Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

On the stratigraphic integrity of leaf-wax biomarkers in loess paleosols

Paleoenvironmental and paleoclimate reconstructions based on molecular proxies, such as those derived from leaf-wax biomarkers, in loess-paleosol sequences represent a promising line of investigation in Quaternary research. The main premise of such reconstructions is the synsedimentary deposition of biomarkers and dust, which has become a debated subject in recent years. This study uses two independent approaches to test the stratigraphic integrity of leaf-wax biomarkers: (i) long-chain n-alkanes and fatty acids are quantified in two sediment-depth profiles in glacial till on the Swiss Plateau, consisting of a Holocene topsoil and the underlying B and C horizons. Since glacial sediments are initially very poor in organic matter, significant amounts of leaf-wax biomarkers in the B and C horizons of those profiles would reflect postsedimentary root-derived or microbial contributions. (ii) Compound-specific radiocarbon measurements are conducted on n-alkanes and n-alkanoic (fatty) acids from several depth intervals in the loess section "Crvenka", Serbia, and the results are compared to independent estimates of sediment age. We find extremely low concentrations of plant-wax n-alkanes and fatty acids in the B and C horizons below the topsoils in the sediment profiles. Moreover, compound-specific radiocarbon analysis yields plant-wax 14C ages that agree well with published luminescence ages and stratigraphy of the Serbian loess deposit. Both approaches confirm that postsedimentary, root-derived or microbial contributions are negligible in the two investigated systems. The good agreement between the ages of odd and even homologues also indicates that reworking and incorporation of fossil leaf waxes is not particularly relevant either.

Improved predictions for μ\to e conversion in nuclei and Higgs-induced lepton flavor violation

Compared to μ→eγ and μ→eee, the process μ→e conversion in nuclei receives enhanced contributions from Higgs-induced lepton flavor violation. Upcoming μ→e conversion experiments with drastically increased sensitivity will be able to put extremely stringent bounds on Higgs-mediated μ→e transitions. We point out that the theoretical uncertainties associated with these Higgs effects, encoded in the couplings of quark scalar operators to the nucleon, can be accurately assessed using our recently developed approach based on SU(2) chiral perturbation theory that cleanly separates two- and three-flavor observables. We emphasize that with input from lattice QCD for the coupling to strangeness fNs, hadronic uncertainties are appreciably reduced compared to the traditional approach where fNs is determined from the pion-nucleon σ term by means of an SU(3) relation. We illustrate this point by considering Higgs-mediated lepton flavor violation in the standard model supplemented with higher-dimensional operators, the two-Higgs-doublet model with generic Yukawa couplings, and the minimal supersymmetric standard model. Furthermore, we compare bounds from present and future μ→e conversion and μ→eγ experiments.

Lobotomy of Flux Compactifications

We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on T6 with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification allowing for critical points. It corresponds to a type IIA background given by a product of two 3-tori with SO(3) twists and results in a unique theory (gauging) with a non-semisimple gauge algebra. Besides the known four AdS solutions surviving the orientifold projection to N = 4 induced by O6-planes, this theory contains a novel AdS solution that requires non-trivial orientifold-odd fluxes, hence being a genuine critical point of the N = 8 theory.

A multi-model comparison of Atlantic multidecadal variability

A multi-model analysis of Atlantic multidecadal variability is performed with the following aims: to investigate the similarities to observations; to assess the strength and relative importance of the different elements of the mechanism proposed by Delworth et al. (J Clim 6:1993–2011, 1993) (hereafter D93) among coupled general circulation models (CGCMs); and to relate model differences to mean systematic error. The analysis is performed with long control simulations from ten CGCMs, with lengths ranging between 500 and 3600 years. In most models the variations of sea surface temperature (SST) averaged over North Atlantic show considerable power on multidecadal time scales, but with different periodicity. The SST variations are largest in the mid-latitude region, consistent with the short instrumental record. Despite large differences in model configurations, we find quite some consistency among the models in terms of processes. In eight of the ten models the mid-latitude SST variations are significantly correlated with fluctuations in the Atlantic meridional overturning circulation (AMOC), suggesting a link to northward heat transport changes. Consistent with this link, the three models with the weakest AMOC have the largest cold SST bias in the North Atlantic. There is no linear relationship on decadal timescales between AMOC and North Atlantic Oscillation in the models. Analysis of the key elements of the D93 mechanisms revealed the following: Most models present strong evidence that high-latitude winter mixing precede AMOC changes. However, the regions of wintertime convection differ among models. In most models salinity-induced density anomalies in the convective region tend to lead AMOC, while temperature-induced density anomalies lead AMOC only in one model. However, analysis shows that salinity may play an overly important role in most models, because of cold temperature biases in their relevant convective regions. In most models subpolar gyre variations tend to lead AMOC changes, and this relation is strong in more than half of the models.

