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The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…
We study the problem of estimating at a central server the mean of a set of vectors distributed across several nodes (one vector per node). When the vectors are high-dimensional, the communication cost of sending entire vectors may be…
In this paper, we propose two nonparametric methods used in the forecasting of functional time-dependent data, namely functional singular spectrum analysis recurrent forecasting and vector forecasting. Both algorithms utilize the results of…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite…
The availability of temporal geospatial data in multiple modalities has been extensively leveraged to enhance the performance of machine learning models. While efforts on the design of adequate model architectures are approaching a level of…
Numerical analytic continuation arises frequently in lattice field theory, particularly in spectroscopy problems. This work shows the equivalence of common spectroscopic problems to certain classes of moment problems that have been studied…
This paper provides quantitative Central Limit Theorems for nonlinear transforms of spherical random fields, in the high frequency limit. The sequences of fields that we consider are represented as smoothed averages of spherical Gaussian…
Spectrum sensing is an essential functionality that enables cognitive radios to detect spectral holes and opportunistically use under-utilized frequency bands without causing harmful interference to primary networks. Since individual…
We present a technique for spatiotemporal data analysis called nonlinear Laplacian spectral analysis (NLSA), which generalizes singular spectrum analysis (SSA) to take into account the nonlinear manifold structure of complex data sets. The…
This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in…
Complex time-varying networks are prominent models for a wide variety of spatiotemporal phenomena. The functioning of networks depends crucially on their connectivity, yet reliable techniques for learning communities in time-evolving…
The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis -…
We examine the constraints of spherically symmetric general relativity with one asymptotically flat region, exploiting both the traditional metric variables and variables constructed from the optical scalars. With respect to the latter…
Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the…
Spectroscopic redshift surveys offer great prospects for constraining the dark sector in cosmology. Future surveys will however be both deep and wide and will thus require an analysis in 3-dimensional spherical geometry. We review and…
Exoplanet research is carried out at the limits of the capabilities of current telescopes and instruments. The studied signals are weak, and often embedded in complex systematics from instrumental, telluric, and astrophysical sources.…
Sampling of a spatiotemporal field for environmental sensing is of interest. Traditionally, a few fixed stations or sampling locations aid in the reconstruction of the spatial field. Recently, there has been an interest in mobile sensing…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
We consider non-local sensing of scalar signals with specific spatial dependence in the Bayesian regime. We design schemes that allow one to achieve optimal scaling and are immune to noise sources with a different spatial dependence than…