Related papers: Symmetry and Contextuality
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
As science and engineering have become increasingly data-driven, the role of optimization has expanded to touch almost every stage of the data analysis pipeline, from signal and data acquisition to modeling and prediction. The optimization…
Symmetry tests provide an important probe for the structure of elementary particle interactions and for the validity of the standard model. However, it is pointed out that in the interpretation of such experiments one must keep in mind that…
Supersymmetry remains compelling theory over 30 years in spite of lack of its discovery. It could be already near the corner our days, therefore present and upcoming experiments are crucial for constraining or even discovery of the…
An asymmetry exists between time and space in the sense that physical systems inevitably evolve over time whereas there is no corresponding ubiquitous translation over space. The asymmetry, which is presumed to be elemental, is represented…
Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters…
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the…
In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel…
The purpose of this article is to show that on an open and dense set, complete integrability implies the existence of symmetry.
Symmetry breaking is a fundamental concept in understanding quantum phases of matter, studied so far mostly through the lens of local order parameters. Recently, a new entanglement-based probe of symmetry breaking has been introduced under…
The concept of an $i$-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of $i$-symmetrizations are introduced and the relations between…
The paper discusses the problem of demarcation between the dimensions of natural and the human sciences in contemporary cosmology. In spite of a common presumption that cosmology is a natural science, the specificity of its alleged subject…
We discuss the applicability of the programme of decoherence -- emergence of approximate classical behaviour through interaction with the environment -- to cases where it was suggested that the presence of symmetries would lead to exact…
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…
The question of the nature of space around us has occupied thinkers since the dawn of humanity, with scientists and philosophers today implicitly assuming that space is something that exists objectively. Here we show that this does not have…
General relativity poses serious problems for counterfactual propositions peculiar to it as a physical theory. Because these problems arise solely from the dynamical nature of spacetime geometry, they are shared by all schools of thought on…