A formula for the number of tilings of an octagon by rhombi

We propose the first algebraic determinantal formula to enumerate tilings of a centro-symmetric octagon of any size by rhombi. This result uses the Gessel-Viennot technique and generalizes to any octagon a formula given by Elnitsky in a special case.Comment: New title. Minor improvements. To appear in Theoretical Computer Science, special issue on "Combinatorics of the Discrete Plane and Tilings

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

Highly sensitive frequency metrology for optical anisotropy measurements

In this paper we present a novel apparatus aimed at measuring very small birefringences and anisotropies, based on frequency metrology and not on polarimetry as usual. In our experiment, a very high finesse resonant cavity is used to convert the phase difference into a resonance frequency difference, which can then be measured with very high accuracy. We describe the set-up and present the results of experimental tests which exhibited a sensitivity dn ~ 2 x 10?18, allowing for the measurement of long-predicted magneto-electro-optical effects in gases. Since the shotnoise limited sensitivity of our apparatus lies well below the state-of-the-art sensitivity, frequency metrology appears as a promising technique for small birefringence measurements.Comment: Accepted for publication in Review of Scientific Instrument

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

Gravitino Dark Matter and the Cosmic Lithium Abundances

Supersymmetric extensions of the standard model of particle physics assuming the gravitino to be the lightest supersymmetric particle (LSP), and with the next-to-LSP decaying to the gravitino during Big Bang nucleosynthesis, are analyzed. Particular emphasis is laid on their potential to solve the "Li7 problem", an apparent factor 2-4 overproduction of Li7 in standard Big Bang nucleosynthesis (BBN), their production of cosmologically important amounts of Li6, as well as the resulting gravitino dark matter densities in these models. The study includes several improvements compared to prior studies. Heavy gravitinos in the constrained minimal supersymmetric standard model (CMMSM) are reanalyzed, whereas light gravitinos in gauge-mediated supersymmetry breaking scenarios (GMSB) are studied for the first time. It is confirmed that decays of NLSP staus to heavy gravitinos, while producing all the dark matter, may at the same time resolve the Li7 problem. For NLSP decay times ~ 1000 sec, such scenarios also lead to cosmologically important Li6 (and possibly Be9) abundances. However, as such scenarios require heavy > 1 TeV staus they are likely not testable at the LHC. It is found that decays of NLSP staus to light gravitinos may lead to significant Li6 (and Be9) abundances, whereas NLSP neutralinos decaying into light gravitinos may solve the Li7 problem. Though both scenarios are testable at the LHC they may not lead to the production of the bulk of the dark matter. A section of the paper outlines particle properties required to significantly reduce the Li7 abundance, and/or enhance the Li6 (and possibly Be9) abundances, by the decay of an arbitrary relic particle.Comment: 13 pages (revtex), 9 figures, minor changes, submitted to PR

Reclaiming human machine nature

Extending and modifying his domain of life by artifact production is one of the main characteristics of humankind. From the first hominid, who used a wood stick or a stone for extending his upper limbs and augmenting his gesture strength, to current systems engineers who used technologies for augmenting human cognition, perception and action, extending human body capabilities remains a big issue. From more than fifty years cybernetics, computer and cognitive sciences have imposed only one reductionist model of human machine systems: cognitive systems. Inspired by philosophy, behaviorist psychology and the information treatment metaphor, the cognitive system paradigm requires a function view and a functional analysis in human systems design process. According that design approach, human have been reduced to his metaphysical and functional properties in a new dualism. Human body requirements have been left to physical ergonomics or "physiology". With multidisciplinary convergence, the issues of "human-machine" systems and "human artifacts" evolve. The loss of biological and social boundaries between human organisms and interactive and informational physical artifact questions the current engineering methods and ergonomic design of cognitive systems. New developpment of human machine systems for intensive care, human space activities or bio-engineering sytems requires grounding human systems design on a renewed epistemological framework for future human systems model and evidence based "bio-engineering". In that context, reclaiming human factors, augmented human and human machine nature is a necessityComment: Published in HCI International 2014, Heraklion : Greece (2014

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