arXiv research

Develops Llarull type theorems for 3D and 4D bands with spectral scalar curvature bounds.

Proves the index of a Möbius band in 4D ball equals 5.

The study refines known counterexamples in 4D to satisfy certain inequalities.

Minimal moves for surfaces in 4D discovered, linking planar and spatial moves.

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…

Satellite knots can be trivialized by a single band move.

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

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…

Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.

New rational band moves simplify knot classification.

In cellular systems, the user equipment (UE) can request a change in the frequency band when its rate drops below a threshold on the current band. The UE is then instructed by the base station (BS) to measure the quality of candidate bands, which requires a measurement gap in the data transmission, thus lowering the da…

We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose a…

New 1-parameter family of ovals identified in 4d Ricci flow classification.

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…

We show that a band-connected sum of knots $K_0$ and $K_1$ along a band $b$ is equal to the connected sum $K_0\# K_1$ if and only if $b$ is a trivial band.

Study of 4D Ricci solitons with symmetry, finding precise geometric asymptotics.

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

Many wireless networks, including 5G NR (New Radio) and future beyond 5G cellular systems, are expected to operate on multiple frequency bands. This paper considers the band assignment (BA) problem in dual-band systems, where the basestation (BS) chooses one of the two available frequency bands (centimeter-wave and mil…

Study 4D solitons with specific curvature properties, proving curvature bounds and classifying solutions.

Deep neural networks with convolutional layers usually process the entire spectrogram of an audio signal with the same time-frequency resolutions, number of filters, and dimensionality reduction scale. According to the constant-Q transform, good features can be extracted from audio signals if the low frequency bands ar…

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

New method finds arbitrage opportunities in fluctuating asset bands.

Every classical knot is band-pass equivalent to the unknot or the trefoil. The band-pass class of a knot is a concordance invariant. Every ribbon knot, for example, is band-pass equivalent to the unknot. Here we introduce the long virtual knot concordance group $\mathscr{VC}$. It is shown that for every concordance cla…

We explicitly classify all $S^1$-invariant free boundary minimal annuli and Möbius bands in $\mathbb{B}^n$. This classification is obtained from an analysis of the spectrum of the Dirichlet-to-Neumann map for $S^1$-invariant metrics on the annulus and Möbius band. First, we determine the supremum of the $k$-th normaliz…

Study surfaces in 4-manifolds using banded unlink diagrams.

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

Study negative band numbers in braids and links.

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded…

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

No free boundary Möbius bands exist in a 3D ball.

The functional significance of resting state networks and their abnormal manifestations in psychiatric disorders are firmly established, as is the importance of the cortical rhythms in mediating these networks. Resting state networks are known to undergo substantial reorganization from childhood to adulthood, but wheth…

Band selection, by choosing a set of representative bands in hyperspectral image (HSI), is an effective method to reduce the redundant information without compromising the original contents. Recently, various unsupervised band selection methods have been proposed, but most of them are based on approximation algorithms …

Paper proves rigidity for spin bands with specific conditions.

We prove optimal systolic inequalities on Finsler Mobius bands relating the systole and the height of the Mobius band to its Holmes-Thompson volume. We also establish an optimal systolic in- equality for Finsler Klein bottles of revolution, which we conjecture to hold true for arbitrary Finsler metrics. Extremal metric…

New theorem on embedding Moebius bands in 3D space.

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

Study classifies special 4D shapes with certain curvature.

Improved bound for optimal Moebius band aspect ratio.

The study finds many Möbius bands and annuli on toroids.

Band surgery is an operation relating pairs of knots or links in the three-sphere. We prove that if two quasi-alternating knots $K$ and $K'$ of the same square-free determinant are related by a band surgery, then the absolute value of the difference in their signatures is either 0 or 8. This obstruction follows from a …

Paper proposes a method to estimate confidence bands for survival random forests.

MRI images reconstructed from sub-sampled Cartesian data using deep learning techniques often show a characteristic banding (sometimes described as streaking), which is particularly strong in low signal-to-noise regions of the reconstructed image. In this work, we propose the use of an adversarial loss that penalizes b…

Defines band maps in unoriented link Floer homology forming a skein exact triangle.

Perelman's proof confirmed, new method uses 4D topology.

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

A complete list of irreducible triangulations is identified on the Möbius band.

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…