Related papers: Breaking the Symmetries of Indistinguishable Objec…
In this work, we study the challenging problem of identifying the irregular status of objects from images in an "open world" setting, that is, distinguishing the irregular status of an object category from its regular status as well as…
We study creating and analyzing symmetry and broken symmetry in digital art. Our focus is not so much on computer-generating artistic images, but rather on analyzing concepts and templates for incorporating symmetry and symmetry breaking…
Modeling symmetry breaking is essential for understanding the fundamental changes in the behaviors and properties of physical systems, from microscopic particle interactions to macroscopic phenomena like fluid dynamics and cosmic…
We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced.…
If supersymmetric particles are discovered, an important problem will be to determine how supersymmetry has been broken. At collider energies, supersymmetry breaking can be parameterised by soft supersymmetry breaking parameters. Several…
Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
We introduce detector-level entanglement, a unified entanglement concept for identical particles that takes into account the possible deletion of many-particle which-way information through the detection process. The concept implies a…
In general, objects can be distinguished on the basis of their features, such as color or shape. In particular, it is assumed that similarity judgments about such features can be processed independently in different metric spaces. However,…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
How can we segment varying numbers of objects where each specific object represents its own separate class? To make the problem even more realistic, how can we add and delete classes on the fly without retraining or fine-tuning? This is the…
Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
Humans have a natural instinct to identify unknown object instances in their environments. The intrinsic curiosity about these unknown instances aids in learning about them, when the corresponding knowledge is eventually available. This…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
We consider the problem of optimally insulating a given domain $\Omega$ of ${\mathbb{R}}^d$; this amounts to solve a nonlinear variational problem, where the optimal thickness of the insulator is obtained as the boundary trace of the…
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how…