In the present article, we investigate a possibility of a real-valued map on the space of tuples of commuting trace-class self-adjoint operators, which behaves like the usual trace map on the space of trace-class linear operators. It turns out that such maps are related with continuous group homomorphisms from the Milnor’s K-group of the real numbers into the additive group of real numbers. Usi...

We discuss the first detection of anomalous microwave emission, in the Owens Valley RING5M experiment, and its interpretation in the context of the ground-based cosmicmicrowave background (CMB) experiments of the early 1990s.TheRING5M experiment was one of the first attempts to constrain the anisotropy power on sub-horizon scales, by observing a set of 7-size fields around the North Celestial P...

This paper presents a framework for considering both stereo cues and structural priors to obtain a geometrically representative depth map from a narrow baseline stereo pair. We use stereo pairs captured with a consumer stereo camera and observe that traditional depth estimation using stereo matching techniques encounters difficulties related to the narrow baseline relative to the depth of the s...

DEFINITION 1.1. Let D ⊂ R be a domain, i.e., an open connected set. (i) A time-dependent vector field on D is a pair consisting of a domain V ⊂ D × R together with a continuous map F : V → R. (ii) The time-dependent vector field F is said to be autonomous (or one simply omits the adjective time-dependent) if V = D × R and for each x ∈ D, F (x, ·) is constant. That is to say, a vector field on D...

Cartograms are a well-known technique for showing geography-related statistical information, such as population demographics and epidemiological data. The basic idea is to distort a map by resizing its regions according to a statistical parameter, but in a way that keeps the map recognizable. In this paper, we deal with the problem of making continuous cartograms that strictly retain the topolo...

We define a self-map Pal : F2 → F2 of the free group on two generators a, b, using automorphisms of F2 that form a group isomorphic to the braid group B3. The map Pal restricts to de Luca’s right iterated palindromic closure on the submonoid generated by a, b. We show that Pal is continuous for the profinite topology on F2; it is the unique continuous extension of de Luca’s right iterated palin...

Let K be a closed subset of a smooth manifold M, and let f : K ! K be a continuous self-map of K. We say that f is smoothable if it is conjugate to the restriction of a smooth map by a homeomorphism of the ambient space M. We give a necessary condition for the smoothability of the faithfully innnitely interval-renormalizable homeomorphisms of Cantor sets in the unit interval. This class contain...

We investigate the relation between preimage multiplicity and topological entropy for continuous maps. An argument originated by Misiurewicz and Przytycki shows that if every regular value of a C1 map has at least m preimages then the topological entropy of the map is at least log m. For every integer, there exist continuous maps of the circle with entropy zero for which every point has at leas...

A 3-D invertible map generating a 4-loop solenoid attractor is presented. The attractor of the "standard" 4-solenoid turns out to be "fat" that is, fractal dimensionality exceeds topological dimensionality by more than unity. If a fourth variable that is weakly damped is added to this 3-variable map, a new type of attractor is generated. In a cross section it is a continuous nowheredifTerentiab...

Using sensors to extract gestural information for control parameters of digital audio effects is common practice. There has also been research using machine learning techniques to classify specific gestures based on audio feature analysis. In this paper, we will describe our experiments in training a computer to map the appropriate audio-based features to look like sensor data, in order to pote...