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Recent technological advances including brain imaging (higher resolution in space and
time), miniaturization of integrated circuits (nanotechnologies), and acceleration of
computation speed (Moore’s Law), combined with interpenetration between neuroscience,
mathematics, and physics have led to the development of more biologically plausible
computational models and novel therapeutic strategies. Today, mathematical models of
irreversible medical conditions...
Modeling the movement of cells (bacteria, amoeba) is a long standing subject and partial differential equations have been used several times. The most classical and successful system was proposed by Patlak and Keller & Segel and is formed of parabolic or elliptic equations coupled through a drift term. This model exhibits a very deep mathematical structure because smooth solutions exist for small initial norm (in the appropriate space) and blow-up for large norms. This reflects experiments on...
The paper presents a new technique for cognitive analysis and recognition of pathological wrist bone lesions. This method uses AI techniques and mathematical linguistics allowing us to automatically evaluate the structure of the said bones, based on palm radiological images. Possibilities of computer interpretation of selected images, based on the methodology of automatic medical image understanding, as introduced by the authors, were created owing to the introduction of an original relational description...
Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death...
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