arXiv research

Paper shows that for torus knots, the pinch number equals the unoriented band unknotting number.

Study negative band numbers in braids and links.

New bounds on knot complexity defined via band number and surface diagrams.

We consider a relation between two kinds of unknotting numbers defined by using a band surgery on unoriented knots; the band-unknotting number and H(2)-unknotting number, which we may characterize in terms of the first Betti number of surfaces in S^3 spanning the knot and the trivial knot. We also give several examples…

Every link is shown to be presentable as a boundary of an unknotted flat banded surface. A (flat) banded link is defined as a boundary of an unknotted (flat) banded surface. A link's (flat) band index is defined as the minimum number of bands required to present the link as boundaries of an unknotted (flat) banded surf…

We categorise coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterise the minimal coherent band pathways (with intermediates) between any two knots or 2-component links with small crossing number. We demonstrate these band surgeries for knots and links with small cr…

Optimal clustering framework selects bands for hyperspectral images.

Study shows torsion order bounds band-unlinking number for knot cobordisms.

Paper shows how to embed Möbius bands with many twists and small aspect ratios.

Improved bound for optimal Moebius band aspect ratio.

Attaching a 2-handle to a genus two or greater boundary component of a 3-manifold is a natural generalization of Dehn filling a torus boundary component. We prove that there is an interesting relationship between an essential surface in a sutured 3-manifold, the number of intersections between the boundary of the surfa…

Knots from a specific band sum have similar homologies but are distinct.

The paper makes inference methods available for Gaussian models with banded precision.

A new neural network separates singing voices more effectively.

We describe the genus two knots which admit a genus one, one bridge position. These are divided into several families, one consists of vertical bandings of two genus one $(1,1)$-knots, other consists of vertical bandings of two cross cap number two 2-bridge knots, and the last one consists of genus two tunnel number on…

Study finds new knots that bound Möbius bands in 4D space.

Paper proposes efficient data-driven confidence bands for distributed nonparametric regression.

Study finds new knot distances and chirally cosmetic bands using grid diagrams.

Proves bounds on ribbonlength for various knot types.

Study on nodal components of random band-limited functions on surfaces, finding a universal law.

The paper finds minimal-area metrics on polygons with multiple crossing geodesics.

New method constructs confidence bands for ODE models with unknown regulatory effects.

EGO-MDA identifies optimal spectral-bands for process discrimination.

Confidence bands for tuning curves improve hyperparameter comparison in NLP.

Machine learning predicts band gaps for large organic crystals.

WideBNet learns inverse scattering from wide-band data efficiently and stably.

Floer homology bounds knot properties like bridge index and ribbon distance.

We give an obstruction to unknotting a knot by adding a twisted band, derived from Heegaard Floer homology.

Knots connected via a trivial band sum to connected sum.

Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the collective motion of an ensemble of system trajectories taking into account how traj…

The paper connects Chebyshev polynomials and Gram determinants on Möbius bands.

Satellite knots can be trivialized by a single band move.

Paper proves a noncompact version of Gromov's band-width estimate.

Study on knot unknotting numbers and their behavior under connected sums.

Finding minima of a real valued non-convex function over a high dimensional space is a major challenge in science. We provide evidence that some such functions that are defined on high dimensional domains have a narrow band of values whose pre-image contains the bulk of its critical points. This is in contrast with the…

Deep learning optimizes wireless band switching without measurement gaps.

Paper tackles BA in dual-band systems using ML.

Study shows upper limit for torical band width with spectral curvature bounds.

The goal of this study is to explain and examine the statistical underpinnings of the Bollinger Band methodology. We start off by elucidating the rolling regression time series model and deriving its explicit relationship to Bollinger Bands. Next we illustrate the use of Bollinger Bands in pairs trading and prove the e…

A new geometric framework resolves singularities in anomalous transport.

New rational band moves simplify knot classification.

Let X be a compact 2-manifold with nonempty boundary dX and let f: (X, dX) --> (X, dX) be a boundary-preserving map. Denote by MF_d[f] the minimum number of fixed point among all boundary-preserving maps that are homotopic through boundary-preserving maps to f. The relative Nielsen number N_d(f) is the sum of the numbe…

We will discuss a method for visual presentation of knotted surfaces in the four space, by examining a number and a position of its Morse's critical points. Using this method, we will investigate surface-knot with one critical point of index 1. Then we show infinitely many mutually distinct surface-knots that has an em…

We give a short proof that if a non-trivial band sum of two knots results in a tight fibered knot, then the band sum is a connected sum. In particular, this means that any prime knot obtained by a non-trivial band sum is not tight fibered. Since a positive L-space knot is tight fibered, a non-trivial band sum never yie…

Classifies $S^1$-invariant free boundary minimal annuli and Möbius bands in $\mathbb{B}^n$.

The paper creates nonparametric confidence bands for band-limited functions.

New method removes MRI banding without post-processing.

Complete classification of links up to specific moves.