This paper proves a Nakai-Moishezon criterion for complex Hessian equations.
problem The solvability of complex Hessian equations on Kähler manifolds.
method Establishing a Nakai-Moishezon criterion for Kähler classes on analytic Kähler varieties.
result Proves Lejmi-Szekelyhidi's conjecture for the J-equation. The paper studies the modified J-equation on Kähler manifolds.
problem Solvability of the modified J-equation on compact Kähler manifolds.
method Characterization of solvability via coercivity of the modified J-functional; Nakai-Moishezon criterion formulation and verification.
result Extension of existence criteria for extremal Kähler metrics.
Criterion for solvability of complex 2-Hessian equation on compact Kähler manifolds.
problem Solvability of complex 2-Hessian equation on compact Kähler manifolds.
method Nakai--Moishezon-type criterion associated with the complex 2-Hessian equation.
result Criterion equivalent to existence of a smooth 2-admissible representative in complex dimension three.
Solves open problems for fully nonlinear elliptic equations on manifolds.
problem Solving fully nonlinear elliptic equations on manifolds.
method Analytic slope invariant and Nakai-Moishezon criterion.
result Solves open problems including hessian and hessian quotient equations.
Proves stability condition for Lagrangian sections in toric weak Fano manifolds.
problem Stability of Lagrangian sections in Calabi-Yau fibrations.
method SYZ transform, toric gamma theorem, Nakai-Moishezon criterion.
result Hamiltonian isotopy of Lagrangian sections under stability condition.
Paper characterizes tamed and weakened tamed four-manifolds using a new technique.
problem Characterizing tamed and weakened tamed four-manifolds.
method Using weakly \widetilde{\mathcal{D}}^+_J -closed technique.
result Characterization of tamed and weakened tamed four-manifolds.
The paper characterizes when numerical criteria for PDE solvability fail and provides effective criteria for existence.
problem Characterizing when numerical criteria for PDE solvability fail.
method Finite number of subvarieties violating Nakai type criterion, and their rigidity.
result Finite number of subvarieties violating the Nakai type criterion, and these subvarieties are rigid.
Let X be a complex projective variety and D a reduced divisor on X. Under a natural minimal condition on the singularities of the pair (X, D), which includes the case of smooth X with simple normal crossing D, we ask for geometric criteria guaranteeing various positivity conditions for the log-canonical divisor K_X+D. …
Paper confirms conjecture for projective manifolds in supercritical phase.
problem Stability condition for deformed Hermitian-Yang-Mills equation.
method Establishes stability result not involving uniform constants.
result Confirms conjecture for projective manifolds in supercritical phase.
The paper extends Nakamaye's theorem to non-closed forms on complex manifolds.
problem Analyzing non-closed (1,1)-forms on compact complex manifolds. method Developed analytic technique by Collins and Tosatti to study non-Hermitian loci.
result Non-Hermitian locus equals union of positive-dimensional null subvarieties.
We study Nakai-Moishezon type question and Donaldson's "tamed to compatible" question for almost complex structures on rational four manifolds. By extending Taubes' subvarieties--current--form technique to J−nef genus 0 classes, we give affirmative answers of these two questions for all tamed almost complex structu…
Study disproves a generalized numerical criterion for certain pairs.
problem Generalized numerical criterion for pairs
method Provided counterexamples
result Negative answer to the generalized numerical criterion problem
New polynomial criterion for periodic knots identified.
problem Identifying periodic knots efficiently.
method Examined HOMFLY-PT and Kauffman polynomials of periodic links.
result Criterion is stronger than existing methods.
New algorithms optimize a soft-robust criterion in reinforcement learning, reducing conservatism.
problem Computing robust policies for high-stakes decisions with limited data.
method Soft-robust criterion using risk measures, two algorithms for optimization.
result Our algorithms produce less conservative solutions than existing methods.
We introduce a new criterion to determine the order of an autoregressive model fitted to time series data. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information criterion. When the data is generated from a finite order autoregression, the Bay…
Modified Bakry-Émery criterion inequality for Tsallis entropy monotonicity.
problem Establishing improved logarithmic Sobolev inequalities and monotonicity of Tsallis entropy.
method Proving a one-parameter family of weighted Bakry-Émery Γ2 criterion inequalities and a modified inequality. result Yields a family of sharp Sobolev inequalities and monotonicity of Tsallis entropy.
