Local time and first return time for periodic semi-flows

We study Z^d-periodic semi-flows, which are versions in continuous time of Z^d-extensions of dynamical systems. These systems are defined by an underlying dynamical system, a step time (the time to wait before the system makes a move), and a step function (the displacement in Z^d at each step). We are interested in two statistics related to these semi-flows: the local time, i.e., the time spent in some subset, and the first return time to the origin. We get some partial results under spectral conditions on the transfer operator of the underlying dynamical system. If the underlying dynamics is Gibbs–Markov, and under additional constraints on the step time and step function, we get distributional asymptotics for the local time, and an equivalent of the tail of the first return time.     

Symplectic hypersurfaces in the complement of an isotropic submanifold

Using Donaldson's approximately holomorphic techniques, we construct symplectic hypersurfaces lying in the complement of any given compact isotropic submanifold of a compact symplectic manifold. We discuss the connection with rational convexity results in the K?hler case and various applications. Received: 9 January 2001 / Published online: 19 October 2001     

Minimal arithmetic thickness connecting discrete planes

While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the three-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector , we provide algorithms either to determine whether a given arithmetic discrete plane with as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector is connected.     

A measurable-group-theoretic solution to von Neumann’s problem

We give a positive answer, in the measurable-group-theory context, to von Neumann’s problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get an embedding result of the free-group von Neumann factor into restricted wreath product factors. D. Gaboriau’s research was supported by CNRS. R. Lyons’ research was supported partially by NSF grant DMS-0705518 and Microsoft Research.     

An uncountable family of nonorbit equivalent actions of

For each , we construct an uncountable family of free ergodic measure preserving actions of the free group on the standard probability space such that any two are nonorbit equivalent (in fact, not even stably orbit equivalent). These actions are all ``rigid' (in the sense of Popa), with the IIfactors mutually nonisomorphic (even nonstably isomorphic) and in the class

     

Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs

A careful look at rough path topology applied to Brownian motion reveals new possible properties of the well-known Lévy area, in particular the presence of an intrinsic drift of this area. Using renormalization limit of Markov chains on periodic graphs, we present a construction of such a non-trivial drift and give an explicit formula for it. Several examples with explicit computations are included.     

How Fast Is the Bandit?

Abstract

In this article we investigate the rate of convergence of the so-called two-armed bandit algorithm. The behavior of the algorithm turns out to be highly non standard: no central limit theorem, possible occurrence of two different rates of convergence with positive probability.     

Dynamics of the infinitely-thin kink

We consider the dynamics of the domain-wall kink soliton, in particular we study the zero mode of translation. In the infinitely-thin kink limit, we show that the zero mode is almost completely frozen out, the only remnant being a dynamically constrained four-dimensional mode of a single but arbitrary frequency. In relation to this result, we show that the usual mode expansion for dealing with zero modes - implicit collective coordinates - is not in fact a completely general expansion, and that one must use instead a traditional generalised Fourier analysis.     

Compaction of single-chain DNA by histone-inspired nanoparticles

We elaborated a versatile experimental model of chromatin which consists of a single chain of long duplex DNA that interacts with well-defined cationic nanoparticles of various sizes. We found that the DNA compaction by nanoparticles is stepwise and progressive at the single-chain level. It is controlled by the ability of DNA to wrap nanoparticles, which is more efficient for larger particles and, similar to DNA-histone interaction, is optimal at a physiological salt concentration.     

Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy

In combination of direct phase retrieval of coherent x-ray diffraction patterns with a novel tomographic reconstruction algorithm, we, for the first time, carried out quantitative 3D imaging of a heat-treated GaN particle with each voxel corresponding to 17 x 17 x 17 nm3. We observed the platelet structure of GaN and the formation of small islands on the surface of the platelets, and successfully captured the internal GaN-Ga2O3 core shell structure in three dimensions. This work opens the door for nondestructive and quantitative imaging of 3D morphology and 3D internal structure of a wide range of materials at the nanometer scale resolution that are amorphous or possess only short-range atomic organization.