arXiv research

Study reveals how travel times on cylindrical boundaries can identify spacetime structure.

Evolution of planar curves under a nonlocal geometric equation is investigated. It models the simultaneous contraction and growth of carbonate particles called ooids in geosciences. Using classical ODE results and a bijective mapping we demonstrate that the steady parameters associated with the physical environment det…

New method learns time-invariant rewards from demonstrations.

Paper tests if beta coefficients in AMF model are consistent over time.

A method for learning with autoregressive chain-of-thoughts.

We build a simple diagnostic criterion for approximate factor structure in large cross-sectional equity datasets. Given a model for asset returns with observable factors, the criterion checks whether the error terms are weakly cross-sectionally correlated or share at least one unobservable common factor. It only requir…

New test uncovers causal links in rare event dynamics.

SPAQL improves RL by adaptively partitioning state-action space and learning a time-invariant policy.

Paper derives an error bound for stochastic LTI systems.

The paper tackles joint learning of linear systems, improving accuracy with pooled data.

Paper tackles temporal overfitting in wind power curve modeling.

Recurrent and convolutional neural networks are the most common architectures used for time series forecasting in deep learning literature. These networks use parameter sharing by repeating a set of fixed architectures with fixed parameters over time or space. The result is that the overall architecture is time-invaria…

This paper focuses on using the first curvature $κ(t)$ of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems [Y. Wang, H. Sun, Y. Song et al., arXiv:1808.00290] to $n$-dimensional systems. We prove that for a system $\dot{r}(t)=Ar(t)$, (i) i…

This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $τ(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a measurable set $E_1$ with positive Lebesgue measure, such that $r(0)\in E_1$ implies t…

New model stabilizes asynchronous LTI systems, independent of synchronous stability.

We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the theories of large-deviations and self-normalized martingales, and provide both d…

This work represents an application of constant mean curvature graphs (as solutions of the mean curvature PDE) to non-linear non-Darcy flows in porous media. It relates time invariant pressure distribution graphs to graphs of constant mean curvature surfaces. This differential geometric interpretation provides an impor…

Study static Einstein-Maxwell space invariant by translation.

AR model forecasts partially observed dynamical time series by estimating evolution function and imputing missing variables.

This paper proposes a formal approach to online learning and planning for agents operating in a priori unknown, time-varying environments. The proposed method computes the maximally likely model of the environment, given the observations about the environment made by an agent earlier in the system run and assuming know…

Off-policy evaluation (OPE) in reinforcement learning is notoriously difficult in long- and infinite-horizon settings due to diminishing overlap between behavior and target policies. In this paper, we study the role of Markovian and time-invariant structure in efficient OPE. We first derive the efficiency bounds for OP…

Proposes a method to prove closing of periodic orbits in dynamical systems.

This work introduces sequential neural beamforming, which alternates between neural network based spectral separation and beamforming based spatial separation. Our neural networks for separation use an advanced convolutional architecture trained with a novel stabilized signal-to-noise ratio loss function. For beamformi…

Autoencoder detects subtle changes in time series data.

We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system. Even though the objective function is non-convex, we provide polynomial running …

In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes th…

New method calibrates asynchronous, error-prone covariates for longitudinal data.

We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee $O(\sqrt{T})$ regret under mild assumptions, where $T$ is the time horizon. Our algorithms rely …

Smooth manifolds have equivalent diffeomorphism groups if and only if they are diffeomorphic.

Constructs entropy-minimizing pseudo-Anosov diffeomorphisms on K3 surfaces.

Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their robustness is still yet unclear. In this work, we fill this important gap by expl…

The study proves diffeomorphisms can be localized to simpler submanifolds.

Paper derives explicit expression of Alekseev-Meinrenken diffeomorphism.

According to Pixton, there are Morse-Smale diffeomorphisms of the 3-sphere which have no energy function, that is a Lyapunov function whose critical points are all periodic points of the diffeomorphism. We introduce the concept of quasi-energy function for a Morse-Smale diffeomorphism as a Lyapunov function with the le…

We determine the Riemannian manifolds for which the group of exact volume preserving diffeomorphisms is a totally geodesic subgroup of the group of volume preserving diffeomorphisms, considering right invariant $L^2$-metrics. The same is done for the subgroup of Hamiltonian diffeomorphisms as a subgroup of the group of…

Generalizes $π_2$-diffeomorphism finiteness to non-zero first homotopy groups.

Study on group cocycles for volume-preserving diffeomorphisms.

Book introduces Hofer's metric on symplectic diffeomorphisms.

We consider the problem of learning a realization for a linear time-invariant (LTI) dynamical system from input/output data. Given a single input/output trajectory, we provide finite time analysis for learning the system's Markov parameters, from which a balanced realization is obtained using the classical Ho-Kalman al…

Study local diffeomorphisms of conformal circles in pseudo-Riemannian manifolds.

Survey on foliations and diffeomorphism groups.

New exotic 4D spaces found using knot slicing techniques.

A dynamical system can be regarded as an information processing apparatus that encodes input streams from the external environment to its state and processes them through state transitions. The information processing capacity (IPC) is an excellent tool that comprehensively evaluates these processed inputs, providing de…

The paper proves $n$-transitivity for equivariant diffeomorphisms of manifolds.

Study constructs solutions for evolving hypersurfaces using inverse spacetime mean curvature.

New 4-manifolds with exotic diffeomorphisms found.

Study exotic Dehn twists in 4-manifolds, producing first known exotic diffeomorphisms.

New Lie groups found for Poisson diffeomorphisms.