Addition chains and solutions of l(2n) = l(n) and l(2n − 1) = n + l(n) − 1

AbstractAn addition chain for a positive integer n is a set 1 = a0 < al < … < ar = n of integers such that for each i ⩾ 1. a1 = a1 + a k for some k ⩽ j < i. The smallest length r for which an addition chain for n exists is denoted by l(n). This paper introduces the function h(x) which denotes the number of integers n less than or equal to x for which l(2n) = l(n) and proves that h(x) > (logx)2. A necessary theorem for establishing this result is that there exist infinitely many infinite classes of integers for which l(2n) = l(n). The proof of this theorem is outlined. Also, this paper establishes seven new cases for which l(2n − 1) = n + l(n) − 1. These are cases n=15, 16, 17, 18, 20, 24 and 32

Bat Mortality at Ontario Wind Farms Quantified and Compared Using Four Candidate Estimator Equations

Wind farm development is expanding globally. While wind energy is a low-cost option for new electricity supply, the impacts to wildlife populations, including bats (Chiroptera), are of ecological concern. To quantify these impacts, scientists have developed estimator equations to estimate bat mortality, which vary in assumptions related to correction factors. We compared the results of 4 estimators applied to post-construction monitoring data from Ontario, Canada, wind farms to evaluate the effects of field methods and correction factors on estimator consistency. To conduct our study, we obtained data from 21 wind farms between 2011 and 2017 for a total of 26 wind farm survey years, because some wind farms supplied fatality monitoring data in \u3e1 year, to estimate mortality. The Ontario Ministry of Natural Resources and Forestry estimator (OMNRF) tended to be highest, while the Huso, Schoenfeld-Erickson, and GenEst estimators produced similar results. Huso and Schoenfeld-Erickson estimates tended to fall within 95% confidence intervals for GenEst, while OMNRF estimates tended to be higher than the upper confidence interval for GenEst. The results from the OMNRF estimator were consistent with the other candidates when carcass persistence times were \u3e6.5 days but inconsistent when carcass persistence times were shorter. Our results demonstrated the degree to which mortality estimates can vary among estimators and highlight the need for a consistent estimator in comparative studies. We recommend GenEst for such studies, as this estimator can incorporate more inputs with flexibility to reflect site-specific field conditions and produces highly consistent results. Conversely, the OMNRF estimator produced consistently higher estimates than the other candidate estimators, and assumptions related to carcass persistence were regularly violated. We recommend that these limitations be acknowledged when interpreting results from this estimator and that its use be reconsidered when assumptions related to carcass persistence are not met

17O NMR study of q=0 spin excitations in a nearly ideal S=1/2 1D Heisenberg antiferromagnet, Sr2CuO3, up to 800 K

We used 17O NMR to probe the uniform (wavevector q=0) electron spin excitations up to 800 K in Sr2CuO3 and separate the q=0 from the q=\pm\pi/a staggered components. Our results support the logarithmic decrease of the uniform spin susceptibility below T ~ 0.015J, where J=2200 K. From measurement of the dynamical spin susceptibility for q=0 by the spin-lattice relaxation rate 1/T_{1}, we demonstrate that the q=0 mode of spin transport is ballistic at the T=0 limit, but has a diffusion-like contribution at finite temperatures even for T << J.Comment: Submitted to Phys. Rev. Lett. 4 pages, 4 figure

Destruction of long-range antiferromagnetic order by hole doping

We study the renormalization of the staggered magnetization of a two-dimensional antiferromagnet as a function of hole doping, in the framework of the t-J model. It is shown that the motion of holes generates decay of spin waves into ''particle-hole'' pairs, which causes the destruction of the long-range magnetic order at a small hole concentration. This effect is mainly determined by the coherent motion of holes. The value obtained for the critical hole concentration, of a few percent, is consistent with experimental data for the doped copper oxide high-Tc superconductors.Comment: 12 pages, 2 figure

