Related papers: Position paper: Towards an observer-oriented theor…
The description of an observer's measurement in general relativity and the standard model of particle physics is closely related to the spacetime metric. In order to understand and interpret measurements, which test the metric structure of…
This paper proposes an algebraic observer-based modulating function approach for linear time-variant systems and a class of nonlinear systems with discrete measurements. The underlying idea lies in constructing an observability…
We present a model to measure the similarity in appearance between different materials, which correlates with human similarity judgments. We first create a database of 9,000 rendered images depicting objects with varying materials, shape…
We propose a new visual hierarchical representation paradigm for multi-object tracking. It is more effective to discriminate between objects by attending to objects' compositional visual regions and contrasting with the background…
We consider the problem of adaptive observer design in the settings when the system is allowed to be nonlinear in the parameters, and furthermore they are to satisfy additional feasibility constraints. A solution to the problem is proposed…
The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of…
Topological data analysis provides a collection of tools to encapsulate and summarize the shape of data. Currently it is mainly restricted to \emph{mapper algorithm} and \emph{persistent homology}. In this paper we introduce new…
Measurement is an integral part of modern science, providing the fundamental means for evaluation, comparison, and prediction. In the context of visualization, several different types of measures have been proposed, ranging from approaches…
We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
The description of Wigner-friend scenarios -- in which external agents describe a closed laboratory containing a friend making a measurement -- remains problematic due to the ambiguous nature of quantum measurements. One option is to…
The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the…
This paper deals with the state estimation for max-plus linear systems. This estimation is carried out following the ideas of the observer method for classical linear systems. The system matrices are assumed to be known, and the observation…
We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective…
In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…
In this work we discuss the notion of observable - both quantum and classical - from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann's…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
We present a novel approach to visually locate bodies of research within the sciences, both at each moment of time and dynamically. This article describes how this approach fits with other efforts to locally and globally map scientific…