Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

Selecting object pairs for action: is the active object always first?

Perception is linked to action via two routes: a direct route based on affordance information in the environment and an indirect route based on semantic knowledge about objects. The present study explored the factors modulating the recruitment of the two routes, in particular which factors affecting the selection of paired objects. In Experiment 1, we presented real objects among semantically related or unrelated distracters. Participants had to select two objects that can interact. The presence of distracters affected selection times, but not the semantic relations of the objects with the distracters. Furthermore, participants first selected the active object (e.g. teaspoon) with their right hand, followed by the passive object (e.g. mug), often with their left hand. In Experiment 2, we presented pictures of the same objects with no hand grip, congruent or incongruent hand grip. Participants had to decide whether the two objects can interact. Action decisions were faster when the presentation of the active object preceded the presentation of the passive object, and when the grip was congruent. Interestingly, participants were slower when the objects were semantically but not functionally related; this effect increased with congruently gripped objects. Our data showed that action decisions in the presence of strong affordance cues (real objects, pictures of congruently gripped objects) relied on sensory-motor representation, supporting the direct route from perception-to-action that bypasses semantic knowledge. However, in the case of weak affordance cues (pictures), semantic information interfered with action decisions, indicating that semantic knowledge impacts action decisions. The data support the dual-route account from perception-to-action.

The role of copper in the thermal conductivity of thermoelectric oxychalcogenides: do lone pairs matter?

Understanding the underlying mechanisms that suppress thermal conduction in solids is of paramount importance for the targeted design of materials for thermal management and thermoelectric energy conversion applications. Bismuth copper oxychalcogenides, BiOCuQ (Q = Se, Te), are highly crystalline thermoelectric materials with an unusually low lattice thermal conductivity of approx. 0.5 Wm-1K-1, a value normally found in amorphous materials. Here we unveil the origin of the unusual thermal transport properties of these phases. First principles calculations of the vibrational properties combined with analysis of in-situ neutron diffraction data, demonstrate that weak bonding of copper atoms within the structure leads to an unexpected vibrational mode at low frequencies, which is likely to be a major contributor to the low thermal conductivity of these materials. In addition, we show that anharmonicity and the large Grüneisen parameter in these oxychalcogenides are mainly related to the low frequency copper vibrations, rather than to the Bi3+ lone pairs.