Monochromatic bounded degree subgraph partitions

Abstract Let F = {F1,F2,...} be a sequence of graphs such that Fn is a graph on n vertices with maximum degree at most Δ. We show that there exists an absolute constant C such that the vertices of any 2-edge-colored complete graph can be partitioned into at most 2CΔlogΔ vertex disjoint monochromatic copies of graphs from F. If each Fn is bipartite, then we can improve this bound to 2CΔ; this result is optimal up to the constant C. © 2015 Elsevier B.V

A statistical method for revealing form-function relations in biological networks

Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question "how does function follow form" is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.Comment: To appear in Proc. Natl. Acad. Sci. USA. 17 pages, 9 figures, 2 table

On a two variable class of Bernstein-Szego measures

The one variable Bernstein-Szego theory for orthogonal polynomials on the real line is extended to a class of two variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.Comment: minor change

Assessing the protection provided by facepiece filtering respirator: New model involving spherical porous layer with annular peripheral opening

© Taiwan Association for Aerosol Research.The penetration of aerosol particles inside a facepiece filtering respirator (FFR) was investigated using a novel model, which involved a spherical porous layer representing a filter and an annular peripheral opening representing a faceseal leakage. The model utilized a two-dimensional laminar incompressible flow in a free space and porous zones that are numerically solved by a computational fluid dynamic code FLUENT. Following the model validation, the efficiency of an FFR with an annular faceseal leakage opening was investigated as a function of the inhalation flow rate, particle size, and the ratio of the leak-to-filter areas. The filter material permeability was determined for a conventional N95 filter medium. It was found – for two inhalation flow rates (Qi = 30 and 85 L min–1) and three particle diameters (dp = 50 nm, 100 nm and 1 µm) – that once the faceseal leakage area exceeded 0.1% of the total surface of an N95 facepiece, the respirator was unable to offer the 95% protection – the minimum level that should be provided by its filter. It was demonstrated that under certain leakage condition (partially determined by the inhalation flow rate), the respirator protection level becomes independent on the particle size; furthermore, it is not anymore affected by the efficiency of its filter, and is only influenced by the size of the faceseal leakage

Safety of assisted reproductive techniques in young women harboring germline pathogenic variants in BRCA1/2 with a pregnancy after prior history of breast cancer

Breast cancer fertility; Pregnancy; SurvivalFertilidad y cáncer de mama; Embarazo; SupervivenciaFertilitat i càncer de mama; Embaràs; SupervivènciaBackground Knowledge is growing on the safety of assisted reproductive techniques (ART) in cancer survivors. No data exist, however, for the specific population of breast cancer patients harboring germline BRCA1/2 pathogenic variants. Patients and methods This is a multicenter retrospective cohort study across 30 centers worldwide including women diagnosed at ≤40 years with stage I-III breast cancer, between January 2000 and December 2012, harboring known germline BRCA1/2 pathogenic variants. Patients included in this analysis had a post-treatment pregnancy either achieved through use of ART (ART group) or naturally (non-ART group). ART procedures included ovulation induction, ovarian stimulation for in vitro fertilization or intracytoplasmic sperm injection, and embryo transfer under hormonal replacement therapy. Results Among the 1424 patients registered in the study, 168 were eligible for inclusion in the present analysis, of whom 22 were in the ART group and 146 in the non-ART group. Survivors in the ART group conceived at an older age compared with those in the non-ART group (median age: 39.7 versus 35.4 years, respectively). Women in the ART group experienced more delivery complications compared with those in the non-ART group (22.1% versus 4.1%, respectively). No other apparent differences in obstetrical outcomes were observed between cohorts. The median follow-up from pregnancy was 3.4 years (range: 0.8-8.6 years) in the ART group and 5.0 years (range: 0.8-17.6 years) in the non-ART group. Two patients (9.1%) in the ART group experienced a disease-free survival event (specifically, a locoregional recurrence) compared with 40 patients (27.4%) in the non-ART group. In the ART group, no patients deceased compared with 10 patients (6.9%) in the non-ART group. Conclusion This study provides encouraging safety data on the use of ART in breast cancer survivors harboring germline pathogenic variants in BRCA1/2, when natural conception fails or when they opt for ART in order to carry out preimplantation genetic testing.The present work was supported by the Italian Association for Cancer Research (‘Associazione Italiana per la Ricerca sul Cancro’, AIRC; MFAG 2020 ID 24698) and the Italian Ministry of Health (5 × 1000 funds 2017). MC and ID acknowledge the Fonds National de la Recherche Scientifique (FNRS and Télévie 7.6508.20) and Fonds Erasme for their financial support

Particle Size on Respiratory Protection Provided by Two Types of N95 Respirators on Agricultural Settings

