Law of large numbers for certain cylinder flows

We construct new examples of cylinder flows, given by skew product extensions of irrational rotations on the circle, that are ergodic and rationally ergodic along a subsequence of iterates. In particular, they exhibit a law of large numbers. This is accomplished by explicitly calculating, for a subsequence of iterates, the number of visits to zero, and it is shown that such number has a Gaussian distribution.

Diseño e implementación de un convertidor numérico como aplicación Android

[ES] El Trabajo de Fin de Grado, Diseño e Implementación de un Convertidor Numérico como Aplicación Android es una aplicación desarrollada para terminales móviles con SO Android. Esta desarrollada en el entorno de desarrollo Eclipse, sobre el lenguaje de programación Java y hace uso de diferentes herramientas, las más importante de ellas el SDK TOOLS para Android. El objetivo o principal motivación por el cual he creado dicha aplicación es facilitarle al usuario final una forma más fácil y amena de acceder a toda la información proporcionada por el Servicio Web Números TIP. Esta aplicación podría tener gran uso en el campo de las enseñanzas primarias para enseñar a los niños a escribir números con letras y también podría ser de gran utilidad para las personas que no tengan un dominio extenso de nuestro idioma. La principal funcionalidad de la aplicación es realizar una consulta al Servicio Web Números TIP y luego mostrar por pantalla todos los datos devueltos. Todo el proceso de dibujo de la interfaz de usuario se realiza de manera dinámica y en tiempo de ejecución, logrando de esta manera adaptarnos a los datos que devuelva el servicio web. Para realizar la consulta al Servicio Web Números TIP el usuario introduce una ristra de caracteres sobre la cual se realizan determinadas comprobaciones en el servidor y se dibuja en la interfaz de usuario la respuesta devuelta. Esta ristra de caracteres puede contener cualquier signo, letra o número y el servicio web se encarga de devolver un error o reconocer un número, ya sea en su forma entera, fraccionaria, decimal o romana. La aplicación esta estandarizada para los cuatro tamaños generales reconocidos por Android y para sus densidades. Además se podría decir que la aplicación reconoce el idioma pre configurado en el teléfono y en base a ello solicita al servicio web las respuestas en español o en inglés.

Estimating persistent Betti numbers for discrete shape analysis

Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it. Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.

Lucky numbers: Choice strategies in the Pennsylvania Daily Number game

Examined the amount of money bet during a week of Pennsylvania's Daily Number game. In this game, players receive a predetermined payoff for picking the 3-digit number (000 to 999) drawn on that day. The betting distribution was distinctly nonuniform. Several betting patterns were identified, such as picking triples and avoiding double 9s. In addition, 121 adults and 215 students were asked to rate selected numbers for randomness, luckiness, and perceived history of winning; to categorize numbers; and to free associate to numbers. It is proposed that people seem to choose highly patterned, available, and/or "lucky" numbers. People apparently do not bet numbers that reflect the random process of the game (do not utilize a representativeness heuristic).

Conversion of CT numbers into tissue parameters for Monte Carlo dose calculations: a multi-centre study

The conversion of computed tomography (CT) numbers into material composition and mass density data influences the accuracy of patient dose calculations in Monte Carlo treatment planning (MCTP). The aim of our work was to develop a CT conversion scheme by performing a stoichiometric CT calibration. Fourteen dosimetrically equivalent tissue subsets (bins), of which ten bone bins, were created. After validating the proposed CT conversion scheme on phantoms, it was compared to a conventional five bin scheme with only one bone bin. This resulted in dose distributions D(14) and D(5) for nine clinical patient cases in a European multi-centre study. The observed local relative differences in dose to medium were mostly smaller than 5%. The dose-volume histograms of both targets and organs at risk were comparable, although within bony structures D(14) was found to be slightly but systematically higher than D(5). Converting dose to medium to dose to water (D(14) to D(14wat) and D(5) to D(5wat)) resulted in larger local differences as D(5wat) became up to 10% higher than D(14wat). In conclusion, multiple bone bins need to be introduced when Monte Carlo (MC) calculations of patient dose distributions are converted to dose to water.

