arXiv research

Study of time-dependent metrics and connections in geometry.

This paper presents a new methodology for clustering multivariate time series leveraging optimal transport between copulas. Copulas are used to encode both (i) intra-dependence of a multivariate time series, and (ii) inter-dependence between two time series. Then, optimal copula transport allows us to define two distan…

The aim of this paper is to geometrize time dependent Lagrangian mechanics in a way that the framework of second order tangent bundles plays an essential role. To this end, we first introduce the concepts of time dependent connections and time dependent semisprays on a manifold $M$ and their induced vector bundle struc…

This research evaluates measures of dependence for financial time-series data.

Study on relativistic nonholonomic mechanics with time-dependent constraints.

An approach is proposed to determine structural shift in time-series assuming non-linear dependence of lagged values of dependent variable. Copulas are used to model non-linear dependence of time series components.

The paper analyzes time-dependent streaming data with biased gradient estimates and proposes improved stochastic optimization methods.

Proposes a method to estimate time-dependent probability density functions using binary classifiers.

Paper adapts causal analysis for time-dependent systems, especially energy management.

In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution of the time-dependent heat equation.

Modeling regime shifts in co-evolving time series with interactions and time-dependency.

Extremal dependence between international stock markets is of particular interest in today's global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with modeling extreme value dependence when that dependence is changing over time, o…

DynForest R package predicts outcomes with time-dependent predictors.

The paper analyzes convergence of Langevin dynamics with time-dependent metrics.

Discovering temporal lagged and inter-dependencies in multivariate time series data is an important task. However, in many real-world applications, such as commercial cloud management, manufacturing predictive maintenance, and portfolios performance analysis, such dependencies can be non-linear and time-variant, which …

A new boosting model handles dependent censoring in time-to-event data.

In this article we get a time-dependent Sobolev inequality along the Ricci flow which generalizes the earlier results of Zhang, Ye, Hsu. As an application of the time-dependent Sobolev inequality, we also get a growth of the ratio of bob-collapsing along the Ricci flow.

Combines CNN and Transformer for financial time series forecasting.

Deep neural nets learn from weakly dependent processes.

The usual formulation of time-dependent mechanics implies a given splitting $Y=R\times M$ of an event space $Y$. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The goal is the frame-covariant formulation of time-dependent mechanics on a bundle…

The paper justifies time-dependent loss reweighting schemes for flow matching and diffusion models.

The aim of this paper is to obtain on the dual 1-jet space J^{1*}(R;M) the main geometrical objects used in the dual jet geometry of time-dependent Hamiltonians. We talk about distinguished (d-) tensors, time-dependent semisprays, nonlinear connections and their mathematical connections.

Flexible Cox model for time-dependent covariates with complex sparsity patterns.

The paper extends Marsden-Weinstein reduction to mechanical presymplectic structures for time-dependent Hamiltonian systems.

Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type equations with time dependent parameters and give the general symmetry structure of th…

In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems. In particular, we generalize the cosymplectic structures to time-dependent Nambu-Poisson Hamiltonian systems and corresponding Jacobi's last multiplier for 3D systems. We illustrate our cons…

Learning a good distance measure for distance-based classification in time series leads to significant performance improvement in many tasks. Specifically, it is critical to effectively deal with variations and temporal dependencies in time series. However, existing metric learning approaches focus on tackling variatio…

We study the heat equation on time-dependent metric measure spaces (as well as the dual and the adjoint heat equation) and prove existence, uniqueness and regularity. Of particular interest are properties which characterize the underlying space as a super Ricci flow as previously introduced by the second author. Our ma…

Study heat flow on changing surfaces, proving existence and uniqueness.

We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…

A new RNN model tackles long-time dependencies with fast, invertible, and memory-efficient hidden states.

The book chapter discusses tail risk analysis for financial data using extreme value statistics.

We propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The …

SurvSHAP(t) explains time-dependent survival predictions from machine learning models.

Proposes a Koopman operator method for time-dependent reliability analysis of nonlinear systems.

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…

In this paper we study a collection of jet geometrical concepts, we refer to d-tensors, relativistic time dependent semisprays, harmonic curves and nonlinear connections on the 1-jet space J1(R;M), necessary to the construction of a Miron's-like geometrization for Lagrangians depending on a relativistic time. The geome…

Paper develops semi-analytic method for American options in time-dependent jump-diffusion models.

In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration…

Paper shows how scattering maps of Schrödinger equations relate to metrics.

Overview of high-dimensional time series regression methods.

The usual formulations of time-dependent mechanics start from a given splitting $Y=R\times M$ of the coordinate bundle $Y\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a splitting is broken under reference frame transformations and time-dependent canonical …

In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …

InfoAtlas speeds up MI estimation for real-time data analysis.

We introduce two types of ordinal pattern dependence between time series. Positive (resp. negative) ordinal pattern dependence can be seen as a non-paramatric and in particular non-linear counterpart to positive (resp. negative) correlation. We show in an explorative study that both types of this dependence show up in …

Extends PD-NJ-ODE to noisy observations and dependent observation times.

New method identifies nonstationary causal structures in time series data.

This paper considers an often forgotten relationship, the time delay between a cause and its effect in economies and finance. We treat the case of Foreign Direct Investment (FDI) and economic growth, - measured through a country Gross Domestic Product (GDP). The pertinent data refers to 43 countries, over 1970-2015, - …