Related papers: Discrete Time Elastic Vector Spaces

Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…

We present a relational framework in which temporal structure is not fundamental but emerges from correlations within a globally stationary quantum state. Each subsystem includes an internal clock, and conditional states evolve effectively…

We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a…

Time crystals are many-body states that spontaneously break translation symmetry in time the way that ordinary crystals do in space. While experimental observations have confirmed the existence of discrete or continuous time crystals, these…

Irregularly sampled time series commonly occur in several domains where they present a significant challenge to standard deep learning models. In this paper, we propose a new deep learning framework for probabilistic interpolation of…

Motivated by predicting intraday trading volume curves, we consider two spatio-temporal autoregressive models for matrix time series, in which each column may represent daily trading volume curve of one asset, and each row captures…

Temporal modulation unlocks possibilities to dynamically control and modify the response of electromagnetic systems. Employing explicit dependencies of circuit or surface parameters on time enables the engineering of systems with…

In this article, we extend the study of embedded corrector problems, that we have previously introduced in the context of the homogenization of scalar diffusive equations, to the context of homogenized elastic properties of materials. This…

Time series data is prevalent in a wide variety of real-world applications and it calls for trustworthy and explainable models for people to understand and fully trust decisions made by AI solutions. We consider the problem of building…

We investigate the question, "how does time flow?" and show that time may change by inversions as well. We discuss its implications to a simple class of linear systems. Instead of introducing any unphysical behaviour, inversions can lead to…

The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series…

We establish the existence of local, covariant time ordered products of local Wick polynomials for a free scalar field in curved spacetime. Our time ordered products satisfy all of the hypotheses of our previous uniqueness theorem, so our…

We introduce a new algebraic framework to describe gravitational scrambling, including the semiclassical limit of any out-of-time-order correlation function that is built out of operator insertions separated by approximately the scrambling…

We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restrictions imposed by the associativity…

We define a set inner product to be a function on pairs of convex bodies which is symmetric, Minkowski linear in each dimension, positive definite, and satisfies the natural analogue of the Cauchy-Schwartz inequality (which is not implied…

Existing deep learning models for Predictive Process Monitoring (PPM) struggle with temporal irregularities, particularly stochastic event durations and overlapping timestamps, limiting their adaptability across heterogeneous datasets. We…

Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…

In this work, we introduce a novel deep learning architecture, Variable Length Embeddings (VLEs), an autoregressive model that can produce a latent representation composed of an arbitrary number of tokens. As a proof of concept, we…

Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…

High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most…