Related papers: Abstract Concept of Changeable Set
The most successful "Standard Model" allows one to define the so-called "Elementary Particles". Now from another point of view, philosophical, how can we think of them? Which kind of a status can be attributed to Elementary Particles and…
There is a deeply entrenched view in philosophy and physics, the closed systems view, according to which isolated systems are conceived of as fundamental. On this view, when a system is under the influence of its environment this is…
Model sets (also called cut and project sets) are generalizations of lattices. Here we show how the self-similarities of model sets are a natural replacement for the group of translations of a lattice. This leads us to the concept of…
Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more…
Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or…
We introduce a new concept, `(topological) (vacuum) parallel world, ' which is a new tool to research submanifolds. Roughly speaking, `Observables in (T)QFT' is equal to `a (topological) modification of space-time.' In other words, we give…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
This paper proposes a formal cognitive framework for problem solving based on category theory. We introduce cognitive categories, which are categories with exactly one morphism between any two objects. Objects in these categories are…
In this note one tries to venture into a study of some notions, in the context of a (unital) normed algebra, in particular the algebra of operators on a Hilbert space. Namely, one considers ``moving norms'', i.e.\ norming an element minus a…
From classical mechanics to quantum field theory, the physical facts at one point in space are held to be independent of those at other points in space. I propose that we can usefully challenge this orthodoxy in order to explain otherwise…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity…
We investigate an extension of ZFC set theory (in an extended language) that stipulates the existence of a proper class of indiscernibles over the universe. One of the main results of the paper shows that the purely set-theoretical…
We study scattered piecewise interpretable Hilbert spaces from a model theoretic point of view. We establish strong connections between the Hilbert space structure theorems of [Chevalier Hrushovski 2021] and the model theoretic notions of…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
This paper proposes a novel perspective on learning, positing it as the pursuit of dynamical invariants -- data combinations that remain constant or exhibit minimal change over time as a system evolves. This concept is underpinned by both…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
The set splittability problem is the following: given a finite collection of finite sets, does there exits a single set that contains exactly half the elements from each set in the collection? (If a set has odd size, we allow the floor or…