Putting probabilities first. How Hilbert space generates and constrains them

We use correlation arrays, the workhorse of Bub's (2016) Bananaworld, to analyze the correlations found in an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-1/2 particles. Adopting an approach pioneered by Pitowsky (1989b) and promoted in Bananaworld, we geometrically represent the class of correlations allowed by quantum mechanics in this setup as an elliptope in a non-signaling cube. To determine which of these quantum correlations are allowed by local hidden-variable theories, we investigate which ones we can simulate using raffles with baskets of tickets that have the outcomes for all combinations of measurement settings printed on them. The class of correlations found this way can be represented geometrically by a tetrahedron contained within the elliptope. We use the same Bub-Pitowsky framework to analyze a generalization of the Mermin setup for measurements on the singlet state of two particles with higher spin. The class of correlations allowed by quantum mechanics in this case is still represented by the elliptope; the subclass of those whose main features can be simulated with our raffles can be represented by polyhedra that, with increasing spin, have more and more vertices and facets and get closer and closer to the elliptope. We use these results to advocate for Bubism (not to be confused with QBism), an interpretation of quantum mechanics along the lines of Bananaworld. Probabilities and expectation values are primary in this interpretation. They are determined by inner products of vectors in Hilbert space. Such vectors do not themselves represent what is real in the quantum world. They encode families of probability distributions over values of different sets of observables. As in classical theory, these values ultimately represent what is real in the quantum world. Hilbert space puts constraints on possible combinations of such values, just as Minkowski space-time puts constraints on possible spatio-temporal constellations of events. Illustrating how generic such constraints are, the constraint derived in this paper, the equation for the elliptope, is a general constraint on correlation coefficients that can be found in older literature on statistics and probability theory. Yule (1896) already stated the constraint. De Finetti (1937) already gave it a geometrical interpretation sharing important features with its interpretation in Hilbert space

Vertical migration behaviour of diatom assemblages of Wadden Sea sediments (Dangast, Germany): a study using cryo-scanning electron microscopy

The vertical migration behaviour of diatom assemblages inhabiting Wadden Sea sediments near Dangast (Germany) was investigated using cryoscanning electron microscopy. The diatom assemblages were dominated by small Navicula species. Intertidal sediments which were located at different distances from the high tide level or stayed submerged even throughout low tides were chosen. Samples were prepared and cryofixed in the field. Sampling was restricted to three sets: (i) before the onset of vertical migration, (ii) 3 to 5 h after the onset of vertical migration, and (iii) before the area became flooded again or just prior to dusk. The diatom assemblages inhabiting the different types of sediments did not always show the same response. When the tidal cycle exposed the sediment surfaces during the night cell densities increased in the early morning hours with the onset of light. Later on, although the photon flux density was still increasing, cell densities stayed constant or decreased before the water flooded the areas around noon. In experiments in which the water drained off around noon and the areas became exposed throughout the entire afternoon, cell densities increased even up to dusk when the photon flux density had dropped to values below 20 μM photons m-2s-1. In an experiment in which the last sampling occured at 10.15 pm, when the photon flux density had already declined below 10 μM photons m-2s-1, cell densities had decreased to lower values. This was ca. 1 h before the area was flooded again. Finally, cryo-scanning electron microscopy revealed frequently occuring micropatches of diatom assemblages which could be differentiated into typical areas of lower and higher cell densities further complicating the pattern of light or water cover induced movements

Results at 24 months from the prospective, randomized, multicenter Investigational Device Exemption trial of ProDisc-C versus anterior cervical discectomy and fusion with 4-year follow-up and continued access patients.

BackgroundCervical total disk replacement (TDR) is intended to address pain and preserve motion between vertebral bodies in patients with symptomatic cervical disk disease. Two-year follow-up for the ProDisc-C (Synthes USA Products, LLC, West Chester, Pennsylvania) TDR clinical trial showed non-inferiority versus anterior cervical discectomy and fusion (ACDF), showing superiority in many clinical outcomes. We present the 4-year interim follow-up results.MethodsPatients were randomized (1:1) to ProDisc-C (PDC-R) or ACDF. Patients were assessed preoperatively, and postoperatively at 6 weeks and 3, 6, 12, 18, 24, 36, and 48 months. After the randomized portion, continued access (CA) patients also underwent ProDisc-C implantation, with follow-up visits up to 24 months. Evaluations included Neck Disability Index (NDI), Visual Analog Scale (VAS) for pain/satisfaction, and radiographic and physical/neurologic examinations.ResultsRandomized patients (103 PDC-R and 106 ACDF) and 136 CA patients were treated at 13 sites. VAS pain and NDI score improvements from baseline were significant for all patients (P < .0001) but did not differ among groups. VAS satisfaction was higher at all time points for PDC-R versus ACDF patients (P = .0499 at 48 months). The percentage of patients who responded yes to surgery again was 85.6% at 24 months and 88.9% at 48 months in the PDC-R group, 80.9% at 24 months and 81.0% at 48 months in the ACDF group, and 86.3% at 24 months in the CA group. Five PDC-R patients (48 months) and no CA patients (24 months) had index-level bridging bone. By 48 months, approximately 4-fold more ACDF patients required secondary surgery (3 of 103 PDC-R patients [2.9%] vs 12 of 106 ACDF patients [11.3%], P = .0292). Of these, 6 ACDF patients (5.6%) required procedures at adjacent levels. Three CA patients required secondary procedures (24 months).ConclusionsOur 4-year data support that ProDisc-C TDR and ACDF are viable surgical options for symptomatic cervical disk disease. Although ACDF patients may be at higher risk for additional surgical intervention, patients in both groups show good clinical results at longer-term follow-up

