Regularity of Edge Ideals and Their Powers

We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of $\text{ reg } I(G)$ and the asymptotic linear function $\text{ reg } I(G)^q$, for $q \geq 1,$ in terms of combinatorial data of the given graph $G.$Comment: 31 pages, 15 figure

Compact relaxations for polynomial programming problems

Reduced RLT constraints are a special class of Reformulation- Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform rRLT constraint generation so as to reduce the number of inequality constraints in the relaxation, thereby making it more compact and faster to solve. We present some computational results validating our approach

Unimodality Problems in Ehrhart Theory

Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart $h^*$-vectors and highlight open questions and problems.Comment: Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original versio

Purifying Selection in Deeply Conserved Human Enhancers Is More Consistent than in Coding Sequences

(c) 2014 De Silva et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Sexual expression and cognitive function: gender-divergent associations in older adults

Prior research demonstrates a positive association between sexual activity and cognitive function in later life. However, the relationship between the type of sexual activity and cognitive function in older adulthood remains unclear. This study explores the associations between the frequency of engaging in different types of sexual activities (intercourse, masturbation, and kissing/petting/fondling) and cognitive function in older women and men. Using data from Wave 6 of the English Longitudinal Study of Ageing (ELSA), 1915 women and 2195 men (age range 50-89 years; n = 4110) reporting any type of sexual activity over the past 12 months, were included in the study. Multiple regression controlling for age, education, satisfaction with sex life, cohabiting, wealth, general health, physical activity, depression and loneliness, was used to explore the associations between the frequency of engagement in intercourse, masturbation and kissing/petting/fondling, and two measures of cognitive function; word recall and number sequencing. For women, masturbation was linked to better word recall (p = .008), whilst for men, kissing/petting/fondling was associated with better number sequencing (p = .035). In women (p = .016) and men (p = .018), dissatisfaction with sex life was associated with better number sequencing. The results point to gendered links between sexual activity and cognitive function. These gender-related divergences may reflect differences in biological/neurological mechanisms, or in cognitive lifestyle factors that could influence cognitive reserve in later life. This novel study underscores the need to delineate the underlying mechanisms of the association between sex and cognition in men and women

Efficient and Specific Internal Cleavage of a Retroviral Palindromic DNA Sequence by Tetrameric HIV-1 Integrase

BACKGROUND: HIV-1 integrase (IN) catalyses the retroviral integration process, removing two nucleotides from each long terminal repeat and inserting the processed viral DNA into the target DNA. It is widely assumed that the strand transfer step has no sequence specificity. However, recently, it has been reported by several groups that integration sites display a preference for palindromic sequences, suggesting that a symmetry in the target DNA may stabilise the tetrameric organisation of IN in the synaptic complex. METHODOLOGY/PRINCIPAL FINDINGS: We assessed the ability of several palindrome-containing sequences to organise tetrameric IN and investigated the ability of IN to catalyse DNA cleavage at internal positions. Only one palindromic sequence was successfully cleaved by IN. Interestingly, this symmetrical sequence corresponded to the 2-LTR junction of retroviral DNA circles-a palindrome similar but not identical to the consensus sequence found at integration sites. This reaction depended strictly on the cognate retroviral sequence of IN and required a full-length wild-type IN. Furthermore, the oligomeric state of IN responsible for this cleavage differed from that involved in the 3'-processing reaction. Palindromic cleavage strictly required the tetrameric form, whereas 3'-processing was efficiently catalysed by a dimer. CONCLUSIONS/SIGNIFICANCE: Our findings suggest that the restriction-like cleavage of palindromic sequences may be a general physiological activity of retroviral INs and that IN tetramerisation is strongly favoured by DNA symmetry, either at the target site for the concerted integration or when the DNA contains the 2-LTR junction in the case of the palindromic internal cleavage

Effect of resting pressure on the estimate of cerebrospinal fluid outflow conductance

