Records of past mid-depth ventilation: Cretaceous ocean anoxic event 2 vs. recent oxygen minimum zones

Present day oceans are well ventilated, with the exception of mid-depth oxygen minimum zones (OMZs) under high surface water productivity, regions of sluggish circulation, and restricted marginal basins. In the Mesozoic, however, entire oceanic basins transiently became dysoxic or anoxic. The Cretaceous ocean anoxic events (OAEs) were characterised by laminated organic-carbon rich shales and low-oxygen indicating trace fossils preserved in the sedimentary record. Yet assessments of the intensity and extent of Cretaceous near-bottom water oxygenation have been hampered by deep or long-term diagenesis and the evolution of marine biota serving as oxygen indicators in today's ocean. Sedimentary features similar to those found in Cretaceous strata were observed in deposits underlying Recent OMZs, where bottom-water oxygen levels, the flux of organic matter, and benthic life have been studied thoroughly. Their implications for constraining past bottom-water oxygenation are addressed in this review. We compared OMZ sediments from the Peruvian upwelling with deposits of the late Cenomanian OAE 2 from the north-west African shelf. Holocene laminated sediments are encountered at bottom-water oxygen levels of < 7 µmol/kg under the Peruvian upwelling and < 5 µmol/kg in California Borderland basins and the Pakistan Margin. Seasonal to decadal changes of sediment input are necessary to create laminae of different composition. However, bottom currents may shape similar textures that are difficult to discern from primary seasonal laminae. The millimetre-sized trace fossil Chondrites was commonly found in Cretaceous strata and Recent oxygen-depleted environments where its diameter increased with oxygen levels from 5 to 45 µmol/kg. Chondrites has not been reported in Peruvian sediments but centimetre-sized crab burrows appeared around 10 µmol/kg, which may indicate a minimum oxygen value for bioturbated Cretaceous strata. Organic carbon accumulation rates ranged from 0.7 and 2.8 g C /cm2 /kyr in laminated OAE 2 sections in Tarfaya Basin, Morocco, matching late Holocene accumulation rates of laminated Peruvian sediments under Recent oxygen levels below 5 µmol/kg. Sediments deposited at > 10 µmol/kg showed an inverse exponential relationship of bottom-water oxygen levels and organic carbon accumulation depicting enhanced bioirrigation and decomposition of organic matter with increased oxygen supply. In the absence of seasonal laminations and under conditions of low burial diagenesis, this relationship may facilitate quantitative estimates of palaeo-oxygenation. Similarities and differences between Cretaceous OAEs and late Quaternary OMZs have to be further explored to improve our understanding of sedimentary systems under hypoxic conditions.

Estimadores bayesianos de la fiabilidad con muestreo censurado

El estudio de la fiabilidad de componentes y sistemas tiene gran importancia en diversos campos de la ingenieria, y muy concretamente en el de la informatica. Al analizar la duracion de los elementos de la muestra hay que tener en cuenta los elementos que no fallan en el tiempo que dure el experimento, o bien los que fallen por causas distintas a la que es objeto de estudio. Por ello surgen nuevos tipos de muestreo que contemplan estos casos. El mas general de ellos, el muestreo censurado, es el que consideramos en nuestro trabajo. En este muestreo tanto el tiempo hasta que falla el componente como el tiempo de censura son variables aleatorias. Con la hipotesis de que ambos tiempos se distribuyen exponencialmente, el profesor Hurt estudio el comportamiento asintotico del estimador de maxima verosimilitud de la funcion de fiabilidad. En principio parece interesante utilizar metodos Bayesianos en el estudio de la fiabilidad porque incorporan al analisis la informacion a priori de la que se dispone normalmente en problemas reales. Por ello hemos considerado dos estimadores Bayesianos de la fiabilidad de una distribucion exponencial que son la media y la moda de la distribucion a posteriori. Hemos calculado la expansion asint6tica de la media, varianza y error cuadratico medio de ambos estimadores cuando la distribuci6n de censura es exponencial. Hemos obtenido tambien la distribucion asintotica de los estimadores para el caso m3s general de que la distribucion de censura sea de Weibull. Dos tipos de intervalos de confianza para muestras grandes se han propuesto para cada estimador. Los resultados se han comparado con los del estimador de maxima verosimilitud, y con los de dos estimadores no parametricos: limite producto y Bayesiano, resultando un comportamiento superior por parte de uno de nuestros estimadores. Finalmente nemos comprobado mediante simulacion que nuestros estimadores son robustos frente a la supuesta distribuci6n de censura, y que uno de los intervalos de confianza propuestos es valido con muestras pequenas. Este estudio ha servido tambien para confirmar el mejor comportamiento de uno de nuestros estimadores. SETTING OUT AND SUMMARY OF THE THESIS When we study the lifetime of components it's necessary to take into account the elements that don't fail during the experiment, or those that fail by reasons which are desirable to exclude from consideration. The model of random censorship is very usefull for analysing these data. In this model the time to failure and the time censor are random variables. We obtain two Bayes estimators of the reliability function of an exponential distribution based on randomly censored data. We have calculated the asymptotic expansion of the mean, variance and mean square error of both estimators, when the censor's distribution is exponential. We have obtained also the asymptotic distribution of the estimators for the more general case of censor's Weibull distribution. Two large-sample confidence bands have been proposed for each estimator. The results have been compared with those of the maximum likelihood estimator, and with those of two non parametric estimators: Product-limit and Bayesian. One of our estimators has the best behaviour. Finally we have shown by simulation, that our estimators are robust against the assumed censor's distribution, and that one of our intervals does well in small sample situation.

Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons.

We study the dynamical states of a small-world network of recurrently coupled excitable neurons, through both numerical and analytical methods. The dynamics of this system depend mostly on both the number of long-range connections or ?shortcuts?, and the delay associated with neuronal interactions. We find that persistent activity emerges at low density of shortcuts, and that the system undergoes a transition to failure as their density reaches a critical value. The state of persistent activity below this transition consists of multiple stable periodic attractors, whose number increases at least as fast as the number of neurons in the network. At large shortcut density and for long enough delays the network dynamics exhibit exceedingly long chaotic transients, whose failure times follow a stretched exponential distribution. We show that this functional form arises for the ensemble-averaged activity if the failure time for each individual network realization is exponen- tially distributed

Recurrence interval statistics of cellular automaton seismicity models

The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.

A Modified Model of Risk Business

2000 Mathematics Subject Classification: 60K10, 62P05

An Estimate of the Probability Pr(X

2000 Mathematics Subject Classification: 33C90, 62E99

An inverse time admittance relay for fault detection in distribution networks containing DGs

Isolation of a faulted segment, from either side of a fault, in a radial feeder that has several converter interfaced DGs is a challenging task when current sensing protective devices are employed. The protective device, even if it senses a downstream fault, may not operate if fault current level is low due to the current limiting operation of converters. In this paper, a new inverse type relay is introduced based on line admittance measurement to protect a distribution network, which has several converter interfaced DGs. The basic operation of this relay, its grading and reach settings are explained. Moreover a method is proposed to compensate the fault resistance such that the relay operation under this condition is reliable. Then designed relay performances are evaluated in a radial distribution network. The results are validated through PSCAD/EMTDC simulation and MATLAB calculations.

Developing a numerical inverse-theory-based extraction of orientation-dependent relaxation rates from partially- relaxed spectra

Second-rank tensor interactions, such as quadrupolar interactions between the spin- 1 deuterium nuclei and the electric field gradients created by chemical bonds, are affected by rapid random molecular motions that modulate the orientation of the molecule with respect to the external magnetic field. In biological and model membrane systems, where a distribution of dynamically averaged anisotropies (quadrupolar splittings, chemical shift anisotropies, etc.) is present and where, in addition, various parts of the sample may undergo a partial magnetic alignment, the numerical analysis of the resulting Nuclear Magnetic Resonance (NMR) spectra is a mathematically ill-posed problem. However, numerical methods (de-Pakeing, Tikhonov regularization) exist that allow for a simultaneous determination of both the anisotropy and orientational distributions. An additional complication arises when relaxation is taken into account. This work presents a method of obtaining the orientation dependence of the relaxation rates that can be used for the analysis of the molecular motions on a broad range of time scales. An arbitrary set of exponential decay rates is described by a three-term truncated Legendre polynomial expansion in the orientation dependence, as appropriate for a second-rank tensor interaction, and a linear approximation to the individual decay rates is made. Thus a severe numerical instability caused by the presence of noise in the experimental data is avoided. At the same time, enough flexibility in the inversion algorithm is retained to achieve a meaningful mapping from raw experimental data to a set of intermediate, model-free

A bayesian analysis for the parameters of the exponential-logarithmic distribution

The exponential-logarithmic is a new lifetime distribution with decreasing failure rate and interesting applications in the biological and engineering sciences. Thus, a Bayesian analysis of the parameters would be desirable. Bayesian estimation requires the selection of prior distributions for all parameters of the model. In this case, researchers usually seek to choose a prior that has little information on the parameters, allowing the data to be very informative relative to the prior information. Assuming some noninformative prior distributions, we present a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. Jeffreys prior is derived for the parameters of exponential-logarithmic distribution and compared with other common priors such as beta, gamma, and uniform distributions. In this article, we show through a simulation study that the maximum likelihood estimate may not exist except under restrictive conditions. In addition, the posterior density is sometimes bimodal when an improper prior density is used. © 2013 Copyright Taylor and Francis Group, LLC.

Topics in geometry, analysis and inverse problems

The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.

Inverse table of the exponential integral /

Mode of access: Internet.