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

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

Toxin-Based Therapeutic Approaches

Protein toxins confer a defense against predation/grazing or a superior pathogenic competence upon the producing organism. Such toxins have been perfected through evolution in poisonous animals/plants and pathogenic bacteria. Over the past five decades, a lot of effort has been invested in studying their mechanism of action, the way they contribute to pathogenicity and in the development of antidotes that neutralize their action. In parallel, many research groups turned to explore the pharmaceutical potential of such toxins when they are used to efficiently impair essential cellular processes and/or damage the integrity of their target cells. The following review summarizes major advances in the field of toxin based therapeutics and offers a comprehensive description of the mode of action of each applied toxin

Allogeneic Mesenchymal Precursor Cells in Type 2 Diabetes: A Randomized, Placebo-Controlled, Dose-Escalation Safety and Tolerability Pilot Study

OBJECTIVE: To assess the safety, tolerability, and feasibility of adult allogeneic bone marrow–derived mesenchymal precursor cells (MPCs) in type 2 diabetes inadequately controlled with metformin either alone or with one additional oral antidiabetic agent. RESEARCH DESIGN AND METHODS: The study was a dose-escalating randomized placebo-controlled trial assessing one intravenous (IV) infusion of MPCs (rexlemestrocel-L; Mesoblast Inc.) 0.3 × 10(6)/kg (n = 15), 1.0 × 10(6)/kg (n = 15), or 2.0 × 10(6)/kg (n = 15) or placebo (n = 16). Study duration was 12 weeks. RESULTS: Subjects (21 women, 40 men) with a mean ± SD baseline HbA(1c) 8.3 ± 1.0% (67 ± 10.9 mmol/mol), BMI 33.5 ± 5.5 kg/m(2), and diabetes duration 10.1 ± 6.0 years were enrolled at 18 U.S. sites. No acute adverse events (AEs) were associated with infusion. No serious AEs, serious hypoglycemia AEs, or discontinuations due to AEs over 12 weeks were found. No subjects developed donor-specific anti-HLA antibodies or became sensitized. The safety profile was comparable among treatment groups. Compared with placebo, a single IV infusion of rexlemestrocel-L reduced HbA(1c) at all time points after week 1. The adjusted least squares mean ± SE dose-related differences in HbA(1c) from placebo in the rexlemestrocel-L groups ranged from −0.1 ± 0.2% (−1.1 ± 2.2 mmol/mol) to −0.4 ± 0.2% (4.4 ± 2.2 mmol/mol) at 8 weeks and from 0.0 ± 0.25% to −0.3 ± 0.25% (−3.3 ± −2.7 mmol/mol) at 12 weeks (P < 0.05 for 2.0 × 10(6)/kg dose at 8 weeks). The clinical target HbA(1c) <7% (53 mmol/mol) was achieved by 33% (5 of 15) of the subjects who received the 2.0 × 10(6)/kg dose vs. 0% of those who received placebo (P < 0.05). CONCLUSIONS: This short-term study demonstrates the safety and feasibility of up to 246 million MPCs in subjects with type 2 diabetes