A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Can You Solve Closest String Faster than Exhaustive Search?

We study the fundamental problem of finding the best string to represent a given set, in the form of the Closest String problem: Given a set $X \subseteq \Sigma^d$ of $n$ strings, find the string $x^*$ minimizing the radius of the smallest Hamming ball around $x^*$ that encloses all the strings in $X$. In this paper, we investigate whether the Closest String problem admits algorithms that are faster than the trivial exhaustive search algorithm. We obtain the following results for the two natural versions of the problem: $\bullet$ In the continuous Closest String problem, the goal is to find the solution string $x^*$ anywhere in $\Sigma^d$. For binary strings, the exhaustive search algorithm runs in time $O(2^d poly(nd))$ and we prove that it cannot be improved to time $O(2^{(1-\epsilon) d} poly(nd))$, for any $\epsilon > 0$, unless the Strong Exponential Time Hypothesis fails. $\bullet$ In the discrete Closest String problem, $x^*$ is required to be in the input set $X$. While this problem is clearly in polynomial time, its fine-grained complexity has been pinpointed to be quadratic time $n^{2 \pm o(1)}$ whenever the dimension is $\omega(\log n) < d < n^{o(1)}$. We complement this known hardness result with new algorithms, proving essentially that whenever $d$ falls out of this hard range, the discrete Closest String problem can be solved faster than exhaustive search. In the small-$d$ regime, our algorithm is based on a novel application of the inclusion-exclusion principle. Interestingly, all of our results apply (and some are even stronger) to the natural dual of the Closest String problem, called the Remotest String problem, where the task is to find a string maximizing the Hamming distance to all the strings in $X$

On Complexity of 1-Center in Various Metrics

We consider the classic 1-center problem: Given a set P of n points in a metric space find the point in P that minimizes the maximum distance to the other points of P. We study the complexity of this problem in d-dimensional $\ell_p$-metrics and in edit and Ulam metrics over strings of length d. Our results for the 1-center problem may be classified based on d as follows. $\bullet$ Small d: We provide the first linear-time algorithm for 1-center problem in fixed-dimensional $\ell_1$ metrics. On the other hand, assuming the hitting set conjecture (HSC), we show that when $d=\omega(\log n)$, no subquadratic algorithm can solve 1-center problem in any of the $\ell_p$-metrics, or in edit or Ulam metrics. $\bullet$ Large d. When $d=\Omega(n)$, we extend our conditional lower bound to rule out sub quartic algorithms for 1-center problem in edit metric (assuming Quantified SETH). On the other hand, we give a $(1+\epsilon)$-approximation for 1-center in Ulam metric with running time $\tilde{O_{\epsilon}}(nd+n^2\sqrt{d})$. We also strengthen some of the above lower bounds by allowing approximations or by reducing the dimension d, but only against a weaker class of algorithms which list all requisite solutions. Moreover, we extend one of our hardness results to rule out subquartic algorithms for the well-studied 1-median problem in the edit metric, where given a set of n strings each of length n, the goal is to find a string in the set that minimizes the sum of the edit distances to the rest of the strings in the set

Pharmacokinetics of epinephrine in patients with septic shock: modelization and interaction with endogenous neurohormonal status

Introduction In septic patients, an unpredictable response to epinephrine may be due to pharmacodynamic factors or to non-linear pharmacokinetics. The purpose of this study was to investigate the pharmacokinetics of epinephrine and its determinants in patients with septic shock. Methods Thirty-eight consecutive adult patients with septic shock were prospectively recruited immediately before epinephrine infusion. A baseline blood sample (C0) was taken to assess endogenous epinephrine, norepinephrine, renin, aldosterone, and plasma cortisol levels before epinephrine infusion. At a fixed cumulative epinephrine dose adjusted to body weight and under steady-state infusion, a second blood sample (C1) was taken to assess epinephrine and norepinephrine concentrations. Data were analyzed using the nonlinear mixed effect modeling software program NONMEM. Results Plasma epinephrine concentrations ranged from 4.4 to 540 nmol/L at steady-state infusion (range 0.1 to 7 mg/hr; 0.026 to 1.67 μg/kg/min). A one-compartment model adequately described the data. Only body weight (BW) and New Simplified Acute Physiologic Score (SAPSII) at intensive care unit admission significantly influenced epinephrine clearance: CL (L/hr) = 127 × (BW/70)0.60 × (SAPS II/50)-0.67. The corresponding half-life was 3.5 minutes. Endogenous norepinephrine plasma concentration significantly decreased during epinephrine infusion (median (range) 8.8 (1 – 56.7) at C0 vs. 4.5 (0.3 – 38.9) nmol/L at C1, P &lt; 0.001). Conclusions Epinephrine pharmacokinetics is linear in septic shock patients, without any saturation at high doses. Basal neurohormonal status does not influence epinephrine pharmacokinetics. Exogenous epinephrine may alter the endogenous norepinephrine metabolism in septic patients

