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.
Proves Yoshikawa eighth move's independence and finds minimal band moves.
problem Proving the independence of Yoshikawa eighth move and finding minimal generating set of band moves.
method Defining twisted diagrams and mirror cut surfaces, using surface-link groups.
result Proves independence of Yoshikawa eighth move and finds minimal generating set of band moves.
New bounds on knot complexity defined via band number and surface diagrams.
problem Understanding the complexity of knots and their generalizations.
method Defining and analyzing band number, using broken surface diagrams and 3-manifold embeddings.
result Band number is an upper bound on double slice genus, a knot complexity measure.
Study finds new knot distances and chirally cosmetic bands using grid diagrams.
problem Computing distances and identifying chirally cosmetic bands between knots.
method Using grid diagrams to explore non-coherent band attachments between knots.
result Discovery of 33 new H(2)-distance one pairs for knots up to 8 crossings.
The abstract extends Reidemeister theorem to 3-manifolds using diagrams of links and bands.
problem Extending Reidemeister theorem to 3-manifolds.
method Defines diagrams for links and bands on spines and flow-spines of 3-manifolds and describes combinatorial moves.
result Reproves and extends Brand et al. result on 3-manifolds.
The paper studies isotopies of surfaces in 4-manifolds using banded unlink diagrams.
problem Isotopies of surfaces in 4-manifolds.
method Complete set of moves relating banded unlink diagrams of isotopic surfaces.
result Bridge trisections of isotopic surfaces in a trisected 4-manifold are related by a sequence of perturbations and deperturbations.
A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary cir…
Axel Seeliger tabulated ribbon knots and found non-symmetric examples.
problem Identifying non-symmetric ribbon knots.
method Tabulated symmetric union presentations and band diagrams for ribbon knots.
result Found non-symmetric ribbon knots with 11 and 12 crossings.
A new invariant for links in lens spaces with advantages over traditional methods.
problem Invariants for links in lens spaces.
method Constructing a virtual quandle for links in lens spaces L(p,1). result The virtual quandle is an essential invariant and its presentation can be easily written from a link's band diagram.
Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right zero semigroups and rectangular bands. The ideal properties of higher order rect…
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 n-valent graph is the spine of a bridge multisection for an unknotted surface. We introduce a matrix representation of a chord on a tangle which leads us to representing tangle chord diagrams as stacks of matrices that we call books. We show that band sum moves, Reidemeister moves as well as orientation changes are implemented on \widetilde{Z}_f - a framed link invariant constructed from the Kont…
Classical and welded knot moves are classified and their interrelationships discussed.
problem Classical and welded knot moves and their interrelationships.
method Algebraic classification and topological interpretations of local moves.
result All local moves are unknotting operations for welded knots.
Develops robust persistence diagrams using kernel methods.
problem Persistence diagrams are sensitive to data perturbations.
method Constructs robust persistence diagrams from superlevel filtrations of robust density estimators using reproducing kernels.
result Robust persistence diagrams are consistent estimators in bottleneck distance.
The paper explores methods to construct knots with diffeomorphic 0-traces.
problem Constructing knots with diffeomorphic 0-traces. method Survey of Gompf-Miyazaki's dualizable pattern, Abe-Jong-Omae-Takeuchi's band presentation, and RGB-diagram.
result A sufficient condition for two knots obtained by Abe-Jong-Omae-Takeuchi's method to coincide.
Researchers find minimal-area metrics on surfaces with constraints.
problem Finding the conformal metric of least area on surfaces with length conditions.
method Numerical convex programs to solve the minimal-area problem.
result The metric is positively curved in some regions and flat in others.
