We provide notions of numerical effectiveness and numerical flatness for Higgs vector bundles on compact Kähler manifolds in terms of fibre metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they…
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48 results for “numerically effective”
Kähler-Ricci flow singularity type is independent of initial metric.
problem Independence of singularity type for Kähler-Ricci flows.
method Analyzing solutions to the Kähler-Ricci flow on numerically effective manifolds.
result The singularity type of solutions is independent of the initial metric.
Kaehler manifolds with numerically effective Ricci class and maximal first Betti number are torimath.DG
Let M be an n-dimensional Kähler manifold with numerically effective Ricci class. In this note we prove that, if the first Betti number b_1(M)=2n, then M is biholomorphic to the complex torus T^n_C.
Study uses neural networks to solve complex equations efficiently.
problem Solving parametric partial differential equations.
method Machine learning and deep neural networks.
result Performance of the model is independent of parameter space dimension.
A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factorsstat.ML
Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and relate them via a multiresponse cross-covariance matrix. We introduce a substantiall…
A new method corrects weight values to improve treatment effect estimation.
problem Estimating heterogeneous treatment effects in high-dimensional data with sample selection bias.
method Differentiable Pareto-Smoothed Weighting (DPSW) framework.
result Our method outperforms existing methods in treatment effect estimation.
A new framework improves tensor completion accuracy by considering numerical priors.
problem Tensor completion accuracy loss due to ignoring numerical priors.
method Generalized CP Decomposition Tensor Completion (GCDTC) framework incorporating numerical priors.
result GCDTC framework outperforms state-of-the-arts in non-negative tensor completion.
Let X be a compact connected Kaehler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly, Peternell and Schenider says that there is a finite unramified Galois covering M --> X, a complex torus T, and a holomorphic surjective submersion f: M --> T, such that the fibers o…
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high accuracy. Upon recasting the problem into a function approximation problem, we …
Proposes a new model for estimating individual treatment effects.
problem Estimating individual treatment effects from observational data is challenging.
method Integrates diffusion modeling and conformal inference with propensity score and covariate approximation.
result Establishes rigorous theoretical guarantees and demonstrates competitive performance.
Method learns dynamics of slow variables from stochastic data.
problem Modeling unknown multiscale stochastic systems with limited data.
method Data-driven approach to learn effective dynamics from bursts of observation data.
result Generative model accurately captures effective dynamics of slow variables.
In this paper, we study numerically flat holomorphic vector bundles over a compact non-Kähler manifold with the Hermitian metric satisfying the Gauduchon and Astheno-Kähler conditions. We prove that numerically flatness is equivalent to numerically effectiveness with vanishing first Chern number, semistabl…
Paper approximates fractional harmonic maps with numerical methods.
problem Approximating fractional harmonic maps with constraints and nonlocality.
method Weak compactness results and numerical methods for various PDEs.
result Convergence of numerical approximations for fractional harmonic maps.
Financial companies continuously analyze the state of the markets to rethink and adjust their investment strategies. While the analysis is done on the digital form of data, decisions are often made based on graphical representations in white papers or presentation slides. In this study, we examine whether binary decisi…
In our work, we bridge deep neural network design with numerical differential equations. We show that many effective networks, such as ResNet, PolyNet, FractalNet and RevNet, can be interpreted as different numerical discretizations of differential equations. This finding brings us a brand new perspective on the design…
Despite the importance of handwritten numeral classification, a robust and effective method for a widely used language like Arabic is still due. This study focuses to overcome two major limitations of existing works: data diversity and effective learning method. Hence, the existing Arabic numeral datasets have been mer…
Numerical issues in maximum likelihood parameter estimation for Gaussian process interpolationstat.ML
Investigates numerical issues in GP interpolation parameter estimation.
problem Numerical issues in maximum likelihood parameter estimation for Gaussian process interpolation.
method Investigates and proposes strategies to improve open-source software implementations.
result Improves reliability and reproducibility of studies relying on GP implementations.
