Simple and Nearly Optimal Polynomial Root-finding by Means of Root Radii Approximation

We propose a new simple but nearly optimal algorithm for the approximation of all sufficiently well isolated complex roots and root clusters of a univariate polynomial. Quite typically the known root-finders at first compute some crude but reasonably good approximations to well-conditioned roots (that is, those isolated from the other roots) and then refine the approximations very fast, by using Boolean time which is nearly optimal, up to a polylogarithmic factor. By combining and extending some old root-finding techniques, the geometry of the complex plane, and randomized parametrization, we accelerate the initial stage of obtaining crude to all well-conditioned simple and multiple roots as well as isolated root clusters. Our algorithm performs this stage at a Boolean cost dominated by the nearly optimal cost of subsequent refinement of these approximations, which we can perform concurrently, with minimum processor communication and synchronization. Our techniques are quite simple and elementary; their power and application range may increase in their combination with the known efficient root-finding methods.Comment: 12 pages, 1 figur

Metabolic pathways inferred from a bacterial marker gene illuminate ecological changes across South Pacific frontal boundaries

Global oceanographic monitoring initiatives originally measured abiotic essential ocean variables but are currently incorporating biological and metagenomic sampling programs. There is, however, a large knowledge gap on how to infer bacterial functions, the information sought by biogeochemists, ecologists, and modelers, from the bacterial taxonomic information (produced by bacterial marker gene surveys). Here, we provide a correlative understanding of how a bacterial marker gene (16S rRNA) can be used to infer latitudinal trends for metabolic pathways in global monitoring campaigns. From a transect spanning 7000 km in the South Pacific Ocean we infer ten metabolic pathways from 16S rRNA gene sequences and 11 corresponding metagenome samples, which relate to metabolic processes of primary productivity, temperature-regulated thermodynamic effects, coping strategies for nutrient limitation, energy metabolism, and organic matter degradation. This study demonstrates that low-cost, high-throughput bacterial marker gene data, can be used to infer shifts in the metabolic strategies at the community scale

A class of efficient high-order iterative methods with memory for nonlinear equations and their dynamics

[EN] In this paper we obtain some theoretical results about iterative methods with memory for nonlinear equations. The class of algorithms we consider focus on incorporating memory without increasing the computational cost of the algorithm. This class uses for the predictor step of each iteration a quantity that has already been calculated in the previous iteration, typically the quantity governing the slope from the previous corrector step. In this way we do not introduce any extra computation, and more importantly, we avoid new function evaluations, allowing us to obtain high-order iterative methods in a simple way. A specific class of methods of this type is introduced, and we prove the convergence order is 2(n) + 2(n-2) with n + 1 function evaluations. An exhaustive efficiency study is performed to show the competitiveness of these methods. Finally, we test some specific examples and explore the effect that this predictor may have on the convergence set by setting a dynamical study.Ministerio de Economia y Competitividad de Espana, Grant/Award Number: MTM2014-52016-C2-2-P; Generalitat Valenciana Prometeo, Grant/Award Number: /2016/089Howk, CL.; Hueso, J.; Martínez Molada, E.; Teruel-Ferragud, C. (2018). A class of efficient high-order iterative methods with memory for nonlinear equations and their dynamics. Mathematical Methods in the Applied Sciences. 41(17):7263-7282. https://doi.org/10.1002/mma.4821S72637282411

A compendium and functional characterization of mammalian genes involved in adaptation to Arctic or Antarctic environments

Many mammals are well adapted to surviving in extremely cold environments. These species have likely accumulated genetic changes that help them efficiently cope with low temperatures. It is not known whether the same genes related to cold adaptation in one species would be under selection in another species. The aims of this study therefore were: to create a compendium of mammalian genes related to adaptations to a low temperature environment; to identify genes related to cold tolerance that have been subjected to independent positive selection in several species; to determine promising candidate genes/pathways/organs for further empirical research on cold adaptation in mammals

Interstellar Turbulence II: Implications and Effects

Interstellar turbulence has implications for the dispersal and mixing of the elements, cloud chemistry, cosmic ray scattering, and radio wave propagation through the ionized medium. This review discusses the observations and theory of these effects. Metallicity fluctuations are summarized, and the theory of turbulent transport of passive tracers is reviewed. Modeling methods, turbulent concentration of dust grains, and the turbulent washout of radial abundance gradients are discussed. Interstellar chemistry is affected by turbulent transport of various species between environments with different physical properties and by turbulent heating in shocks, vortical dissipation regions, and local regions of enhanced ambipolar diffusion. Cosmic rays are scattered and accelerated in turbulent magnetic waves and shocks, and they generate turbulence on the scale of their gyroradii. Radio wave scintillation is an important diagnostic for small scale turbulence in the ionized medium, giving information about the power spectrum and amplitude of fluctuations. The theory of diffraction and refraction is reviewed, as are the main observations and scintillation regions.Comment: 46 pages, 2 figures, submitted to Annual Reviews of Astronomy and Astrophysic

