Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

The Patterson-Sullivan embedding and minimal volume entropy for outer space

"Vegeu el resum a l'inici del document del fitxer adjunt."

Marx's analysis of the falling rate of profit on the first version of volume III of capital

The paper provides a description and analysis of the Hodgskin section of Theories of Surplus Value and the general law section of the first version of Volume III of Capital. It then considers Part III of Volume III, the evolution of Marx's thought and various interpretations of his theory in the light of this analysis. It is suggested that Marx thought that the rate of profit must fall and even in the 1870s hoped to be able to provide a demonstration of this. However the main conclusions are: 1. Marx's major attempt to show that the rate of profit must fall occurred in the general law section. 2. Part III does not contain a demonstration that the rate of profit must fall. 3. Marx was never able to demonstrate that the rate of profit must fall and he was aware of this.

High tidal volume ventilation affects neuronal activation in mechanically ventilated rats

Els malalts crítics presenten sovint seqüeles cognitives a llarg termini, l’aplicació de ventilació mecànica (VM) pot contribuir al seu desenvolupament. El principal objectiu del nostre estudi fou investigar l’efecte de dos patrons de ventilació (volum corrent elevat/baix) en l’activació neuronal (expressió de c-fos) en determinades àrees cerebrals en un model en rates. Després de 3 hores sota VM, es va trobar activació neuronal; la seva intensitat va ser superior al grup de volum corrent elevat, suggerint un efecte iatrogènic de la VM al cervell. Aquests resultats suggereixen que cal aprofundir en l’estudi del crosstalk cervell-pulmó en malalts crítics sota VM.

A new automated method versus continuous positive airway pressure method for measuring pressure-volume curves in patients with acute lung injury

Objective: To compare pressure–volume (P–V) curves obtained with the Galileo ventilator with those obtained with the CPAP method in patients with ALI or ARDS receiving mechanical ventilation. P–V curves were fitted to a sigmoidal equation with a mean R2 of 0.994 ± 0.003. Lower (LIP) and upper inflection (UIP), and deflation maximum curvature (PMC) points calculated from the fitted variables showed a good correlation between methods with high intraclass correlation coefficients. Bias and limits of agreement for LIP, UIP and PMC obtained with the two methods in the same patient were clinically acceptable.

On the impact of leverage constraints on asset prices and trading volume

Researchers have used stylized facts on asset prices and trading volumein stock markets (in particular, the mean reversion of asset returnsand the correlations between trading volume, price changes and pricelevels) to support theories where agents are not rational expected utilitymaximizers. This paper shows that this empirical evidence is in factconsistent with a standard infite horizon perfect information expectedutility economy where some agents face leverage constraints similar tothose found in todays financial markets. In addition, and in sharpcontrast to the theories above, we explain some qualitative differencesthat are observed in the price-volume relation on stock and on futuresmarkets. We consider a continuous-time economy where agents maximize theintegral of their discounted utility from consumption under both budgetand leverage con-straints. Building on the work by Vila and Zariphopoulou(1997), we find a closed form solution, up to a negative constant, for theequilibrium prices and demands in the region of the state space where theconstraint is non-binding. We show that, at the equilibrium, stock holdingsvolatility as well as its ratio to stock price volatility are increasingfunctions of the stock price and interpret this finding in terms of theprice-volume relation.

Micropatterning of single endothelial cell shape reveals a tight coupling between nuclear volume in G1 and proliferation

Shape-dependent local differentials in cell proliferation are considered to be a major driving mechanism of structuring processes in vivo, such as embryogenesis, wound healing, and angiogenesis. However, the specific biophysical signaling by which changes in cell shape contribute to cell cycle regulation remains poorly understood. Here, we describe our study of the roles of nuclear volume and cytoskeletal mechanics in mediating shape control of proliferation in single endothelial cells. Micropatterned adhesive islands were used to independently control cell spreading and elongation. We show that, irrespective of elongation, nuclear volume and apparent chromatin decondensation of cells in G1 systematically increased with cell spreading and highly correlated with DNA synthesis (percent of cells in the S phase). In contrast, cell elongation dramatically affected the organization of the actin cytoskeleton, markedly reduced both cytoskeletal stiffness (measured dorsally with atomic force microscopy) and contractility (measured ventrally with traction microscopy), and increased mechanical anisotropy, without affecting either DNA synthesis or nuclear volume. Our results reveal that the nuclear volume in G1 is predictive of the proliferative status of single endothelial cells within a population, whereas cell stiffness and contractility are not. These findings show that the effects of cell mechanics in shape control of proliferation are far more complex than a linear or straightforward relationship. Our data are consistent with a mechanism by which spreading of cells in G1 partially enhances proliferation by inducing nuclear swelling and decreasing chromatin condensation, thereby rendering DNA more accessible to the replication machinery.

