E-tec calculates topological entropy of chaotic systems using an ensemble of trajectories.
problem Quantifying the complexity of chaotic dynamics in two-dimensional systems.
method E-tec uses an ensemble of trajectories and a rubber band to estimate topological entropy.
result E-tec provides a computationally efficient method to estimate topological entropy.
We consider coupled nonholonomic LR systems on the product of Lie groups. As examples, we study n n n -dimensional variants of the spherical support system and the rubber Chaplygin sphere. For a special choice of the inertia operator, it is proved that the rubber Chaplygin sphere, after reduction and a time reparametrizat…
Two types of differentials are shown equivalent for compactifying moduli spaces.
problem Compactifying moduli spaces of curves with prescribed orders of zeros and poles.
method Equivalence of multi-scale and logarithmic differentials, isomorphism of moduli stacks, explicit blowups.
result Multi-scale and logarithmic differentials are equivalent and isomorphic.
Integrable geodesics found on special orthogonal group.
problem Analyzing normal geodesics on the special orthogonal group.
method Adapted Lax pair and bi-Hamiltonian structure.
result Almost all normal geodesics are completely integrable.
We relate a Chaplygin type system to a Cartan decomposition of a real semi-simple Lie group. The resulting system is described in terms of the structure theory associated to the Cartan decomposition. It is shown to possess a preserved measure and when internal symmetries are present these are factored out via a process…
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.
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.
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 S 1 S^1 S 1 -invariant free boundary minimal annuli and Möbius bands in B n \mathbb{B}^n B n .
problem Classifying S 1 S^1 S 1 -invariant free boundary minimal annuli and Möbius bands in B n \mathbb{B}^n B n . method Analysis of the spectrum of the Dirichlet-to-Neumann map for S 1 S^1 S 1 -invariant metrics. result Existence and classification of S 1 S^1 S 1 -invariant free boundary minimal annuli and Möbius bands in B n \mathbb{B}^n B n . 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.
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 μ μ μ -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 V C \mathscr{VC} VC . 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.
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…
Simple proof shows uncountable Möbius bands are impossible in space.
problem Proving the impossibility of uncountably many disjoint Möbius bands in 3D space.
method Algebraic proof
result Proves uncountable Möbius bands are impossible in R 3 \mathbb{R}^3 R 3 and higher dimensions. A 2-link with trivial components has a nonribbon band-sum.
problem Characterizing nonribbon 2-links.
method Examining specific 2-links and their band-sums.
result Found a nonribbon 2-link with trivial components and a nonribbon band-sum.
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.
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.
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.
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.
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 W W W -Killing spinors. result Obtains slight generalizations of known rigidity results.
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.
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…
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.
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.
The paper makes inference methods available for Gaussian models with banded precision.
problem Efficient inference for Gaussian models with banded precision.
method Develops linear algebra operators for banded matrices within automatic differentiation frameworks.
result The operators enable efficient variational inference and gradient-based sampling for Gaussian models with banded precision.
Beta and gamma rhythms mediate different maturation trajectories of cortical networks.
problem Understanding how distinct cortical rhythms influence network maturation.
method Magnetoencephalography (MEG) to map frequency band-specific maturation from age 7 to 29 in 162 participants.
result Beta band mediated networks follow a linear trajectory, while gamma band networks follow an asymptotic one.
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 3 − ( 1 / 26 ) \sqrt 3-(1/26) 3 − ( 1/26 ) , 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.
Paper proposes a method to estimate confidence bands for survival random forests.
problem No statistically valid and computationally feasible approach for estimating confidence bands for survival random forests.
method Extending recent developments in infinite-order incomplete U-statistics, the paper proposes an unbiased confidence band estimation.
result The proposed method accurately estimates the confidence band and achieves desired coverage rate.
Defines band maps in unoriented link Floer homology forming a skein exact triangle.
problem Understanding unoriented link Floer homology through band maps.
method Defines and analyzes band maps in unoriented link Floer homology.
result Band maps form an unoriented skein exact triangle.
Band-limited training reduces resource usage without sacrificing accuracy.
problem Resource constraints in training Convolutional Neural Networks (CNNs).
method Artificially constraining the frequency spectra of convolutional filters during training.
result CNNs can leverage lower-frequency components effectively, reducing resource usage.
EGO-MDA identifies optimal spectral-bands for process discrimination.
problem Optimal spectral-bands for process discrimination.
method EGO-MDA, an unsupervised method using EGO and Mixture Discriminant Analysis.
result EGO-MDA achieves at least 70% improvement in median deviance.