Nuclear spin relaxation rates in two-leg spin ladders

Using the transfer-matrix DMRG method, we study the nuclear spin relaxation rate 1/T_1 in the two-leg s=1/2 ladder as function of the inter-chain (J_{\perp}) and intra-chain (J_{|}) couplings. In particular, we separate the q_y=0 and \pi contributions and show that the later contribute significantly to the copper relaxation rate ^{63}(1/T_1) in the experimentally relevant coupling and temperature range. We compare our results to both theoretical predictions and experimental measures on ladder materials.Comment: Few modifications from the previous version 4 pages, 5 figures, accepted for publication in PR

Coral-associated bacteria demonstrate phylosymbiosis and cophylogeny

Scleractinian corals' microbial symbionts influence host health, yet how coral microbiomes assembled over evolution is not well understood. We survey bacterial and archaeal communities in phylogenetically diverse Australian corals representing more than 425 million years of diversification. We show that coral microbiomes are anatomically compartmentalized in both modern microbial ecology and evolutionary assembly. Coral mucus, tissue, and skeleton microbiomes differ in microbial community composition, richness, and response to host vs. environmental drivers. We also find evidence of coral-microbe phylosymbiosis, in which coral microbiome composition and richness reflect coral phylogeny. Surprisingly, the coral skeleton represents the most biodiverse coral microbiome, and also shows the strongest evidence of phylosymbiosis. Interactions between bacterial and coral phylogeny significantly influence the abundance of four groups of bacteria-including Endozoicomonas-like bacteria, which divide into host-generalist and host-specific subclades. Together these results trace microbial symbiosis across anatomy during the evolution of a basal animal lineage

Direct inversion of S-P differential arrival-times for Vp/Vs ratio in SE Asia

Open Access via Jisc Wiley agreementPeer reviewedPublisher PD

How linear features alter predator movement and the functional response

In areas of oil and gas exploration, seismic lines have been reported to alter the movement patterns of wolves (Canis lupus). We developed a mechanistic first passage time model, based on an anisotropic elliptic partial differential equation, and used this to explore how wolf movement responses to seismic lines influence the encounter rate of the wolves with their prey. The model was parametrized using 5 min GPS location data. These data showed that wolves travelled faster on seismic lines and had a higher probability of staying on a seismic line once they were on it. We simulated wolf movement on a range of seismic line densities and drew implications for the rate of predator–prey interactions as described by the functional response. The functional response exhibited a more than linear increase with respect to prey density (type III) as well as interactions with seismic line density. Encounter rates were significantly higher in landscapes with high seismic line density and were most pronounced at low prey densities. This suggests that prey at low population densities are at higher risk in environments with a high seismic line density unless they learn to avoid them

A Systems Approach for Tumor Pharmacokinetics

Recent advances in genome inspired target discovery, small molecule screens, development of biological and nanotechnology have led to the introduction of a myriad of new differently sized agents into the clinic. The differences in small and large molecule delivery are becoming increasingly important in combination therapies as well as the use of drugs that modify the physiology of tumors such as anti-angiogenic treatment. The complexity of targeting has led to the development of mathematical models to facilitate understanding, but unfortunately, these studies are often only applicable to a particular molecule, making pharmacokinetic comparisons difficult. Here we develop and describe a framework for categorizing primary pharmacokinetics of drugs in tumors. For modeling purposes, we define drugs not by their mechanism of action but rather their rate-limiting step of delivery. Our simulations account for variations in perfusion, vascularization, interstitial transport, and non-linear local binding and metabolism. Based on a comparison of the fundamental rates determining uptake, drugs were classified into four categories depending on whether uptake is limited by blood flow, extravasation, interstitial diffusion, or local binding and metabolism. Simulations comparing small molecule versus macromolecular drugs show a sharp difference in distribution, which has implications for multi-drug therapies. The tissue-level distribution differs widely in tumors for small molecules versus macromolecular biologic drugs, and this should be considered in the design of agents and treatments. An example using antibodies in mouse xenografts illustrates the different in vivo behavior. This type of transport analysis can be used to aid in model development, experimental data analysis, and imaging and therapeutic agent design.National Institutes of Health (U.S.) (grant T32 CA079443

Great Bahama Bank

p. 181-228, [13] p. of plates (1 folded) : ill., maps ; 27 cm.Includes bibliographical references (p. 226-228)