Satellite knots can be trivialized by a single band move.
problem Satellite knots and their trivialization.
method Infinite family of satellite knots and a single band move.
result No disjoint band unknotting exists for satellite knots.
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48 results for “trivial band”
Knots connected via a trivial band sum to connected sum.
problem Conditions for band-connected sum to equal connected sum.
method Analyzing knots and bands to determine conditions for equality.
result A band is trivial if and only if a band-connected sum equals a connected sum.
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…
There is a nonribbon 2-link all of whose components are trivial 2-knots and one of whose band-sums is a nonribbon 2-knot.
Proves special alternating knots cannot be decomposed as non-trivial band sums.
problem Understanding the structure and properties of special alternating knots.
method Analyzes concordance properties and uses band sums to restrict knot decompositions.
result Conjecture that special alternating knots are ribbon concordance minimal is verified in many cases.
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…
Knots from a specific band sum have similar homologies but are distinct.
problem Cosmetic crossing conjecture for knots from a specific band sum.
method Analyzing knot homologies (Heegaard, instanton, Khovanov) to verify distinctness.
result Knots from the band sum are distinct despite similar homologies.
The Rosenberg index vanishes if a manifold admits a wide Riemannian band or cube-like domain.
problem Proving the Rosenberg index does not vanish for certain manifolds.
method Analyzing isometric immersions of wide Riemannian bands and cube-like domains on spin manifolds.
result Closed spin manifolds with infinite -width have non-vanishing Rosenberg index.
In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML estimator, three approximate algorithms are presented: a binary quadratic programming (BQP) algorit…
We prove the following results (1) (2) (3) on relations between -links and their components. (1) Let L=(L_1, L_2) be a (4k+1)-link (4k+1\geq 5). Then we have Arf L=Arf L_1+Arf L_2. (2) Let L=(L_1, L_2) be a (4k+3)-link (4k+3\geq3). Then we have σL=σL_1+σL_2. (3) Let n\geq1. Then there is a nonribbon n-link L=(L_1, L…
We give a classification of -component links up to -move. In order to prove this classification, we characterize Brunnian links, and have that a Brunnian link is ambient isotopic to a band sum of trivial link and Milnor's links.
Paper proves uniqueness of bridge multisections for surfaces in 4-space.
problem Tackles the combinatorial description of surface links in 4-space.
method Develops a surgery operation called band surgery to prove uniqueness.
result Proves any -valent graph is the spine of a bridge multisection for an unknotted surface.
The paper provides bounds on the CDF of a variable under nonstationary conditions.
problem Estimating the complete distribution of a random variable under nonstationary conditions.
method Time-uniform and value-uniform bounds on the CDF of the running averaged conditional distribution.
result Presented computationally efficient bounds that are always valid and sometimes trivial.
The paper examines cosmetic two-strand twists on fibered knots and their properties.
problem When does a two-strand twist of a fibered knot produce an isotopic knot?
method Generalized crossing changes and non-coherent band surgeries were defined and analyzed.
result Fibered knots in rational homology spheres admit no cosmetic generalized crossing changes.
Hodge Topology of Semiclassical Transport: A Coordinate-Free Geometric Framework for the Anomalous Hall Effect and Non-Linear Berry Dipolecond-mat.mes-hall
A new geometric framework resolves singularities in anomalous transport.
problem Mathematical singularities in quantum Berry connections.
method Hodge-de Rham decomposition of the Brillouin zone.
result A smooth geometric proxy potential for anomalous transport.
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…
Virtual Knot Cobordismmath.GT
This paper defines a theory of cobordism for virtual knots and studies this theory for standard and rotational virtual knots and links. Non-trivial examples of virtual slice knots are given. Determinations of the four-ball genus of positive virtual knots are given using the results of a companion paper by the author an…
A flat plumbing basket is a surface consisting a disk and finitely many bands which are contained in distinct pages of the trivial open book decomposition of . In this paper, we construct a Legendrian link from a flat plumbing basket, and we describe a relation among the self-linking number, the Thursto…
Paper proves a noncompact version of Gromov's band-width estimate.
problem Proving a precise upper bound for noncompact Riemannian bands.
method Developed a quantitative partitioned manifold index theory.
result Proved a version of Gromov's band-width estimate for noncompact Riemannian bands.
Deep learning optimizes wireless band switching without measurement gaps.
problem Wireless networks waste data during band switching due to measurement gaps.
method Online-learning based classifier models exploiting spatial and spectral correlation.
result 30% improvement in mean effective rates compared to industry standard.
New classification of Serrin domains using algebraic curves and periodic solutions.
problem Classifying Serrin planar domains with specific boundary conditions.
method Algebraic geometry and mKdV hierarchy analysis.
result Ordered Serrin ring domains into finite complexity levels with detailed examples.
Study shows upper limit for torical band width with spectral curvature bounds.
problem Understanding the band width of torical bands with spectral curvature constraints.
method Used the warped \( μ\)-bubble method with spectral curvature bounds.
result Upper bound for the band width of torical bands is established.