Relating in situ gas measurements to the surface outgassing properties of cometary nuclei

The sensitivity of the gas flow field to changes in different initial conditions has been studied for the case of a highly simplified cometary nucleus model. The nucleus model simulated a homogeneously outgassing sphere with a more active ring around an axis of symmetry. The varied initial conditions were the number density of the homogeneous region, the surface temperature, and the composition of the flow (varying amounts of H2O and CO2) from the active ring. The sensitivity analysis was performed using the Polynomial Chaos Expansion (PCE) method. Direct Simulation Monte Carlo (DSMC) was used for the flow, thereby allowing strong deviations from local thermal equilibrium. The PCE approach can be used to produce a sensitivity analysis with only four runs per modified input parameter and allows one to study and quantify non-linear responses of measurable parameters to linear changes in the input over a wide range. Hence the PCE allows one to obtain a functional relationship between the flow field properties at every point in the inner coma and the input conditions. It is for example shown that the velocity and the temperature of the background gas are not simply linear functions of the initial number density at the source. As probably expected, the main influence on the resulting flow field parameter is the corresponding initial parameter (i.e. the initial number density determines the background number density, the temperature of the surface determines the flow field temperature, etc.). However, the velocity of the flow field is also influenced by the surface temperature while the number density is not sensitive to the surface temperature at all in our model set-up. Another example is the change in the composition of the flow over the active area. Such changes can be seen in the velocity but again not in the number density. Although this study uses only a simple test case, we suggest that the approach, when applied to a real case in 3D, should assist in identifying the sensitivity of gas parameters measured in situ by, for example, the Rosetta spacecraft to the surface boundary conditions and vice versa.

First πK atom lifetime and πK scattering length measurements

The results of a search for hydrogen-like atoms consisting of π∓K±π∓K± mesons are presented. Evidence for πK atom production by 24 GeV/c protons from CERN PS interacting with a nickel target has been seen in terms of characteristic πK pairs from their breakup in the same target (178±49178±49) as well as in terms of produced πK atoms (653±42653±42). Using these results, the analysis yields a first value for the πK atom lifetime of View the MathML sourceτ=(2.5−1.8+3.0) fs and a first measurement of the S-wave isospin-odd πK scattering length View the MathML source|a0−|=13|a1/2−a3/2|=(0.11−0.04+0.09)Mπ−1 (aIaI for isospin I).

CODE’s new solar radiation pressure model for GNSS orbit determination

The Empirical CODE Orbit Model (ECOM) of the Center for Orbit Determination in Europe (CODE), which was developed in the early 1990s, is widely used in the International GNSS Service (IGS) community. For a rather long time, spurious spectral lines are known to exist in geophysical parameters, in particular in the Earth Rotation Parameters (ERPs) and in the estimated geocenter coordinates, which could recently be attributed to the ECOM. These effects grew creepingly with the increasing influence of the GLONASS system in recent years in the CODE analysis, which is based on a rigorous combination of GPS and GLONASS since May 2003. In a first step we show that the problems associated with the ECOM are to the largest extent caused by the GLONASS, which was reaching full deployment by the end of 2011. GPS-only, GLONASS-only, and combined GPS/GLONASS solutions using the observations in the years 2009–2011 of a global network of 92 combined GPS/GLONASS receivers were analyzed for this purpose. In a second step we review direct solar radiation pressure (SRP) models for GNSS satellites. We demonstrate that only even-order short-period harmonic perturbations acting along the direction Sun-satellite occur for GPS and GLONASS satellites, and only odd-order perturbations acting along the direction perpendicular to both, the vector Sun-satellite and the spacecraft’s solar panel axis. Based on this insight we assess in the third step the performance of four candidate orbit models for the future ECOM. The geocenter coordinates, the ERP differences w. r. t. the IERS 08 C04 series of ERPs, the misclosures for the midnight epochs of the daily orbital arcs, and scale parameters of Helmert transformations for station coordinates serve as quality criteria. The old and updated ECOM are validated in addition with satellite laser ranging (SLR) observations and by comparing the orbits to those of the IGS and other analysis centers. Based on all tests, we present a new extended ECOM which substantially reduces the spurious signals in the geocenter coordinate z (by about a factor of 2–6), reduces the orbit misclosures at the day boundaries by about 10 %, slightly improves the consistency of the estimated ERPs with those of the IERS 08 C04 Earth rotation series, and substantially reduces the systematics in the SLR validation of the GNSS orbits.

