An Evening Spent with Bill van Zwet

Willem Rutger van Zwet was born in Leiden, the Netherlands, on March 31, 1934. He received his high school education at the Gymnasium Haganum in The Hague and obtained his Masters degree in Mathematics at the University of Leiden in 1959. After serving in the army for almost two years, he obtained his Ph.D. at the University of Amsterdam in 1964, with Jan Hemelrijk as advisor. In 1965, he was appointed Associate Professor of Statistics at the University of Leiden and promoted to Full Professor in 1968. He remained in Leiden until his retirement in 1999, while also serving as Associate Professor at the University of Oregon (1965), William Newman Professor at the University of North Carolina at Chapel Hill (1990--1996), frequent visitor and Miller Professor (1997) at the University of California at Berkeley, director of the Thomas Stieltjes Institute of Mathematics in the Netherlands (1992--1999), and founding director of the European research institute EURANDOM (1997--2000). At Leiden, he was Dean of the School of Mathematics and Natural Sciences (1982--1984). He served as chair of the scientific council and member of the board of the Mathematics Centre at Amsterdam (1983--1996) and the Leiden University Fund (1993--2005).Comment: Published in at http://dx.doi.org/10.1214/08-STS261 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inverted and mirror repeats in model nucleotide sequences

We analytically and numerically study the probabilistic properties of inverted and mirror repeats in model sequences of nucleic acids. We consider both perfect and non-perfect repeats, i.e. repeats with mismatches and gaps. The considered sequence models are independent identically distributed (i.i.d.) sequences, Markov processes and long range sequences. We show that the number of repeats in correlated sequences is significantly larger than in i.i.d. sequences and that this discrepancy increases exponentially with the repeat length for long range sequences.Comment: 12 pages, 6 figure

High fidelity sorting of remarkably similar components via metal-mediated assembly.

Subtle differences in ligand coordination angle and rigidity lead to high fidelity sorting between individual components displaying identical coordination motifs upon metal-mediated self-assembly. Narcissistic self-sorting can be achieved between highly similar ligands that vary minimally in rigidity and internal coordination angle upon combination with Fe(ii) ions and 2-formylpyridine. Selective, sequential cage formation can be precisely controlled in a single flask from a mix of three different core ligands (and 33 total components) differing only in the hybridization of one group that is uninvolved in the metal coordination process

Least Squares and Shrinkage Estimation under Bimonotonicity Constraints

In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonotone r-by-s matrices. These algorithms can be used, for instance, to estimate a bimonotone regression function via least squares or (a smooth approximation of) least absolute deviations. Another application is shrinkage estimation in image denoising or, more generally, regression problems with two ordinal factors after representing the data in a suitable basis which is indexed by pairs (i,j) in {1,...,r}x{1,...,s}. Various numerical examples illustrate our methods

A Markov Chain based method for generating long-range dependence

This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov Modulated Process based upon an infinite Markov chain is described. The work described is motivated by applications in telecommunications where LRD is a known property of time-series measured on the internet. The process can generate a time series exhibiting LRD with known parameters and is particularly suitable for modelling internet traffic since the time series is in terms of ones and zeros which can be interpreted as data packets and inter-packet gaps. The method is extremely simple computationally and analytically and could prove more tractable than other methods described in the literatureComment: 8 pages, 2 figure

The Composite Fermion Hierarchy: Condensed States of Composite Fermion Excitations?

A composite Fermion hierarchy theory is constructed in a way related to the original Haldane picture by applying the composite Fermion (CF) transformation to quasiparticles of Jain states. It is shown that the Jain theory coincides with the Haldane hierarchy theory for principal CF fillings. Within the Fermi liquid approach for few electron systems on the sphere a simple interpretation of many-quasiparticle spectra is given and provides an explanation of failure of CF hierarchy picture when applied to the hierarchical $4/11$ state.Comment: 6 pages, Revtex, 4 figures in PostScript, submitted to Phys. Rev. Let

Modeling long-range memory with stationary Markovian processes

In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate transformation of a specific power-law correlated additive process x(t), already known in the literature, whose pdf shows power-law tails 1/x^a. We give analytical and numerical evidence that although the new processes (i) are Markovian and (ii) have gaussian or exponential tails their autocorrelation function still shows a power-law decay =1/T^b where b grows with a with a law which is compatible with b=a/2-c, where c is a numerical constant. When a<2(1+c) the process y(t), although Markovian, is long-range correlated. Our results help in clarifying that even in the context of Markovian processes long-range dependencies are not necessarily associated to the occurrence of extreme events. Moreover, our results can be relevant in the modeling of complex systems with long memory. In fact, we provide simple processes associated to Langevin equations thus showing that long-memory effects can be modeled in the context of continuous time stationary Markovian processes.Comment: 5 figure

Non-optimality of unitary operations for dense coding

One of the primary goals of information theory is to provide limits on the amount of information it is possible to send through various types of communication channels, and to understand the encoding methods that will allow one to achieve such limits. An early surprise in the study of \textit{quantum} information theory was the discovery of dense coding, which demonstrated that it is possible to achieve higher rates for communicating classical information by transmitting quantum systems, rather than classical ones. To achieve the highest possible rate, the transmitted quantum system must initially be maximally entangled with another that is held by the receiver, and the sender can achieve this rate by encoding her messages with unitary operations. The situation where these two systems are not maximally entangled has been intensively studied in recent years, and to date it has appeared as though unitary encoding might well be optimal in all cases. Indeed, this optimality of unitary operations for quantum communication protocols has been found to hold under far more general conditions, extending well beyond the special case of dense coding. Nonetheless, we here present strong numerical evidence supported by analytical arguments that indicate there exist circumstances under which one can encode strictly more classical information using dense coding with non-unitary, as opposed to unitary, operations.Comment: 10 pages, 1 figure, comments welcom