arXiv research

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

We prove that the Witten--Reshetikhin--Turaev $\mathrm{SU}(2)$ quantum representations of mapping class groups are always irreducible in the case of surfaces equipped with colored banded points, provided that at least one banded point is colored by one. We thus generalize a well--known result due to J. Roberts.

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…

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…

Study proves rigidity of harmonic maps from 2-torus to complex projective space.

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…

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

Inspired by Gromov's work on 'Metric inequalities with scalar curvature' we establish band width inequalities for Riemannian bands of the form $(V=M\times[0,1],g)$, where $M^{n-1}$ is a closed manifold. We introduce a new class of orientable manifolds we call filling enlargeable and prove: If $M$ is filling enlargeable…

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 study the problem of defining maps on link Floer homology induced by unoriented link cobordisms. We provide a natural notion of link cobordism, disoriented link cobordism, which tracks the motion of index zero and index three critical points. Then we construct a map on unoriented link Floer homology associated to a …

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…

As adversarial attacks pose a serious threat to the security of AI system in practice, such attacks have been extensively studied in the context of computer vision applications. However, few attentions have been paid to the adversarial research on automatic path finding. In this paper, we show dominant adversarial exam…

The paper proves rigidity for certain product spaces and bounds for band widths.

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 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.

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…

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.

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

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…

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.

A new geometric framework resolves singularities in anomalous transport.

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

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.

The paper explores surgeries on lens spaces and their knot properties.

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.

Let $B$ be a Möbius band and $f:B \to \mathbb{R}$ be a Morse map taking a constant value on $\partial B$, and $\mathcal{S}(f,\partial B)$ be the group of diffeomorphisms $h$ of $B$ fixed on $\partial B$ and preserving $f$ in the sense that $f\circ h = f$. Under certain assumptions on $f$ we compute the group $π_0\mathc…

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…

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

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