Almost all trees are almost graceful

The Graceful Tree Conjecture of Rosa from 1967 asserts that the vertices of each tree T of order n can be injectively labeled by using the numbers {1,2,…,n} in such a way that the absolute differences induced on the edges are pairwise distinct. We prove the following relaxation of the conjecture for each γ>0 and for all n>n 0(γ). Suppose that (i) the maximum degree of T is bounded by (Formula presented.)), and (ii) the vertex labels are chosen from the set {1,2,…,⌈(1+γ)n⌉}. Then there is an injective labeling of V(T) such that the absolute differences on the edges are pairwise distinct. In particular, asymptotically almost all trees on n vertices admit such a labeling. The proof proceeds by showing that a certain very natural randomized algorithm produces a desired labeling with high probability

Biological life-history and farming scenarios of marine aquaculture to help reduce wild marine fishing pressure

Aquaculture (freshwater and marine) has largely supplemented fisheries, but in theory could help reduce fishing pressure on wild stocks. Although not the sole factors, some potential benefits depend on aquaculture pressures on fished species, including collection of wild ‘seed’ material—earlier to later life stages—for rearing in captivity and the capacity of aquaculture to increase. Here we first classify 203 marine (saltwater and brackish) animal species as being produced by either open-cycle capture-based aquaculture (CBA) or closed-cycle domesticated aquaculture (DA)—based on their likely reliance on wild seed—and assess the extent to which these forms of aquaculture could support seafood production and greater wild biomass. Using a data-limited modelling approach, we find evidence that current aquaculture practices are not necessarily helping reduce fishing to sustainable levels for their wild counterparts—consistent with emerging scientific research. However, if some wild capture species (87 equivalent spp.) were instead produced through CBA, almost a million extra tonnes could theoretically be left in the wild, without reducing seafood production. Alternatively, if reliance on wild seed inputs is further reduced by shifting to DA production, then a little less than doubling of aquaculture of the overexploited species in our study could help fill the ‘production gap’ to support fishing at maximum sustainable levels. While other ecological (e.g. escapes), social and economic considerations (e.g. market substitution) are important, we focused on a critical biological linkage between wild fisheries and aquaculture that provides another aspect on how to improve management alignment of the sectors

Introduction of Empirical Topology in Construction of Relationship Networks of Informative Objects

Understanding the structure of relationships between objects in a given database is one of the most important problems in the field of data mining. The structure can be defined for a set of single objects (clustering) or a set of groups of objects (network mapping). We propose a method for discovering relationships between individuals (single or groups) that is based on what we call the empirical topology, a system-theoretic measure of functional proximity. To illustrate the suitability and efficiency of the method, we apply it to an astronomical data base

Genome-wide enrichment analysis between endometriosis and obesity-related traits reveals novel susceptibility loci

Endometriosis is a chronic inflammatory condition in women that results in pelvic pain and subfertility, and has been associated with decreased body mass index (BMI). Genetic variants contributing to the heritable component have started to emerge from genome-wide association studies (GWAS), although the majority remain unknown. Unexpectedly, we observed an intergenic locus on 7p15.2 that was genome-wide significantly associated with both endometriosis and fat distribution (waist-to-hip ratio adjusted for BMI; WHRadjBMI) in an independent meta-GWAS of European ancestry individuals. This led us to investigate the potential overlap in genetic variants underlying the aetiology of endometriosis, WHRadjBMI and BMI using GWAS data. Our analyses demonstrated significant enrichment of common variants between fat distribution and endometriosis (P = 3.7 × 10(-3)), which was stronger when we restricted the investigation to more severe (Stage B) cases (P = 4.5 × 10(-4)). However, no genetic enrichment was observed between endometriosis and BMI (P = 0.79). In addition to 7p15.2, we identify four more variants with statistically significant evidence of involvement in both endometriosis and WHRadjBMI (in/near KIFAP3, CAB39L, WNT4, GRB14); two of these, KIFAP3 and CAB39L, are novel associations for both traits. KIFAP3, WNT4 and 7p15.2 are associated with the WNT signalling pathway; formal pathway analysis confirmed a statistically significant (P = 6.41 × 10(-4)) overrepresentation of shared associations in developmental processes/WNT signalling between the two traits. Our results demonstrate an example of potential biological pleiotropy that was hitherto unknown, and represent an opportunity for functional follow-up of loci and further cross-phenotype comparisons to assess how fat distribution and endometriosis pathogenesis research fields can inform each other

Clinical and laboratory variability in a cohort of patients diagnosed with type 1 VWD in the United States

Von Willebrand disease (VWD) is the most common inherited bleeding disorder, and type 1 VWD is the most common VWD variant. Despite its frequency, diagnosis of type 1 VWD remains the subject of much debate. In order to study the spectrum of type 1 VWD in the United States, the Zimmerman Program enrolled 482 subjects with a previous diagnosis of type 1 VWD without stringent laboratory diagnostic criteria. VWF laboratory testing and full length VWF gene sequencing were performed for all index cases and healthy control subjects in a central laboratory. Bleeding phenotype was characterized using the ISTH Bleeding Assessment Tool. At study entry, 64% of subjects had VWF:Ag or VWF:RCo below the lower limit of normal, while 36% had normal VWF levels. VWF sequence variations were most frequent in subjects with VWF:Ag < 30 IU/dL (82%) while subjects with type 1 VWD and VWF:Ag ≥ 30 IU/dL had an intermediate frequency of variants (44%). Subjects whose VWF testing was normal at study entry had a similar rate of sequence variations as the healthy controls at 14% of subjects. All subjects with severe type 1 VWD and VWF:Ag ≤ 5 IU/dL had an abnormal bleeding score, but otherwise bleeding score did not correlate with VWF:Ag level. Subjects with a historical diagnosis of type 1 VWD had similar rates of abnormal bleeding scores compared to subjects with low VWF levels at study entry. Type 1 VWD in the United States is highly variable, and bleeding symptoms are frequent in this population

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics

A model for pion Delta electroproduction on the proton

We have extended a model for the $\gamma N\to \pi\pi N$ reaction to virtual photons and selected the diagrams which have a $\Delta$ in the final state. With this model we have evaluated cross sections for the virtual photon cross section as a function of $Q^2$ for different energies. The agreement found with the $\gamma_v p\to\Delta^0\pi^+$ and $\gamma_v p\to\Delta^{++}\pi^-$ reactions is good. The sensitivity of the results to $N\Delta$ transition form factors is also studied. The present reaction, selecting a particular final state, is an extra test for models of the $\gamma_{v} N\to \pi\pi N$ amplitude. The experimental measurement of the different isospin channels for this reaction are encouraged as a means to unravel the dynamics of the two pions photoproduction processes.Comment: 30 pages, 10 figures (ps files). Major changes added. To be published in Nucl. Phys.

Shadowing in Inelastic Scattering of Muons on Carbon, Calcium and Lead at Low XBj

Nuclear shadowing is observed in the per-nucleon cross-sections of positive muons on carbon, calcium and lead as compared to deuterium. The data were taken by Fermilab experiment E665 using inelastically scattered muons of mean incident momentum 470 GeV/c. Cross-section ratios are presented in the kinematic region 0.0001 < XBj <0.56 and 0.1 < Q**2 < 80 GeVc. The data are consistent with no significant nu or Q**2 dependence at fixed XBj. As XBj decreases, the size of the shadowing effect, as well as its A dependence, are found to approach the corresponding measurements in photoproduction.Comment: 22 pages, incl. 6 figures, to be published in Z. Phys.