Josep Ginebra

Setting Reaction and Hardening of an Apatitic Calcium Phosphate Cement

The combination of self-setting and biocompatibility makes calcium phosphate cements potentially useful materials for a variety of dental applications. The objective of this study was to investigate the setting and hardening mechanisms of a cement-type reaction leading to the formation of calcium-deficient hydroxyapatite at low temperature. Reactants used were a-tricalcium phosphate containing 17 wt% β-tricalcium phosphate, and 2 wt% of precipitated hydroxyapatite as solid phase and an aqueous solution 2.5 wt% of disodium hydrogen phosphate as liquid phase. The transformation of the mixture was stopped at selected times by a freeze-drying technique, so that the cement properties at various stages could be studied by means of x-ray diffraction, infrared spectroscopy, and scanning electron microscopy. Also, the compressive strength of the cement was measured as a function of time. The results showed that: (1) the cement setting was the result of the a-tricalcium phosphate hydrolysis, giving as a product calcium-deficient hydroxyapatite, while β-tricalcium phosphate did not participate in the reaction; (2) the extent of conversion of a-TCP was nearly 80% after 24 hr; (3) both the extent of conversion and the compressive strength increased initially linearly with time, subsequently reaching a saturation level, with a strong correlation observed between them, indicating that the microstructural changes taking place as the setting reaction proceeded were responsible for the mechanical behavior of the cement; and (4) the microstructure of the set cement consisted of clusters of big plates with radial or parallel orientations in a matrix of small plate-like crystals.

Kinetic study of the setting reaction of a calcium phosphate bone cement

The setting reaction of a calcium phosphate bone cement consisting of a mixture of 63.2 wt % alpha-tertiary calcium phosphate (TCP)[alpha-Ca3(PO4)2], 27.7 wt % dicalcium phosphate (DCP) (CaHPO4), and 9.1 wt % of precipitated hydroxyapatite [(PHA) used as seed material] was investigated. The cement samples were prepared at a liquid-to-powder ratio of: L/P = 0.30 ml/g. Bi-distilled water was used as liquid solution. After mixing the powder and liquid, some samples were molded and aged in Ringers solution at 37 degrees C. At fixed time intervals they were unmolded and then immediately frozen in liquid nitrogen at a temperature of TN = -196 degrees C, lyofilized, and examined by X-ray diffraction as powder samples. The compressive strength versus time was also measured in setting samples of this calcium phosphate bone cement. The crystal entanglement morphology was examined by scanning electron microscopy. The results showed that: 1) alpha-TCP reacted to a calcium-deficient hydroxyapatite (CDHA), Ca9(HPO4)(PO4)5O H, whereas DCP did not react significantly; 2) the reaction was nearly finished within 32 h, during which both the reaction percentage and the compressive strength increased versus time, with a strong correlation between them; and 3) the calcium phosphate bone cement showed in general a structure of groups of interconnected large plates distributed among agglomerations of small crystal plates arranged in very dense packings.

Bayesian Analysis of a Multinomial Sequence and Homogeneity of Literary Style

To help settle the debate around the authorship of Tirant lo Blanc, all words in each chapter are categorized according to their length, and the appearances of certain words are counted, thus forming two contingency tables of ordered rows. A Bayesian multinomial change-point analysis of the sequence of rows, reveals a clear stylistic boundary, estimated to be near chapters 371 and 382. A Bayesian cluster analysis of these rows confirms the existence of that boundary, and reveals a few chapters that are misclassified by the estimated change-point. The statistical evidence supports the hypotheses of one main author writing about four fifths of the book, with a second author finishing the book by filling in material, mainly at the end of it.

On the measure of the information in a statistical experiment

Setting aside experimental costs, the choice of an experiment is usu- ally formulated in terms of the maximization of a measure of information, often presented as an optimality design criterion. However, there does not seem to be a universal agreement on what objects can qualify as a valid measure of the in- formation in an experiment. In this article we explicitly state a minimal set of requirements that must be satised by all such measures. Under that framework, the measure of the information in an experiment is equivalent to the measure of the variability of its likelihood ratio statistics or which is the same, it is equivalent to the measure of the variability of its posterior to prior ratio statistics and to the measure of the variability of the distribution of the posterior distributions yielded by it. The larger that variability, the more peaked the likelihood functions and posterior distributions that tend to be yielded by the experiment, and the more informative the experiment is. By going through various measures of variability, this paper uncovers the unifying link underlying well known information measures as well as information measures that are not yet recognized as such. The measure of the information in an experiment is then related to the measure of the information in a given observation from it. In this framework, the choice of experiment based on statistical merit only, is posed as a decision problem where the reward is a likelihood ratio or posterior distribution, the utility function is convex, the utility of the reward is the information observed, and the expected utility is the information in an experiment. Finally, the information in an experiment is linked to the information and to the uncertainty in a probability distribution, and we nd that the measure of the information in an experiment is not always interpretable as the uncertainty in the prior minus the expected uncertainty in the posterior.

