Small Noise Research Articles

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation.

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional (8D) limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

Health Prognosis for Equipment Based on ACO-K-Means and MCS-SVM under Small Sample Noise Unbalanced Data

Health Prognosis for Equipment Based on ACO-K-Means and MCS-SVM under Small Sample Noise Unbalanced Data

Impact of the combination and replacement of SLR-based low-degree gravity field coefficients in GRACE solutions

GRACE and GRACE Follow-On (FO) missions provide time-variable gravity field models of unprecedented quality that allow for the hydrological, oceanic, and ice mass change studies on a global scale. However, the very low-degree coefficients derived from GRACE and GRACE-FO are of inferior quality due to thermal effects acting on satellites and malfunctioning of the onboard accelerometers. Therefore, C20 and C30 coefficients describing the Earth’s oblateness and the pear shape of the Earth, respectively, are being replaced by values derived from satellite laser ranging (SLR) in the standard GRACE solutions. This study assesses the impact of the replacement of low-degree gravity field coefficients in GRACE/GRACE-FO solutions by SLR data on the trend and seasonal signals of ice mass changes in Greenland and Antarctica. We found that the replacement of the low-degree gravity field coefficients changes the estimates of trends by 4, 8, and 22 Gt/year in Greenland, West, and East Antarctica, respectively, depending on the source of SLR coefficients and period for which the coefficients are replaced. In SLR and GRACE solutions, all coefficients of the same order and the same parity of degrees are strongly correlated. Therefore, replacing only two selected coefficients may lead to a biased solution. Thus, we propose to combine GRACE with SLR solutions up to a degree and order 10 × 10 to properly consider the sensitivity of each of the techniques to gravity field coefficients, instead of replacing two coefficients from SLR in GRACE solutions. The combined solution reduces the residual trend of post-glacial rebound from 1.2 to 0.9 Gt/year and from − 57.8 to − 57.0 Gt/year in Scandinavia and South Canada, respectively, when compared to GRACE/GRACE-FO solutions with the replacement of coefficients. The SLR-GRACE combination reduces the noise in the GRACE/GRACE-FO solutions by 8%, from 38 to 35 Gt, in the Fennoscandia region. In the periods when GRACE is at the end of its mission and observations are disrupted, the weights adjust the contribution from SLR and GRACE based on relative ratio of variances from each techniques. Thus, the combined solutions are more consistent with independent geophysical models of glacial isostatic adjustment, and the combinations are affected by smaller noise than the standard GRACE solutions and properly account for different sensitivities of SLR and GRACE techniques to low-degree time-variable gravity field coefficients.

BASS: Broad Network Based on Localized Stochastic Sensitivity.

The training of the standard broad learning system (BLS) concerns the optimization of its output weights via the minimization of both training mean square error (MSE) and a penalty term. However, it degrades the generalization capability and robustness of BLS when facing complex and noisy environments, especially when small perturbations or noise appear in input data. Therefore, this work proposes a broad network based on localized stochastic sensitivity (BASS) algorithm to tackle the issue of noise or input perturbations from a local perturbation perspective. The localized stochastic sensitivity (LSS) prompts an increase in the network's noise robustness by considering unseen samples located within a Q -neighborhood of training samples, which enhances the generalization capability of BASS with respect to noisy and perturbed data. Then, three incremental learning algorithms are derived to update BASS quickly when new samples arrive or the network is deemed to be expanded, without retraining the entire model. Due to the inherent superiorities of the LSS, extensive experimental results on 13 benchmark datasets show that BASS yields better accuracies on various regression and classification problems. For instance, BASS uses fewer parameters (12.6 million) to yield 1% higher Top-1 accuracy in comparison to AlexNet (60 million) on the large-scale ImageNet (ILSVRC2012) dataset.

