We prove some criteria for uniform K-stability of log Fano pairs. In particular, we show that uniform K-stability is equivalent to -invariant having a positive lower bound. Then we study the relation between optimal destabilization conjecture and the conjectural equivalence between uniform K-stability and K-stabilit…
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48 results for “stability criteria”
Proposes a new stability measure for model fitting on similar feature data sets.
problem Model fitting on data sets with similar features is challenging.
method Tuning hyperparameters in a multi-criteria fashion with predictive accuracy and feature selection stability.
result Our approach achieves similar or better predictive performance than single-criteria and stability selection approaches.
Let be a Kähler manifold and let be a compact group that acts on in a Hamiltonian fashion. We study the action of on probability measures on . First of all we identify an abstract setting for the momentum mapping and give numerical criteria for stability, semi-stability and polystabili…
We study the stability of partitions involving two or more phases in convex domains under the assumption of at most two-phase contact, thus excluding in particular triple junctions. We present a detailed derivation of the second variation formula with particular attention to the boundary terms, and then study the sign …
We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not only extends but also provides a new approach (and proofs) to the classical stabili…
The paper develops stability criteria for real reductive Lie groups acting on manifolds.
problem Analyzing stability of real reductive Lie group actions on manifolds.
method Introduced a gradient map and maximal weight function to characterize stability conditions.
result Characterized stability, semistability, and polystability using numerical criteria.
New stability and isolation results for Einstein manifolds.
problem Stability and isolation of Einstein manifolds.
method Conditions on Weyl tensor for AH and ALE manifolds, Bochner tensor for Kähler and Sasaki manifolds.
result Established new stability criteria and isolation results for various types of Einstein manifolds.
From the work of Dervan-Keller, there exists a quantization of the critical equation for the J-flow. This leads to the notion of J-balanced metrics. We prove that the existence of J-balanced metrics has a purely algebro-geometric characterization in terms of Chow stability, complementing the result of Dervan-Keller. We…
Uniform criteria for stability of fixed points in various geometric structures.
problem Stability of fixed points in Poisson geometry and higher Lie theory.
method Uniform approach to criteria for stability, using differential graded Lie algebras and cohomology.
result Vanishing of a finite-dimensional cohomology group implies stability of fixed points.
S3VDC improves DC methods for scalability, stability, and simplicity.
problem Poor scalability, instability, and lack of simplicity in DC methods.
method Four algorithmic improvements: initial -training, periodic -annealing, mini-batch GMM initialization, and inverse min-max transform. S3VDC incorporates all improvements.
result S3VDC outperforms state-of-the-art methods on benchmark and industrial datasets.
We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical Q-divisors. First, we propose a condition in terms of certain anticanonical Q-divisors of given Fano variety, which we conjecture to be equivalent to the K-stability. We prove that …
Solves complex Hessian equations in unstable cases, proving unique canonical solutions with singularities.
problem Existence of smooth solutions to complex Hessian equations in unstable cases.
method Parabolic flows and moment-map energy functionals, focusing on J-equation and deformed Hermitian Yang-Mills equation.
result Proves existence of unique canonical solutions with singularities on Kahler surfaces.
On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examplesmath.PR
We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a non-deterministic and time inhomogeneous compensator. The BSDE generator function c…
Paper presents a novel method to assess boundedness and stability of nonlinear systems with variable delays.
problem Challenges in assessing boundedness and stability of vector nonlinear systems with variable delays and coefficients.
method Develops a novel framework to evaluate the evolution of solution norms in such systems by constructing scalar counterparts.
result Introduces new criteria for boundedness and stability and estimates the radii of containing balls for history functions.
On the use of artificial intelligence in financial regulations and the impact on financial stabilityecon.GN
AI threatens financial stability through misuse and stealth adoption.
problem Misuse and stealth adoption of AI in financial regulations.
method Analysis of AI's potential risks and criteria for AI suitability.
result AI will likely become widely used by stealth, affecting high-level financial functions.
