Lowness of higher randomness notions

We study randomness notions given by higher recursion theory, establishing the relationships Π ₁ ¹ -randomness ? Π ₁ ¹ -Martin-Löf randomness ? Δ ₁ ¹ -randomness = Δ ₁ ¹ -Martin-Löf randomness. We characterize the set of reals that are low for Δ ₁ ¹ randomness as precisely those that are Δ ₁ ¹ -traceable. We prove that there is a perfect set of such reals.     

Preconditioning trace coupled 3d‐1d systems using fractional Laplacian

Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains of different dimensionality. In this work, we consider a simplified model problem of a 3d‐1d coupling and the main objective is to construct algorithms that may utilize standard multilevel algorithms for the 3d domain, which has the dominating computational complexity. Preconditioning for a system of two elliptic problems posed, respectively, in a three‐dimensional domain and an embedded one dimensional curve and coupled by the trace constraint is discussed. Investigating numerically the properties of the well‐defined discrete trace operator, it is found that negative fractional Sobolev norms are suitable preconditioners for the Schur complement of the system. The norms are employed to construct a robust block diagonal preconditioner for the coupled problem.     

Deformations of the hemisphere that increase scalar curvature

Consider a compact Riemannian manifold M of dimension n whose boundary ?M is totally geodesic and is isometric to the standard sphere S ^n?1. A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n?1), then M is isometric to the hemisphere $S_{+}^{n}$ equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. In this paper, we construct counterexamples to Min-Oo??s Conjecture in dimension n??3.     

Transient absorption spectra of 2-hydroxybenzophenone photostabilizers

Transient absorption spectra (400–600 nm) of 2-hydroxybenzophenone and the methyl methacrylate copolymer of 2-hydroxy, 3-allyl, 4,4'-dimethoxybenzophenone following 355 nm excitation (7–480 ps delay) are reported. A short-lived, 435 nm transient (τ ≈ 10 ps in CH₂Cl₂) for both molecules is assigned to the lowest excited singlet before internal proton transfer. Weaker, broad T-T absorption is observed after 480 ps.     

A spatial scan statistic for case event data based on connected components

We propose a new spatial scan statistic based on graph theory as a method for detecting irregularly-shaped clusters of events over space. A graph-based method is proposed for identifying potential clusters in spatial point processes. It relies on linking the events closest than a given distance and thus defining a graph associated to the point process. The set of possible clusters is then restricted to windows including the connected components of the graph. The concentration in each of these possible clusters is measured through classical concentration indices based on likelihood ratio and also through a new concentration index which does not depend on any alternative hypothesis. These graph-based spatial scan tests seem to be very powerful against any arbitrarily-shaped cluster alternative, whatever the dimension of the data. These results have applications in various fields, such as the epidemiological study of rare diseases or the analysis of astrophysical data.     

Some limit theorems for negatively associated random variables

Let {X _n , n ≥ 1} be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the L ^p -convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables.     

BDD-based heuristics for binary optimization

In this paper we introduce a new method for generating heuristic solutions to binary optimization problems. We develop a technique based on binary decision diagrams. We use these structures to provide an under-approximation to the set of feasible solutions. We show that the proposed algorithm delivers comparable solutions to a state-of-the-art general-purpose optimization solver on randomly generated set covering and set packing problems.     

Chemical kinetics at high pressure

Abstract

Numerous studies have demonstrated the importance to include pressure as a kinetic parameter in the elucidation of inorganic reaction mechanisms. These studies have specially led to a better understanding and a systematic classification of solvent exchange and ligand substitution reactions of octahedral complexes of transition metal elements. The mechanistic picture for substution reactions on square planar complexes is well established and involves a concurrent bimolecular attack by solvent and the nucleophile on the substrate with a considerable discrimination among different entering groups. The search for factor promoting the conversion of the normal associative mode of activation into a dissociative process has then attracted much attention. Two attempts to induce dissociation, as studied by high-pressure NMR, are presented: one is to prevent the formation by means of sterically hindered ligands, the other one is to promote bond weakening at the leaving group.     

Transition from the ballistic to the diffusive regime in a turbid medium

By varying the absorption coefficient and width of an intralipid-India ink solution in a quasi-one-dimensional experiment, we investigate the transition between the ballistic and the diffusive regimes. The medium's attenuation coefficient changes abruptly between two different values within a single mean free path. This problem is analyzed both experimentally and theoretically, and it is demonstrated that the transition location depends on the scattering coefficient as well as on the measuring solid angle.