Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis

In this paper, we discuss the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrödinger equation and Heisenberg uncertainty principles are structured within local fractional operators.

Self-similarity principle: the reduced description of randomness

A new general fitting method based on the Self-Similar (SS) organization of random sequences is presented. The proposed analytical function helps to fit the response of many complex systems when their recorded data form a self-similar curve. The verified SS principle opens new possibilities for the fitting of economical, meteorological and other complex data when the mathematical model is absent but the reduced description in terms of some universal set of the fitting parameters is necessary. This fitting function is verified on economical (price of a commodity versus time) and weather (the Earth’s mean temperature surface data versus time) and for these nontrivial cases it becomes possible to receive a very good fit of initial data set. The general conditions of application of this fitting method describing the response of many complex systems and the forecast possibilities are discussed.

Maximum likelihood detection for OFDM signals with strong nonlinear distortion effects

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

The application of the controllability principle in Electricidade dos Açores, SA

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

Development of principle culture medium formulations for Saccharomyces cerevisiae

Saccharomyces cerevisiae as well as other microorganisms are frequently used in industry with the purpose of obtain different kind of products that can be applied in several areas (research investigation, pharmaceutical compounds, etc.). In order to obtain high yields for the desired product, it is necessary to make an adequate medium supplementation during the growth of the microorganisms. The higher yields are typically reached by using complex media, however the exact formulation of these media is not known. Moreover, it is difficult to control the exact composition of complex media, leading to batch-to-batch variations. So, to overcome this problem, some industries choose to use defined media, with a defined and known chemical composition. However these kind of media, many times, do not reach the same high yields that are obtained by using complex media. In order to obtain similar yield with defined media the addition of many different compounds has to be tested experimentally. Therefore, the industries use a set of empirical methods with which it is tried to formulate defined media that can reach the same high yields as complex media. In this thesis, a defined medium for Saccharomyces cerevisiae was developed using a rational design approach. In this approach a given metabolic network of Saccharomyces cerevisiae is divided into a several unique and not further decomposable sub networks of metabolic reactions that work coherently in steady state, so called elementary flux modes. The EFMtool algorithm was used in order to calculate the EFM’s for two Saccharomyces cerevisiae metabolic networks (amino acids supplemented metabolic network; amino acids non-supplemented metabolic network). For the supplemented metabolic network 1352172 EFM’s were calculated and then divided into: 1306854 EFM’s producing biomass, and 18582 EFM’s exclusively producing CO2 (cellular respiration). For the non-supplemented network 635 EFM’s were calculated and then divided into: 215 EFM’s producing biomass; 420 EFM’s producing exclusively CO2. The EFM’s of each group were normalized by the respective glucose consumption value. After that, the EFMs’ of the supplemented network were grouped again into: 30 clusters for the 1306854 EFMs producing biomass and, 20 clusters for the 18582 EFM’s producing CO2. For the non-supplemented metabolic network the respective EFM’s of each metabolic function were grouped into 10 clusters. After the clustering step, the concentrations of the other medium compounds were calculated by considering a reasonable glucose amount and by accounting for the proportionality between the compounds concentrations and the glucose ratios. The approach adopted/developed in this thesis may allow a faster and more economical way for media development.

Hierarchical modelling of timber reference properties using probabilistic methods: Maximum Likelihood Method, Bayesian Methods and Probability Networks

In recent decades, an increased interest has been evidenced in the research on multi-scale hierarchical modelling in the field of mechanics, and also in the field of wood products and timber engineering. One of the main motivations for hierar-chical modelling is to understand how properties, composition and structure at lower scale levels may influence and be used to predict the material properties on a macroscopic and structural engineering scale. This chapter presents the applicability of statistic and probabilistic methods, such as the Maximum Likelihood method and Bayesian methods, in the representation of timber’s mechanical properties and its inference accounting to prior information obtained in different importance scales. These methods allow to analyse distinct timber’s reference properties, such as density, bending stiffness and strength, and hierarchically consider information obtained through different non, semi or destructive tests. The basis and fundaments of the methods are described and also recommendations and limitations are discussed. The methods may be used in several contexts, however require an expert’s knowledge to assess the correct statistic fitting and define the correlation arrangement between properties.

Исследование возможной связи между изменениями электротеллурического поля и активацией сейсмотектонических процессов с использованием принципа максимального правдоподобия

ჩატარდა ელექტროტელურული ველის ცვალებადობის შესაძლო კავშირის კვლევა სეისმოტექტონიკური პროცესების აქტიურობასთან მიმართებაში მაქსიმალური დასაჯერებლობის პრინციპის გამოყენებით. 1982 წელს ელექტროტელურული ველის ურთიერთმართობული მდგენელების ინტენსივობის წლიურ-ყოველსაათიან ცვალებადობას და დუშეთიდან ასორმოცდაათი კილომეტრის რადიუსით შემოსაზღვრულ არეში მომხდარი არასუსტი მიწისძვრების მაგნიტუდების ცვალებადობას შორის არსებობს შესაძლო კავშირი.

On convergence of the maximum likelihood estimator in adaptive designs

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Dissertation, 2016

Likelihood inferences with interval-censored data

En l’anàlisi de la supervivència el problema de les dades censurades en un interval es tracta, usualment,via l’estimació per màxima versemblança. Amb l’objectiu d’utilitzar una expressió simplificada de la funció de versemblança, els mètodes estàndards suposen que les condicions que produeixen la censura no afecten el temps de fallada. En aquest article formalitzem les condicions que asseguren la validesa d’aquesta versemblança simplificada. Així, precisem diferents condicions de censura no informativa i definim una condició de suma constant anàloga a la derivada en el context de censura per la dreta. També demostrem que les inferències obtingudes amb la versemblançaa simplificada són correctes quan aquestes condicions són certes. Finalment, tractem la identificabilitat de la funció distribució del temps de fallada a partir de la informació observada i estudiem la possibilitat de contrastar el compliment de la condició de suma constant.

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

A note on the separability principle in economies with single-peaked

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and continuity (with respect to the social endowment). We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of continuity. Furthermore, we prove that Pareto optimality, equal division lower bound, and separability imply no-envy. Using this result, we strengthen one of Chun's (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, equal división lower bound, separability, and either continuity or duplication-invariance.

Likelihood-based approaches to modeling demand for medical care

We review recent likelihood-based approaches to modeling demand for medical care. A semi-nonparametric model along the lines of Cameron and Johansson's Poisson polynomial model, but using a negative binomial baseline model, is introduced. We apply these models, as well a semiparametric Poisson, hurdle semiparametric Poisson, and finite mixtures of negative binomial models to six measures of health care usage taken from the Medical Expenditure Panel survey. We conclude that most of the models lead to statistically similar results, both in terms of information criteria and conditional and unconditional prediction. This suggests that applied researchers may not need to be overly concerned with the choice of which of these models they use to analyze data on health care demand.