Study geometric quantum confinement on special incomplete Riemannian manifolds.
problem Characterize quantum confinement on Grushin-type manifolds.
method Constant-fibre direct integral scheme combined with Weyl's analysis.
result Fully characterizes essential self-adjointness of Laplace-Beltrami operator.
This paper summarizes closed-form relations for SE(3) maps and their derivatives.
problem Closed-form expressions for SE(3) maps and their derivatives are scattered in the literature.
method Summarizes and provides proofs for relevant closed-form relations of the exponential and Cayley map on SE(3).
result Provides an implicit generalized-alpha scheme for rigid/flexible multibody systems using the Cayley map.
We review properties of so-called special conformal Killing tensors on a Riemannian manifold (Q,g) and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle TQ. We then address the question of generalizing this concept to a Finsler space, where the metric tensor field comes from a regular La…
Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a …
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 …
The paper efficiently solves a complex option valuation equation for two assets.
problem Valuation of European options under a two-asset Kou jump-diffusion model.
method Extends an efficient algorithm for a one-dimensional integral to a two-dimensional one, using operator splitting schemes for time discretization.
result The method achieves optimal computational cost and stable convergence for various operator splitting schemes.
A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are applied to hyperbolic systems of differential-geometric origin, like the sine-Go…
Given a representation up to homotopy of a Lie algebroid on a 2-term complex of vector bundles, we define the corresponding holonomy as a strict 2-functor from a Weinstein path 2-groupoid to the gauge 2-groupoid of the underlying 2-term complex. We construct a corresponding transformation 2-groupoid and we prove that t…
This paper proposes a new method to learn integration schemes for complex ODEs.
problem Learning efficient integration schemes for non-linear ODEs and their identification.
method A novel framework to learn integration schemes that minimize an integration-related cost function.
result The proposed learning-based approach provides integration schemes close to analytical solutions.
The paper develops and tests operator splitting schemes for American options in a complex model.
problem Efficient numerical solution of American options under a two-asset Merton jump-diffusion model.
method Adaptation of IMEX and ADI operator splitting schemes to solve the two-dimensional PIDCP.
result Investigates and compares the convergence and performance of eight operator splitting methods.
JKO scheme adds deceleration in rapidly changing metric curvature directions.
problem Understanding the implicit bias of the JKO scheme in Wasserstein gradient flow.
method Characterized the implicit bias of the JKO scheme at second order in η, modifying the energy functional.
result JKO scheme adds deceleration in directions where metric curvature of J is rapidly changing.
TOPNet integrates task-based evaluation into machine learning models.
problem Non-differentiable task-based evaluation criteria in real-world applications.
method Task-Oriented Prediction Network (TOPNet) with learnable surrogate loss function.
result TOPNet significantly outperforms traditional and heuristic models in financial prediction tasks.
MixUp explained as a special adversarial training technique.
problem Improving model robustness against adversarial attacks.
method Introducing directional adversarial training (DAT) and proving MixUp's equivalence to a specific subclass of DAT.
result The family of Untied MixUp schemes is equivalent to the entire class of DAT schemes and can improve upon MixUp.
New sampling method for Heston model reduces complexity.
problem Efficient sampling for Heston model's time integrated variance.
method Series expansion, change of measure, Chebyshev polynomial approximations.
result Strong, efficient sampling scheme established for Heston model.
Predicts solar dynamics with diffusion models, improving long-range dependencies.
problem Predicting solar dynamics with limited observable data.
method Multiscale inference scheme for diffusion models.
result Improved long-range predictions with reduced bias.
Via the transverse Hilbert scheme construction, we associate a holomorphic completely integrable system to a surface S endowed with a holomorphic symplectic form ω and a projection onto C. We provide a full characterization of the completely integrable systems that arise in this way.
Proposes exact inference for continuous-time Gaussian process dynamics.
problem Inexact inference methods for continuous-time Gaussian process dynamics are impractical for irregularly-sampled data.
method Uses higher-order numerical integrators to discretize dynamics with arbitrary accuracy and proposes multistep and Taylor integrators for exact inference.
result Demonstrates accurate representation of continuous-time systems through exact GP inference.
Study of Tannakian categories for integrable connections on Kaehler manifolds.
problem Understanding Tannakian categories for integrable connections on Kaehler manifolds.
method Analyzing pairs (E, D) where E is a trivial holomorphic vector bundle and D is an integrable holomorphic connection.
result The pro-algebraic affine group scheme uniquely determines the isomorphism class of compact Riemann surfaces.
A new simulation method for Volterra processes improves convergence for rough kernels.
problem Simulating Volterra processes with singular kernels.
method iVi (integrated Volterra implicit) scheme based on Inverse Gaussian distribution.
result The iVi scheme achieves weak convergence with few time steps, especially for rough kernels.
New symplectic scheme speeds up RMHMC.
problem Reducing computational burden in RMHMC.
method Explicit symplectic integration for non-separable Hamiltonians.
result Significant reduction in higher-order derivative calculations.
The paper compares numerical schemes for nonholonomic systems using retraction maps.
problem Optimal control of nonholonomic systems with numerical approximations.
method Retraction maps used as seed for geometric integrators of Hamilton equations.
result Performance comparison of symplectic and non-symplectic integrators.