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…
New rational band moves simplify knot classification.
problem Classifying knots using rational moves.
method Introduced oriented rational band moves and proved their effectiveness.
result Knots that can be unlinkified by rational moves are rationally slice.
Classifies -invariant free boundary minimal annuli and Möbius bands in .
problem Classifying -invariant free boundary minimal annuli and Möbius bands in .
method Analysis of the spectrum of the Dirichlet-to-Neumann map for -invariant metrics.
result Existence and classification of -invariant free boundary minimal annuli and Möbius bands in .
Optimal clustering framework selects bands for hyperspectral images.
problem Efficiently choosing representative bands in hyperspectral images.
method Proposes an optimal clustering framework (OCF) and rank on clusters strategy (RCS) for band selection.
result Significantly outperforms other methods on various data sets.
Nonparametric, Nonasymptotic Confidence Bands with Paley-Wiener Kernels for Band-Limited Functionsstat.ML
The paper creates nonparametric confidence bands for band-limited functions.
problem Estimating confidence bands for band-limited functions with finite samples and unknown noise.
method Uses Paley-Wiener reproducing kernel Hilbert spaces and gradient-perturbation methods.
result Non-asymptotic guarantees for confidence regions without assuming a parametric model.
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…
New method removes MRI banding without post-processing.
problem MRI banding in reconstructed images.
method Adversarial training to penalize banding structures.
result Superior banding removal compared to baseline.
A new neural network separates singing voices more effectively.
problem Separating singing voices from mixed signals with high accuracy.
method MBR-FCN that processes different frequency bands with varying resolutions and filters.
result The MBR-FCN achieves better performance with fewer parameters.
Paper shows that for torus knots, the pinch number equals the unoriented band unknotting number.
problem Determining the minimum number of band surgeries to unknot torus knots.
method Used the torsion order of unoriented knot Floer homology.
result Pinch number and unoriented band unknotting number coincide for torus knots.
New method finds arbitrage opportunities in fluctuating asset bands.
problem Finding arbitrage opportunities in fluctuating asset bands.
method Formulate as maximizing volatility within a price band, using convex-concave optimization.
result Approximately solves non-convex optimization problem for moving-band arbitrage.
Develops Llarull type theorems for 3D and 4D bands with spectral scalar curvature bounds.
problem Bounding scalar curvature and metric on 3D and 4D bands simultaneously.
method Warped -bubble method
result Establishes 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 . It is shown that for every concordance cla…
Study surfaces in 4-manifolds using banded unlink diagrams.
problem Representing and manipulating immersed surfaces in 4-manifolds.
method Singular banded unlink diagrams and associated moves.
result Every immersed surface can be represented uniquely by a singular banded unlink diagram.
The paper improves nonparametric confidence bands for band-limited functions.
problem Constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees.
method Based on Paley-Wiener reproducing kernel Hilbert spaces, the paper relaxes assumptions, improves noise estimation, and tightens constraints.
result Enhanced confidence bands with improved efficiency and tighter constraints.
On the negative band numbermath.GT
Study negative band numbers in braids and links.
problem Characterizing braids with negative band numbers.
method Using Birman, Ko, and Lee's left-canonical form.
result Characterize strongly and almost strongly quasipositive braids.
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.
problem Finding the smallest aspect ratio for Möbius bands with many twists.
method Constructs a folded paper ribbon knot to bound the aspect ratio.
result Paper Möbius bands and annuli with any number of half-twists can be embedded with aspect ratio less than 8.
Maturation Trajectories of Cortical Resting-State Networks Depend on the Mediating Frequency Bandq-bio.NC
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…
No free boundary Möbius bands exist in a 3D ball.
problem Proving the non-existence of Möbius bands with free boundaries in a 3D ball.
method Analytical proof based on geometric properties.
result Proves the non-existence of free boundary Möbius bands in the unit three-ball.
The paper establishes new band width inequalities for Riemannian bands.
problem Band width inequalities for Riemannian bands.
method Introduced filling enlargeable manifolds and used them to prove band width inequalities.
result If a manifold is filling enlargeable, then the band width is bounded.
Paper proves rigidity for spin bands with specific conditions.
problem Proving rigidity for initial data sets on spin bands.
method Using Dirac operator techniques and lightlike imaginary -Killing spinors.
result Obtains slight generalizations of known rigidity results.
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.
problem Proving the impossibility of placing uncountably many disjoint Moebius bands in 3D space.
method Generalization of Grushin and Palamodov's result to tame subsets in R^N and arbitrary topological embeddings in R^3.
result The impossibility of embedding uncountably many pairwise disjoint Moebius bands in 3D space, even for arbitrary topological embeddings.
Improved bound for optimal Moebius band aspect ratio.
problem Finding the optimal aspect ratio of a Moebius band.
method Optimization problem to find the smallest possible aspect ratio of a smoothly embedded Moebius band.
result The new bound is at least , significantly improving on previous bounds.
The study finds many Möbius bands and annuli on toroids.
problem Finding minimal surfaces on toroids.
method Equivariant variational methods.
result Linear growth of surface areas with symmetry order.
Band surgery is an operation relating pairs of knots or links in the three-sphere. We prove that if two quasi-alternating knots and 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 …