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Dropping the ambient noise from microseismic signals is very important for disaster monitoring such as a rockburst and early warning system using microseismic monitoring techniques in the mine and coal mines. Currently, it is still a challenge to remove high and low-frequency noise simultaneously without losing the useful information of microseismic signal. The aim of this paper is to remove the low-frequency noise contained in microseismic signal effectively, while preserving the useful signal information by using a stochastic approach. We first statistically model the wavelet coefficients in the approximation subband of noisy microseismic signal. In addition, we evaluate qualitatively and quantitatively the fitness of Gauss–Laplace mixture distribution and the statistical modeling of data. Then, we propose a novel denoising algorithm to remove the ambient noise effectively from the noisy microseismic signals in wavelet domain. This algorithm removes the low-frequency noise by using a stochastic approach and the high-frequency noise by using a traditional wavelet thresholding method. The low-frequency noise is removed by using a closed-form shrinkage function based on Gauss–Laplace mixture distribution, while the high-frequency noise is removed by using a threshold function combined with Garrote and hyperbolic threshold functions. Next, we evaluated the ambient denoising performance of our novel denoising algorithm by comparing it with various denoising methods with different test signals. Experimental results show that the ambient denoising performance of the proposed method is better than the other seven existing methods. [ABSTRACT FROM AUTHOR]

In order to achieve image denoising in high-noise environment, this paper proposes an image denoising algorithm based on improved wavelet thresholding algorithm.The algorithm first improves the problem of fixed threshold.Secondly, an improved wavelet threshold function is proposed for the traditional hard and soft threshold function.Finally, the combination of improved threshold function and threshold can improve the accuracy of wavelet threshold judgment, and realize the effective separation of image and noise. Experimental results show that the proposed algorithm can not only effectively remove image noise in noisy environment, but also obtain higher(Peak signal-to-noise ratio, PSNR) and smaller (Mean Squared Error, MSE). [ABSTRACT FROM AUTHOR]

The efficiency of threshold and no-threshold wavelet noise filtering methods in processing radar signals is analyzed. Three methods of wavelet analysis are considered: a method with a general limit threshold for wavelet coefficients of detail; a method with a universal threshold for all wavelet decompositions; and a method without a threshold, based on zeroing the coefficients of detail at certain levels of the wavelet decomposition of the signal. The efficiency of wavelet filtering by the signal-to-noise ratio before and after filtering, signal entropy, and the model's mean squared error (MSE) are evaluated. It is found that over a wide range of high noise from –12 dB to –7.5 dB, the common-threshold method provides more efficient noise filtering than the other methods. [ABSTRACT FROM AUTHOR]

Image denoising is a significant procedure in image processing, and a good denoising method can improve the image quality. This study focuses on enhancing the estimation model of wavelet coefficients by improving the threshold function. Thus, a general construction method for a class of threshold functions is introduced, and sufficient conditions are given to ensure that the threshold functions are continuous, first-order differentiable and higher-order differentiable. It makes an existing class of improved threshold functions a particular case and enables the construction of other needed threshold functions based on this general approach. Experiments have shown that using the new threshold functions yields better denoising results for images containing salt and pepper noise, Gaussian noise and speckle noise. Moreover, as the smoothness of the threshold function is enhanced, the denoising effect is also improved. The improved wavelet coefficients estimation model can effectively boost the quality of image denoising, further enhancing the accuracy and effectiveness of computer vision algorithms. [ABSTRACT FROM AUTHOR]

System identification is an effective method to model a wireless power transfer system when it is used for wireless charging of electric vehicles. However, system identification using raw data directly is often unsatisfactory due to the inevitable noise interference from system operation and signal acquisition. This study proposes an improved wavelet threshold denoising (WTD) algorithm with optimized algorithm parameters and design methods. First, the number of decomposition layers is determined based on the signal spectrum diagram. Second, adaptive thresholds are designed for different decomposition layers. Third, the hierarchical threshold is combined with the hardness adjustable threshold function. Last, recursive least squares is employed to obtain a system model with the data denoised by the proposed method. Experiments demonstrate that the improved WTD method increases the accuracy of system identification to 85.42%, which verifies the effectiveness of the proposed method. An internal model controller is also designed based on the obtained model. [ABSTRACT FROM AUTHOR]

