Testing Monotonicity

at arguments of its choice, the test always accepts a monotone f, and rejects f with high probability if it is ε-far from being monotone (i.e., every monotone function differs from f on more than an ε fraction of the domain). The complexity of the test is O(n/ε). The analysis of our algorithm relates two natural combinatorial quantities that can be measured with respect to a Boolean function; one being global to the function and the other being local to it. A key ingredient is the use of a switching (or sorting) operator on functions. Received March 29, 1999     

A-posteriori KAM theory with optimal estimates for partially integrable systems

In this paper we present a-posteriori KAM results for existence of d-dimensional isotropic invariant tori for n-DOF Hamiltonian systems with additional $n?d$ independent first integrals in involution. We carry out a covariant formulation that does not require the use of action-angle variables nor symplectic reduction techniques. The main advantage is that we overcome the curse of dimensionality avoiding the practical shortcomings produced by the use of reduced coordinates, which may cause difficulties and underperformance when quantifying the hypotheses of the KAM theorem in such reduced coordinates. The results include ordinary and (generalized) iso-energetic KAM theorems. The approach is suitable to perform numerical computations and computer assisted proofs.     

Stable Extrapolation of Analytic Functions

Foundations of Computational Mathematics - This paper examines the problem of extrapolation of an analytic function for $$x > 1$$ given $$N+1$$ perturbed samples from an equally spaced grid...     

The Dirichlet series for the exterior square <Emphasis Type="Italic">L</Emphasis>-function on GL(<Emphasis Type="Italic">n</Emphasis>)

We present an elementary derivation of the Jacquet–Shalika construction for the exterior square L-function on GL(n), as a classical Dirichlet series in the Fourier coefficients A(m ₁,…,m _n−1).     

No-arbitrage conditions,scenario trees,and multi-asset financial optimization

Many numerical optimization methods use scenario trees as a discrete approximation for the true (multi-dimensional) probability distributions of the problem’s random variables. Realistic specifications in financial optimization models can lead to tree sizes that quickly become computationally intractable. In this paper we focus on the two main approaches proposed in the literature to deal with this problem: scenario reduction and state aggregation. We first state necessary conditions for the node structure of a tree to rule out arbitrage. However, currently available scenario reduction algorithms do not take these conditions explicitly into account. State aggregation excludes arbitrage opportunities by relying on the risk-neutral measure. This is, however, only appropriate for pricing purposes but not for optimization. Both limitations are illustrated by numerical examples. We conclude that neither of these methods is suitable to solve financial optimization models in asset–liability or portfolio management.     

A hierarchical multi-label classification ant colony algorithm for protein function prediction

This paper proposes a novel ant colony optimisation (ACO) algorithm tailored for the hierarchical multi-label classification problem of protein function prediction. This problem is a very active research field, given the large increase in the number of uncharacterised proteins available for analysis and the importance of determining their functions in order to improve the current biological knowledge. Since it is known that a protein can perform more than one function and many protein functional-definition schemes are organised in a hierarchical structure, the classification problem in this case is an instance of a hierarchical multi-label problem. In this type of problem, each example may belong to multiple class labels and class labels are organised in a hierarchical structure—either a tree or a directed acyclic graph structure. It presents a more complex problem than conventional flat classification, given that the classification algorithm has to take into account hierarchical relationships between class labels and be able to predict multiple class labels for the same example. The proposed ACO algorithm discovers an ordered list of hierarchical multi-label classification rules. It is evaluated on sixteen challenging bioinformatics data sets involving hundreds or thousands of class labels to be predicted and compared against state-of-the-art decision tree induction algorithms for hierarchical multi-label classification.     

Semi-Markov Modelling for Multi-State Systems

In this work we focus on multi state systems that we model by means of semi-Markov processes. The sojourn times are seen to be independent not identically distributed random variables and assumed to belong to a general class of distributions that includes several popular reliability distributions like the exponential, Weibull, and Pareto. We obtain maximum likelihood estimators of the parameters of interest and investigate their asymptotic properties. Plug-in type estimators are furnished for various quantities related to the system under study.     

Theoretical predictions of the electronic and optical properties of single and coupled (In,Ga)As/GaAs quantum dots

We show how an atomistic pseudopotential plus many-body configuration interaction theory can address the main spectroscopic features of self-assembled dots including, excitons, trions, biexcitons, fine-structure, charging spectra as well as electric-field dependence of entanglement in dot molecules.