Paper proposes a method to improve circular coordinate representation for detecting changes in high-dimensional datasets.
problem Detecting changes in high-dimensional datasets with preserved topological structures.
method Adapt circular coordinate framework using a generalized penalty function instead of an L2 penalty.
result Circular coordinates with generalized penalty can detect changes in high-dimensional datasets under different sampling schemes.
Projected random forests improve circular data prediction with adaptive arc length and finite-sample coverage.
problem Regression with circular responses.
method Adapting linear-response models to circular data using projection and random forest out-of-bag mechanism.
result Projected random forest out-of-bag conformal prediction sets are more efficient and shorter than alternative methods.
ANGLE tackles circular data regression, improving predictive performance.
problem Geometrically misleading traditional regression for circular data.
method Generative map optimized via GCES loss for non-parametric distributional regression.
result Unified toolbox for circular statistics challenges.
Curves become nearly circular over time without initial assumptions.
problem Understanding the asymptotic behavior of area-preserving flows.
method Proving asymptotic circularity without additional assumptions.
result Immortal solutions become asymptotically circular without initial assumptions.
Study circular tractrices and pseudospheres in 3D space.
problem Geometric properties of circular tractrices and pseudospheres.
method Exploration of geometric properties through analysis.
result Characterization of circular tractrices and pseudospheres.
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by extending some standard probabilistic modelling tools to the circular domain. First w…
The paper defines circular orderability for quandles and explores their properties.
problem Understanding the structure of quandles through circular orderings.
method Introduced circular orderability for quandles, showed embedding properties, and provided examples.
result Spaces of circular orderings embed in the space of all orderings, and examples of non-circularly orderable quandles are given.
Paper studies geometric and combinatorial properties of circular snakes.
problem Exploring geometric and combinatorial properties of circular snakes.
method Definition and investigation of outer Lipschitz geometry, decomposition of Valette link, construction of combinatorial objects, weakly outer Lipschitz classification.
result Existence of canonical decomposition and necessary/sufficient criteria for removing segments or Hölder triangles.
Paper tackles circularity issues in machine learning predictions.
problem Circularity problems in machine learning predictions.
method Not specified in the abstract.
result Not specified in the abstract.
New algorithm for robust circular coordinates in recurrent time series data.
problem Inefficient and sensitive methods for finding circular coordinates on recurrent data.
method Subsampling, aligning, and averaging to correct uneven sampling density.
result More robust and efficient circular coordinates for neuronal recordings.
The study identifies surfaces with Maslovian normal bundles.
problem Characterizing surfaces with specific geometric properties.
method Proving equivalence to round spheres, cylinders, or cones.
result Surfaces with Maslovian normal bundles are limited to specific shapes.
New hexagonal circular 3-webs with reducible curves classified.
problem Classifying hexagonal circular 3-webs with reducible polar curves of degree 3.
method New examples and classifications presented.
result Classification of hexagonal circular 3-webs with reducible polar curves of degree 3.
CVNN outperforms RVNN on non-circular data.
problem Classifying complex-valued data with statistical dependence.
method Comparison of CVNN and RVNN on non-circular data.
result CVNN outperforms RVNN in accuracy and generalization.
Circular nets with spherical parameter lines have geometric properties related to Darboux cyclides and terminating Laplace sequences.
problem Discretizing surfaces with spherical curvature lines.
method Lie-geometric discretisation in terms of principal contact element nets.
result Circular nets with two families of spherical parameter lines are related to Darboux cyclides.
The paper studies circular evolutes and involutes of framed curves in Euclidean space.
problem Investigating properties of framed curves and their evolutes and involutes.
method Definition and analysis of circular evolutes and involutes of framed curves, properties of normal surfaces, and their relations.
result Circular evolutes and involutes of framed curves are opposite operations under suitable assumptions, similar to fronts in the Euclidean plane.
It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using the Bergman mapping, we prove that every origin-preserving automorphism of normal …
CDFD analyzes circularity and directionality in weighted directed networks.
problem Analyzing circularity and directionality in weighted directed networks.
method CDFD framework separates flow into circular and acyclic components.
result CDFD yields a normalized circularity index capturing flow in cycles and directionality.
