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 Various strands of evidence are converging on this conclusion, but further progress has been hampered by an outdated theory of perceptual experience.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

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

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

Symmetry Breaking of Relativistic Multiconfiguration Methods in the Nonrelativistic Limit

The multiconfiguration Dirac-Fock method allows to calculate the state of relativistic electrons in atoms or molecules. This method has been known for a long time to provide certain wrong predictions in the nonrelativistic limit. We study in full mathematical details the nonlinear model obtained in the nonrelativistic limit for Be-like atoms. We show that the method with sp+pd configurations in the J=1 sector leads to a symmetry breaking phenomenon in the sense that the ground state is never an eigenvector of L^2 or S^2. We thereby complement and clarify some previous studies.Comment: Final version, to appear in Nonlinearity. Nonlinearity (2010) in pres