The objective of this study was to compare size-selective workplace protection factors (WPFs) of an N95 elastomeric respirator (ER) and an N95 filtering facepiece respirator (FFR) in agricultural environments. Twenty-five healthy farm workers ranging in age from 20 to 30 years voluntarily participated in the study. Altogether eight farms were included representing three different types: two horse farms, three pig barns, and three grain handling sites. Subjects wore the ER and FFR while performing their daily activities, such as spreading hay, feeding livestock, and shoveling. Aerosol concentrations in an optical particle size range of 0.7–10 µm were determined simultaneously inside and outside of the respirator during the first and last 15 minutes of a 60-minute experiment. For every subject, size-selective WPFs were calculated in one-minute intervals and averaged over 30 minutes. For the ER, geometric mean WPFs were 172, 321, 1013, 2097 and 2784 for particles of 0.7–1.0, 1.0–2.0, 2.0–3.0, 3.0–5.0, and 5.0–10.0 µm, respectively. Corresponding values for the FFR were 69, 127, 324, 893, and 1994. The 5th percentiles for the ER and FFR were higher than the Assigned Protection Factor of 10 and varied from 28 to 250 and from 16 to 225, respectively. The results show that the N95 ER and FFR tested in the study provided expected level of protection for workers on agricultural farms against particles ranging from 0.7 to 10 µm. The WPFs for the ER were higher than those for the FFR in all size ranges, and the WPFs for both respirators increased with increasing particle size

Comparison of Workplace Protection Factors for Different Biological Contaminants

This study compared workplace protection factors (WPFs) for five different contaminants (endotoxin, fungal spores, (1→3)-β-D-glucan, total particle mass, and total particle number) provided by an N95 elastomeric respirator (ER) and an N95 filtering facepiece respirator (FFR). We previously reported size-selective WPFs for total particle numbers for the ER and FFR, whereas the current article is focused on WPFs for bioaerosols and total particle mass. Farm workers (n = 25) wore the ER and FFR while performing activities at eight locations representing horse farms, pig barns, and grain handling facilities. For the determination of WPFs, particles were collected on filters simultaneously inside and outside the respirator during the first and last 15 min of a 60-min experiment. One field blank per subject was collected without actual sampling. A reporting limit (RL) was established for each contaminant based on geometric means (GMs) of the field blanks as the lowest possible measurable values. Depending on the contaminant type, 38–48% of data points were below the RL. Therefore, a censored regression model was used to estimate WPFs (WPFcensored). The WPFcensored provided by the two types of respirators were not significantly different. In contrast, significant differences were found in the WPFcensored for different types of contaminants. GMs WPFscensored for the two types of respirators combined were 154, 29, 18, 19, and 176 for endotoxin, fungal spore count, (1→3)-β-D-glucan, total particle mass, and total particle number, respectively. The WPFcensored was more strongly associated with concentrations measured outside the respirator for endotoxin, fungal spores, and total particle mass except for total particle number. However, when only data points with outside concentrations higher than 176×RL were included, the WPFs increased, and the association between the outside concentrations and the WPFs became weaker. Results indicate that difference in WPFs observed between different contaminants may be attributed to differences in the sensitivity of analytical methods to detect low inside concentrations, rather than the nature of particles (biological or non-biololgical)

Blood-Brain Barrier Breakdown in a Single Post-stroke Rodent Brain

Stroke is a major cause of global morbidity and mortality. Middle cerebral artery occlusion (MCAO) has historically been the most common animal model of simulating ischemic stroke. The extent of neurological injury after MCAO is typically measured by cerebral edema, infarct zone, and blood-brain barrier (BBB) permeability. A significant limitation of these methods is that separate sets of brains must be used for each measurement. Here we examine an alternative method of measuring cerebral edema, infarct zone and BBB permeability following MCAO in the same set of brain samples. Ninety-six rats were randomly divided into three experimental groups. Group 1 (n = 27) was used for the evaluation of infarct zone and brain edema in rats post-MCAO (n = 17) vs. sham-operated controls (n = 10). Group 2 (n = 27) was used for the evaluation of BBB breakdown in rats post-MCAO (n = 15) vs. sham-operated controls (n = 10). In Group 3 (n = 42), all three parameters were measured in the same set of brain slices in rats post-MCAO (n = 26) vs. sham-operated controls (n = 16). The effect of Evans blue on the accuracy of measuring infarct zone by 2,3,5-triphenyltetrazolium chloride (TTC) staining was determined by measuring infarct zone with and without an applied blue filter. The effects of various concentrations of TTC (0, 0.05, 0.35, 0.5, 1, and 2%) on the accuracy of measuring BBB permeability was also assessed. There was an increase in infarct volume (p < 0.01), brain edema (p < 0.01) and BBB breakdown (p < 0.01) in rats following MCAO compared to sham-operated controls, whether measured separately or together in the same set of brain samples. Evans blue had an effect on measuring infarct volume that was minimized by the application of a blue filter on scanned brain slices. There was no difference in the Evans blue extravasation index for the brain tissue samples without TTC compared to brain tissue samples incubated in TTC. Our results demonstrate that measuring cerebral edema, infarct zone and BBB permeability following MCAO can accurately be measured in the same set of brain samples