Characterizes functions in Carnot groups of step 2.
problem Understanding intrinsic Lipschitz functions in Carnot groups.
method Characterization via intrinsic distributional gradients.
result Characterization of locally intrinsic Lipschitz functions in Carnot groups of step 2.
Characterizes intrinsic Lorentzian spaces using midpoint properties.
problem Deciding if a metric is length-based in Lorentzian spaces.
method Adapting midpoint criteria from metric geometry to Lorentzian pre-length spaces.
result Spaces with specific midpoint properties are strictly or merely intrinsic.
The study characterizes generalized Berwald surfaces with topological constraints.
problem Topological constraints on generalized Berwald surfaces.
method Intrinsic characterization and examples.
result Results on topological obstructions for the base manifold.
Criterion for flat circle bundles using intrinsically harmonic forms.
problem Characterizing flat circle bundles.
method Criterion based on intrinsic harmonicity of a specific form.
result Flatness of a principal circle bundle is equivalent to intrinsic harmonicity of a certain form.
Study uniformly differentiable graphs in Carnot groups, proving area formulas.
problem Characterize uniformly differentiable intrinsic graphs in Carnot groups.
method Characterize uniform intrinsic differentiability via Hölder properties of projections of vector fields.
result Explicit area formula for uniformly intrinsically differentiable maps in Carnot groups.
The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental proje…
The paper characterizes biconservative surfaces in hyperbolic 4-space.
problem Characterizing biconservative surfaces in hyperbolic 4-space.
method Establishing intrinsic conditions and analyzing geometric properties.
result Biconservative surfaces in hyperbolic 4-space satisfy a specific intrinsic condition.
We show that every p-fold strictly-cyclic branched covering of a b-bridge link in the 3-sphere admits a p-symmetric Heegaard splitting of genus g=(b-1)(p-1). This gives a complete converse to a result of Birman and Hilden, and gives an intrinsic characterization of p-symmetric Heegaard splittings as p-fold strictly-cyc…
We examine graphs that contain a non-trivial link in every embedding into real projective space, using a weaker notion of unlink than was used by Flapan, et al. We call such graphs intrinsically linked in projective space. We fully characterize such graphs with connectivity 0,1 and 2. We also show that only one Peterse…
New metric measure space theory for Lipschitz constants.
problem Defining and characterizing Cheeger energy in metric measure spaces.
method Adapting Cheeger theory to intrinsically Lipschitz sections.
result Characterization of intrinsic Cheeger energy in terms of relaxed slope.
Study provides bounds for estimating intrinsic dimension using Gaussian kernels.
problem Estimating intrinsic dimension from data.
method Finite-sample concentration and anti-concentration bounds for Gaussian kernel sums.
result Explicit dependence on sample size, bandwidth, and geometric parameters.
Cylinders in warped product spaces have zero curvature.
problem Characterizing cylinders in warped product spaces.
method Proving cylinders have zero extrinsic and intrinsic curvatures.
result Cylinders in M2imesRn have zero curvature. In this paper we provide a characterization of intrinsic Lipschitz graphs in the sub-Riemannian Heisenberg groups in terms of their distributional gradients. Moreover, we prove the equivalence of different notions of continuous weak solutions to the equation φ_y+ [φ^{2}/2]_t=w, where w is a bounded function depending o…
Study on predicting sequences with Gaussian constraints, linking to intrinsic volumes and metric complexity.
problem Predicting sequences almost as well as the best Gaussian distribution with mean in a given subset.
method Expressed minimax regret in terms of intrinsic volumes, established comparison inequality for Wills functional, characterized global covering numbers and local Gaussian widths.
result Sharp estimates on the log-Laplace transform of intrinsic volume sequence for a general nonconvex set.
Develops intrinsic curved cosets for Cartan geometries.
problem Defines curved cosets for arbitrary Cartan geometries.
method Defines intrinsic holonomy group and curved cosets.
result Curved cosets retain characteristics of homogeneous counterparts and behave well under automorphisms.
Characterizes density-valued symplectic forms on multisymplectic manifolds.
problem Understanding density-valued symplectic forms on multisymplectic manifolds.
method Intrinsic characterization and Darboux-type theorems.
result Proves Darboux-type theorems for density-valued symplectic forms.
New algorithm estimates intrinsic dimension of discrete datasets.
problem Inaccuracies in using continuous methods for discrete datasets.
method Introduced an algorithm to infer intrinsic dimension of discrete spaces.
result Demonstrated accuracy on benchmark datasets and found a small intrinsic dimension in a metagenomic dataset.
