Optimal Belief Approximation

In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it is to communicate a given approximation. We reproduce and discuss an old proof showing that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. The loss function that is obtained in the derivation is equal to the Kullback-Leibler divergence when normalized. This loss function is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. The correct order ensures that the recipient of a communication is only deprived of the minimal amount of information. We hope that the elementary derivation settles the apparent confusion. For example when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many suggested computational schemes.Comment: made improvements on the proof and the languag

Quantification of Cell Subpopulations, Fractions of Dead Cells and Debris in Cell Suspensions by Laser Diffractometry

Laser diffractometry was employed for size analysis in liver cell and blood cell suspensions to assess its suitability for characterizing cell populations. The method proved sensitive to detect subpopulations in liver cells (bimodal or trimodal distributions) and to quantify their volume fractions. Cell debris and aggregates of cells could also be quantified, dead cell populations recognized by their shift in the mean cell diameter. Laser diffractometry is therefore suitable for determining the quality of cell isolations (e.g. by liver perfusion) or for following alterations in cell populations during culture of cells in suspension. Analysis of human blood allowed differenciations to be made between thrombocytes and other blood cells. No peak separation was obtained for the populations of erythrocytes and granulocytes due to their similarity in size. Monocytes could not be detected due to their extremely low number in the blood indicating the limit of the metho

A geometric protocol for a robust Majorana magic gate

A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this manuscript we present a protocol that achieves the missing, so called, $\pi/8$ 'magic' phase gate. The protocol is based on the manipulation of geometric phases in a universal manner, and does not require fine tuning for distinct physical realizations. The protocol converges exponentially with the number of steps in the geometric path. Furthermore, the magic gate protocol relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to any-phase-gate, where $\pi/8$ is substituted by any $\alpha$.Comment: 14 pages, 8 figures (including appendices), v3: simplified derivation, more explicit connection between topological protection and exponential convergenc

Adjustment of the basin-scale circulation at 26 degrees N to variations in Gulf Stream, deep western boundary current and Ekman transports as observed by the Rapid array

The Rapid instrument array across the Atlantic Ocean along 26 degrees N provides unprecedented monitoring of the basin-scale circulation. A unique feature of the Rapid array is the combination of full-depth moorings with instruments measuring temperature, salinity, pressure time series at many depths with co-located bottom pressure measurements so that dynamic pressure can be measured from surface to bottom. Bottom pressure measurements show a zonally uniform rise (and fall) of bottom pressure of 0.015 dbar on a 5 to 10 day time scale, suggesting that the Atlantic basin is filling and draining on a short time scale. After removing the zonally uniform bottom pressure fluctuations, bottom pressure variations at 4000 m depth against the western boundary compensate instantaneously for baroclinic fluctuations in the strength and structure of the deep western boundary current so there is no basin-scale mass imbalance resulting from variations in the deep western boundary current. After removing the mass compensating bottom pressure, residual bottom pressure fluctuations at the western boundary just east of the Bahamas balance variations in Gulf Stream transport. Again the compensation appears to be especially confined close to the western boundary. Thus, fluctuations in either Gulf Stream or deep western boundary current transports are compensated in a depth independent (barotropic) manner very close to the continental slope off the Bahamas. In contrast, compensation for variations in wind-driven surface Ekman transport appears to involve fluctuations in both western basin and eastern basin bottom pressures, though the bottom pressure difference fluctuations appear to be a factor of 3 too large, perhaps due to an inability to resolve small bottom pressure fluctuations after removal of larger zonal average, baroclinic, and Gulf Stream pressure components. For 4 tall moorings where time series dynamic height (geostrophic pressure) profiles can be estimated from sea surface to ocean bottom and bottom pressure can be added, there is no general correlation between surface dynamic height and bottom pressure. Dynamic height on each mooring is strongly correlated with sea surface height from satellite observations and the variability in both dynamic height and satellite sea surface height decrease sharply as the western boundary is approached

Chiral Bogoliubons in Nonlinear Bosonic Systems

We present a versatile scheme for creating topological Bogoliubov excitations in weakly interacting bosonic systems. Our proposal relies on a background stationary field that consists of a Kagome vortex lattice, which breaks time-reversal symmetry and induces a periodic potential for Bogoliubov excitations. In analogy to the Haldane model, no external magnetic field or net flux is required. We construct a generic model based on the two-dimensional (2D) nonlinear Schr\"odinger equation and demonstrate the emergence of topological gaps crossed by chiral Bogoliubov edge modes. Our scheme can be realized in a wide variety of physical systems ranging from nonlinear optical systems to exciton-polariton condensates.Comment: 6 pages, 3 figures; with Supplemental Material (5 pages; in source

Inductively coupled plasma- and glow discharge plasma-sector field mass spectrometry

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Data congruence, paedomorphosis and salamanders

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background: The retention of ancestral juvenile characters by adult stages of descendants is called paedomorphosis. However, this process can mislead phylogenetic analyses based on morphological data, even in combination with molecular data, because the assessment if a character is primary absent or secondary lost is difficult. Thus, the detection of incongruence between morphological and molecular data is necessary to investigate the reliability of simultaneous analyses. Different methods have been proposed to detect data congruence or incongruence. Five of them (PABA, PBS, NDI, LILD, DRI) are used herein to assess incongruence between morphological and molecular data in a case study addressing salamander phylogeny, which comprises several supposedly paedomorphic taxa. Therefore, previously published data sets were compiled herein. Furthermore, two strategies ameliorating effects of paedomorphosis on phylogenetic studies were tested herein using a statistical rigor. Additionally, efficiency of the different methods to assess incongruence was analyzed using this empirical data set. Finally, a test statistic is presented for all these methods except DRI