Abstract:
Young (7 week-old) db/db mice were randomized and assigned to receive diets supplemented with or without EGCG or rosiglitazone for 10 weeks. Fasting blood glucose, body weight and food intake was measured along the treatment. Glucose and insulin levels were determined during an oral glucose tolerance test after 10 weeks of treatment. Pancreata were sampled at the end of the study for blinded histomorphometric analysis. Islets were isolated and their mRNA expression analyzed by quantitative RT-PCR.The results show that, in db/db mice, EGCG improves glucose tolerance and increases glucose-stimulated insulin secretion. EGCG supplementation reduces the number of pathologically changed islets of Langerhans, increases the number and the size of islets, and heightens pancreatic endocrine area. These effects occurred in parallel with a reduction in islet endoplasmic reticulum stress markers, possibly linked to the antioxidative capacity of EGCG.This study shows that the green tea extract EGCG markedly preserves islet structure and enhances glucose tolerance in genetically diabetic mice. Dietary supplementation with EGCG could potentially contribute to nutritional strategies for the prevention and treatment of type 2 diabetes.The WHO and CDC (U.S. Center for Disease Control) predict that by today some 26 million people in the U.S. only are afflicted by diabetes (http://www.cdc.gov/diabetes/ webcite). Previously viewed as a disease of the elderly, type 2 diabetes is now seen in ever-younger age groups. In the U.S. about one third of all newly diagnosed diabetes in children and adolescents (age 10-19 years) now is type 2, an alarming scenario considering the magnitude of premature cardiovascular and cerebrovascular morbidity in these individuals. Recent estimates by the CDC indicate that the life-time risk of getting diabetes is not less than 40% for people born in 2000 in the U.S., with certain ethnic groups being significantly overrepresented (http://www.cdc.gov/diabetes web

Abstract:
Ground-motion prediction equations (GMPE) are essential in probabilistic seismic hazard studies for estimating the ground motions generated by the seismic sources. In low seismicity regions, only weak motions are available in the lifetime of accelerometric networks, and the equations selected for the probabilistic studies are usually models established from foreign data. Although most ground-motion prediction equations have been developed for magnitudes 5 and above, the minimum magnitude often used in probabilistic studies in low seismicity regions is smaller. Desaggregations have shown that, at return periods of engineering interest, magnitudes lower than 5 can be contributing to the hazard. This paper presents the testing of several GMPEs selected in current international and national probabilistic projects against weak motions recorded in France (191 recordings with source-site distances up to 300km, 3.8\leqMw\leq4.5). The method is based on the loglikelihood value proposed by Scherbaum et al. (2009). The best fitting models (approximately 2.5\leqLLH\leq3.5) over the whole frequency range are the Cauzzi and Faccioli (2008), Akkar and Bommer (2010) and Abrahamson and Silva (2008) models. No significant regional variation of ground motions is highlighted, and the magnitude scaling could be predominant in the control of ground-motion amplitudes. Furthermore, we take advantage of a rich Japanese dataset to run tests on randomly selected low-magnitude subsets, and check that a dataset of ~190 observations, same size as the French dataset, is large enough to obtain stable LLH estimates. Additionally we perform the tests against larger magnitudes (5-7) from the Japanese dataset. The ranking of models is partially modified, indicating a magnitude scaling effect for some of the models, and showing that extrapolating testing results obtained from low magnitude ranges to higher magnitude ranges is not straightforward.

Abstract:
Geometric Singular Perturbation Theory (GSPT) and Conley Index Theory are two powerful techniques to analyze dynamical systems. Conley already realized that using his index is easier for singular perturbation problems. In this paper, we will revisit Conley's results and prove that the GSPT technique of Fenichel Normal Form can be used to simplify the application of Conley index techniques even further. We also hope that our results provide a better bridge between the different fields. Furthermore we show how to interpret Conley's conditions in terms of averaging. The result are illustrated by the two-dimensional van der Pol equation and by a three-dimensional Morris-Lecar model.

Abstract:
An analytically tractable model is introduced which exhibits both, a glass--like freezing transition, and a collection of double--well configurations in its zero--temperature potential energy landscape. The latter are generally believed to be responsible for the anomalous low--temperature properties of glass-like and amorphous systems via a tunneling mechanism that allows particles to move back and forth between adjacent potential energy minima. Using mean--field and replica methods, we are able to compute the distribution of asymmetries and barrier--heights of the double--well configurations {\em analytically}, and thereby check various assumptions of the standard tunneling model. We find, in particular, strong correlations between asymmetries and barrier--heights as well as a collection of single--well configurations in the potential energy landscape of the glass--forming system --- in contrast to the assumptions of the standard model. Nevertheless, the specific heat scales linearly with temperature over a wide range of low temperatures.

