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Time series anomaly detection is important in modern large-scale systems and is applied in a variety of domains to analyze and monitor the operation of diverse systems. Unsupervised approaches have received widespread interest, as they do…

We consider a new type of defect in the scope of linear elasticity theory, using geometrical methods. This defect is produced by a spherically symmetric dislocation, or ball dislocation. We derive the induced metric as well as the affine…

Spatiotemporal graph neural networks have shown to be effective in time series forecasting applications, achieving better performance than standard univariate predictors in several settings. These architectures take advantage of a graph…

Deep forecasting models often suffer from attenuated periodic perception and entangled trend-noise representations as network depth increases. Moreover, the widely adopted channel-independent paradigm, while improving training stability,…

Given a set of synchronous time series, each associated with a sensor-point in space and characterized by inter-series relationships, the problem of spatiotemporal forecasting consists of predicting future observations for each point.…

We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the {\it tendency} of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale…

In modelling time series data coming from different sources, frequencies can easily vary since some variable can be measured at higher frequencies, others, at lower frequencies. Given data measured over spatial units and at varying…

Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications,…

Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…

Encoder-decoder recurrent neural network models (RNN Seq2Seq) have achieved great success in ubiquitous areas of computation and applications. It was shown to be successful in modeling data with both temporal and spatial dependencies for…

Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…

We introduce persistence spheres, a novel functional representation of persistence diagrams. Unlike existing embeddings (such as persistence images, landscapes, or kernel methods), persistence spheres provide a bi-continuous mapping: they…

Many astrophysical phenomena are time-varying, in the sense that their brightness change over time. In the case of periodic stars, previous approaches assumed that changes in period, amplitude, and phase are well described by either…

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…

A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the $d$-dimensional Euclidean space with $d\geq 2$. Spheres arrive sequentially at…

Spatiotemporal forecasting is critical for real-world applications like traffic management, yet capturing reliable interactions remains challenging under noisy and non-stationary conditions. Existing methods primarily rely on historical…

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Predicting high-dimensional dynamical systems with irregular time steps presents significant challenges for current data-driven algorithms. These irregularities arise from missing data, sparse observations, or adaptive computational…

There exists a correlation between geospatial activity temporal patterns and type of land use. A novel self-supervised approach is proposed to stratify landscape based on mobility activity time series. First, the time series signal is…

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…