Study establishes time functions in Lorentzian spaces without requiring manifold structure.
problem Existence and properties of time functions in Lorentzian spaces.
method Characterization of time functions by K-causality, modified volume functions, and global hyperbolicity.
result No manifold structure is needed for suitable time functions in Lorentzian spaces.
Two new methods improve forecasting of functional time series data.
problem Forecasting of functional time-dependent data.
method Functional Singular Spectrum Analysis (FSFA) based forecasting methods.
result Our methods outperform existing algorithms for periodic stochastic processes.
This study improves estimation of locally stationary functional time series using NW method.
problem Accurately capturing time-dependence in locally stationary functional time series with time-varying covariates.
method Nadaraya-Watson (NW) estimation procedure for the conditional distribution of LSFTS.
result Established convergence rates of NW estimator for LSFTS with respect to Wasserstein distance.
Paper introduces a new time separation function for C0 spacetimes.
problem Lower semicontinuity of time separation function for C0 spacetimes. method Introduced nearly timelike curves to ensure lower semicontinuity.
result Lower semicontinuous time separation function for C0 spacetimes. Develops probabilistic forecasting for Sea Level Anomalies using Conformal Prediction on functional time series.
problem Forecasting and uncertainty quantification for Sea Level Anomalies.
method Functional data analysis, Conformal Prediction, Functional Autoregressive Processes.
result Proposed method provides accurate probabilistic predictions and uncertainty quantification for Sea Level Anomalies.
The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime (M,g) admits a smooth time function τ whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth…
Proposes a new model for non-linear regression of multivariate time series data.
problem Regression models for non-scalar variables, especially time series, have limitations.
method Develops a non-linear function-on-function model using neural networks.
result Demonstrates effectiveness through real-world applications.
Sequential modelling with self-attention has achieved cutting edge performances in natural language processing. With advantages in model flexibility, computation complexity and interpretability, self-attention is gradually becoming a key component in event sequence models. However, like most other sequence models, self…
Meta-learning for Koopman spectral analysis with short time-series data.
problem Lack of long time-series for training embedding functions in Koopman spectral analysis.
method Meta-learning approach using bidirectional LSTM and neural network to estimate embedding functions from short time-series.
result The proposed method achieves better performance in eigenvalue estimation and future prediction compared to existing methods.
DF2M uses deep neural networks within a factor model for high-dimensional functional time series forecasting.
problem Forecasting high-dimensional functional time series with explainability and accuracy.
method Bayesian nonparametric model based on Indian Buffet Process and multi-task Gaussian Process, incorporating a deep kernel function.
result DF2M provides better explainability and superior predictive accuracy compared to conventional deep learning models.
Novel method converts time series data into functional data for high dimensional classification.
problem Small sample size problem in high dimensional time series data.
method Classwise Functional Principal Component Analysis (PCA) followed by Bayesian linear classifier.
result Demonstrated efficacy on synthetic and real data sets.
Continuous-time Q-learning theory developed for reinforcement learning.
problem Continuous-time reinforcement learning challenges.
method Entropy-regularized, exploratory diffusion process formulation; first-order approximation of Q-function; martingale conditions.
result Developed a q-learning theory independent of time discretization.
Let (M,g) be a time oriented Lorentzian manifold and d the Lorentzian distance on M. The function τ(q):=supp<qd(p,q) is the cosmological time function of M, where as usual p<q means that p is in the causal past of q. This function is called regular iff τ(q)<∞ for all q and also $τ\to 0…
We give a geometrically intrinsic construction of a global time function for relatively compact diamond-shaped regions in arbitrary spacetimes. In the case of Minkowski spacetime, the flow of diffeomorphisms associated to a suitably normalized gradient of this time function becomes the conformal isotropy subgroup of th…
Study dynamic risk measures and performance indices using distortion functions.
problem Investigate time consistency of dynamic risk measures and performance indices generated by distortion functions.
method Analyze dynamic coherent risk measures (DCRMs) and dynamic weighted value at risk measures, proving their equivalence. Establish properties of families of DCRMs generated by distortion functions and define corresponding dynamic coherent acceptability indices (DCAIs). Examine time consistency of DCRMs and DCAIs.
result DCRM generated by distortion functions are sub-martingale time consistent but not super-martingale time consistent and not weakly acceptance time consistent.
