The covering radius problem for sets of perfect matchings

Consider the family of all perfect matchings of the complete graph $K_{2n}$ with $2n$ vertices. Given any collection $\mathcal M$ of perfect matchings of size $s$, there exists a maximum number $f(n,x)$ such that if $s\leq f(n,x)$, then there exists a perfect matching that agrees with each perfect matching in $\mathcal M$ in at most $x-1$ edges. We use probabilistic arguments to give several lower bounds for $f(n,x)$. We also apply the Lov\'asz local lemma to find a function $g(n,x)$ such that if each edge appears at most $g(n, x)$ times then there exists a perfect matching that agrees with each perfect matching in $\mathcal M$ in at most $x-1$ edges. This is an analogue of an extremal result vis-\'a-vis the covering radius of sets of permutations, which was studied by Cameron and Wanless (cf. \cite{cameron}), and Keevash and Ku (cf. \cite{ku}). We also conclude with a conjecture of a more general problem in hypergraph matchings.Comment: 10 page

Baseline values of canine tear production determined by schirmer tear and phenol red thread tests.

Although research on canine tear production and dry eye has been reported in temperate countries in different breeds, there is no Malaysian data. On the average, at least two new cases of dry eye are diagnosed weekly at the University Veterinary Hospital (UVH) of the Faculty of Veterinary Medicine, Universiti Putra Malaysia. Currently in UVH the guidelines for the diagnosis of keratoconjunctivitis (KCS) and monitoring of response to treatment are based on recommendations for temperate countries. Thus the objectives of this study were to determine the Malaysian baseline values for canine tear levels using Schirmer tear test (STT) and phenol red thread test (PRTT), the relationship between and diurnal effect on STT and PRTT in dogs. The average baseline values for canine tear production in healthy local dogs in Malaysia with normal tear film breakup time (TBUT) were within the range of average baseline values reported in temperate countries. The average STT value for both eyes was approximately 22 mm/min and the PRTT was approximately 26 mm/15 s. There was poor relationship between STT and PRTT. This might be due to the presence of one or more confounding factors. The red colour change in PRTT was more intense when STT was performed first followed by PRTT and vice versa. The intensity of red colour change in PRTT was even more when performed in KCS dogs. This is because the intensity of the colour change in the phenol red thread is due to increasing alkalinity. Thus, KCS dogs had more alkaline tears than normal dogs. The lowest tear level was in the afternoon when diurnal study was conducted. Hence, KCS tests should be performed in the afternoon in order to obtain a more accurate measurement of tear level. Tear levels fluctuate when normal dogs were exposed in clinic with air-conditioned environment. Therefore, KCS tests should be performed immediately when dogs arrived at the clinic

Anatomical features, fiber morphological, physical and mechanical properties of three years old new hybrid Paulownia: green Paulownia

Objective: Green Paulownia (hybridization of Paulownia elongata × Paulownia fotunei and tropical Paulownia spp.) is new hybrid claimed as one of the fast-growing woody plants with the high potential as a fiber material or lignocellulosic material. The material for this study originates from the area of Nanning in China. Methodology: Cell morphology and anatomical appearances were observed and evaluated under the image analysis system (Leica DMLS). Physical and mechanical properties were evaluated based on the American Society for Testing and Materials (ASTM) standards. Results: From the results, average value of the mean fiber length was 0.905 mm, mean fiber length 34.59 μm, lumen thickness 26.80 μm and cell wall thickness 3.89 μm. Fiber dimensions of green Paulownia are in the normal range for hardwoods. The physical and mechanical properties of 3 years old green Paulownia have similar properties than those 7-11 years old Paulownia published in China. Conclusion: The 3 years old green Paulownia timbers can be used as materials for furniture

General Analysis of Antideuteron Searches for Dark Matter

Low energy cosmic ray antideuterons provide a unique low background channel for indirect detection of dark matter. We compute the cosmic ray flux of antideuterons from hadronic annihilations of dark matter for various Standard Model final states and determine the mass reach of two future experiments (AMS-02 and GAPS) designed to greatly increase the sensitivity of antideuteron detection over current bounds. We consider generic models of scalar, fermion, and massive vector bosons as thermal dark matter, describe their basic features relevant to direct and indirect detection, and discuss the implications of direct detection bounds on models of dark matter as a thermal relic. We also consider specific dark matter candidates and assess their potential for detection via antideuterons from their hadronic annihilation channels. Since the dark matter mass reach of the GAPS experiment can be well above 100 GeV, we find that antideuterons can be a good indirect detection channel for a variety of thermal relic electroweak scale dark matter candidates, even when the rate for direct detection is highly suppressed.Comment: 44 pages, 15 Figure

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio

Subcellular heterogeneity of ryanodine receptor properties in ventricular myocytes with low T-tubule density

