Bentley’s conjecture on popularity toplist turnover under random copying

Bentley et al. studied the turnover rate in popularity toplists in a ‘random copying’ model of cultural evolution. Based on simulations of a model with population size N, list length ? and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: $\ell \sqrt{\mu}$ . Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.     

Lecture Hall Partitions II

For a non-decreasing integer sequence a=(a₁,...,a_n) we define L_a to be the set of n-tuples of integers = (₁,...,_n) satisfying . This generalizes the so-called lecture hall partitions corresponding to a_i=i and previously studied by the authors and by Andrews. We find sequences a such that the weight generating function for these a-lecture hall partitions has the remarkable form In the limit when n tends to infinity, we obtain a family of identities of the kind the number of partitions of an integer m such that the quotient between consecutive parts is greater than is equal to the number of partitions of m into parts belonging to the set P, for certain real numbers and integer sets P. We then underline the connection between lecture hall partitions and Ehrhart theory and discuss some reciprocity results.     

Towards a kinetic theory for fermions with quantum coherence

A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation is finding new spectral solutions for the 2-point Green's functions written in the Wigner representation, that are carrying the information of the quantum coherence. Physically observable density matrix is then defined from the bare singular 2-point function by convoluting it with the extrenous information about the state of the system. The formalism is shown to reproduce familiar results from the Dirac equation approach, like Klein problem and nonlocal reflection from a mass wall. The notion of the particle number in the presence of quantum coherence is shown to be particularly transparent in the current picture. We extend the formalism to the case of mixing fields and show how the usual flavour mixing and oscillation of neutrinos emerges again from a singular shell structure. Finally, we show how the formalism can be extended to include decohering interactions.     

Minimal technicolor on the lattice

We present results from a lattice study of SU(2) gauge theory with 2 flavors of Dirac fermions in adjoint representation. This is a candidate for a minimal (simplest) walking technicolor theory, and has been predicted to possess either an IR fixed point (where the physics becomes conformal) or a coupling which evolves very slowly, so-called walking coupling. In this initial part of the study we investigate the lattice phase diagram and the excitation spectrum of the theory.     

Average-optimal string matching

The exact string matching problem is to find the occurrences of a pattern of length m from a text of length n symbols. We develop a novel and unorthodox filtering technique for this problem. Our method is based on transforming the problem into multiple matching of carefully chosen pattern subsequences. While this is seemingly more difficult than the original problem, we show that the idea leads to very simple algorithms that are optimal on average. We then show how our basic method can be used to solve multiple string matching as well as several approximate matching problems in average optimal time. The general method can be applied to many existing string matching algorithms. Our experimental results show that the algorithms perform very well in practice.     

There exists no (15,5,4) RBIBD

An (n, M, d)_q code is a q‐ary code of length n, cardinality M, and minimum distance d. We show that there exists no (15,5,4) resolvable balanced incomplete block design (RBIBD) by showing that there exists no (equidistant) (14,15,10)₃ code. This is accomplished by an exhaustive computer search using an orderly algorithm combined with a maximum clique algorithm. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 227–232, 2001     

Time-dependent physical spectra of Gaussian Schell-model pulses

The time-dependent physical spectra introduced by Eberly and Wódkiewicz [J. Opt. Soc. Am. 67 (1977) 1252], observable with a photon-counting detector placed behind a Fabry-Perot filter, are evaluated for a class of temporally partially coherent non-stationary fields known as Gaussian Schell-model plane-wave pulses. Numerical comparisons between source spectra and observed spectra are provided and discussed, and several general features such as initial spectral broadening at the arrival of the pulse and a temporal pulse tail are illustrated. Closed-form approximations are obtained for the time evolution of the observable spectrum by evaluating the leading terms in an appropriate series expansion.     

Miscellaneous classification results for 2-designs

An orderly algorithm combined with clique searching is used to show that there are—up to isomorphism, in all cases—325,062 resolvable 2-(16,4,2) designs with 339,592 resolutions, 19,072,802 2-(13,6,5) designs, and 15,111,019 2-(14,7,6) designs. Properties of the classified designs are further discussed.     

Photoinduced electron transfer in Langmuir-Blodgett monolayers of porphyrin-fullerene dyads

A series of electron donor-acceptor (DA) dyads, composed of a porphyrin donor and a fullerene acceptor covalently linked with two molecular chains, were used to fabricate solid molecular films with the Langmuir-Blodgett (LB) technique. By means of the LB technique, the DA molecules can be oriented perpendicular to the plane of the substrate. In DHD6ee and its zinc derivative hydrophilic groups are attached to the phenyl moieties in the porphyrin end of the molecule; while in the other three dyads, TBD6a, TBD6hp, and TBD4hp, the hydrophilic groups are in the fullerene end of the molecule. This makes it possible to alternate the orientation of the molecules in two opposite directions with respect to the air-water interface and to fabricate molecular assemblies in which the direction of the primary photoinduced vectorial electron transfer can be controlled both by the deposition direction of the LB monolayer and by the selection of the used DA molecule. This was proved by the time-resolved Maxwell displacement charge measurements. The spectroscopic properties of the DA films were studied with the steady-state absorption and fluorescence methods. In addition, the time correlated single photon counting technique was used to determine the fluorescence properties of the dyad films.