Competition in growth and urns

We study survival among two competing types in two settings: a planar growth model related to two‐neighbor bootstrap percolation, and a system of urns with graph‐based interactions. In the planar growth model, uncolored sites are given a color at rate 0, 1 or , depending on whether they have zero, one, or at least two neighbors of that color. In the urn scheme, each vertex of a graph G has an associated urn containing some number of either blue or red balls (but not both). At each time step, a ball is chosen uniformly at random from all those currently present in the system, a ball of the same color is added to each neighboring urn, and balls in the same urn but of different colors annihilate on a one‐for‐one basis. We show that, for every connected graph G and every initial configuration, only one color survives almost surely. As a corollary, we deduce that in the two‐type growth model on , one of the colors only infects a finite number of sites with probability one. We also discuss generalizations to higher dimensions and multi‐type processes, and list a number of open problems and conjectures.     

A quantitative criterion validating coupling power proportionality in statistical energy analysis

The response of two general spring-coupled elements is investigated to develop a unifying approach to the weak coupling criterion in Statistical Energy Analysis (SEA). First, the coupled deterministic equations of motion are expressed in the bases given by the uncoupled elements’ eigenmodes. Then, an iterative solution is expressed as a succession of exchanges between elements, where uncoupled motion provides the start approximation, converging if the ‘coupling eigenvalue’ is less than unity, in which case coupling is said to be weak. This definition is related to whether response is ‘local’ or ‘global’, encompassing a number of previously defined coupling strength definitions, applying for deterministically described structures. A stochastic ensemble is defined by that its members are equal to the investigated structure but the elements have random frequencies. It is required that the coupling eigenvalue be less than unity for all members of the ensemble. This requirement generates the title subject of the article: ‘the modal interaction strength’. It is similar to the previously defined coupling strength criterion characterising the ensemble average energy flow in uni-dimensional waveguides. Finally, SEA models are formulated in terms of the uncoupled elements’ modal data.     

On smallest triangles

Pick n points independently at random in ?², according to a prescribed probability measure μ, and let Δ ≤ Δ ≤ … be the areas of the () triangles thus formed, in nondecreasing order. If μ is absolutely continuous with respect to Lebesgue measure, then, under weak conditions, the set {n³Δ : i ≥ 1} converges as n → ∞ to a Poisson process with a constant intensity κ(μ). This result, and related conclusions, are proved using standard arguments of Poisson approximation, and may be extended to functionals more general than the area of a triangle. It is proved in addition that if μ is the uniform probability measure on the region S, then κ(μ) ≤ 2/|S|, where |S| denotes the area of S. Equality holds in that κ(μ) = 2/|S| if S is convex, and essentially only then. This work generalizes and extends considerably the conclusions of a recent paper of Jiang, Li, and Vitányi. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 206–223, 2003     

On certain quotients of Hardy spaces

The quotient space of a Hardy space on a half-plane Imz> modulo the subspace of elements containing a factore ^iz is in some sense independent of . A formula is derived which exhibits a correspondence between any two such quotient spaces.Supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine.     

Using chemometrics for navigating in the large data sets of genomics, proteomics, and metabonomics (gpm)

This article describes the applicability of multivariate projection techniques, such as principal-component analysis (PCA) and partial least-squares (PLS) projections to latent structures, to the large-volume high-density data structures obtained within genomics, proteomics, and metabonomics. PCA and PLS, and their extensions, derive their usefulness from their ability to analyze data with many, noisy, collinear, and even incomplete variables in both X and Y. Three examples are used as illustrations: the first example is a genomics data set and involves modeling of microarray data of cell cycle-regulated genes in the microorganism Saccharomyces cerevisiae. The second example contains NMR-metabonomics data, measured on urine samples of male rats treated with either of the drugs chloroquine or amiodarone. The third and last data set describes sequence-function classification studies in a set of G-protein-coupled receptors using hierarchical PCA.     

Vibronic coupling in the ground and excited states of the naphthalene cation

The hole-vibrational coupling in naphthalene is studied using high-resolution gas-phase photoelectron spectroscopy and density functional theory calculations (DFT), and a remarkable increase of the coupling with low-frequency vibrations is observed in the excited states.     

The Deletion Method For Upper Tail Estimates

We present a new method to show concentration of the upper tail of random variables that can be written as sums of variables with plenty of independence. We compare our method with the martingale method by Kim and Vu, which often leads to similar results.Some applications are given to the number X _G of copies of a graph G in the random graph (n,p). In particular, for G = K ₄ and G = C ₄ we improve the earlier known upper bounds on —ln (X _G 2 X _G ) in some range of p = p(n).* Research of the second author supported by KBN grants 2 P03A 032 16 and 2 P03A 015 23.