Metric trees of generalized roundness one

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify some large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual combinatorial metric (SSTs). Using a simple geometric argument we show how to determine decent upper bounds on the generalized roundness of finite SSTs that depend only on the downward degree sequence of the tree in question. By considering limits it follows that if the downward degree sequence $(d_{0}, d_{1}, d_{2}...)$ of a SST $(T,\rho)$ satisfies $|\{j \, | \, d_{j} > 1 \}| = \aleph_{0}$, then $(T,\rho)$ has generalized roundness one. Included among the trees that satisfy this condition are all complete $n$-ary trees of depth $\infty$ ($n \geq 2$), all $k$-regular trees ($k \geq 3$) and inductive limits of Cantor trees. The remainder of the paper deals with two classes of countable metric trees of generalized roundness one whose members are not, in general, spherically symmetric. The first such class of trees are merely required to spread out at a sufficient rate (with a restriction on the number of leaves) and the second such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table

Euclidean Distances, soft and spectral Clustering on Weighted Graphs

We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow data, properly conditioned, illustrate the procedure as well as visualization aspects.Comment: accepted for presentation (and further publication) at the ECML PKDD 2010 conferenc

Transformation elastodynamics and active exterior acoustic cloaking

This chapter consists of three parts. In the first part we recall the elastodynamic equations under coordinate transformations. The idea is to use coordinate transformations to manipulate waves propagating in an elastic material. Then we study the effect of transformations on a mass-spring network model. The transformed networks can be realized with "torque springs", which are introduced here and are springs with a force proportional to the displacement in a direction other than the direction of the spring terminals. Possible homogenizations of the transformed networks are presented, with potential applications to cloaking. In the second and third parts we present cloaking methods that are based on cancelling an incident field using active devices which are exterior to the cloaked region and that do not generate significant fields far away from the devices. In the second part, the exterior cloaking problem for the Laplace equation is reformulated as the problem of polynomial approximation of analytic functions. An explicit solution is given that allows to cloak larger objects at a fixed distance from the cloaking device, compared to previous explicit solutions. In the third part we consider the active exterior cloaking problem for the Helmholtz equation in 3D. Our method uses the Green's formula and an addition theorem for spherical outgoing waves to design devices that mimic the effect of the single and double layer potentials in Green's formula.Comment: Submitted as a chapter for the volume "Acoustic metamaterials: Negative refraction, imaging, lensing and cloaking", Craster and Guenneau ed., Springe

Modern weathering in outcrop samples versus ancient paleoredox information in drill core samples from a Mesoarchaean marine oxygen oasis in Pongola Supergroup, South Africa

There is growing evidence from Mo and Fe stable isotope tracers that shallow-water sediments of the 2.95 Ga Mozaan Group (Pongola Supergroup) in South Africa were deposited under oxidizing conditions, while mineralogical, elemental and S isotopic evidence favors the contemporaneous atmosphere to have remained reducing. In contrast, the first reported Cr-stable isotope data for White Mfolozi riverbed outcrop samples of the Ijzermijn iron formation (IF), Mozaan Group, and drill core samples of the underlying paleosol of the Nsuze Group were interpreted to require oxidative weathering conditions during the time of deposition. More recent Cr-isotope data of at least the Ijzermijn IF samples of the same White Mfolozi riverbed outcrop, however, suggested that modern weathering effects can superimpose oxidative signatures on paleo-redox proxies. This study compares (234U/238U) activity ratios along with stable Mo and Fe isotope data of corresponding drill core and White Mfolozi riverbed outcrop samples in order (i) to test (234U/238U) disequilibria as a potential tool to identify samples affected by modern weathering and (ii) to further investigate weathering effects on outcrop samples, particularly with regard to the stable Mo and Fe isotope systematics. All drill core samples from the Ijzermijn IF have (234U/238U) activity ratios that are within uncertainties of secular equilibrium (i.e. a value of 1), and thus were not significantly affected by modern weathering-related U gain or loss or other sub-recent rock-water interaction. By contrast, the outcrop IF and shale samples from the White Mfolozi riverbed show very strong deviations from the secular equilibrium (234U/238U) activity ratio. Furthermore, these deviations are accompanied by the observations that (i) outcrop samples have on average heavier δ56/54Fe values (−0.96‰) than drill cores (−1.59‰), and (ii) positive correlations in drill core samples between log[Fe/Mn] and δ98/95Mo or δ56/54Fe are disrupted by inclusion of the outcrop samples, as are negative correlations between log[MnO] and δ98/95Mo. However, δ56/54Fe and δ98/95Mo of our outcrop samples do not correlate with the extent of (234U/238U) disequilibria. As such, (234U/238U) activity ratios fail to act as a direct identification tool for modern weathering effects on stable Fe and Mo isotopes in outcrop samples. Overall, this study confirms the adsorption of isotopically light Mo onto MnO2 particles in oxic surface water conditions in the epicontinental Pongola Sea. Reduction of the Mn-oxides together with microbial Fe reduction in the reduced sediment pile of the Pongola basin led to the formation of Mn- and Fe-carbonates during early diagenesis storing the observed stable Fe and Mo isotopic signatures. We thus extend the so-called MnO2-shuttle first proposed for the Neoarchean 2.46 Ga old Koegas IF to late Mesoarchean shallow-marine depositional settings.</p

Effects of MTOR-IS on malignancy and survival following renal transplantation: A systematic review and meta-analysis of randomized trials with a minimum follow-up of 24 months.

<div><p>Background</p><p>mTOR-Is positively influence the occurrence and course of certain tumors after solid organ transplantation. The effect of mTOR-Is on the overall incidence of tumors irrespective of their origin is not entirely clear. Furthermore, conflicting data have been shown on mortality under mTOR-Is.</p><p>Methods</p><p>The current literature was searched for prospective randomized controlled renal transplantation trials. There were 1415 trials screened of which 13 could be included (pts. = 5924). A minimum follow-up of 24 months was mandatory for inclusion. Incidence of malignancies and patient survival was assessed in meta-analyses.</p><p>Results</p><p>The average follow-up of all trials was 40.6 months. Malignancy was significantly reduced under mTOR-Is compared to CNIs (RR 0.70, CI 0.49–0.99, p = 0.046). This effect remained stable when combined with CNIs (RR 0.58, CI 0.34–1.00, p = 0.05). When NMSCs were excluded the risk for malignancy remained significantly reduced under mTOR-I therapy (mono and combi) (RR 0.43, CI 0.24–0.77, p = 0.0046). Graft survival was minimally decreased under mTOR-Is (RR 0.99, CI 0.98–1.00, p = 0.054). This effect was abrogated when mTOR-Is were combined with CNIs (RR 0.99, CI 0.97–1.02, p = 0.50). Patient survival was not different (RR 1.00, CI 0.99–1.01, p = 0.54).</p><p>Conclusions</p><p>Posttransplant patients have a lower incidence of malignancy when treated with an mTOR-I no matter if it is used in combination with CNIs or not. This beneficial effect remains significant even when NMSCs are excluded. With currently used mTOR-I-based regimen patient and graft survival is not different compared to CNI therapies.</p></div