A novel robust meta-analysis model using the distribution for outlier accommodation and detectionstat.ME
A new meta-analysis model detects and accommodates outliers.
problem Outliers in meta-analysis studies can skew results.
method Proposes a novel Meta model using the distribution for robustness.
result Demonstrates superior performance in detecting and accommodating outliers.
We introduce a Vasicek-type short rate model which has two additional parameters representing memory effect. This model presents better results in yield curve fitting than the classical Vasicek model. We derive closed-form expressions for the prices of bonds and bond options. Though the model is non-Markov, there exist…
Paper introduces ENZ to measure significant coefficients in sparse recovery, improving over classical methods.
problem Numerical noise creates long tails of negligible coefficients in sparse recovery.
method Entropy-based notion of effective sparsity (ENZ) to measure significant coefficients, proving stability under restricted isometry condition.
result ENZ decomposes into support cardinality and efficiency factor, providing a precise measure of sparsity.
Machine learning models predict the behavior of negatively buoyant jets from wastewater.
problem Minimizing harmful effects of negatively buoyant jets during wastewater discharge.
method Training machine learning models (ANN, XGBoost, CatBoost, LightGBM) on OpenFOAM simulations and experimental data.
result Artificial Neural Network provided the best prediction with R2 0.98 and RMSE 0.28.
New method combines ODE filters and numerical quadrature to propagate model uncertainty.
problem Propagation of model uncertainty in ODE solutions with uncertain parameters.
method Combining ODE filters with numerical quadrature.
result Effective propagation of both numerical and parametric uncertainty.
In this paper we define a set of numerical criteria for a handlebody link to be irreducible. It provides an effective, easy-to-implement method to determine the irreducibility of handlebody links; particularly, it recognizes the irreducibility of all handlebody knots in the Ishii-Kishimoto-Moriuchi-Suzuki knot table an…
In this paper, a novel approach for coding nominal data is proposed. For the given nominal data, a rank in a form of complex number is assigned. The proposed method does not lose any information about the attribute and brings other properties previously unknown. The approach based on these knew properties can been used…
LLMs struggle with arithmetic tasks unless they use high numerical precision.
problem Improving arithmetical reasoning capabilities of LLMs.
method Theoretical analysis and empirical experiments on numerical precision.
result LLMs require high numerical precision to efficiently handle arithmetic tasks.
This work studies scaling laws for low-precision training in high-dimensional linear regression.
problem Optimizing trade-off between model quality and training costs in high-dimensional linear regression.
method Theoretical study of scaling laws for low-precision training within a high-dimensional sketched linear regression framework, analyzing multiplicative and additive quantization.
result Multiplicative quantization maintains full-precision model size, while additive quantization reduces effective model size.
Adversarial attacks against neural networks in a regression setting are a critical yet understudied problem. In this work, we advance the state of the art by investigating adversarial attacks against regression networks and by formulating a more effective defense against these attacks. In particular, we take the perspe…
Parallel-in-time solver reduces ODE simulation time from linear to logarithmic.
problem Efficiently solving ordinary differential equations (ODEs) with reduced computational cost.
method Formulated a parallel-in-time probabilistic numerical ODE solver using time-parallel formulation of iterated extended Kalman smoothers.
result Reduces span cost from linear to logarithmic in the number of time steps.
A new scheme for FBSDEs simplifies computation without Monte Carlo.
problem Numerical solution for decoupled FBSDEs with reduced complexity.
method Recursive marginal quantization for fully quantization-based scheme.
result Effective numerical procedure for financial applications.
Improved financial sentiment analysis using simple instruction tuning of LLMs.
problem Lack of accurate financial sentiment analysis by large language models.
method Instruction tuning of general-purpose LLMs with a small portion of financial sentiment data.
result Significant improvement in financial sentiment analysis, especially in complex scenarios.