Basket links are shown to be isotopic to T(2,n+1).
problem Understanding isotopy of basket links to torus links.
method Using symmetrized Seifert form congruence to An matrix. result Basket links are isotopic to T(2,n+1). Let L be an oriented link with an alternating diagram D. It is known that L is a fibered link if and only if the surface R obtained by applying Seifert's algorithm to D is a Hopf plumbing. Here, we call R a Hopf plumbing if R is obtained by successively plumbing finite number of Hopf bands to a disk. In t…
In this paper the properties of the Kauffman bracket skein module of L(p,q) are investigated. Links in lens spaces are represented both through band and disk diagrams. The possibility to transform between the diagrams enables us to compute the Kauffman bracket skein module on an interesting class of examples consisti…
In 1993 K. Habiro defined Ck-move of oriented links and around 1994 he proved that two oriented knots are transformed into each other by Ck-moves if and only if they have the same Vassiliev invariants of order ≤k−1. In this paper we define Vassiliev invariant of type (k1,...,kl), and show that, for $k=k…
We study the ribbon discs that arise from a symmetric union presentation of a ribbon knot. A natural notion of symmetric ribbon number is introduced and compared with the classical ribbon number. We show that the gap between these numbers can be arbitrarily large by constructing an infinite family of ribbon knots with …
The abstract introduces a method to compute surface invariants in 4-manifolds.
problem Computing invariants of surfaces embedded in 4-manifolds.
method Using a nested pair of ribbon fusion categories and banded-link presentations.
result The method provides an invariant sensitive to both genus and knotting.
Minimal moves for surfaces in 4D discovered, linking planar and spatial moves.
problem Finding the minimal set of moves for surfaces in 4D.
method Derived minimal generating set of spatial moves, translated into planar moves.
result Minimal generating set of spatial moves for surfaces in 4D.
The paper compares isotopic and diffeomorphic links in lens spaces.
problem Comparing isotopic and diffeomorphic links in lens spaces.
method Provides a set of moves on disk, band, and grid diagrams to connect diffeomorphic links.
result There are up to four isotopy equivalent links in each diffeo equivalence class.
This paper computes the Homflypt skein module of lens spaces using braids.
problem Computing the Homflypt skein module of lens spaces L(p,1). method Using Lambropoulou invariant and braid band moves on a basis of the solid torus.
result Established the connection and computed the Homflypt skein module of lens spaces.
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…
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 generalize bridge trisections to surfaces in four-manifolds, linking them to braided links.
problem Embedding surfaces in four-manifolds and understanding their braiding.
method Introducing bridge trisections, isotoping surfaces, and using trisections and open-book decompositions.
result Any neatly embedded surface can be isotoped to lie in bridge trisection position with respect to any trisection of the four-manifold.
New invariant shows fifth move is unique and extends biquandle theory for surface-links.
problem Reproduce Yoshikawa's fifth move using other moves and isotopies.
method Develops a semi-invariant and biquandle-based invariant for surface-links.
result Yoshikawa's fifth move is unique and cannot be reproduced by other moves.
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.
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.
The paper finds and visualizes unique geometric polyhedra and tori with few vertices.
problem Finding and visualizing geometric polyhedra and tori with specific vertex configurations.
method Using Schlegel diagrams and geometric realization in 3D and 4D space.
result Identifies and visualizes 12 triangulations of the 2-torus and 12 triangulations of the 2D projective plane.
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.
Paper tackles BA in dual-band systems using ML.
problem Choosing the best frequency band for communication in dual-band systems.
method Formulated as binary classification problem, proposed supervised ML solutions.
result Analytical and Viterbi Algorithm-based solutions for directional BA.
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.
Band surgery affects knot signatures by 0 or 8.
problem Understanding how band surgery impacts knot signatures.
method Using Heegaard Floer d-invariants and L-space properties.
result The absolute value of signature difference is 0 or 8 for quasi-alternating knots related by band surgery.
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 S1-invariant free boundary minimal annuli and Möbius bands in Bn.
problem Classifying S1-invariant free boundary minimal annuli and Möbius bands in Bn. method Analysis of the spectrum of the Dirichlet-to-Neumann map for S1-invariant metrics. result Existence and classification of S1-invariant free boundary minimal annuli and Möbius bands in Bn. 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.
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.
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.
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.
Study of cosmetic bandings on knots and links, including a counterexample.
problem Cosmetic bandings on knots and links and their impact on knot types.
method Examples and counterexamples of cosmetic bandings, hyperbolic knot analysis.
result A counterexample to a conjecture about chirally cosmetic surgeries.
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 group shows knots can't always be simplified.
problem Understanding concordance in long virtual knots.
method Introduced long virtual knot concordance group and proved a band-pass invariant not a concordance invariant.
result For every concordance class, there exists a knot not band-pass equivalent to the original or other specific 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.