New ANN method for imputing rounded zeros in compositional data.
problem Imputing missing values in compositional data with rounded zeros.
method Artificial Neural Networks (ANNs) for imputation of compositional data.
result ANNs are competitive or better than conventional methods for imputing rounded zeros.
A theory of cellwise contamination for compositional data using log-ratios.
problem Contamination in compositional data analysis.
method Develops a theory combining contamination model and propagation theorem.
result Reduction in cellwise breakdown value by (D−1)/D for certain estimators. TDX predicts evolving distributions from streaming data.
problem Predicting density at future time points in evolving data.
method Dynamic basis expansion with isometric log-ratio transformation.
result TDX accurately captures monotonous drift patterns.
Proposes CLUB for reliable MI minimization in high dimensions.
problem Estimating and minimizing mutual information in high-dimensional spaces.
method Contrastive Log-ratio Upper Bound (CLUB) for MI minimization.
result CLUB provides reliable estimation of mutual information.
This paper extends compositional data analysis using graph signal processing.
problem Traditional log-ratios between all variables are not suitable for specific variable relationships.
method Linking compositional data analysis with graph signal processing, it considers only selected log-ratios.
result The approach retains desirable properties of scale invariance and compositional coherence.
Adapts Altman's model to compositional data for bankruptcy prediction.
problem Predicting business default using standard financial ratios has issues.
method Uses compositional data methodology with log-ratios and machine learning.
result Compositional methods improve predictive performance, especially random forests.
ADPO optimizes relative advantage in reinforcement learning from human feedback.
problem Optimizing policy alignment in reinforcement learning from human preferences.
method ADPO explicitly parameterizes the optimal structure through anchored logits, decoupling response quality from prior popularity.
result Empirically, ADPO achieves state-of-the-art performance on reasoning tasks, outperforming GRPO by 30.9 percent.
Geometry-aware KDE model improves multiclass quantification.
problem Accurately estimating class prevalence for label shift adaptation.
method Log-ratio representations and Aitchison geometry for compositional data, shrinkage regularization.
result Competitive with state-of-the-art quantifiers, often improving over standard KDE-based baselines.
Paper optimizes change detection in unnormalized distributions.
problem Detecting changes in unnormalized pre- and post-change distributions.
method Log-Partition Approximation Cumulative Sum (LPA-CUSUM) algorithm based on thermodynamic integration.
result Asymptotically optimal performance achieved through unbiased estimation of CUSUM statistics.
A new geometry-preserving method for interpreting compositional data.
problem Statistical challenges in high-dimensional compositional data.
method Geometry-preserving framework for dimension reduction of compositional data.
result Identification of a central compositional subspace for compositional predictors.
FORE evaluates occupancy ratios without requiring Bellman completeness.
problem Offline reinforcement learning occupancy ratio estimation.
method Fitted occupancy-ratio evaluation (FORE) using adjoint Bellman recursion.
result FORE achieves convergence in KL without Bellman completeness.
Study reveals clusters of resilient and vulnerable Spanish agri-food firms post-Ukraine-Russia war.
problem Financial resilience of agri-food companies in Spain during the Ukraine-Russia conflict.
method Cluster analysis using centred log-ratios for compositional data of financial ratios.
result Increase in resilient firms by 2023, highlighting sectoral adaptation to economic challenges.
Isometric embeddings of Teichmüller spaces are derived from branched coverings.
problem Characterizing isometric embeddings of Teichmüller spaces.
method Holomorphic isometric embeddings induced by branched coverings.
result All isometric embeddings of Teichmüller spaces of dimension at least 2 arise from branched coverings.
VarGrad reduces variance in ELBO gradient estimation for variational inference.
problem Improving the variance of gradient estimators in variational inference.
method VarGrad uses a new log-variance loss to estimate the ELBO gradient, achieving lower variance than the score function method.
result VarGrad offers a lower variance gradient estimator compared to other methods.
Proof that specific groups are quasi-isometrically rigid.
problem Quasi-isometric rigidity of specific groups.
method Proof of quasi-isometric rigidity for Kleinian and three-manifold groups.
result Finitely generated Kleinian and three-manifold groups are quasi-isometrically rigid.
