相关论文: Fundamental component enhancement via adaptive non…

We demonstrate that a superoscillating in time signal may be obtained as a nonlinear response on a harmonic low-frequency input. Using the realization of a superoscillating function proposed by (Huang et al. 2007 J. Opt. A: Pure Appl. Opt.…

We present a simple nonlinear resonant analog circuit which demonstrates quantization of resonating amplitudes, for a given excitation level. The system is a simple RLC resonator where C is an active capacitor whose value is related to the…

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

Computer vision models normally witness degraded performance when deployed in real-world scenarios, due to unexpected changes in inputs that were not accounted for during training. Data augmentation is commonly used to address this issue,…

The power spectrum of primordial tensor perturbations $\mathcal{P}_t$ increases rapidly in high frequency region if the spectral index $n_t>0$. It is shown that the amplitude of relic gravitational wave $h_t$($5\times10^9$Hz) varies from…

Time-frequency representation (TFR) is often used for non-stationary signal analysis. The most intuitive and interpretable TFR is the spectrogram. Recently, a concept of non-negative matrix factorization (NMF) has been successfully applied…

We investigate two classes of inflationary models, which lead to a stiff period after inflation that boosts the signal of primordial gravitational waves (GWs). In both families of models studied, we consider an oscillating scalar…

We investigate energy transfer and localization in a linear time-invariant oscillator chain weakly coupled to a forced nonlinear actuator. Two types of perturbation are studied: (1) harmonic forcing with a constant frequency is applied to…

Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…

Optical properties of components in a linac can be reconstructed from analysis of the orbit response matrix, composed from responses of BPMs to changes in currents of dipole correctors. An efficient way to record such response, discussed in…

In this report, we lay the foundation for amplitude noise and phase noise analysis in nonlinear devices. We build a theoretical framework that helps us to analyze extremely difficult problems which include both nonlinearity and noise of…

A nonlinear oscillator with an abruptly inhomogeneous restoring force driven by an uniform oscillating force exhibits stochastic properties under specific resonance conditions. This behaviour elucidates the elementary mechanism of the…

We develop methods to calculate the curvature power spectrum in models where features in the inflaton potential nonlinearly excite modes and generate high frequency features in the spectrum. The first nontrivial effect of excitations…

Adapting vision transformer foundation models through parameter-efficient fine-tuning (PEFT) methods has become increasingly popular. These methods optimize a limited subset of parameters, enabling efficient adaptation without the need to…

A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore…

An astonishingly simple analytical frequency approximation formula for a class of strongly nonlinear oscillators is derived and applied to various example systems yielding useful quick estimates.

Non-negative matrix factorization is a popular tool for decomposing data into feature and weight matrices under non-negativity constraints. It enjoys practical success but is poorly understood theoretically. This paper proposes an algorithm…

Here we present a one-degree-of-freedom model of a nonlinear parametrically-driven resonator in the presence of a small added ac signal that has spectral responses similar to a frequency comb. The proposed nonlinear resonator has a spread…

This paper resolves a pivotal open problem on nonparametric inference for nonlinear functionals of volatility matrix. Multiple prominent statistical tasks can be formulated as functionals of volatility matrix, yet a unified statistical…

We propose a novel activation function that implements piece-wise orthogonal non-linear mappings based on permutations. It is straightforward to implement, and very computationally efficient, also it has little memory requirements. We…