Related papers: Braid analysis of (low-dimensional) chaos
Gravitational anomalies can be realized on the boundary of topologically ordered states in one higher dimension and are described by topological orders in one higher dimension. In this paper, we try to develop a general theory for both…
The Standard Model of particle physics provides very accurate predictions of phenomena occurring at the sub-atomic level, but the reason for the choice of symmetry group and the large number of particles considered elementary, is still…
We propose an algorithm for deciding whether a given braid is pseudo-Anosov, reducible, or periodic. The algorithm is based on Garside's weighted decomposition and is polynomial-time in the word-length of an input braid. Moreover, a…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…
Using the ordered analogue of Farley-Sabalka's discrete gradient field on the configuration space of a graph, we unravel a levelwise behavior of the generators of the pure braid group on a tree. This allows us to generalize Farber's…
Graph theory has drawn a lot of attention in the field of Neuroscience during the last decade, mainly due to the abundance of tools that it provides to explore the interactions of elements in a complex network like the brain. The local and…
We study simple branched coverings of degree d of the 2- and 3- dimensional sphere branched over oriented links. We demonstrate how to use braid charts to develop embeddings of these into $S^k \times D^2$ for $k=2,3 when $d=2,3$. This is an…
We define an action of Artin's braid group on a finite dimensional algebra.
We give an algorithm to decide if a given braid is a product of two factors which are conjugates of given powers of standard generators of the braid group. The same problem is solved in a certain class of Garside groups including Artin-Tits…
The deep connection among braids, knots and topological physics has provided valuable insights into studying topological states in various physical systems. However, identifying distinct braid groups and knot topology embedded in…
Topological phases of noninteracting particles are distinguished by global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses…
Physics concepts have often been borrowed and independently developed by other fields of science. In this perspective a significant example is that of entropy in Information Theory. The aim of this paper is to provide a short and…
Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
Random braids that are formed by multiplying randomly chosen permutation braids are studied by analyzing their behavior under Garside's weighted decomposition and cycling. Using this analysis, we propose a polynomial-time algorithm to the…
In this paper we present a detailed study of \emph{bonded knots} and their related structures, integrating recent developments into a single framework. Bonded knots are classical knots endowed with embedded bonding arcs modeling physical or…
We study interactions amongst topologically conserved excitations of quantum theories of gravity, in particular the braid excitations of four-valent spin networks. These have been shown previously to propagate and interact under evolution…
Algebraic topology (homology) is used to analyze the weakly turbulent state of spiral defect chaos in both laboratory experiments and numerical simulations of Rayleigh-Benard convection.The analysis reveals topological asymmetries that…
The spin network quantum simulator relies on the su(2) representation ring (or its q-deformed counterpart at q= root of unity) and its basic features naturally include (multipartite) entanglement and braiding. In particular, q-deformed spin…