The letter states "the errors within IHMS' medication processes are manifold, represent significant risk to patients and likely to constitute medical negligence".
The notion that the manifold represents an independently existing thing is quite natural in the realist view of physical theories.
Leibniz Equivalence tells us that different spreadings of metrical and matter fields on the spacetime manifold represent the same physical spacetime.
A slight and very popular variant allows that each event of the manifold represents a physical spacetime event, but which physical event that might be depends on the spreading of metric and matter fields on the manifold.
The manifold represents an amorphous four-dimensional differentiable continuum in the sense of analysis situs and has no properties besides those that fall under the concept of a manifold.
Some claim which goes beyond conceptual analysis has to be made, according to Weyl, in order to prove that among the various types of possible metrical structures that can be put on a differentiable manifold representing physical space, the Pythagorean-Riemannian form is unique.
At its core are Einstein's equations, which describe the relation between the geometry of a four-dimensional, pseudo-Riemannian manifold representing spacetime, and the energy momentum contained in that spacetime.
Attractors represent differentiated states (in agreement with earlier postulates, [ 1, 13, 14, 41- 46]), separatrices form the ridges between the valleys, which are formed by unstable manifolds representing their associated chreodes (see Figure 1B, panels 3 and 4), and the flow is represented by the steepness of the slopes on the landscape.
To do this, each manifold is represented by a Laplacian matrix which models the similarity of instances with others who share the same label.
When each MGMCM is treated as a probability distribution lying on a multinomial manifold, we represent per object image as a point on a product multinomial manifold.