A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an overestimating term of a widely applicable Bayesian information criterion. Adjustment of…
New criterion improves predictive evaluation in weighted inference scenarios.
problem Improving predictive evaluation in scenarios with different likelihoods for estimation and evaluation.
method Developed the posterior covariance information criterion (PCIC) to handle weighted likelihood inference.
result PCIC is asymptotically unbiased for quasi-Bayesian generalization error in weighted inference.
Criterion for stopping conjugacy class enumeration in triangle groups.
problem Enumerating all conjugacy classes in cocompact triangle groups.
method Encoding by P. Dehornoy and T. Pinsky; stopping criterion based on geometric length.
result Stopping criterion for the generation of conjugacy classes in cocompact triangle groups.
In [D.A. Fedoseev, V.O. Manturov, A sliceness criterion for odd free knots,arXiv:1707.04923], the authors proved a sliceness criterion for odd free knots: free knots with odd chords. In the present paper we give a similar criterion for stably odd free knots. Some additional results on knot sliceness and cobordism are g…
New criterion for solving inverse Hessian equations, including J-equation.
problem Existence of solutions to inverse Hessian equations, including J-equation.
method Stability of pairs in the sense of Paul, formulated in terms of GIT criterion.
result New numerical criterion for existence of solutions to inverse Hessian equations.
Criterion for nilpotent Lie groups to have nilsolitons.
problem Existence of nilsolitons in nilpotent Lie groups.
method Algebraic criterion for nilpotent Lie algebras, proving necessary and sufficient condition for nilsolitons.
result Criterion provides a necessary and sufficient condition for nilpotent Lie groups to admit nilsolitons.
Study proposes a stopping criterion for active learning based on error stability.
problem Improving predictive performance in active learning by adaptively annotating samples.
method Proposes a stopping criterion based on error stability for Bayesian active learning.
result Demonstrates the proposed criterion stops active learning at the appropriate timing for various models and datasets.
Clarifies boundary criterion for non-one-ended subgroups in cubulation theory.
problem Boundary criterion for relative cubulation in non-one-ended subgroups.
method Showed that if boundary criterion is satisfied for a relatively hyperbolic group, the group admits a relatively geometric action on a CAT(0) cube complex.
result The refinement of the boundary criterion is useful for constructing new relative cubulations.
Extends Kelly Criterion to more complex betting scenarios.
problem Maximizing long-term growth in complex betting models.
method Generalizes Kelly Criterion to Lévy processes and high-frequency limits.
result Improved strategies for high-frequency betting.
Derives criteria for Kähler structures on holomorphic submersions.
problem Criteria for Kähler structures on holomorphic submersions.
method Derives a criterion for Kähler structures using holomorphic submersions.
result Proves Kähler structures for certain holomorphic submersions.
Partial answer to affineness of entire Grauert tubes, with Stein manifold criterion.
problem Affineness of entire Grauert tubes
method Generalized Demailly's criterion for Stein manifolds
result Complement of a codimension-one subset is affine
Optimizes recommendation models using skew normal distribution.
problem Improving personalized recommendation systems.
method Develops a new optimization criterion based on skew normal distribution.
result Significantly outperforms state-of-the-art models.
Paper explains why small-loss criterion works for learning from noisy labels.
problem Learning from noisy labels in deep learning with limited labeled data.
method Theoretical analysis and reformulation of the small-loss criterion.
result Theoretical explanation and reformulation of the small-loss criterion.
New criterion assesses cluster separability for validation.
problem Validating cluster analysis results and determining the number of clusters.
method Distinguishability criterion, combined loss function-based framework.
result Validated cluster configurations and determined the number of clusters.
Criterion found for Teichmüller extremal maps on infinite Riemann surfaces.
problem Finding necessary and sufficient conditions for Teichmüller extremal maps.
method Established a criterion for Teichmüller-type extremal maps.
result Criterion for Teichmüller extremal maps on infinite Riemann surfaces.
Criterion for subgroup separability in outer automorphism groups.
problem Subgroup separability in outer automorphism groups.
method Criterion for separability of subgroups.
result Strengthening and generalizing a previous result on mapping class groups.