Increased numbers of spontaneous SCLC metastasis in absence of NK cells after subcutaneous inoculation of different SCLC cell lines into pfp/rag2 double knock out mice

Spontaneous metastases in small cell lung cancer (SCLC) occur regularly in patients but seldom if any in conventional xenograft mouse models. To overcome this problem, SCLC cells were grafted subcutaneously onto pore forming protein and recombination activating gene 2 double knock out (pfp/rag2) mice and in severe combined immunodeficient (scid) mice. Primary tumours grew well in both mouse strains, while metastases occurred frequently in the pfp/rag2 mice and infrequently in scid mice. Hence NK cells, which are inactive in pfp/rag2 mice, play an important role in SCLC metastasis formation in xenograft models. This observation is in agreement with clinical studies, where a high NK cell number in the blood is correlated with a better prognosis of the patient.

In vitro differentiation of near-unlimited numbers of functional mouse basophils using conditional Hoxb8

Background: Basophils constitute a rare leukocyte population known for their effector functions in inflammation and allergy, as well as more recently described immunoregulatory roles. Besides their low frequency, functional analysis of basophils is hindered by a short life span, inefficient ex vivo differentiation protocols, and lack of suitable cell models. A method to produce large quantities of basophils in vitro would facilitate basophil research and constitute a sought-after tool for diagnostic and drug testing purposes. Methods: A method is described to massively expand bone marrow–derived basophils in vitro. Myeloid progenitors are conditionally immortalized using Hoxb8 in the presence of interleukin-3 (IL-3) and outgrowing cell lines selected for their potential to differentiate into basophils upon shutdown of Hoxb8 expression. Results: IL-3-dependent, conditional Hoxb8-immortalized progenitor cell lines can be expanded and maintained in culture for prolonged periods. Upon shutdown of Hoxb8 expression, near-unlimited numbers of mature functional basophils can be differentiated in vitro within six days. The cells are end-differentiated and short-lived and express basophil-specific surface markers and proteases. Upon IgE- as well as C5a-mediated activation, differentiated basophils release granule enzymes and histamine and secrete Th2-type cytokines (IL-4, IL-13) and leukotriene C4. IL-3-deprivation induces apoptosis correlating with upregulation of the BH3-only proteins BCL-2-interacting mediator of cell death (BIM) and p53 upregulated modulator of apoptosis (PUMA) and downregulation of proviral integration site for Moloney murine leukemia virus 1 kinase (PIM-1). Conclusion: A novel method is presented to generate quantitative amounts of mouse basophils in vitro, which moreover allows genetic manipulation of conditionally immortalized progenitors. This approach may represent a useful alternative method to isolating primary basophils.

Sample size in orthodontic randomized controlled trials: are numbers justified?

Sample size calculations are advocated by the Consolidated Standards of Reporting Trials (CONSORT) group to justify sample sizes in randomized controlled trials (RCTs). This study aimed to analyse the reporting of sample size calculations in trials published as RCTs in orthodontic speciality journals. The performance of sample size calculations was assessed and calculations verified where possible. Related aspects, including number of authors; parallel, split-mouth, or other design; single- or multi-centre study; region of publication; type of data analysis (intention-to-treat or per-protocol basis); and number of participants recruited and lost to follow-up, were considered. Of 139 RCTs identified, complete sample size calculations were reported in 41 studies (29.5 per cent). Parallel designs were typically adopted (n = 113; 81 per cent), with 80 per cent (n = 111) involving two arms and 16 per cent having three arms. Data analysis was conducted on an intention-to-treat (ITT) basis in a small minority of studies (n = 18; 13 per cent). According to the calculations presented, overall, a median of 46 participants were required to demonstrate sufficient power to highlight meaningful differences (typically at a power of 80 per cent). The median number of participants recruited was 60, with a median of 4 participants being lost to follow-up. Our finding indicates good agreement between projected numbers required and those verified (median discrepancy: 5.3 per cent), although only a minority of trials (29.5 per cent) could be examined. Although sample size calculations are often reported in trials published as RCTs in orthodontic speciality journals, presentation is suboptimal and in need of significant improvement.

Plasma-functionalized electrospun matrix for biograft development and cardiac function stabilization.

