Active learning framework for strict partial orders from concept prerequisite relations.
problem Lack of large-scale labels for mining strict partial order relations.
method Active learning framework incorporating relational reasoning.
result Framework improves classification performance with same query budget.
Strict convexity is essential for compact minimal surfaces in curved spaces.
problem Conditions for compact minimal surfaces in curved spaces.
method Analysis of minimal surfaces in curved manifolds with free boundaries.
result Strict convexity of the boundary is necessary for compact minimal surfaces.
Paper proposes a new method to predict partial rankings from crowdsourced data.
problem Ambiguity in pairwise comparisons leads to incomplete rankings, requiring a better method.
method Margin-based Maximum Likelihood Estimate (MLE) framework for probabilistic partial order learning.
result The proposed MLE method improves accuracy over traditional algorithms.
Let X be a norm curve in the SL(2,C)-character variety of a knot exterior M. Let t = || b || / || a || be the ratio of the Culler-Shalen norms of two distinct non-zero classes a, b in H_1(\partial M, Z). We demonstrate that either X has exactly two associated strict boundary slopes \pm t, or else there are strict bound…
Strict convexity of graphs with constant mean curvature is proven under certain conditions.
problem Proving strict convexity of graphs with constant mean curvature.
method Analyzing the Dirichlet problem for graphs with normalized constant mean curvature and planar boundary.
result The optimal solvability condition for the mean curvature of the boundary suffices to prove the strict convexity of the graph.
Develops a test for strict stationarity in stochastic processes.
problem Testing strict stationarity of discrete time stochastic processes.
method Window averaged sample estimate of second order cumulant spectrum, asymptotic complex standard normal distribution test.
result Test statistic derived and demonstrated with 137Cs gamma ray decay data.
Defines a strict order on plat presentation classes for links.
problem Ordering and classification of link presentation classes.
method Dehornoy order applied to braid group classes.
result Induces a strict total order on bridge isotopy classes of n-bridge positions.
Local minimality proven for stable free-boundary minimal hypersurfaces.
problem Proving local minimality for stable free-boundary minimal hypersurfaces.
method Using relative current setting and strict stability, proving local minimality among relative cycles.
result Local minimality of stable free-boundary minimal hypersurfaces in a small tubular neighborhood.
New tensor recovery method improves efficiency under strict complementarity.
problem Efficiently recovering low-rank tensors using tensor nuclear norm.
method Developed strict complementarity condition for tensor nuclear norm ball and applied to gradient methods.
result Standard gradient methods achieve linear convergence and nearly linear runtime under strict complementarity.
We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are available at regular primes, but we seek more conceptual answers in terms of lo…
Strong geodesic convex function and strong monotone vector field of order m m m on Riemannian manifolds have been established. A characterization of strong geodesic convex function of order m m m for the continuously differentiable functions has been discussed. The relation between the solution of a new variational inequal…
New proof shows how to identify DAGs with weakly increasing errors.
problem Identifying the true DAG in models with weakly increasing error variances.
method Minimum-trace DAG method and hill climbing algorithm with R2R neighborhood.
result Hill climbing algorithm without strict local optima under weakly increasing error variances.
New theory explains how momentum SGD helps avoid saddle points in nonconvex optimization.
problem Understanding convergence properties of Momentum SGD in nonconvex optimization.
method Diffusion approximations for nonconvex optimization problems with strict saddle points and isolated local optima.
result Momentum helps escape from saddle points but hurts convergence near optima.
Develops measures for non-Borel Anosov groups on Furstenberg boundary.
problem Measuring non-Borel Anosov groups on the Furstenberg boundary.
method Theory of Patterson--Sullivan measures, strict convexity, entropy rigidity.
result Existence, uniqueness, and ergodicity of measures on Furstenberg boundary.
Decomposes harmonic forms on almost Kähler manifolds, revealing non-trivial structure.
problem Primitive decomposition of harmonic forms on compact almost Kähler manifolds.
method Primitive decomposition of ∂ ˉ , ∂ \bar \partial, \partial ∂ ˉ , ∂ , Bott-Chern and Aeppli-harmonic ( k , k ) (k,k) ( k , k ) -forms. result Primitive components of harmonic forms are constants multiples of ω k ω^k ω k . The paper establishes conditions for strict power concavity in convolutions.
problem Conditions for strict power concavity in convolutions.
method Analyzes sufficient conditions for strict parabolic power concavity of convolutions.
result Establishes sufficient conditions for strict power concavity of convolutions.
