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This mapping is known as a Riemann mapping. [1] Intuitively, the condition that be simply connected means that does not contain any “holes”. The fact that is biholomorphic implies that it is a conformal map and therefore angle-preserving. Such a map may be interpreted as preserving the shape of any sufficiently small figure, while possibly ...
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.
According to the definition established in 2013 by Society for Brain Mapping and Therapeutics (SBMT), brain mapping is specifically defined, in summary, as the study of the anatomy and function of the brain and spinal cord through the use of imaging, immunohistochemistry, molecular & optogenetics, stem cell and cellular biology, engineering ...
Relieved of the requirement to map the position of an olfactory stimulus in space, the olfactory system employs spatial segregation of sensory input to encode the quality of an odorant. [ 7 ] The topographic map revealed in the olfactory system differs in quality from the orderly representation inherent in the retinotopic, tonotopic, or ...
Cognitive biology is an emerging science that regards natural cognition as a biological function. [1] It is based on the theoretical assumption that every organism —whether a single cell or multicellular —is continually engaged in systematic acts of cognition coupled with intentional behaviors, i.e., a sensory-motor coupling . [ 2 ]
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 ...
Since du is non-zero and the square of the Hodge star operator is −1 on 1-forms, du and dv must be linearly independent, so that u and v give local isothermal coordinates. 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 ...
Such a mapping defines both a first fundamental form and second fundamental form. The Laplacian (also called tension field) is defined via the second fundamental form, and its vanishing is the condition for the map to be harmonic. The definitions extend without modification to the setting of pseudo-Riemannian manifolds.