Related papers: Uniform stationary phase estimate with limited smo…
We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…
We analyze an intermediate collective regime where amplitude oscillators distribute themselves along a closed, smooth, time-dependent curve $\mathcal{C}$, thereby maintaining the typical ordering of (identical) phase oscillators. This is…
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…
We study the convergence properties of state estimates of an oscillating qubit being monitored by a sequence of \textit{discrete}, unsharp measurements. Our method derives a differential equation determining the evolution of the estimation…
Synchronization of coupled oscillators is a paradigm for complexity in many areas of science and engineering. Any realistic network model should include noise effects. We present a description in terms of phase and amplitude deviation for…
In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of $L^2 \mapsto L^2$ type for the operator, as well as for the corresponding maximal function. If…
We have developed a new methodology and a time-domain software package for the estimation of the oscillation frequency and the phase noise spectrum of non-linear noisy microwave circuits based on the direct integration of the system of…
This paper is devoted to the proof of uniform H\"older and Lipschitz estimates close to oscillating boundaries, for divergence form elliptic systems with periodically oscillating coefficients. Our main point is that no structure is assumed…
A novel method for decomposing a nonstationary signal into amplitude- and frequency-modulated (AM-FM) oscillations and discontinuous (jump) components is proposed. Current nonstationary signal decomposition methods are designed to either…
We study the position estimation of a mechanical oscillator undergoing both detuned parametric amplification and continuous quantum measurement. This model, which can be utilised to produce squeezed states, is applied to a general…
We consider the problem of estimating the fractional order of a L\'{e}vy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a…
Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern,…
The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for…
We consider the following model of degenerate and singular oscillatory integral operators: \begin{equation*} Tf(x)=\int_{\mathbb{R}} e^{i\lambda S(x,y)}K(x,y)\psi(x,y)f(y)dy, \end{equation*} where the phase functions are homogeneous…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
In this paper we present a theory that predicts the phase noise characteristics of self-sustained optomechanical oscillators. By treating the cavity optomechanical system as a feedback loop consisting of an optical cavity and a mechanical…
This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
We use broad-narrow method to estabish the sharp $L^4$ decay estimate for a class of degenerate oscillatory integral operators in $(2+1)$ dimensions. Especially, the model phase function is \[xt^2+y^2t,\] a cubic homogeneous polynomial…
We prove that the density function of the gradient of a sufficiently smooth function $S : \Omega \subset \mathbb{R}^d \rightarrow \mathbb{R}$, obtained via a random variable transformation of a uniformly distributed random variable, is…