Ribbon cobordism forms a partial order in 3-manifolds.
problem Understanding partial orders in 3-manifolds.
method Utilizing recent methods from Ian Agol's work on knot concordance.
result Ribbon rational homology cobordism forms a partial order.
In a Markovian model for a financial market, we characterize the best arbitrage with respect to the market portfolio that can be achieved using nonanticipative investment strategies, in terms of the smallest positive solution to a parabolic partial differential inequality; this is determined entirely on the basis of th…
New method speeds up NIR spectroscopy calibration by 400x.
problem Efficient preprocessing selection in NIR spectroscopy.
method Operator-adaptive PLS and Ridge regression.
result Significant reduction in fitting time with comparable prediction quality.
Optimal maps exist in very strict C D ( K , ∞ ) CD(K,\infty) C D ( K , ∞ ) spaces despite plan uniqueness issues.
problem Existence of optimal transport maps in very strict C D ( K , ∞ ) CD(K,\infty) C D ( K , ∞ ) spaces. method Introduced a more restrictive C D ( K , ∞ ) CD(K,\infty) C D ( K , ∞ ) condition and showed existence of optimal maps. result Existence of optimal maps in very strict C D ( K , ∞ ) CD(K,\infty) C D ( K , ∞ ) spaces. Geometric proof shows regularity of anisotropic minimal surfaces in 2D.
problem Regularity of anisotropic minimal surfaces in 2D.
method Geometric proof using surface energy and strict convexity.
result All anisotropic surface minimizers in 2D are locally disjoint unions of line segments.
Optimal online learning algorithms for label-efficient prediction and bandits.
problem Efficient prediction in online learning with limited information.
method Optimistic online mirror descent with second order corrections and hybrid regularizers.
result Improved regret bounds for label-efficient prediction and bandits.
We consider a Poisson process η η η on a measurable space $(\BY,\mathcal{Y})$ equipped with a partial ordering, assumed to be strict almost everwhwere with respect to the intensity measure λ λ λ of η η η . We give a Clark-Ocone type formula providing an explicit representation of square integrable martingales (defined with re…
Paper defines a partial order on multibranched surfaces in 3-manifolds.
problem Classifying and ordering essential multibranched surfaces in 3-manifolds.
method Introducing a partial order on neighborhood equivalence classes of multibranched surfaces.
result Atoroidal and acylindrical surfaces are minimal in the partial order.
Partial soft-matching distance improves neural representation comparison by allowing some neurons to remain unmatched.
problem Neural representations are noisy and contain outliers, making traditional matching methods unreliable.
method Extends soft-matching distance to a partial optimal transport setting, allowing some neurons to remain unmatched.
result Partial soft-matching provides robust correspondences that are more reliable under noise and outliers.
The paper studies strict equivalence in multi-virtual linkoids with new invariants.
problem Understanding strict equivalence in multi-virtual linkoids.
method Utilizing multi-virtual knot theory, defining strict virtual linkoids, and studying invariants.
result New invariants for strict virtual linkoids are defined.
Ribbon cobordisms form a partial order on 3-manifolds.
problem Understanding the partial order structure of 3-manifolds.
method Building on Agol's proof for knots, we extend the partial order to 3-manifolds.
result Ribbon rational homology cobordism forms a partial order.
Riemannian gradient descent escapes some spurious critical points on low-rank matrix manifold.
problem Spurious critical points on the boundary of low-rank matrix manifold.
method Riemannian gradient descent with dynamical low-rank approximation and rescaled gradient flow.
result Riemannian gradient descent escapes some spurious critical points on the boundary of the manifold.
Study strict stability of cones with isolated singularities.
problem Stability of cones with isolated singularities.
method Analyzes special Lagrangian and coassociative cones, provides examples for the complex case.
result Proves strict stability for special Lagrangian and coassociative cones.
Extends Mallows model to handle item indifference in rankings.
problem Real data often contains item indifference, challenging strict preference assumptions.
method Proposes Clustered Mallows Model (CMM) to accommodate item indifference.
result CMM provides a flexible representation of rank collections with ordered clusters.
FedAvg converges linearly to global minimum in federated learning with partial participation.
problem Challenges in federated learning with partial client participation.
method Federated averaging (FedAvg) method for over-parameterized neural networks.
result FedAvg converges to global minimum at a linear rate after t iterations.
Prove strong ribbon concordance induces a partial order on links, certify minimality for a handful of knots, and find minimal ribbon minimal knots.
problem Prove strong ribbon concordance induces a partial order on links.
method Use results from knot Floer homology to certify minimality under the ribbon partial order.
result Certify minimality for a handful of knots and find minimal ribbon minimal knots.
