A SIMULATION STUDY OF THE SIZE AND POWER OF SOME TWO-SAMPLE TESTS FOR UNEQUALLY CENSORED SURVIVAL DATA (RANK TESTS, LOGRANK, PROPORTIONAL HAZARDS, WILCOXON TESTS, EXPONENTIAL DISTRIBUTION)

Sizes and power of selected two-sample tests of the equality of survival distributions are compared by simulation for small samples from unequally, randomly-censored exponential distributions. The tests investigated include parametric tests (F, Score, Likelihood, Asymptotic), logrank tests (Mantel, Peto-Peto), and Wilcoxon-Type tests (Gehan, Prentice). Equal sized samples, n = 18, 16, 32 with 1000 (size) and 500 (power) simulation trials, are compared for 16 combinations of the censoring proportions 0%, 20%, 40%, and 60%. For n = 8 and 16, the Asymptotic, Peto-Peto, and Wilcoxon tests perform at nominal 5% size expectations, but the F, Score and Mantel tests exceeded 5% size confidence limits for 1/3 of the censoring combinations. For n = 32, all tests showed proper size, with the Peto-Peto test most conservative in the presence of unequal censoring. Powers of all tests are compared for exponential hazard ratios of 1.4 and 2.0. There is little difference in power characteristics of the tests within the classes of tests considered. The Mantel test showed 90% to 95% power efficiency relative to parametric tests. Wilcoxon-type tests have the lowest relative power but are robust to differential censoring patterns. A modified Peto-Peto test shows power comparable to the Mantel test. For n = 32, a specific Weibull-exponential comparison of crossing survival curves suggests that the relative powers of logrank and Wilcoxon-type tests are dependent on the scale parameter of the Weibull distribution. Wilcoxon-type tests appear more powerful than logrank tests in the case of late-crossing and less powerful for early-crossing survival curves. Guidelines for the appropriate selection of two-sample tests are given. ^

Determination of sulfite and manganese in sediments from the K/T boundary

The solid-state-physics technique of electron spin resonance (ESR) has been employed in an exploratory study of marine limestones and impact-related deposits from Cretaceous-Tertiary (KT) boundary sites including Spain (Sopelana and Caravaca), New Jersey (Bass River), the U.S. Atlantic continental margin (Blake Nose, ODP Leg 171B/1049/A), and several locations in Belize and southern Mexico within -600 km of the Chicxulub crater. The ESR spectra of SO3(1-) (a radiation-induced point defect involving a sulfite ion substitutional for CO3(2-) which has trapped a positive charge) and Mn(2+) in calcite were singled out for analysis because they are unambiguously interpretable and relatively easy to record. ESR signal strengths of calcite-related SO3(1-) and Mn(2+) have been studied as functions of stratigraphic position in whole-rock samples across the KT boundary at Sopelana, Caravaca, and Blake Nose. At all three of these sites, anomalies in SO3(1-) and/or Mn(2+) intensities are noted at the KT boundary relative to the corresponding background levels in the rocks above and below. At Caravaca, the SO3(1-) background itself is found to be lower by a factor of 2.7 in the first 30,000 years of the Tertiary relative to its steady-state value in the last 15,000 years of the Cretaceous, indicating either an abrupt and quasi-permanent change in ocean chemistry (or temperature) or extinction of the marine biota primarily responsible for fixing sulfite in the late Cretaceous limestones. An exponential decrease in the Mn(2+) concentration per unit mass calcite, [Mn(2+)], as the KT boundary at Caravaca is approached from below (1/e characteristic length =1.4 cm) is interpreted as a result of post-impact leaching of the seafloor. Absolute ESR quantitative analyses of proximal impact deposits from Belize and southern Mexico group naturally into three distinct fields in a twodimensional [SO3(1-)]-versus-[Mn(2+)] scatter plot. These fields contain (I) limestone ejecta clasts, (II) accretionary lapilli, and (III) a variety of SO3(1-) -depleted/Mn(2+) enriched impact deposits. Data for the investigated non-impact-related Cretaceous and Tertiary marine limestones (Spain and Blake Nose) fall outside of these three fields. With reference to thes enon-impact deposits, fields I, II, and III can be respectively characterized as Mn(2+) -depleted, SO3(1-) -enhanced, and SO3(1-) -depleted. It is proposed that (1) field I represents calcites from the Yucatin Platform, and that the Mn(2+) -depleted signature can be used as an indicator of primary Chicxulub ejecta in deep marine environments and (2) field II represents calcites that include a component formed in the vapor plume, either from condensation in the presence of CO2/SO3(1-) -rich vapors, or reactions between CaO and CO2/SO3 rich vapors, and that this SO3(1-) -enhanced signature can be used as an indicator of impact vapor plume deposits. Given these two propositions, the ESR data for the Blake Nose deposits are ascribed to the presence of basal coarse calcitic Chicxulub ejecta clasts, while the finer components that are increasingly represented toward the top are interpreted to contain high- SO3(1-) calcite from the vapor plume. The apparently-undisturbed Bass River deposit may contain even higher concentrations of vapor-plume calcite. None of the three components included in field III appear to be represented at distal, deep marine KT-boundary sites; this field may include several types of impact-related deposits of diverse origins and diagenetic histories.