A study to guide breeding of new cultivars of organic cherry tomato following a consumer-driven approach.

Agricultural studies focusing on the development and/or improvement of new varieties of fruits and vegetables usually prioritize the productivity, disease resistance, response to fertilization, and higher nutrient content. However, new product development needs to take into account not only flavour preference, but also consumer preference for appearance since without tasting products, consumers have to make decisions based on the way a product looks. The present study evaluated the sensory characteristics and consumer preference of ten promising accessions of organic cherry tomato for fresh consumption aiming at identifying the sensory attributes related to appearance that contributed to consumer liking/disliking the fruit. More specifically, the objective of the study was to guide producers regarding the target appearance attributes that play a role on consumer acceptance of cherry tomatoes. Ten accessions of organic cherry tomatoes were evaluated by a trained panel using the QDA methodology, and also by 80 tomato consumers for the acceptance of appearance and intention to purchase. The results achieved after integrating these two data sets (from the trained panel and consumers) in a multidimensional map allowed the elucidation of consumer liking of tomatoes in relation to the appearance, i.e. drivers of liking/disliking were identified. Results revealed that tomatoes with round shape and red colour (reddish) (cultivar ENAS 1031, ENAS 1010, ?Perinha Agua Branca?, Super Sweet, and ?Joana?) were the most liked cherry tomatoes. Those genotypes were also liked by the smallest segment (17.5% of participants) but for them unusual shapes (oblong and pear), orange-yellow colour, and bigger size were also liked. Despite the small number of participants in this study (80 consumers), new shapes and colours for the organic cherry tomatoes could be considered promising alternatives in the Brazilian market, and can be an opportunity for the producers of the state of Rio de Janeiro

Gestión ambiental de los sistemas agroforestales en el Valle de Paraíba del Sur, Estado de Sao Paulo, Brasil.

En el año de 2011 se analizó el desempeño ambiental de la finca Coruputuba, en Pindamonhangaba, Estado de São Paulo, Brasil. La metodología utilizada fué el sistema APOIA-NovoRural, con 62 indicadores de sustentabilidad en el contexto para el análisis de la implementación de los sistemas agroforestales con Calophyllum braziliense y Acacia mangium. Antes de la implementación de los sistemas agroforestales, la finca estuvo plantada con arroz en el valle y eucalipto en las terrazas. Con el proyecto se logró sustituir 10 ha en el valle y 4 ha de terraza con Calophyllum, especie que ofrece una madera fina. Otra especie que se introdujo en la terraza fue la acacia (50 ha), sustituta del eucalipto. La finca aporta un valor agregado a la gestión dirigida a procesos de recuperación de la viabilidad económica y ambiental mediante el rescate de la vocación agrícola. Se fue reintroducido la Manihot esculenta, Maranta arundinaceae, Colocasia esculenta, Euterpe edulis, Musa sp., Cajanus cajan, y especies forestales en asociación con Calophyllum: Inga sp., Schinnus terebinthifolius, Alchornea triplinervia, Sesbania sp., repartidas entre 159 ha productivas y 50 ha para hábitats naturales de conservación. Las variables como efecto de los sistemas agroforestales estuvieron repartidas en suelos, caracteristicas productivas, apropiación y mejoramiento de las condicones de los trabajadores, aspectos ambientales y socioeconónicos que en conjunto arrojaron indices de desempeño para el sistema APOIA-NovoRural. Se encontraron contribuciones de los sistemas agroforestales para la sustentabilidad, destacándose la calidad del agua con índice (0,94) comparado con (0,85) obtenido en los sedimentos que drenan del cultivo de arroz; valores económicos (0,85) y de ecología del paisaje (0,77). El índice integrado medio, llegó a 0,79 en una escala de 0 a 10, con referencia de 0,70. La Finca Coruputuba estuvo entre los cinco valores más altos de desempeño ambiental de un universo de 178 casos

