For one, from integrals of multivalued functions on configuration spaces of points.
Riemann argued that the fundamental ingredients for geometry are a space of points (called today a manifold) and a way of measuring distances along curves in the space.
It was assumed, with anticipation that there is frequently such a thing in nature, that a transformation T relates members of the series by successively transforming an underlying space of points ω according to a rule.
The term X denotes an abstract mathematical space of points.
Let X be a space of points with generic elements of X denoted by x and I = [ 0, 1 ].
Much of the modeling of physical systems takes place in what is called state space, an abstract mathematical space of points where each point represents a possible state of the system.
Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function.
Some general methods for deriving such equations are the master equation approach and an approach that relies upon coarse-graining the phase space of points representing the micro-states of the system into finite cells and assuming fixed transition probabilities from cell to cell (Markov assumption).
In this model, the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures in order to take the time since detection into account.
A large spacing of control points allows modeling of global deformation with large displacement, and hence, one control point will influence the deformation of large local areas, while a small spacing of control points allows modeling of local deformation within small areas.
