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.
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. 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.
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.
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. …
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.
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.
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.
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…
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 give some general criteria of being a homeomorphism for continuous mappings of topological manifolds, as well as criteria of being a diffeomorphism for smooth mappings of smooth manifolds. As an illustration, we apply these criteria to the problems arising in two- and three-dimensional grid generation.
The study reveals flaws in pruning criteria and proposes a new assumption for better filter selection.
problem Flaws in existing pruning criteria for CNNs.
method Empirical experiments and Convolutional Weight Distribution Assumption.
result The Convolutional Weight Distribution Assumption improves filter selection in pruning.
New method finds optimal hyperparameters for multiple tasks and criteria.
problem Finding optimal hyperparameters for multiple tasks and criteria.
method Multi-Task Multi Criteria (MTMC) method that provides Pareto-optimal solutions.
result The method selects optimal hyperparameters based on given criteria significance coefficients.
New criteria for Heegaard splittings ensure strong irreducibility and finite Goeritz groups.
problem Determining strong irreducibility and finite Goeritz groups of Heegaard splittings.
method Two diagrammatic criteria for Heegaard splittings, accepting arbitrary disk systems.
result Criteria ensure strong irreducibility and finite Goeritz groups for Heegaard splittings.
Multi-criteria recommender systems have been increasingly valuable for helping consumers identify the most relevant items based on different dimensions of user experiences. However, previously proposed multi-criteria models did not take into account latent embeddings generated from user reviews, which capture latent se…
Develops scenario theory for multi-criteria decision making.
problem Need for robustness assessment with multiple criteria and datasets.
method Collectively treats risks associated with individual criteria for multi-criteria decision problems.
result More accurate robustness certificates and sharper quantification of simultaneous criterion satisfaction.
We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single criterion, such as Euclidean distance. However, in many cases there may not exist …
The paper evaluates criteria for selecting cryptocurrencies based on historical data.
problem High risk of cryptocurrencies due to volatility.
method Characterized returns and risks using historical data in short time windows (7 and 15 days). Analyzed the importance of criteria using various methods.
result Importance of criteria for selecting cryptocurrencies is analyzed and evaluated.
We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or…
When sufficient labeled data are available, classical criteria based on Receiver Operating Characteristic (ROC) or Precision-Recall (PR) curves can be used to compare the performance of un-supervised anomaly detection algorithms. However , in many situations, few or no data are labeled. This calls for alternative crite…
The paper analyzes performance criteria for competing fund managers in Ito-diffusion markets.
problem Analyzing performance of competing fund managers in Ito-diffusion markets.
method Developed forward relative performance criteria and forward Nash equilibrium for passive and competitive cases.
result Extended performance criteria for investment problems in Ito-diffusion markets.
Paper defines numerical criteria to test handlebody link irreducibility.
problem Determining the irreducibility of handlebody links.
method A set of numerical criteria to test handlebody links for irreducibility.
result Effective method to recognize irreducibility of handlebody knots and most handlebody links.
We shall give useful criteria of lips, beaks and swallowtail singularities of smooth map from the plane into the plane. As an application of criteria, we will discuss the singularities of Cauchy problem of single conservation law.
A new method for multi-criteria recommender systems using graph attention networks.
problem Lack of nuanced relationships between users and items based on specific criteria.
method MDGAT, a multi-edge bipartite graph with dual attention networks and contrastive learning.
result MDGAT achieves higher accuracy in predicting item ratings compared to baseline methods.
New framework for resilient bi-criteria optimization under noisy feedback.
problem Bi-criteria combinatorial optimization with noisy function evaluations.
method Introducing (α,β,δ,extttN)-resilience and developing a black-box framework. result Achieves sublinear regret and constraint violation for bi-criteria bandit problems.
New algorithms minimize risk in MNL bandits, achieving near-optimal performance.
problem Minimizing risk in multi-armed bandit problems.
method Designing algorithms for various risk criteria (e.g., CVaR, Sharpe ratio, entropy risk).
result Near-optimal regret for the designed algorithms.
A game-theoretic approach to multi-criteria ranking from ordinal data.
problem Ranking objects from ordinal data with multiple criteria.
method Generalizing von Neumann winner to multi-criteria setting using Blackwell's approachability.
result The Blackwell winner can be computed as a convex optimization problem and achieves near-optimal sample complexity.
Stress, edge crossings, and crossing angles play an important role in the quality and readability of graph drawings. Most standard graph drawing algorithms optimize one of these criteria which may lead to layouts that are deficient in other criteria. We introduce an optimization framework, Stress-Plus-X (SPX), that sim…
Recent work on fairness in machine learning has focused on various statistical discrimination criteria and how they trade off. Most of these criteria are observational: They depend only on the joint distribution of predictor, protected attribute, features, and outcome. While convenient to work with, observational crite…
Criteria found for graph drawings on surfaces.
problem Graph drawings on surfaces.
method Criteria for integer and modulo 2 embeddability.
result Found criteria for graph drawings on surfaces.
