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The fitting of spectral lines is a common step in the analysis of line observations and simulations. However, the observational noise, the presence of multiple velocity components, and potentially large data sets make it a non-trivial task.…
Spectral characterization of noise environments that lead to the decoherence of qubits is critical to developing robust quantum technologies. While dynamical decoupling offers one of the most successful approaches to characterize noise…
Particle tracing through numerical integration is a well-known approach to generating pathlines for visualization. However, for particle simulations, the computation of pathlines is expensive, since the interpolation method is complicated…
This note considers the problem of approximating the locations of dominant spikes for a probability measure from noisy spectrum measurements under the condition of residue signal, significant noise level, and no minimum spectrum separation.…
Ultra-wideband (UWB) based positioning with fewer anchors has attracted significant research interest in recent years, especially under energy-constrained conditions. However, most existing methods rely on discrete-time representations and…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
For transient sources with timescales of 1-100 seconds, standardized imaging for all observations at each time step become impossible as large modern interferometers produce significantly large data volumes in this observation time frame.…
In this article we revisit the auxiliary variable method introduced in Smith and kohn (1996) for the fitting of P-th order spline regression models with an unknown number of knot points. We introduce modifications which allow the location…
Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…
Addressing the optical communication systems employing the nonlinear Fourier transform (NFT) for the data modulation/demodulation, we provide an explicit proof for the properties of the signals emerging in the so-called b-modulation method,…
In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…
There is a need for fast adaptation in spike sorting algorithms to implement brain-machine interface (BMIs) in different applications. Learning and adapting the functionality of the sorting process in real-time can significantly improve the…
Quantitative MRI methods that estimate multiple physical parameters simultaneously often require the fitting of a computational complex signal model defined through the Bloch equations. Repeated Bloch simulations can be avoided by matching…
Neuromorphology is crucial to identifying neuronal subtypes and understanding learning. It is also implicated in neurological disease. However, standard morphological analysis focuses on macroscopic features such as branching frequency and…
We present an improved neural field architecture for solving partial differential equations (PDEs). Current physics-informed neural networks (PINNs) provide a flexible framework for solving PDEs, but they struggle to achieve highly accurate…
Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to traditional numerical solvers for partial differential equations (PDEs). However, PINNs often struggle to learn high-frequency and multi-scale…
Recently, there is growing attention on one-stage panoptic segmentation methods which aim to segment instances and stuff jointly within a fully convolutional pipeline efficiently. However, most of the existing works directly feed the…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
Splines are useful building blocks when constructing priors on nonparametric models indexed by functions. Recently it has been established in the literature that hierarchical priors based on splines with a random number of equally spaced…
We present a constructive approximation framework for analyzing the expressive power of Fourier residual networks in approximating a broad class of one-dimensional functions. Our study covers both piecewise continuous functions -- including…