Brownian motion on the Sierpinski carpet

We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpinski carpet that is invariant with respect to the local symmetries of the carpet. Consequently for each such fractal the law of Brownian motion is uniquely determined and the Laplacian is well defined

Challenges in Reconciling Different Views of Neuroanatomy in a Reference Ontology of Anatomy

A fundamental requirement for integrating neuroscience data is a well-structured ontology that can incorporate, accommodate and reconcile different neuroanatomical views. Here we describe the challenges in creating such ontology, and, because of its principled design, illustrate the potential of the Foundational Model of Anatomy to be that ontology

The electronic Hamiltonian for cuprates

A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations

Dissociation of Action and Object Naming: Evidence From Cortical Stimulation Mapping

This cortical stimulation mapping study investigates the neural representation of action and object naming. Data from 13 neurosurgical subjects undergoing awake cortical mapping is presented. Our findings indicate clear evidence of differential disruption of noun and verb naming in the context of this naming task. At the individual level, evidence was found for punctuate regions of perisylvian cortex subserving noun and verb function. Across subjects, however, the location of these sites varied. This finding may help explain discrepancies between lesion and functional imaging studies of noun and verb naming. In addition, an alternative coding of these data served to highlight the grammatical class vulnerability of the target response. The use of this coding scheme implicates a role for the supramarginal gyrus in verb-naming behavior. These data are discussed with respect to a functional-anatomical pathway underlying verb naming