Dynamic functional time-series methods improve forecast accuracy for foreign exchange implied volatility surfaces.
problem Forecasting implied volatility surfaces in foreign exchange markets.
method Dynamic functional principal component analysis and multivariate functional time-series methods.
result Dynamic univariate functional time-series method shows the greatest improvement in forecast accuracy.
In this paper, we propose two discontinuous dynamical systems in continuous time with guaranteed prescribed finite-time local convergence to strict local minima of a given cost function. Our approach consists of exploiting a Lyapunov-based differential inequality for differential inclusions, which leads to finite-time …
Study optimal portfolio strategies with time-varying discount rates.
problem Optimizing portfolio decisions with a non-constant discount rate.
method Introduced subgame perfect strategies to handle time inconsistency, using fixed point iteration to find the utility-weighted discount rate.
result Subgame perfect strategies are equivalent to optimal strategies under certain utility function assumptions.
Bayesian method tests Granger causality in functional time series.
problem Testing Granger causality between functional time series.
method Bayesian dynamic linear models (DLM) and Bayes Factor.
result Captures Granger causality between yield curves and weather conditions.
NeuTSFlow models continuous functions behind time series forecasting.
problem Forecasting treats time series as discrete sequences, ignoring their continuous nature.
method NeuTSFlow uses Neural Operators to learn the transition between historical and future function families.
result NeuTSFlow outperforms traditional methods in forecasting accuracy and robustness.
RST improves environmental time series classification accuracy using randomized B-spline trees.
problem Improving accuracy in classifying complex environmental time series.
method Randomized Spline Trees (RST) integrates randomized functional representations into ensemble learning.
result RST variants outperform standard Random Forests and Gradient Boosting on most environmental time series datasets.
Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.
problem Optimal stopping problems with finite-time horizon and state-dependent discounting.
method Linear diffusion process, time-homogeneous gain function, fine regularity properties, continuity and strict monotonicity proof.
result Proves continuity and strict monotonicity of the optimal stopping boundary under mild assumptions.
SurvFD and SurvSHAP-IQ provide interpretable survival models by analyzing feature interactions.
problem Non-additivity of hazard and survival functions limits standard additive explanation methods.
method SurvFD decomposes higher-order effects into time-dependent and time-independent components, extending Shapley interactions to time-indexed functions.
result SurvFD and SurvSHAP-IQ offer a new perspective on survival explanations, explicitly characterizing feature interactions.
AR model forecasts partially observed dynamical time series by estimating evolution function and imputing missing variables.
problem Forecasting dynamical time series with missing variables.
method Autoregressive with slack time series (ARS) model.
result ARS model forecasts future time series with time-invariant and linear assumptions.
The paper defines the time function of stock prices using a mathematical model.
problem Understanding the movement and predictability of stock prices over time.
method Empirical evidence and mathematical modeling of white noise.
result Derives auto-correlation function, displacement formula, and power spectral density of stock price movement.
This short note suggests a heuristic method for detecting the dependence of random time series that can be used in the case when this dependence is relatively weak and such that the traditional methods are not effective. The method requires to compare some special functionals on the sample characteristic functions with…
New algorithm learns value and advantage functions for continuous-time Markov processes without structural assumptions.
problem Learning value and advantage functions for continuous-time Markov processes without structural assumptions.
method Proposes Sobolev-prox fitted q-learning algorithm based on Hilbert-space positive definiteness and boundedness properties of Bellman operators. result Identifies ellipticity as a key structural property enabling reinforcement learning for Markov diffusions.
A new algorithm optimizes time-varying functions with non-constant evaluation times.
problem Optimizing functions that change over time with varying evaluation times.
method Proposes a novel time-varying Bayesian optimization algorithm.
result Establishes a regret bound for the proposed algorithm.
The paper contains a geometrization of the autonomous multi-time Lagrangian function of electrodynamics. We point out that this multi-time Lagrangian function comes from electrodynamics and the theory of bosonic strings.
