Related papers: Vector-Valued Spectral Analysis of Space-Time Data

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a…

Formal verification provides a powerful framework for proving that dynamical systems satisfy their specifications. However, these techniques face scalability challenges in high-dimensional settings, as they often rely on state-space…

In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a gamma-filter explicitly in a reproducing kernel Hilbert…

We provide one theorem of spectral equivalence of Koopman operators of an original dynamical system and its reconstructed one through the delay-embedding technique. The theorem is proved for measure-preserving maps (e.g. dynamics on compact…

In carbon capture and sequestration, building an effective monitoring method is a crucial step to detect and respond to CO2 leakage. CO2 leakage detection methods rely on geophysical observations and monitoring sensor network. However,…

We propose {\delta}-MAPS, a method that analyzes spatio-temporal data to first identify the distinct spatial components of the underlying system, referred to as "domains", and second to infer the connections between them. A domain is a…

We address the problem of data-driven pattern identification and outlier detection in time series. To this end, we use singular value decomposition (SVD) which is a well-known technique to compute a low-rank approximation for an arbitrary…

We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstrate that time delays shape the spectrum of a matrix…

Wind direction plays an important role in the spread of pollutant levels over a geographical region. We discuss how to include wind directional information in the covariance function of spatial models. We follow the spatial convolution…

Pedestrian detection is a critical task in robot perception. Multispectral modalities (visible light and thermal) can boost pedestrian detection performance by providing complementary visual information. Several gaps remain with…

Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…

High resolution satellite image sequences are multidimensional signals composed of spatio-temporal patterns associated to numerous and various phenomena. Bayesian methods have been previously proposed in (Heas and Datcu, 2005) to code the…

We develop a detector-based framework in which quantum theory and spacetime geometry arise within a common inferential structure. Detector states and a detector kernel assign amplitudes to measurement events, allowing quantum theory to be…

By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…

Semantic segmentation from RGB cameras is essential to the perception of autonomous flying vehicles. The stability of predictions through the captured videos is paramount to their reliability and, by extension, to the trustworthiness of the…

This article presents a quantum computing approach to designing of similarity measures and kernels for classification of stochastic symbolic time series. In the area of machine learning, kernels are important components of various…

The development of unsupervised Video Anomaly Detection (VAD) relies on technologies in the field of signal processing. Since the anomaly is quite ambiguous and unbounded, different detection demands may often be raised even in one…

In this review, we discuss the use of continuous variable spectroscopy techniques for investigating quantum coherence and light-matter interactions in semiconductor systems with ultrafast dynamics. We focus on multichannel homodyne…

Volterra analysis and its variants have long been prominent among methods for modeling multi-input non-linear systems. The product of Volterra analysis, the Volterra kernels, are particularly suited to quantifying intra- and inter-input…

Speckle patterns produced by coherent X-ray have a close relationship with the internal structure of materials but quantitative inversion of the relationship to determine structure from speckle patterns is challenging. Here, we investigate…