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.     

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.     

Optimal Operations Management and Network Planning of a District Heating System with a Combined Heat and Power Plant

District heating plants are becoming more common in European cities. These systems make it possible to furnish users with warm water while locating the production plants in the outskirts having the double benefit of lowering the impact of pollution on the center of the city and achieving better conversion performances. In order to amortize the costs throughout the year, the system often includes a combined heat and power (CHP) plant, to exploit the energy during the summer as well, when the demand for warm water decreases. A linear programming model for the optimal resource management of such a plant is presented and some results for a real case are reported. A distribution network design problem is also addressed and solved by means of mixed integer linear programming.     

Simulation of dynamic speckle sequences and its application to the analysis of transient processes

Dynamic speckle has been used in recent years to analyse several transient processes that are produced in industrial and biological applications. We present here a numerical simulation to generate a temporal sequence of dynamic speckle patterns which is based on a model used for speckle formation by the superposition of waves from discrete scattering centres. It is demonstrated that the first and second statistics of the intensity of each speckle image, the time history of the speckle pattern, the temporal evolution of the correlation coefficient, and the power spectral density of the intensity generated by the proposed model reproduce quite well those obtained from experimentally recorded data. The process of a fast drying paint is presented as an example of the application of the proposed numerical model.     

Stereoselective synthesis of (Z)-axino- and (Z)-debromoaxinohydantoin

(Z)-Axinohydantoin and (Z)-debromoaxinohydantoin, two pyrrole-imidazole alkaloids isolated from different marine sponges, possess moderate activities in inhibiting the progress of the cell cycle at different phases. A stereoselective synthesis of both natural products was achieved. The key step in the synthetic pathway was the installation of the hydantoin northern ring by using 1-benzoyl-2-methylsulfanyl-1,5-dihydroimidazol-4-one.