Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

A review on the combination of binary classifiers in multiclass problems

Several real problems involve the classification of data into categories or classes. Given a data set containing data whose classes are known, Machine Learning algorithms can be employed for the induction of a classifier able to predict the class of new data from the same domain, performing the desired discrimination. Some learning techniques are originally conceived for the solution of problems with only two classes, also named binary classification problems. However, many problems require the discrimination of examples into more than two categories or classes. This paper presents a survey on the main strategies for the generalization of binary classifiers to problems with more than two classes, known as multiclass classification problems. The focus is on strategies that decompose the original multiclass problem into multiple binary subtasks, whose outputs are combined to obtain the final prediction.

A real-time polymerase chain reaction assay for the identification and quantification of American Leishmania species on the basis of glucose-6-phosphate dehydrogenase

A real-time polymerase chain reaction (PCR) test was developed on the basis of the Leishmania glucose-6-phosphate dehydrogenase locus that enables identification and quantification of parasites. Using two independent pairs of primers in SYBR-Green assays, the test identified etiologic agents of cutaneous leishmaniasis belonging to both subgenera, Leishmania (Viannia) and Leishmania (Leishmania) in the Americas. Furthermore, use of TaqMan probes enables distinction between L. (V.) braziliensis or L. (V.) peruviania from the other L. (Viannia) species. All assays were negative with DNA of related trypanosomatids, humans, and mice. The parasite burden was estimated by normalizing the number of organisms per total amount of DNA in the sample or per host glyceraldehyde-3-phosphate dehydrogenase copies. The real-time PCR assay for L. (Leishmania) subgenus showed a good linear correlation with quantification on the basis of a limiting dilution assay in experimentally infected mice. The test successfully identifies and quantifies Leishmania in human biopsy specimens and represents a new tool to study leishmaniasis.

A note on the eigenvalues of a special class of matrices

In the analysis of stability of a variant of the Crank-Nicolson (C-N) method for the heat equation on a staggered grid a class of non-symmetric matrices appear that have an interesting property: their eigenvalues are all real and lie within the unit circle. In this note we shall show how this class of matrices is derived from the C-N method and prove that their eigenvalues are inside [-1, 1] for all values of m (the order of the matrix) and all values of a positive parameter a, the stability parameter sigma. As the order of the matrix is general, and the parameter sigma lies on the positive real line this class of matrices turns out to be quite general and could be of interest as a test set for eigenvalue solvers, especially as examples of very large matrices. (C) 2010 Elsevier B.V. All rights reserved.