Maps Lie 2-groups to Weil algebras, showing cohomology isomorphisms.
problem Cohomology of strict Lie 2-groups.
method Constructs van Est map using double complex and Weil algebra.
result Induces isomorphisms in cohomology under connectedness.
Proves integrability of strict Lie 2-algebras using cohomological methods.
problem Integrability of strict Lie 2-algebras.
method Van Est theorems relating cohomologies of Lie 2-groups and algebras.
result Proves integrability of Lie 2-algebras.
Rational homology ribbon cobordism defines a partial order on 3-manifolds.
problem Classifying 3-manifolds based on their homology
method Proving a partial order on homeomorphism classes of 3-manifolds
result Closed, connected, oriented 3-manifolds are partially ordered by rational homology ribbon cobordism.
The paper computes torsion invariants for groups acting on complexes.
problem Computing torsion invariants for groups acting on complexes.
method Analyzes residually finite groups acting cocompactly on contractible complexes with specific stabilizers.
result Torsion limits to the torsion of the boundary subcomplex, independent of the chain of subgroups.
Differentiable relaxation for inferring partial orders from noisy linear data.
problem Inference of partial orders from linear data with noisy observations.
method Introducing a differentiable relaxation to model noisy linear extensions, replacing discontinuous precedence and feasibility with smooth surrogates.
result Smooth posterior that preserves partial-order semantics, supports gradient-based inference, and converges to hard likelihood.
We study strict local martingales via h-transforms, a method which first appeared in Delbaen-Schachermayer. We show that strict local martingales arise whenever there is a consistent family of change of measures where the two measures are not equivalent to one another. Several old and new strict local martingales are i…
The paper uses belief propagation to analyze rankings and partial orders from partial information.
problem Analyzing rankings and partial orders from incomplete data.
method Continuous spin system and belief propagation algorithm.
result Computes marginal distribution and approximates number of linear extensions.
Abstract shows entropy and convexity definitions of very strict C D ( K , N ) CD(K,N) C D ( K , N ) spaces are equivalent.
problem Equivalence of definitions of very strict C D ( K , N ) CD(K,N) C D ( K , N ) spaces. method Showed equivalence of definitions using entropy functionals and full displacement convexity class.
result Equivalence of definitions of very strict C D ( K , N ) CD(K,N) C D ( K , N ) spaces. In an earlier work, we constructed the almost strict Morse n n n -category X \mathcal X X which extends Cohen & \& & Jones & \& & Segal's flow category. In this article, we define two other almost strict n n n -categories V \mathcal V V and W \mathcal W W where V \mathcal V V is based on homomorphisms between real vector spaces and $\ma…
Study calculates eigenvalues and eigenfunctions for spherical triangles and finds fundamental gap behavior.
problem Understanding eigenvalues and gaps in spherical triangles.
method Explicit computation of Dirichlet eigenvalues and eigenfunctions for spherical lunes and triangles.
result Fundamental gap of spherical triangles increases as the angle of the lune decreases.
Paper proposes methods to learn DAGs from partial orderings.
problem Learning DAGs from partial orderings is challenging.
method General estimation framework and efficient algorithms for low- and high-dimensional problems.
result Efficient estimation of DAGs from partial orderings is possible.
The paper proves strict convexity of the Mabuchi functional for geodesics connecting energy minimizers.
problem Proving strict convexity of the Mabuchi functional for geodesics.
method Explicit formula for the complex Hessian of the weighted log-Bergman kernel, and proof by showing geodesics must be non-degenerate and smooth.
result Strict convexity of the Mabuchi functional along geodesics connecting energy minimizers.
Study contact partial order on non-compact manifolds.
problem Understanding contact partial order on non-compact manifolds.
method Analyzing orbits of adjoint action on Lie algebras of contactomorphism groups.
result Remnants of contact partial order on orbits of adjoint action.
Algorithm improves reinforcement learning in MDPs with partial order policies.
problem Improving reinforcement learning in MDPs with partial order policies.
method Epoch-based reinforcement learning algorithm leveraging a partial order over policy class.
result Achieves an O ( w log ( ∣ Θ ∣ ) T ) O(\sqrt{w \log(|Θ|) T}) O ( w log ( ∣Θ∣ ) T ) regret bound, independent of state and action space sizes. Proximal methods avoid local minima in weakly convex problems.
problem Weakly convex optimization problems with strict saddle properties.
method Proximal methods on nonsmooth functions with strict saddle guarantees.
result Proximal methods converge to local minimizers only, when initialized randomly.
It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…