相关论文: Fundamental component enhancement via adaptive non…
Non-linear activation functions are crucial in Convolutional Neural Networks. However, until now they have not been well described in the frequency domain. In this work, we study the spectral behavior of ReLU, a popular activation function.…
Driven non-linear resonators can display sharp resonances or even multistable behaviours amenable to induce strong enhancements of weak signals. Such enhancements can make use of the phenomenon of vibrational resonance whereby a weak…
Convolutional neural networks have been successful in solving many socially important and economically significant problems. This ability to learn complex high-dimensional functions hierarchically can be attributed to the use of nonlinear…
In the field of numerical integration, methods specially tuned on oscillating functions, are of great practical importance. Such methods are needed in various branches of natural sciences, particularly in physics, since a lot of physical…
A subject's heart beat can be nearly invisible in a spectrum, when that spectrum is generated using conventional methods of Fourier analysis. The phenomenon has been observed in records of both electrocardiography type and…
Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct…
A general procedure for introducing parametric, learned, nonlinearity into activation functions is found to enhance the accuracy of representative neural networks without requiring significant additional computational resources. Examples…
The high-sensitivity quantum detection of a resonant classical force acting on a quantum oscillator can be substantially enhanced through the use of a resonant optical parametric transducer. We demonstrate that this approach not only…
The Frequency Response Functions (FRFs) are the most widely used functions to characterise the dynamic behaviour of structures. The natural frequencies and damping behaviour can be easily and quickly detected from a Bode diagram. The modal…
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…
Time series anomaly detection is critical for system monitoring and risk identification, across various domains, such as finance and healthcare. However, for most reconstruction-based approaches, detecting anomalies remains a challenge due…
Periodic activation functions, often referred to as learned Fourier features have been widely demonstrated to improve sample efficiency and stability in a variety of deep RL algorithms. Potentially incompatible hypotheses have been made…
Incremental processing allows interactive systems to respond based on partial inputs, which is a desirable property e.g. in dialogue agents. The currently popular Transformer architecture inherently processes sequences as a whole,…
The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to…
Many industrial and real life problems exhibit highly nonlinear periodic behaviors and the conventional methods may fall short of finding their analytical or closed form solutions. Such problems demand some cutting edge computational tools…
The nonlinearity of activation functions used in deep learning models are crucial for the success of predictive models. There are several commonly used simple nonlinear functions, including Rectified Linear Unit (ReLU) and Leaky-ReLU…
A nonlinear frequency response based adaptive vibration controller is proposed for a class of nonlinear mechanical systems. In order to obtain the nonlinear Frequency Response Function (FRF), the convergence properties of the system are…
Functional linear regression is a widely used approach to model functional responses with respect to functional inputs. However, classical functional linear regression models can be severely affected by outliers. We therefore introduce a…
The frequency flicker of an oscillator, which appears as a 1/f^3 line in the phase noise spectral density, and as a floor on the Allan variance plot, originates from two basic phenomena, namely: (1) the 1/f phase noise turned into 1/f…
Frequency response function (FRF) measurements are widely used in Gravitational Wave (GW) detectors, e.g., for the design of controllers, calibrating signals and diagnostic problems with system dynamics. The aim of this paper is to present…