We consider a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics, and we study the linear stability of those solutions relative to the flow. After deriving various criteria that imply linear stability, we turn our attention to left-invariant soliton metrics on (non-compac…
Suffocating Fire Salesq-fin.RM
Mathematical framework investigates fire sales amplification and stability.
problem Market instability caused by fire sales amplification.
method Developed a mathematical framework to investigate system characteristics and resilience.
result Characterized systems resilient to small shocks for financial stability assessment.
MOSS optimizes decision rules for accuracy and stability.
problem Constructing stable sets of decision rules.
method Multi-objective optimization framework incorporating sparsity, accuracy, and stability.
result MOSS outperforms state-of-the-art rule ensembles in predictive performance and stability.
We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of non-compact real reductive Lie groups on topological spaces that admit functions similar to the Kempf-Ness function. The point of this…
New methods improve stability of Sinkhorn algorithm in machine learning.
problem Stability of Sinkhorn semigroups in high-dimensional settings.
method Semigroup analysis based on contraction coefficients and Lyapunov-type operator-theoretic techniques.
result Unified and simplified arguments in Sinkhorn algorithm stability.
New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.
problem Characterizing cyclicity in weighted Besov spaces.
method Defining cyclicity indices based on potential theory and capacity, studying stability under perturbations, and linking zero set structure to cyclicity.
result Novel invariants and conditions for cyclicity in various function spaces.
New stability criteria for Fano varieties using generalized b-divisors.
problem Characterizing uniform -stability in Fano varieties.
method Introducing a new function and formalism for -stability, proving stability conditions for Kähler-Einstein metrics.
result Existence of a unique Kähler-Einstein metric implies uniform -log -stability when .
We present a new implementation of anisotropic mean curvature flow for contour recognition. Our procedure couples the mean curvature flow of planar closed smooth curves, with an external field from a potential of point-wise charges. This coupling constrains the motion when the curve matches a picture placed as backgrou…
Comparison of Lattice-Free and Lattice-Based Sequence Discriminative Training Criteria for LVCSReess.AS
Sequence discriminative training criteria have long been a standard tool in automatic speech recognition for improving the performance of acoustic models over their maximum likelihood / cross entropy trained counterparts. While previously a lattice approximation of the search space has been necessary to reduce computat…
The paper studies conjugate points on Lie groups with specific metrics.
problem Existence and properties of conjugate points on Lie groups with left-invariant metrics.
method Using reformulated index form in terms of adjoint action, the paper proves sufficient conditions for conjugate points and provides bounds and criteria.
result All geodesics in compact semisimple Lie groups have conjugate points, with upper and lower bounds on conjugate times.
New stability criteria for vector bundles linked to Hermite-Einstein geometry.
problem Stability of higher-rank vector bundles and their moduli spaces.
method Introducing -positivity and a smooth function for coherent subbundles, linking to Hermite-Einstein geometry.
result Hermite-Einstein bundles are uniformly semi-stable, and new stability conditions are established.
Characterizes geometric actions on graphs with flexible stabilizers.
problem Understanding geometric actions on flexible stabilizers.
method Defining generalized fine actions and proving relative quasi-convexity criteria.
result Characterizes Bowditch boundary points in relatively geometric actions.
Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that minimize the prediction error on a held out dataset. We argue that error reduction is o…
In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in inputs lead to unacceptably large variation in outputs. Our approach uses multi…
Functionals involving surface curvature are important across a range of scientific disciplines, and their extrema are representative of physically meaningful objects such as atomic lattices and biomembranes. Inspired in particular by the relationship of the Willmore energy to lipid bilayers, we consider a general funct…
This work examines the stability of GD and SGD near minima, revealing nonlinear dynamics that differ from linear analysis.
problem The stability of optimization algorithms like GD and SGD near minima is not well understood.
method The authors derive an exact criterion for stable oscillations of GD near minima in the multivariate setting, considering high-order derivatives.
result Nonlinear dynamics can diverge in expectation even if a single batch is unstable, challenging linear analysis.
The paper classifies Toda equations for noncompact symmetric spaces and their solutions.
problem Classifying Toda equations for noncompact symmetric spaces.
method Interpreting Toda equations as equations for metrics on holomorphic principal bundles and using stability criteria.
result Existence of solutions to geometric Toda equations for totally noncompact pairs.
