Topological invariants of spatial databases (i.e., finite structures that capture thetopological properties of the database) are receiving increasing attention since theycan act as a basic structure to tackle relevant problems in the field (e.g., assessmentof the topological equivalence). In this paper, the novel notion of boundary decom-position of a topological invariant is in...

Isomap is one of widely-used low-dimensional embedding methods, where geodesic distances on a weighted graph are incorporated with the classical scaling (metric multidimensional scaling). In this paper we pay our attention to two critical issues that were not considered in Isomap, such as: (1) generalization property (projection property); (2) topological stability. Then we present a robust ker...

We show the existence of an infinite monothetic Polish topological group G with the fixed point on compacta property. Such a group provides a positive answer to a question of Mitchell who asked whether such groups exist, and a negative answer to a problem of R. Ellis on the isomorphism of L(G), the universal point transitive G-system (for discrete G this is the same as PG the Stonetech compacti...

This paper presents a novel layout model and floorplanning tool particularly suitable for taking into account user defined layout constraints on specific sets of modules and specific locations. The user defined layout constraints can be the setting of any common topological property associated with a group of specific modules such as the neighboring property for example. Or the use of any topol...

A match-to-sample task was performed, in which observers compared configurations of line segments presented stereoscopically in different three-dimensional orientations. Several different structural properties of these configurations were manipulated, including the relative orientations of line segments (a Euclidean property), their coplanarity (an affine property), and their patterns of cointe...

The underlying idea of the ESOM [2] is to incorporate the topological neighborhood preserving property of Self-Organizing Map (SOM) and the convex-hull property (a global optimality) of TSP together. The learning rule of its generalized version is as follows: ! w j(t+ 1) = cj(t) [ ! w j(t) + j(t) ( ! x t !w j(t))] where !w j is the weight of jth neuron, !x t the input city coordinate, cj(t) the...

We study mixing properties (topological mixing and weak mixing of arbitrary order) for nonautonomous linear dynamical systems that are induced by the corresponding dynamics on certain invariant sets. The type of nonautonomous systems considered here can be defined by a sequence (Ti)i∈N of linear operators Ti : X → X on a topological vector space X such that there is an invariant set Y for which...

This paper presents a compression scheme for digital still images, by using the Kohonen's neural network algorithm, not only for its vector quantization feature, but also for its topological property. This property allows an increase of about 80% for the compression rate. Compared to the JPEG standard, this compression scheme shows better performances (in terms of PSNR) for compression rates hi...

A topological group G has the Approximate Fixed Point (AFP) property on a bounded convex subset C of a locally convex space if every continuous affine action of G on C admits a net ( x i ) , x i ∈ C , such that x i - g ⁢ x i ⟶ 0 for all g ∈ G . In this work, we study the relationship between this property and amenability.