Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocks based on compositional statistics is introduced. It improves and generalizes the common joins-count statistics known from map analysis in geographic information systems. Assigning phases independently to objects in RD is modelled by a single-trial multinomial random function Z(x), where the probabilities of phases add to one and are explicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistencies of the tests based on the conventional joins{count statistics and their possibly contradictory interpretations are avoided. In practical applications we assume that the probabilities of phases do not depend on the location but are identical everywhere in the domain of de nition. Thus, the model involves the sum of r independent identical multinomial distributed 1-trial random variables which is an r-trial multinomial distributed random variable. The probabilities of the distribution of the r counts can be considered as a composition in the Q-part simplex SQ. They span the so called Hardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This is a generalisation of the well-known Hardy-Weinberg law of genetics. If the assignment of phases accounts for some kind of spatial dependence, then the r-trial probabilities do not remain on H. This suggests the use of the Aitchison distance between observed probabilities to H to test dependence. Moreover, when there is a spatial uctuation of the multinomial probabilities, the observed r-trial probabilities move on H. This shift can be used as to check for these uctuations. A practical procedure and an algorithm to perform the test have been developed. Some cases applied to simulated and real data are presented. Key words: Spatial distribution of crystals in rocks, spatial distribution of phases, joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinberg manifold, Aitchison geometry

Assessing the uncertainty associated with intermittent rainfall fields

[1] In many practical situations where spatial rainfall estimates are needed, rainfall occurs as a spatially intermittent phenomenon. An efficient geostatistical method for rainfall estimation in the case of intermittency has previously been published and comprises the estimation of two independent components: a binary random function for modeling the intermittency and a continuous random function that models the rainfall inside the rainy areas. The final rainfall estimates are obtained as the product of the estimates of these two random functions. However the published approach does not contain a method for estimation of uncertainties. The contribution of this paper is the presentation of the indicator maximum likelihood estimator from which the local conditional distribution of the rainfall value at any location may be derived using an ensemble approach. From the conditional distribution, representations of uncertainty such as the estimation variance and confidence intervals can be obtained. An approximation to the variance can be calculated more simply by assuming rainfall intensity is independent of location within the rainy area. The methodology has been validated using simulated and real rainfall data sets. The results of these case studies show good agreement between predicted uncertainties and measured errors obtained from the validation data.

Estimation or simulation? That is the question

The issue of smoothing in kriging has been addressed either by estimation or simulation. The solution via estimation calls for postprocessing kriging estimates in order to correct the smoothing effect. Stochastic simulation provides equiprobable images presenting no smoothing and reproducing the covariance model. Consequently, these images reproduce both the sample histogram and the sample semivariogram. However, there is still a problem, which is the lack of local accuracy of simulated images. In this paper, a postprocessing algorithm for correcting the smoothing effect of ordinary kriging estimates is compared with sequential Gaussian simulation realizations. Based on samples drawn from exhaustive data sets, the postprocessing algorithm is shown to be superior to any individual simulation realization yet, at the expense of providing one deterministic estimate of the random function.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Agreement Abstractions in Anonymous and Homonymous Distributed Systems Prone to Failures

The distributed computing models typically assume every process in the system has a distinct identifier (ID) or each process is programmed differently, which is named as eponymous system. In such kind of distributed systems, the unique ID is helpful to solve problems: it can be incorporated into messages to make them trackable (i.e., to or from which process they are sent) to facilitate the message transmission; several problems (leader election, consensus, etc.) can be solved without the information of network property in priori if processes have unique IDs; messages in the register of one process will not be overwritten by others process if this process announces; it is useful to break the symmetry. Hence, eponymous systems have influenced the distributed computing community significantly either in theory or in practice. However, every thing in the world has its own two sides. The unique ID also has disadvantages: it can leak information of the network(size); processes in the system have no privacy; assign unique ID is costly in bulk-production(e.g, sensors). Hence, homonymous system is appeared. If some processes share the same ID and programmed identically is called homonymous system. Furthermore, if all processes shared the same ID or have no ID is named as anonymous system. In homonymous or anonymous distributed systems, the symmetry problem (i.e., how to distinguish messages sent from which process) is the main obstacle in the design of algorithms. This thesis is aimed to propose different symmetry break methods (e.g., random function, counting technique, etc.) to solve agreement problem. Agreement is a fundamental problem in distributed computing including a family of abstractions. In this thesis, we mainly focus on the design of consensus, set agreement, broadcast algorithms in anonymous and homonymous distributed systems. Firstly, the fault-tolerant broadcast abstraction is studied in anonymous systems with reliable or fair lossy communication channels separately. Two classes of anonymous failure detectors AΘ and AP∗ are proposed, and both of them together with a already proposed failure detector ψ are implemented and used to enrich the system model to implement broadcast abstraction. Then, in the study of the consensus abstraction, it is proved the AΩ′ failure detector class is strictly weaker than AΩ and AΩ′ is implementable. The first implementation of consensus in anonymous asynchronous distributed systems augmented with AΩ′ and where a majority of processes does not crash. Finally, a general consensus problem– k-set agreement is researched and the weakest failure detector L used to solve it, in asynchronous message passing systems where processes may crash and recover, with homonyms (i.e., processes may have equal identities), and without a complete initial knowledge of the membership.

