Related papers: The Resonance Bias Framework: Resonance, Structure…
This paper addresses the problem of deriving the asymptotic performance of adaptive Low Rank (LR) filters used in target detection embedded in a disturbance composed of a LR Gaussian noise plus a white Gaussian noise. In this context, we…
Fractional cumulative residual inaccuracy (FCRI) measure allows to determine regions of discrepancy between systems, depending on their respective fractional and chaotic map parameters. Most of the theoretical results and applications…
In future gravitational-wave (GW) detections, a large number of overlapping GW signals will appear in the data stream of detectors. When extracting information from one signal, the presence of other signals can cause large parameter…
Vibrational resonance focuses on the resonance behavior of a nonlinear system when it is subjected to both a weak low-frequency characteristic signal and a high-frequency auxiliary signal. A traditional Duffing system has a fixed natural…
This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization,…
Resonance is instrumental in modern optics and photonics for novel phenomena such as cavity quantum electrodynamics and electric-field-induced transparency. While one can use numerical simulations to sweep geometric and material parameters…
Implicit Neural Representation (INR), which utilizes a neural network to map coordinate inputs to corresponding attributes, is causing a revolution in the field of signal processing. However, current INR techniques suffer from the…
In this paper we present the framework of symmetry in nonparametric regression. This generalises the framework of covariate sparsity, where the regression function depends only on at most $s < d$ of the covariates, which is a special case…
Neural network architectures designed for function parameterization, such as the Bag-of-Functions (BoF) framework, bridge the gap between the expressivity of deep learning and the interpretability of classical signal processing. However,…
Two-wave with diffuse power (TWDP) is one of the most promising distribution for description of a small-scale fading in the emerging mmWave band. However, traditional error performance analysis in these channels faces two fundamental…
The Rosenfeld functional provides excellent results for the prediction of the fluid phase of hard convex particle systems but fails beyond the freezing point. The reason for this limitation is the neglect of orientational and distance…
In this paper, we construct a quadrature scheme to numerically solve the nonlocal diffusion equation $(\mathcal{A}^\alpha+b\mathcal{I})u=f$ with $\mathcal{A}^\alpha$ the $\alpha$-th power of the regularly accretive operator $\mathcal{A}$.…
We present a generalization of the RBF-FD method that computes RBF-FD weights in finite-sized neighborhoods around the centers of RBF-FD stencils by introducing an overlap parameter $\delta \in [0,1]$ such that $\delta=1$ recovers the…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…
Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…
Intrinsic random functions (IRF) provide a versatile approach when the assumption of second-order stationarity is not met. Here, we develop the IRF theory on the circle with its universal kriging application. Unlike IRF in Euclidean spaces,…
The search for the optimal shape parameter for Radial Basis Function (RBF) kernel approximation has been an outstanding research problem for decades. In this work, we establish a theoretical framework for this problem by leveraging a…
We study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal…
Interferometry can measure the shape or the material density of a system that could not be measured otherwise by recording the difference between the phase change of a signal and a reference phase. This difference is always between $-\pi$…