The paper examines the effectiveness of threshold and non-threshold wavelet noise filtering methods in processing radar signals. Three methods of wavelet analysis are analyzed: a method with a general threshold for limiting wavelet coefficients of detail; a method with a universal threshold for all wavelet decompositions; and a method without a threshold, based on zeroing the coefficients of detail at certain levels of the wavelet decomposition of the signal. The effectiveness of wavelet filtering is evaluated by the signal-to-noise ratio before and after filtering, signal entropy, and the model’s mean square error (MSE) value. It is found that over a wide range of high noise from –12 dB to –7.5 dB, the common threshold method provides more effective noise filtering than other methods. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract Background The surface electromyography (sEMG) signal presents significant challenges for the dynamic analysis and subsequent examination of muscle movements due to its low signal energy, broad frequency distribution, and inherent noise interference. However, the conventional wavelet threshold filtering techniques for sEMG signals are plagued by the Gibbs-like phenomenon and an overall decrease in signal amplitude, leading to signal distortion. Purpose This article aims to establish an improved wavelet thresholding method that can filter various types of signals, with a particular emphasis on sEMG signals, by adjusting two independent factors. Hence, it generates the filtered signal with a higher signal-to-noise ratio (SNR), a lower mean square error (MSE), and better signal quality. Results After denoising Doppler and Heavysine signals, the filtered signal exhibits a higher SNR and lower MSE than the signal generated from traditional filtering algorithms. The filtered sEMG signal has a lower noise baseline while retaining the peak sEMG signal strength. Conclusion The empirical evaluation results show that the quality of the signal processed by the new noise reduction algorithm is better than the traditional hard thresholding, soft thresholding, and Garrote thresholding methods. Moreover, the filtering performance on the sEMG signal is improved significantly, which enhances the accuracy and reliability of subsequent experimental analyses.

A wavelet packet filtering algorithm has been developed, which includes cyclic movement along the branches of the wavelet packet tree with a constraint on each branch of the approximation and detail coefficients until the minimum root-mean-square error is attained, with the optimal parameters of the wavelet threshold and threshold function. To calculate the root-mean-square error of filtering, the signal is reconstructed in the time domain after each cycle of processing of the wavelet decomposition coefficients. In the next cycle, the received signal is decomposed into approximation and detail coefficients until the root-mean-square error reaches a minimum for all possible values of the basic wavelet threshold and the threshold function. The study was conducted with 20 of the most commonly used signals, including signals with linear and non-linear frequencies. To confirm the efficiency of wavelet packet filtering, a comparative analysis with the well-known methods based on a common threshold of detail coefficients at all levels of wavelet decomposition is given. [ABSTRACT FROM AUTHOR]

A wavelet packet filtering algorithm has been developed, which includes cyclic movement along the branches of the wavelet packet tree with a constraint on each branch of the approximation and detail coefficients until the minimum root-mean-square error is attained, with the optimal parameters of the wavelet threshold and threshold function. To calculate the root-mean-square error of filtering, after each cycle of processing the wavelet decomposition coefficients, the signal is reconstructed in the time domain. In the next cycle, the received signal is decomposed into approximation and detail coefficients until the root-mean-square error reaches a minimum for all possible values of the basic wavelet-threshold and the threshold function. The study was conducted with twenty of the most commonly used signals, including signals with linear and non-linear frequencies. To confirm the efficiency of packet wavelet filtering, a comparative analysis with the known methods based on a common threshold of detail coefficients at all levels of wavelet decomposition is given. [ABSTRACT FROM AUTHOR]

