A Well Stated Time Domain Integral Representation for Elastodynamic Analysis and Applications

This article discusses three possible ways to derive time domain boundary integral representations for elastodynamics. This discussion points out possible difficulties found when using those formulations to deal with practical applications. The discussion points out recommendations to select the convenient integral representation to deal with elastodynamic problems and opens the possibility of deriving simplified schemes. The proper way to take into account initial conditions applied to the body is an interesting topict shown. It illustrates the main differences between the discussed boundary integral representation expressions, their singularities and possible numerical problems. The correct way to use collocation points outside the analyzed domain is carefully described. Some applications are shown at the end of the paper, in order to demonstrate the capabilities of the technique when properly used.

A conceptual and practical overview of cDNA microarray technology: implications for basic and clinical sciences

cDNA microarray is an innovative technology that facilitates the analysis of the expression of thousands of genes simultaneously. The utilization of this methodology, which is rapidly evolving, requires a combination of expertise from the biological, mathematical and statistical sciences. In this review, we attempt to provide an overview of the principles of cDNA microarray technology, the practical concerns of the analytical processing of the data obtained, the correlation of this methodology with other data analysis methods such as immunohistochemistry in tissue microarrays, and the cDNA microarray application in distinct areas of the basic and clinical sciences.

Rationality in children: the first steps

Not all categorization is conceptual. Many of the experimental findings concerning infant and animal categorization invite the hypothesis that the subjects form abstract perceptual representations, mental models or cognitive maps that are not composed of concepts. The paper is a reflection upon the idea that conceptual categorization involves the ability to make categorical judgements under the guidance of norms of rationality. These include a norm of truth-seeking and a norm of good evidence. Acceptance of these norms implies willingness to defer to cognitive authorities, unwillingness to commit oneself to contradictions, and knowledge of how to reorganize one's representational system upon discovering that one has made a mistake. It is proposed that the cognitive architecture required for basic rationality is similar to that which underlies pretend-play. The representational system must be able to make room for separate 'mental spaces' in which alternatives to the actual world are entertained. The same feature underlies the ability to understand modalities, time, the appearance-reality distinction, other minds, and ethics. Each area of understanding admits of degrees, and mastery (up to normal adult level) takes years. But rational concept-management, at least in its most rudimentary form, does not require a capacity to form second-order representations. It requires knowledge of how to operate upon, and compare, the contents of different mental spaces.