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Keywords Control · Regulation · Biological information · Three-dimensional geometry · Principle of life · Biological process · Complexity Introduction This is an essay about the conceptual foundations of modern biology and the role that mathematics can play for biology. Traditionally, two aspects have been considered as funda-
18 Αυγ 2020 · More and more analyses of biological shapes are using the techniques of geometric morphometrics based on configurations of landmarks in two or three dimensions. A fundamental concept at the core of these analyses is Kendall’s shape space and local approximations to it by shape tangent spaces.
1 Ιαν 2014 · Geometry (Ancient Greek: γεωμετρία; geo “earth,” metron “measurement”) is a mathematical area concerned with the space around us, with the shapes in the space, their properties, and different “patterns” and “thinking patterns” for which they serve as trigger and basis.
Here we review the building blocks of modern geometric morphometrics: the representation of organismal geometry by landmarks and semilandmarks, the computation of shape or form variables via superimposition, the visualization of statistical results as actual shapes or forms, the decomposition of shape variation into symmetric and asymmetric ...
18 Οκτ 1999 · This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of …
28 Αυγ 2020 · LUCS greatly expands the designable structure space and offers a new paradigm for designing proteins with tunable geometries that may be customizable for novel functions. The design of proteins with new and useful architectures and functions requires precise control over molecular geometries (1, 2).
7 Σεπ 2001 · The deduction of the explicit geometry of shape space given experimental affinity data provides new ways to quantify the similarity of antibodies to antibodies, antigens to antigens, and the affinity of antigens to antibodies.