Lepton Acceleration in Pulsar Wind Nebulae

Pulsar Wind Nebulae (PWNe) act as calorimeters for the relativistic pair winds emanating from within the pulsar light cylinder. Their radiative dissipation in various wavebands is significantly different from that of their pulsar central engines: the broadband spectra of PWNe possess characteristics distinct from those of pulsars, thereby demanding a site of lepton acceleration remote from the pulsar magnetosphere. A principal candidate for this locale is the pulsar wind termination shock, a putatively highly-oblique, ultra-relativistic MHD discontinuity. This paper summarizes key characteristics of relativistic shock acceleration germane to PWNe, using predominantly Monte Carlo simulation techniques that compare well with semi-analytic solutions of the diffusion-convection equation. The array of potential spectral indices for the pair distribution function is explored, defining how these depend critically on the parameters of the turbulent plasma in the shock environs. Injection efficiencies into the acceleration process are also addressed. Informative constraints on the frequency of particle scattering and the level of field turbulence are identified using the multiwavelength observations of selected PWNe. These suggest that the termination shock can be comfortably invoked as a principal injector of energetic leptons into PWNe without resorting to unrealistic properties for the shock layer turbulence or MHD structure.Comment: 19 pages, 5 figures, invited review to appear in Proc. of the inaugural ICREA Workshop on "The High-Energy Emission from Pulsars and their Systems" (2010), eds. N. Rea and D. Torres, (Springer Astrophysics and Space Science series

Monoubiquitination of syntaxin 3 leads to retrieval from the basolateral plasma membrane and facilitates cargo recruitment to exosomes

Syntaxin 3 (Stx3), a SNARE protein located and functioning at the apical plasma membrane of epithelial cells, is required for epithelial polarity. A fraction of Stx3 is localized to late endosomes/lysosomes, although how it traffics there and its function in these organelles is unknown. Here we report that Stx3 undergoes monoubiquitination in a conserved polybasic domain. Stx3 present at the basolateral—but not the apical—plasma membrane is rapidly endocytosed, targeted to endosomes, internalized into intraluminal vesicles (ILVs), and excreted in exosomes. A nonubiquitinatable mutant of Stx3 (Stx3-5R) fails to enter this pathway and leads to the inability of the apical exosomal cargo protein GPRC5B to enter the ILV/exosomal pathway. This suggests that ubiquitination of Stx3 leads to removal from the basolateral membrane to achieve apical polarity, that Stx3 plays a role in the recruitment of cargo to exosomes, and that the Stx3-5R mutant acts as a dominant-negative inhibitor. Human cytomegalovirus (HCMV) acquires its membrane in an intracellular compartment and we show that Stx3-5R strongly reduces the number of excreted infectious viral particles. Altogether these results suggest that Stx3 functions in the transport of specific proteins to apical exosomes and that HCMV exploits this pathway for virion excretion

The Borwein brothers, Pi and the AGM

We consider some of Jonathan and Peter Borweins' contributions to the high-precision computation of $\pi$ and the elementary functions, with particular reference to their book "Pi and the AGM" (Wiley, 1987). Here "AGM" is the arithmetic-geometric mean of Gauss and Legendre. Because the AGM converges quadratically, it can be combined with fast multiplication algorithms to give fast algorithms for the $n$-bit computation of $\pi$, and more generally the elementary functions. These algorithms run in almost linear time $O(M(n)\log n)$, where $M(n)$ is the time for $n$-bit multiplication. We outline some of the results and algorithms given in Pi and the AGM, and present some related (but new) results. In particular, we improve the published error bounds for some quadratically and quartically convergent algorithms for $\pi$, such as the Gauss-Legendre algorithm. We show that an iteration of the Borwein-Borwein quartic algorithm for $\pi$ is equivalent to two iterations of the Gauss-Legendre quadratic algorithm for $\pi$, in the sense that they produce exactly the same sequence of approximations to $\pi$ if performed using exact arithmetic.Comment: 24 pages, 6 tables. Changed style file and reformatted algorithms in v

Serum antibodies against p53 in relation to cancer risk and prognosis in breast cancer: a population-based epidemiological study

To perform an epidemiological evaluation of the predictive value of p53 autoantibodies in breast cancer, we measured antibodies against p53 in serum samples from 165 breast cancer patients in comparison with serum samples from 330 healthy controls, selected from the same population as the cases and matched for age, sex and specimen storage time. Median age of patients was 51 years (range 25–64 years). Presence of serum p53 autoantibodies was analysed by enzyme-linked immunosorbent assay (ELISA) and confirmed by Western blotting. The lower ELISA reactivities were similar for cases and controls, but presence of high-level reactivity was more common among cases than among controls [odds ratio (OR) 9.03, 95% confidence interval (CI) 2.40–50.43]. Presence of Western blot-detected p53 autoantibodies had a very similar association (OR 10.8, CI 3.0–59.4). Among the cases, we also studied whether there was any correlation between level of anti-p53 antibodies and stage of the disease or survival. There was no significant correlation between presence of antibodies and stage of the disease. There was a significant negative correlation between presence of p53 antibodies and survival (P= 0.003). A stepwise multivariate Cox regression analysis showed that T-stage, age and presence of anti-p53 antibodies were significant independent prognostic variables, with a dose-dependent negative effect on survival for all three variables. We conclude that presence of anti-p53 antibodies are of significance both for the risk of having breast cancer and the risk of dying from breast cancer. 1999 Cancer Research Campaig