For reaction networks arising in systems biology, the capacity for two or more steady states, that is, multistationarity, is an important property that underlies biochemical switches. Another property receiving much attention recently is absolute concentration robustness (ACR), which means that some species concentration is the same at all positive steady states. In this work, we investigate the prevalence of each property while paying close attention to when the properties occur together. Specifically, we consider a stochastic block framework for generating random networks and prove edge-probability thresholds at which, with high probability, multistationarity appears and ACR becomes rare. We also show that the small window in which both properties occur only appears in networks with many species. Taken together, our results confirm that, in random reversible networks, ACR and multistationarity together, or even ACR on its own, is highly atypical. Our proofs rely on two prior results, one pertaining to the prevalence of networks with deficiency zero and the other "lifting"" multistationarity from small networks to larger ones. [ABSTRACT FROM AUTHOR]

Multimodal signals are susceptible to external environmental disturbances, such as weather conditions, electromagnetic interference, etc., which may affect the accuracy and stability of the data. This paper utilizes the characteristics of continuous and discrete wavelet transforms to study the wavelet threshold denoising algorithm in-depth, and by adjusting the parameters therein, it avoids the problem that the traditional threshold function is set to zero when the wavelet coefficients are smaller than the threshold value. Then, the deep learning algorithm in artificial intelligence is used to complete the signal adaptive denoising and realize the suppression of deceptive signal interference. The test results show that the adaptive denoising optimization model based on the deep learning algorithm has significantly improved signal characteristics compared to the original signal. Under a 15% noise environment, the average error of the model is less than 0.1, and the signal-to-noise gain of the signal is 5.0547 dB, which can reliably complete the interference suppression of both multiple interference and single interference and realize the adaptive anti-jamming optimization of the signal.

Background: The surface electromyography (sEMG) signal presents significant challenges for the dynamic analysis and subsequent examination of muscle movements due to its low signal energy, broad frequency distribution, and inherent noise interference. However, the conventional wavelet threshold filtering techniques for sEMG signals are plagued by the Gibbs-like phenomenon and an overall decrease in signal amplitude, leading to signal distortion. Purpose: This article aims to establish an improved wavelet thresholding method that can filter various types of signals, with a particular emphasis on sEMG signals, by adjusting two independent factors. Hence, it generates the filtered signal with a higher signal-to-noise ratio (SNR), a lower mean square error (MSE), and better signal quality. Results: After denoising Doppler and Heavysine signals, the filtered signal exhibits a higher SNR and lower MSE than the signal generated from traditional filtering algorithms. The filtered sEMG signal has a lower noise baseline while retaining the peak sEMG signal strength. Conclusion: The empirical evaluation results show that the quality of the signal processed by the new noise reduction algorithm is better than the traditional hard thresholding, soft thresholding, and Garrote thresholding methods. Moreover, the filtering performance on the sEMG signal is improved significantly, which enhances the accuracy and reliability of subsequent experimental analyses. [ABSTRACT FROM AUTHOR]

The paper proposes a fast method for the multidimensional parameter estimation of a polarization-sensitive array. Compared with conventional methods (e.g., MUSIC algorithm), the proposed method applies an iterative approach based on Newton's method to obtain joint estimation results instead of a spectral search and dimension reduction. It also extends the original Newton method to the 4D scale using the Hessian matrix. To reduce the complexity of establishing the aim function, Nystrom's method is applied to process the covariance matrix. A new threshold is also proposed to select the results, which can accomplish the parameter estimation with a small number of iterations while guaranteeing a high estimation accuracy. Finally, the proposed algorithm is analyzed in detail and the numerical simulations of various algorithms are compared to verify its effectiveness. [ABSTRACT FROM AUTHOR]

In this article, we investigate the stabilization and fault detection problem for discrete‐time switched systems with all modes unstable. A set of mode‐dependent fault detection filters are designed with respect to each subsystem and combined with the switched system into an augmented switched system. Sufficient conditions for both guaranteeing globally uniformly asymptotically stable (GUAS) and H−/H∞$$ {H}_{-}/{H}_{\infty } $$ performance of the augmented switched system are derived by utilizing the discretized Lyapunov function technique and dwell time (DT) switching strategy. A novel pair of the residual evaluation function and threshold function are also provided for improving the sensitivity and practicability of fault detection logic. Numerical experiments demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Because the traditional pulse laser high-precision ranging method has the problems of low ranging accuracy and long ranging time, a pulse laser high-precision ranging algorithm under low signal-to-noise ratio is proposed. Based on the analysis of the basic principle of pulse laser ranging, the pulse laser signal under low signal-to-noise ratio is obtained by modeling the pulse laser echo analog signal waveform. The wavelet denoising method of improved threshold function is used to denoise the pulse laser signal under low signal-to-noise ratio. According to the processing results, the pulse laser high-precision ranging is carried out through sinusoidal amplitude time conversion. The simulation results show that the proposed algorithm has high precision and short ranging time.