Abstract:
We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by Rodgers and Bray. Due attention is payed to the issue of localization. Our approach is not restricted to matrices defined on graphs with Poissonian degree distribution. Matrices defined on regular random graphs or on scale-free graphs, are easily handled. We also look at matrices with row constraints such as discrete graph Laplacians. Our approach naturally allows to unfold the total density of states into contributions coming from vertices of different local coordination.

Abstract:
We compute spectra of large stochastic matrices $W$, defined on sparse random graphs, where edges $(i,j)$ of the graph are given positive random weights $W_{ij}>0$ in such a fashion that column sums are normalized to one. We compute spectra of such matrices both in the thermodynamic limit, and for single large instances. The structure of the graphs and the distribution of the non-zero edge weights $W_{ij}$ are largely arbitrary, as long as the mean vertex degree remains finite in the thermodynamic limit and the $W_{ij}$ satisfy a detailed balance condition. Knowing the spectra of stochastic matrices is tantamount to knowing the complete spectrum of relaxation times of stochastic processes described by them, so our results should have many interesting applications for the description of relaxation in complex systems. Our approach allows to disentangle contributions to the spectral density related to extended and localized states, respectively, allowing to differentiate between time-scales associated with transport processes and those associated with the dynamics of local rearrangements.

Abstract:
Alternating patterns of small and large amplitude oscillations occur in a wide variety of physical, chemical, biological and engineering systems. These mixed-mode oscillations (MMOs) are often found in systems with multiple time scales. Previous differential equation modeling and analysis of MMOs has mainly focused on local mechanisms to explain the small oscillations. Numerical continuation studies reported different MMO patterns based on parameter variation. This paper aims at improving the link between local analysis and numerical simulation. Our starting point is a numerical study of a singular return map for the Koper model which is a prototypical example for MMOs that also relates to local normal form theory. We demonstrate that many MMO patterns can be understood geometrically by approximating the singular maps with affine and quadratic maps. Motivated by our numerical analysis we use abstract affine and quadratic return map models in combination with two local normal forms that generate small oscillations. Using this decomposition approach we can reproduce many classical MMO patterns and effectively decouple bifurcation parameters for local and global parts of the flow. The overall strategy we employ provides an alternative technique for understanding MMOs.

Abstract:
Recent studies have shown that adaptive networks driven by simple local rules can organize into "critical" global steady states, providing another framework for self-organized criticality (SOC). We focus on the important convergence to criticality and show that noise and time-scale optimality are reached at finite values. This is in sharp contrast to the previously believed optimal zero noise and infinite time scale separation case. Furthermore, we discover a noise induced phase transition for the breakdown of SOC. We also investigate each of the three new effects separately by developing models. These models reveal three generically low-dimensional dynamical behaviors: time-scale resonance (TR), a new simplified version of stochastic resonance - which we call steady state stochastic resonance (SSR) - as well as noise-induced phase transitions.

Abstract:
Hopf bifurcations in fast-slow systems of ordinary differential equations can be associated with surprising rapid growth of periodic orbits. This process is referred to as canard explosion. The key step in locating a canard explosion is to calculate the location of a special trajectory, called a maximal canard, in parameter space. A first-order asymptotic expansion of this location was found by Krupa and Szmolyan in the framework of a "canard point"-normal-form for systems with one fast and one slow variable. We show how to compute the coefficient in this expansion using the first Lyapunov coefficient at the Hopf bifurcation thereby avoiding use of this normal form. Our results connect the theory of canard explosions with existing numerical software, enabling easier calculations of where canard explosions occur.

Abstract:
Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent standard software packages are available for ODEs, there are - for good reasons - no standard numerical continuation toolboxes available for partial differential equations (PDEs), which cover a broad range of different classes of PDEs automatically. A natural approach to this problem is to look for efficient gluing computation approaches, with independent components developed by researchers in numerical analysis, dynamical systems, scientific computing and mathematical modelling. In this paper, we shall study several elliptic PDEs (Lane-Emden-Fowler, Lane-Emden-Fowler with microscopic force, Caginalp) via the numerical continuation software pde2path and develop a gluing component to determine a set of starting solutions for the continuation by exploting the variational structures of the PDEs. In particular, we solve the initialization problem of numerical continuation for PDEs via a minimax algorithm to find multiple unstable solution. Furthermore, for the Caginalp system, we illustrate the efficient gluing link of pde2path to the underlying mesh generation and the FEM MatLab pdetoolbox. Even though the approach works efficiently due to the high-level programming language and without developing any new algorithms, we still obtain interesting bifurcation diagrams and directly applicable conclusions about the three elliptic PDEs we study, in particular with respect to symmetry-breaking. In particular, we show for a modified Lane-Emden-Fowler equation with an asymmetric microscopic force, how a fully connected bifurcation diagram splits up into C-shaped isolas on which localized pattern deformation appears towards two different regimes.