Rationale: In ventricular myocytes of large mammals, not all ryanodine receptor (RyR) clusters are associated with T-tubules (TTs); this fraction increases with cellular remodeling after myocardial infarction (MI). Objective: To characterize RyR functional properties in relation to TT proximity, at baseline and after MI. Methods: Myocytes were isolated from left ventricle of healthy pigs (CTRL) or from the area adjacent to a myocardial infarction (MI). Ca2+ transients were measured under whole-cell voltage clamp during confocal linescan imaging (fluo-3) and segmented according to proximity of TTs (sites of early Ca2+ release, F>F50 within 20 ms) or their absence (delayed areas). Spontaneous Ca2+ release events during diastole, Ca2+ sparks, reflecting RyR activity and properties, were subsequently assigned to either category. Results: In CTRL, spark frequency was higher in proximity of TTs, but spark duration was significantly shorter. Block of Na+/Ca2+ exchanger (NCX) prolonged spark duration selectively near TTs, while block of Ca2+ influx via Ca2+ channels did not affect sparks properties. In MI, total spark mass was increased in line with higher SR Ca2+ content. Extremely long sparks (>47.6 ms) occurred more frequently. The fraction of near-TT sparks was reduced; frequency increased mainly in delayed sites. Increased duration was seen in near-TT sparks only; Ca2+ removal by NCX at the membrane was significantly lower in MI. Conclusion: TT proximity modulates RyR cluster properties resulting in intracellular heterogeneity of diastolic spark activity. Remodeling in the area adjacent to MI differentially affects these RyR subpopulations. Reduction of the number of sparks near TTs and reduced local NCX removal limit cellular Ca2+ loss and raise SR Ca2+ content, but may promote Ca2+ waves

Cytotoxic polyfunctionality maturation of cytomegalovirus-pp65-specific CD4 + and CD8 + T-cell responses in older adults positively correlates with response size

Cytomegalovirus (CMV) infection is one of the most common persistent viral infections in humans worldwide and is epidemiologically associated with many adverse health consequences during aging. Previous studies yielded conflicting results regarding whether large, CMV-specific T-cell expansions maintain their function during human aging. In the current study, we examined the in vitro CMV-pp65-reactive T-cell response by comprehensively studying five effector functions (i.e., interleukin-2, tumor necrosis factor-α, interferon-γ, perforin, and CD107a expression) in 76 seropositive individuals aged 70 years or older. Two data-driven, polyfunctionality panels (IL-2-associated and cytotoxicity-associated) derived from effector function co-expression patterns were used to analyze the results. We found that, CMV-pp65-reactive CD8 + and CD4 + T cells contained similar polyfunctional subsets, and the level of polyfunctionality was related to the size of antigen-specific response. In both CD8 + and CD4 + cells, polyfunctional cells with high cytotoxic potential accounted for a larger proportion of the total response as the total response size increased. Notably, a higher serum CMV-IgG level was positively associated with a larger T-cell response size and a higher level of cytotoxic polyfunctionality. These findings indicate that CMV-pp65-specific CD4 + and CD8 + T cell undergo simultaneous cytotoxic polyfunctionality maturation during aging

Definition of the σW regulon of Bacillus subtilis in the absence of stress

Bacteria employ extracytoplasmic function (ECF) sigma factors for their responses to environmental stresses. Despite intensive research, the molecular dissection of ECF sigma factor regulons has remained a major challenge due to overlaps in the ECF sigma factor-regulated genes and the stimuli that activate the different ECF sigma factors. Here we have employed tiling arrays to single out the ECF σW regulon of the Gram-positive bacterium Bacillus subtilis from the overlapping ECF σX, σY, and σM regulons. For this purpose, we profiled the transcriptome of a B. subtilis sigW mutant under non-stress conditions to select candidate genes that are strictly σW-regulated. Under these conditions, σW exhibits a basal level of activity. Subsequently, we verified the σW-dependency of candidate genes by comparing their transcript profiles to transcriptome data obtained with the parental B. subtilis strain 168 grown under 104 different conditions, including relevant stress conditions, such as salt shock. In addition, we investigated the transcriptomes of rasP or prsW mutant strains that lack the proteases involved in the degradation of the σW anti-sigma factor RsiW and subsequent activation of the σW-regulon. Taken together, our studies identify 89 genes as being strictly σW-regulated, including several genes for non-coding RNAs. The effects of rasP or prsW mutations on the expression of σW-dependent genes were relatively mild, which implies that σW-dependent transcription under non-stress conditions is not strictly related to RasP and PrsW. Lastly, we show that the pleiotropic phenotype of rasP mutant cells, which have defects in competence development, protein secretion and membrane protein production, is not mirrored in the transcript profile of these cells. This implies that RasP is not only important for transcriptional regulation via σW, but that this membrane protease also exerts other important post-transcriptional regulatory functions