A linear ordering (X,≺) is a Debreu chain (or has the Debreu property) if each subordering (Y,≺) of X can be embedded into X with an injective function that is both order-preserving and continuous with respect to the order topology on X and Y . The most typical example of a Debreu chain is the linearly ordered topological space (R, <, τ<) of real numbers endowed with its usual order < and the o...

Recent work has led to the ability to perform space efficient, approximate counting over large vocabularies in a streaming context. Motivated by the existence of data structures of this type, we explore the computation of associativity scores, otherwise known as pointwise mutual information (PMI), in a streaming context. We give theoretical bounds showing the impracticality of perfect online PM...

We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

We show that a pointwise convergent sequence (n) n2IN of continuous collineations of a compact projective plane converges uniformly if and only if the pointwise limit of (n) n2IN has a quadrangle in its image. Moreover is then a continuous collineation. Furthermore, we derive that a homomorphism between topological projective planes is continuous if and only if it is continuous at some point.

We propose using (bilinear) sum-of-squares programming for obtaining inner bounds of regionsof-attraction and outer bounds of attractive invariant sets for dynamical systems with polynomial vector fields. We search for composite Lyapunov functions, comprised of pointwise maximums and pointwise minimums of polynomial functions. Excellent results for some examples are obtained using the proposed ...

1. Pointwise. Each point in the dest is determined from the corresponding point in the src. We start with 3 points specifying the initial coordinate space and the 3 corresponding points that specify the transformed coordinate space, and transform an entire image pointwise by the transformation (1). 2. Sequential. The entire image is successively transformed by a sequence of shear, scale and tra...

This paper conducts a stability, robustness and sensitivity analysis on a pointwise-optimal control law developed for dynamical systems. Many dynamical systems are described by complex nonlinear equations, which makes it difficult to design controllers for them. Pointwise-optimal control emerges as a viable design for such systems. We quantify the sources of errors for dynamical systems and pro...

Weprovide a generalmechanism for obtaining uniform information from pointwise data. A sample result is that if a diffeomorphism of a compact Riemannian manifold has pointwise expanding and contracting continuous invariant cone families, then the diffeomorphism is an Anosov diffeomorphism, i.e., the entire manifold is uniformly hyperbolic.