3,854 research outputs found
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, '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 is substituted by any .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
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
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