Estimates intrinsic dimension of data manifolds using local angle statistics.
problem Estimating intrinsic dimension of data on manifolds.
method Local angle statistics to estimate variance of angles between vectors near a point on the manifold.
result Consistency and asymptotic distribution of the local dimension estimator established.
Proposes LARS and LASSO methods for generalized linear models.
problem Sparse estimation for generalized linear models.
method Transforms statistical model manifold into tangent space, applies LARS and LASSO algorithms.
result Efficient and performs well, similar to l1-regularized maximum likelihood estimation. The paper models protein dihedral angles using BVM mixtures.
problem Modeling protein dihedral angles using directional data.
method Bayesian minimum message length (MML) for mixture model selection.
result MML provides a better model selection than traditional methods.
GANs with NCE improve dihedral angle prediction accuracy.
problem Inaccurate distribution of predicted dihedral angles.
method Introduced NCE-GAN to estimate density of GAN models and proposed residue-wise variants of AC-GAN and Semi-supervised GAN.
result Improved distribution of predicted angles, most similar to real angles with Semi-supervised GAN.
A new method reduces model complexity in DMD using LARS.
problem Building accurate reduced-order models from data.
method Least Angle Regression (LARS) for Dynamic Mode Decomposition (DMD).
result LARS4DMD produces comparable performance to DMDSP with less complexity.
Dynamic angles estimated from noisy measurements over time with smoothness constraints.
problem Recovering angles from noisy pairwise measurements over time.
method Three algorithms for joint estimation of angles under smoothness constraints.
result MSE converges to zero as T increases under milder conditions. Develops a new tensor model for clustering with degree correction.
problem Clustering with unknown degree heterogeneity in multiway data.
method Degree-corrected tensor block model with estimation guarantees.
result Demonstrates an intrinsic statistical-to-computational gap for tensors of order three or greater.
New method identifies latent relationships in deep models without additional constraints.
problem Latent representations in deep latent variable models are not statistically identifiable.
method Identifies relationships between latent variables (distances, angles, volumes) under mild model conditions.
result Empirically demonstrates more reliable latent distances without additional labeled data.
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.
Study constant angle surfaces in 4D Minkowski space, proving their properties.
problem Characterize surfaces in 4D Minkowski space with constant angle between tangent planes.
method Define complex angle, prove curvature properties, use PDE methods, analyze special cases.
result Constant angle surfaces have vanishing Gauss and normal curvatures; not complete for ψeq0 [π/2]. Sequential regression procedures can include spurious variables early, even in sparse settings.
problem Sequential regression procedures can select spurious variables early in rankings.
method Analysis of three sequential procedures: forward stepwise, lasso, and least angle regression.
result The first spurious variable is selected earlier as coefficients become denser.
The paper extends Lagrangian and Kähler angles to immersed surfaces in complex plane and proves pinching results.
problem Extending Lagrangian and Kähler angles to immersed surfaces in complex plane.
method Extending Lagrangian angle, Maslov form, and Maslov class to immersed surfaces in C2; proving pinching results for Kähler angle. result Two pinching results for the Kähler angle imply rigidity theorems of self-shrinkers with Kähler angle.
Defines Kahler angle for a broader context.
problem Generalizing results about Kahler angle.
method Provides a general definition of Kahler angle.
result Generalized results about Kahler angle.
Study angle structures on pseudo 3-manifolds, proving existence for some cases.
problem Determining if hyperbolic 3-manifolds can have angle structures.
method Examined triangulated pseudo 3-manifolds with area-curvature angle structures, establishing sufficient and necessary conditions.
result Compact hyperbolic 3-manifolds with totally geodesic boundary can have angle structures.
New refit strategy improves probability estimation for multicategory angle-based classifiers.
problem Improving probability estimation for multicategory angle-based classifiers in high dimensional applications.
method Proposes a new refit strategy for multicategory angle-based classifiers, adding small computation cost.
result Significant improvement in probability estimation with minimal additional computation.
Introduces a new geometry based on difference angles, showing unique properties.
problem Defining angles independently of circles or rotations.
method Axiomatic system for difference angles, defining new geometric constructs.
result Explicit confirmation of the concurrency of the parabolic Miquel configuration.
