Fibonacci-Lucas SIC-POVMs

We present a conjectured family of SIC-POVMs which have an additional symmetry group whose size is growing with the dimension. The symmetry group is related to Fibonacci numbers, while the dimension is related to Lucas numbers. The conjecture is supported by exact solutions for dimensions d=4,8,19,48,124,323, as well as a numerical solution for dimension d=844.Comment: The fiducial vectors can be obtained from http://sicpovm.markus-grassl.de as well as from the source files. v2: precision for the numerical solution in dimension 844 increased to 150 digits and new exact solution for dimension 323 adde

Hypotheses in Marketing Science: Literature Review and Publication Audit

We examined three approaches to research in marketing: exploratory hypotheses, dominant hypothesis, and competing hypotheses. Our review of empirical studies on scientific methodology suggests that the use of a single dominant hypothesis lacks objectivity relative to the use of exploratory and competing hypotheses approaches. We then conducted a publication audit of over 1,700 empirical papers in six leading marketing journals during 1984-1999. Of these, 74% used the dominant hypothesis approach, while 13 % used multiple competing hypotheses, and 13% were exploratory. Competing hypotheses were more commonly used for studying methods (25%) than models (17%) and phenomena (7%). Changes in the approach to hypotheses since 1984 have been modest; there was a slight decrease in the percentage of competing hypotheses to 11%, which is plained primarily by an increasing proportion of papers on phenomena. Of the studies based on hypothesis testing, only 11 % described the conditions under which the hypotheses would apply, and dominant hypotheses were below competing hypotheses in this regard. Marketing scientists differed substantially in their opinions about what types of studies should be published and what was published. On average, they did not think dominant hypotheses should be used as often as they were, and they underestimated their use

Massive Galileon Positivity Bounds

The EFT coefficients in any gapped, scalar, Lorentz invariant field theory must satisfy positivity requirements if there is to exist a local, analytic Wilsonian UV completion. We apply these bounds to the tree level scattering amplitudes for a massive Galileon. The addition of a mass term, which does not spoil the non-renormalization theorem of the Galileon and preserves the Galileon symmetry at loop level, is necessary to satisfy the lowest order positivity bound. We further show that a careful choice of successively higher derivative corrections are necessary to satisfy the higher order positivity bounds. There is then no obstruction to a local UV completion from considerations of tree level 2-to-2 scattering alone. To demonstrate this we give an explicit example of such a UV completion.Comment: 31 page

Positivity Bounds for Scalar Theories

Assuming the existence of a local, analytic, unitary UV completion in a Poincar\'{e} invariant scalar field theory with a mass gap, we derive an infinite number of positivity requirements using the known properties of the amplitude at and away from the forward scattering limit. These take the form of bounds on combinations of the pole subtracted scattering amplitude and its derivatives. In turn, these positivity requirements act as constraints on the operator coefficients in the low energy effective theory. For certain theories these constraints can be used to place an upper bound on the mass of the next lightest state that must lie beyond the low energy effective theory if such a UV completion is to ever exist.Comment: 5 page

Mitofusins Mfn1 and Mfn2 coordinately regulate mitochondrial fusion and are essential for embryonic development

Mitochondrial morphology is determined by a dynamic equilibrium between organelle fusion and fission, but the significance of these processes in vertebrates is unknown. The mitofusins, Mfn1 and Mfn2, have been shown to affect mitochondrial morphology when overexpressed. We find that mice deficient in either Mfn1 or Mfn2 die in midgestation. However, whereas Mfn2 mutant embryos have a specific and severe disruption of the placental trophoblast giant cell layer, Mfn1-deficient giant cells are normal. Embryonic fibroblasts lacking Mfn1 or Mfn2 display distinct types of fragmented mitochondria, a phenotype we determine to be due to a severe reduction in mitochondrial fusion. Moreover, we find that Mfn1 and Mfn2 form homotypic and heterotypic complexes and show, by rescue of mutant cells, that the homotypic complexes are functional for fusion. We conclude that Mfn1 and Mfn2 have both redundant and distinct functions and act in three separate molecular complexes to promote mitochondrial fusion. Strikingly, a subset of mitochondria in mutant cells lose membrane potential. Therefore, mitochondrial fusion is essential for embryonic development, and by enabling cooperation between mitochondria, has protective effects on the mitochondrial population

Beneath the Baselines: Detecting Molecular Emission from Submillimeter Galaxies with the GBT