Treatment of post-partum haemorrhage with sublingual misoprostol versus oxytocin in women not exposed to oxytocin during labour: a double-blind, randomised, non-inferiority trial

Gynuity

Evaluation of cover crops based on characteristics of nitrogen use, and aerial and root growth

La caracterización de los cultivos cubierta (cover crops) puede permitir comparar la idoneidad de diferentes especies para proporcionar servicios ecológicos como el control de la erosión, el reciclado de nutrientes o la producción de forrajes. En este trabajo se estudiaron bajo condiciones de campo diferentes técnicas para caracterizar el dosel vegetal con objeto de establecer una metodología para medir y comparar las arquitecturas de los cultivos cubierta más comunes. Se estableció un ensayo de campo en Madrid (España central) para determinar la relación entre el índice de área foliar (LAI) y la cobertura del suelo (GC) para un cultivo de gramínea, uno de leguminosa y uno de crucífera. Para ello se sembraron doce parcelas con cebada (Hordeum vulgare L.), veza (Vicia sativa L.), y colza (Brassica napus L.). En 10 fechas de muestreo se midieron el LAI (con estimaciones directas y del LAI-2000), la fracción interceptada de la radiación fotosintéticamente activa (FIPAR) y la GC. Un experimento de campo de dos años (Octubre-Abril) se estableció en la misma localización para evaluar diferentes especies (Hordeum vulgare L., Secale cereale L., x Triticosecale Whim, Sinapis alba L., Vicia sativa L.) y cultivares (20) en relación con su idoneidad para ser usadas como cultivos cubierta. La GC se monitorizó mediante análisis de imágenes digitales con 21 y 22 muestreos, y la biomasa se midió 8 y 10 veces, respectivamente para cada año. Un modelo de Gompertz caracterizó la cobertura del suelo hasta el decaimiento observado tras las heladas, mientras que la biomasa se ajustó a ecuaciones de Gompertz, logísticas y lineales-exponenciales. Al final del experimento se determinaron el C, el N y el contenido en fibra (neutrodetergente, ácidodetergente y lignina), así como el N fijado por las leguminosas. Se aplicó el análisis de decisión multicriterio (MCDA) con objeto de obtener un ranking de especies y cultivares de acuerdo con su idoneidad para actuar como cultivos cubierta en cuatro modalidades diferentes: cultivo de cobertura, cultivo captura, abono verde y forraje. Las asociaciones de cultivos leguminosas con no leguminosas pueden afectar al crecimiento radicular y a la absorción de N de ambos componentes de la mezcla. El conocimiento de cómo los sistemas radiculares específicos afectan al crecimiento individual de las especies es útil para entender las interacciones en las asociaciones, así como para planificar estrategias de cultivos cubierta. En un tercer ensayo se combinaron estudios en rhizotrones con extracción de raíces e identificación de especies por microscopía, así como con estudios de crecimiento, absorción de N y 15N en capas profundas del suelo. Las interacciones entre raíces en su crecimiento y en el aprovisionamiento de N se estudiaron para dos de los cultivares mejor valorados en el estudio previo: uno de cebada (Hordeum vulgare L. cv. Hispanic) y otro de veza (Vicia sativa L. cv. Aitana). Se añadió N en dosis de 0 (N0), 50 (N1) y 150 (N2) kg N ha-1. Como resultados del primer estudio, se ajustaron correctamente modelos lineales y cuadráticos a la relación entre la GC y el LAI para todos los cultivos, pero en la gramínea alcanzaron una meseta para un LAI>4. Antes de alcanzar la cobertura total, la pendiente de la relación lineal entre ambas variables se situó en un rango entre 0.025 y 0.030. Las lecturas del LAI-2000 estuvieron correlacionadas linealmente con el LAI, aunque con tendencia a la sobreestimación. Las correcciones basadas en el efecto de aglutinación redujeron el error cuadrático medio del LAI estimado por el LAI-2000 desde 1.2 hasta 0.5 para la crucífera y la leguminosa, no siendo efectivas para la cebada. Esto determinó que para los siguientes estudios se midieran únicamente la GC y la biomasa. En el segundo experimento, las gramíneas alcanzaron la mayor cobertura del suelo (83-99%) y la mayor biomasa (1226-1928 g m-2) al final del mismo. Con la mayor relación C/N (27-39) y contenido en fibra digestible (53-60%) y la menor calidad de residuo (~68%). La mostaza presentó elevadas GC, biomasa y absorción de N en el año más templado en similitud con las gramíneas, aunque escasa calidad como forraje en ambos años. La veza presentó la menor absorción de N (2.4-0.7 g N m-2) debido a la fijación de N (9.8-1.6 g N m-2) y escasa acumulación de N. El tiempo térmico hasta alcanzar el 30% de GC constituyó un buen indicador de especies de rápida cubrición. La cuantificación de las variables permitió hallar variabilidad entre las especies y proporcionó información para posteriores decisiones sobre la selección y manejo de los cultivos cubierta. La agregación de dichas variables a través de funciones de utilidad permitió confeccionar rankings de especies y cultivares para cada uso. Las gramíneas fueron las más indicadas para los usos de cultivo de cobertura, cultivo captura y forraje, mientras que las vezas fueron las mejor como abono verde. La mostaza alcanzó altos valores como cultivo de cobertura y captura en el primer año, pero el segundo decayó debido a su pobre actuación en los inviernos fríos. Hispanic fue el mejor cultivar de cebada como cultivo de cobertura y captura, mientras que Albacete como forraje. El triticale Titania alcanzó la posición más alta como cultiva de cobertura, captura y forraje. Las vezas Aitana y BGE014897 mostraron buenas aptitudes como abono verde y cultivo captura. El MCDA permitió la comparación entre especies y cultivares proporcionando información relevante para la selección y manejo de cultivos cubierta. En el estudio en rhizotrones tanto la mezcla de especies como la cebada alcanzaron mayor intensidad de raíces (RI) y profundidad (RD) que la veza, con valores alrededor de 150 cruces m-1 y 1.4 m respectivamente, comparados con 50 cruces m-1 y 0.9 m para la veza. En las capas más profundas del suelo, la asociación de cultivos mostró valores de RI ligeramente mayores que la cebada en monocultivo. La cebada y la asociación obtuvieron mayores valores de densidad de raíces (RLD) (200-600 m m-3) que la veza (25-130) entre 0.8 y 1.2 m de profundidad. Los niveles de N no mostraron efectos claros en RI, RD ó RLD, sin embargo, el incremento de N favoreció la proliferación de raíces de veza en la asociación en capas profundas del suelo, con un ratio cebada/veza situado entre 25 a N0 y 5 a N2. La absorción de N de la cebada se incrementó en la asociación a expensas de la veza (de ~100 a 200 mg planta-1). Las raíces de cebada en la asociación absorbieron también más nitrógeno marcado de las capas profundas del suelo (0.6 mg 15N planta-1) que en el monocultivo (0.3 mg 15N planta-1). ABSTRACT Cover crop characterization may allow comparing the suitability of different species to provide ecological services such as erosion control, nutrient recycling or fodder production. Different techniques to characterize plant canopy were studied under field conditions in order to establish a methodology for measuring and comparing cover crops canopies. A field trial was established in Madrid (central Spain) to determine the relationship between leaf area index (LAI) and ground cover (GC) in a grass, a legume and a crucifer crop. Twelve plots were sown with either barley (Hordeum vulgare L.), vetch (Vicia sativa L.), or rape (Brassica napus L.). On 10 sampling dates the LAI (both direct and LAI-2000 estimations), fraction intercepted of photosynthetically active radiation (FIPAR) and GC were measured. A two-year field experiment (October-April) was established in the same location to evaluate different species (Hordeum vulgare L., Secale cereale L., x Triticosecale Whim, Sinapis alba L., Vicia sativa L.) and cultivars (20) according to their suitability to be used as cover crops. GC was monitored through digital image analysis with 21 and 22 samples, and biomass measured 8 and 10 times, respectively for each season. A Gompertz model characterized ground cover until the decay observed after frosts, while biomass was fitted to Gompertz, logistic and linear-exponential equations. At the end of the experiment C, N, and fiber (neutral detergent, acid and lignin) contents, and the N fixed by the legumes were determined. Multicriteria