Copyright of Petroleum Geology & Recovery Efficiency is the property of Petroleum Geology & Recovery Efficiency and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Measurement Science & Instrumentation is the property of Journal of Measurement Science & Instrumentation and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The existing estimators for the drift coefficient in the diffusion model with jumps involve jump components and possess larger boundary error. How to effectively estimate the drift function is an important issue that faces challenges and has theoretical significance. In this paper, the gamma asymmetric kernel for boundary correction and threshold function eliminating jump impacts are combined to estimate the unknown drift coefficient in the jump diffusion process of interest rate. The asymptotic large sample property and the better finite sample property through the Monte Carlo numerical simulation experiment and the empirical analysis of SHIBOR and LIBOR for the corresponding estimator are considered in detail. It is found that the estimator proposed in this paper can correct the estimation error near or far away from the origin point, which provides a more asymptotic unbiased estimator for the drift function in diffusion models with jumps. [ABSTRACT FROM AUTHOR]

Ground-penetrating radar will be disturbed by various noise signals in the actual use process, and to solve this problem, a ground-penetrating radar denoising was proposed based on wavelet adaptive thresholding method. Conventional wavelet thresholding algorithms for ground-penetrating radar B-scan images may cause image distortion due to the difference in wavelet coefficients before and after processing. In order to make the target signal clearer and eliminate interference such as noise, wavelet thresholds were improved by the way of selecting wavelet thresholds and the threshold function, and the thresholds were identified with the length of subbands of different layers of wavelet transform to achieve adaptive and accurate quantization of thresholds. The experimental results show that the method is applicable to ground-penetrating radar signal processing and improves the good continuity and stability of the threshold function compared with the ordinary wavelet thresholding algorithm, further improves the direct wave removal and noise reduction effects, and better preserves the details of the target image. Comparing the results with other methods shows that the algorithm proposed in this paper improves the peak signal-to-noise ratio and reduces the image entropy. The research results show that the method has a certain application value in the practical use case of ground-penetrating radar. [ABSTRACT FROM AUTHOR]

Variable energy constraints affect the implementations of neural networks on battery-operated embedded systems. This paper describes a learning algorithm for randomization-based neural networks with hard-limit activation functions. The approach adopts a novel cost function that balances accuracy and network complexity during training. From an energy-specific perspective, the new learning strategy allows to adjust, dynamically and in real time, the number of operations during the network's forward phase. The proposed learning scheme leads to efficient predictors supported by digital architectures. The resulting digital architecture can switch to approximate computing at run time, in compliance with the available energy budget. Experiments on 10 real-world prediction testbeds confirmed the effectiveness of the learning scheme. Additional tests on limited-resource devices supported the implementation efficiency of the overall design approach. [ABSTRACT FROM AUTHOR]

The occurrence of a macroeconomic policy would lead to a jump of financial data and the presence of jump behaviors might make the statistical methods for high-frequency sampling data to face new challenges. This paper will use the threshold function technique to disentangle the continuous part and the jump part from the high frequency financial data. Moreover, in the financial practices, the abnormal observations contained in the data could cause bias from nonparametric estimation based on least squares. The paper will employ the local M estimation to provide a robust estimator for the unknown diffusion coefficient of the diffusion model with jumps under high frequency sampling data. Under certain conditions for the initial values, this paper further considers one-step local M estimation for the unknown diffusion coefficient which can reduce the calculation quantity under the estimation efficiency. The Monte Carlo numerical simulation results verify that compared with the local linear threshold estimator, the threshold one-step local M estimator is more accurate and more robust. Finally, the threshold one-step local M estimator in this paper is applied to the Shanghai composite index of 2015 and 2020 in China and the Nasdaq index of 2020 in USA, which illustrates the method considered in this paper possesses good finite sample properties. [ABSTRACT FROM AUTHOR]