Characterizes isolated compact subgroups in Lie groups.
problem Identifying isolated compact subgroups in Lie groups.
method Characterization based on intrinsic structure, irrelevant ambient group details.
result Characterization of isolated compact subgroups depends only on intrinsic structure.
A non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the non-convex optimization problem as transformations of Euclidean conditional expectation. …
Conformally compact asymptotically hyperbolic metrics have been intensively studied. The goal of this note is to understand what intrinsic conditions on a complete Riemannian manifold (M,g) will ensure that g is asymptotically hyperbolic in this sense. We use the geodesic compactification by asymptotic geodesic rays to…
Catenaries defined on any Riemannian surface using intrinsic distance.
problem Defining catenaries on Riemannian surfaces.
method Defining catenaries as critical points of a potential functional, calculating potential with intrinsic distance, and characterizing using curvature.
result Characterization of catenaries on various Riemannian surfaces.
Extends Anosov subgroup definitions to more general groups.
problem Characterize subgroups of semisimple Lie groups.
method Relativizes characterizations of Anosov subgroups.
result Proves implications and equivalences between relativized characterizations.
Understanding and characterizing the subspaces of adversarial examples aid in studying the robustness of deep neural networks (DNNs) to adversarial perturbations. Very recently, Ma et al. (ICLR 2018) proposed to use local intrinsic dimensionality (LID) in layer-wise hidden representations of DNNs to study adversarial s…
Sharp estimates for Finsler metrics in convex domains.
problem Estimating distances in Finsler metrics near convex points.
method Sharp estimates for intrinsic distances of Finsler metrics.
result Characterization of k-quasi hyperbolic metric in convex geometry. Characterizes projective special complex manifolds using c-projective structures.
problem Characterizing projective special complex manifolds.
method Defining S1-bundles and constructing conical special complex manifolds. result Intrinsic characterization of projective special complex manifolds.
The aim of the present paper is to provide an intrinsic investigation of two special Finsler spaces whose defining properties are related to Berwald connection, namely, Finsler space of scalar curvature and of constant curvature. Some characterizations of a Finsler space of scalar curvature are proved. Necessary and su…
This paper analyzes deep federated learning for low-dimensional data, revealing intrinsic dimensionality's role in convergence rates.
problem Insufficient investigation of generalization error in heterogeneous federated learning, especially for low-dimensional data.
method Statistical analysis of deep federated regression in a two-stage sampling model.
result Intrinsic dimensionality, characterized by entropic dimension, determines convergence rates for deep learners.
The article presents a new entropy model for assessing stock market interest.
problem Assessing investor interest and market sentiment in exchange-traded securities.
method Intrinsic entropy model using actual trading data, without exogenous factors.
result Empirical evidence supports the model's ability to predict trading activity.
The study defines and characterizes extrinsic catenaries in hyperbolic space.
problem Understanding catenaries in hyperbolic geometry.
method Defined extrinsic catenaries in hyperbolic plane, characterized them, and proved their relation to minimal surfaces.
result Extrinsic catenaries in hyperbolic space are critical points of a potential functional and generating curves of minimal surfaces.
CrossLID evaluates GAN quality by comparing intrinsic dimensions.
problem Measuring GAN quality and detecting mode collapse.
method CrossLID measures local intrinsic dimensionality of real-world data vs. GAN-generated samples.
result CrossLID correlates with GAN training progress and is robust to noise.
Study Alexander polynomials of ribbon and virtual knots using ribbon's intrinsic singularity.
problem Determining Alexander polynomials for ribbon and virtual knots.
method Using ribbon's intrinsic singularity information, defining half Alexander polynomial, and developing simplified formulas.
result New formulas for Alexander polynomials of general knots and virtual knots in terms of Gauss diagrams.
A new method classifies almost contact metric manifolds using intrinsic endomorphisms.
problem Difficult classification of almost contact metric manifolds into 2^12 classes.
method Introducing intrinsic endomorphisms S and h, providing a flowchart based on algebraic conditions.
result A more natural classification scheme with fewer classes, including H-parallel manifolds. The n-dimensional torus is uniquely characterized by specific harmonic forms.
problem Characterizing the n-dimensional torus via harmonic forms.
method Analyzing closed 1-forms on the torus to determine unique properties.
result The n-dimensional torus is the unique manifold supporting a linearly independent set of (n-1) closed 1-forms whose product determines a non-zero cohomological class.
