New method for freezing sets in arbitrary dimensions.
problem Creating freezing sets for digital images in arbitrary dimensions.
method Using c1 and cn adjacencies to obtain freezing sets in Zn. result Demonstrated freezing sets for digital images in arbitrary dimensions.
Proves existence of maps with arbitrary ends and conditions for maxfaces.
problem Existence of maps with a specific number of ends and maxfaces.
method Proves existence through maximal maps and conditions for maxfaces.
result Existence of genus-zero complete maximal maps with arbitrary ends.
Researchers prove positive mass theorem for manifolds with arbitrary ends.
problem Proving the positive mass theorem for manifolds with non-compact ends.
method Developed techniques to handle non-compact singular sets and used Wloc1,p metrics. result Established positive mass theorem for C0 arbitrary ends with Wloc1,p metrics. In this paper, we prove a classification theorem for self-shrinkers of the mean curvature flow with ∣A∣2≤1 in arbitrary codimension. In particular, this implies a gap theorem for self-shrinkers in arbitrary codimension.
Since J. L. Lagrange initiated in 1760 the study of minimal surfaces of Euclidean 3-space, minimal surfaces in real space forms have been studied extensively by many mathematicians during the last two and half centuries. In contrast, so far very few results on minimal Lorentz surfaces in indefinite space forms are know…
Sharp estimate for flow in any dimension.
problem Interior gradient estimate for graphical mean curvature flow.
method Proving sharp interior gradient estimate for area decreasing graphical mean curvature flow in arbitrary codimension.
result Generalized result in arbitrary codimension.
New metric reduces arbitrariness in fair binary classification predictions.
problem Variance in predictions leads to arbitrary decisions in fair classification.
method Developed a self-consistency metric and an abstention algorithm.
result Fair binary classification is often close to fair due to variance, not interventions.
Proves mass theorem for manifolds with arbitrary ends.
problem Proving the positive mass theorem for manifolds with various ends.
method Quantitative analysis of scalar curvature on manifolds with arbitrary ends.
result Proves the positive mass theorem for a wide class of manifolds.
Paper analyzes TD(λ) convergence rates for arbitrary features.
problem Convergence rates for linear TD(λ) under arbitrary features. method Developed a novel stochastic approximation result for arbitrary features.
result Established L2 convergence rates for linear TD(λ) without linearly independent features assumption. Posterior Matching enables VAEs to model arbitrary conditional densities.
problem Modeling conditional dependencies in unsupervised learning.
method Posterior Matching framework for arbitrary conditioning.
result Posterior Matching enables VAEs to perform arbitrary conditioning without modification.
We prove that an arbitrary Poisson structure omega^{ij}(u) and an arbitrary closed 3-form T_{ijk}(u) generate the local Poisson structure A^{ij}(u,u_x) = M^i_s(u,u_x)omega^{sj}(u), where M^i_s(u,u_x)(delta^s_j + omega^{sp}(u)T_{pjk}(u)u^k_x) = delta^i_j, on the corresponding loop space. We obtain also a special graded …
The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…
The paper extends end concepts to arbitrary groups and spaces.
problem Extending end concepts to arbitrary groups and spaces.
method Description of maximal coarse compactification and geometric proof of end properties.
result Generalization of Stallings' theorem and definition of ends for coarse spaces.
Culler-Shalen theory extended to arbitrary characteristic.
problem Understanding essential surfaces in 3-manifolds over arbitrary fields.
method Using character varieties and group actions on trees over arbitrary algebraically closed fields.
result Examples show changes in the A-polynomial and essential surfaces in characteristic 2. Classifies Killing forms of arbitrary degree on specific nilpotent Lie groups.
problem Classifying Killing forms of arbitrary degree on specific Lie groups.
method Analyzing left-invariant Killing forms on simply connected 2-step nilpotent Lie groups with left-invariant metrics.
result Classified Killing forms when center is at most 2-dimensional.