We introduce the technique combining the features of integration schemes for SDYM equations and multidimensional dispersionless integrable equations to get SDYM equations on the conformally self-dual background. Generating differential form is defined, the dressing scheme is developed. Some special cases and reductions…
Detects and traces masterminds behind cryptocurrency pump-and-dump schemes.
problem Identifying and tracing the entities organizing cryptocurrency manipulation.
method Collects real-time data from social networks and cryptocurrency markets, constructs temporal attributed graphs, and uses GNN to identify masterminds.
result Achieves higher F1 scores and precision than state-of-the-art fraud detection methods, detects 438 masterminds.
We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the computational efficiency gains achieved by the sparse grid combination technique.
Proposes a multi-view architecture for drug-target interaction prediction.
problem Representing compound-target pairs in deep learning models.
method Integrates differentiable and predefined molecular descriptors using an adversarial multi-view architecture.
result Demonstrates potential of the proposed approach on clinically relevant datasets.
Efficient simulation scheme for rough Heston model reduces computational cost.
problem Accurate and efficient simulation of the rough Heston model for option pricing.
method Weak simulation scheme based on Markovian approximations of the rough Heston process.
result The new scheme exhibits second order weak convergence with linear computational cost.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are …
This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a criterion of integrability for distributions on such convenient manifolds which are locally direct limits of particular sequences of Banach anc…
New clustering methods use motifs to organize networks.
problem Organizing directed graphs efficiently.
method Construct clustering methods parametrized by motifs.
result New clustering methods can organize networks.
Enhances HNNs for conservative systems with noisy data.
problem Modeling conservative systems with neural networks.
method Proposes a deep hidden physics model for continuous-time trajectory estimation.
result Integration scheme works well for HNNs, especially with low sampling rates.
We introduce a simulation scheme for Brownian semistationary processes, which is based on discretizing the stochastic integral representation of the process in the time domain. We assume that the kernel function of the process is regularly varying at zero. The novel feature of the scheme is to approximate the kernel fu…
Study shows thresholding scheme converges for mean curvature flow of convex sets.
problem Analyzing convergence of thresholding scheme for mean curvature flow.
method Time discretization using Merriman, Bence and Osher's scheme, focusing on two-phase mean convex settings.
result Time-integrated energy of approximation converges to limit's energy in minimizing movements interpretation.
Efficiently simulates the Heston model with large time steps using a novel method.
problem Challenges in simulating the Heston model with large time steps.
method Implicit integrated variance scheme exploiting the near-linear nature between stochastic driver and conditional integrated variance process.
result Achieves near-exact accuracy with coarse discretizations, efficient for large time steps.
ContinuousNet generalizes ResNets to continuous dynamical systems.
problem ResNets fail to be meaningful dynamical integrators.
method Embedding continuous dynamical systems into higher-order numerical integration schemes (Runge Kutta).
result ContinuousNet exhibits invariance to discrete time step sizes and numerical integration schemes.
Efficiently simulates SABR model with novel sampling methods.
problem Sampling integrated variance and terminal forward price in SABR model.
method Moment-matched shifted lognormal approximation for integrated variance, CEV approximation for terminal forward price.
result Enhanced simulation scheme is highly efficient, accurate, and reliable.
Paper develops a finite dimensional approximation scheme for Riemannian manifolds.
problem Integration on Riemannian manifolds.
method New finite dimensional approximation scheme motivated by categorical colimit.
result Establishes a generalization for L1-functionals on Riemannian manifolds. Geodesic flows with specific integrals are linked to special 4-webs.
problem Characterizing geodesic flows with commuting quadratic integrals.
method Characterization through geodesic 4-webs and geometric hypothesis.
result Metrics of Stäckel type for geodesic flows with specific integrals.
The paper integrates Gaussian processes into numerical integration schemes to improve accuracy and uncertainty quantification.
problem Improving the accuracy and uncertainty quantification in numerical integration schemes.
method Embedding Gaussian process regression into numerical integration schemes (Bulirsch-Stoer algorithm).
result Gaussian process regression can provide robust solutions even in scenarios where traditional polynomial extrapolation fails.
New integration method improves BSDE-based PDE solvers.
problem Discretization bias in standard BSDE-based solvers.
method Proposed Stratonovich-based BSDE formulation with stochastic Heun integration.
result Eliminates bias issues and outperforms EM-based variants.
Study uses FEM for HJB in option pricing with borrowing fees, improving accuracy and efficiency.
problem Optimal control problems in financial markets with frictions.
method Finite element method with non-uniform mesh, theta-scheme time integration, Newton-type algorithm.
result Efficient and accurate solution to HJB equation for option pricing with borrowing fees.
Research covers geometry, analysis, and integration on infinite-dimensional spaces.
problem Exploring geometric and analytical structures in infinite-dimensional settings.
method Analyzes numerical schemes, Lie groups, connections, and integration theory.
result Developed new methods for integration and analysis on infinite-dimensional manifolds.
We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie group integrators leads to global error estimates.
In the framework of path integral the evolution operator kernel for the Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-known Black-Scholes result. Possible approximation numerical schemes for path integral calculations are proposed.
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. We will assume that we can sample from the distribution of the process from time…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds a…
In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single time frames, followed by the application of a suitable kinetic model to time activity curves (TACs) at the voxel or region-of-interest level. The relatively new field of 4D PET dire…
Proposes a new method for medical image segmentation.
problem Medical image segmentation challenges.
method Decompose-and-Integrate Learning.
result Improves segmentation performance on multiple datasets.