In this paper a new intrinsic geometric characterization of the symmetric square of a curve and of the ordinary product of two curves is given. More precisely it is shown that the existence on a surface of general type S of irregularity q of an effective divisor D having self-intersection D^2>0 and arithmetic genus q i…
In this paper, geometric characterizations of conformally flat and radially flat hypersurfaces in Sn×R and Hn×R are given by means of their extrinsic geometry. Under suitable conditions on the shape operator, we classify conformally flat hypersurfaces in terms of …
Curves in Rn for which the ratios between two consecutive curvatures are constant are characterized by the fact that their tangent indicatrix is a geodesic in a flat torus. For n=3,4, spherical curves of this kind are also studied and compared with intrinsic helices in the sphere.
Study characterizes quasi-isometric embeddings of maps from cusped surfaces into moduli space.
problem Characterizing quasi-isometric embeddings of maps from cusped surfaces into moduli space.
method Investigates shrinking maps from a cusped hyperbolic surface into the moduli space of closed Riemann surfaces, considering quasi-isometric embeddings with respect to Teichmüller distance and intrinsic distance.
result Characterizations of quasi-isometric embeddings are solely determined by the map's monodromy under mild conditions.
The paper studies new curvature properties in Finsler geometry.
problem Properties of projectively equivalent Finsler metrics and their curvature structures.
method Introducing new characterizations of quadratic curvature properties in Finsler manifolds.
result Novel insights into curvature behavior under generalized projective sprays.
Develops a new method to compare data distributions on manifolds.
problem Existing techniques for comparing data distributions are limited and uni-scale.
method Intrinsic and multi-scale method using spectral Gromov-Wasserstein distance.
result Effective at discerning data manifold structure and evaluating generative models.
The collective phenomena of a liquid market is characterized in terms of a particle system scenario. This physical analogy enables us to disentangle intrinsic features from purely stochastic ones. The latter are the result of environmental changes due to a `heat bath' acting on the many-asset system, quantitatively des…
We show some characterizations of hyperspheres in the (n+1)-dimensional Euclidean space En+1 with intrinsic and extrinsic properties such as the n-dimensional area of the sections cut off by hyperplanes, the (n+1)-dimensional volume of regions between parallel hyperplanes, and the n-dimensional surf…
Conformal Autoencoders infer intrinsic dimensionality and impose invariance.
problem Detecting intrinsic dimensionality and imposing invariance in nonlinear manifold data.
method Imposing orthogonality conditions on latent variables to infer intrinsic dimensionality and build coordinate invariance.
result The method can infer intrinsic dimensionality and build coordinate invariance on submanifolds.
Characterizes metrics on triangulated surfaces using glued Euclidean triangles.
problem Describing metrics on triangulated surfaces constructed from glued Euclidean triangles.
method Carefully constructing polyhedral metrics and proving their uniqueness.
result Polyhedral metrics are the only intrinsic metrics preserving Euclidean triangle lengths.
We characterize the differentiable points of the distance function from a closed subset N of an arbitrary dimensional Finsler manifold in terms of the number of N-segments. In the case of a 2-dimensional Finsler manifold, we prove the structure theorem of the cut locus of a closed subset N, namely that it is a lo…
Study characterizes SU(3)-structures with special Lagrangian 3-folds as minimal.
problem Characterizing SU(3)-structures with special Lagrangian 3-folds.
method Derivation of mean curvature formulas and analysis of SU(3)-structures.
result Obtained formulas for mean curvature and characterized SU(3)-structures.
New method detects intrinsic cross-correlations in non-stationary time series affected by common factors.
problem Bias in cross-correlation analysis due to common external factors.
method Multifractal temporally weighted detrended partial cross-correlation analysis (MF-TWDPCCA).
result MF-TWDPCCA accurately detects intrinsic cross-correlations between non-stationary time series.
Two new exploration methods for multi-agent systems improve team performance.
problem Exploration in transition-dependent multi-agent settings.
method EITI and EDTI, using mutual information and VoI to encourage coordinated exploration.
result Significant improvement in multi-agent performance through coordinated exploration.
W2S FT often outperforms weak teachers due to low intrinsic dimensionality.
problem Understanding why weak-to-strong finetuning outperforms weak models.
method Analyzing W2S in ridgeless regression setting, focusing on variance reduction.
result Weak teacher's variance is inherited by strong student in shared feature subspace, reduced in discrepancy subspace.