The paper examines rigidity in geometric actions of Coxeter groups on Croke-Kleiner spaces.
problem The rigidity of geometric actions of Coxeter groups compared to their quasi-isometric counterparts.
method Study of right-angled Coxeter groups acting geometrically on Croke-Kleiner spaces.
result Right-angled Coxeter groups have more rigid geometric actions than their quasi-isometric counterparts.
Stiefel-Whitney classes of moment-angle manifolds are trivial.
problem Analyzing the topological properties of moment-angle manifolds.
method Proving triviality of Stiefel-Whitney classes for moment-angle manifolds, including partial quotients.
result Stiefel-Whitney classes of moment-angle manifolds are trivial.
New method certifies images against transformations like rotations and translations.
problem Certifying robustness of images against transformations like rotations and translations.
method Randomized smoothing with three different kinds of defenses.
result Individual certificates can be obtained via statistical error bounds or efficient online inverse computation.
Uniqueness of quasi-roots explored in right-angled Artin groups.
problem Uniqueness of quasi-roots in right-angled Artin groups.
method Introducing quasi-roots and studying their uniqueness.
result Uniqueness of quasi-roots established in right-angled Artin groups.
This note generalizes the visual angle to convex sets in 3D space.
problem Analyzing geometric properties of convex sets in 3D space.
method Generalizing the visual angle to convex sets in Euclidean space and expressing geometric quantities in terms of integrals of functions related to the solid angle.
result Invariant quantities of the original convex set can be expressed by integrals of functions related to the solid angle.
Study proves existence of weak mean curvature flow with contact angle.
problem Existence of weak mean curvature flow with prescribed contact angle.
method Compactness theorem for varifolds and Ilmanen's regularization extended to capillarity.
result Existence of weak mean curvature flow with contact angle for general θ. Improved volume estimates for right-angled polyhedra in hyperbolic space.
problem Estimating volumes of right-angled polyhedra in hyperbolic space.
method Combining Andreev theorem and Atkinson's results, improved upper volume estimates.
result Upper volume estimates for both compact and ideal right-angled polyhedra improved.
This paper explores historical and philosophical aspects of angles and solid angles, inspired by Euler's work.
problem Understanding the historical context and philosophical implications of angles and solid angles.
method Historical review and analysis of mathematical and philosophical works.
result Questions raised by Euler about angles and solid angles are timeless and relevant to modern mathematics.
Real moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic.
problem Uniqueness of smooth structures on real moment-angle manifolds.
method Arguments from calculus applied to results from complex moment-angle manifolds.
result Real moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic.
Defines Lorentzian angles for null vectors in geometry.
problem Handling angles involving null vectors in geometry.
method Introduces Lorentzian angles for null directions.
result Provides a proof for the Lorentzian Gauss-Bonnet theorem.
Agol recently introduced the notion of a veering triangulation, and showed that such triangulations naturally arise as layered triangulations of fibered hyperbolic 3-manifolds. We prove, by a constructive argument, that every veering triangulation admits positive angle structures, recovering a result of Hodgson, Rubins…
We provide a congruence theorem for minimal surfaces in S5 with constant contact angle using Gauss-Codazzi-Ricci equations. More precisely, we prove that Gauss-Codazzi-Ricci equations for minimal surfaces in S5 with constant contact angle satisfy an equation for the Laplacian of the holomorphic angle. Also, we wi…
Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational fans, the manifold Z is the total space of a holomorphic bundle over a toric variet…
Surveying connections between graph combinatorics and algebraic right-angled Artin groups.
problem Understanding the relationship between graph structures and algebraic properties of right-angled Artin groups.
method Analyzing the defining and extension graphs of right-angled Artin groups.
result Discovers connections to geometric group theory and complexity theory.
The paper extends circle pattern theory to include obtuse angles.
problem Existence and rigidity of circle patterns with non-obtuse exterior intersection angles.
method Topological degree theory, variational principle, Teichmüller theory, Sard's Theorem.
result The Circle Pattern Theorem is generalized to include obtuse angles.
Survey on RAAGs in low-dimensional manifold diffeomorphisms.
problem Role of RAAGs in diffeomorphism groups of low-dimensional manifolds.
method Subgroup structure, algebraic structure, compactness, regularity analysis.
result RAAGs have diverse actions on low-dimensional manifolds, with restrictions on higher regularity.
