Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).

The aid of machine learning to overcome the classification of real health discharge reports written in Spanish

Hospitals attached to the Spanish Ministry of Health are currently using the International Classification of Diseases 9 Clinical Modification (ICD9-CM) to classify health discharge records. Nowadays, this work is manually done by experts. This paper tackles the automatic classification of real Discharge Records in Spanish following the ICD9-CM standard. The challenge is that the Discharge Records are written in spontaneous language. We explore several machine learning techniques to deal with the classification problem. Random Forest resulted in the most competitive one, achieving an F-measure of 0.876.

Morphological classification of microtidal sand and gravel beaches

A new classification of microtidal sand and gravel beaches with very different morphologies is presented below. In 557 studied transects, 14 variables were used. Among the variables to be emphasized is the depth of the Posidonia oceanica. The classification was performed for 9 types of beaches: Type 1: Sand and gravel beaches, Type 2: Sand and gravel separated beaches, Type 3: Gravel and sand beaches, Type 4: Gravel and sand separated beaches, Type 5: Pure gravel beaches, Type 6: Open sand beaches, Type 7: Supported sand beaches, Type 8: Bisupported sand beaches and Type 9: Enclosed beaches. For the classification, several tools were used: discriminant analysis, neural networks and Support Vector Machines (SVM), the results were then compared. As there is no theory for deciding which is the most convenient neural network architecture to deal with a particular data set, an experimental study was performed with different numbers of neuron in the hidden layer. Finally, an architecture with 30 neurons was chosen. Different kernels were employed for SVM (Linear, Polynomial, Radial basis function and Sigmoid). The results obtained for the discriminant analysis were not as good as those obtained for the other two methods (ANN and SVM) which showed similar success.

An updated evolutionary classification of CRISPR–Cas systems

The evolution of CRISPR–cas loci, which encode adaptive immune systems in archaea and bacteria, involves rapid changes, in particular numerous rearrangements of the locus architecture and horizontal transfer of complete loci or individual modules. These dynamics complicate straightforward phylogenetic classification, but here we present an approach combining the analysis of signature protein families and features of the architecture of cas loci that unambiguously partitions most CRISPR–cas loci into distinct classes, types and subtypes. The new classification retains the overall structure of the previous version but is expanded to now encompass two classes, five types and 16 subtypes. The relative stability of the classification suggests that the most prevalent variants of CRISPR–Cas systems are already known. However, the existence of rare, currently unclassifiable variants implies that additional types and subtypes remain to be characterized.

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.