Análisis de la evolución temporal de la mortalidad mediante modelos lineales generalizados

En este trabajo se muestra como los modelos lineales generalizados permiten describir eficientemente diferentes patrones de evolucion temporal de datos de mortalidad y, a su vez, llevar a cabo una facil interpretacion. Como aplicacion practica se analiza la evolucion de la mortalidad por cancer de mama en las mujeres de Cataluna entre 1986 y 2000. De los resultados destaca que la mortalidad por cancer de mama experimenta un aumento y un posterior descenso para todos los grupos de edad. El ano en que se inicia el descenso es mas reciente en los grupos de edad mayor.

Change-point estimation in a multinomial sequence and homogeneity of literary style

To help settle the debate around the authorship of Tirant lo Blanc, all the words in each chapter of that book are categorized according to their length and the appearance of various words is counted. The graphical exploration of the sequences of multinomial observations obtained reveals a clear single sudden change point that is consistently estimated to be between chapters 371 and 382 and might indicate a switch of author. Correspondence analysis indicates that at the end of the book the words tend to be longer and the frequency of various words changes significantly. By doing a cluster analysis of the multinomial observations, the evidence in favor of the existence of that stylistic boundary is strengthened, because the two clusters obtained match very closely the before and after change-point groups; only a few chapters at the end of the book appear to be misclassified by the change point.

Extended truncated Inverse Gaussian–Poisson model

The inverse Gaussian–Poisson mixture model is very useful when modelling highly skewed non-negative integer data in fields as diverse as linguistics, ecology, market research, bibliometry, engineering and insurance. When using this statistical model on the frequency of word or species frequency data, one typically truncates its sample space at zero to accommodate for the ignorance about the number of words or species that are not observed. In this paper, we show that by truncating the sample space of the inverse Gaussian–Poisson model, one is allowed to extend its parameter space and in that way improve its fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. By fitting the extended model to word frequency count data, we find many instances where the maximum likelihood estimates fall in the extension of the parameter space.

Two-level experiments for binary response data

Information in a statistical experiment is often measured through the determinant of its information matrix. Under first order normal linear models, the determinant of the information matrix of a two-level factorial experiment neither depends on where the experiment is centered, nor on how it is oriented, and balanced allocations are more informative than unbalanced ones with the same number of runs. In contrast, under binary response models, none of these properties hold. The performance of two-level experiments for binomial responses is explored by investigating the dependence of the determinant of their information matrix on their location, orientation, range, presence or absence of interactions and on the relative allocation of runs to support points, and in particular, on the type of fractionating involved. Conventional wisdom about two-level factorial experiments, which is deeply rooted on normal response models, does not apply to binomial models. In binary response settings, factorial experiments should not be used for screening or as building blocks for binary response surface exploration, and there is no alternative to the optimal design theory approach to planning experiments.

Diversity of vocabulary and homogeneity of literary style

Abstract To help settle the debate around the authorship of Tirant lo Blanc, we analyse the evolution of the diversity of the vocabulary used in that book, as measured through eight different diversity indices. The exploratory analysis reveals a clear single shift in diversity, that is estimated through change-point techniques to be in chapter 382, and might indicate the existence of one main author writing about four fifths of the book, and of a second author finishing the last one fifth of the book. Before chapter 382, the language is richer and more diverse than after it.

On the measure and the estimation of evenness and diversity

Modelling word or species frequency count data through zero truncated Poisson mixture models allows one to interpret the model mixing distribution as the distribution of the word or species frequencies of the vocabulary or population. As a consequence, estimates of their mixing density can be used as a fingerprint of the style of the author in his texts or of the ecosystem in its samples. Definitions of measure of the evenness and of measure of the diversity within a vocabulary or population are given, and the novelty of these definitions is explained. It is then proposed that the measures of the evenness and of the diversity of a vocabulary or population be approximated through the expectation of these measures under the word or species frequency distribution. That leads to the assessment of the lack of diversity through measures of the variability of the mixing frequency distribution estimates described above.