We establish decoupled functional CLTs for two-time-scale stochastic approximation.
problem Understanding the asymptotic behavior of two-time-scale stochastic approximation.
method Martingale problem approach and auxiliary sequence.
result The limiting dynamics of two-time-scale SA are independent of each other.
A new Bayesian method optimizes time-dependent expensive functions with lookahead.
problem Maximizing a time-dependent, expensive oracle with limited evaluations.
method Recursive, two-step lookahead expected payoff (r2LEY) acquisition function.
result r2LEY outperforms myopic methods in synthetic and real-world datasets.
The paper classifies hypersurfaces in H2imesH2 with constant curvature.
problem Classifying hypersurfaces in H2imesH2 with constant sectional curvature. method Analyzing the geometry of H2imesH2 and constructing specific examples. result Examples of hypersurfaces in H2imesH2 with non-constant product angle function. A function that optimally aligns a timelike vector field with its gradients
problem Finding a time function that aligns a timelike vector field with its gradients
method Introducing a functional that penalizes null gradients and minimizes misalignment
result Proving the existence of a unique alignment time function under suitable conditions
Essentially, some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein.
A method for noise reduction in functional time series using FPCA.
problem Noise contamination in functional time series.
method Extending FPCA to separate signal and noise components.
result Optimal projection minimizes mean integrated squared error.
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.
The paper develops methods for time-varying constrained online convex optimization.
problem Time-varying loss and constraint functions in online convex optimization.
method Model-based augmented Lagrangian methods (MALM) for time-varying and delayed feedback.
result Sublinear regret and constraint violation for both time-varying and delayed feedback scenarios.
TVBO optimizes time-varying functions with asymptotically vanishing regret.
problem Understanding the asymptotic performance of TVBO for time-varying black-box functions.
method Provided upper and lower bounds for cumulative regret of TVBO algorithms.
result TVBO algorithms can achieve asymptotically vanishing regret under certain conditions.
We develop a new approach to the existence of time functions on Lorentzian manifolds, based on Conley's work regarding Lyapunov functions for dynamical systems. We recover Hawking's result that a stably causal admits a time function through a more general result giving the existence of a continuous function that is non…
Proves globally hyperbolic spacetimes via null distance completeness.
problem No Hopf-Rinow Theorem in Lorentzian Geometry.
method Observation of null distances and their behavior with time functions.
result Proves globally hyperbolic spacetimes via null distance completeness.
Proves Arnold-Thom conjecture for surfaces' arrival times.
problem Existence of limit tangents for gradient flow lines of surfaces.
method Gradient flow lines of mean curvature flows with neck or cylindrical singularities.
result Proves Arnold's conjecture for all mean convex mean curvature flows of surfaces.
This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension n≥3 with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes admit a globally defined constant mean curvature time function precisely when they a…
This paper explores the relation between convex functions and the geometry of space-times and semi-Riemannian manifolds (an investigation initiated by Gibbons-Ishibashi). Specifically, we study geodesic connectedness. We give geometric-topological proofs of geodesic connectedness for classes of space-times to which kno…
The goal of dynamic time warping is to transform or warp time in order to approximately align two signals together. We pose the choice of warping function as an optimization problem with several terms in the objective. The first term measures the misalignment of the time-warped signals. Two additional regularization te…
We discuss the minimum of Willmore functional of torus in a Riemannian manifold N, especially for the case that N is a product manifold. We show that when N=S2×S1, the minimum of W(T2) is 0, and when N=R2×S1, there exists no torus having least Willmore functional. When N=H2(−c)×S1, …
Neural network models improve survival analysis with reduced computation time.
problem Limited expressiveness of standard survival models.
method Piecewise neural network models of hazard and density functions.
result Models outperform state-of-the-art models with less computation time.
Improved SVRG for quadratic functions achieves better performance and running times.
problem Minimizing quadratic functions with a specific type of Hessian matrix.
method Variant of SVRG algorithm for quadratic functions with improved analysis.
result Improved performance and running times for quadratic functions compared to state-of-the-art methods.
We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a deterministic part increasing with execution volume and a positive stochastic noise pa…