We consider the problem of sampling elements with some desired property from a large set, without testing the property of interest, but with the (probabilistic) assurance to have at least one match among the random sample. Like in ranked set sampling (RSS), we consider an infinite population under study, whose properties of interest are too expensive and/or time-consuming to measure. Unlike RSS, we are void of a ranking mechanism, so our sampling is done entirely blind. We show how it is nonetheless doable to assure, with controllably large likelihood, to either have at least one of the interesting elements in a random sample, or, contrarily, sample with the likewise assurance of not having one of the interesting elements in the sample. Our technique utilizes density bounds for distributions and threshold functions from random graph theory. • Algorithm for sampling elements of a set with a desired property, but without ever testing this property. • Construction of a formal language that is poly-time "sampleable" in the above respect. • Provides a new algorithmic application of threshold functions from random graph theory. • Has possible applications for the construction of "hard" problems for cryptography. [ABSTRACT FROM AUTHOR]

Copyright of Light Industry Machinery is the property of Light Industry Machinery Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Due to the existence of SAR interferogram noise, the quality of the interferogram is seriously affected. Therefore, to suppress the influence of phase noise, many scholars have carried out a lot of research on SAR interferogram noise reduction, but existing studies have difficulty maintaining edge details while also considering effective noise reduction. Therefore, we proposed an improved wavelet denoising algorithm for SAR interferogram using fast nonlocal means filtering. The algorithm was divided into three steps. First, the appropriate wavelet basis was selected and the decomposition level was determined by white noise detection to achieve wavelet decomposition. Then, after non-local processing of wavelet coefficients, the threshold denoising rule was constructed by improving the threshold function to achieve the first denoising. Finally, fast non-local means filtering was used for the second denoising. To verify the effectiveness and superiority of the proposed method, experimental verification of simulated data and real data was conducted. Experimental results show that the proposed method can obtain a more ideal SAR interferogram after noise reduction and has better qualitative and quantitative evaluation than the competitive methods, which indicates that the proposed method can achieve effective denoising for SAR interferograms while preserving the detailed features at smaller window settings. [ABSTRACT FROM AUTHOR]

A complex square matrix is a ray pattern matrix if each of its nonzero entries has modulus 1. A ray pattern matrix naturally corresponds to a weighted-digraph. A ray pattern matrix A is ray nonsingular if for each entry-wise positive matrix K, A ∘ K is nonsingular. A random model of ray pattern matrices with order n is introduced, where a uniformly random ray pattern matrix B is defined to be the adjacency matrix of a simple random digraph D n , p whose arcs are weighted with i.i.d. random variables uniformly distributed over the unit circle in the complex plane. It is shown that p ∗ (n) = 1 n is a threshold function for the random matrix M = I−B to be ray nonsingular, which is the same as the threshold function of the appearance of giant strong components in D n , p . [ABSTRACT FROM AUTHOR]

In this paper we study decision tree models with various types of queries. For a given function it is usually not hard to determine the complexity in the standard decision tree model (each query evaluates a variable). However in more general settings showing tight lower bounds is substantially harder. Threshold functions often have non-trivial complexity in such models and can be used to provide interesting examples. Standard decision trees can be viewed as a computational model in which each query depends on only one input bit. In the first part of the paper we consider natural generalization of standard decision tree model: we address decision trees that are allowed to query any function depending on two input bits. We show the first lower bound of the form n − o(n) for an explicit function (namely, the majority function) in this model. We also show that in the decision tree model with AND and OR queries of arbitrary fan-in the complexity of the majority function is n − 1. In the second part of the paper we address parity decision trees that are allowed to query arbitrary parities of input bits. There are various lower bound techniques for parity decision trees complexity including analytical techniques (degree over F 2 , Fourier sparsity, granularity) and combinatorial techniques (generalizations of block sensitivity and certificate complexity). These techniques give tight lower bounds for many natural functions. We give a new inductive argument tailored specifically for threshold functions. A combination of this argument with granularity lower bound allows us to provide a simple example of a function for which all previously known lower bounds are not tight. [ABSTRACT FROM AUTHOR]

