Spectral Statistics of "Cellular" Billiards

For a bounded planar domain $\Omega^0$ whose boundary contains a number of flat pieces $\Gamma_i$ we consider a family of non-symmetric billiards $\Omega$ constructed by patching several copies of $\Omega^0$ along $\Gamma_i$'s. It is demonstrated that the length spectrum of the periodic orbits in $\Omega$ is degenerate with the multiplicities determined by a matrix group $G$. We study the energy spectrum of the corresponding quantum billiard problem in $\Omega$ and show that it can be split in a number of uncorrelated subspectra corresponding to a set of irreducible representations $\alpha$ of $G$. Assuming that the classical dynamics in $\Omega^0$ are chaotic, we derive a semiclassical trace formula for each spectral component and show that their energy level statistics are the same as in standard Random Matrix ensembles. Depending on whether ${\alpha}$ is real, pseudo-real or complex, the spectrum has either Gaussian Orthogonal, Gaussian Symplectic or Gaussian Unitary types of statistics, respectively.Comment: 18 pages, 4 figure

Robust Chauvenet Outlier Rejection

Sigma clipping is commonly used in astronomy for outlier rejection, but the number of standard deviations beyond which one should clip data from a sample ultimately depends on the size of the sample. Chauvenet rejection is one of the oldest, and simplest, ways to account for this, but, like sigma clipping, depends on the sample's mean and standard deviation, neither of which are robust quantities: Both are easily contaminated by the very outliers they are being used to reject. Many, more robust measures of central tendency, and of sample deviation, exist, but each has a tradeoff with precision. Here, we demonstrate that outlier rejection can be both very robust and very precise if decreasingly robust but increasingly precise techniques are applied in sequence. To this end, we present a variation on Chauvenet rejection that we call "robust" Chauvenet rejection (RCR), which uses three decreasingly robust/increasingly precise measures of central tendency, and four decreasingly robust/increasingly precise measures of sample deviation. We show this sequential approach to be very effective for a wide variety of contaminant types, even when a significant -- even dominant -- fraction of the sample is contaminated, and especially when the contaminants are strong. Furthermore, we have developed a bulk-rejection variant, to significantly decrease computing times, and RCR can be applied both to weighted data, and when fitting parameterized models to data. We present aperture photometry in a contaminated, crowded field as an example. RCR may be used by anyone at https://skynet.unc.edu/rcr, and source code is available there as well.Comment: 62 pages, 48 figures, 7 tables, accepted for publication in ApJ

Semiclassical approach to discrete symmetries in quantum chaos

We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to irreducible representations of the corresponding symmetry group. We show that for (spinless) time reversal invariant systems the statistics inside these subspectra depend on the type of irreducible representation. For real representations the spectral statistics agree with those of the Gaussian Orthogonal Ensemble (GOE) of Random Matrix Theory (RMT), whereas complex representations correspond to the Gaussian Unitary Ensemble (GUE). For systems without time reversal invariance all subspectra show GUE statistics. There are no correlations between non-degenerate subspectra. Our techniques generalize recent developments in the semiclassical approach to quantum chaos allowing one to obtain full agreement with the two-point correlation function predicted by RMT, including oscillatory contributions.Comment: 26 pages, 8 Figure

GSE statistics without spin

Energy levels statistics following the Gaussian Symplectic Ensemble (GSE) of Random Matrix Theory have been predicted theoretically and observed numerically in numerous quantum chaotic systems. However in all these systems there has been one unifying feature: the combination of half-integer spin and time-reversal invariance. Here we provide an alternative mechanism for obtaining GSE statistics that is based on geometric symmetries of a quantum system which alleviates the need for spin. As an example, we construct a quantum graph with a particular discrete symmetry given by the quaternion group Q8. GSE statistics is then observed within one of its subspectra.Comment: 5 pages, 6 figure

Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations

To treat the spectral statistics of quantum maps and flows that are fully chaotic classically, we use the rigorous Riemann-Siegel lookalike available for the spectral determinant of unitary time evolution operators $F$. Concentrating on dynamics without time reversal invariance we get the exact two-point correlator of the spectral density for finite dimension $N$ of the matrix representative of $F$, as phenomenologically given by random matrix theory. In the limit $N\to\infty$ the correlator of the Gaussian unitary ensemble is recovered. Previously conjectured cancellations of contributions of pseudo-orbits with periods beyond half the Heisenberg time are shown to be implied by the Riemann-Siegel lookalike

Application of phenotypic microarrays to environmental microbiology

Environmental organisms are extremely diverse and only a small fraction has been successfully cultured in the laboratory. Culture in micro wells provides a method for rapid screening of a wide variety of growth conditions and commercially available plates contain a large number of substrates, nutrient sources, and inhibitors, which can provide an assessment of the phenotype of an organism. This review describes applications of phenotype arrays to anaerobic and thermophilic microorganisms, use of the plates in stress response studies, in development of culture media for newly discovered strains, and for assessment of phenotype of environmental communities. Also discussed are considerations and challenges in data interpretation and visualization, including data normalization, statistics, and curve fitting

Finite pseudo orbit expansions for spectral quantities of quantum graphs

We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irreducible and where the total number of bonds is less than or equal to the number of bonds of the graph appear, analogous to a cut off at half the Heisenberg time. The calculation simplifies previous approaches to pseudo orbit expansions on graphs. We formulate coefficients of the characteristic polynomial and derive a secular equation in terms of the irreducible pseudo orbits. From the secular equation, whose roots provide the graph spectrum, the zeta function is derived using the argument principle. The spectral zeta function enables quantities, such as the spectral determinant and vacuum energy, to be obtained directly as finite expansions over the set of short irreducible pseudo orbits.Comment: 23 pages, 4 figures, typos corrected, references added, vacuum energy calculation expande

Small and mighty: adaptation of superphylum Patescibacteria to groundwater environment drives their genome simplicity.