Classifies hexagonal circular 3-webs with cubic polar curves.
problem Classifying hexagonal circular 3-webs with algebraic polar curves of degree three.
method Analyzes hexagonal circular 3-webs on unit sphere with polar points on a twisted cubic.
result Completes the classification of hexagonal circular 3-webs with algebraic polar curves of degree three.
Study geometrically characterizes piecewise circular curves with decreasing curvature.
problem Characterizing piecewise circular curves with decreasing curvature.
method Introducing moduli spaces and relating them to Legendrian polygons.
result Proves the moduli space contains a connected component homeomorphic to the Fock-Goncharov space of positive flags.
Bayesian model predicts circular data with fast Gibbs sampling.
problem Predicting circular data in scientific fields.
method Expressive von Mises quasi-processes with Stratonovich augmentation for posterior inference.
result Fast Gibbs sampling for posterior inference.
A new machine learning framework called machine collaboration improves prediction accuracy.
problem Improving prediction accuracy in machine learning.
method Machine Collaboration (MaC) framework, which uses a circular and interactive learning approach.
result Machine Collaboration framework significantly outperforms other state-of-the-art methods in most cases.
Numerous studies have been carried out to measure wind pressures around circular cylinders since the early 20th century due to its engineering significance. Consequently, a large amount of wind pressure data sets have accumulated, which presents an excellent opportunity for using machine learning (ML) techniques to tra…
Study finds a limiting distribution for free path lengths on flat surfaces with circular obstacles.
problem Understanding free path lengths on flat surfaces with circular obstacles.
method Proved the existence of a limiting distribution using radius of obstacles as a parameter.
result Relates the limiting distribution to heights of zippered rectangle decompositions.
We show that circular width is preserved under connected sum of knots for some cases.
The paper classifies and studies symplectic and contact properties of circular spherical divisors.
problem Investigating symplectic and contact topology of circular spherical divisors.
method Classification and analysis of concave circular spherical divisors, including embedding, Stein fillability, and rational homology type determination.
result All concave circular spherical divisors up to toric equivalence are realized as symplectic log Calabi-Yau pairs with minimal complements.
The paper explores circular orderability in 3-manifold groups, related to the L-space conjecture.
problem Circular orderability of 3-manifold groups and its relation to the L-space conjecture.
method Investigation of finite cyclic covers and Dehn surgeries to establish circular orderability.
result Circularly orderable fundamental groups of compact, connected, P^2-irreducible 3-manifolds are characterized.
Derives conformal parameters of curves using inscribed circular polygons.
problem Characterizing conformal invariants of smooth curves in 3D.
method Limiting process with inscribed circular polygons, based on elementary geometry.
result Derives conformal length, curvature, and torsion via a novel method.
For a knot K⊂S3, its exterior E(K)=S3\η(K) has a singular foliation by Seifert surfaces of K derived from a circle-valued Morse function f:E(K)→S1. When f is self-indexing and has no critical points of index 0 or 3, the regular levels that separate the index-1 and index-2 critica…
Angular measurements are often modeled as circular random variables, where there are natural circular analogues of moments, including correlation. Because a product of circles is a torus, a d-dimensional vector of circular random variables lies on a d-dimensional torus. For such vectors we present here a class of graph…
This article provides sufficient conditions for a closed hyperbolic 3-manifold M with non zero first Betti number to fiber over the circle, and to find a fiber in M. Those conditions are formulated in terms of the behavior the circular characteristic in finite regular covers of M. We define the circular character…
A regular circle-valued Morse function on the knot complement C(K) = S^3\K is a function f from C(K) to S^1 which separates critical points and which behaves nicely in a neighborhood of the knot. Such a function induces a handle decomposition on the knot exterior E(K) = S^3\N (K), with the property that every regular l…
We study relations of some classes of k-convex, k-visible bodies in Euclidean spaces. We introduce and study \textrm{circular projections} in normed linear spaces and classes of bodies related with families of such maps, in particular, \textrm{k-circular convex} and \textrm{k-circular visible} ones. Investigati…
New conditions for circular orderability of direct products, linking to left-orderability of groups.
problem Conditions for circular orderability of direct products GimesZ/nZ. method Cohomological conditions and characterizations for left-orderability.
result New characterization for left-orderability of fundamental groups of rational homology 3-spheres.
