Unimodality of steady state distributions of growing cell populations

We consider an equation for the evolution of growing and dividing cells, and show, using a result of Kato and McLeod, that the probability density function for the stationary size distribution is necessarily unimodal

Universal features of the order-parameter fluctuations : reversible and irreversible aggregation

We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the finite-size scaling analysis. The relation between order parameter, criticality and scaling law of fluctuations has been established and the connexion between the scaling function and the critical exponents has been found. We give examples in out-of-equilibrium aggregation models such as the Smoluchowski kinetic equations, or of at-equilibrium Ising and percolation models.Comment: 19 pages, 10 figure

The BCS Functional for General Pair Interactions

The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.Comment: Revised Version. To appear in Commun. Math. Phys

Degradation and healing in a generalized neo-Hookean solid due to infusion of a fluid

The mechanical response and load bearing capacity of high performance polymer composites changes due to diffusion of a fluid, temperature, oxidation or the extent of the deformation. Hence, there is a need to study the response of bodies under such degradation mechanisms. In this paper, we study the effect of degradation and healing due to the diffusion of a fluid on the response of a solid which prior to the diffusion can be described by the generalized neo-Hookean model. We show that a generalized neo-Hookean solid - which behaves like an elastic body (i.e., it does not produce entropy) within a purely mechanical context - creeps and stress relaxes when infused with a fluid and behaves like a body whose material properties are time dependent. We specifically investigate the torsion of a generalized neo-Hookean circular cylindrical annulus infused with a fluid. The equations of equilibrium for a generalized neo-Hookean solid are solved together with the convection-diffusion equation for the fluid concentration. Different boundary conditions for the fluid concentration are also considered. We also solve the problem for the case when the diffusivity of the fluid depends on the deformation of the generalized neo-Hookean solid.Comment: 24 pages, 10 figures, submitted to Mechanics of Time-dependent Material

Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: a Review and Extensions of Tests for the Painlev\'e Property

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable equations have the Painlev\'e property, that is, all solutions are single-valued around all movable singularities. In this expository article, we review methods for analysing such singularity structure. In particular, we describe well known techniques of nonlinear regular-singular-type analysis, i.e. the Painlev\'e tests for ordinary and partial differential equations. Then we discuss methods of obtaining sufficiency conditions for the Painlev\'e property. Recently, extensions of \textit{irregular} singularity analysis to nonlinear equations have been achieved. Also, new asymptotic limits of differential equations preserving the Painlev\'e property have been found. We discuss these also.Comment: 40 pages in LaTeX2e. To appear in the Proceedings of the CIMPA Summer School on "Nonlinear Systems," Pondicherry, India, January 1996, (eds) B. Grammaticos and K. Tamizhman

The analytic continuation of the resolvent kernel and scattering operator associated with the Schroedinger operator,

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33406/1/0000807.pd

A type 2 diabetes subtype responsive to ACCORD intensive glycemia treatment

OBJECTIVE Current type 2 diabetes (T2D) management contraindicates intensive glycemia treatment in patients with high cardiovascular disease (CVD) risk and is partially motivated by evidence of harms in the Action to Control Cardiovascular Risk in Diabetes (ACCORD) trial. Heterogeneity in response to intensive glycemia treatment has been observed, suggesting potential benefit for some individuals. RESEARCH DESIGN AND METHODS ACCORD was a randomized controlled trial that investigated whether intensively treating glycemia in individuals with T2D would reduce CVD outcomes. Using a novel approach to cluster HbA1c trajectories, we identified groups in the intensive glycemia arm with modified CVD risk. Genome-wide analysis and polygenic score (PS) were developed to predict group membership. Mendelian randomization was performed to infer causality. RESULTS We identified four clinical groupings in the intensive glycemia arm, and clinical group 4 (C4) displayed fewer CVD (hazard ratio [HR] 0.34; P 5 2.01 × 10-3) and microvascular outcomes (HR 0.86; P 5 0.015) than those receiving standard treatment. A singlenucleotide polymorphism, rs220721, in MAS1 reached suggestive significance in C4 (P 5 4.343 10-7). PS predicted C4 with high accuracy (area under the receiver operating characteristic curve 0.98), and this predicted C4 displayed reduced CVD risk with intensive versus standard glycemia treatment (HR 0.53; P 5 4.02 × 10-6), but not reduced risk of microvascular outcomes (P < 0.05). Mendelian randomization indicated causality between PS, on-trial HbA1c, and reduction in CVD outcomes (P < 0.05). CONCLUSIONS We found evidence of a T2D clinical group in ACCORD that benefited from intensive glycemia treatment, and membership in this group could be predicted using genetic variants. This study generates new hypotheses with implications for precision medicine in T2D and represents an important development in this landmark clinical trial warranting further investigation

Au+Au Reactions at the AGS: Experiments E866 and E917

Particle production and correlation functions from Au+Au reactions have been measured as a function of both beam energy (2-10.7AGeV) and impact parameter. These results are used to probe the dynamics of heavy-ion reactions, confront hadronic models over a wide range of conditions and to search for the onset of new phenomena.Comment: 12 pages, 14 figures, Talk presented at Quark Matter '9

Genetic variants in CPA6 and PRPF31 are associated with variation in response to metformin in individuals with type 2 diabetes

Metformin is the first-line treatment for type 2 diabetes (T2D). Although widely prescribed, the glucose-lowering mechanism for metformin is incompletely understood. Here, we used a genome-wide association approach in a diverse group of individuals with T2D from the Action to Control Cardiovascular Risk in Diabetes (ACCORD) clinical trial to identify common and rare variants associated with HbA 1c response to metformin treatment and followed up these findings in four replication cohorts. Common variants in PRPF31 and CPA6 were associated with worse and better metformin response, respectively (P &lt; 5 3 10 26 ), and meta-analysis in independent cohorts displayed similar associations with metformin response (P = 1.2 3 10 2 8 and P = 0.005, respectively). Previous studies have shown that PRPF31(+/2) knockout mice have increased total body fat (P = 1.78 3 10 26 ) and increased fasted circulating glucose (P = 5.73 3 10 26 ). Furthermore, rare variants in STAT3 associated with worse metformin response (q &lt;0.1). STAT3 is a ubiquitously expressed pleiotropic transcriptional activator that participates in the regulation of metabolism and feeding behavior. Here, we provide novel evidence for associations of common and rare variants in PRPF31, CPA6, and STAT3 with metformin response that may provide insight into mechanisms important for metformin efficacy in T2D