Efficient Learning of a One-dimensional Density Functional Theory

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In addition, the computational result---energy and charge density distribution of the ground state---is useful for electronic properties of solids mostly when reduced to a band structure interpretation based on the Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can help to free density functional theory from these limitations. We study a theory of spinless fermions on a one-dimensional lattice. The density functional is implicitly represented by a neural network, which predicts, besides the ground-state energy and density distribution, density-density correlation functions. At no point do we require a band structure interpretation. The training data, obtained via exact diagonalization, feeds into a learning scheme inspired by active learning, which minimizes the computational costs for data generation. We show that the network results are of high quantitative accuracy and, despite learning on random potentials, capture both symmetry-breaking and topological phase transitions correctly.Comment: 5 pages, 3 figures; 4+ pages appendi

Multi-camera Realtime 3D Tracking of Multiple Flying Animals

Automated tracking of animal movement allows analyses that would not otherwise be possible by providing great quantities of data. The additional capability of tracking in realtime - with minimal latency - opens up the experimental possibility of manipulating sensory feedback, thus allowing detailed explorations of the neural basis for control of behavior. Here we describe a new system capable of tracking the position and body orientation of animals such as flies and birds. The system operates with less than 40 msec latency and can track multiple animals simultaneously. To achieve these results, a multi target tracking algorithm was developed based on the Extended Kalman Filter and the Nearest Neighbor Standard Filter data association algorithm. In one implementation, an eleven camera system is capable of tracking three flies simultaneously at 60 frames per second using a gigabit network of nine standard Intel Pentium 4 and Core 2 Duo computers. This manuscript presents the rationale and details of the algorithms employed and shows three implementations of the system. An experiment was performed using the tracking system to measure the effect of visual contrast on the flight speed of Drosophila melanogaster. At low contrasts, speed is more variable and faster on average than at high contrasts. Thus, the system is already a useful tool to study the neurobiology and behavior of freely flying animals. If combined with other techniques, such as `virtual reality'-type computer graphics or genetic manipulation, the tracking system would offer a powerful new way to investigate the biology of flying animals.Comment: pdfTeX using libpoppler 3.141592-1.40.3-2.2 (Web2C 7.5.6), 18 pages with 9 figure

A Reference-Free Algorithm for Computational Normalization of Shotgun Sequencing Data

Deep shotgun sequencing and analysis of genomes, transcriptomes, amplified single-cell genomes, and metagenomes has enabled investigation of a wide range of organisms and ecosystems. However, sampling variation in short-read data sets and high sequencing error rates of modern sequencers present many new computational challenges in data interpretation. These challenges have led to the development of new classes of mapping tools and {\em de novo} assemblers. These algorithms are challenged by the continued improvement in sequencing throughput. We here describe digital normalization, a single-pass computational algorithm that systematizes coverage in shotgun sequencing data sets, thereby decreasing sampling variation, discarding redundant data, and removing the majority of errors. Digital normalization substantially reduces the size of shotgun data sets and decreases the memory and time requirements for {\em de novo} sequence assembly, all without significantly impacting content of the generated contigs. We apply digital normalization to the assembly of microbial genomic data, amplified single-cell genomic data, and transcriptomic data. Our implementation is freely available for use and modification

Arbuscular mycorrhizae of Mojave Desert plants

Roots of 15 Mojave Desert plant species were assessed for arbuscular mycorrhizal (AM) colonization in spring and autumn 1999. Another 19 species were assessed in autumn only. Perennial species were AM colonized, whereas annual species contained very low levels of AM hyphae or were nonmycorrhizal. The nonnative tree Tamarix ramosissima was also nonmycorrhizal. Levels of hyphae changed over the season in 2 species, arbuscle levels increased in 1 species, and vesicles decreased in 7 species. Mycorrhizal inoculum potential (MIP) was assessed in the soils associated with spring-collected plants. All soils were found to contain MIP. MIP values were not correlated with AM root colonization

A novel platform for two-dimensional chiral topological superconductivity

We show that the surface of an $s$-wave superconductor decorated with a two-dimensional lattice of magnetic impurities can exhibit chiral topological superconductivity. If impurities order ferromagnetically and the superconducting surface supports a sufficiently strong Rashba-type spin-orbit coupling, Shiba sub-gap states at impurity locations can hybridize into Bogoliubov bands with non-vanishing, sometimes large, Chern number $C$. This topological superconductor supports $C$ chiral Majorana edge modes. We construct phase diagrams for model two-dimensional superconductors, accessing the dilute and dense magnetic impurity limits analytically and the intermediate regime numerically. To address potential experimental systems, we identify stable configurations of ferromagnetic iron atoms on the Pb (111) surface and conclude that ferromagnetic adatoms on Pb surfaces can provide a versatile platform for two-dimensional topological superconductivity