Agreement Abstractions in Anonymous and Homonymous Distributed Systems Prone to Failures

The distributed computing models typically assume every process in the system has a distinct identifier (ID) or each process is programmed differently, which is named as eponymous system. In such kind of distributed systems, the unique ID is helpful to solve problems: it can be incorporated into messages to make them trackable (i.e., to or from which process they are sent) to facilitate the message transmission; several problems (leader election, consensus, etc.) can be solved without the information of network property in priori if processes have unique IDs; messages in the register of one process will not be overwritten by others process if this process announces; it is useful to break the symmetry. Hence, eponymous systems have influenced the distributed computing community significantly either in theory or in practice. However, every thing in the world has its own two sides. The unique ID also has disadvantages: it can leak information of the network(size); processes in the system have no privacy; assign unique ID is costly in bulk-production(e.g, sensors). Hence, homonymous system is appeared. If some processes share the same ID and programmed identically is called homonymous system. Furthermore, if all processes shared the same ID or have no ID is named as anonymous system. In homonymous or anonymous distributed systems, the symmetry problem (i.e., how to distinguish messages sent from which process) is the main obstacle in the design of algorithms. This thesis is aimed to propose different symmetry break methods (e.g., random function, counting technique, etc.) to solve agreement problem. Agreement is a fundamental problem in distributed computing including a family of abstractions. In this thesis, we mainly focus on the design of consensus, set agreement, broadcast algorithms in anonymous and homonymous distributed systems. Firstly, the fault-tolerant broadcast abstraction is studied in anonymous systems with reliable or fair lossy communication channels separately. Two classes of anonymous failure detectors AΘ and AP∗ are proposed, and both of them together with a already proposed failure detector ψ are implemented and used to enrich the system model to implement broadcast abstraction. Then, in the study of the consensus abstraction, it is proved the AΩ′ failure detector class is strictly weaker than AΩ and AΩ′ is implementable. The first implementation of consensus in anonymous asynchronous distributed systems augmented with AΩ′ and where a majority of processes does not crash. Finally, a general consensus problem– k-set agreement is researched and the weakest failure detector L used to solve it, in asynchronous message passing systems where processes may crash and recover, with homonyms (i.e., processes may have equal identities), and without a complete initial knowledge of the membership.

The Effect of nutritional supplementation on subjective and objective measures of visual and retinal function:a random controlled trial

In industrialised countries age-related macular disease (ARMD) is the leading cause of visual loss in older people. Because oxidative stress is purported to be associated with an increased risk of disease development the role of antioxidant supplementation is of interest. Lutein is a carotenoid antioxidant that accumulates within the retina and is thought to filter blue light. Increased levels of lutein have been associated with reduced risk of developing ARMD and improvements in visual and retinal function in eyes with ARMD. The aim of this randomised controlled trial (RCT) was to investigate the effect of a lutein-based nutritional supplement on subjective and objective measures of visual function in healthy eyes and in eyes with age-related maculopathy (ARM) – an early form of ARMD. Supplement withdrawal effects were also investigated. A sample size of 66 healthy older (HO), healthy younger (HY), and ARM eyes were randomly allocated to receive a lutein-based supplement or no treatment for 40 weeks. The supplemented group then stopped supplementation to look at the effects of withdrawal over a further 20 weeks. The primary outcome measure was multifocal electroretinogram (mfERG) N1P1 amplitude. Secondary outcome measures were mfERG N1, P1 and N2 latency, contrast sensitivity (CS), Visual acuity (VA) and macular pigment optical density (MPOD). Sample sizes were sufficient for the RCT to have an 80% power to detect a significant clinical effect at the 5% significance level for all outcome measures when the healthy eye groups were combined, and CS, VA and mfERG in the ARM group. This RCT demonstrates significant improvements in MPOD in HY and HO supplemented eyes. When HY and HO supplemented groups were combined, MPOD improvements were maintained, and mfERG ring 2 P1 latency became shorter. On withdrawal of the supplement mfERG ring 1 N1P1 amplitude reduced in HO eyes. When HO and HY groups were combined, mfERG ring 1 and ring 2 N1P1 amplitudes were reduced. In ARM eyes, ring 3 N2 latency and ring 4 P1 latency became longer. These statistically significant changes may not be clinically significant. The finding that a lutein-based supplement increases MPOD in healthy eyes, but does not increase mfERG amplitudes contrasts with the CARMIS study and contributes to the debate on the use of nutritional supplementation in ARM.

