Asymmetric flow networks

This paper provides a new model of network formation that bridges the gap between the two benchmark game-theoretic models by Bala and Goyal (2000a) – the one-way flow model, and the two-way flow model – and includes both as limiting cases. As in both the said models, a link can be initiated unilaterally by any player with any other in what we call an “asymmetric flow” network, and the flow through a link towards the player who supports it is perfect. Unlike those models, there is friction or decay in the opposite direction. When this decay is complete there is no flow and this corresponds to the one-way flow model. The limit case when the decay in the opposite direction (and asymmetry) disappears corresponds to the two-way flow model. We characterize stable and strictly stable architectures for the whole range of parameters of this “intermediate” and more general model. A study of the efficiency of these architectures shows that in general stability and efficiency do not go together. We also prove the convergence of Bala and Goyal’s dynamic model in this context.     

Viscosity Characterization of the Value Function of an Investment-Consumption Problem in Presence of an Illiquid Asset

We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded and observed at discrete random times corresponding to the jumps of a Poisson process. The problem is a nonstandard mixed discrete/continuous optimal control problem, which we face by the dynamic programming approach. The main goal of the paper is the characterization of the value function as unique viscosity solution of an associated Hamilton–Jacobi–Bellman equation. We then use such a result to build a numerical algorithm, allowing one to approximate the value function and so to measure the cost of illiquidity.     

The Fried Average Entropy and Slow Entropy for Actions of Higher Rank Abelian Groups

We consider two numerical entropy-type invariants for actions of \({\mathbb{Z}^k}\) , invariant under a choice of generators and well-adapted for smooth actions whose individual elements have positive entropy. We concentrate on the maximal rank case, i.e. \({\mathbb{Z}^k,\,k \geq 2}\) actions on k + 1-dimensional manifolds. In this case we show that for a fixed dimension (or, equivalently, rank) each of the invariants determines the other and their values are closely related to regulators in algebraic number fields. In particular, in contrast with the classical case of \({{\mathbb Z}}\) actions the entropies of ergodic maximal rank actions take only countably many values. Our main result is the dichotomy that is best expressed under the assumption of weak mixing or, equivalently, no periodic factors: either both invariants vanish, or their values are bounded away from zero by universal constants. Furthermore, the lower bounds grow with dimension: for the first invariant (the Fried average entropy) exponentially, and for the second (the slow entropy) linearly.     

Metric-Induced Wrinkling of a Thin Elastic Sheet

We study the wrinkling of a thin elastic sheet caused by a prescribed non-Euclidean metric. This is a model problem for the patterns seen, for example, in torn plastic sheets and the leaves of plants. Following the lead of other authors, we adopt a variational viewpoint, according to which the wrinkling is driven by minimization of an elastic energy subject to appropriate constraints and boundary conditions. We begin with a broad introduction, including a discussion of key examples (some well-known, others apparently new) that demonstrate the overall character of the problem. We then focus on how the minimum energy scales with respect to the sheet thickness \(h\) for certain classes of displacements. Our main result is that when deformations are subject to certain hypotheses, the minimum energy is of order \(h^{4/3}\) . We also show that when deformations are subject to more restrictive hypotheses, the minimum energy is strictly larger – of order \(h\) ; it follows that energy minimization in the more restricted class is not a good model for the applications that motivate this work. Our results do not explain the cascade of wrinkles seen in some experimental and numerical studies, and they leave open the possibility that an energy scaling law better than \(h^{4/3}\) could be obtained by considering a larger class of deformations.     

Generalization bounds for function approximation from scattered noisy data

We consider the problem of approximating functions from scattered data using linear superpositions of non-linearly parameterized functions. We show how the total error (generalization error) can be decomposed into two parts: an approximation part that is due to the finite number of parameters of the approximation scheme used; and an estimation part that is due to the finite number of data available. We bound each of these two parts under certain assumptions and prove a general bound for a class of approximation schemes that include radial basis functions and multilayer perceptrons. This revised version was published online in June 2006 with corrections to the Cover Date.     

Testing optimality for quadratic 0-1 problems

Received June 4, 1996 / Revised version received November 19, 1997 Published online November 24, 1998     

First report of non‐coloured flavonoids in Echium plantagineum bee pollen: differentiation of isomers by liquid chromatography/ion trap mass spectrometry

Apicultural products have been widely used in diet complements as well as in phytotherapy. Bee pollen from Echium plantagineum was analysed by high‐performance liquid chromatography/photodiode‐array detection coupled to ion trap mass spectrometry (HPLC‐PAD‐MSⁿ) with an electrospray ionisation interface. The structures have been determined by the study of the ion mass fragmentation, which characterises the interglycosidic linkage in glycosylated flavonoids and differentiates positional isomers. Twelve non‐coloured flavonoids were characterised, being kaempferol‐3‐O‐neohesperidoside the major compound, besides others in trace amounts. These include quercetin, kaempferol and isorhamnetin glycosides, with several of them being isomers. Acetylated derivatives are also described. This is the first time that non‐coloured flavonoids are reported from this pollen, with MS fragmentation proving to be most useful in the elucidation of isomeric structures. Copyright © 2010 John Wiley & Sons, Ltd.     

Efficient method to prepare diethylphosphonacetamides

An efficient and versatile synthetic method is described to synthesize diethylphosphonacetamides in a single step.