We study almost Kähler manifolds whose curvature tensor satisfies the second curvature condition of Gray (shortly ). This condition is interpreted in terms of the first canonical Hermitian connection. It turns out that this condition forces the torsion of this connection to be parallel in directions ortho…
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48 results for “AK model”
We study special almost Kaehler manifolds whose curvature tensor satisfies the second curvature condition of Gray. It is shown that for such manifolds, the torsion of the first canonical Hermitian is parallel. This enables us to show that every AK_2-manifold has parallel torsion. Some applications of this result, conce…
We define a large class of integrable nonlinear PDE's, \emph{-symmetric AKS systems}, whose solutions evolve on finite dimensional subalgebras of loop algebras, and linearize on an associated algebraic curve. We prove that periodicity of the associated algebraic data implies a type of quasiperiodicity for the soluti…
Let be a complete non-compact Riemannian surface. We consider operators of the form , where is the non-negative Laplacian, the Gaussian curvature, a locally integrable function, and a positive real number. Assuming that the positive part of is integrable, we address the question "…
The main purpose of this article is to prove that there exist no proper -manifold of dimension with vanishing Tricerri-Vanhecke Bochner curvature tensor and constant scalar curvature.
Active Kriging Monte Carlo simulation method with conformal certification for failure probability estimation
problem Failure probability estimation in structural reliability analysis
method Active learning framework with conformal prediction
result Improved uncertainty quantification and reliability of failure probability estimates
Modeling pollution from competing firms using mean-field games.
problem Pollution regulation of competitive firms producing similar goods.
method Developed a mean-field game model with cap-and-trade regulation.
result Explicit solutions found through Riccati differential equations.
New active learning method for kernel selection improves efficiency and accuracy.
problem Real-world applications where acquiring true labels is costly or time-consuming.
method Active Multiple Kernel Learning (AMKL) with adaptive kernel selection (AMKL-AKS).
result AMKL-AKS achieves optimal sublinear regret and better performance with fewer labeled data.
In this paper we study the analytic realisation of the discrete series representations for the group as a subspace of the space of square integrable sections in a homogeneous vector bundle over the symmetric space . We use the Szegö map to give expressions for the restric…
Recent research in economic theory attempts to study optimal economic growth and spatial location of economic activity in a unified framework. So far, the key result of this literature - asymptotic convergence, even in the absence of decreasing returns to capital - relies on specific assumptions about the objective of …
In this paper, we deal with the linear Weingarten factorable surfaces in the isotropic 3-space I^{3} satisfying the relation aK+bH=c, where K is the relative curvature and H the isotropic mean curvature, a,b,cR. We obtain a complete classification for such surfaces in I^{3}. As a further study, we classify all graph su…
Weingarten type surfaces in and math.DG
In this article, we study complete surfaces , isometrically immersed in the product space or having positive extrinsic curvature . Let denote the intrinsic curvature of . Assume that the equation holds for some real constants $…
Enhances GNNs to better capture local graph structures.
problem Limited expressiveness of GNNs due to star-shaped message passing.
method Extends local aggregation to subgraph patterns using GNN encoders.
result Significantly improved performance on graph ML tasks.
Generalized Ricci surfacesmath.DG
The study explores surfaces with curvature satisfying a specific relation, leading to isometric immersions and topological obstructions.
problem Curvature relations on smooth Riemannian surfaces and their geometric implications.
method Properties of log-harmonic functions and isometric immersions theorems.
result Characterization of surfaces that locally admit minimal isometric immersions into constant curvature manifolds.
We construct large families of new collapsing hyperkähler metrics on the K3 surface. The limit space is the quotient of a flat 3-torus by an involution. Away from finitely many exceptional points the collapse occurs with bounded curvature. There are at most 24 exceptional points where the curvature concentrates, which …
Arctic coastal morphology is governed by multiple factors, many of which are affected by climatological changes. As the season length for shorefast ice decreases and temperatures warm permafrost soils, coastlines are more susceptible to erosion from storm waves. Such coastal erosion is a concern, since the majority of …
Effective detection of fake news has recently attracted significant attention. Current studies have made significant contributions to predicting fake news with less focus on exploiting the relationship (similarity) between the textual and visual information in news articles. Attaching importance to such similarity help…
The paper explores the identifiability and interpretability of Gaussian process models using different kernel structures.
problem Identifiability and interpretability issues in Gaussian process models.
method The paper examines both single-output and multi-output Gaussian process models using additive and multiplicative mixtures of Matérn kernels.
result The smoothness of a mixture of Matérn kernels is determined by the least smooth component, and none of the mixing weights or parameters are identifiable.