Watercourses and roadways commonly intersect in their layout at many locations through bridges, drainages, and fords. During heavy rain events, watercourses may overflow causing serious disturbance toward traffic movement. Under such circumstances, attempting to drive through these intersections can be extremely dangerous. Therefore, understanding the responses of the vehicles moving through floodwaters is of utmost importance. Between 1967 and 2021, several studies have been published investigating the stability of static flooded vehicles. However, studies on the stability of vehicles in the movement are not sufficient at which only few experimental studies were published. Herein, for the very first time numerical simulations were conducted to investigate the hydrodynamic forces on a full‐scale medium‐size passenger vehicle moving perpendicular to the incoming floodwaters. Sliding and floating instability modes were observed by detecting the position of the vehicle centre of mass at each time step. Further, horizontal (FH) and vertical (FV) forces were measured and plotted against the governing flow parameters. Finally, it was observed that the critical flow depth was 0.38 m, while the minimum depth×velocity threshold function was 0.39 m2/s, for the tested vehicle. Later, a comparison between simulation outcomes and previously published experimental work was performed and a good agreement was observed. [ABSTRACT FROM AUTHOR]

Abstract Watercourses and roadways commonly intersect in their layout at many locations through bridges, drainages, and fords. During heavy rain events, watercourses may overflow causing serious disturbance toward traffic movement. Under such circumstances, attempting to drive through these intersections can be extremely dangerous. Therefore, understanding the responses of the vehicles moving through floodwaters is of utmost importance. Between 1967 and 2021, several studies have been published investigating the stability of static flooded vehicles. However, studies on the stability of vehicles in the movement are not sufficient at which only few experimental studies were published. Herein, for the very first time numerical simulations were conducted to investigate the hydrodynamic forces on a full‐scale medium‐size passenger vehicle moving perpendicular to the incoming floodwaters. Sliding and floating instability modes were observed by detecting the position of the vehicle centre of mass at each time step. Further, horizontal (FH) and vertical (FV) forces were measured and plotted against the governing flow parameters. Finally, it was observed that the critical flow depth was 0.38 m, while the minimum depth×velocity threshold function was 0.39 m2/s, for the tested vehicle. Later, a comparison between simulation outcomes and previously published experimental work was performed and a good agreement was observed.

The paper proposes a fast method for the multidimensional parameter estimation of a polarization-sensitive array. Compared with conventional methods (e.g., MUSIC algorithm), the proposed method applies an iterative approach based on Newton’s method to obtain joint estimation results instead of a spectral search and dimension reduction. It also extends the original Newton method to the 4D scale using the Hessian matrix. To reduce the complexity of establishing the aim function, Nystrom’s method is applied to process the covariance matrix. A new threshold is also proposed to select the results, which can accomplish the parameter estimation with a small number of iterations while guaranteeing a high estimation accuracy. Finally, the proposed algorithm is analyzed in detail and the numerical simulations of various algorithms are compared to verify its effectiveness.

A vertex-colored path P is rainbow if its internal vertices have distinct colors; whereas P is monochromatic if its internal vertices are colored the same. For a vertex-colored connected graph G, the rainbow vertex-connection number rvc(G) is the minimum number of colors used such that there is a rainbow path joining any two vertices of G; whereas the monochromatic vertex-connection number mvc(G) is the maximum number of colors used such that any two vertices of G are connected by a monochromatic path. These two opposite concepts are the vertex-versions of rainbow connection number rc(G) and monochromatic connection number mc(G) respectively. The study on rc(G) and mc(G) of random graphs drew much attention, and there are few results on the rainbow and monochromatic vertex-connection numbers. In this paper, we consider these two vertex-connection numbers of random graphs and establish sharp threshold functions for them, respectively. [ABSTRACT FROM AUTHOR]