We report the first detection of a submillimeter galaxy (SMG) in CO(1 →0) emission using the GBT. We identify a line with Δv_(FWHM) ~1000 kms^(−1) in the 1 cm spectrum of SMM J13120+4242 at z = 3.408, which is significantly greater than the width of the previously detected CO(4→3) line. If the observed CO(1→0) line profile arises from a single object and not several merging objects, the CO(4 →3)/CO(1→0) brightness temperature ratio of ~0.26 suggests n(H_2) > 10^3 cm^(−3) and the presence of sub-thermally excited gas. The 10σ integrated line flux implies a cold molecular gas mass M(H2) ~10^(11)M_⊙, comparable to the dynamical mass estimate and four times larger than the H_2 mass found from the CO(4 →3) line. While our observations confirm that this SMG is massive and highly gas-rich, they also suggest that J_(upper) > 3 transitions of CO may not accurately trace cold, diffuse molecular gas in SMGs

The oral-aboral axis of a sea urchin embryo is specified by first cleavage

Several lines of evidence suggest that the oral-aboral axis in Strongylocentrotus purpuratus embryos is specified at or before the 8-cell stage. Were the oral-aboral axis specified independently of the first cleavage plane, then a random association of this plane with the blastomeres of the four embryo quadrants in the oral-aboral plane (viz. oral, aboral, right and left) would be expected. Lineage tracer dye injection into one blastomere at the 2-cell stage and observation of the resultant labeling patterns demonstrates instead a strongly nonrandom association. In at least ninety percent of cases, the progeny of the aboral blastomeres are associated with those of the left lateral blastomeres and the progeny of the oral blastomeres with the right lateral ones, respectively. Thus, ninety percent of the time the oral pole of the future oral-aboral axis lies 45 degrees clockwise from the first cleavage plane as viewed from the animal pole. The nonrandom association of blastomeres after labeling of the 2-cell stage implies that there is a mechanistic relation between axis specification and the positioning of the first cleavage plane

Macromere cell fates during sea urchin development

This paper examines the cell lineage relationships and cell fates in embryos of the sea urchin Strongylocentrotus purpuratus leading to the various cell types derived from the definitive vegetal plate territory or the veg_2 tier of cells. These cell types are gut, pigment cells, basal cells and coelomic pouches. They are cell types that constitute embryonic structures through cellular migration or rearrangement unlike the relatively non-motile ectoderm cell types. For this analysis, we use previous knowledge of lineage to assign macromeres to one of four types: VOM, the oral macromere; VAM, the aboral macromere, right and left VLM, the lateral macromeres. Each of the four macromeres contributes progeny to all of the cell types that descend from the definitive vegetal plate. Thus in the gut each macromere contributes to the esophagus, stomach and intestine, and the stripe of labeled cells descendant from a macromere reflects the re-arrangement of cells that occurs during archenteron elongation. Pigment cell contributions exhibit no consistent pattern among the four macromeres, and are haphazardly distributed throughout the ectoderm. Gut and pigment cell contributions are thus radially symmetrical. In contrast, the VOM blastomere contributes to both of the coelomic pouches while the other three macromeres contribute to only one or the other pouch. The total of the macromere contribution amounts to 60% of the cells constituting the coelomic pouches

Regional requirements for Dishevelled signaling during Xenopus gastrulation: separable effects on blastopore closure, mesendoderm internalization and archenteron formation

During amphibian gastrulation, the embryo is transformed by the combined actions of several different tissues. Paradoxically, many of these morphogenetic processes can occur autonomously in tissue explants, yet the tissues in intact embryos must interact and be coordinated with one another in order to accomplish the major goals of gastrulation: closure of the blastopore to bring the endoderm and mesoderm fully inside the ectoderm, and generation of the archenteron. Here, we present high-resolution 3D digital datasets of frog gastrulae, and morphometrics that allow simultaneous assessment of the progress of convergent extension, blastopore closure and archenteron formation in a single embryo. To examine how the diverse morphogenetic engines work together to accomplish gastrulation, we combined these tools with time-lapse analysis of gastrulation, and examined both wild-type embryos and embryos in which gastrulation was disrupted by the manipulation of Dishevelled (Xdsh) signaling. Remarkably, although inhibition of Xdsh signaling disrupted both convergent extension and blastopore closure, mesendoderm internalization proceeded very effectively in these embryos. In addition, much of archenteron elongation was found to be independent of Xdsh signaling, especially during the second half of gastrulation. Finally, even in normal embryos, we found a surprising degree of dissociability between the various morphogenetic processes that occur during gastrulation. Together, these data highlight the central role of PCP signaling in governing distinct events of Xenopus gastrulation, and suggest that the loose relationship between morphogenetic processes may have facilitated the evolution of the wide variety of gastrulation mechanisms seen in different amphibian species