In this note we prove that any monohedral tiling of the closed circular unit disc with k≤3 topological discs as tiles has a k-fold rotational symmetry. This result yields the first nontrivial estimate about the minimum number of tiles in a monohedral tiling of the circular disc in which not all tiles contain t…
We show a non existence result for solutions of the prescribed mean curvature equation in the product manifold H2×R, where H2 is the real hyperbolic plane. More precisely we prove a-priori estimates for graphs with constant mean curvature h∈(0,1/2] on circular annuli of $\mathbb{H…
Method detects neural network equivalence via matrix ensembles and spectral analysis.
problem Detecting equivalence among different deep learning architectures.
method Generating Mixed Matrix Ensembles (MMEs) and matching to conjugate circular ensembles.
result Empirical evidence shows vanishing differences in spectral densities with long tail decay rates.
Vector-valued neural learning has emerged as a promising direction in deep learning recently. Traditionally, training data for neural networks (NNs) are formulated as a vector of scalars; however, its performance may not be optimal since associations among adjacent scalars are not modeled. In this paper, we propose a n…
Elliptic bouquets defined for spin manifolds with circular actions.
problem Defining integration in elliptic cohomology.
method Introducing elliptic bouquets of germs of holomorphic equivariant cohomology classes, integrating them as in K-theory.
result Witten's rigidity theorem follows from integration of elliptic bouquets.
Study stability and bifurcation of liquid interfaces in cylindrical supports.
problem Stability and bifurcation of liquid interfaces in cylindrical support surfaces.
method Analysis of eigenvalues of the Jacobi operator, Plateau-Rayleigh instability, bifurcation theory.
result Conditions for the emergence of new morphologies and bifurcations from circular cylinders.
Study convex embeddability in linear and circular orders, applying to knots.
problem Understanding the quasi-order of convex embeddability in linear and circular orders.
method Combinatorial and descriptive set-theoretic methods applied to arcs and knots.
result Established combinatorial properties and lower bounds for knot complexity.
We provide a way to infer about existence of topological circularity in high-dimensional data sets in Rd from its projection in R2 obtained through a fast manifold learning map as a function of the high-dimensional dataset X and a particular choice of a positive real σ known as band…
The method for approximation of planar curve by circular arcs with length preservation, proposed by I.Kh. Sabitov and A.V. Slovesnov, is analyzed. We extend the applicability of the method, and consider some corollaries, not related to the approximation problem. Inequalities for the length of a convex spiral arc with p…
We present a 2x2 Lax representation for discrete circular nets of constant negative Gauß curvature. It is tightly linked to the 4D consistency of the Lax representation of discrete K-nets (in asymptotic line parametrization). The description gives rise to Bäcklund transformations and an associated family. All the membe…
Method selects interpretable circular coordinates from data.
problem Abstract circular coordinates are hard to interpret.
method Minimum-weight basis problem in vector matroid for selecting interpretable circle-valued coordinates.
result Proves consistency of cochain inner product estimator.
We use technology from sutured manifold theory and the theory of Heegaard splittings to relate genus reducing crossing changes on knots in S^3 to twists on surfaces arising in circular Heegaard splittings for knot complements. In a separate paper, currently in preparation, we prove that these circular Heegaard splittin…
Motivated by well known results in low-dimensional topology, we introduce and study a topology on the set CO(G) of all left-invariant circular orders on a fixed countable and discrete group G. CO(G) contains as a closed subspace LO(G), the space of all left-invariant linear orders of G, as first topologized by Sikora. …
A privacy-preserving framework detects faults in circular economy processes.
problem Lack of shared data across company borders due to privacy concerns.
method Federated Principal Component Analysis (PCA) and Secure Multiparty Computation.
result The proposed FedMSPC framework outperforms standard PCA in fault detection.
The paper introduces a method to decorrelate circular coordinates using lattice reduction.
problem Geometric correlation between circle-valued maps when multiple cohomology classes are used.
method Systematic procedure using the Lenstra--Lenstra--Lovász algorithm for constructing low energy torus-valued maps.
result A method to obtain less correlated maps from cohomology classes using integer linear combinations.