decision analysis (MCDA) was applied in order to rank the species and cultivars according to their suitability to perform as cover crops in four different modalities: cover crop, catch crop, green manure and fodder. Intercropping legumes and non-legumes may affect the root growth and N uptake of both components in the mixture. The knowledge of how specific root systems affect the growth of the individual species is useful for understanding the interactions in intercrops as well as for planning cover cropping strategies. In a third trial rhizotron studies were combined with root extraction and species identification by microscopy and with studies of growth, N uptake and 15N uptake from deeper soil layers. The root interactions of root growth and N foraging were studied for two of the best ranked cultivars in the previous study: a barley (Hordeum vulgare L. cv. Hispanic) and a vetch (Vicia sativa L. cv. Aitana). N was added at 0 (N0), 50 (N1) and 150 (N2) kg N ha-1. As a result, linear and quadratic models fitted to the relationship between the GC and LAI for all of the crops, but they reached a plateau in the grass when the LAI > 4. Before reaching full cover, the slope of the linear relationship between both variables was within the range of 0.025 to 0.030. The LAI-2000 readings were linearly correlated with the LAI but they tended to overestimation. Corrections based on the clumping effect reduced the root mean square error of the estimated LAI from the LAI-2000 readings from 1.2 to less than 0.50 for the crucifer and the legume, but were not effective for barley. This determined that in the following studies only the GC and biomass were measured. In the second experiment, the grasses reached the highest ground cover (83- 99%) and biomass (1226-1928 g/m2) at the end of the experiment. The grasses had the highest C/N ratio (27-39) and dietary fiber (53-60%) and the lowest residue quality (~68%). The mustard presented high GC, biomass and N uptake in the warmer year with similarity to grasses, but low fodder capability in both years. The vetch presented the lowest N uptake (2.4-0.7 g N/m2) due to N fixation (9.8-1.6 g N/m2) and low biomass accumulation. The thermal time until reaching 30% ground cover was a good indicator of early coverage species. Variable quantification allowed finding variability among the species and provided information for further decisions involving cover crops selection and management. Aggregation of these variables through utility functions allowed ranking species and cultivars for each usage. Grasses were the most suitable for the cover crop, catch crop and fodder uses, while the vetches were the best as green manures. The mustard attained high ranks as cover and catch crop the first season, but the second decayed due to low performance in cold winters. Hispanic was the most suitable barley cultivar as cover and catch crop, and Albacete as fodder. The triticale Titania attained the highest rank as cover and catch crop and fodder. Vetches Aitana and BGE014897 showed good aptitudes as green manures and catch crops. MCDA allowed comparison among species and cultivars and might provide relevant information for cover crops selection and management. In the rhizotron study the intercrop and the barley attained slightly higher root intensity (RI) and root depth (RD) than the vetch, with values around 150 crosses m-1 and 1.4 m respectively, compared to 50 crosses m-1 and 0.9 m for the vetch. At deep soil layers, intercropping showed slightly larger RI values compared to the sole cropped barley. The barley and the intercropping had larger root length density (RLD) values (200-600 m m-3) than the vetch (25-130) at 0.8-1.2 m depth. The topsoil N supply did not show a clear effect on the RI, RD or RLD; however increasing topsoil N favored the proliferation of vetch roots in the intercropping at deep soil layers, with the barley/vetch root ratio ranging from 25 at N0 to 5 at N2. The N uptake of the barley was enhanced in the intercropping at the expense of the vetch (from ~100 mg plant-1 to 200). The intercropped barley roots took up more labeled nitrogen (0.6 mg 15N plant-1) than the sole-cropped barley roots (0.3 mg 15N plant-1) from deep layers.