Implementation of Image Recognition for Human detection in Underwater Images

Recent advances in deep learning have resolved the challenges of detection of objects underwater. Specialized methods have been developed as a result of the particular characteristics of small, fuzzy objects and heterogeneous noise. The Sample-Weighted Network (SWIPE Net) for small object recognition is one of them, as are frameworks with feature enhancement and anchor refining. Additionally, upgraded versions of the attention processes and YOLOv7 have been released. These advancements help with tracking the effects of clean energy technologies, developing accurate and reliable underwater object detection systems, bridging the communication gap between the deaf and hearing-impaired, and automating the analysis of underwater imagery for the extraction of ecological data.

What is the Simplest Linear Ramp?

We discuss conditions under which a deterministic sequence of real numbers, interpreted as the set of eigenvalues of a Hamiltonian, can exhibit features usually associated to random matrix spectra. A key diagnostic is the spectral form factor (SFF) — a linear ramp in the SFF is often viewed as a signature of random matrix behavior. Based on various explicit examples, we observe conditions for linear and power law ramps to arise in deterministic spectra. We note that a very simple spectrum with a linear ramp is En ~ log n. Despite the presence of ramps, these sequences do not exhibit conventional level repulsion, demonstrating that the lore about their concurrence needs refinement. However, when a small noise correction is added to the spectrum, they lead to clear level repulsion as well as the (linear) ramp. We note some remarkable features of logarithmic spectra, apart from their linear ramps: they are closely related to normal modes of black hole stretched horizons, and their partition function with argument s = β + it is the Riemann zeta function ζ(s). An immediate consequence is that the spectral form factor is simply −ζ|(it)|2. Our observation that log spectra have a linear ramp, is closely related to the Lindelöf hypothesis on the growth of the zeta function. With elementary numerics, we check that the slope of a best fit line through |ζ(it)|2 on a log-log plot is indeed 1, to the fourth decimal. We also note that truncating the Riemann zeta function sum at a finite integer N causes the would-be-eternal ramp to end on a plateau.

Stochastic evolutionary p-Laplace equation: Large deviation principles and transportation cost inequality

We establish a large deviation principle for the strong solution of the evolutionary p-Laplace equation driven by small multiplicative Brownian noise, where the weak convergence approach plays a key role. Moreover, by using the Girsanov transformation along with the L1-contraction approach, we show the quadratic transportation cost inequality for the strong solution to the underlying problem.

Detection and prediction of pathogenic microorganisms in aquaculture (Zhejiang Province, China).

The detection and prediction of pathogenic microorganisms play a crucial role in the sustainable development of the aquaculture industry. Currently, researchers mainly focus on the prediction of water quality parameters such as dissolved oxygen for early warning. To provide early warning directly from the pathogenic source, this study proposes an innovative approach for the detection and prediction of pathogenic microorganisms based on yellow croaker aquaculture. Specifically, a method based on quantitative polymerase chain reaction (qPCR) is designed to detect the Cryptocaryon irritans (Cri) pathogenic microorganisms. Furthermore, we design a predictive combination model for small samples and high noise data to achieve early warning. After performing wavelet analysis to denoise the data, two data augmentation strategies are used to expand the dataset and then combined with the BP neural network (BPNN) to build the fusion prediction model. To ensure the stability of the detection method, we conduct repeatability and sensitivity tests on the designed qPCR detection technique. To verify the validity of the model, we compare the combined BPNN to long short-term memory (LSTM). The experimental results show that the qPCR method provides accurate quantitative measurement of Cri pathogenic microorganisms, and the combined model achieves a good level. The prediction model demonstrates higher accuracy in predicting Cri pathogenic microorganisms compared to the LSTM method, with evaluation indicators including mean absolute error (MAE), recall rate, and accuracy rate. Especially, the accuracy of early warning is increased by 54.02%.

Adaptive Image Compression via Optimal Mesh Refinement

Abstract The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces a quasi-optimal subdivision grid for a given error norm with high probability. This subdivision can be stored with very little overhead and thus leads to an efficient compression algorithm. We demonstrate experimentally, that the new algorithm can achieve better compression ratios than standard JPEG compression with no visible loss of quality on many images. The mathematical core of this work shows that Binev’s optimal tree approximation algorithm is applicable to image compression with high probability, when we assume small additive Gaussian noise on the pixels of the image.