Correction of aberration in holographic optical tweezers using a Shack-Hartmann sensor

Optical aberration due to the nonflatness of spatial light modulators used in holographic optical tweezers significantly deteriorates the quality of the trap and may easily prevent stable trapping of particles. We use a Shack-Hartmann sensor to measure the distorted wavefront at the modulator plane; the conjugate of this wavefront is then added to the holograms written into the display to counteract its own curvature and thus compensate the optical aberration of the system. For a Holoeye LC-R 2500 reflective device, flatness is improved from 0.8¿ to ¿/16 (¿=532 nm), leading to a diffraction-limited spot at the focal plane of the microscope objective, which makes stable trapping possible. This process could be fully automated in a closed-loop configuration and would eventually allow other sources of aberration in the optical setup to be corrected for.

Adding functionalities to precomputed holograms with random mask multiplexing in holographic optical tweezers

In this study, we present a method designed to generate dynamic holograms in holographic optical tweezers. The approach combines our random mask encoding method with iterative high-efficiency algorithms. This hybrid method can be used to dynamically modify precalculated holograms, giving them new functionalities¿temporarily or permanently¿with a low computational cost. This allows the easy addition or removal of a single trap or the independent control of groups of traps for manipulating a variety of rigid structures in real time.

Holographic phase transitions with fundamental matter

The holographic dual of a finite-temperature gauge theory with a small number of flavors typically contains D-brane probes in a black hole background. At low temperature, the branes sit outside the black hole and the meson spectrum is discrete and possesses a mass gap. As the temperature increases, the branes approach a critical solution. Eventually, they fall into the horizon and a phase transition occurs. In the new phase, the meson spectrum is continuous and gapless. At large Nc and large't Hooft coupling, we show that this phase transition is always first order. In confining theories with heavy quarks, it occurs above the deconfinement transition for the glue.

Simple holographic polarogram

A new technique capable of obtaining quantitative values of the rotation angle of the polarization vector by using holography is presented. This is a two-stage holographic process; during the recording stage a hologram of the object of interest is obtained. The reference beam is composed of two beams that form a small angle between them and keep their polarization states at right angles to each other. In the reconstruction stage of the hologram, two images from the hologram are obtained along two different angles. As a result of the interference between these two images, a set of parallel fringes is formed at the image plane. The fringe contrast on the reconstruction is related to the angle of the polarization vector of the light at each position on the image plane. Measurements of the rotation of the polarization angle of a fraction of a degree were obtained. The main application of this technique is in the study of transient phenomena, where single-shot measurements are the only means of obtaining reliable data.

Holographic collisions in confining theories

We study the gravitational dual of a high-energy collision in a confining gauge theory. We consider a linearized approach in which two point particles traveling in an AdS-soliton background suddenly collide to form an object at rest (presumably a black hole for large enough center-of-mass energies). The resulting radiation exhibits the features expected in a theory with a mass gap: late-time power law tails of the form t −3/2, the failure of Huygens" principle and distortion of the wave pattern as it propagates. The energy spectrum is exponentially suppressed for frequencies smaller than the gauge theory mass gap. Consequently, we observe no memory effect in the gravitational waveforms. At larger frequencies the spectrum has an upward-stairway structure, which corresponds to the excitation of the tower of massive states in the confining gauge theory. We discuss the importance of phenomenological cutoffs to regularize the divergent spectrum, and the aspects of the full non-linear collision that are expected to be captured by our approach.

Positional stability of holographic optical traps

The potential of digital holography for complex manipulation of micron-sized particles with optical tweezers has been clearly demonstrated. By contrast, its use in quantitative experiments has been rather limited, partly due to fluctuations introduced by the spatial light modulator (SLM) that displays the kinoforms. This is an important issue when high temporal or spatial stability is a concern. We have investigated the performance of both an analog-addressed and a digitally-addressed SLM, measuring the phase fluctuations of the modulated beam and evaluating the resulting positional stability of a holographic trap. We show that, despite imparting a more unstable modulation to the wavefront, our digitally-addressed SLM generates optical traps in the sample plane stable enough for most applications. We further show that traps produced by the analog-addressed SLM exhibit a superior pointing stability, better than 1 nm, which is comparable to that of non-holographic tweezers. These results suggest a means to implement precision force measurement experiments with holographic optical tweezers (HOTs).

Holographic optical tweezers combined with back-focal-plane displacement detection

A major problem with holographic optical tweezers (HOTs) is their incompatibility with laser-based position detection methods, such as back-focal-plane interferometry (BFPI). The alternatives generally used with HOTs, like high-speed video tracking, do not offer the same spatial and temporal bandwidths. This has limited the use of this technique in precise quantitative experiments. In this paper, we present an optical trap design that combines digital holography and back-focal-plane displacement detection. We show that, with a particularly simple setup, it is possible to generate a set of multiple holographic traps and an additional static non-holographic trap with orthogonal polarizations and that they can be, therefore, easily separated for measuring positions and forces with the high positional and temporal resolutions of laser-based detection. We prove that measurements from both polarizations contain less than 1% crosstalk and that traps in our setup are harmonic within the typical range. We further tested the instrument in a DNA stretching experiment and we discuss an interesting property of this configuration: the small drift of the differential signal between traps.