Upper bounds for second Robin eigenvalue on Riemannian surfaces.
problem Bounding the second Robin eigenvalue of Schrödinger operators on Riemannian surfaces.
method Geometric upper bound via Hersch balancing argument on capped surfaces.
result Sharp geometric restrictions for minimal surfaces in negatively curved manifolds.
The paper optimizes risk-sensitive RL with CVaR, achieving near-minimax-optimal results.
problem Optimizing risk-sensitive reinforcement learning with CVaR objective.
method Developed algorithms for multi-arm bandits and online RL in MDPs, achieving near-minimax-optimal regret.
result Achieved near-minimax-optimal regret of for constant .
Survey and framework for efficient active learning in structural reliability.
problem Efficiently solving complex structural reliability problems.
method Generalized modular framework combining surrogate model, reliability estimation algorithm, learning function, and stopping criterion.
result 39 strategies for solving 20 reliability benchmark problems, highlighting the importance of surrogates and algorithms.
Near-optimal per-action regret bounds for sleeping bandits are derived.
problem Optimizing performance in sleeping bandits where arms and losses are chosen by an adversary.
method Directly minimizing per-action regret using generalized versions of EXP3, EXP3-IX, and FTRL with Tsallis entropy.
result Near-optimal bounds of order and are obtained.
New bounds on manifold widths and essential curves in high dimensions.
problem Bounding the -widths of submanifolds in Euclidean space.
method Introducing a new approach to systolic geometry involving non-linear complexes and averaging over isometries.
result Proved upper bounds on -widths and existence of essential curves in cubes.
The paper introduces BCART models for aggregate claim amount, improving frequency-severity and joint modeling.
problem Modeling aggregate claim amount with frequency-severity and joint dependencies.
method Developed three types of BCART models: frequency-severity, sequential, and joint models. Used various distributions for claim severity data.
result Weibull distribution outperforms gamma and lognormal for right-skewed, heavy-tailed claim severity data.
The paper uses model-based trees to create interpretable surrogate models for complex machine learning models.
problem Interpreting complex machine learning models.
method Using model-based trees to partition feature space and create interpretable models.
result Model-based trees generate optimal surrogate models that balance interpretability and performance.
Gauge Flow Modelscs.LG
Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.
problem Improving generative model performance.
method Integrates a learnable Gauge Field into Flow ODEs.
result Gauge Flow Models outperform traditional Flow Models in Flow Matching experiments.
The study examines how model predictions hold up under model extensions.
problem Model predictions may not be robust under model extensions, limiting their applicability.
method The study uses causal ordering to assess robustness of qualitative model predictions and characterizes model extensions that preserve predictions.
result Conditions and techniques are provided to assess robustness of model predictions under model extensions.
Revises Bayesian model averaging for foundation models.
problem Ensemble pre-trained and lightly-finetuned foundation models for improved classification performance.
method Introduces trainable linear classifiers and computationally cheaper model averaging scheme (OMA).
result Ensembled models can better predict on various datasets.
Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
New method to handle credit portfolio model uncertainties.
problem Model risk in credit portfolio models.
method Demonstrates comprehensive yet easy-to-implement approach to uncertainty in model parameters.
result Comprehensive method to deal with model uncertainties.
The paper tests stock return models and uses LSTM to predict stock returns.
problem Validating stock return models and predicting stock returns.
method Used Fama-French three-factor, four-factor, and five-factor models; also used LSTM model.
result Fama-French five-factor model shows better validity for stock returns.
Researchers review challenges in interpreting additive models, especially neural additive models.
problem Challenges in interpreting additive models, particularly neural additive models.
method Review of generalized additive models and discussion of nonidentifiability.
result Challenges in claiming interpretability or suitability for safety-critical applications of additive models.
