Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, sometimes by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We review, discuss and benchmark state-of-the-art representations and relations between them, including smooth overlap of atomic positions, many-body tensor representation, and symmetry functions. For this, we use a unified mathematical framework based on many-body functions, group averaging and tensor products, and compare energy predictions for organic molecules, binary alloys and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method and hyper-parameter optimization

Non-Universal Behavior of the k-Body Embedded Gaussian Unitary Ensemble of Random Matrices

Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the $k$-body embedded unitary ensemble in the limit of large matrix dimension. We identify the transition point between semicircle and Gaussian shape. The transition also affects the spectral fluctuations which deviate from Wigner-Dyson form and become Poissonian in the limit $k << m << l$. Here $m$ is the number of Fermions and $l$ the number of degenerate single-particle states.Comment: 4 pages, no figures, revised version including a new proof of one of our main claim

Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons

We investigate the shape of the spectrum and the spectral fluctuations of the $k$-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the number of Bosons $m \to \infty$ while both $k$, the rank of the interaction, and $l$, the number of single-particle states, are kept fixed. We show that the relative fluctuations of the low spectral moments do not vanish in this limit, proving that the ensemble is non-ergodic. Numerical simulations yield spectra which display a strong tendency towards picket-fence type. The wave functions also deviate from canonical random-matrix behaviourComment: 7 pages, 5 figures, uses epl.cls (included

Parent Resource Packet - A Guide for New Parents

PDF pages: 8

Information content of colored motifs in complex networks

We study complex networks in which the nodes of the network are tagged with different colors depending on the functionality of the nodes (colored graphs), using information theory applied to the distribution of motifs in such networks. We find that colored motifs can be viewed as the building blocks of the networks (much more so than the uncolored structural motifs can be) and that the relative frequency with which these motifs appear in the network can be used to define the information content of the network. This information is defined in such a way that a network with random coloration (but keeping the relative number of nodes with different colors the same) has zero color information content. Thus, colored motif information captures the exceptionality of coloring in the motifs that is maintained via selection. We study the motif information content of the C. elegans brain as well as the evolution of colored motif information in networks that reflect the interaction between instructions in genomes of digital life organisms. While we find that colored motif information appears to capture essential functionality in the C. elegans brain (where the color assignment of nodes is straightforward) it is not obvious whether the colored motif information content always increases during evolution, as would be expected from a measure that captures network complexity. For a single choice of color assignment of instructions in the digital life form Avida, we find rather that colored motif information content increases or decreases during evolution, depending on how the genomes are organized, and therefore could be an interesting tool to dissect genomic rearrangements.Comment: 21 pages, 8 figures, to appear in Artificial Lif

Photon-propagation model with random background field: Length scales and Cherenkov limits

We present improved experimental bounds on typical length scales of a photon-propagation model with a frozen (time-independent) random background field, which could result from anomalous effects of a static, multiply connected spacetime foam.Comment: 6 pages with revtex4; v3: final versio

Infidels.

Infidels is a short story collection dealing with a myriad of themes, most centrally of failed parenting, love, and yearning for the divine through spiritual brotherhood. The world the characters of Infidels inhabit is one of psychological wilderness. In the story, Squatting, for instance, a son watches helplessly as his father realizes that he cannot successfully raise his child as a homeless field squatter. Gnosis shows a physics professor experiencing cognitive breakdown as he struggles to rectify or even realize the pain he's causing his wife. In God Will Hear You, the half-Nepali, half-American protagonist only reveals to himself his love for his wife after driving her into a feigned state of catatonia. The collection culminates with Elohim, a story about an isolated young man's attempt to experience the divine after discovering companionship in two poorly recovering methamphetamine addicts. More than anything, however, Infidels explores beauty in the most putrid and dysfunctional landscapes of contemporary American life.--Abstract