The fundamental problem in science is that of using measurements and observations to draw conclusions that at rst appear to be hidden from the observer. The task of turning raw measurements into useful conclusions is exactly the task underlying data driven modeling. The full task involves the ability to turn various assumptions into useful constraints which allow the data to be converted into c...

In this paper I will give a summary of the description of State Vector reduction using Topos Theory put forward by Isham in [1]. I will first briefly explain some mathematical concepts regarding Categories and Topoi. For a more detailed and complete explanation of the subjects of Topos and Category Theory the readers should refer to Topos-Physics and reference therein. I would like to point out...

The anatomy of model species is described in ontologies, which are used to standardize the annotations of experimental data, such as gene expression patterns. To compare such data between species, we need to establish relationships between ontologies describing different species. Ontology matching is a kind of solutions to find semantic correspondences between entities of different ontologies. ...

Currently, anesthesiologists use clinical parameters to directly measure the depth of anesthesia (DoA). This clinical standard of monitoring is often combined with brain monitoring for better assessment of the hypnotic component of anesthesia. Brain monitoring devices provide indices allowing for an immediate assessment of the impact of anesthetics on consciousness. However, questions remain re...

A new method, MUNIN (Multi-dimensional NMR spectra interpretation), is introduced for the automated interpretation of three-dimensional NMR spectra. It is based on a mathematical concept referred to as three-way decomposition. An NMR spectrum is decomposed into a sum of components, with each component corresponding to one or a group of peaks. Each component is defined as the direct product of t...

In his book, Analytical Archaeology, Clarke (1968:512-513) noted three ways in which mathematical concepts are relevant to what he calls archaeological ideology: "(i) The need for entitation and quantification ... using ... descriptive statistics"; "(ii) The need to handle relationship concepts ... using analytical inductive statistics"; "(iii) The need to handle the regularities in complex dat...

Computational models have become an integral part of basic neuroscience and have facilitated some of the major advances in the field. More recently, such models have also been applied to the understanding of disruptions in brain function. In this review, using examples and a simple analogy, we discuss the potential for computational models to inform our understanding of brain function and dysfu...

Introduction It is now possible to employ a fully communicative approach to language teaching while at the same time attending to grammatical structure, but only if one can decisively abandon a mindset in which structure consists of rules governing form only and fully adopt instead a view that structure consists of forms that encode meanings, which speakers choose in order to communicate messag...

Large amounts of various biological networks exist for representing different types of interaction data, such as genetic, metabolic, gene regulatory, and protein-protein relationships. Recent approaches on biological network study are based on different mathematical concepts. It is necessary to construct a uniform framework to judge the functionality of biological networks. We recently introduc...

Multiresolution is a general mathematical concept that allows us to study a property by means of several changes of resolution. From a fixed resolution, a coarser projection can be calculated and then the changes between a finer resolution and a coarser one can be studied. That information can give a good knowledge about the problem under consideration. Also using multiresolution techniques it ...