Solitary waves for nonconvex FPU lattices

Belgium Herbarium image of Meise Botanic Garden

On selection criteria for problems with moving inhomogeneities

We study mechanical problems with multiple solutions and introduce a thermodynamic framework to formulate two different selection criteria in terms of macroscopic energy productions and fluxes. Studying simple examples for lattice motion we then compare the implications for both resting and moving inhomogeneities.Comment: revised version contains new introduction, numerical simulations of Riemann problems, and a more detailed discussion of the causality principle; 18 pages, several figure

Solitary waves for nonconvex FPU lattices

Solitary waves in a one-dimensional chain of atoms {q j} j∈Z are investigated. The potential energy is required to be monotone and grow super-quadratically. The existence of solitary waves with a prescribed asymptotic strain is shown under certain assumptions on the asymptotic strain and the wave speed. It is demonstrated the invariance of the equations allows one to transform a system with non-convex potential energy density to the situation under consideration

A systems biology approach uncovers the core gene regulatory network governing iridophore fate choice from the neural crest.

Multipotent neural crest (NC) progenitors generate an astonishing array of derivatives, including neuronal, skeletal components and pigment cells (chromatophores), but the molecular mechanisms allowing balanced selection of each fate remain unknown. In zebrafish, melanocytes, iridophores and xanthophores, the three chromatophore lineages, are thought to share progenitors and so lend themselves to investigating the complex gene regulatory networks (GRNs) underlying fate segregation of NC progenitors. Although the core GRN governing melanocyte specification has been previously established, those guiding iridophore and xanthophore development remain elusive. Here we focus on the iridophore GRN, where mutant phenotypes identify the transcription factors Sox10, Tfec and Mitfa and the receptor tyrosine kinase, Ltk, as key players. Here we present expression data, as well as loss and gain of function results, guiding the derivation of an initial iridophore specification GRN. Moreover, we use an iterative process of mathematical modelling, supplemented with a Monte Carlo screening algorithm suited to the qualitative nature of the experimental data, to allow for rigorous predictive exploration of the GRN dynamics. Predictions were experimentally evaluated and testable hypotheses were derived to construct an improved version of the GRN, which we showed produced outputs consistent with experimentally observed gene expression dynamics. Our study reveals multiple important regulatory features, notably a sox10-dependent positive feedback loop between tfec and ltk driving iridophore specification; the molecular basis of sox10 maintenance throughout iridophore development; and the cooperation between sox10 and tfec in driving expression of pnp4a, a key differentiation gene. We also assess a candidate repressor of mitfa, a melanocyte-specific target of sox10. Surprisingly, our data challenge the reported role of Foxd3, an established mitfa repressor, in iridophore regulation. Our study builds upon our previous systems biology approach, by incorporating physiologically-relevant parameter values and rigorous evaluation of parameter values within a qualitative data framework, to establish for the first time the core GRN guiding specification of the iridophore lineage

Action minimizing fronts in general FPU-type chains

We study atomic chains with nonlinear nearest neighbour interactions and prove the existence of fronts (heteroclinic travelling waves with constant asymptotic states). Generalizing recent results of Herrmann and Rademacher we allow for non-convex interaction potentials and find fronts with non-monotone profile. These fronts minimize an action integral and can only exists if the asymptotic states fulfil the macroscopic constraints and if the interaction potential satisfies a geometric graph condition. Finally, we illustrate our findings by numerical simulations.Comment: 19 pages, several figure

Evolution equations of curvature tensors along the hyperbolic geometric flow

We consider the hyperbolic geometric flow $\frac{\partial^2}{\partial t^2}g(t)=-2Ric_{g(t)}$ introduced by Kong and Liu [KL]. When the Riemannian metric evolve, then so does its curvature. Using the techniques and ideas of S.Brendle [Br,BS], we derive evolution equations for the Levi-Civita connection and the curvature tensors along the hyperbolic geometric flow. The method and results are computed and written in global tensor form, different from the local normal coordinate method in [DKL1]. In addition, we further show that any solution to the hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.Comment: 15 page

Oporność na kwas acetylosalicylowy we wtórnej prewencji udaru mózgu

Wstęp. Autorzy zbadali czynność płytek krwi u pacjentów po udarze mózgu leczonych kwasem acetylosalicylowym (ASA, acetylsalicylic acid), w celu zapobieżenia kolejnemu udarowi. Okres obserwacji wynosił 1 rok. Metoda. W badaniu prospektywnym wzięło udział 291 pacjentów, u których po raz pierwszy włączono ASA (300 mg/d.) w celu wtórnej prewencji udaru mózgu. Pomiary agregacji płytek wykonano po 24 godzinach, 3, 6 i 12 miesiącach od rozpoczęcia leczenia. Wyniki. Dwudziestu jeden pacjentów (7,2%) spośród 291 uznano za pierwotnie nieodpowiadających na ASA (początkowa niewystarczająca inhibicja płytek), a 4,1% jako wtórnie nieodpowiadających (niewystarczająca inhibicja płytek w czasie obserwacji). Nie stwierdzono istotnych różnic w odniesieniu do wieku, płci, czynników ryzyka i typu udaru między grupami pacjentów odpowiadajacych i nieodpowiadających na leczenie ASA. Wniosek. Oporność na ASA wśród pacjentów po udarze mózgu nie jest zjawiskiem rzadkim. Kliniczną przydatność rutynowych testów czynności płytek powinno się ocenić w przyszłych badaniach klinicznych

Controlled variations in stimulus similarity during learning determine visual discrimination capacity in freely moving mice

The mouse is receiving growing interest as a model organism for studying visual perception. However, little is known about how discrimination and learning interact to produce visual conditioned responses. Here, we adapted a two-alternative forced-choice visual discrimination task for mice and examined how training with equiprobable stimuli of varying similarity influenced conditioned response and discrimination performance as a function of learning. Our results indicate that the slope of the gradients in similarity during training determined the learning rate, the maximum performance and the threshold for successful discrimination. Moreover, the learning process obeyed an inverse relationship between discrimination performance and discriminative resolution, implying that sensitivity within a similarity range cannot be improved without sacrificing performance in another. Our study demonstrates how the interplay between discrimination and learning controls visual discrimination capacity and introduces a new training protocol with quantitative measures to study perceptual learning and visually-guided behavior in freely moving mice