Paper solves a complex portfolio selection problem with time-inconsistent preferences.
problem Time-inconsistent preferences in portfolio selection.
method Unified framework with minimal assumptions, proving existence and uniqueness of solution.
result Existence and uniqueness of square-integrable solution for the integral equation.
Simplified uHMC with time integration improves accuracy and efficiency.
problem Improving the efficiency and accuracy of Hamiltonian Monte Carlo algorithms.
method Randomized time integrator for uHMC with stratified Monte Carlo.
result Achieves more accurate approximations with fewer gradient evaluations.
New method samples from time-integrated stochastic bridges using neural networks.
problem Sampling from time-integrated stochastic bridges with high accuracy and speed.
method Polynomial chaos expansion and artificial neural networks.
result Robust, data-driven Monte Carlo sampling with thousands of samples in milliseconds.
We prove that a Ricci flow cannot develop a finite time singularity assuming the boundedness of a suitable space-time integral norm of the curvature tensor. Moreover, the extensibility of the flow is proved under a Ricci lower bound and the boundedness of a space-time integral norm of the scalar curvature.
Path integral method calculates PDBS option prices with time-dependent parameters.
problem Pricing proportional double-barrier step options with time-dependent interest rates and volatilities.
method Path integral method applied to a quantum mechanical analogy of barrier options.
result Derivation of pricing kernel for PDBS options with time-dependent parameters.
HF-opt uses Hamiltonian dynamics to optimize functions, achieving accelerated rates with randomized integration time.
problem Optimizing functions efficiently and accelerating convergence rates.
method Randomized Hamiltonian flow (RHF) with accelerated convergence rates.
result RHGD achieves accelerated convergence rates similar to Nesterov's AGD.
In this note, we first prove that the solution of mean curvature flow on a finite time interval [0,T) can be extended over time T if the space-time integration of the norm of the second fundamental form is finite. Secondly, we prove that the solution of certain mean curvature flow on a finite time interval [0,T) …
The anomaly flow on a complex 3-fold is studied with integral Shi-type estimates and long-time existence conditions.
problem Long-time existence of the anomaly flow on a compact complex 3-fold.
method Integral Shi-type estimates adapted from integration-by-parts arguments, with a smallness condition on the slope parameter.
result Long-time existence of the anomaly flow on a compact complex 3-fold under a smallness condition on the slope parameter.
Theory of space-time currents for geometric evolutions.
problem Analysis of geometric evolutions driven by dislocations.
method Development of space-time integral currents with bounded variation, introduction of Lipschitz deformation distance.
result Agreement of Lipschitz deformation distance with integral Whitney flat metric for boundaryless currents.
Develops integrators for Hamiltonian systems in Jacobi manifolds.
problem Modeling conservative systems with dissipative and thermodynamic phenomena.
method Constructs structure-preserving integrators for Hamiltonian systems in Jacobi manifolds.
result Proposes a numerical integration technique compatible with Jacobi dynamics.
Proves long-time Ricci flow existence and topological rigidity for pinched integral curvature manifolds.
problem Proving long-time existence and topological rigidity for manifolds with pinched scale-invariant integral curvature.
method Proves long-time existence of Ricci flow for manifolds with bounded curvature and pinched scale-invariant integral curvature, converging to a flat metric.
result Flow converges to a flat metric, implying topological rigidity of the manifold.
Many introductory courses in quantum mechanics include Feynman's time-slicing definition of the path integral, with a complete derivation of the propagator in the simplest of cases. However, attempts to generalize this, for instance to non-quadratic potentials, encounter formidable analytic issues in showing the succes…
Continuous-time distributed mirror descent with integral feedback converges to global optimum.
problem Distributed optimization of a global strongly convex function with local convex components.
method Continuous-time distributed mirror descent with integral feedback.
result Asymptotic convergence to global optimum with constant step-size.
Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary time, N=1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interprete…
We find a simple expression for the probability density of ∫exp(Bs−s/2)ds in terms of its distribution function and the distribution function for the time integral of exp(Bs+s/2). The relation is obtained with a change of measure argument where expectations over events determined by the time integral…
Counterexample shows Ito integrand needn't be locally square integrable.
problem Ito integrand's square integrability condition is not always met.
method Provided a counterexample to Ito's Lemma's integrability condition.
result Ito integrand needn't be locally square integrable.
We study holomorphic integrable systems on the hyperkähler manifold G×Sreg, where G is a complex semisimple Lie group and Sreg is the Slodowy slice determined by a regular sl2(C)-triple. Our main result is that this manifold carries a canonical \textit{abstract int…
A new adaptive binarization technique using fuzzy integrals improves image quality.
problem Improving image thresholding quality.
method FLAT (Fuzzy Local Adaptive Thresholding) based on fuzzy integrals.
result The proposed FLAT method produces better image quality than traditional algorithms and neural networks.
DDD reformulated for sparse matrices, integrating trajectory and snapshot time series data.
problem Efficiently integrate trajectory and snapshot time series data.
method Reformulate DDD to use compact basis functions, reducing parameter scaling.
result Inference of sparse matrices reduces the number of parameters in DDD.
Improved efficiency in HMC samplers reduces dissipative behavior.
problem Reducing dissipative behavior in HMC samplers.
method Variable integration time and partial velocity refreshment.
result Efficiency improved by a √κ factor in Wasserstein-2 distance.
RHMC accelerates sampling from log-concave distributions.
problem Sampling from log-concave probability distributions efficiently.
method RHMC uses simulated Hamiltonian dynamics with random integration times.
result RHMC converges exponentially fast in KL divergence for log-concave distributions.
New method calculates geometric Brownian motion with affine drift and its integral.
problem Calculating the distribution of geometric Brownian motion with affine drift and its integral.
method Laplace transform approach and Heun differential equation.
result Joint distribution of geometric Brownian motion with affine drift and its integral can be determined.
This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable processes to the space of continuous adapted processes. It is characterized in te…
Study short-time existence of Ricci-DeTurck flow from rough metrics with Morrey-type integrability.
problem Short-time existence of Ricci-DeTurck flow from rough metrics with specific integrability condition.
method Rough existence theory, preservation and improvement of scalar curvature bounds.
result Preservation and improvement of distributional scalar curvature lower bounds under certain conditions.
Efficiently integrates stiff ODEs with vectorized methods.
problem Stiff systems and sparse training data in ODEs.
method Implicit, vectorized time integration with adjoint method.
result Achieves speed ups of greater than 100x on modern GPUs.
We introduce a "minimal" Kontsevich integral that generates the original Kontsevich integral while at the same time producing ribbons whose boundaries are the braids on which the minimal Kontsevich integral is evaluated. We generalize the definition of the Kontsevich integral to that of graphs in R^3 and study the beha…
We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous spaces SO(n)/SO(k1)×...×SO(kr), for any choice of k1,...,kr, k1+...+kr≤n. In particular, a new proof of the integrability of a Manakov symmetric rigid body motion around a fixed point is presented…
Study null curves and their motion in 3D flat space-time, leading to integrable hierarchies.
problem Understanding null curves and their motion in 3D flat space-time.
method Analyzing the motion of null curves and their surfaces, deriving integrability conditions and hierarchies.
result Obtained one- and two-soliton surfaces associated with the MKdV equation, showing singularities in finite time.
Survival MDN uses invertible functions to speed up survival analysis models.
problem Training neural ODEs for survival analysis is computationally expensive.
method Survival MDN applies an invertible positive function to MDN outputs.
result Survival MDN outperforms or matches other models on concordance, Brier score, and log-likelihood.
AdaPID optimizes diffusion-based samplers by dynamically adjusting schedules.
problem Optimizing the intermediate-time dynamics in diffusion-based samplers.
method Develops a time-varying stiffness schedule using Piece-Wise-Constant (PWC) parametrizations and a hierarchical refinement approach.
result QoS-driven PWC schedules consistently improve sampling fidelity and accuracy.
