Related papers: Topological computation analysis of meteorological…
Spatio-temporal problems exist in many areas of knowledge and disciplines ranging from biology to engineering and physics. However, solution strategies based on classical statistical techniques often fall short due to the large number of…
Tensor time series (TTS) data, a generalization of one-dimensional time series on a high-dimensional space, is ubiquitous in real-world scenarios, especially in monitoring systems involving multi-source spatio-temporal data (e.g.,…
In this article, we review the interdisciplinary techniques (borrowed from physics, mathematics, statistics, machine-learning, etc.) and methodological framework that we have used to understand climate systems, which serve as examples of…
It is common for researchers to record long, multiple time series from experiments or calculations. But sometimes there are no good models for the systems or no applicable mathematical theorems that can tell us when there are basic…
We introduce Multivariate Multiscale Graph-based Dispersion Entropy (mvDEG), a novel, computationally efficient method for analyzing multivariate time series data in graph and complex network frameworks, and demonstrate its application in…
Argo floats measure seawater temperature and salinity in the upper 2,000 m of the global ocean. Statistical analysis of the resulting spatio-temporal dataset is challenging due to its nonstationary structure and large size. We propose…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-time…
Energy system models involve various input data sets representing the generation, consumption and transport infrastructure of electricity. Especially energy system models with a focus on the transmission grid require time series of…
The ground states of noninteracting fermions in one-dimension with chiral symmetry form a class of topological band insulators, described by a topological invariant that can be related to the Zak phase. Recently, a generalization of this…
Spatial heteroskedasticity refers to stochastically changing variances and covariances in space. Such features have been observed in, for example, air pollution and vegetation data. We study how volatility modulated moving averages can…
A strategy is presented to incorporate prior information from conceptual geological models in probabilistic inversion of geophysical data. The conceptual geological models are represented by multiple-point statistics training images (TIs)…
A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths --- the rare trajectories that transit between the folded and unfolded ensembles --- using only thermodynamic information, such as a…
Precipitation is a complex physical process that varies in space and time. Predictions and interpolations at unobserved times and/or locations help to solve important problems in many areas. In this paper, we present a hierarchical Bayesian…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
Spatiotemporal forecasting is critical in applications such as traffic prediction, climate modeling, and environmental monitoring. However, the prevalence of missing data in real-world sensor networks significantly complicates this task. In…
The Grey System Theory (GST) is a powerful mathematical framework employed for modeling systems with uncertain or incomplete information. This paper proposes an integration of the GST with time scales, a generalized approach that…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…
A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…