The emergence of 4-cycles in polynomial maps over the extended integers

Let $f(x) \in \mathbb{Z}[x]$; for each integer $\alpha$ it is interesting to consider the number of iterates $n_{\alpha}$, if possible, needed to satisfy $f^{n_{\alpha}}(\alpha) = \alpha$. The sets $\{\alpha, f(\alpha), \ldots, f^{n_{\alpha} - 1}(\alpha), \alpha\}$ generated by the iterates of $f$ are called cycles. For $\mathbb{Z}[x]$ it is known that cycles of length 1 and 2 occur, and no others. While much is known for extensions to number fields, we concentrate on extending $\mathbb{Z}$ by adjoining reciprocals of primes. Let $\mathbb{Z}[1/p_1, \ldots, 1/p_n]$ denote $\mathbb{Z}$ extended by adding in the reciprocals of the $n$ primes $p_1, \ldots, p_n$ and all their products and powers with each other and the elements of $\mathbb{Z}$. Interestingly, cycles of length 4, called 4-cycles, emerge for polynomials in $\mathbb{Z}\left[1/p_1, \ldots, 1/p_n\right][x]$ under the appropriate conditions. The problem of finding criteria under which 4-cycles emerge is equivalent to determining how often a sum of four terms is zero, where the terms are $\pm 1$ times a product of elements from the list of $n$ primes. We investigate conditions on sets of primes under which 4-cycles emerge. We characterize when 4-cycles emerge if the set has one or two primes, and (assuming a generalization of the ABC conjecture) find conditions on sets of primes guaranteed not to cause 4-cycles to emerge.Comment: 14 pages, 1 figur

Living with HIV after Release from Prison: An Evaluation of the Long-term Health of Formerly Incarcerated Individuals who used Michigan’s Community Reentry Service

In 2003, Michigan implemented a reentry service to assist HIV-infected people incarcerated in state prisons in linking to HIV medical care immediately upon their release. We examined whether formerly incarcerated people were linked to care successfully, remained in care, and were in good health 3 years after their date of release. In all, 190 people used the service over the 5 years following its inception. Only a minority of those who were alive and not reincarcerated at the time of the evaluation engaged consistently with medical care. Unsurprisingly given low rates of engagement in care, 3 years after their release only 27% had achieved viral suppression. Concerted efforts to support formerly incarcerated HIV-infected individuals’ engagement in care over the long term are urgently needed

Advanced stitching head for making stitches in a textile article having variable thickness

A stitching head for a computer numerically controlled stitching machine includes a thread tensioning mechanism for automatically adjusting thread tension according to the thickness of the material being stitched. The stitching head also includes a mechanism for automatically adjusting thread path geometry according to the thickness of the material being stitched

Environmental Dependence of the Fundamental Plane of Galaxy Clusters

Galaxy clusters approximate a planar (FP) distribution in a three-dimensional parameter space which can be characterized by optical luminosity, half-light radius, and X-ray luminosity. Using a high-quality catalog of cluster redshifts, we find the nearest neighbor cluster for those common to an FP study and the cluster catalog. Examining scatter about the FP, we find 99.2% confidence that it is dependent on nearest neighbor distance. Our study of X-Ray clusters finds that those with high central gas densities are systematically closer to neighbor clusters. If we combine results here with those of Fritsch and Buchert, we find an explanation for some of our previous conclusions: Clusters in close proximity to other clusters are more likely to have massive cooling flows because they are more relaxed and have higher central gas densities.Comment: Accepted for publication in Astrophysical Journal Letters. Moderate revisions, including more statistical analysis and discussion. Latex, 7 page

Experimental field studies to measure behavioral responses of cetaceans to sonar

Funding was provided by a variety of military and governmental funding sources from several nations acknowledged within referenced publications, notably the US Office of Naval Research, US Navy Living Marine Resources Program, and the navies of the USA, Norway, and the Netherlands. P.L.T. acknowledges the support of the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) in the completion of this study. MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.Substantial recent progress has been made in directly measuring behavioral responses of free-ranging marine mammals to sound using controlled exposure experiments. Many studies were motivated by concerns about observed and potential negative effects of military sonar, including stranding events. Well-established experimental methods and increasingly sophisticated technologies have enabled fine-resolution measurement of many aspects of baseline behavior and responses to sonar. Studies have considered increasingly diverse taxa, but primarily odontocete and mysticete cetaceans that are endangered, particularly sensitive, or frequently exposed to sonar. This review focuses on recent field experiments studying cetacean responses to simulated or actual active military sonars in the 1 to 8 kHz band. Overall results demonstrate that some individuals of different species display clear yet varied responses, some of which have negative implications, while others appear to tolerate relatively high levels, although such exposures may have other consequences not measured. Responses were highly variable and may not be fully predictable with simple acoustic exposure metrics (e.g. received sound level). Rather, differences among species and individuals along with contextual aspects of exposure (e.g. behavioral state) appear to affect response probability. These controlled experiments provide critically needed documentation of identified behavioral responses occurring upon known sonar exposures, and they directly inform regulatory assessments of potential effects. They also inform more targeted opportunistic monitoring of potential responses of animals during sonar operations and have stimulated adaptations of field methods to consider increasingly realistic exposure scenarios and how contextual factors such as behavioral state and source proximity influence response type and probability.Publisher PDFPeer reviewe

The Global Implications of the Hard Excess II: Analysis of the Local population of Radio Quiet AGN

Active galactic nuclei (AGN) show evidence for reprocessing gas, outflowing from the accreting black hole. The combined effects of absorption and scattering from the circumnuclear material likely explains the `hard excess' of X-ray emission above 20 keV, compared with extrapolation of spectra from lower X-ray energies. In a recent {\it Suzaku} study, we established the ubiquitous hard excess in hard X-ray-selected, radio-quiet type\,1 AGNs to be consistent with reprocessing of the X-ray continuum an ensemble of clouds, located tens to hundreds of gravitational radii from the nuclear black hole. Here we add hard X-ray-selected, type\,2 AGN to extend our original study and show that the gross X-ray spectral properties of the entire local population of radio quiet AGN may be described by a simple unified scheme. We find a broad, continuous distribution of spectral hardness ratio and Fe\,K$\alpha$ equivalent width across all AGN types, which can be reproduced by varying the observer's sightline through a single, simple model cloud ensemble, provided the radiative transfer through the model cloud distribution includes not only photoelectric absorption but also 3D Compton scattering. Variation in other parameters of the cloud distribution, such as column density or ionisation, should be expected between AGN, but such variation is not required to explain the gross X-ray spectral properties.Comment: 24 pages, 6 figure

Alcohol-related adverse consequences: cross-cultural variations in attribution process among young adults

Background: Social norms around what is culturally accepted in terms of alcohol consumption and drunken comportment appear important regarding the acceptance of alcohol-related adverse consequences; however, investigations often neglect to consider differences in terms of attribution. This study aims at assessing cross-cultural differences in the reporting of alcohol-related adverse consequences. It also considers differences across consequences that might explain which type of consequences (mainly acute or mainly chronic) are most affected by an attribution process. Methods: Conditional regression models were estimated based on data from eight European countries participating in the Gender, Alcohol and Culture—An International Study (GENACIS) project. Cases were matched to controls based on usual drinking patterns in order to control for average volume of alcohol and frequency of ‘risky single occasion drinking' (RSOD). Results: Differences among the patterns of associations between countries and consequences were evident. The distinction between Nordic and other European countries was persistent. A higher variability of associations was observed for some consequences, namely the mainly acute instances. Finally, the Isle of Man and Switzerland showed specific trends with associations across consequences. Conclusion: Reporting of alcohol-related adverse consequences seemed strongly affected by cultural norms. The latter may be exemplified by viewing drinking as ‘time-out' behaviour. Respondents in countries with a stereotypical history of being ‘dry' or with a stereotyped ‘binge' drinking culture were more likely to attribute consequences to their alcohol consumption than people in ‘wet' countries. This was particularly true for consequences that related to episodic ‘time-out' heavy drinkin

Lipid coated liquid crystal droplets for the on-chip detection of antimicrobial peptides

We describe a novel biosensor based on phospholipid-coated nematic liquid crystal (LC) droplets and demonstrate the detection of Smp43, a model antimicrobial peptide (AMP) from the venom of North African scorpion Scorpio maurus palmatus. Mono-disperse lipid-coated LC droplets of diameter 16.7 ± 0.2 μm were generated using PDMS microfluidic devices with a flow-focusing configuration and were the target for AMPs. The droplets were trapped in a bespoke microfluidic trap structure and were simultaneously treated with Smp43 at gradient concentrations in six different chambers. The disruption of the lipid monolayer by the Smp43 was detected (<6 μM) at concentrations well within its biologically active range, indicated by a dramatic change in the appearance of the droplets associated with the transition from a typical radial configuration to a bipolar configuration, which is readily observed by polarizing microscopy. This suggests the system has feasibility as a drug-discovery screening tool. Further, compared to previously reported LC droplet biosensors, this LC droplet biosensor with a lipid coating is more biologically relevant and its ease of use in detecting membrane-related biological processes and interactions has the potential for development as a reliable, low-cost and disposable point of care diagnostic tool

Ionization structure and Fe Kα\alpha energy for irradiated accretion disks

We study the radial ionization structure at the surface of an X-ray illuminated accretion disk. We plot the expected iron K$\alpha$ line energy as a function of the Eddington ratio and of the distance of the emitting matter from the central source, for a non-rotating and a maximally-rotating black hole. We compare the predicted disk line energies with those measured in an archival sample of active galactic nuclei observed with {\it Chandra}, {\it XMM-Newton} and {\it Suzaku}, and discuss whether the line energies are consistent with the radial distances inferred from reverberation studies. We also suggest using rapidly-variable iron K$\alpha$ lines to estimate the viscosity parameter of an accretion disk. There is a forbidden region in the line energy versus Eddington ratio plane, at low Eddington ratios, where an accretion disk cannot produce highly-ionized iron K$\alpha$ lines. If such emission is observed in low-Eddington-ratio sources, it is either coming from a highly-ionized outflow, or is a blue-shifted component from fast-moving neutral matter.Comment: 5 pages, 2 figures, accepted by MNRA