Proves positive mass theorem for specific manifold types.
problem Positive mass theorem for manifolds with arbitrary ends.
method Proof for asymptotically flat and Euclidean manifolds.
result Validates positive mass theorem in new manifold types.
We construct the first explicit finite presentations for a family of Kähler groups with arbitrary finiteness properties, answering a question of Suciu.
This paper studies eigenvalues of the buckling problem of arbitrary order on bounded domains in Euclidean spaces and spheres. We prove universal bounds for the k-th eigenvalue in terms of the lower ones independent of the domains. Our results strengthen the recent work in [28] and generalize Cheng-Yang's recent estimat…
Paper proves timelike minimal surfaces with any number of ends exist.
problem Existence of timelike minimal surfaces with arbitrary ends.
method Analyzes asymptotic behavior and topology of constructed surfaces.
result Timelike minimal surfaces with arbitrary ends exist.
Linear bound on Betti numbers of negatively curved orbifolds.
problem Bounding Betti numbers of negatively curved orbifolds.
method Quantitative bound on the homology of spherical quotients.
result Linear growth of Betti numbers with volume, arbitrary field coefficients.
Extends positive mass theorem to arbitrary dimensions using a new inductive scheme.
problem Overcoming singularities in the Schoen-Yau proof for arbitrary dimensions.
method Inductive scheme combining shielding principle, conformal blow-up, and Cheeger-Naber bound.
result Proof of positive mass theorem in arbitrary dimensions.
This paper examines fairness and arbitrariness in bias mitigation methods.
problem Understanding how different bias mitigation strategies affect individual predictions and whether they introduce arbitrariness.
method FRAME framework to evaluate bias mitigation through five dimensions: Impact Size, Change Direction, Decision Rates, Affected Subpopulations, and Neglected Subpopulations.
result Significant differences in the behaviors of debiasing methods were exhibited, highlighting the limitations of current fairness criteria and the inherent arbitrariness in the debiasing process.
We prove that polyharmonic maps of arbitrary order from complete nonparabolic Riemannian manifolds to arbitrary Riemannian manifolds must be harmonic if certain smallness and integrability conditions hold.
The geography of minimal symplectic 4-manifolds with arbitrary fundamental group and symplectic 6-manifolds with abelian fundamental group of small rank, and with arbitrary fundamental group are addressed.
The paper extends inequalities for projection bodies to arbitrary measures.
problem Sharp bounds for volume ratios of convex bodies and their projection bodies.
method Generalizations of Zhang's inequality to arbitrary measures and extensions of the projection body operator.
result New Zhang-type inequalities for arbitrary measures and functions.
We employ min-max techniques to show that the unit ball in R3 contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus.
We solve the Cauchy-Dirichlet problem for the minimal surface system in arbitrary dimension and codimension assuming a condition on the variation of the initial submanifold .
Existence proof of noncompact self-shrinkers with arbitrary genus.
problem Existence of noncompact self-shrinkers with arbitrary genus.
method Employing min-max techniques to rigorously prove existence.
result Confirmation of one asymptotically conical end for large genus self-shrinkers.
We exhibit pseudo Riemannian manifolds which are Szabó nilpotent of arbitrary order, or which are Osserman nilpotent of arbitrary order, or which are Ivanov-Petrova nilpotent of order 3.
Transformers can interpolate between arbitrary measures.
problem Understanding the expressive power of Transformers as measure-to-measure maps.
method Provided an explicit choice of parameters for a single Transformer to match N arbitrary input measures to N arbitrary target measures.
result A single Transformer can interpolate between arbitrary measures.
We obtain universal inequalities for eigenvalues of the buckling problem of arbitrary order on bounded domains in M×R.