Novel hybrid modeling combines ML and physics for real-time diagnosis.
problem Real-time diagnosis of complex systems.
method Combines machine learning and physics-based models to create reduced-order models.
result Generated models are two orders of magnitude simpler, improving efficiency.
CRS model improves ranking data modeling with theoretical guarantees.
problem Lack of rich, multimodal models for ranking data.
method Contextual Repeated Selection (CRS) model for multimodal ranking data.
result CRS model significantly outperforms existing methods in various ranking contexts.
Sigma models linked to Gross-Neveu models via quiver varieties.
problem Understanding the relationship between sigma models and Gross-Neveu models.
method Exploring the mathematical correspondence between sigma models and Gross-Neveu models, including their geometric and trigonometric/elliptic deformations.
result Sigma models are mathematically equivalent to Gross-Neveu models under certain conditions.
Interpretable machine learning has become a strong competitor for traditional black-box models. However, the possible loss of the predictive performance for gaining interpretability is often inevitable, putting practitioners in a dilemma of choosing between high accuracy (black-box models) and interpretability (interpr…
Simple models are preferred over complex models, but over-simplistic models could lead to erroneous interpretations. The classical approach is to start with a simple model, whose shortcomings are assessed in residual-based model diagnostics. Eventually, one increases the complexity of this initial overly simple model a…
Matryoshka hides secret models in a carrier model, achieving high capacity and robustness.
problem Stealing functionality of private ML data by hiding models in a carrier model.
method Parameter sharing approach exploiting the learning capacity of the carrier model.
result Hides a 26x larger secret model or 8 secret models in the carrier model.
Seq2Seq models speed up epidemic model predictions.
problem Complex epidemic models are computationally expensive.
method Used deep seq2seq models as surrogates for complex models.
result Surrogates predict scenarios up to several thousand times faster.
This work develops scalable model selection methods with fast update and selection.
problem Efficient model selection for large pools of candidate models.
method Isolated model embedding, which supports asymptotically fast update and selection.
result Standardized Embedder achieves competitive model selection performances.
Paper proposes BMPO to optimize policies using bidirectional models.
problem Model-based reinforcement learning's reliance on forward model accuracy.
method Develops BMPO using both forward and backward models for policy optimization.
result BMPO outperforms state-of-the-art methods in sample efficiency and asymptotic performance.
Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?q-fin.RM
Copulas outperform marginal models in multivariate risk forecasting, reducing model risk by narrowing down the set of models.
problem Model risk in multivariate risk forecasting, especially during crises.
method Comprehensive empirical study comparing Copula-GARCH models with fixed marginals, copulas, or neither.
result Model risk is almost entirely due to copula choice, not marginal models.
BayesBlend blends multiple models' predictions for better insurance loss predictions.
problem Improving insurance loss predictions by combining multiple models.
method Pseudo-Bayesian model averaging, stacking, and hierarchical stacking.
result BayesBlend provides a user-friendly way to blend model predictions and estimate weights.
The paper identifies when larger models improve predictions and proposes a switcher model.
problem Understanding when larger models benefit from added complexity.
method Numerical studies on T5 architecture to analyze predictive uncertainty and model performance.
result Large models improve on examples where small models are uncertain, but not on certain examples.
Improved diffusion model generation speed with speculative sampling.
problem Generating samples from computationally expensive diffusion models.
method Extending speculative sampling to diffusion models, using fast draft models for candidate token generation.
result Significant speedup in generation, halving the number of function evaluations.
We propose a generalization of neural network sequence models. Instead of predicting one symbol at a time, our multi-scale model makes predictions over multiple, potentially overlapping multi-symbol tokens. A variation of the byte-pair encoding (BPE) compression algorithm is used to learn the dictionary of tokens that …
The paper extends statistical inference methods for black-box generative models.
problem Understanding and validating black-box generative models without access to their internal data.
method Develops model-level statistical inference tasks using generative model representations.
result Model-level representations are effective for multiple inference tasks.
PMM uses Bayesian inference to generate data from noisy approximations.
problem Creating flexible generative models for various data types.
method Bayesian inference and conjugate pairs of distributions.
result PMM achieves performance competitive with existing generative models.