This paper examines the integration process of the Japanese major rice markets (Tokyo and Osaka) from 1881 to 1932. Using a non-Bayesian time-varying vector error correction model, we argue that the process strongly depended on the government's policy on the network system of the telegram and telephone; rice traders wi…
Extends integrability to cosymplectic manifolds.
problem Integrability of Hamiltonian systems on cosymplectic manifolds.
method Extended Arnold-Liouville and noncommutative integrability to cosymplectic manifolds, proved a variant of non-commutative integrability for specific fields, constructed action-angle variables.
result Variant of non-commutative integrability for evaluation and Reeb vector fields on cosymplectic manifolds.
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.
A novel symplectic integrator for Hamiltonian equations on $S_2^n \times T^{\ast} \RR^m$ is developed and studied. Partitioned Runge--Kutta methods for Hamiltonian systems on products of Hamiltionian manifolds are studied, specifically, algebraic conditions for their symplecticity are derived.
Improved path integral method for financial derivatives pricing.
problem Analytical intractability of financial derivative pricing models.
method Generalized semi-classical path integral approach to time-dependent Hamiltonians.
result Accuracy and computational efficiency of the path integral approach for derivatives pricing.
Study on surfaces in product space with curvature inequality.
problem Characterizing surfaces in SnimesR with total mean curvature. method Defined differential operators and proved integral inequalities.
result Integral inequality for closed stationary H-surfaces in SnimesR. We give time-slicing path integral formulas for solutions to the heat equation corresponding to a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold with boundary. More specifically, we show that such a solution can be approximated by integrals over finite-dimens…
We classify all integrable complex structures on 6-dimensional Lie algebras of the form g×g.
We consider solutions (M,g(t)), 0 <= t <T, to Ricci flow on compact, four dimensional manifolds without boundary. We prove integral curvature estimates which are valid for any such solution. In the case that the scalar curvature is bounded and T is finite, we show that these estimates imply that the (spatial) integral …
Gradient flow preserves speed for integral Menger curvature curves.
problem Optimizing curves with integral Menger curvature constraints.
method Projected Sobolev gradient flow in Hilbert space.
result Long-time existence and C1,1-bounds for the flow. This paper deals with the evaluation of double line integrals of the squared exponential covariance function. We propose a new approach in which the double integral is reduced to a single integral using the error function. This single integral is then computed with efficiently implemented numerical techniques. The perf…
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.
Improved time series forecasting with expert loss integration.
problem Enhancing time series forecasting accuracy and efficiency.
method Adaptive Mixture-of-Experts framework with expert-specific loss integration and online learning.
result Significantly improved forecasting accuracy and computational efficiency.
We study a time reparametrisation of the Newton type equations on Riemannian manifolds slightly modifying the Chaplygin multiplier method, allowing us to consider the Chaplygin method and the Maupertuis principle within a unified framework. As an example, the reduced nonholonomic problem of rolling without slipping and…
Derives integral representations for a Lévy process and its extremum, hitting time, with fast evaluation.
problem Efficiently evaluating the joint probability density function of a Lévy process, its supremum, and hitting time.
method Integral representations, Laplace-Fourier transforms, summation by parts, conformal deformation, trapezoid rules, Gaver-Wynn-Rho algorithm.
result Explicit calculations and fast evaluation of the joint cpdf for Lévy processes.
The aim of this note is to present simple proofs of the completeness of Manakov's integrals for a motion of a rigid body fixed at a point in Rn, as well as for geodesic flows on a class of homogeneous spaces SO(n)/SO(n1)×⋯×SO(nr).
New method for pricing American options in time-dependent models, improving accuracy and efficiency.
problem Pricing American options in time-dependent models with improved accuracy and efficiency.
method Semi-analytical pricing using a nonlinear Volterra integral equation and numerical methods.
result Improved accuracy and efficiency in pricing American options compared to forward finite difference solvers.
In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both the perpetual timer call options and the finite time-horizon timer call options…