We survey the analytic theory of matrix orthogonal polynomials. MSC: 42C05, 47B36, 30C10 keywords: orthogonal polynomials, matrix-valued measures, block Jacobi matrices, block CMV matrices

We prove the existence of absolutely continuous invariant measures for piecewise real-analytic expanding maps on bounded regions in the plane.

Brascamp–Lieb-type, weighted Poincaré-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general κ-concave probability measures (in the hierarchy of convex measures). In analogy with the limiting (infinitedimensional log-concave) Gaussian model, the weighted inequalities fully describe the measure concentration and large deviation properties of...

Brascamp–Lieb-type, weighted Poincaré-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general κ-concave probability measures (in the hierarchy of convex measures). In analogy with the limiting (infinite-dimensional log-concave) Gaussian model, the weighted inequalities fully describe the measure concentration and large deviation properties o...

In this study, we derived analytic expressions for the elliptical truncated moment generating function (MGF), the zeroth-, first-, and second-order moments of quadratic forms of the multivariate normal, Student’s t, and generalised hyperbolic distributions. The resulting formulae were tested in a numerical application to calculate an analytic expression of the expected shortfall of quadratic po...

Recent research has indicated a negative relation between the propensity for analytic reasoning and religious beliefs and practices. Here, we propose conflict detection as a mechanism underlying this relation, on the basis of the hypothesis that more-analytic people are less religious, in part, because they are more sensitive to conflicts between immaterial religious beliefs and beliefs about t...

Developmental and individual differences in the tendency to favor analytic responses over heuristic responses were examined in children of two different ages (10- and 11-year-olds versus 13-year-olds), and of widely varying cognitive ability. Three tasks were examined that all required analytic processing to override heuristic processing: inductive reasoning, deductive reasoning under condition...

Two intervention procedures for the rehabilitation of elderly adults with hearing impairment were evaluated: analytic auditory training and active listening training. Seventy-eight older adults with hearing loss served as subjects. Twenty-six subjects received no training, 26 received analytic training, and 26 received active listening training. The effectiveness of the audiologic rehabilitatio...

In our response, we clarify important theoretical differences between basic emotion and psychological construction approaches. We evaluate the empirical status of the basic emotion approach, addressing whether it requires brain localization, whether localization can be observed with better analytic tools, and whether evidence for basic emotions exists in other types of measures. We then revisit...