Large deviations for small noise diffusions over long time

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers (LLN) of the empirical measure in this asymptotic regime is given by the unique equilibrium of the noiseless dynamics. Due to degeneracy of the noise in the limit, the methods of Donsker and Varadhan [Comm. Pure Appl. Math. 29 (1976), pp. 389–461] are not directly applicable and new ideas are needed. Second, we study a system of slow-fast diffusions where both the slow and the fast components have vanishing noise on their natural time scales. This time the LLN is governed by a degenerate averaging principle in which local equilibria of the noiseless system obtained from the fast dynamics describe the asymptotic evolution of the slow component. We establish a large deviation principle that describes probabilities of divergence from this behavior. On the one hand our methods require stronger assumptions than the nondegenerate settings, while on the other hand the rate functions take simple and explicit forms that have striking differences from their nondegenerate counterparts.

Multilevel Monte Carlo EM scheme for MV-SDEs with small noise

Multilevel Monte Carlo EM scheme for MV-SDEs with small noise

The Power of Passivity: A Note on the Hirshleifer Contest Under Small Noise

The Power of Passivity: A Note on the Hirshleifer Contest Under Small Noise

ACTIVE TRANSMITTER SIGNAL CANCELLATION IN RECEIVE SIGNAL PATH FOR SDR

Elimination of receiver (RX) band-pass filters is actual task for construction of next generation New Radio Wireless Transceivers and other modern equipment (Multiple Input Multiple Output systems, radar applications, etc.) based on software-defined radio. Unfortunately, some new problems with electromagnetic compatibility arise. Main problem start up with Frequency Division Duplex mode, were part of high power transmitter (TX) signal came to high sensitivity RX input through duplexer with limited isolation. In presence of high TX signal RX mixer could come into non-linear working area and RX sensitivity is decreases. This problem may be solved by cancellation of TX signal from RX path. This article provides a preliminary approach to the problem of active TX signal cancellation in RX signal path with cancellation is at least 25 dB, and relatively small additional power consumption and noise. After critical parameters identifying, based on mathematical expressions, the requirements for cancellation blocks parameters are determined. Simplest implementations of the proposed structure are simulated.

A New Method for Integrating a Deep Learning Module into Special Object Classification Software

The article discusses a method for integrating a deep learning module into special software based on classical computer vision methods. This software implements the functions of creating panoramic images and their subsequent comparison with the ability to highlight different areas. The integration of deep learning methods is aimed at automating the classification of found objects and solving problems associated with identifying a large number of small objects and noise anomalies. In the process of carrying out the research, an additional neural network generative model was created that improves the quality of classification by increasing the size of the training dataset. This model was implemented in the form of an ensemble of variational autoencoders, which made it possible to simplify the learning process and fine-tuning of neural networks. Also, in order to assess the quality of the ensemble of variational autoencoders, a new method for checking the generated synthetic data was developed. The result of the integration was improved special software capable of classifying the detected found objects of interest with high accuracy.

Rapid visual detection method of highway pavement sag based on improved Yolov7-tiny

Different weather and light conditions will affect the detection of pavement sag. And the camera field of view is limited, can not fully cover the entire highway road surface, resulting in higher difficulty in road sag detection. Therefore, a rapid visual detection method for highway pavement sag based on improved Yolov7-tiny is proposed. The structure elements are determined, and the small noise points in the image are removed by etching operation, and the morphology of the highway surface is completed. Input the processed highway pavement sag image into YOLOv7-tiny network, improve the input module and backbone network, and output the irregular shape of the sag image target. Fuzzy C-Means (FCM) clustering algorithm is introduced and objective function is established to realize the morphological feature visual detection of highway pavement depression. The experimental results show that: The method has smaller entropy, larger fuzzy coefficient, higher peak signal-to-noise ratio, and clearer features of pavement depression images.

