Related papers: Position paper: Towards an observer-oriented theor…
Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The…
The perception-related origins of physical measures and standards are considered within the framework of the general observer theory. The impact of observer characteristics on the development of observer-centric physics, physical concepts…
We propose a formal framework for understanding and unifying the concept of observers across physics, computer science, philosophy, and related fields. Building on cybernetic feedback models, we introduce an operational definition of…
In both quantum mechanics and relativity theory, the concept of the observer plays a critical role. However, there is no consensus on the definition of observer in these theories. Following Einstein's thought experiments, one could ask:…
Mathematical theory of an observer is elaborated upon the basis of A.Poincare's ideas on the nature of geometry and the role of observer's perceptive space. The said theory is generalizing reference frames theory in GR. Physical structure…
This paper is a small step towards the goal of constructing a coherent theory of physic and mathematics together. It is based on two ideas, the localization of mathematical systems in space or space time, and the separation of the concepts…
The motivation for using qualitative shape descriptions is as follows: qualitative shape descriptions can implicitly act as a schema for measuring the similarity of shapes, which has the potential to be cognitively adequate. Then, shapes…
A quantum mechanical observer might be describable as having a reference system that is a superposition of classical inertial reference frames. The present paper suggests a possible weighting function in such superpositions, determined by…
In previous work, we introduced a method for modeling a configuration of objects in 2D and 3D images using a mathematical "medial/skeletal linking structure." In this paper, we show how these structures allow us to capture positional…
This paper frames a general prediction system as an observer traveling around a continuous space, measuring values at some locations, and predicting them at others. The observer is completely agnostic about any particular task being solved;…
Physical systems are characterized by their structure and dynamics. But the physical laws only express relations, and their symmetries allow any possible relational structure to be also possible in a different parametrization or basis of…
Relying on the equivalence principle, a first approach of the general theory of relativity is presented using the spacetime metric of an observer with a constant proper acceleration. Within this non inertial frame, the equation of motion of…
The paper \cite{Dance0601} tentatively suggested a physical picture that might underlie string theories. The string parameters $\tau $ and $\sigma_i $ were interpreted as spacetime dimensions which a simple quantum mechanical observer can…
For arbitrary linear time-invariant systems, the existence of a strong functional observer is investigated. Such observer determines, from the available measurement on the plant, an estimate of a function of the state and the input. This…
Position representation is crucial for building position-aware representations in Transformers. Existing position representations suffer from a lack of generalization to test data with unseen lengths or high computational cost. We…
The purpose of this paper is to give an overview of the operator structure of frames, where the operator belongs to certain classes of linear operators and the element belongs to $H$. We discuss the size of the set of such elements. Also,…
The personal spatial structure of an observer is introduced as a central element in the positioning of objects in space. The link between a reference frame used by an observer and his personal spatial structure is discussed. Research on…
Interpretations of quantum theory have traditionally assumed a "Galilean" observer, a bare "point of view" implemented physically by a quantum system. This paper investigates the consequences of replacing such an…
The concept of {\em complexity} (as a quantity) has been plagued by numerous contradictory and confusing definitions. By explicitly recognising a role for the observer of a system, an observer that attaches meaning to data about the system,…
This paper utilizes the recently proposed cubic observer to estimate the state of a class of nonlinear systems. The cubic observer is proposed as an alternative to linear observers for improved convergence rate and robustness. It is shown…