It is well known that multi-chart parameterization methods introduce seams over the object being parameterized. This causes serious problems for several applications, like texture filtering and simulations in texture domain (e.g. fluid simulations). In this paper we present a set of two techniques, collectively known as ’Continuity Mapping’, that when used together make a multi-chart parameteri...

The stability of optimal plans with respect to information is studied given the representation of information as sub-σ -fields of a probability space. A decision maker is constrained to choose a plan measurable with respect to her information. Continuity is derived by characterizing the continuity of the measurability constraint correspondence and then applying a generalized maximum theorem. Th...

1 Homework Assignment # 1 1. Show that the -δ definition of continuity of a map f : X → Y between metric spaces is equivalent to the definition of continuity in terms of open subsets. Proof. Suppose f is -δ-continuous (i.e., continuous in the sense of the -δ definition of continuity) and that U is an open subset of Y . We need to show that f−1(U) is an open subset of X. The definition of an ope...

Let t 7→ A(t) for t ∈ T be a C -mapping with values unbounded operators with compact resolvents and common domain of definition which are self-adjoint or normal. Here C stands for C (real analytic), a quasianalytic or non-quasianalytic Denjoy-Carleman class, C∞, or a Hölder continuity class C. The parameter domain T is either R or R or an infinite dimensional convenient vector space. We prove a...

State space equations that constrain the values of related variables within individual states are often used in models of continuous dynamical systems such as ordinary differential equations . These models do not allow the representation of non-local information constraining the behavior of the system across time except through the application of continuity . Qualitative simulation (Kuipers, 19...

Fliess operators as input–output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory. In the classical analysis of these operators, certain growth conditions on the coe3cients in their series representations insure uniform and absolute convergence, provided every input is uniformly bounded by some 4xed upperbound. In some emerging applica...

A family of spatio-temporal scale-spaces suitable for a moving observer is developed. The scale-spaces are required to be time causal for being usable for real time measurements, and to be “velocity adapted”, i.e. to have Galilean covariance to avoid favoring any particular motion. Furthermore standard scale-space axioms: linearity, positivity, continuity, translation invariance, scaling covari...

The intention of my paper, The Attentional Theory of Cinematic Continuity (AToCC; this volume) was to bring together disparate lines of research on cinematic continuity and make an intentionally provocative first stab at theorising a cognitive foundation for the continuity editing conventions that pervade film. If our understanding of film cognition is to progress, clear hypotheses need to be p...

In this paper, we study the properties of the metric projection operator (the nearest point projection operator) and its continuity. Then we use it to solve variational inequalities in general Banach spaces and to approximate the solutions in uniformly convex and uniformly smooth Banach spaces.