Absolutely Continuous Spectrum for the Anderson Model on Some Tree-like Graphs

We prove persistence of absolutely continuous spectrum for the Anderson model on a general class of tree-like graphs.Comment: Some clarifications were added in the introduction and an extra appendix was adde

The direct perception hypothesis: perceiving the intention of another’s action hinders its precise imitation

We argue that imitation is a learning response to unintelligible actions, especially to social conventions. Various strands of evidence are converging on this conclusion, but further progress has been hampered by an outdated theory of perceptual experience. Comparative psychology continues to be premised on the doctrine that humans and nonhuman primates only perceive others’ physical ‘surface behavior’, while mental states are perceptually inaccessible. However, a growing consensus in social cognition research accepts the Direct Perception Hypothesis: primarily we see what others aim to do; we do not infer it from their motions. Indeed, physical details are overlooked – unless the action is unintelligible. On this basis we hypothesize that apes’ propensity to copy the goal of an action, rather than its precise means, is largely dependent on its perceived intelligibility. Conversely, children copy means more often than adults and apes because, uniquely, much adult human behavior is completely unintelligible to unenculturated observers due to the pervasiveness of arbitrary social conventions, as exemplified by customs, rituals, and languages. We expect the propensity to imitate to be inversely correlated with the familiarity of cultural practices, as indexed by age and/or socio-cultural competence. The Direct Perception Hypothesis thereby helps to parsimoniously explain the most important findings of imitation research, including children’s over-imitation and other species-typical and age-related variations

Enacting Productive Dialogue: Addressing the Challenge that Non-Human Cognition Poses to Collaborations Between Enactivism and Heideggerian Phenomenology

This chapter uses one particular proposal for interdisciplinary collaboration – in this case, between early Heideggerian phenomenology and enactivist cognitive science – as an example of how such partnerships may confront and negotiate tensions between the perspectives they bring together. The discussion begins by summarising some of the intersections that render Heideggerian and enactivist thought promising interlocutors for each other. It then moves on to explore how Heideggerian enactivism could respond to the challenge of reconciling the significant differences in the ways that each discourse seeks to apply the structures it claims to uncover

Carleman estimates and absence of embedded eigenvalues

Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.Comment: 26 page

Multiconfiguration electron density function for the ATSP2K-package

A new ATSP2K module is presented for evaluating the electron density function of any multiconfiguration Hartree-Fock or configuration interaction wave function in the non relativistic or relativistic Breit-Pauli approximation. It is first stressed that the density function is not a priori spherically symmetric in the general open shell case. Ways of building it as a spherical symmetric function are discussed, from which the radial electron density function emerges. This function is written in second quantized coupled tensorial form for exploring the atomic spherical symmetry. The calculation of its expectation value is performed using the angular momentum theory in orbital, spin, and quasispin spaces, adopting a generalized graphical technique. The natural orbitals are evaluated from the diagonalization of the density matrix

On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials

We consider discrete one-dimensional random Schroedinger operators with decaying matrix-valued, independent potentials. We show that if the l^2-norm of this potential has finite expectation value with respect to the product measure then almost surely the Schroedinger operator has an interval of purely absolutely continuous (ac) spectrum. We apply this result to Schroedinger operators on a strip. This work provides a new proof and generalizes a result obtained by Delyon, Simon, and Souillard.Comment: (1 figure

Transient rectification of Brownian diffusion with asymmetric initial distribution

In an ensemble of non-interacting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the equation for the first moment of velocity to couple to moments of higher order. The effect may be relevant when a complex system dissociates in a viscous medium with conservation of momentum

Numerical Optimal Transport from 1D to 2D using a Non-local Monge-Amp\`ere Equation

We consider the numerical solution of the optimal transport problem between densities that are supported on sets of unequal dimension. Recent work by McCann and Pass reformulates this problem into a non-local Monge-Amp\`ere type equation. We provide a new level set framework for interpreting this non-linear PDE. We also propose a novel discretisation that combines carefully constructed monotone finite difference schemes with a variable-support discrete version of the Dirac delta function. The resulting method is consistent and monotone. These new techniques are described and implemented in the setting of 1D to 2D transport, but can easily be generalised to higher dimensions. Several challenging computational tests validate the new numerical method

Exploring Biorthonormal Transformations of Pair-Correlation Functions in Atomic Structure Variational Calculations

Multiconfiguration expansions frequently target valence correlation and correlation between valence electrons and the outermost core electrons. Correlation within the core is often neglected. A large orbital basis is needed to saturate both the valence and core-valence correlation effects. This in turn leads to huge numbers of CSFs, many of which are unimportant. To avoid the problems inherent to the use of a single common orthonormal orbital basis for all correlation effects in the MCHF method, we propose to optimize independent MCHF pair-correlation functions (PCFs), bringing their own orthonormal one-electron basis. Each PCF is generated by allowing single- and double- excitations from a multireference (MR) function. This computational scheme has the advantage of using targeted and optimally localized orbital sets for each PCF. These pair-correlation functions are coupled together and with each component of the MR space through a low dimension generalized eigenvalue problem. Nonorthogonal orbital sets being involved, the interaction and overlap matrices are built using biorthonormal transformation of the coupled basis sets followed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energies that are lower than the ones from traditional CAS-MCHF calculations using large orbital active sets. It is fair to say that we now have the possibility to account for, in a balanced way, correlation deep down in the atomic core in variational calculations

Role of HRM in knowledge integration: Towards a conceptual framework

Knowledge integration (KI) is a source of sustained competitive advantage for firms. This paper draws upon the knowledge-based view of the firm and ability-motivation-opportunity framework to develop a theoretical and empirical model showing the role of human resource management (HRM) practices in achieving KI. Findings suggest three ability-enhancing practices (training and development, focused hiring, and knowledge questioning values), four motivation-enhancing practices (project-specific performance, competency-based performance management, project-based information dissemination, and information and knowledge sharing forums) and five opportunity-enhancing practices (team working, information and knowledge sharing, verticalisation of business, geographical information and knowledge sharing, and structural change) that facilitate KI. The paper concludes with managerial implications, directions for future research and the study's limitations