Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.

PDFOS: PDF estimation based over-sampling for imbalanced two-class problems

This contribution proposes a novel probability density function (PDF) estimation based over-sampling (PDFOS) approach for two-class imbalanced classification problems. The classical Parzen-window kernel function is adopted to estimate the PDF of the positive class. Then according to the estimated PDF, synthetic instances are generated as the additional training data. The essential concept is to re-balance the class distribution of the original imbalanced data set under the principle that synthetic data sample follows the same statistical properties. Based on the over-sampled training data, the radial basis function (RBF) classifier is constructed by applying the orthogonal forward selection procedure, in which the classifier’s structure and the parameters of RBF kernels are determined using a particle swarm optimisation algorithm based on the criterion of minimising the leave-one-out misclassification rate. The effectiveness of the proposed PDFOS approach is demonstrated by the empirical study on several imbalanced data sets.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Assessment of the relative reinforcing strength of cocaine in socially housed monkeys using a choice procedure.

Position in the social hierarchy can influence brain dopamine function and cocaine reinforcement in nonhuman primates during early cocaine exposure. With prolonged exposure, however, initial differences in rates of cocaine self-administration between dominant and subordinate monkeys dissipate. The present studies used a choice procedure to assess the relative reinforcing strength of cocaine in group-housed male cynomolgus monkeys with extensive cocaine self-administration histories. Responding was maintained under a concurrent fixed-ratio 50 schedule of food and cocaine (0.003-0.1 mg/kg per injection) presentation. Responding on the cocaine-associated lever increased as a function of cocaine dose in all monkeys. Although response distribution was similar across social rank when saline or relatively low or high cocaine doses were the alternative to food, planned t tests indicated that cocaine choice was significantly greater in subordinate monkeys when choice was between an intermediate dose (0.01 mg/kg) and food. When a between-session progressive-ratio procedure was used to increase response requirements for the preferred reinforcer (either cocaine or food), choice of that reinforcer decreased in all monkeys. The average response requirement that produced a shift in response allocation from the cocaine-associated lever to the food-associated lever was higher in subordinates across cocaine doses, an effect that trended toward significance (p = 0.053). These data indicate that despite an extensive history of cocaine self-administration, most subordinate monkeys were more sensitive to the relative reinforcing strength of cocaine than dominant monkeys.