Paper finds isometric timelike minimal surfaces with unique properties.
problem Rigidity of isometric timelike minimal surfaces in Lorentz-Minkowski space.
method Analyzes symmetries and deformations of timelike minimal surfaces.
result Existence of isometric timelike minimal surfaces not congruent to associated family.
The paper explores rigidity and flexibility of isometric extensions with critical Hölder exponent.
problem The critical Hölder exponent in isometric extensions and its implications.
method Convex integration and construction of isometric extensions.
result The Hölder exponent $θ_0= rac12$ is critical, with extensions violating the tangential connection for $θ< rac12$.
Paper classifies pillow box isometric deformations preserving crease patterns.
problem Classifying pillow box isometric deformations preserving crease patterns.
method Continuous isometric deformations from pillow boxes to double rectangles, preserving crease patterns.
result Such deformations necessarily change pillow box topology.
In this paper we consider the Cauchy problem for isometric immersions. More precisely, given a smooth isometric immersion of a codimension one submanifold we construct C1,α isometric extensions for any α<n(n+1)+11 via the method of convex integration.
In this paper we study critial isometric and minimal isometric embeddings of classes of Riemannian metrics which we call {\it quasi-k-curved metrics}. Quasi-k-curved metrics generalize the metrics of space forms. We construct explicit examples and prove results about existence and rigidity.
Study on isometric submanifolds with preserved Gauss map metrics.
problem Investigating isometric immersions with preserved Gauss map metrics.
method Local analysis of isometric immersions and deformations in Euclidean space.
result Local characterization of non-minimal and non-reducible isometric immersions.
We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taki…
Heat kernels map RCD spaces to Riemannian manifolds.
problem Mapping RCD spaces to Riemannian manifolds using heat kernels.
method Using heat kernels to map RCD spaces into L2 space and then normalizing to achieve isometric immersions. result Compact RCD spaces with isometrically heat kernel immersions are isometric to unweighted smooth Riemannian manifolds.
Study extends isometric immersions using submanifolds.
problem General extension problem for isometric immersions.
method Establishing Cartan-Ambrose-Hicks theorems based on submanifolds.
result Geometric constructions of isometric extensions.
We provide conditions under which an isometric immersion of a (warped) product of manifolds into a space form must be a (warped) product of isometric immersions.
In trying to generalize Bianchi's Bäcklund transformation of quadrics to Bäcklund transformations of isometric deformations of other (classes of) surfaces, we investigate basic features of the isometric deformation of surfaces via the Bäcklund transformation with isometric correspondence of leaves of a general nature (…
The paper improves the approximation of isometric immersions in high codimension.
problem Isometric immersions in high codimension.
method Uniform approximation of short immersions by C1,θ isometric immersions. result Achieved C1,θ regularity for isometric immersions in local settings. Proves isometric correspondence of leaves for generic rolling distributions.
problem Isometric correspondence of leaves in generic rolling distributions.
method Uses Bäcklund transformation for proof.
result Requires Bäcklund transformation for isometric correspondence of leaves.
The paper examines isometric timelike surfaces in 4D Minkowski space.
problem Analyzing geometric properties of isometric timelike surfaces.
method Study of Bour's theorem for four kinds of timelike helicoidal surfaces, analysis of geometric properties, presentation of parametrizations.
result Introduction of isometric pairs of timelike surfaces with same Gauss map.
Explains isometric immersions and their applications.
problem Isometric immersions and their applications in math and physics.
method Historical overview and applications.
result Explains the importance and applications of isometric immersions.
The paper examines rigidity of metric constructions in Wasserstein spaces.
problem Isometric rigidity of metric constructions in Wasserstein spaces.
method Analyzes spaces like Hilbert, rays, half-cylinders, and spherical suspensions.
result Different spaces exhibit varying levels of isometric rigidity in Wasserstein spaces.
New findings on minimal isometric immersions of flat n-tori into spheres.
problem Conditions for minimal isometric immersions of flat n-tori into spheres.
method Analyzes rationality conditions and derives upper bounds for algebraic irrationality degree.
result Upper bound for algebraic irrationality degree of minimal isometric immersions is sharp and equals 4 for n=3.