1,25-Dihydroxycholecalciferol (calcitriol) modifies uptake and release of 25-hydroxycholecalciferol in skeletal muscle cells in culture

© 2017 Elsevier Ltd The major circulating metabolite of vitamin D 3 , 25-hydroxycholecalciferol [25(OH)D], has a remarkably long half-life in blood for a (seco)steroid. Data from our studies and others are consistent with the hypothesis that there is a role for skeletal muscle in the maintenance of vitamin D status. Muscle cells internalise vitamin D-binding protein (DBP) from the circulation by means of a megalin/cubilin plasma membrane transport mechanism. The internalised DBP molecules then bind to actin and thus provide an intracellular array of high affinity binding sites for its specific ligand, 25(OH)D. There is evidence that the residence time for DBP in muscle cells is short and that it undergoes proteolytic degradation, releasing bound 25(OH)D. The processes of internalisation of DBP and its intracellular residence time, bound to actin, appear to be regulated. To explore whether 1,25-dihydroxycholecalciferol (calcitriol) has any effect on this process, cell cultures of myotubes and primary skeletal muscle fibers were incubated in a medium containing 10 −10 M calcitriol but with no added DBP. After 3 h pre-incubation with calcitriol, the net uptake of 25(OH)D by these calcitriol-treated cells over a further 4 h was significantly greater than that in vehicle-treated control cells. This was accompanied by a significant increase in intracellular DBP protein. However, after 16 h of pre-incubation with calcitriol, the muscle cells showed a significantly depressed ability to accumulate 25(OH)D compared to control cells over a further 4 or 16 hours. These effects of pre-incubation with calcitriol were abolished in fibers from VDR-knockout mice. The effect was also abolished by the addition of 4,4\u27-diisothiocyano-2,2\u27-stilbenedisulfonic acid (DIDS), which inhibits chloride channel opening. Incubation of C2 myotubes with calcitriol also significantly reduced retention of previously accumulated 25(OH)D after 4 or 8 h. It is concluded from these in vitro studies that calcitriol can modify the DBP-dependent uptake and release of 25(OH)D by skeletal muscle cells in a manner that suggests some inducible change in the function of these cells

Skeletal muscle and the maintenance of vitamin d status

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. Vitamin D, unlike the micronutrients, vitamins A, E, and K, is largely obtained not from food, but by the action of solar ultraviolet (UV) light on its precursor, 7-dehydrocholesterol, in skin. With the decline in UV light intensity in winter, most skin production of vitamin D occurs in summer. Since no defined storage organ or tissue has been found for vitamin D, it has been assumed that an adequate vitamin D status in winter can only be maintained by oral supplementation. Skeletal muscle cells have now been shown to incorporate the vitamin D-binding protein (DBP) from blood into the cell cytoplasm where it binds to cytoplasmic actin. This intracellular DBP provides an array of specific binding sites for 25-hydroxyvitamin D (25(OH)D), which diffuses into the cell from the extracellular fluid. When intracellular DBP undergoes proteolytic breakdown, the bound 25(OH)D is then released and diffuses back into the blood. This uptake and release of 25(OH)D by muscle accounts for the very long half-life of this metabolite in the circulation. Since 25(OH)D concentration in the blood declines in winter, its cycling in and out of muscle cells appears to be upregulated. Parathyroid hormone is the most likely factor enhancing the repeated cycling of 25(OH)D between skeletal muscle and blood. This mechanism appears to have evolved to maintain an adequate vitamin D status in winter