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An interesting example of a compact Hausdorff space that is often presented in beginning courses in topology is the unit square [0, 1]× [0, 1] with the lexicographic order topology. The closed subspac...
An understanding of stream network topology is necessary for a landscape-level perspective of stream hydrology and ecology. We present a method for quantifying stream network topology that overcomes c...
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relationwith GromovWitten theory and integrable systems
SGDM (Sphere Grid Data Model) is an efficient method to deal with the global data because of the advantages of multi-resolution and hierarchy. However, SGDM has no distinct descriptions and lack of r...
In this paper we present a method for synthesis of decentralized controllers for multiple identical systems interconnected on a graph. We develop a synthesis procedure for controllers which will stabi...
In this paper we present a method for synthesis of decentralized controllers for systems interconnected on a graph. We develop a synthesis procedure which will achieve a specified level of performance...
We consider the design of optimal controllers for a networked system (or a spatio-temporal system), where the dynamics of each subsystem may affect those of other subsystems with some propagation dela...
An understanding of stream network topology is necessary for a landscape-level perspective of stream hydrology and ecology. We present a method for quantifying stream network topology that overcomes c...
Modern spaceborne SAR sensors like TerraSAR-X offer ground resolution of up to one meter in range and azimuth direction. Buildings, roads, bridges, and other man-made structures appear in such data of...
This paper is a follow-up to the author's work "Topology of probability measure space, I" devoted to investigation of the functors $\hat P$ and $P_\tau$ of spaces of probability $\tau$-smooth and Rado...
For a non-empty set $X$, the collection $Top(X)$ of all topologies on $X$ sits inside the Boolean lattice $\PP(\PP(X))$ (when ordered by set-theoretic inclusion) which in turn can be naturally identif...
Abstract: The standard representation of c*-algebra is used to describe fields in compactified space-time dimensions characterized by topologies of the type $ \Gamma_{D}^{d}=(\mathbb{S}^{1})^{d}\times...
The return to the quiescent state of the Anomalous X-ray pulsar XTE J1810-197 following its 2003 outburst represents a unique opportunity to probe the surface emission properties of a magnetar. The qu...
Abstract: For a finite set of points $P$ in $R^d$, the function $d_P:R^d \to R_+$ measures Euclidean distance to the set $P$. We study the number of critical points of $d_P$ when $P$ is random. In par...
Abstract: Consider the mean curvature flow of an (n+1)-dimensional, compact, mean convex region in Euclidean space (or, if n<7, in a Riemannian manifold). We prove that elements of the m-th homotopy g...

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