Delocalization-localization transition of plasmons in random (GaAs)(m)(Al(0.3)Ga(0.7)As)(6) superlattices

The transition of plasmons from propagating to localized state was studied in disordered systems formed in GaAs/AlGaAs superlattices by impurities and by artificial random potential. Both the localization length and the linewidth of plasmons were measured by Raman scattering. The vanishing dependence of the plasmon linewidth on the disorder strength was shown to be a manifestation of the strong plasmon localization. The theoretical approach based on representation of the plasmon wave function in a Gaussian form well accounted for by the obtained experimental data.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Random regression models to estimate test-day milk yield genetic parameters Holstein cows in Southeastern Brazil

A total of 152,145 weekly test-day milk yield records from 7317 first lactations of Holstein cows distributed in 93 herds in southeastern Brazil were analyzed. Test-day milk yields were classified into 44 weekly classes of DIM. The contemporary groups were defined as herd-year-week of test-day. The model included direct additive genetic, permanent environmental and residual effects as random and fixed effects of contemporary group and age of cow at calving as covariable, linear and quadratic effects. Mean trends were modeled by a cubic regression on orthogonal polynomials of DIM. Additive genetic and permanent environmental random effects were estimated by random regression on orthogonal Legendre polynomials. Residual variances were modeled using third to seventh-order variance functions or a step function with 1, 6,13,17 and 44 variance classes. Results from Akaike`s and Schwarz`s Bayesian information criterion suggested that a model considering a 7th-order Legendre polynomial for additive effect, a 12th-order polynomial for permanent environment effect and a step function with 6 classes for residual variances, fitted best. However, a parsimonious model, with a 6th-order Legendre polynomial for additive effects and a 7th-order polynomial for permanent environmental effects, yielded very similar genetic parameter estimates. (C) 2008 Elsevier B.V. All rights reserved.

The critical power function is dependent on the duration of the predictive exercise tests chosen

The linear relationship between work accomplished (W-lim) and time to exhaustion (t(lim)) can be described by the equation: W-lim = a + CP.t(lim). Critical power (CP) is the slope of this line and is thought to represent a maximum rate of ATP synthesis without exhaustion, presumably an inherent characteristic of the aerobic energy system. The present investigation determined whether the choice of predictive tests would elicit significant differences in the estimated CP. Ten female physical education students completed, in random order and on consecutive days, five art-out predictive tests at preselected constant-power outputs. Predictive tests were performed on an electrically-braked cycle ergometer and power loadings were individually chosen so as to induce fatigue within approximately 1-10 mins. CP was derived by fitting the linear W-lim-t(lim) regression and calculated three ways: 1) using the first, third and fifth W-lim-t(lim) coordinates (I-135), 2) using coordinates from the three highest power outputs (I-123; mean t(lim) = 68-193 s) and 3) using coordinates from the lowest power outputs (I-345; mean t(lim) = 193-485 s). Repeated measures ANOVA revealed that CPI123 (201.0 +/- 37.9W) > CPI135 (176.1 +/- 27.6W) > CPI345 (164.0 +/- 22.8W) (P < 0.05). When the three sets of data were used to fit the hyperbolic Power-t(lim) regression, statistically significant differences between each CP were also found (P < 0.05). The shorter the predictive trials, the greater the slope of the W-lim-t(lim) regression; possibly because of the greater influence of 'aerobic inertia' on these trials. This may explain why CP has failed to represent a maximal, sustainable work rate. The present findings suggest that if CP is to represent the highest power output that an individual can maintain for a very long time without fatigue then CP should be calculated over a range of predictive tests in which the influence of aerobic inertia is minimised.

The application of adaptive partitioned random search in feature selection problem

Feature selection is one of important and frequently used techniques in data preprocessing. It can improve the efficiency and the effectiveness of data mining by reducing the dimensions of feature space and removing the irrelevant and redundant information. Feature selection can be viewed as a global optimization problem of finding a minimum set of M relevant features that describes the dataset as well as the original N attributes. In this paper, we apply the adaptive partitioned random search strategy into our feature selection algorithm. Under this search strategy, the partition structure and evaluation function is proposed for feature selection problem. This algorithm ensures the global optimal solution in theory and avoids complete randomness in search direction. The good property of our algorithm is shown through the theoretical analysis.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.