Mathematical Algorithm (mathematical + algorithm)

Distribution by Scientific Domains

Selected Abstracts

Toward a better understanding of the pathophysiology of OCD SSRI responders: QEEG source localization

T. G. Bolwig
Objective:, To demonstrate the utility of three-dimensional source localization of the scalp-recorded electroencephalogram (EEG) for the identification of the most probable underlying brain dysfunction in patients with obsessive,compulsive disorder (OCD). Method:, Eyes-closed resting EEG data was recorded from the scalp locations of the International 10/20 System. Variable resolution electromagnetic tomography (VARETA) was applied to artifact-free EEG data. This mathematical algorithm estimates the source generators of EEG recorded from the scalp. Results:, An excess in the alpha range was found with sources in the corpus striatum, in the orbito-frontal and temporo-frontal regions in untreated OCD patients. This abnormality was seen to decrease following successful treatment with paroxetine. Conclusion:, The VARETA findings of an activation/deactivation pattern in cortical and subcortical structures in paroxetine-responsive patients are in good accordance with data obtained in previously published positron emission tomography studies related to current hypotheses of a thalamo-striatal-frontal feedback loop being relevant for understanding the pathophysiology of OCD. [source]

Investigating Global and Local Categorical Map Configuration Comparisons Based on Coincidence Matrices

T. K. Remmel
The simple and intuitive nature of the coincidence matrix has not only made it the current "gold standard" for accuracy assessment (based on a sample of map pixels), but also a common tool for describing difference between two categorical maps (when all pixels are enumerated). It is this latter case of map comparison that this article explores. Coincidence matrices, although providing significant information regarding thematic agreement between two categorical maps (composition), can lack significantly in terms of conveying information about differences or similarities in the spatial arrangement (configuration) of those map categories in geographic space. This article introduces means for distilling the available configuration information from a coincidence matrix while demonstrating some simple categorical map comparisons. Specifically, while the coincidence matrix summarizes per-pixel compositional persistence or change, the introduced technique further quantifies the global and local configurational uncertainty between compared maps. I demonstrate how this quantification of configurational uncertainty can be used to gauge which thematic mismatch types are most significant and how to measure/present local configurational uncertainty in a spatial context. Implementation is through a straightforward mathematical algorithm in R that is illustrated by several examples. La sencillez y características las matrices de confusión (tablas de contingencia o de error) no sólo la ha convertido en (1) el estándar por excelencia para la evaluación de confiabilidad (veracidad o validez) de mapas temáticos en escala nominal (en base de una muestra de pixeles en un mapa), sino también en (2) una herramienta común para describir la diferencia entre dichos mapas (cuando todos los pixeles son tomados en cuenta). Este segundo uso de las matrices de confusión es el tema explorado por el presente artículo. A pesar de proporcionar información importante acerca de la confiabilidad temática entre dos mapas de categorías nominales (composición), las matrices de confusión sufren de limitaciones importantes cuando el objetivo es extraer información acerca del patrón o arreglo espacial (configuración) de las categorías del mapa. El presente artículo presenta herramientas para destilar la información de configuración espacial disponible a partir de una matriz de confusión, y al mismo tiempo, ilustra algunas comparaciones entre mapas de categorías nominales. En términos más concretos, la matriz de confusión resume la persistencia o cambio en la composición a nivel de cada pixel. La nueva técnica presentada en este estudio incluye además la cuantificación de la incertidumbre en la configuración de los mapas comparados. El autor demuestra cómo esta cuantificación puede ser utilizada para darse una idea de cuáles tipos de errores temáticos son más importantes, y cómo se puede medir e ilustrar la incertidumbre de la configuración local en el contexto espacial. La implementación del método se realiza a través de un algoritmo matemático sencillo en lenguaje R, el mismo que es ilustrado con varios ejemplos. [source]

Retrieving low- and medium-resolution structural features of macromolecules directly from the diffraction intensities , a real-space approach to the X-ray phase problem

Wu-Pei Su
A simple mathematical algorithm is proposed to generate electron-density functions whose Fourier amplitudes match the diffraction intensities. The function is by construction everywhere positive. Using appropriate averaging procedures, the high-density regions of such functions could yield important structural information about macromolecular crystals. Trial calculations on protein crystals show that the protein envelope plus other structural motifs such as barrels and secondary structures could be recognized in the density maps. As such, the algorithm could provide a basis for new phasing methods or supplement existing phasing methods. [source]

Zur Modellierung von Zerkleinerungsprozessen,

Dr.-Ing., K. Husemann Prof., habil.
Abstract Die Bedeutung der Zerkleinerung für die industrielle Stoffwandlung ist groß und die Angebotspalette an Zerkleinerungsmaschinen , angepasst an die Festigkeit/Härte des Mahlgutes, die Ausgangsmaterial- und Mahlproduktfeinheit, den notwendigen Durchsatz u.,a. , breit. Die Beschreibung der Zerkleinerung ist auch heute trotz der erreichten Fortschritte bei den Grundlagen der Zerkleinerung und den Kenntnissen der Vorgänge in Zerkleinerungsmaschinen nur eingeschränkt möglich. Vor diesem Hintergrund ist die Modellierung der Zerkleinerung von der Modellvorstellung bis zum mathematischen Algorithmus notwendig und hilfreich. Im Beitrag werden verschiedene Modellierungsmöglichkeiten dargestellt und dabei zwischen Regressionsmodellen für die Prozesse in Zerkleinerungsmaschinen, Modellvorstellungen aus den Grundlagen der Zerkleinerung und Modellen für die Zerkleinerung aus der allgemeinen Prozessgleichung der mechanischen Verfahrenstechnik unterschieden. Modeling of Comminution Processes The importance of comminution processes for industrial material processing is crucial and the available selection of crushers and mills , adapted to strength/hardness of the material to be ground, the fineness of the feed and product, the throughput required, etc. , is wide. The description of a comminution process is also nowadays , despite the progress as to the fundamentals of comminution and as to the knowledge of the processes in comminution equipment , possible only to a limited extent. In this respect, modeling and simulation of comminution from the model to a mathematical algorithm is necessary and helpful. In this contribution, several possible models are presented: regression models, models derived from the fundamentals of comminution processes and, finally, models related to the general process equation of mechanical process engineering. [source]