Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions

Three-dimensional integer partitions provide a convenient representation of codimension-one three-dimensional random rhombus tilings. Calculating the entropy for such a model is a notoriously difficult problem. We apply transition matrix Monte Carlo simulations to evaluate their entropy with high precision. We consider both free- and fixed-boundary tilings. Our results suggest that the ratio of free- and fixed-boundary entropies is $\sigma_{free}/\sigma_{fixed}=3/2$, and can be interpreted as the ratio of the volumes of two simple, nested, polyhedra. This finding supports a conjecture by Linde, Moore and Nordahl concerning the ``arctic octahedron phenomenon'' in three-dimensional random tilings

Synergistic interaction between the Arp2/3 complex and cofilin drives stimulated lamellipod extension

Both the Arp2/3 complex and cofilin are believed to be important for the generation of protrusive force at the leading edge; however, their relative contributions have not been explored in vivo. Our results with living cells show that cofilin enters the leading edge immediately before the start of lamellipod extension, slightly earlier than Arp2/3, which begins to be recruited slightly later as the lamellipod is extended. Blocking either the Arp2/3 complex or cofilin function in cells results in failure to extend broad lamellipods and inhibits free barbed ends, suggesting that neither factor on its own can support actin polymerization-mediated protrusion in response to growth factor stimulation. High-resolution analysis of the actin network at the leading edge supports the idea that both the severing activity of cofilin and the specific branching activity of the Arp2/3 complex are essential for lamellipod protrusion. These results are the first to document the relative contributions of cofilin and Arp2/3 complex in vivo and indicate that cofilin begins to initiate the generation of free barbed ends that act in synergy with the Arp2/3 complex to create a large burst in nucleation activity

Two-dimensional random tilings of large codimension: new progress

Two-dimensional random tilings of rhombi can be seen as projections of two-dimensional membranes embedded in hypercubic lattices of higher dimensional spaces. Here, we consider tilings projected from a $D$-dimensional space. We study the limiting case, when the quantity $D$, and therefore the number of different species of tiles, become large. We had previously demonstrated [ICQ6] that, in this limit, the thermodynamic properties of the tiling become independent of the boundary conditions. The exact value of the limiting entropy and finite $D$ corrections remain open questions. Here, we develop a mean-field theory, which uses an iterative description of the tilings based on an analogy with avoiding oriented walks on a random tiling. We compare the quantities so-obtained with numerical calculations. We also discuss the role of spatial correlations.Comment: Proceedings of the 7th International Conference on Quasicrystals (ICQ7, Stuttgart), 4 pages, 4 figure

B\,^1\Sigma^{+}_{u} and EF\,^{1}\Sigma^{+}_{g} level energies of D2_{2}

Accurate absolute level energies of the B\,^1\Sigma^{+}_{u}, $v=0-8, N$ and EF\,^{1}\Sigma^{+}_{g}, $v=0-21, N$ rovibrational quantum states of molecular deuterium are derived by combining results from a Doppler-free two-photon laser excitation study on several lines in the $EF\,{}^{1}\Sigma_{g}^{+}-X\,{}^{1}\Sigma_{g}^{+}$ (0,0) band, with results from a Fourier-transform spectroscopic emission study on a low-pressure hydrogen discharge. Level energy uncertainties as low as 0.0005 cm$^{-1}$ are obtained for some low-lying E\,^{1}\Sigma^{+}_{g} inner-well rovibrational levels, while uncertainties for higher-lying rovibrational levels and those of the F\,^{1}\Sigma^{+}_{g} outer-well states are nominally 0.005 cm$^{-1}$. Level energies of B\,^1\Sigma^{+}_{u} rovibrational levels, for $v \leq 8$ and $N \leq 10$ are determined at an accuracy of 0.001 cm$^{-1}$. Computed wavelengths of D$_2$ Lyman transitions in the B\,^1\Sigma^{+}_{u}-X\,^{1}\Sigma^{+}_{g} ($v,0$) bands are also tabulated for future applications.Comment: appears in Journal of Molecular Spectroscopy (2014

Actin at cell-cell junctions is composed of two dynamic and functional populations