BackgroundThe newly defined superphylum Patescibacteria such as Parcubacteria (OD1) and Microgenomates (OP11) has been found to be prevalent in groundwater, sediment, lake, and other aquifer environments. Recently increasing attention has been paid to this diverse superphylum including > 20 candidate phyla (a large part of the candidate phylum radiation, CPR) because it refreshed our view of the tree of life. However, adaptive traits contributing to its prevalence are still not well known.ResultsHere, we investigated the genomic features and metabolic pathways of Patescibacteria in groundwater through genome-resolved metagenomics analysis of > 600 Gbp sequence data. We observed that, while the members of Patescibacteria have reduced genomes (~ 1 Mbp) exclusively, functions essential to growth and reproduction such as genetic information processing were retained. Surprisingly, they have sharply reduced redundant and nonessential functions, including specific metabolic activities and stress response systems. The Patescibacteria have ultra-small cells and simplified membrane structures, including flagellar assembly, transporters, and two-component systems. Despite the lack of CRISPR viral defense, the bacteria may evade predation through deletion of common membrane phage receptors and other alternative strategies, which may explain the low representation of prophage proteins in their genomes and lack of CRISPR. By establishing the linkages between bacterial features and the groundwater environmental conditions, our results provide important insights into the functions and evolution of this CPR group.ConclusionsWe found that Patescibacteria has streamlined many functions while acquiring advantages such as avoiding phage invasion, to adapt to the groundwater environment. The unique features of small genome size, ultra-small cell size, and lacking CRISPR of this large lineage are bringing new understandings on life of Bacteria. Our results provide important insights into the mechanisms for adaptation of the superphylum in the groundwater environments, and demonstrate a case where less is more, and small is mighty

Colwellia psychrerythraea Strains from Distant Deep Sea Basins Show Adaptation to Local Conditions

Many studies have shown that microbes, which share nearly identical 16S rRNA genes, can have highly divergent genomes. Microbes from distinct parts of the ocean also exhibit biogeographic patterning. Here we seek to better understand how certain microbes from the same species have adapted for growth under local conditions. The phenotypic and genomic heterogeneity of three strains of Colwellia psychrerythraeawas investigated in order to understand adaptions to local environments. Colwellia are psychrophilic heterotrophic marine bacteria ubiquitous in cold marine ecosystems. We have recently isolated two Colwellia strains: ND2E from the Eastern Mediterranean and GAB14E from the Great Australian Bight. The 16S rRNA sequence of these two strains were greater than 98.2% identical to the well-characterized C. psychrerythraea 34H, which was isolated from arctic sediments. Salt tolerance, and carbon source utilization profiles for these strains were determined using Biolog Phenotype MicoArrays. These strains exhibited distinct salt tolerance, which was not associated with the salinity of sites of isolation. The carbon source utilization profiles were distinct with less than half of the tested carbon sources being metabolized by all three strains. Whole genome sequencing revealed that the genomes of these three strains were quite diverse with some genomes having up to 1600 strain-specific genes. Many genes involved in degrading strain-specific carbon sources were identified. There appears to be a link between carbon source utilization and location of isolation with distinctions observed between the Colwellia isolate recovered from sediment compared to water column isolates

Statistical modeling of ground motion relations for seismic hazard analysis

We introduce a new approach for ground motion relations (GMR) in the probabilistic seismic hazard analysis (PSHA), being influenced by the extreme value theory of mathematical statistics. Therein, we understand a GMR as a random function. We derive mathematically the principle of area-equivalence; wherein two alternative GMRs have an equivalent influence on the hazard if these GMRs have equivalent area functions. This includes local biases. An interpretation of the difference between these GMRs (an actual and a modeled one) as a random component leads to a general overestimation of residual variance and hazard. Beside this, we discuss important aspects of classical approaches and discover discrepancies with the state of the art of stochastics and statistics (model selection and significance, test of distribution assumptions, extreme value statistics). We criticize especially the assumption of logarithmic normally distributed residuals of maxima like the peak ground acceleration (PGA). The natural distribution of its individual random component (equivalent to exp(epsilon_0) of Joyner and Boore 1993) is the generalized extreme value. We show by numerical researches that the actual distribution can be hidden and a wrong distribution assumption can influence the PSHA negatively as the negligence of area equivalence does. Finally, we suggest an estimation concept for GMRs of PSHA with a regression-free variance estimation of the individual random component. We demonstrate the advantages of event-specific GMRs by analyzing data sets from the PEER strong motion database and estimate event-specific GMRs. Therein, the majority of the best models base on an anisotropic point source approach. The residual variance of logarithmized PGA is significantly smaller than in previous models. We validate the estimations for the event with the largest sample by empirical area functions. etc