Asymptotic analysis of an elastic rod with rounded ends

We derive a one-dimensional model for an elastic shuttle, that is, a thin rod with rounded ends and small fixed terminals, by means of an asymptotic procedure of dimension reduction. In the model, deformation of the shuttle is described by a system of ordinary differential equations with variable degenerating coefficients, and the number of the required boundary conditions at the end points of the one-dimensional image of the rod depends on the roundness exponent m is an element of(0,1). Error estimates are obtained in the case m is an element of(0,1/4) by using an anisotropic weighted Korn inequality, which was derived in an earlier paper by the authors. We also briefly discuss boundary layer effects, which can be neglected in the case m is an element of(0,1/4) but play a crucial role in the formulation of the limit problem for m >= 1/4.Peer reviewe

How Many Subpopulations is Too Many? Exponential Lower Bounds for Inferring Population Histories

Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, like the seminal work of Li and Durbin (Nature, 2011), attempt to solve this problem using sequence data but have no rigorous guarantees. Determining the amount of data needed to correctly reconstruct population histories is a major challenge. Using a variety of tools from information theory, the theory of extremal polynomials, and approximation theory, we prove new sharp information-theoretic lower bounds on the problem of reconstructing population structure -- the history of multiple subpopulations that merge, split and change sizes over time. Our lower bounds are exponential in the number of subpopulations, even when reconstructing recent histories. We demonstrate the sharpness of our lower bounds by providing algorithms for distinguishing and learning population histories with matching dependence on the number of subpopulations. Along the way and of independent interest, we essentially determine the optimal number of samples needed to learn an exponential mixture distribution information-theoretically, proving the upper bound by analyzing natural (and efficient) algorithms for this problem.Comment: 38 pages, Appeared in RECOMB 201

Increased Membrane Cholesterol in Lymphocytes Diverts T-Cells toward an Inflammatory Response

Cell signaling for T-cell growth, differentiation, and apoptosis is initiated in the cholesterol-rich microdomains of the plasma membrane known as lipid rafts. Herein, we investigated whether enrichment of membrane cholesterol in lipid rafts affects antigen-specific CD4 T-helper cell functions. Enrichment of membrane cholesterol by 40–50% following squalene administration in mice was paralleled by an increased number of resting CD4 T helper cells in periphery. We also observed sensitization of the Th1 differentiation machinery through co-localization of IL-2Rα, IL-4Rα, and IL-12Rβ2 subunits with GM1 positive lipid rafts, and increased STAT-4 and STAT-5 phosphorylation following membrane cholesterol enrichment. Antigen stimulation or CD3/CD28 polyclonal stimulation of membrane cholesterol-enriched, resting CD4 T-cells followed a path of Th1 differentiation, which was more vigorous in the presence of increased IL-12 secretion by APCs enriched in membrane cholesterol. Enrichment of membrane cholesterol in antigen-specific, autoimmune Th1 cells fostered their organ-specific reactivity, as confirmed in an autoimmune mouse model for diabetes. However, membrane cholesterol enrichment in CD4+ Foxp3+ T-reg cells did not alter their suppressogenic function. These findings revealed a differential regulatory effect of membrane cholesterol on the function of CD4 T-cell subsets. This first suggests that membrane cholesterol could be a new therapeutic target to modulate the immune functions, and second that increased membrane cholesterol in various physiopathological conditions may bias the immune system toward an inflammatory Th1 type response