavioral Assessment of Acute Inhibition of System x\u3csub\u3ec\u3c/sub\u3e\u3csup\u3e -\u3c/sup\u3e in rats

Rationale Gaps in our understanding of glutamatergic signaling may be key obstacles in accurately modeling complex CNS diseases. System xc - is an example of a poorly understood component of glutamate homeostasis that has the potential to contribute to CNS diseases. Objectives This study aims to determine whether system xc - contributes to behaviors used to model features of CNS disease states. Methods In situ hybridization was used to map mRNA expression of xCT throughout the brain. Microdialysis in the prefrontal cortex was used to sample extracellular glutamate levels; HPLC was used to measure extracellular glutamate and tissue glutathione concentrations. Acute administration of sulfasalazine (8–16 mg/kg, IP) was used to decrease system xc - activity. Behavior was measured using attentional set shifting, elevated plus maze, open-field maze, Porsolt swim test, and social interaction paradigm. Results The expression of xCT mRNA was detected throughout the brain, with high expression in several structures including the basolateral amygdala and prefrontal cortex. Doses of sulfasalazine that produced a reduction in extracellular glutamate levels were identified and subsequently used in the behavioral experiments. Sulfasalazine impaired performance in attentional set shifting and reduced the amount of time spent in an open arm of an elevated plus maze and the center of an open-field maze without altering behavior in a Porsolt swim test, total distance moved in an open-field maze, or social interaction. Conclusions The widespread distribution of system xc - and involvement in a growing list of behaviors suggests that this form of nonvesicular glutamate release is a key component of excitatory signaling

Gluon Propagator in the Infrared Region

The gluon propagator is calculated in quenched QCD for two different lattice sizes (16^3x48 and 32^3x64) at beta=6.0. The volume dependence of the propagator in Landau gauge is studied. The smaller lattice is instrumental in revealing finite volume and anisotropic lattice artefacts. Methods for minimising these artefacts are developed and applied to the larger lattice data. New structure seen in the infrared region survives these conservative cuts to the lattice data. This structure serves to rule out a number of models that have appeared in the literature. A fit to a simple analytical form capturing the momentum dependence of the nonperturbative gluon propagator is also reported.Comment: 13 pages, 9 figures, using RevTeX. Submitted to Phys. Rev. D. This and related papers can also be obtained from http://www.physics.adelaide.edu.au/~jskuller/papers

Development of a networked photonic‐enabled staring radar testbed for urban surveillance

Urban surveillance of slow-moving small targets such as drones and birds in low to medium airspace using radar presents significant challenges. Detecting, locating and identifying such low observable targets in strong clutter requires both innovation in radar hardware design and optimisation of processing algorithms. To this end, the University of Birmingham (UoB) has set-up a testbed of two L-band staring radars to support performance benchmarking using datasets of target and clutter from realistic urban environment. This testbed is also providing the vehicle to understand how novel radar architectures can enhance radar capabilities. Some of the challenges in installing the radar at the UoB campus are highlighted. Detailed benchmarking results are provided from urban monostatic and bistatic field trials that form the basis for performance comparison against future hardware modification. The solution to the challenge of interfacing the radar to the external oscillators is described and stand-alone bench tests with the candidate oscillators are reported. The testbed provides a valuable capability to undertake detailed analysis of performance of Quantum photonic-enabled radar and allows for its comparison with conventional oscillator technology for surveillance of low observable targets in the presence of urban clutter

Functional Dissection of the Neural Substrates for Sexual Behaviors in Drosophila melanogaster

The male-specific Fruitless proteins (FruM) act to establish the potential for male courtship behavior in Drosophila melanogaster and are expressed in small groups of neurons throughout the nervous system. We screened ∼1000 GAL4 lines, using assays for general courtship, male–male interactions, and male fertility to determine the phenotypes resulting from the GAL4-driven inhibition of FruM expression in subsets of these neurons. A battery of secondary assays showed that the phenotypic classes of GAL4 lines could be divided into subgroups on the basis of additional neurobiological and behavioral criteria. For example, in some lines, restoration of FruM expression in cholinergic neurons restores fertility or reduces male–male courtship. Persistent chains of males courting each other in some lines results from males courting both sexes indiscriminately, whereas in other lines this phenotype results from apparent habituation deficits. Inhibition of ectopic FruM expression in females, in populations of neurons where FruM is necessary for male fertility, can rescue female infertility. To identify the neurons responsible for some of the observed behavioral alterations, we determined the overlap between the identified GAL4 lines and endogenous FruM expression in lines with fertility defects. The GAL4 lines causing fertility defects generally had widespread overlap with FruM expression in many regions of the nervous system, suggesting likely redundant FruM-expressing neuronal pathways capable of conferring male fertility. From associations between the screened behaviors, we propose a functional model for courtship initiation