The paper provides guarantees for clustering validity without distributional assumptions.
problem Validating clustering results without distributional assumptions.
method Generic method to obtain post-inference guarantees of near-optimality and stability for clustering.
result The guarantees do not depend on distributional assumptions but depend on the data set admitting a stable clustering.
Minimal surfaces in 4D space are stable if their Gauss map spherical area is less than 2π.
problem Stability of minimal surfaces in 4D space.
method Geometric criteria based on the Gauss map of minimal surfaces in terms of the spherical area.
result Minimal surfaces in 4D space are stable if their Gauss map spherical area is less than 2π.
Smooth actions on manifolds can be globally defined under certain conditions.
problem Globalizing partial smooth actions of Lie groupoids on smooth manifolds.
method Providing necessary and sufficient conditions for globalizability and analyzing orbit and stabilizer spaces.
result There exists a unique differentiable structure on the quotient space for free and proper actions.
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical stability as well as transitions between different stable states are found. This comb…
The paper studies deformations of Kundt metrics using nil-Killing vector fields.
problem Deformations of Kundt metrics in the direction of type III tensors.
method Characterizations within the Kundt class using nil-Killing vector fields.
result Theorem classifying algebraic stability of tensors and sufficient criteria for preserving spi's.
Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We address this limitation for the first time and develop a …
Structural Limits of OHLCV-Based Intraday Signals in MNQ Futures: A Systematic Falsification Studyq-fin.TR
Study finds no statistically significant trading edge in MNQ futures signals from OHLCV data.
problem Testing intraday momentum signals from OHLCV data in MNQ futures under realistic execution constraints.
method 947 trading days of five-minute data, 14 signal families evaluated, strict institutional criteria applied.
result No signal satisfies all criteria simultaneously, gross edge insufficient to overcome costs.
RENT selects stable features for robust model interpretation.
problem Stability in feature selection for robust model interpretation.
method RENT uses an ensemble of elastic net models trained on distinct subsets of data.
result RENT selects features with high stability improving model robustness.
The new business paradigms originate a strong necessity to re-think the theory of the firm with the aim to get a better understanding on the organizational and functional principles of the firm, operating in the investment economies in the prosperous societies. In this connection, we make the innovative research to adv…
Robo-advisors use MPC to create dynamic investment strategies.
problem Static allocation methods limit robo-advisors' effectiveness.
method Combines MPC with Hidden Markov Model and Black-Litterman for dynamic asset allocation.
result MPC-based strategies outperform static approaches in dynamic and risk-budgeting criteria.
Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on the tuning parameters that balance the trade-off between model fitting and model s…
High-dimensional models become unstable when sample size falls below a critical level, leading to a phase transition.
problem Instability in high-dimensional learning models when sample size is insufficient.
method Proved the necessity of a Fisher eigenvalue threshold for stability, introduced Fisher floor for verification.
result A sharp phase transition between reliable concentration and inevitable failure in high-dimensional learning.
We describe a new technique which minimizes the amount of neurons in the hidden layer of a random recurrent neural network (rRNN) for time series prediction. Merging Takens-based attractor reconstruction methods with machine learning, we identify a mechanism for feature extraction that can be leveraged to lower the net…
We propose the Margin Adaptation for Generative Adversarial Networks (MAGANs) algorithm, a novel training procedure for GANs to improve stability and performance by using an adaptive hinge loss function. We estimate the appropriate hinge loss margin with the expected energy of the target distribution, and derive princi…
Constructs stable bundles on K3 surfaces using monad construction.
problem Stability of bundles on K3 surfaces.
method Monad construction, Generalised Hoppe Criterion, computer aid.
result Examples of real stable bundles constructed on K3 surfaces.
A surface of constant mean curvature (CMC) equal to in a sub-Riemannian -manifold is strongly stable if it minimizes the functional up to second order. In this paper we obtain some criteria ensuring strong stability of surfaces in Sasakian -manifolds. We also produce new exampl…