Evaluating accuracy of community detection using the relative normalized mutual informationphysics.soc-ph
The Normalized Mutual Information (NMI) has been widely used to evaluate the accuracy of community detection algorithms. However in this article we show that the NMI is seriously affected by systematic errors due to finite size of networks, and may give a wrong estimate of performance of algorithms in some cases. We gi…
We study numerical restricted volumes of (1,1) classes on compact Kahler manifolds, as introduced by Boucksom. Inspired by work of Ein-Lazarsfeld-Mustata-Nakamaye-Popa on restricted volumes of line bundles on projective manifolds, we pose a natural conjecture to the effect that irreducible components of the non-Kahler …
New method uses SEMs to uncover cause-effect in manufacturing processes.
problem Complex cause-and-effect relationships in manufacturing processes.
method Using Structural Equation Models with non-linear relationships.
result More informative cause-effect relationships derived from data.
Develops numerical methods for pricing exchange options in a market with limited liquidity.
problem Pricing European style exchange options in a market with finite liquidity.
method Integrates price impact into the dynamics of correlated assets using a controlled variate approach.
result Numerical pricing methods for exchange options are developed and validated.
This paper improves change-point detection for complex data streams using denoising score matching.
problem Timely identification of distributional shifts in high-dimensional, complex data streams.
method Score-based CUSUM change-point detection with denoising score matching.
result Denoising score matching enhances detection power by effectively controlling noise scale.
This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock's price. Thus, we consider a full-feedback model in which price impact is fully incorporated into the model. The price …
We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. F…
Calibration of stochastic local volatility (SLV) models to their underlying local volatility model is often performed by numerically solving a two-dimensional non-linear forward Kolmogorov equation. We propose a novel finite volume (FV) discretization in the numerical solution of general 1D and 2D forward Kolmogorov eq…
In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier options. For getting the static hedging formula, the underlying process needs to have…
FBSJNN solves PIDEs and FBSDEJs with deep learning, offering theoretical and numerical efficiency.
problem Solving Partial Integro-Differential Equations and Forward-Backward Stochastic Differential Equations with Jumps.
method FBSJNN framework using a single neural network for both solution approximation and non-local integral.
result FBSJNN achieves numerical solutions with a relative error of , demonstrating efficiency.
Some recent studies have suggested using GANs for numeric data generation such as to generate data for completing the imbalanced numeric data. Considering the significant difference between the dimensions of the numeric data and images, as well as the strong correlations between features of numeric data, the convention…
The paper analyzes the intrinsic exploration terms in policy-gradient algorithms.
problem Exploration in policy-gradient algorithms and its impact on policy optimization.
method Numerical optimization criteria and stochastic gradient analysis.
result Exploration techniques improve policy optimization by smoothing the learning objective and modifying gradient estimates.
New neural network model improves treatment effect estimation.
problem Estimating treatment effects from observational data.
method Proposes a neural network model leveraging covariates and neighboring instances.
result Reports better treatment effect estimation performance.
New method for estimating heterogeneous treatment effects in panel data.
problem Estimating heterogeneous treatment effects in non-stationary, temporally dependent panel data.
method Proposes H1SL and H2SL, synthetic learners for panel data, based on existing non-panel data estimators.
result Established convergence rates for proposed estimators and demonstrated superior performance.
We consider the general Kähler-Ricci flows which exist for all time. The zeroth order control on the flow metric potential for various infinite time singularities is the focus. The possible semi-amplness for numerically effective classes serves as the main motivation.
Proves solution uniqueness for biomembrane shape prediction.
problem Proving solution uniqueness for the genus one Canham variational problem.
method Combining numeric analytic continuation and singularity analysis to prove non-negativity of a sequence.
result Proves positivity of the sequence, leading to solution uniqueness.
An efficient adaptive direct numerical integration (DNI) algorithm is developed for computing high quantiles and conditional Value at Risk (CVaR) of compound distributions using characteristic functions. A key innovation of the numerical scheme is an effective tail integration approximation that reduces the truncation …
With broad applications in various public services like aviation management and urban disaster warning, numerical precipitation prediction plays a crucial role in weather forecast. However, constrained by the limitation of observation and conventional meteorological models, the numerical precipitation predictions are o…