Expression of myriapod pair rule gene orthologs

Background Segmentation is a hallmark of the arthropods; most knowledge about the molecular basis of arthropod segmentation comes from work on the fly Drosophila melanogaster. In this species a hierarchic cascade of segmentation genes subdivides the blastoderm stepwise into single segment wide regions. However, segmentation in the fly is a derived feature since all segments form virtually simultaneously. Conversely, in the vast majority of arthropods the posterior segments form one at a time from a posterior pre-segmental zone. The pair rule genes (PRGs) comprise an important level of the Drosophila segmentation gene cascade and are indeed the first genes that are expressed in typical transverse stripes in the early embryo. Information on expression and function of PRGs outside the insects, however, is scarce. Results Here we present the expression of the pair rule gene orthologs in the pill millipede Glomeris marginata (Myriapoda: Diplopoda). We find evidence that these genes are involved in segmentation and that components of the hierarchic interaction of the gene network as found in insects may be conserved. We further provide evidence that segments are formed in a single-segment periodicity rather than in pairs of two like in another myriapod, the centipede Strigamia maritima. Finally we show that decoupling of dorsal and ventral segmentation in Glomeris appears already at the level of the PRGs. Conclusions Although the pair rule gene network is partially conserved among insects and myriapods, some aspects of PRG interaction are, as suggested by expression pattern analysis, convergent, even within the Myriapoda. Conserved expression patterns of PRGs in insects and myriapods, however, may represent ancestral features involved in segmenting the arthropod ancestor

Polarimetric Geometric Modeling for mm-VLBI Observations of Black Holes

The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric "m-ring" model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT.Comment: 34 pages, 15 figures, published in The Astrophysical Journal Letter

Regional Climate Trends and Scenarios for the U.S. National Climate Assessment Part 4. Climate of the U.S. Great Plains

This document is one of series of regional climate descriptions designed to provide input that can be used in the development of the National Climate Assessment (NCA). As part of a sustained assessment approach, it is intended that these documents will be updated as new and well-vetted model results are available and as new climate scenario needs become clear. It is also hoped that these documents (and associated data and resources) are of direct benefit to decision makers and communities seeking to use this information in developing adaptation plans. There are nine reports in this series, one each for eight regions defined by the NCA, and one for the contiguous U.S. The eight NCA regions are the Northeast, Southeast, Midwest, Great Plains, Northwest, Southwest, Alaska, and Hawai‘i/Pacific Islands. These documents include a description of the observed historical climate conditions for each region and a set of climate scenarios as plausible futures – these components are described in more detail below. While the datasets and simulations in these regional climate documents are not, by themselves, new, (they have been previously published in various sources), these documents represent a more complete and targeted synthesis of historical and plausible future climate conditions around the specific regions of the NCA. There are two components of these descriptions. One component is a description of the historical climate conditions in the region. The other component is a description of the climate conditions associated with two future pathways of greenhouse gas emissions

Periodic and discrete Zak bases

Weyl's displacement operators for position and momentum commute if the product of the elementary displacements equals Planck's constant. Then, their common eigenstates constitute the Zak basis, each state specified by two phase parameters. Upon enforcing a periodic dependence on the phases, one gets a one-to-one mapping of the Hilbert space on the line onto the Hilbert space on the torus. The Fourier coefficients of the periodic Zak bases make up the discrete Zak bases. The two bases are mutually unbiased. We study these bases in detail, including a brief discussion of their relation to Aharonov's modular operators, and mention how they can be used to associate with the single degree of freedom of the line a pair of genuine qubits.Comment: 15 pages, 3 figures; displayed abstract is shortened, see the paper for the complete abstrac

Bisulfite sequencing with Daphnia highlights a role for epigenetics in regulating stress response to Microcystis through preferential differential methylation of serine and threonine amino acids

Little is known about the influence that environmental stressors may have on genome-wide methylation patterns, and to what extent epigenetics may be involved in environmental stress response. Yet, studies of methylation patterns under stress could provide crucial insights on stress response and toxicity pathways. Here, we focus on genome-wide methylation patterns in the microcrustacean Daphnia magna, a model organism in ecotoxicology and risk assessment, exposed to the toxic cyanobacterium Microcystis aeruginosa. Bisulfite sequencing of exposed and control animals highlighted differential methylation patterns in Daphnia upon exposure to Microcystis primarily in exonic regions. These patterns are enriched for serine/threonine amino acid codons and genes related to protein synthesis, transport and degradation. Furthermore, we observed that genes with differential methylation corresponded well with genes susceptible to alternative splicing in response to Microcystis stress. Overall, our results suggest a complex mechanistic response in Daphnia characterized by interactions between DNA methylation and gene regulation mechanisms. These results underscore that DNA methylation is modulated by environmental stress and can also be an integral part of the toxicity response in our study species

Short-time scaling behavior of growing interfaces

The short-time evolution of a growing interface is studied within the framework of the dynamic renormalization group approach for the Kadar-Parisi-Zhang (KPZ) equation and for an idealized continuum model of molecular beam epitaxy (MBE). The scaling behavior of response and correlation functions is reminiscent of the ``initial slip'' behavior found in purely dissipative critical relaxation (model A) and critical relaxation with conserved order parameter (model B), respectively. Unlike model A the initial slip exponent for the KPZ equation can be expressed by the dynamical exponent z. In 1+1 dimensions, for which z is known exactly, the analytical theory for the KPZ equation is confirmed by a Monte-Carlo simulation of a simple ballistic deposition model. In 2+1 dimensions z is estimated from the short-time evolution of the correlation function.Comment: 27 pages LaTeX with epsf style, 4 figures in eps format, submitted to Phys. Rev.