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In complex analysis, the Riemann mapping theorem states that if is a non-empty simply connected open subset of the complex number plane which is not all of , then there exists a biholomorphic mapping (i.e. a bijective holomorphic mapping whose inverse is also holomorphic) from onto the open unit disk
Shapes in Computational Anatomy (CA) are studied via the use of diffeomorphic mapping for establishing correspondences between anatomical coordinate systems. In this setting, 3-dimensional medical images are modelled as diffeomorphic transformations of some exemplar, termed the template I t e m p {\displaystyle I_{temp}} , resulting in the ...
Cognitive mapping is the implicit, mental mapping the explicit part of the same process. In most cases, a cognitive map exists independently of a mental map, an article covering just cognitive maps would remain limited to theoretical considerations. Mental mapping is typically associated with landmarks, locations, and geography when demonstrated.
Computational anatomy is an interdisciplinary field of biology focused on quantitative investigation and modelling of anatomical shapes variability. [1] [2] It involves the development and application of mathematical, statistical and data-analytical methods for modelling and simulation of biological structures.
There are several equivalent definitions of a Riemann surface. A Riemann surface X is a connected complex manifold of complex dimension one. This means that X is a connected Hausdorff space that is endowed with an atlas of charts to the open unit disk of the complex plane: for every point x ∈ X there is a neighbourhood of x that is homeomorphic to the open unit disk of the complex plane, and ...
The existence of isothermal coordinates can be proved by other methods, for example using the general theory of the Beltrami equation, as in Ahlfors (2006), or by direct elementary methods, as in Chern (1955) and Jost (2006). From this correspondence with compact Riemann surfaces, a classification of closed orientable Riemannian 2-manifolds ...
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The term "psychobiology" has been used in a variety of contexts, emphasizing the importance of biology, which is the discipline that studies organic, neural and cellular modifications in behavior, plasticity in neuroscience, and biological diseases in all aspects, in addition, biology focuses and analyzes behavior and all the subjects it is ...