<p>Abstract</p> <p>Background</p> <p>A lumbar infusion test is commonly used as a predictive test for patients with normal pressure hydrocephalus and for evaluation of cerebrospinal fluid (CSF) shunt function. Different infusion protocols can be used to estimate the outflow conductance (<it>C</it>_out) or its reciprocal the outflow resistance (<it>R</it>_out), with or without using the baseline resting pressure, <it>P</it>_r. Both from a basic physiological research and a clinical perspective, it is important to understand the limitations of the model on which infusion tests are based. By estimating <it>C</it>_out using two different analyses, with or without <it>P</it>_r, the limitations could be explored. The aim of this study was to compare the <it>C</it>_out estimates, and investigate what effect <it>P</it>_rhad on the results.</p> <p>Methods</p> <p>Sixty-three patients that underwent a constant pressure infusion protocol as part of their preoperative evaluation for normal pressure hydrocephalus, were included (age 70.3 ± 10.8 years (mean ± SD)). The analysis was performed without (<it>C</it>_{excl Pr}) and with (<it>C</it>_{incl Pr}) P_r. The estimates were compared using Bland-Altman plots and paired sample <it>t</it>-tests (<it>p </it>< 0.05 considered significant).</p> <p>Results</p> <p>Mean <it>C</it>_out for the 63 patients was: <it>C</it>_{excl Pr}= 7.0 ± 4.0 (mean ± SD) μl/(s kPa) and <it>C</it>_{incl Pr} = 9.1 ± 4.3 μl/(s kPa) and <it>R</it>_out was 19.0 ± 9.2 and 17.7 ± 11.3 mmHg/ml/min, respectively. There was a positive correlation between methods (r = 0.79, n = 63, <it>p </it>< 0.01). The difference, Δ<it>C</it>_out= -2.1 ± 2.7 μl/(s kPa) between methods was significant (<it>p </it>< 0.01) and Δ<it>R</it>_outwas 1.2 ± 8.8 mmHg/ml/min). The Bland-Altman plot visualized that the variation around the mean difference was similar all through the range of measured values and there was no correlation between Δ<it>C</it>_outand <it>C</it>_out.</p> <p>Conclusions</p> <p>The difference between <it>C</it>_outestimates, obtained from analyses with or without <it>P</it>_r, needs to be taken into consideration when comparing results from studies using different infusion test protocols. The study suggests variation in CSF formation rate, variation in venous pressure or a pressure dependent <it>C</it>_outas possible causes for the deviation from the CSF absorption model seen in some patients.</p

Kyphosis and paraspinal muscle composition in older men: a cross-sectional study for the osteoporotic fractures in men (MrOS) research group

BACKGROUND: The prevalence of hyperkyphosis is increased in older men; however, risk factors other than age and vertebral fractures are not well established. We previously reported that poor paraspinal muscle composition contributes to more severe kyphosis in a cohort of both older men and women. METHODS: To specifically evaluate this association in older men, we conducted a cross-sectional study to evaluate the association of paraspinal muscle composition and degree of thoracic kyphosis in an analytic cohort of 475 randomly selected participants from the Osteoporotic Fractures in Men (MrOS) study with baseline abdominal quantitative computed tomography (QCT) scans and plain thoracic radiographs. Baseline abdominal QCT scans were used to obtain abdominal body composition measurements of paraspinal muscle and adipose tissue distribution. Supine lateral spine radiographs were used to measure Cobb angle of kyphosis. We examined the linear association of muscle volume, fat volume and kyphosis using loess plots. Multivariate linear models were used to investigate the association between muscle and kyphosis using total muscle volume, as well as individual components of the total muscle volume, including adipose and muscle compartments alone, controlling for age, height, vertebral fractures, and total hip bone mineral density (BMD). We examined these associations among those with no prevalent vertebral fracture and those with BMI < 30 kg/m(2). RESULTS: Among men in the analytic cohort, means (SD) were 74 (SD = 5.9) years for age, and 37.5 (SD = 11.9) degrees for Cobb angle of kyphosis. Men in the lowest tertile of total paraspinal muscle volume had greater mean Cobb angle than men in the highest tertile, although test of linear trend across tertiles did not reach statistical significance. Neither lower paraspinal skeletal muscle volume (p-trend = 0.08), or IMAT (p-trend = 0.96) was associated with greater kyphosis. Results were similar among those with no prevalent vertebral fractures. However, among men with BMI < 30 kg/m(2), those in the lowest tertile of paraspinal muscle volume had greater adjusted mean kyphosis (40.0, 95% CI: 37.8 – 42.1) compared to the highest tertile (36.3, 95% CI: 34.2 – 38.4). CONCLUSIONS: These results suggest that differences in body composition may potentially influence kyphosis

Search for Gravitational Waves from Low Mass Compact Binary Coalescence in LIGO's Sixth Science Run and Virgo's Science Runs 2 and 3

We report on a search for gravitational waves from coalescing compact binaries using LIGO and Virgo observations between July 7, 2009 and October 20, 2010. We searched for signals from binaries with total mass between 2 and 25 solar masses; this includes binary neutron stars, binary black holes, and binaries consisting of a black hole and neutron star. The detectors were sensitive to systems up to 40 Mpc distant for binary neutron stars, and further for higher mass systems. No gravitational-wave signals were detected. We report upper limits on the rate of compact binary coalescence as a function of total mass, including the results from previous LIGO and Virgo observations. The cumulative 90%-confidence rate upper limits of the binary coalescence of binary neutron star, neutron star- black hole and binary black hole systems are 1.3 x 10^{-4}, 3.1 x 10^{-5} and 6.4 x 10^{-6} Mpc^{-3}yr^{-1}, respectively. These upper limits are up to a factor 1.4 lower than previously derived limits. We also report on results from a blind injection challenge.Comment: 11 pages, 5 figures. For a repository of data used in the publication, go to: . Also see the announcement for this paper on ligo.org at: <http://www.ligo.org/science/Publication-S6CBCLowMass/index.php