Linear Stability Analysis of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem

We apply the symmetry reduction method of Roberts to numerically analyze the linear stability of a one-parameter family of symmetric periodic orbits with regularizable simultaneous binary collisions in the planar pairwise symmetric four-body problem with a mass $m\in(0,1]$ as the parameter. This reduces the linear stability analysis to the computation of two eigenvalues of a $3\times 3$ matrix for each $m\in(0,1]$ obtained from numerical integration of the linearized regularized equations along only the first one-eighth of each regularized periodic orbit. The results are that the family of symmetric periodic orbits with regularizable simultaneous binary collisions changes its linear stability type several times as $m$ varies over $(0,1]$, with linear instability for $m$ close or equal to 0.01, and linear stability for $m$ close or equal to 1.Comment: 13 pages, 1 figur

Relative Equilibria and Periodic Orbits in a Binary Asteroid Model

We present a planar four-body model, called the Binary Asteroid Problem, for the motion of two asteroids (having small but positive masses) moving under the gravitational attraction of each other, and under the gravitational attraction of two primaries (with masses much larger than the two asteroids) moving in uniform circular motion about their center of mass. We show the Binary Asteroid Model has (at least) 6 relative equilibria and (at least) 10 one-parameter families of periodic orbits, two of which are of Hill-type. The existence of six relative equilibria and 8 one-parameter families of periodic orbits is obtained by a reduction of the Binary Asteroid Problem in which the primaries have equal mass, the asteroids have equal mass, and the positions of the asteroids are symmetric with respect to the origin. The remaining two one-parameter families of periodic orbits, which are of comet-type, are obtained directly in the Binary Asteroid Problem.Comment: 34 page, 8 figure

Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem

We extend our previous analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized fully symmetric equal mass four-body problem to the analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar pairwise symmetric equal mass four-body problem. We then use a continuation method to numerically find symmetric periodic simultaneous binary collision orbits in a regularized planar pairwise symmetric 1, m, 1, m four-body problem for $m$ between 0 and 1. Numerical estimates of the the characteristic multipliers show that these periodic orbits are linearly stability when $0.54\leq m\leq 1$, and are linearly unstable when $0<m\leq0.53$.Comment: 6 figure

Linear Stability for Some Symmetric Periodic Simultaneous Binary Collision Orbits in the Four-Body Problem

We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four body problem with masses 1, m, m, 1, and also in a symmetric planar four-body problem with equal masses. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability.Comment: 16 pages, 4 figure

Genetic Variation in the Familial Mediterranean Fever Gene (MEFV) and Risk for Crohn's Disease and Ulcerative Colitis

BACKGROUND AND AIMS: The familial Mediterranean fever (FMF) gene (MEFV) encodes pyrin, a major regulator of the inflammasome platform controlling caspase-1 activation and IL-1beta processing. Pyrin has been shown to interact with the gene product of NLRP3, NALP3/cryopyrin, also an important active member of the inflammasome. The NLRP3 region was recently reported to be associated with Crohn's disease (CD) susceptibility. We therefore sought to evaluate MEFV as an inflammatory bowel disease (IBD) susceptibility gene. METHODOLOGY AND RESULTS: MEFV colonic mucosal gene expression was significantly increased in experimental colitis mice models (TNBS p<0.0003; DSS p<0.006), in biopsies from CD (p<0.02) and severe ulcerative colitis (UC) patients (p<0.008). Comprehensive genetic screening of the MEFV region in the Belgian exploratory sample set (440 CD trios, 137 UC trios, 239 CD cases, 96 UC cases, and 107 healthy controls) identified SNPs located in the MEFV 5' haplotype block that were significantly associated with UC (rs224217; p = 0.003; A allele frequency: 56% cases, 45% controls), while no CD associations were observed. Sequencing and subsequent genotyping of variants located in this associated haplotype block identified three synonymous variants (D102D/rs224225, G138G/rs224224, A165A/rs224223) and one non-synonymous variant (R202Q/rs224222) located in MEFV exon 2 that were significantly associated with UC (rs224222: p = 0.0005; A allele frequency: 32% in cases, 23% in controls). No consistent associations were observed in additional Canadian (256 CD trios, 91 UC trios) and Scottish (495 UC, 370 controls) sample sets. We note that rs224222 showed marginal association (p = 0.012; G allele frequency: 82% in cases, 70% in controls) in the Canadian sample, but with a different risk allele. None of the NLRP3 common variants were associated with UC in the Belgian-Canadian UC samples and no significant interactions were observed between NLRP3 and MEFV that could explain the observed flip-flop of the rs224222 risk allele. CONCLUSION: The differences in association levels observed between the sample sets may be a consequence of distinct founder effects or of the relative small sample size of the cohorts evaluated in this study. However, the results suggest that common variants in the MEFV region do not contribute to CD and UC susceptibility.Journal ArticleResearch Support, N.I.H. ExtramuralResearch Support, Non-U.S. Gov'tSCOPUS: ar.jinfo:eu-repo/semantics/publishe

