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. 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.
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. Algorithm finds small confidence sets for arbitrary distributions.
problem Learning high-density regions in arbitrary distributions.
method Competitive with sets from a concept class with bounded VC-dimension.
result Algorithm finds a confidence set with volume exp(ildeO(d1/2)) competitive with optimal ball. 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.
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…
Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
problem Proving the positive mass theorem for spin initial data sets with various ends and energy shields.
method Modification of Witten's approach involving an additional independent timelike direction in the spinor bundle.
result Positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
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.
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.
Study generalizes Möbius energy to non-smooth sets in arbitrary dimensions.
problem Investigate Möbius-invariant energies on non-smooth subsets of arbitrary dimensions.
method Show local finite energy implies embedded Lipschitz submanifold, and low fractional Sobolev regularity guarantees finite energy.
result Local graph structure of low fractional Sobolev regularity on a set is sufficient to guarantee finite energy.
Simplified identification methods for causal inference with arbitrary interventional distributions.
problem Estimating cause-effect relationships from data with experimental interventions.
method Using Single World Intervention Graphs and nested model factorization, we provide algorithms for identifying causal parameters from mixed observational and interventional distributions.
result Our algorithms are complete for certain types of interventional marginal distributions.
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.
Proves spacetime positive mass theorem in all dimensions.
problem Proving the spacetime positive mass theorem in arbitrary dimensions.
method Using Brendle--Wang's Riemannian positive mass theorem approach.
result Proves the spacetime positive mass theorem for all dimensions.
In an earlier paper of the authors it was shown that the sheaf theoretically based recently developed abstract differential geometry of the first author can in an easy and natural manner incorporate singularities on arbitrary closed nowhere dense sets in Euclidean spaces, singularities which therefore can have arbitrar…
New method for triclustering with reduced arbitrariness.
problem Need for reduced arbitrariness in specifying cluster size.
method Spectral decomposition of tensor slices and intersection of clusters.
result Effective triclustering on synthetic and real-world data.
Generalizes Fenchel conjugation to nonlinear functions on arbitrary sets.
problem Extending Fenchel conjugation to functions on arbitrary sets without structure.
method Replacing linear test functions with nonlinear ones, investigating properties including biconjugation.
result Derived further results on smooth manifolds and Lie groups, relating to convexity.
Given an arbitrary closed set A of Rn, we establish the relation between the eigenvalues of the approximate differential of the spherical image map of A and the principal curvatures of A introduced by Hug-Last-Weil, thus extending a well known relation for sets of positive reach by Federer and Zaehle. The…
Efficiently samples arbitrary compact bodies with polynomial complexity.
problem Uniform sampling from arbitrary compact bodies efficiently.
method Warm start algorithm under isoperimetry and volume growth condition.
result Substantial generalization of known results for convex and star-shaped bodies.
The paper constructs stable minimal hypersurfaces with specific singularities.
problem Creating minimal hypersurfaces with controlled singularities.
method Constructing hypersurfaces with a given singular set in a modified Euclidean space.
result Embedded minimal hypersurfaces with stable properties and specified singularities.
Algorithm learns arbitrary ReLU neurons under Gaussian inputs.
problem Learn an arbitrary ReLU activation over Gaussian marginals.
method Statistical Query (SQ) algorithm that outputs a ReLU activation achieving O(OPT)+ε loss. result First constant factor approximation for arbitrary bias in polynomial time.
Efficient algorithm for sampling from arbitrary compact bodies.
problem Sampling from arbitrary compact bodies efficiently.
method Warm start algorithm with polynomial complexity.
result Substantial generalization of known results for convex and star-shaped bodies.
Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed. In particular, the first variational fo…
Unordered feature sets are a nonstandard data structure that traditional neural networks are incapable of addressing in a principled manner. Providing a concatenation of features in an arbitrary order may lead to the learning of spurious patterns or biases that do not actually exist. Another complication is introduced …
We study the existence and uniqueness of smooth mean curvature flow, in arbitrary dimension and co-dimension, emanating from so called k-dimensional (ε,R) Reifenberg flat sets in Rn. Our results generalize the ones from a previous paper by the author, in which the co-dimension one case (i.e. $…
Understanding the dependencies among features of a dataset is at the core of most unsupervised learning tasks. However, a majority of generative modeling approaches are focused solely on the joint distribution p(x) and utilize models where it is intractable to obtain the conditional distribution of some arbitrary sub…
Employing a notion of curvature for arbitrary closed sets we prove an ABP-type estimate for a class of singular submanifolds of arbitrary codimension and bounded mean curvature recently introduced by B. White. A weak-Harnack-type estimate is then derived using the ABP estimate. These results generalize analogous result…
The paper sets lower bounds for adversarial robustness in multiclass classification.
problem Adversarial robustness in multiclass classification with arbitrary loss functions.
method Dual and barycentric reformulations for robust risk minimization.
result Sharp lower bounds for adversarial risks are computed efficiently.
