Maximum likelihood estimator consistency for a ballistic random walk in a parametric random environment

We consider a one dimensional ballistic random walk evolving in an i.i.d. parametric random environment. We provide a maximum likelihood estimation procedure of the parameters based on a single observation of the path till the time it reaches a distant site, and prove that the estimator is consistent as the distant site tends to infinity. Our main tool consists in using the link between random walks and branching processes in random environments and explicitly characterising the limiting distribution of the process that arises. We also explore the numerical performance of our estimation procedure.     

A mixed basis approach in the SGP-limit

A perturbation method for computing quick estimates of the echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit is presented. The perturbation basis involves (relatively few) dipole distributions on the boundaries generating a small perturbation matrix in O(s²) time, where s denotes the number of boundary elements. Several approximate eigenvalues and eigenfunctions to the diffusion operator are retrieved. The method is applied to 1D and 2D systems with Neumann boundary conditions.     

Universal bound on N-point correlations from inflation

Models of inflation in which non-Gaussianity is generated outside the horizon, such as curvaton models, generate distinctive higher-order correlation functions in the cosmic microwave background and other cosmological observables. Testing for violation of the Suyama-Yamaguchi inequality τ(NL) ≥ (6/5f (NL))(2), where f(NL) and f(NL) denote the amplitude of the three-point and four-point functions in certain limits, has been proposed as a way to distinguish qualitative classes of models. This inequality has been proved for a wide range of models, but only weaker versions have been proved in general. In this Letter, we give a proof that the Suyama-Yamaguchi inequality is always satisfied. We discuss scenarios in which the inequality may appear to be violated in an experiment such as Planck and how this apparent violation should be interpreted.     

Dimerization of Pyramidalized 3,4,8,9‐Tetramethyltetracyclo [4.4.0.03,9.04,8]dec‐1(6)‐ene to a Hydrocarbon Featuring Four Cyclohexane Rings in Boat Conformations

The synthesis, chemical trapping, and dimerization of a highly pyramidalized alkene is reported. Its dimer is a unique nonacycle featuring three planar cyclobutane rings, four cyclopentane rings, and four cyclohexane rings in boat conformations. The X‐ray diffraction analysis showed a H–H distance between the flagpole hydrogen atoms of 1.999 Å and a separation of 2.619 Å between the two flagpole carbon atoms. The three cyclobutane rings of the dimer were thermally stable.     

n -Heptane and methylcyclohexane transformation over a HMCM-22 zeolite. Origin of the features typical of large-or of medium-pore zeolites

The main features of methylcyclohexane (mch) and n-heptane (n-C₇) transformation at 350°C were compared for fresh samples of HMWW, HMFI and HFAU zeolites. With both reactions, the behavior of HMWW was between those of the medium HMFI and large pore HFAU zeolites. Thus, the values of turnover frequency (TOF) and of the TOF_mch/n-C7 ratio were similar with HMWW and HMFI and much higher with HFAU. In contrast, small differences were found between product distributions over HMWW and HFAU but large differences between HMWW and HMFI. These observations can be explained by alkane transformation in the large supercages with 10-MR apertures of HMWW: the narrow apertures limit diffusion of the mch within the supercages, but not the diffusion of the products which are therefore typical of the transformation within large cages hence without any steric limitation.     

Colorful Strips

We study the following geometric hypergraph coloring problem: given a planar point set and an integer k, we wish to color the points with k colors so that any axis-aligned strip containing sufficiently many points contains all colors. We show that if the strip contains at least 2k − 1 points, such a coloring can always be found. In dimension d, we show that the same holds provided the strip contains at least k(4 ln k + ln d) points. We also consider the dual problem of coloring a given set of axis-aligned strips so that any sufficiently covered point in the plane is covered by k colors. We show that in dimension d the required coverage is at most d(k − 1) + 1. This complements recent impossibility results on decomposition of strip coverings with arbitrary orientations. From the computational point of view, we show that deciding whether a three-dimensional point set can be 2-colored so that any strip containing at least three points contains both colors is NP-complete. This shows a big contrast with the planar case, for which this decision problem is easy.