The Gibbs ensemble of a vortex filament

 We introduce a statistical ensemble for a single vortex filament of a three dimensional incompressible fluid. The core of the vortex is modeled by a quite generic stochastic process. We prove the existence of the partition function for both positive and a limited range of negative temperatures. Received: 31 July 2000 / Revised version: 6 March 2001 / Published online: 20 December 2001     

Investment using evolutionary learning methods and technical rules

In this paper, I propose a genetic learning approach to generate technical trading systems for stock timing. The most informative technical indicators are selected from a set of almost 5000 signals by a multi-objective genetic algorithm with variable string length. Successively, these signals are combined into a unique trading signal by a learning method. I test the expert weighting solution obtained by the plurality voting committee, the Bayesian model averaging and Boosting procedures with data from the S&P 500 Composite Index, in three market phases, up-trend, down-trend and sideways-movements, covering the period 2000–2006. Computational results indicate that the near-optimal set of rules varies among market phases but presents stable results and is able to reduce or eliminate losses in down-trend periods.     

The Ontology of Products

We speak of products in two senses: in one, we speak of types of products, in the other we speak of the particular objects that are instances of those types. I argue that types of products have the same ontological status as that of material stuffs, like water and gold, which have a non-particular level of existence. I also argue that the relationship between types of products and their instances is logically similar to the relation of constitution, which holds between, say, gold and a ring made of gold. In my approach, types of products are concrete entities, having spatiotemporal properties. This picture fits our commonplace conception of types of products better than alternative approaches according to which types of products are universal, abstract, or mereological entities.     

On optimal regularity of free boundary problems and a conjecture of De Giorgi

We present a general theory to study optimal regularity for a large class of nonlinear elliptic systems satisfying general boundary conditions and in the presence of a geometric transmission condition on the free boundary. As an application we give a full positive answer to a conjecture of De Giorgi on the analyticity of local minimizers of the Mumford‐Shah functional. © 2004 Wiley Periodicals, Inc.     

A priori estimates for rough PDEs with application to rough conservation laws

We introduce a general weak formulation for PDEs driven by rough paths, as well as a new strategy to prove well-posedness. Our procedure is based on a combination of fundamental a priori estimates with (rough) Gronwall-type arguments. In particular this approach does not rely on any sort of transformation formula (flow transformation, Feynman–Kac representation formula etc.) and is therefore rather flexible. As an application, we study conservation laws driven by rough paths establishing well–posedness for the corresponding kinetic formulation.     

Reactivity of lithium 2,3-dihydro-1-benzothiophene-1-oxide toward aldehydes and imines and DFT calculations

The sulfinyl carbanion derived from 2,3-dihydro-1-benzothiophene-1-oxide and its lithium salt has been investigated by DFT calculations. The lithium carbanion was treated with aldehydes and imines to give chiral hydroxy and amino derivatives, with high stereoselectivity at the carbon α to the sulfoxide group (trans diastereoisomers), but with low diastereoselectivity at the hydroxyl or amine group. DFT calculations were used to rationalize the different stereochemical behavior of cyclic and acyclic lithiated sulfoxides in the reaction with aldehydes and azomethines.     

Pedestrian flows and non‐classical shocks

We present a model for the flow of pedestrians that describes features typical of this flow, such as the fall due to panic in the outflow of people through a door. The mathematical techniques essentially depend on the use of non‐classical shocks in scalar conservation laws. Copyright © 2005 John Wiley & Sons, Ltd.     

Cantor families of periodic solutions for wave equations via a variational principle

We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation—variational in nature—defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to “small divisors” phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical “Arnold non-degeneracy condition” of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities.