Measuring cell adhesion forces with the atomic force microscope at the molecular level

In the past 25 years many techniques have been developed to characterize cell adhesion and to quantify adhesion forces. Atomic force microscopy (AFM) has been used to measure forces in the pico-newton range, an experimental technique known as force spectroscopy. We modified such an AFM to measure adhesion forces between live cells or between cells and surfaces. This strategy required functionalizing the surface of the sensors for immobilizing the cell. We used Dictyostelium discoideum cells which respond to starvation by surface expression of the adhesion molecule csA and consequent aggregation to measure the adhesion force of a single csA-csA bond. Relevant experimental parameters include the duration of contact between the interacting surfaces, the force against which this contact is maintained, the number and specificity of interacting adhesion molecules and the constituents of the medium in which the interaction occurs. This technology also permits the measurement of the viscoelastic properties of single cells or cell layers. Copyright (C) 2002 S, Karger AG, Basel

Stochastic averaging lemmas for kinetic equations

We develop a class of averaging lemmas for stochastic kinetic equations. The velocity is multiplied by a white noise which produces a remarkable change in time scale. Compared to the deterministic case and as far as we work in $L^2$, the nature of regularity on averages is not changed in this stochastic kinetic equation and stays in the range of fractional Sobolev spaces at the price of an additional expectation. However all the exponents are changed; either time decay rates are slower (when the right hand side belongs to $L^2$), or regularity is better when the right hand side contains derivatives. These changes originate from a different space/time scaling in the deterministic and stochastic cases. Our motivation comes from scalar conservation laws with stochastic fluxes where the structure under consideration arises naturally through the kinetic formulation of scalar conservation laws

Scalar conservation laws with rough (stochastic) fluxes

We develop a pathwise theory for scalar conservation laws with quasilinear multiplicative rough path dependence, a special case being stochastic conservation laws with quasilinear stochastic dependence. We introduce the notion of pathwise stochastic entropy solutions, which is closed with the local uniform limits of paths, and prove that it is well posed, i.e., we establish existence, uniqueness and continuous dependence, in the form of pathwise $L^1$-contraction, as well as some explicit estimates. Our approach is motivated by the theory of stochastic viscosity solutions, which was introduced and developed by two of the authors, to study fully nonlinear first- and second-order stochastic pde with multiplicative noise. This theory relies on special test functions constructed by inverting locally the flow of the stochastic characteristics. For conservation laws this is best implemented at the level of the kinetic formulation which we follow here

Scalar conservation laws with rough (stochastic) fluxes; the spatially dependent case

We continue the development of the theory of pathwise stochastic entropy solutions for scalar conservation laws in $\R^N$ with quasilinear multiplicative ''rough path'' dependence by considering inhomogeneous fluxes and a single rough path like, for example, a Brownian motion. Following our previous note where we considered spatially independent fluxes, we introduce the notion of pathwise stochastic entropy solutions and prove that it is well posed, that is we establish existence, uniqueness and continuous dependence in the form of a (pathwise) $L^1$-contraction. Our approach is motivated by the theory of stochastic viscosity solutions, which was introduced and developed by two of the authors, to study fully nonlinear first- and second-order stochastic pde with multiplicative noise. This theory relies on special test functions constructed by inverting locally the flow of the stochastic characteristics. For conservation laws this is best implemented at the level of the kinetic formulation which we follow here

Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy

Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.Comment: 11 pages, 4 figure

Spectral properties of near-Earth and Mars-crossing asteroids using Sloan photometry

The nature and origin of the asteroids orbiting in near-Earth space, including those on a potentially hazardous trajectory, is of both scientific interest and practical importance. We aim here at determining the taxonomy of a large sample of near-Earth (NEA) and Mars-crosser (MC) asteroids and analyze the distribution of these classes with orbit. We use this distribution to identify their source regions and to study the strength of planetary encounters to refresh asteroid surfaces. We measure the photometry of these asteroids over four filters at visible wavelengths on images taken by the SDSS. These colors are used to classify the asteroids into a taxonomy consistent with the widely used Bus-DeMeo taxonomy based on spectroscopy. We report here on the taxonomic classification of 206 NEAs and 776 MCs determined from SDSS photometry, representing an increase of 40% and 663% of known taxonomy classifications in these populations. Using the source region mapper by Greenstreet et al. (2012), we compare the taxonomic distribution among NEAs and main-belt asteroids of similar diameters. Both distributions agree at the few percent level for the inner part of the Main Belt and we confirm this region as a main source of near-Earth objects. The effect of planetary encounters on asteroid surfaces are also studied by developing a simple model of forces acting on a surface grain during planetary encounter, which provides the minimum distance at which a close approach should occur to trigger resurfacing events. By integrating numerically the orbit of the 519 S-type and 46 Q-type asteroids back in time and monitoring their encounter distance with planets, we seek to understand the conditions for resurfacing events. The population of Q-type is found to present statistically more encounters with Venus and the Earth than S-types, although both types present the same amount of encounters with Mars.Comment: Accepted for publication in Icarus. 45 pages, 11 figures, 4 tables, 2 tables in appendix (supplementary material

Canard-like phenomena in piecewise-smooth Van der Pol systems

We show that a nonlinear, piecewise-smooth, planar dynamical system can exhibit canard phenomena. Canard solutions and explosion in nonlinear, piecewise-smooth systems can be qualitatively more similar to the phenomena in smooth systems than piecewise-linear systems, since the nonlinearity allows for canards to transition from small cycles to canards ``with heads." The canards are born of a bifurcation that occurs as the slow-nullcline coincides with the splitting manifold. However, there are conditions under which this bifurcation leads to a phenomenon called super-explosion, the instantaneous transition from a globally attracting periodic orbit to relaxations oscillations. Also, we demonstrate that the bifurcation---whether leading to canards or super-explosion---can be subcritical.Comment: 17 pages, 11 figure

Specialization of the rostral prefrontal cortex for distinct analogy processes

Analogical reasoning is central to learning and abstract thinking. It involves using a more familiar situation (source) to make inferences about a less familiar situation (target). According to the predominant cognitive models, analogical reasoning includes 1) generation of structured mental representations and 2) mapping based on structural similarities between them. This study used functional magnetic resonance imaging to specify the role of rostral prefrontal cortex (PFC) in these distinct processes. An experimental paradigm was designed that enabled differentiation between these processes, by temporal separation of the presentation of the source and the target. Within rostral PFC, a lateral subregion was activated by analogy task both during study of the source (before the source could be compared with a target) and when the target appeared. This may suggest that this subregion supports fundamental analogy processes such as generating structured representations of stimuli but is not specific to one particular processing stage. By contrast, a dorsomedial subregion of rostral PFC showed an interaction between task (analogy vs. control) and period (more activated when the target appeared). We propose that this region is involved in comparison or mapping processes. These results add to the growing evidence for functional differentiation between rostral PFC subregions