An update of the Worldwide Integrated Assessment (WIA) on systemic insecticides. Part 2: impacts on organisms and ecosystems

New information on the lethal and sublethal effects of neonicotinoids and fipronil on organisms is presented in this review, complementing the previous WIA in 2015. The high toxicity of these systemic insecticides to invertebrates has been confirmed and expanded to include more species and compounds. Most of the recent research has focused on bees and the sublethal and ecological impacts these insecticides have on pollinators. Toxic effects on other invertebrate taxa also covered predatory and parasitoid natural enemies and aquatic arthropods. Little, while not much new information has been gathered on soil organisms. The impact on marine coastal ecosystems is still largely uncharted. The chronic lethality of neonicotinoids to insects and crustaceans, and the strengthened evidence that these chemicals also impair the immune system and reproduction, highlights the dangers of this particular insecticidal classneonicotinoids and fipronil. , withContinued large scale – mostly prophylactic – use of these persistent organochlorine pesticides has the potential to greatly decreasecompletely eliminate populations of arthropods in both terrestrial and aquatic environments. Sublethal effects on fish, reptiles, frogs, birds and mammals are also reported, showing a better understanding of the mechanisms of toxicity of these insecticides in vertebrates, and their deleterious impacts on growth, reproduction and neurobehaviour of most of the species tested. This review concludes with a summary of impacts on the ecosystem services and functioning, particularly on pollination, soil biota and aquatic invertebrate communities, thus reinforcing the previous WIA conclusions (van der Sluijs et al. 2015)

Antiinflammatory Therapy with Canakinumab for Atherosclerotic Disease

Background: Experimental and clinical data suggest that reducing inflammation without affecting lipid levels may reduce the risk of cardiovascular disease. Yet, the inflammatory hypothesis of atherothrombosis has remained unproved. Methods: We conducted a randomized, double-blind trial of canakinumab, a therapeutic monoclonal antibody targeting interleukin-1β, involving 10,061 patients with previous myocardial infarction and a high-sensitivity C-reactive protein level of 2 mg or more per liter. The trial compared three doses of canakinumab (50 mg, 150 mg, and 300 mg, administered subcutaneously every 3 months) with placebo. The primary efficacy end point was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death. RESULTS: At 48 months, the median reduction from baseline in the high-sensitivity C-reactive protein level was 26 percentage points greater in the group that received the 50-mg dose of canakinumab, 37 percentage points greater in the 150-mg group, and 41 percentage points greater in the 300-mg group than in the placebo group. Canakinumab did not reduce lipid levels from baseline. At a median follow-up of 3.7 years, the incidence rate for the primary end point was 4.50 events per 100 person-years in the placebo group, 4.11 events per 100 person-years in the 50-mg group, 3.86 events per 100 person-years in the 150-mg group, and 3.90 events per 100 person-years in the 300-mg group. The hazard ratios as compared with placebo were as follows: in the 50-mg group, 0.93 (95% confidence interval [CI], 0.80 to 1.07; P = 0.30); in the 150-mg group, 0.85 (95% CI, 0.74 to 0.98; P = 0.021); and in the 300-mg group, 0.86 (95% CI, 0.75 to 0.99; P = 0.031). The 150-mg dose, but not the other doses, met the prespecified multiplicity-adjusted threshold for statistical significance for the primary end point and the secondary end point that additionally included hospitalization for unstable angina that led to urgent revascularization (hazard ratio vs. placebo, 0.83; 95% CI, 0.73 to 0.95; P = 0.005). Canakinumab was associated with a higher incidence of fatal infection than was placebo. There was no significant difference in all-cause mortality (hazard ratio for all canakinumab doses vs. placebo, 0.94; 95% CI, 0.83 to 1.06; P = 0.31). Conclusions: Antiinflammatory therapy targeting the interleukin-1β innate immunity pathway with canakinumab at a dose of 150 mg every 3 months led to a significantly lower rate of recurrent cardiovascular events than placebo, independent of lipid-level lowering. (Funded by Novartis; CANTOS ClinicalTrials.gov number, NCT01327846.

Structure of group invariants of a quasiperiodic flow

It is shown that the multiplier representation of the generalized symmetry group of a quasiperiodic flow induces a semidirect product structure on certain group invariants (including the generalized symmetry group) of the flow's smooth conjugacy class