Fairness in machine learning has predominantly been studied in static classification settings without concern for how decisions change the underlying population over time. Conventional wisdom suggests that fairness criteria promote the long-term well-being of those groups they aim to protect. We study how static fairne…
The paper introduces risk consistency properties for credit ratings.
problem Promoting prudent investment decisions in credit ratings.
method Introducing and studying risk consistency properties in the framework of Choquet rating criteria.
result Characterization of Choquet risk measures and rating criteria satisfying risk consistency properties.
Many machine learning frameworks, such as resource-allocating networks, kernel-based methods, Gaussian processes, and radial-basis-function networks, require a sparsification scheme in order to address the online learning paradigm. For this purpose, several online sparsification criteria have been proposed to restrict …
Study tackles criterion collapse in learning criteria, showing conditions for loss minimization.
problem Criterion collapse in optimization, focusing on error probability minimizers.
method Analyzes various learning criteria, including DRO, OCE risks, and non-monotonic criteria.
result Non-monotonic criteria can avoid collapse, while monotonic ones cannot.
Simple criteria for codimension two surface singularities.
problem Identifying singularities in surfaces of codimension two.
method Provided criteria for singularities in surfaces of codimension less than or equal to two.
result Conditions for codimension two singularities in ruled surfaces and center maps.
Managing risk in dynamic decision problems is of cardinal importance in many fields such as finance and process control. The most common approach to defining risk is through various variance related criteria such as the Sharpe Ratio or the standard deviation adjusted reward. It is known that optimizing many of the vari…
Study finite-type solutions of elliptic sinh-Gordon equation with Durham boundary conditions.
problem Finite-type solutions of elliptic sinh-Gordon equation with Durham boundary conditions.
method Determine rationality criteria for Durham conditions and analyze spectral curve properties.
result Rationality criteria are sufficient for finite-type solutions with complementary boundary conditions.
We give criteria for Morin singularities into higher dimensions. As an application, we study the number of A-isotopy classes of Morin singularities.
A government has to finance a risk for its population. It shares the charges among the population with a fixed scale based on economic criteria. Various organisms have to collect and to redistribute fairly the subsidies. Under these conditions, when the size of the organisms is varied, the distribution's laws of the cr…
This work compares data reduction criteria for online Gaussian Processes.
problem The computational complexity of Gaussian Processes limits their applicability to small datasets and streaming scenarios.
method Unified comparison of several data reduction criteria, analyzing computational complexity and reduction behavior.
result Practical guidelines for choosing a suitable data reduction criterion for online Gaussian Processes.
Study on algebraic curves' invariants and vanishing criteria.
problem Vanishing criteria for Griffiths infinitesimal invariants of algebraic curves.
method Analysis of moduli space of smooth genus 4 curves, study of normal functions.
result Vanishing criteria for the Griffiths infinitesimal invariants of Ceresa normal function.
Solves Skopenkov's problem on graph embedding criteria.
problem Criteria for toroidal embedding of one-vertex ribbon graphs.
method Analyzes one-vertex ribbon graphs with additional disc structure.
result Provides solutions to Skopenkov's problem.
We give criteria for Morin singularities for germs of maps into lower dimensions. As an application, we study the bifurcation of Lefschetz singularities.
Curvature criteria for A-simple singularities and their parallel curves identified.
problem Determining singularity types of A-simple singularities and their parallel curves.
method Defined curvature parameters and criteria for A-simple singularities.
result Criteria to determine singularity types of A-simple singularities and their parallel curves.
In this paper we extend temporal difference policy evaluation algorithms to performance criteria that include the variance of the cumulative reward. Such criteria are useful for risk management, and are important in domains such as finance and process control. We propose both TD(0) and LSTD(lambda) variants with linear…
A method to select validation data from a dataset using statistical criteria.
problem Selecting a validation basis from a full dataset for machine learning model validation.
method Adopting a 'design of experiments' point of view and using statistical criteria, particularly Maximum Mean Discrepancy criteria.
result The 'support points' concept is particularly relevant for selecting validation data.
The paper provides criteria and curvatures for singularities of curves in R^N.
problem Tackles the classification and characterization of singularities of curves in R^N.
method Systematic procedure for constructing criteria, explicit criteria for multiplicities 2-4, generalized curvatures.
result Generalized curvatures reinterpret Fukui's theorem for curves of finite multiplicities.