Surface modification of ZnO nanowires using single walled carbon nanotubes for efficient UV–visible broadband photodetection

A UV–visible broadband photodetector (PD) based on single walled carbon nanotube (SWCNT)/Zinc oxide nanowire (ZnO NW) hybrid is being reported. This work focuses on designing a stable, fast, efficient and reliable hybrid broadband PD by surface modification of ZnO NWs using SWCNT. The study shows that spectral response of the hybrid heterostructure (HS) spans beyond the UV spectrum and into the visible region which is due to the integration of SWCNTs. Photoluminescence (PL) study reveals surface plasmon (SP) mediated resonance phenomenon resulting in an increase in PL intensity. High nanotube charge carrier mobility and conductivity allows the hybrid HS to attain high values of spectral responsivity (R λ = 187.77 A W−1), external quantum efficiency (EQE = 5.82 × 104%), specific detectivity (D* = 7.04 × 1011 Jones) and small noise equivalent power (NEP = 4.77 × 10−12 W) values for the SWCNT/ZnO NW hybrid HS. The device also gives quick rise (t rise = 0.43 s) and fall (t fall = 0.60 s) time values.

Hardware and software for automated examination of defects of hard tissues of teeth after endodontic intervention for fatigue and destruction

The work developed circuit engineering, design and software of the loading machine for automated examination of dental hard tissue defects after endodontics intervention for fatigue and destruction. The advantage of this development is the combination as cyclic loading methods simulating chewing movements and force effects on compression in a compact small-sized case, with low power consumption and small noise level. Thanks to the use of a screw transmission and a stepper motor in combination with a sensitive tensoresistive force sensor, it was possible to achieve high accuracy and resolution of 0.1 microns.
 A series of tests was conducted on real samples of endodontically treated teeth restored using fiberglass pins and cast metal stump inserts. It is shown that methods of restoring incisors and premolars of the upper jaw with the help of fiberglass pins have an advantage when the residual structure of the tooth is lacking due to a more uniform distribution of deformation stresses, since their elastic modulus is close to the elastic modulus of dentin.

On near-martingales and a class of anticipating linear stochastic differential equations

The goals of this paper are to prove a near-martingale optional stopping theorem and establish solvability and large deviations for a class of anticipating linear stochastic differential equations. For a class of anticipating linear stochastic differential equations, we prove the existence and uniqueness of solutions using two approaches: (1) Ayed–Kuo differential formula using an ansatz, and (2) a braiding technique by interpreting the integral in the Skorokhod sense. We establish a Freidlin–Wentzell type large deviations result for the solution of such equations. In addition, we prove large deviation results for small noise where the initial conditions are random.

Identification of switched dynamic system for electric multiple unit train modeling

A new iterative algorithm is proposed to identify the high-speed train model which is described as a switched dynamic system including a fast switched nonlinear static subsystem followed by a non-switched linear dynamic subsystem. The non-switched property of the linear part leads to a more complex dynamics of the whole system, compared to the switched Hammerstein system which linear part switches synchronously with its nonlinear part. The proposed iterative algorithm alternates between identifying the switched nonlinear static subsystem and the linear dynamic subsystem. The switched nonlinear subsystem identification incorporates a quadratic error bound constraint with respect to nominal values of model parameters, and is formulated as a second-order cone program. Properties of convergence and asymptotic unbiasedness of the obtained estimates are proved under some necessary assumptions. With real data and simulation examples, the proposed iterative algorithm produces convergent and asymptotically unbiased estimates. In the simulation results, incorporating the quadratic error bounds results in a fast convergence rate in the presence of a small noise variance, and also produces a smaller identification error in the presence of colored noises with a non-zero mean and a large variance.

Statistical inference for discretely sampled stochastic functional differential equations with small noise

Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast function is based on a local-Gauss approximation to the transition probability density of the process. We show consistency and asymptotic normality of the minimum-contrast estimator when a small dispersion coefficient ε→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon \\rightarrow 0$$\\end{document} and sample size n→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\rightarrow \\infty $$\\end{document} simultaneously.