Cardiac tissue engineering approaches can deliver large numbers of cells to the damaged myocardium and have thus increasingly been considered as a possible curative treatment to counteract the high prevalence of progressive heart failure after myocardial infarction (MI). Optimal scaffold architecture and mechanical and chemical properties, as well as immune- and bio-compatibility, need to be addressed. We demonstrated that radio-frequency plasma surface functionalized electrospun poly(ɛ-caprolactone) (PCL) fibres provide a suitable matrix for bone-marrow-derived mesenchymal stem cell (MSC) cardiac implantation. Using a rat model of chronic MI, we showed that MSC-seeded plasma-coated PCL grafts stabilized cardiac function and attenuated dilatation. Significant relative decreases of 13% of the ejection fraction (EF) and 15% of the fractional shortening (FS) were observed in sham treated animals; respective decreases of 20% and 25% were measured 4 weeks after acellular patch implantation, whereas a steadied function was observed 4 weeks after MSC-patch implantation (relative decreases of 6% for both EF and FS).

ATP-gated ionotropic P2X7 receptor controls follicular T helper cell numbers in Peyer's patches to promote host-microbiota mutualism.

Microbial colonization of the gut induces the development of gut-associated lymphoid tissue (GALT). The molecular mechanisms that regulate GALT function and result in gut-commensal homeostasis are poorly defined. T follicular helper (Tfh) cells in Peyer's patches (PPs) promote high-affinity IgA responses. Here we found that the ATP-gated ionotropic P2X7 receptor controls Tfh cell numbers in PPs. Lack of P2X7 in Tfh cells enhanced germinal center reactions and high-affinity IgA secretion and binding to commensals. The ensuing depletion of mucosal bacteria resulted in reduced systemic translocation of microbial components, lowering B1 cell stimulation and serum IgM concentrations. Mice lacking P2X7 had increased susceptibility to polymicrobial sepsis, which was rescued by Tfh cell depletion or administration of purified IgM. Thus, regulation of Tfh cells by P2X7 activity is important for mucosal colonization, which in turn results in IgM serum concentrations necessary to protect the host from bacteremia.

Vertical distribution of relative numbers of the main groups of sound-scattering fishes in the Central Indian Ocean

Findings made in 31 catches with an Isaacs-Kidd midwater trawl in the light (09.00-16.00) and dark (21.00-04.00) periods of a day within a survey area of about 100 sq. miles with approximate center coordinates of 13°S and 78°E have been used to investigate vertical distribution of the main groups of sound-scattering fishes (35 species of the family Myctophidae and 16 species of other families). It has been shown that during daylight hours all fishes sink to depths deeper than 400 m. Data are presented concerning the fish population of night-time sound-scattering layers at depths of 70-150 m and about 400 m and of the daytime ones at depths of about 450 m.

Petrology and geochemistry of the basement boninite series of ODP Site 125-786

The 720 m of igneous basement that was penetrated at Site 786 of Ocean Drilling Program Leg 125 consists of boninite-series volcanics. Bronzite andesites dominate the lithology and primitive magmas of high-Ca, intermediate-Ca, and low-Ca boninite are present in subordinate amounts. Sparsely phyric boninites typically contain olivine and orthopyroxene phenocrysts with Mg numbers [= Mg/(Mg + Fe) in moles] between 86% and 87%. Their high whole-rock Mg numbers, and the absence of zonation in the phenocrysts, imply equilibration at temperatures probably between 1200° and 1250°C, and 20° to 50°C below their liquidus. Equilibrium olivine and orthopyroxene have identical Mg numbers, and Mg/Fe partitioning between these minerals and the melt thus can be described with a single Kd. The invariably phenocryst-rich bronzite andesites contain Plagioclase that has spectacular zoning and mafic phases that can be as magnesian as those of the boninite parent. The most evolved melts are rhyolites with hypersthene, Plagioclase (An50), and magnetite. Eruption temperatures for the rhyolites are estimated at about 1000°C. Some magmas contain ferroactinolite in the groundmass, which is most likely a secondary, low-temperature phase. The locally large contrasts in degree of alteration are consistent with multiple episodes of magmatic activity. However, all igneous events produced boninite volcanics. Only the first, the edifice-building episode, gave rise to differentiated magmas. Differentiation of parental boninites took place by limited fractional crystallization, producing bronzite andesites. The erupted andesites, dacites and rhyolites are filter pressed extracts from these bronzite andesite magmas, which, as a result, have accumulated crystals. Subsequent younger igneous events produced high-Ca and intermediate-Ca boninites which intruded as dikes and sills throughout the basement sequence. The mineralogy of the dikes and sills reflects variable degrees of subliquidus cooling of the magma before emplacement.