New activation functions achieve arbitrary-accuracy Sobolev approximation by fixed-size neural networks.
problem Approximation of Sobolev functions by neural networks
method Elementary Universal Activation Function and Differentiable Universal Activation Functions
result Arbitrary-accuracy Sobolev approximation by fixed-size neural networks
Differentiable optimization bridges arbitrary metrics to tree metrics.
problem Designing algorithms to convert arbitrary metrics to tree metrics with guarantees.
method DeltaZero framework, leveraging differentiable Gromov hyperbolicity.
result DeltaZero consistently achieves state-of-the-art distortion on synthetic and real-world datasets.
In the regression problem, L1 and L2 are the most commonly used loss functions, which produce mean predictions with different biases. However, the predictions are neither robust nor adequate enough since they only capture a few conditional distributions instead of the whole distribution, especially for small datasets. …
Researchers create BPS monopoles with any desired symmetry breaking.
problem Creating monopoles with specific symmetry breaking patterns.
method Using a new class of Nahm data to construct finite energy BPS monopoles.
result Arbitrary symmetry breaking monopoles can be constructed.
We define toric contact manifolds in arbitrary codimension and give a description of such manifolds in terms of a kind of labelled polytope embedded into a grassmannian, analogous to the Delzant polytope of a toric symplectic manifold.
New algorithm tackles adversarial bandits with arbitrary strategies.
problem Adversarial bandit problem against arbitrary strategies.
method Adopted master-base framework using online mirror descent method (OMD). Proposed adaptive learning rates for OMD.
result Achieved improved regret bounds compared to previous methods.
The paper constructs CR manifolds with arbitrary Levi nondegeneracy.
problem Creating CR manifolds with specific Levi nondegeneracy properties.
method Using CR algebras from su(2) representations, studying iterated Levi forms, and local model equations. result Explicit construction and analysis of homogeneous CR manifolds with arbitrary Levi nondegeneracy.
Generalizes halfspace theorems to higher dimensions for self-shrinkers.
problem Limitations of halfspace theorems in higher dimensions for self-shrinkers.
method Extends codimension 1 results to arbitrary codimension.
result Establishes new halfspace theorems for self-shrinkers in arbitrary codimension.
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.
We give explicit representation formulas for marginally trapped submanifolds of co-dimension two in pseudo-Riemannian spaces with arbitrary signature and constant sectional curvature. This paper is dedicated to the memory of Franki Dillen, 1963-2013.
Introduces a new tensor for electrostatic systems in arbitrary dimensions.
problem Developing a tensor for electrostatic systems in various dimensions.
method Comparison of Cotton and Weyl decompositions of the Riemann curvature tensor.
result The tensor is totally trace-free and satisfies symmetries of the Cotton tensor.
We determine the automorphisms and the continuous endomorphisms of the Einstein gyrogroup in arbitrary dimension. This generalizes a recent result of Lajos Molnár and Dániel Virosztek, who have determined the continuous endomorphisms in the three-dimensional case.
We consider the timelike minimal surface problem in Minkowski spacetimes and show local and global existence of such surfaces having arbitrary dimension ≥2 and arbitrary co-dimension, provided they are initially close to a flat plane.
Algorithm estimates mixtures of arbitrary Gaussians robustly in presence of corruptions.
problem Estimating mixtures of arbitrary Gaussians in the presence of a constant fraction of arbitrary corruptions.
method Polynomial-time algorithm using partial clustering and tensor decomposition.
result Resolves the main open problem in several previous works on algorithmic robust statistics.
Proves spacetime positive mass theorem for spin initial data sets with arbitrary ends.
problem Proving the spacetime positive mass theorem for specific spacetime configurations.
method Solving a mixed boundary value problem for the Dirac-Witten operator with a Callias potential.
result Established spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends.
In this article, we investigate the stability of leaves of minimal foliations of arbitrary codimension. We also study relations between Jacobi fields and vector fields which preserves a foliation and we use these results to Killing fields.
Newtonian dynamical systems which accept the normal shift on an arbitrary Riemannian manifold are considered. For them the determinating equations making the weak normality condition are derived. The expansion for the algebra of tensor fields is constructed.