arXiv research

This research improves deep neural networks for parameter identification and prediction in stochastic Volterra integral equations.

Path integral method calculates PDBS option prices with time-dependent parameters.

Paper proposes adaptive parameter selection for KGD algorithms.

Study integrability of quantized six-vertex model on torus.

Proposes a method to integrate learner models robustly against misspecifications.

Overview of integrable systems with symmetries, focusing on toric and semitoric systems.

The aim of this paper is to describe a class of conservative systems on $S^2$ possessing an integral cubic in momenta. We prove that this class of systems consists off the case of Goryachev-Chaplygin, the one-parameter family of systems which has been found by the author in the previous paper (dg-ga/9711005) and a new …

The anomaly flow on a complex 3-fold is studied with integral Shi-type estimates and long-time existence conditions.

We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the discontinuity of the stocha…

The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.

The paper discusses a new method for constructing two-step Darboux transforms of isothermic surfaces.

New integrable systems derived from Nijenhuis geometry.

Note on failure of Martingale Wasserstein Inequality in higher dimensions.

New framework discovers PDEs from sparse, noisy data.

Background: Pharmacokinetic evaluation is one of the key processes in drug discovery and development. However, current absorption, distribution, metabolism, excretion prediction models still have limited accuracy. Aim: This study aims to construct an integrated transfer learning and multitask learning approach for deve…

We introduce a novel systematic construction for integrable (3+1)-dimensional dispersionless systems using nonisospectral Lax pairs that involve contact vector fields. In particular, we present new large classes of (3+1)-dimensional integrable dispersionless systems associated to the Lax pairs which are polynomial and …

We prove nonexistence of a nontrivial integral that is polynomial in momenta of degree less than 7 for the Zipoy-Voorhees spacetime with the parameter $δ=2$

We prove that the quantum SO(3)-invariant of an arbitrary 3-manifold $M$ is always an algebraic integer, if the order of the quantum parameter is co-prime with the order of the torsion part of $H_1(M,\BZ)$. An even stronger integrality, known as cyclotomic integrality, was established by Habiro for integral homology 3-…

A new method simulates square-root processes efficiently.

Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other Monte Carlo methods, incurs a significant computational cost as it requires explic…

There is a well-known example of integrable conservative system on $S^2$, the case of Kovalevskaya in the dynamics of a rigid body, possessing an integral of fourth degree in momenta. Goryachev proposed a one-parameter family of examples of conservative systems on $S^2$ possessing an integral of fourth degree in moment…

Researchers compute Greeks for rough Volterra SV models using Malliavin calculus.

Paper explores robust regression methods and their bias-variance trade-off.

Integrates estimation and optimization for uncertain parameters.

Extends robust methods for causal inference, improving estimator performance.

An integrated and extendable approach for stress-testing loan portfolios

This work introduces a fixed-point optimization for variational inference.

The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the HMCA, we find that the 2MNI is more efficient than the conventional leapfrog integr…

We introduce a model for the dynamics of stock prices based on a non quadratic path integral. The model is a generalization of Ilinski's path integral model, more precisely we choose a different action, which can be tuned to different time scales. The result is a model with a very small number of parameters that provid…

We introduce the Variational Holder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to the variational parameters, the VH bound involves minimization of a convex upper bound to the intract…

Squared families are a new model class derived from linear transformations, offering convenient properties and universal approximation.

Construct Lax pairs for BKM equations and related integrable hierarchies.

Kernelised flows improve density estimation and generation with fewer parameters.

Equations of dispersionless Hirota type have been thoroughly investigated in the mathematical physics and differential geometry literature. It is known that the parameter space of integrable Hirota type equations in 3D is 21-dimensional and the action of the natural equivalence group Sp(6, R) on the parameter space has…

New equations reveal moduli space rigidity in geometric deformations.

In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a Hamilton-Jacobi-Bellman (HJB) partial differential equation, which we solve for bo…

Mathai-Quillen forms are used to give an integral formula for the Lefschetz number of a smooth map of a closed manifold. Applied to the identity map, this formula reduces to the Chern-Gauss-Bonnet theorem. The formula is computed explicitly for constant curvature metrics. There is in fact a one-parameter family of inte…

We construct an extension of the Kontsevich integral of knots to knotted trivalent graphs, which commutes with orientation switches, edge deletions, edge unzips, and connected sums. In 1997 Murakami and Ohtsuki [MO] first constructed such an extension, building on Drinfel'd's theory of associators. We construct a step …

It has been proved that on 2-dimensional orientable compact manifolds of genus $g>1$ there is no integrable geodesic flow with an integral polynomial in momenta. There is a conjecture that all integrable geodesic flows on $T^2$ possess an integral quadratic in momenta. All geodesic flows on $S^2$ and $T^2$ possessing i…

Improved KLMC for sampling under various conditions.

Integrable symmetries of diffieties are studied, leading to local morphisms.

Defines new bi-flat structures from integrable systems and flat coordinates.

We investigate centers of a body (the closure of a bounded open set) defined as maximum points of potentials. In particular, we study centers defined by the Riesz potential and by Poisson's integral. These centers, in general, depend on parameters and move with respect to the parameters. We give a necessary and suffici…

We prove an estimate for spherical functions $\varphi_λ(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $λ$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.…

A theorem proves integrability of Fréchet tangent distributions.

We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal…

The classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop parameter. As a matter of fact, the same result holds for $k$-symmetric spa…

Bayesian neural networks improve likelihood-free inference efficiency.