The Inverted Phantom Giant

In his famous children’s book, “Jim Button and Luke the Engine Driver”, Michael Ende describes a curious character: A phantom giant. Clothed in rags and with a long beard, the phantom giant appears enormous from far away, but shrinks to normal size as one gets closer. Most people avoid the poor creature, but the ones that dare approach it encounter a gentle, lonely being called Mr. Tur Tur. Chemical ecology is just the opposite of Mr. Tur Tur: A phantom dwarf. Or, in other words, an inverted phantom giant. From a distance, chemical ecology appears like a slightly odd, marginal section of biology and chemistry. But, as the interested scholar approaches, it starts growing and very quickly reaches gigantic dimensions, because all life is explained by chemistry, and all biological chemistry is guided by ecological principles. Herein lies the difficulty with chemical ecology: As it is not perceived well by biologists and chemists, few approach it to understand its significance, and the ones that do find themselves in front of a giant that defies their attempts to define and contain it. This is where the Journal of Chemical Ecology comes in: It invites us to take a closer look at an underestimated discipline and supports us to explore it and deal with its multidimensionality through the promotion of knowledge and methods. These services are unique and make the journal stand out of the crowd of scientific journals. Writing children’s books has become difficult in the era of information technology. And, so has the job of the Journal of Chemical Ecology. Young scientists gather information through accessible, dynamic websites and social platforms. They want articles that are available through a single mouse click, anywhere, anytime. They prefer advanced interactive hypertext protocols over clumsy pdf files. They care about transparency, non-profit and open access just as much as about traditional journal properties. In my view, reaching “the kids” is the major challenge of the Journal over the next years. Promoting an inverted phantom giant in the 21st century requires a combination of high-quality information and boosted visibility. In Michael Ende’s book, Jim and Luke follow exactly this strategy with Mr. Tur Tur: They become friends and offer him a job as a living lighthouse to protect their small island. They combine a quality relationship with high visibility, et voilà, the story ends well! I am looking forward to seeing if the Journal of Chemical Ecology will follow a similar path to reach the next generation of biologists and chemists. If yes, there is a good chance that in 40 years from now, somebody will write a laudation and refer to another famous book by Michael Ende: “The Neverending Story”.

CRTC2 polymorphism as a risk factor for the incidence of metabolic syndrome in patients with solid organ transplantation.

Metabolic syndrome after transplantation is a major concern following solid organ transplantation (SOT). The CREB-regulated transcription co-activator 2 (CRTC2) regulates glucose metabolism. The effect of CRTC2 polymorphisms on new-onset diabetes after transplantation (NODAT) was investigated in a discovery sample of SOT recipients (n1=197). Positive results were tested for replication in two samples from the Swiss Transplant Cohort Study (STCS, n2=1294 and n3=759). Obesity and other metabolic traits were also tested. Associations with metabolic traits in population-based samples (n4=46'186, n5=123'865, n6>100,000) were finally analyzed. In the discovery sample, CRTC2 rs8450-AA genotype was associated with NODAT, fasting blood glucose and body mass index (Pcorrected<0.05). CRTC2 rs8450-AA genotype was associated with NODAT in the second STCS replication sample (odd ratio (OR)=2.01, P=0.04). In the combined STCS replication samples, the effect of rs8450-AA genotype on NODAT was observed in patients having received SOT from a deceased donor and treated with tacrolimus (n=395, OR=2.08, P=0.02) and in non-kidney transplant recipients (OR=2.09, P=0.02). Moreover, rs8450-AA genotype was associated with overweight or obesity (n=1215, OR=1.56, P=0.02), new-onset hyperlipidemia (n=1007, OR=1.76, P=0.007), and lower high-density lipoprotein-cholesterol (n=1214, β=-0.08, P=0.001). In the population-based samples, a proxy of rs8450G>A was significantly associated with several metabolic abnormalities. CRTC2 rs8450G>A appears to have an important role in the high prevalence of metabolic traits observed in patients with SOT. A weak association with metabolic traits was also observed in the population-based samples.The Pharmacogenomics Journal advance online publication, 8 December 2015; doi:10.1038/tpj.2015.82.

The Osr1 and Osr2 genes act in the pronephric anlage downstream of retinoic acid signaling and upstream of Wnt2b to maintain pectoral fin development.

Vertebrate odd-skipped related genes (Osr) have an essential function during the formation of the intermediate mesoderm (IM) and the kidney structures derived from it. Here, we show that these genes are also crucial for limb bud formation in the adjacent lateral plate mesoderm (LPM). Reduction of zebrafish Osr function impairs fin development by the failure of tbx5a maintenance in the developing pectoral fin bud. Osr morphant embryos show reduced wnt2b expression, and increasing Wnt signaling in Osr morphant embryos partially rescues tbx5a expression. Thus, Osr genes control limb bud development in a non-cell-autonomous manner, probably through the activation of Wnt2b. Finally, we demonstrate that Osr genes are downstream targets of retinoic acid (RA) signaling. Therefore, Osr genes act as a relay within the genetic cascade of fin bud formation: by controlling the expression of the signaling molecule Wnt2ba in the IM they play an essential function transmitting the RA signaling originated in the somites to the LPM.

Lipschitz extensions of maps between Heisenberg groups

Let $\H^n$ be the Heisenberg group of topological dimension 2n+1 . We prove that if n is odd, the pair of metric spaces $(\H^n, \H^n)$ does not have the Lipschitz extension property.