Growth Rates for Monotone Subsequence

The growth rate of the largest monotone subsequence of a uniformly distributed sequence is obtained. For an - na mod 1 with a algebraic irrational the exponent of growth is found to be precisely the same as for a random sequence

Hammersley\u27s Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers

The analogue of Hammersley\u27s theorem on the length of the longest monotonic subsequence of independent, identically, and continuously distributed random variables is obtained for the pseudorandom van der Corput sequence. In this case there is no limit but the precise limits superior and inferior are determined. The constants obtained are closely related to those established in the independent case by Logan and Shepp, and Vershik and Kerov

Complexity for extended dynamical systems

We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, epsilon-entropy and topological entropy per unit time and volume have been introduced previously. In this paper we use the notion of Kolmogorov complexity to introduce, for extended dynamical systems, a notion of complexity per unit time and volume which plays the same role as the metric entropy for classical dynamical systems. We introduce this notion as an almost sure limit on orbits of the system. Moreover we prove a kind of variational principle for this complexity.Comment: 29 page

Rigidity and Non-recurrence along Sequences

Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main focus in this article is to characterize explicitly the structural properties of sequences which can be rigidity sequences or non-recurrent sequences for some weakly mixing dynamical system. For ergodic transformations generally and for weakly mixing transformations in particular there are both parallels and distinctions between the class of rigid sequences and the class of non-recurrent sequences. A variety of classes of sequences with various properties are considered showing the complicated and rich structure of rigid and non-recurrent sequences

Uniformity in the Wiener-Wintner theorem for nilsequences

We prove a uniform extension of the Wiener-Wintner theorem for nilsequences due to Host and Kra and a nilsequence extension of the topological Wiener-Wintner theorem due to Assani. Our argument is based on (vertical) Fourier analysis and a Sobolev embedding theorem.Comment: v3: 18 p., proof that the cube construction produces compact homogeneous spaces added, measurability issues in the proof of Theorem 1.5 addressed. We thank the anonymous referees for pointing out these gaps in v

Revista de Vertebrados de la Estación Biológica de Doñana

Ritmo diario de actividad social en (Gambusia affinis)Sobre la herpetofauna de la Sierra de Estrella (Portugal) con especial referencia a Coronella austriaca austriaca y Vipera latastiNuevos datos sobre la distribución geográfica de los anfibios y reptiles ibéricosBiogeografía en la evolución de un grupo de formas de Coluber en el Paleártico OccidentalDatos sobre la alimentación de ofidiosEstructura de las galerías de nidificación del Abejaruco (Merops apiaster) en DoñanaComportamiento de la Perdiz Moruna ( Alectoris barbara) en cautividadEl paso otoñal de Sylvia borin y Sylvia conmmunis en la Reserva de DoñanaSobre el lirón Gris (Glis glis pyrenaicus Cabrera, 1908) en España.Sobre alimentación y biología de la Gineta (Genetta genetta lo) en EspañaEliomys quercinus valverdei, un nuevo lirón careto del noroeste de la Península IbéricaPeer reviewe

Determinación de las variables más representativas para la organización y el control de la reproducción en sistemas vacunos lecheros

A five-point scale survey with a Likert response format (1976) was anonymously answered by 35 experts in livestock reproduction from Camagüey province, Cuba, in order to determine the most representative variables in organizing and managing dairy cattle reproduction. A reliability test (Cronbach’s alpha index = 0,89) and a cluster analysis were performed to evaluate and validate the survey results. Experts considered birth number, birth rate, pregnant females, and on-reproduction females the most outstanding variables, while no consensus was registered on non-pregnant females, no-calving index, and off-production females criteria. Reproduction indexes for data analysis, decision making, and predictions scored a lower mark compared to on-production females, reproductive categories (except non-pregnant and off-production females), and estrus detection variables (females gathering at first estrus and at every estrus). Based on the survey results, the latter constitute the most representative variables in organizing and managing dairy cattle reproduction in Camagüey province.Para determinar los elementos más representativos del sistema de variables utilizado para la organización y el control de la reproducción en sistemas vacunos lecheros, se empleó una encuesta en formato de respuesta tipo Likert (1976) con escala de cinco puntos, aplicada a 35 expertos en el trabajo de la reproducción bovina de la provincia de Camagüey, Cuba; la misma fue respondida de forma anónima. Se realizaron análisis de fiabilidad (alfa de Cronbach = 0,89) y por cluster para validar y evaluar, respectivamente, los resultados de la encuesta. Se identificaron como las variables más importantes: los nacimientos, el índice de natalidad, las hembras gestantes y las hembras en la reproducción. No coincidieron los criterios con respecto a las hembras vacías, el índice de no parto y las bajas. Los indicadores reproductivos para el análisis de la información, la toma de decisiones y los pronósticos obtuvieron una calificación inferior a la otorgada a las hembras en la reproducción, las categorías reproductivas (excepto para hembras vacías y las bajas de la reproducción) y a las variables representativas de la detección de estros (recogida de hembras en primer celo y recogida en total celos) que, sobre la base de los resultados de la encuesta, constituyeron las variables más representativas del sistema de organización y control de la reproducción en los sistemas lecheros en las condiciones de la provincia de Camagüey, Cuba

Statistical machines for trauma hospital outcomes research: Application to the PRospective, Observational, Multi-center Major trauma Transfusion (PROMMTT) study

Improving the treatment of trauma, a leading cause of death worldwide, is of great clinical and public health interest. This analysis introduces flexible statistical methods for estimating center-level effects on individual outcomes in the context of highly variable patient populations, such as those of the PRospective, Observational, Multi-center Major Trauma Transfusion study. Ten US level I trauma centers enrolled a total of 1,245 trauma patients who survived at least 30 minutes after admission and received at least one unit of red blood cells. Outcomes included death, multiple organ failure, substantial bleeding, and transfusion of blood products. The centers involved were classified as either large or small-volume based on the number of massive transfusion patients enrolled during the study period. We focused on estimation of parameters inspired by causal inference, specifically estimated impacts on patient outcomes related to the volume of the trauma hospital that treated them. We defined this association as the change in mean outcomes of interest that would be observed if, contrary to fact, subjects from large-volume sites were treated at small-volume sites (the effect of treatment among the treated). We estimated this parameter using three different methods, some of which use data-adaptive machine learning tools to derive the outcome models, minimizing residual confounding by reducing model misspecification. Differences between unadjusted and adjusted estimators sometimes differed dramatically, demonstrating the need to account for differences in patient characteristics in clinic comparisons. In addition, the estimators based on robust adjustment methods showed potential impacts of hospital volume. For instance, we estimated a survival benefit for patients who were treated at large-volume sites, which was not apparent in simpler, unadjusted comparisons. By removing arbitrary modeling decisions from the estimation process and concentrating on parameters that have more direct policy implications, these potentially automated approaches allow methodological standardization across similar comparativeness effectiveness studies