Extremal dependence measure and extremogram: the regularly varying case

The dependence of large values in a stochastic process is an important topic in risk, insurance and finance. The idea of risk contagion is based on the idea of large value dependence. The Gaussian copula notoriously fails to capture this phenomenon. Two notions in a process or vector context which summarize extremal dependence in a function comparable to a correlation function are the extremal dependence measure (EDM) and the extremogram. We review these ideas and compare the two tools and end with a central limit theorem for a natural estimator of the EDM which allows drawing confidence bands comparable to those provided by Bartlett’s formula in a classical context of sample correlation functions.     

Oxygen initiated combustion: Thermochemistry and kinetics of unsaturated hydrocarbons

The thermochemistry and kinetics of the initiation reactions involved in the oxidation of unsaturated fuels are explored. The thermochemistry of intermediate radicals, diradicals, and molecular species involved are estimated using group additivity with some assistance from bond additivity. Kinetic parameters are estimated with the techniques of thermochemical kinetics. In the case of acetylene, estimated rate constants are in excellent agreement with experimental results on the induction period and flame speed. It is shown that the route initiated by O₂ addition to an unsaturated carbon atom to produce a 1,4 diradical is faster than any other path available to form radicals capable of propagating a chain. The 1,4 diradicals so produced can generally cyclize to form a dioxetane which exothermically opens to a dialdehyde which is the ultimate radical source. Below 1000 K unsaturates will always initiate oxidation faster than saturated fuels. © 1996 John Wiley & Sons, Inc.     

Noncanonical RNA Nucleosides as Molecular Fossils of an Early Earth—Generation by Prebiotic Methylations and Carbamoylations

The RNA‐world hypothesis assumes that life on Earth started with small RNA molecules that catalyzed their own formation. Vital to this hypothesis is the need for prebiotic routes towards RNA. Contemporary RNA, however, is not only constructed from the four canonical nucleobases (A, C, G, and U), it also contains many chemically modified (noncanonical) bases. A still open question is whether these noncanonical bases were formed in parallel to the canonical bases (chemical origin) or later, when life demanded higher functional diversity (biological origin). Here we show that isocyanates in combination with sodium nitrite establish methylating and carbamoylating reactivity compatible with early Earth conditions. These reactions lead to the formation of methylated and amino acid modified nucleosides that are still extant. Our data provide a plausible scenario for the chemical origin of certain noncanonical bases, which suggests that they are fossils of an early Earth.     

Ordinal algorithms for packing with target center of gravity

The problem of arranging N unit length weights on a line segment of length N, given a target center of gravity on this line segment, is examined under the assumption that the only information we have about the weights is their order, i.e., a ₁ a ₂ ... a _N . Lower bounds on worst case performance of algorithms for this problem are developed, and algorithms (permutations) which come close to achieving these bounds are provided.This work was partially supported under Natural Sciences and Engineering Research Council (NSERC) of Canada research grant number OGP0002507.     

Are All Uniform Algebras Amnm?

A Banach algebra a is AMNM if whenever a linear functional on a and a positive number satisfy |(ab)–(a)(b)|||a||·||b||for all a, b a, there is a multiplicative linear functional on a such that ||–||=o(1) as 0. K. Jarosz [1] asked whetherevery Banach algebra, or every uniform algebra, is AMNM. B.E. Johnson [3] studied the AMNM property and constructed a commutativesemisimple Banach algebra that is not AMNM. In this note weconstruct uniform algebras that are not AMNM. 1991 MathematicsSubject Classification 46J10.