Revisits Weyl's problem on isometric immersions of spheres into 3D manifolds.
problem Isometric immersions of S² into 3D Riemannian manifolds with non-negative Gauss curvature.
method Utilizes the framework of J-holomorphic curves developed by Labourie.
result Exhibits a sufficient condition for the existence of global C¹¹ isometric immersions.
Maps between Hadamard manifolds are quasi-isometric to harmonic maps.
problem Understanding the relationship between quasi-isometric maps and harmonic maps on Hadamard manifolds.
method Extending a previous result to quotient spaces of Hadamard manifolds by convex cocompact discrete groups.
result Locally quasi-isometric maps to Hadamard manifolds are within bounded distance from a unique harmonic map.
We study quasi-isometric embeddings of symmetric spaces and non-uniform irreducible lattices in semisimple higher rank Lie groups. We show that any quasi-isometric embedding between symmetric spaces of the same rank can be decomposed into a product of quasi-isometric embeddings into irreducible symmetric spaces. We thu…
Study holomorphic isometric embeddings of a Grassmannian into quadrics.
problem Holomorphic isometric embeddings of complex Grassmannian into quadrics.
method Generalization of do Carmo--Wallach theory to study moduli space.
result Moduli space of embeddings up to equivalence discussed.
Stability result for nearly isometric subspaces and Finsler surfaces.
problem Stability of normed spaces and Finsler surfaces under near-isometric conditions.
method Refined topological argument and explicit quantification using Banach-Mazur distance.
result A 2-dimensional surface with near-monochromatic Finsler metric is approximately Riemannian.
The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian metrics. With this motivation we study the isometric immersion problem in strip a…
Characterizes quasi-isometric embeddings in coarsely Lipschitz category.
problem Understanding quasi-isometric embeddings in geometric terms.
method Formalizes quasi-isometric embeddings as regular monomorphisms in coarsely Lipschitz category.
result Quasi-isometric embeddings are equivalently characterised as effective, strong, or extremal monomorphisms.
In this article, we study holomorphic isometric embeddings between bounded symmetric domains. In particular, we show the total geodesy of any holomorphic isometric embedding between reducible bounded symmetric domains with the same rank.
We investigate the structure of real hypersurfaces with isometric Reeb flow in Kaehler manifolds. As an application we classify real hypersurfaces with isometric Reeb flow in irreducible Hermitian symmetric spaces of compact type.
Study minimal Kähler submanifolds in product of space forms.
problem Existence and properties of minimal isometric immersions of Kähler manifolds into product spaces.
method Analyse obstruction conditions and prove existence results for minimal immersions into Sm−1imesR and Hm−1imesR. result Only minimal isometric immersions of Riemannian surfaces into Sm−1imesR and Hm−1imesR exist. Long spacelike embeddings can be approximated by isometric ones.
problem Approximating long embeddings to isometric embeddings in Lorentzian spaces.
method Proving approximation by constructing C1 isometric embeddings. result Long spacelike embeddings can be C0-approximated by C1 isometric embeddings. We study isometric Lie group actions on the compact exceptional groups E6, E7, E8, F4 and G2 endowed with a biinvariant metric. We classify polar actions on these groups. We determine all isometric actions of cohomogeneity less than three on E6, E7, F4 and all isometric actions of cohomogeneity less than 20 on E8. More…
We present some results on reductions and the copolarity of isometric group actions, which we obtained in our thesis. We also describe a resolution construction for isometric actions with respect to a reduction and give examples.
Research shows arc complex is not quasi-isometric to sphere complex.
problem Comparing quasi-isometry of arc complex and sphere complex.
method Simple proof of quasi-isometric rigidity of arc complex.
result Arc complex is not quasi-isometric to sphere complex.
Authors create non-isometric 3-orbifolds with identical topology and volume.
problem Finding non-isometric hyperbolic 3-orbifolds with the same topological type and volume.
method Constructing pairs of non-isometric hyperbolic 3-orbifolds with the same topological type and volume.
result Demonstrated the existence of non-isometric hyperbolic 3-orbifolds with the same topological type and volume.
First explicit isometric immersion of a flat Klein bottle in 3D space.
problem Finding an isometric embedding of a Klein bottle in 3D.
method Piecewise-linear map from a Klein bottle to Euclidean 3-space.
result Explicit numerical data for a flat Klein bottle isometrically immersed in 3D.