The ability of epithelial cells to polarize requires cell-cell adhesion mediated by cadherin receptors. During cell-cell contact, the mechanism via which a flat, spread cell shape is changed into a tall, cuboidal epithelial morphology is not known. We found that cadherin-dependent adhesion modulates actin dynamics by triggering changes in actin organization both locally at junctions and within the rest of the cell. Upon induction of cell-cell contacts, two spatial actin populations are distinguishable: junctional actin and peripheral thin bundles. With time, the relative position of these two populations changes and becomes indistinguishable to form a cortical actin ring that is characteristic of mature, fully polarized epithelial cells. Junctional actin and thin actin bundles differ in their actin dynamics and mechanism of formation, and interestingly, have distinct roles during epithelial polarization. Whereas junctional actin stabilizes clustered cadherin receptors at cell-cell contacts, contraction of peripheral actin bundle is essential for an increase in the maximum height at the lateral domain during polarization (cuboidal morphology). Thus, both junctional actin and thin bundles are necessary, and cooperate with each other to generate a polarized epithelial morphology

Reduced dimension modeling of leading edge turbulent interaction noise

A computational aeroacoustics approach is used to model the effects of real airfoil geometry on leading edge turbulent interaction noise for symmetric airfoils at zero angle of attack. For the first time, one-component (transverse), two-component (transverse and streamwise), and three-component (transverse, streamwise, and spanwise) synthesized turbulent disturbances are modeled instead of single frequency transverse gusts, which previous computational studies of leading edge noise have been confined to. The effects of the inclusion of streamwise and spanwise disturbances on the noise are assessed, and it is shown that accurate noise predictions for symmetric airfoils can be made by modeling only the transverse disturbances, which reduces the computational expense of simulations. Additionally, the two-component turbulent synthesis method is used to model the effects of airfoil thickness on the noise for thicknesses ranging from 2% to 12%. By using sufficient airfoil thicknesses to show trends, it is found that airfoil thickness will reduce the noise at high frequency, and that the sound power P will reduce linearly with increasing airfoil thickness

Protention and retention in biological systems

This paper proposes an abstract mathematical frame for describing some features of cognitive and biological time. We focus here on the so called "extended present" as a result of protentional and retentional activities (memory and anticipation). Memory, as retention, is treated in some physical theories (relaxation phenomena, which will inspire our approach), while protention (or anticipation) seems outside the scope of physics. We then suggest a simple functional representation of biological protention. This allows us to introduce the abstract notion of "biological inertia".Comment: This paper was made possible only as part of an extended collaboration with Francis Bailly (see references), a dear friend and "ma\^itre \'a penser", who contributed to the key ideas. Francis passed away in february 2008: we continue here our inspiring discussions and joint wor

The BMV project: Search for photon oscillations into massive particles

In this contribution to PSAS08 we report on the research activities developed in our Toulouse group, in the framework of the BMV project, concerning the search for photon oscillations into massive particles, such as axion-like particles in the presence of a strong transverse magnetic field. We recall our main result obtained in collaboration with LULI at \'Ecole Polytechnique (Palaiseau, France). We also present the very preliminary results obtained with the BMV experiment which is set up at LNCMP (Toulouse, France).Comment: Proceedings of PSAS'08, to be published in Can. J. Phy

Direct multiple shooting and direct collocation perform similarly in biomechanical predictive simulations

Direct multiple shooting (DMS) and direct collocation (DC) are two common transcription methods for solving optimal control problems (OCP) in biomechanics and robotics. They have rarely been compared in terms of solution and speed. Through five examples of predictive simulations solved using five transcription methods and 100 initial guesses in the Bioptim software, we showed that not a single method outperformed systematically better. All methods converged to almost the same solution (cost, states, and controls) in all but one OCP, with several local minima being found in the latter. Nevertheless, DC based on fourth-order Legendre polynomials provided overall better results, especially in terms of dynamic consistency compared to DMS based on a fourth-order Runge-Kutta method. Furthermore, expressing the rigid-body constraints using inverse dynamics was usually faster than forward dynamics. DC with dynamics constraints based on inverse dynamics converged to better and less variable solutions. Consequently, we recommend starting with this transcription to solve OCPs but keep testing other methods.Comment: 19 pages, 4 figure