A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

The Malthusian parameter of ascents: What prevents the exponential increase of one’s ancestors?

The reason that the indefinite exponential increase in the number of one’s ancestors does not take place is found in the law of sibling interference, which can be expressed by the following simple equation:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\begin{matrix}{\mathit{N}}_{{\mathit{n}}} \enskip & \\ {\mathit{{\blacksquare}}} \enskip & \\ {\mathit{ASZ}} \enskip & \end{matrix} {\mathrm{\hspace{.167em}{\times}\hspace{.167em}2\hspace{.167em}=\hspace{.167em}}}{\mathit{N_{n+1},}}\end{equation*}\end{document} where Nn is the number of ancestors in the nth generation, ASZ is the average sibling size of these ancestors, and Nn+1 is the number of ancestors in the next older generation (n + 1). Accordingly, the exponential increase in the number of one’s ancestors is an initial anomaly that occurs while ASZ remains at 1. Once ASZ begins to exceed 1, the rate of increase in the number of ancestors is progressively curtailed, falling further and further behind the exponential increase rate. Eventually, ASZ reaches 2, and at that point, the number of ancestors stops increasing for two generations. These two generations, named AN SA and AN SA + 1, are the most critical in the ancestry, for one’s ancestors at that point come to represent all the progeny-produced adults of the entire ancestral population. Thereafter, the fate of one’s ancestors becomes the fate of the entire population. If the population to which one belongs is a successful, slowly expanding one, the number of ancestors would slowly decline as you move toward the remote past. This is because ABZ would exceed 2. Only when ABZ is less than 2 would the number of ancestors increase beyond the AN SA and AN SA + 1 generations. Since the above is an indication of a failing population on the way to extinction, there had to be the previous AN SA involving a far greater number of individuals for such a population. Simulations indicated that for a member of a continuously successful population, the AN SA ancestors might have numbered as many as 5.2 million, the AN SA generation being the 28th generation in the past. However, because of the law of increasingly irrelevant remote ancestors, only a very small fraction of the AN SA ancestors would have left genetic traces in the genome of each descendant of today.

Meta-analysis of short term low dose prednisolone versus placebo and non-steroidal anti-inflammatory drugs in rheumatoid arthritis

Objective: To determine whether short term, oral low dose prednisolone (⩽15 mg daily) is superior to placebo and non-steroidal anti-inflammatory drugs in patients with rheumatoid arthritis.

Exponential increases of RNA virus fitness during large population transmissions.

The great adaptability shown by RNA viruses is a consequence of their high mutation rates. Here we investigate the kinetics of virus fitness gains during repeated transfers of large virus populations in cell culture. Results always show that fitness increases exponentially. Low fitness clones exhibit regular increases observed as biphasic periods of exponential evolutionary improvement, while neutral clones show monophasic kinetics. These results are significant for RNA virus epidemiology, optimal handling of attenuated live virus vaccines, and routine laboratory procedures.

On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

Privileged Regions in Critical Strips of Non-lattice Dirichlet Polynomials

This paper shows, by means of Kronecker’s theorem, the existence of infinitely many privileged regions called r -rectangles (rectangles with two semicircles of small radius r ) in the critical strip of each function Ln(z):= 1−∑nk=2kz , n≥2 , containing exactly [Tlogn2π]+1 zeros of Ln(z) , where T is the height of the r -rectangle and [⋅] represents the integer part.

Direct versus indirect channels: Differentiated loss aversion in a high‐involvement, non‐frequently purchased hedonic product

Purpose – This article aims to investigate whether intermediaries reduce loss aversion in the context of a high-involvement non-frequently purchased hedonic product (tourism packages). Design/methodology/approach – The study incorporates the reference-dependent model into a multinomial logit model with random parameters, which controls for heterogeneity and allows representation of different correlation patterns between non-independent alternatives. Findings – Differentiated loss aversion is found: consumers buying high-involvement non-frequently purchased hedonic products are less loss averse when using an intermediary than when dealing with each provider separately and booking their services independently. This result can be taken as identifying consumer-based added value provided by the intermediaries. Practical implications – Knowing the effect of an increase in their prices is crucial for tourism collective brands (e.g. “sun and sea”, “inland”, “green destinations”, “World Heritage destinations”). This is especially applicable nowadays on account of the fact that many destinations have lowered prices to attract tourists (although, in the future, they will have to put prices back up to their normal levels). The negative effect of raising prices can be absorbed more easily via indirect channels when compared to individual providers, as the influence of loss aversion is lower for the former than the latter. The key implication is that intermediaries can – and should – add value in competition with direct e-tailing. Originality/value – Research on loss aversion in retailing has been prolific, exclusively focused on low-involvement and frequently purchased products without distinguishing the direct or indirect character of the distribution channel. However, less is known about other types of products such as high-involvement non-frequently purchased hedonic products. This article focuses on the latter and analyzes different patterns of loss aversion in direct and indirect channels.

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.