Method constructs confidence regions for linear models with arbitrary predictors.
problem Constructing confidence regions for linear models with non-linear predictors.
method Mixed Integer Linear Programming for constraints.
result Empty confidence regions for hypothesis testing.
The Dirichlet Laplacian in curved tubes of arbitrary cross-section rotating with respect to the Tang frame along infinite curves in Euclidean spaces of arbitrary dimension is investigated. If the reference curve is not straight and its curvatures vanish at infinity, we prove that the essential spectrum as a set coincid…
The paper tackles entry prediction in row/column-exchangeable matrices with arbitrary missing data.
problem Prediction in matrices with arbitrary missing data.
method Proposes two practical algorithms: one for fast emulation and another for acceleration using algorithmic stability.
result Demonstrates superior performance in synthetic and real-world data sets.
This paper generalizes neural transport learning for free energy estimation in arbitrary state spaces.
problem Efficient estimation of free energy in various state spaces.
method Generalized neural transport learning approach for arbitrary state spaces.
result Validation of the proposed method's effectiveness and efficiency in diverse settings.
Study on homeomorphism groups of manifolds using set theory.
problem Relationship between set theory and homeomorphism groups of manifolds.
method First-order rigidity, type versus conjugacy, axiom of constructibility, projective determinacy.
result Under V=L, homeomorphism groups of manifolds are first-order rigid and conjugacy class is determined by type.
Dynamic acquisition of features improves predictions with limited data.
problem Limited or uncertain data requires additional relevant information for accurate assessments.
method Proposes models that dynamically acquire new features using conditional mutual information and arbitrary conditional flow.
result Demonstrates superior performance over baselines in multiple settings.
Sharp generalization of boundary regularity for area minimizing currents with arbitrary multiplicity.
problem Boundary regularity of area minimizing currents with multiplicity.
method Sharp generalization of Allard's boundary regularity theorem to higher multiplicity settings.
result The set of density Q/2 singular boundary points of T is Hm−3-rectifiable. Algorithm learns from both labeled and arbitrary test examples, giving guarantees for bounded VC dimension classes.
problem Learning from arbitrary test examples, not just perturbations.
method Selective transductive learning algorithm that outputs abstaining predictions.
result Nontrivial guarantees for bounded VC dimension classes with arbitrary train and test distributions.
Let G be a finite group and let M be a G-manifold. We introduce the concept of generalized orbifold invariants of M/G associated to an arbitrary group Gamma, an arbitrary Gamma-set, and an arbitrary covering space of a connected manifold Sigma whose fundamental group is Gamma. Our orbifold invariants have a natural and…
We develop a method for user-controllable semantic image inpainting: Given an arbitrary set of observed pixels, the unobserved pixels can be imputed in a user-controllable range of possibilities, each of which is semantically coherent and locally consistent with the observed pixels. We achieve this using a deep generat…
New algorithm estimates eigenspace with faulty nodes, matching performance of existing methods.
problem Estimating eigenspace in distributed systems with node failures.
method Develops an eigenspace estimation algorithm for distributed environments with arbitrary node failures.
result Matches performance of existing non-robust estimator up to an additive error.
An introduction to the applications of algebraic surgery to the structure theory of high-dimensional topological manifolds.
The paper proves the existence of area-minimizing hypersurfaces in AF manifolds of higher dimensions.
problem Existence of area-minimizing hypersurfaces in AF manifolds with arbitrary dimension and ends.
method Positive mass theorem for AF manifolds with arbitrary ends and global behavior for hypersurfaces in AF manifolds of dimension ≤ 8.
result Existence and behavior of area-minimizing hypersurfaces in AF manifolds of higher dimensions.
We consider the problem of learning from distributed data in the agnostic setting, i.e., in the presence of arbitrary forms of noise. Our main contribution is a general distributed boosting-based procedure for learning an arbitrary concept space, that is simultaneously noise tolerant, communication efficient, and compu…
Empirical risk minimization (ERM), with proper loss function and regularization, is the common practice of supervised classification. In this paper, we study training arbitrary (from linear to deep) binary classifier from only unlabeled (U) data by ERM. We prove that it is impossible to estimate the risk of an arbitrar…
Random small feature subsets outperform FS in diverse datasets.
problem The significance of selected features in high-dimensional datasets is questionable.
method Analysis of 28 diverse datasets (microarray, RNA-Seq, etc.).
result Any arbitrary set of features performs as well as or better than selected features across datasets.
We investigate whether a robot arm can learn to pick and throw arbitrary objects into selected boxes quickly and accurately. Throwing has the potential to increase the physical reachability and picking speed of a robot arm. However, precisely throwing arbitrary objects in unstructured settings presents many challenges:…
New bounds on inscribed triangles in arbitrary planar domains.
problem Finding inscribed triangles in arbitrary planar domains with specific angle constraints.
method Proving the existence of uniformly fat triangles and not-too-fat triangles in bounded open sets.
result Existence of a maximal number Θ (between 0 and 60) for inscribed triangles with angles ≥ Θ degrees.
We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new nonconvex algorithm for robust phase retrieval, namely Robust Wirtinger Flow to …