Related papers: An Affine-invariant Time-dependent Triangulation o…

This work presents a complete geometrical characterisation of divisible and indivisible time-evolution at the level of probabilities for systems with two configurations, open or closed. Our new geometrical construction in the space of…

Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as…

We study a classical reparametrization-invariant system, in which ``time'' is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a…

Temporal knowledge graphs represent temporal facts $(s,p,o,\tau)$ relating a subject $s$ and an object $o$ via a relation label $p$ at time $\tau$, where $\tau$ could be a time point or time interval. Temporal knowledge graphs may exhibit…

The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…

Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…

We propose a spatio-temporal data-fusion framework for point data and gridded data with variables observed on different spatial supports. A latent Gaussian field with a Mat\'ern-SPDE prior provides a continuous space representation, while…

The influence of natural image transformations on receptive field responses is crucial for modelling visual operations in computer vision and biological vision. In this regard, covariance properties with respect to geometric image…

This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…

The problem of broad practical interest in spatiotemporal data analysis, i.e., discovering interpretable dynamic patterns from spatiotemporal data, is studied in this paper. Towards this end, we develop a time-varying reduced-rank vector…

Gaussian random fields with Mat\'ern covariance functions are popular models in spatial statistics and machine learning. In this work, we develop a spatio-temporal extension of the Gaussian Mat\'ern fields formulated as solutions to a…

The increasing ability to collect data from urban environments, coupled with a push towards openness by governments, has resulted in the availability of numerous spatio-temporal data sets covering diverse aspects of a city. Discovering…

We propose an off-line approach to explicitly encode temporal patterns spatially as different types of images, namely, Gramian Angular Fields and Markov Transition Fields. This enables the use of techniques from computer vision for feature…

Analyte response is convoluted with instrument response in time resolved fluorescence data. Decoding the desired analyte information from the measurement usually requires iterative numerical convolutions. Here in, we show that time resolved…

Temporal networks -- sequences of time-stamped contacts among nodes -- constitute the finest-grained representation of dynamic interaction data; however, geometric and topological analyses of such networks have remained largely confined to…

Traffic time series forecasting is challenging due to complex spatio-temporal dynamics time series from different locations often have distinct patterns; and for the same time series, patterns may vary across time, where, for example, there…

An alternative data-driven modeling approach has been proposed and employed to gain fundamental insights into robot motion interaction with granular terrain at certain length scales. The approach is based on an integration of dimension…

The ultra-long relaxation time of glass transition makes it difficult to construct atomic models of amorphous materials by conventional methods. We propose a novel method for building such atomic models using data assimilation method by…

We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…

Developmental transcriptional networks in plants and animals operate in both space and time. To understand these transcriptional networks it is essential to obtain whole-genome expression data at high spatiotemporal resolution. Substantial…