Upslope migration of snow avalanches in a warming climate.

Snow is highly sensitive to atmospheric warming. However, because of the lack of sufficiently long snow avalanche time series and statistical techniques capable of accounting for the numerous biases inherent to sparse and incomplete avalanche records, the evolution of process activity in a warming climate remains little known. Filling this gap requires innovative approaches that put avalanche activity into a long-term context.

Tree-ring reconstruction of snow avalanche activity: Does avalanche path selection matter?

In the current context of anthropogenic global warming, one of the purposes of dendrogeomorphic analyses is to provide long and continuous chronologies of mass movements, so as to detect potential trends or shift related to increasing temperatures. However, on documented slopes, the comparison between historical archives and tree-ring records suggests that dendrogeomorphic reconstructions systematically underestimate the natural activity of the process under investigation. In the specific case of snow avalanches, underestimation generally amounts to 50% and the main causes generally given for this difference are related to the magnitude of past events.

The convergence of chaotic integrals.

We review the convergence of chaotic integrals computed by Monte Carlo simulation, the trace method, dynamical zeta function, and Fredholm determinant on a simple one-dimensional example: the parabola repeller. There is a dramatic difference in convergence between these approaches. The convergence of the Monte Carlo method follows an inverse power law, whereas the trace method and dynamical zeta function converge exponentially, and the Fredholm determinant converges faster than any exponential.

Excitation of spirals and chiral symmetry breaking in rayleigh-benard convection.

Spiral-defect populations in low-Prandtl number Rayleigh-Bénard convection with slow rotation about a vertical axis were measured in carbon dioxide at high pressure. The results indicate that spirals act like "thermally excited" defects and that the winding direction of a spiral is analogous to a magnetic spin. Rotation about a vertical axis, the spiral analog of the magnetic field, breaks the zero-rotation chiral symmetry between clockwise and counterclockwise spiral defects.

On the equality of Hausdorff and box counting dimensions.

By viewing the covers of a fractal as a statistical mechanical system, the exact capacity of a multifractal is computed. The procedure can be extended to any multifractal described by a scaling function to show why the capacity and Hausdorff dimension are expected to be equal.

A complex chromosome rearrangement with 10 breakpoints: tentative assignment of the locus for Williams syndrome to 4q33----q35.1.

An unbalanced complex chromosome rearrangement with 10 breakpoints resulting in four derivative chromosomes (1, 2, 4, and 11) was found in a girl with severe phenotypic abnormalities, many of which are characteristic of Williams syndrome. The patient was monosomic for the region 4q33----q35.1 and thus the mapping of the syndrome could tentatively be restricted to this region.

Cycle expansion for the Lyapunov exponent of a product of random matrices.

Using cycle expansion for the thermodynamic zeta function, a formula is derived for the Lyapunov exponent of a product of random hyperbolic matrices chosen from a discrete set. This allows for an accurate numerical solution of the Ising model in one dimension with quenched disorder. The formula is compared with weak disorder expansions and with the microcanonical approximation and shown to apply to matrices with degenerate eigenvalues.