We give a new notion of angle in general metric spaces; more precisely, given a triple a points p,x,q in a metric space (X,d), we introduce the notion of angle cone ∠pxq as being an interval ∠pxq:=[∠pxq−,∠pxq+], where the quantities ∠pxq± are defined in terms o…
The study explores statistical methods to interpret radiological models and identify key features.
problem Interpreting complex radiological models for clinical use.
method Exploration of statistical techniques to assess relationships between radiomic features.
result Identification of key relationships and features for improved interpretability.
The paper studies prescribed angle surfaces in Riemannian manifolds with torse-forming vector fields.
problem Characterizing surfaces with prescribed angles in Riemannian geometry.
method Introducing and analyzing prescribed angle hypersurfaces associated with torse-forming vector fields.
result Classification of prescribed angle surfaces in 3D Riemannian manifolds.
In this paper we classify certain special ruled surfaces in R3 under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle property. Moreover, the natural extension to normal and binormal constant angle sur…
New invariant classifies right-angled Coxeter groups, bounds thickness.
problem Classifying and bounding right-angled Coxeter groups.
method Introducing hypergraph index from defining graph, computing upper bounds.
result Hypergraph index partitions groups into quasi-isometry classes, bounds thickness.
The paper solves a geometric problem involving points in a triangle's plane.
problem Determine points in a triangle's plane corresponding to given cosines of angles.
method Analyzes the geometric constraints and uses trigonometric properties.
result The number of points D satisfying the given conditions is determined. Study on null hypersurfaces with constant angle in Lorentzian manifolds.
problem Understanding constant angle null hypersurfaces in Lorentzian manifolds.
method Introduced constant angle null hypersurfaces, analyzed with respect to a given ambient vector field, and provided classification results.
result Null hypersurfaces have a canonical principal direction when the vector field is closed and conformal.
Study subgroup growth in RAAGs and RAAGs with Coxeter relations.
problem Understanding subgroup growth in RAAGs and RAAGs with Coxeter relations.
method Analyzing the independence number of defining graphs for RAAGs and conjecturing for RAAGs with Coxeter relations.
result Subgroup growth rate depends on the independence number of the defining graph for RAAGs and a conjecture for RAAGs with Coxeter relations.
The paper studies the face angles of tetrahedra with a fixed base.
problem Determine the closure and boundary of the set of face angles of tetrahedra with a given base.
method Analyzes the set of tetrahedra with a given base and calculates the cosine of the angles between the faces.
result The closure and boundary of the set of face angles are determined.
We consider the question of determining whether a given group (especially one generated by involutions) is a right-angled Coxeter group. We describe a group invariant, the involution graph, and we characterize the involution graphs of right-angled Coxeter groups. We use this characterization to describe a process for c…
Establishes a boundary maximum principle for varifolds with fixed contact angle.
problem Boundary behavior of varifolds with contact angle constraints.
method Maximum principle for stationary pairs of varifolds with fixed contact angle condition.
result Boundary maximum principle proven for stationary varifolds.
This notes explores angle structures on ideally triangulated compact 3-manifolds with high genus boundary. We show that the existence of angle structures implies the existence of a hyperbolic metric with totally geodesic boundary, and conversely each hyperbolic 3-manifold with totally geodesic boundary has an ideal…
This paper characterizes a specific type of twisted Artin groups embedded in knot groups.
problem Embedding twisted right-angled Artin groups in knot groups.
method Defined and characterized twisted right-angled Artin groups through mixed graphs and Klein bottle relations.
result Completely determined which twisted right-angled Artin groups can be embedded in knot groups.
The angle defect, which is the standard way to measure curvature at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the literature an axiomatic characterization of the angle defect. We give a characterization …
Hyperbolic links in thickened torus decompose into angled tetrahedra.
problem Hyperbolicity of links in thickened torus.
method Decomposition into torihedra, angled pyramids, and angled tetrahedra.
result Augmented links in thickened torus are hyperbolic.
Fixed angles of convex polygons lead to combinatorially rich polytopes.
problem Understanding the structure of convex polygons with fixed vertex angles.
method Combining combinatorial and geometric approaches, including dual polytopes and Schwarz-Christoffel maps.
result Fixed-angles polytopes are dual to cyclic polytopes under certain conditions.