The study provides a criterion to compute the total Thurston-Bennequin invariant of Legendrian graphs.
problem Computing the total Thurston-Bennequin invariant for Legendrian graphs.
method Generalized criterion for computing the total Thurston-Bennequin invariant from the tb of smaller cycles.
result The criterion holds for graphs with up to 9 vertices and for infinite families of examples.
Paper proposes an algorithm for robust estimation using Huber's criterion.
problem Non-convexity and non-robustness of joint maximum likelihood estimation.
method Block-wise minimization majorization framework with data-adaptive step sizes.
result Improved convergence and robustness in sparse learning.
Extends Milnor's criterion to biharmonic functions.
problem Deciding surface type for biharmonic functions.
method Generalizes Milnor's criterion to biharmonic functions.
result Characterizes whether a surface is hyperbolic or parabolic for biharmonic functions.
New proof of Kobayashi's properness criterion using metric geometry.
problem Properness of L-action on homogeneous spaces. method CAT(0) metric geometry on non-compact Riemannian symmetric spaces.
result Established a similar criterion for properness of L-action on homogeneous spaces. A new criterion for deep active learning selects minimal labeled data points.
problem Efficiently select minimal labeled data points for deep neural networks.
method Diffuses label information over a graph of data representations to switch between exploration and refinement.
result The diffusion-based criterion outperforms existing methods in deep active learning.
Study introduces combinatorial criterion for quasi-isometry groups of Euclidean spaces.
problem Determining quasi-isometries of Euclidean spaces.
method Introduces PLδ-homeomorphisms and combinatorial criterion using vertices and edges of simplicial structures. result The center of the quasi-isometry group QI(Rn) is trivial. We obtain a constructive criterion for robust no-arbitrage in discrete-time market models with transaction costs. This criterion is expressed in terms of the supports of the regular conditional upper distributions of the solvency cones. We also consider the model with a bank account. A method for construction of arbitr…
Study shows the corrected Akaike criterion is inadmissible for estimating Kullback-Leibler discrepancy.
problem Inadmissibility of the corrected Akaike information criterion for estimating Kullback-Leibler discrepancy.
method Loss estimation framework to demonstrate inadmissibility and provide improved estimators.
result Improved estimators of Kullback-Leibler discrepancy are provided and perform well in reduced-rank situations.
New inequality criterion for a mean field equation on spheres.
problem Finding uniqueness in a mean field equation on spheres.
method Established a new Moser-Trudinger-Onofri inequality with a constraint on moments deviation.
result A threshold for deviation is a uniqueness criterion for the mean field equation.
In this paper, we investigate the geometry of a general class of gradient flows with multiple local maxima. we decompose the underlying space into disjoint regions of attraction and establish the adjacency criterion. The criterion states a necessary and sufficient condition for two regions of attraction of stable equil…
This work improves fair tensor decomposition using a kernel criterion.
problem Learning fair low-rank tensor decompositions with statistical parity.
method Regularizes Canonical Polyadic Decomposition with KHSIC to ensure approximate statistical parity.
result The proposed algorithm achieves better fairness and fit than state-of-the-art FATR.
Paper proves a new criterion for time-like geodesics in flat spacetimes.
problem Existence and nature of time-like geodesics in asymptotically flat spacetimes.
method Generalized topological criterion using the Jordan-Brouwer Separation Theorem and differential geometry.
result Conclusively affirms the presence of time-like geodesics intersecting transversally.
Categorical d-separation criterion simplifies probability graph analysis.
problem Detecting causal relationships in probability distributions.
method Introducing categorical definitions for causal models and d-separation.
result Abstract version of d-separation criterion applies to various probability theories.
Physical systems are modelled and investigated within simulation software in an increasing range of applications. In reality an investigation of the system is often performed by empirical test scenarios which are related to typical situations. Our aim is to derive a method which generates diverse test scenarios each re…
We prove by Hilbert-Mumford criterion that a slope stable polarized weighted pointed nodal curve is Chow asymptotic stable. This generalizes the result of Caporaso on stability of polarized nodal curves, and of Hasset on weighted pointed stable curves polarized by the weighted dualizing sheaves. It also solved a questi…
A new pruning criterion reduces model size and improves performance.
problem Overparameterized neural networks are computationally and memory intensive, leading to overfitting.
method Introduces a magnitude and uncertainty (M&U) pruning criterion inspired by statistical Wald test.
result Our M&U pruning criterion leads to more compressed models with less loss in predictive power.