Entropy-scaling search of massive biological data

Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing a dataset's entropy and fractal dimension. We prove that searching scales in time with metric entropy (number of covering hyperspheres), if the fractal dimension of the dataset is low, and scales in space with the sum of metric entropy and information-theoretic entropy (randomness of the data). Using these ideas, we present accelerated versions of standard tools, with no loss in specificity and little loss in sensitivity, for use in three domains---high-throughput drug screening (Ammolite, 150x speedup), metagenomics (MICA, 3.5x speedup of DIAMOND [3,700x BLASTX]), and protein structure search (esFragBag, 10x speedup of FragBag). Our framework can be used to achieve "compressive omics," and the general theory can be readily applied to data science problems outside of biology.Comment: Including supplement: 41 pages, 6 figures, 4 tables, 1 bo

Killing forms on the five-dimensional Einstein-Sasaki Y(p,q) spaces

We present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p,q) spaces. Two new Killing-Yano tensors are identified, associated with the complex volume form of the Calabi-Yau metric cone. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.Comment: 10 pages; improved versio

Harmonic coordinate method for simulating generic singularities

This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such coordinates, the terms in Einstein's equations with the highest number of derivatives take a form similar to that of the wave equation. The application is an exploration of the generic approach to the singularity for this type of matter. The preliminary results indicate that the dynamics as one approaches the singularity is locally the dynamics of the Kasner spacetimes.Comment: 5 pages, 4 figures, Revtex, discussion expanded, references adde

Helicity Removal and Coronal Fe XII Stalks: Evidence That the Axial Field Is Not Ejected but Resubmerged

This is the final version. Available from American Astronomical Society via the DOI in this recordThe magnetic/current helicity of the coronal field is closely associated with the presence of a nonpotential axial component directed along the photospheric polarity inversion line (PIL), which is also the source of the axial/toroidal field in flux ropes and coronal mass ejections (CMEs). To better understand the role of this axial component in the evolution of coronal helicity, we use Fe xii 19.3 nm images and longitudinal magnetograms from the Solar Dynamics Observatory to track active regions (ARs) and their filament channels as they decay due to flux transport processes. We find that the Fe xii loop legs or "stalks," initially oriented almost perpendicular to the PIL, become closely aligned with it after ~1–4 rotations; this alignment is attributed to the progressive cancellation of the transverse field component at the PIL. As the AR flux continues to decay, the PIL becomes ever more distorted and the directions of the stalks are increasingly randomized. These observations suggest that most of the original axial field in ARs is not expelled in CMEs, but instead pinches off after the eruptions and becomes concentrated at the PIL. Because the twist of the field decreases, however, the helicity itself decreases, with CMEs removing a significant fraction of it in the form of disconnected flux ropes. Like most of the AR flux, the bulk of the axial field is eventually canceled/resubmerged, brought to the equator by the subsurface meridional flow, and annihilated (along with the remaining helicity) by merging with its opposite-handed counterpart from the other hemisphere.This work was funded by the Chief of Naval Research

Stationary phase slip state in quasi-one-dimensional rings

The nonuniform superconducting state in a ring in which the order parameter vanishing at one point is studied. This state is characterized by a jump of the phase by $\pi$ at the point where the order parameter becomes zero. In uniform rings such a state is a saddle-point state and consequently unstable. However, for non-uniform rings with e.g. variations of geometrical or physical parameters or with attached wires this state can be stabilized and may be realized experimentally.Comment: 6 pages, 7 figures, RevTex 4.0 styl

Variation in ovulation rate and litter size

An increase in mean prolificacy is a goal for many sheep production systems, but it is also desirable that variation be minimized around the optimum value. Lambs born in litters of 3 or 4 can be reared with intensive management, but at higher input costs than for twins. Thus for a mean litter size (LS) goal of 2.0, producers desire the maximum possible proportion of twins with as few singles and litters of 3 or more as possible. Coefficients of variation for ovulation rate (OR) range from about 22 % for Romanov to about 40 % for Booroola Merinos; breed CV’s for LS vary less. The most uniform LS’s are achieved by populations with a uniform OR and high prenatal survival. Variability in Booroola populations results in part from segregation of a gene with large effect on OR, but variation is high within genotypes (FF or F+). Among breeds where high prolificacy appears to be inherited quantitatively, there are differences in variability, with Romanov quite uniform, Finnsheep intermediate, and D’Man more variable. The possibility of a gene with large effect in the D’Man breed, in addition to many favorable quantitative genes for prolificacy, has not been ruled out. In general, these three breeds (and some others) transmit their prolificacy additively, making it possible to choose a wider range of mean prolificacy values by crossing and backcrossing with such breeds than by use of a major gene such as the Booroola. Data on variability of first and later generation crossbreds between non-prolific and different prolific breeds are now available

Relationships between magnetic foot points and G-band bright structures

Magnetic elements are thought to be described by flux tube models, and are well reproduced by MHD simulations. However, these simulations are only partially constrained by observations. We observationally investigate the relationship between G-band bright points and magnetic structures to clarify conditions, which make magnetic structures bright in G-band. The G-band filtergrams together with magnetograms and dopplergrams were taken for a plage region covered by abnormal granules as well as ubiquitous G-band bright points, using the Swedish 1-m Solar Telescope (SST) under very good seeing conditions. High magnetic flux density regions are not necessarily associated with G-band bright points. We refer to the observed extended areas with high magnetic flux density as magnetic islands to separate them from magnetic elements. We discover that G-band bright points tend to be located near the boundary of such magnetic islands. The concentration of G-band bright points decreases with inward distance from the boundary of the magnetic islands. Moreover, G-band bright points are preferentially located where magnetic flux density is higher, given the same distance from the boundary. There are some bright points located far inside the magnetic islands. Such bright points have higher minimum magnetic flux density at the larger inward distance from the boundary. Convective velocity is apparently reduced for such high magnetic flux density regions regardless of whether they are populated by G-band bright points or not. The magnetic islands are surrounded by downflows.These results suggest that high magnetic flux density, as well as efficient heat transport from the sides or beneath, are required to make magnetic elements bright in G-band.Comment: 9 pages, 14 figures, accepted for publication in A&

Dijet Event Shapes as Diagnostic Tools

Event shapes have long been used to extract information about hadronic final states and the properties of QCD, such as particle spin and the running coupling. Recently, a family of event shapes, the angularities, has been introduced that depends on a continuous parameter. This additional parameter-dependence further extends the versatility of event shapes. It provides a handle on nonperturbative power corrections, on non-global logarithms, and on the flow of color in the final state.Comment: 18 pages, 3 figure