For an integer ℓ≥2 $\ell \ge 2$, the ℓ $\ell $‐connectivity κℓ(G) ${\kappa }_{\ell }(G)$ of a graph G $G$ is defined to be the minimum number of vertices of G $G$ whose removal produces a disconnected graph with at least ℓ $\ell $ components or a graph with fewer than ℓ $\ell $ vertices. The ℓ $\ell $‐edge‐connectivity λℓ(G) ${\lambda }_{\ell }(G)$ of a graph G $G$ is the minimum number of edges whose removal leaves a graph with at least ℓ $\ell $ components if |V(G)|≥ℓ $|V(G)|\ge \ell $, and λℓ(G)=|E(G)| ${\lambda }_{\ell }(G)=|E(G)|$ if |V(G)|<ℓ $|V(G)|\lt \ell $. Given integers k≥0 $k\ge 0$ and ℓ≥2 $\ell \ge 2$, we investigate κℓ(G(n,p)) ${\kappa }_{\ell }(G(n,p))$ and λℓ(G(n,p)) ${\lambda }_{\ell }(G(n,p))$ when np≤logn+kloglogn $np\le \mathrm{log}n+k\mathrm{log}\mathrm{log}n$. Furthermore, our arguments can be used to show that in the random graph process, the hitting times of minimum degree at least k $k$ and of ℓ $\ell $‐connectivity (or ℓ $\ell $‐edge‐connectivity) at least k(ℓ−1) $k(\ell -1)$ coincide with high probability. These results generalize the work of Bollobás and Thomason on classical connectivity. [ABSTRACT FROM AUTHOR]

The existing estimators for the drift coefficient in the diffusion model with jumps involve jump components and possess larger boundary error. How to effectively estimate the drift function is an important issue that faces challenges and has theoretical significance. In this paper, the gamma asymmetric kernel for boundary correction and threshold function eliminating jump impacts are combined to estimate the unknown drift coefficient in the jump diffusion process of interest rate. The asymptotic large sample property and the better finite sample property through the Monte Carlo numerical simulation experiment and the empirical analysis of SHIBOR and LIBOR for the corresponding estimator are considered in detail. It is found that the estimator proposed in this paper can correct the estimation error near or far away from the origin point, which provides a more asymptotic unbiased estimator for the drift function in diffusion models with jumps.

A { 0 , 1 } -valued function on a two-dimensional rectangular grid is called threshold if its sets of zeros and ones are separable by a straight line. In this paper we study 2-threshold functions, i.e. functions representable as the conjunction of two threshold functions. We provide a characterization of 2-threshold functions by pairs of oriented prime segments, where each such segment is defined by an ordered pair of adjacent integer points. [ABSTRACT FROM AUTHOR]

Fast iterative soft threshold algorithm (FISTA) is one of the algorithms for the reconstruction part of compressed sensing (CS). However, FISTA cannot meet the increasing demands for accuracy and efficiency in the signal reconstruction. Thus, an improved algorithm (FIPITA, fast iterative parametric improved threshold algorithm) based on mended threshold function, restart adjustment mechanism and parameter adjustment is proposed. The three parameters used to generate the gradient in the FISTA are carefully selected by assessing the impact of them on the performance of the algorithm. The developed threshold function is used to replace the soft threshold function to reduce the reconstruction error and a restart mechanism is added at the end of each iteration to speed up the algorithm. The simulation experiment is carried out on one-dimensional signal and the FISTA, RadaFISTA and RestartFISTA are used as the comparison objects, with the result that in one case, for example, the residual rate of FIPITA is about 6.35% lower than those three and the number of iterations required to achieve the minimum error is also about 102 less than that of FISTA. [ABSTRACT FROM AUTHOR]

Robust detection of patterns at low signal-to-noise ratios (SNRs) is a fundamental challenge of analysing high-frequency data, particularly in water quality monitoring. When conducting water quality data analysis, an indispensable step is to clean the data noise. In this paper, a new method named ADAPTIVE-EWT-MFE, based on empirical wavelet transform (EWT) and multiscale fuzzy entropy (MFE), is proposed to implement time series data cleaning. EWT-MFE can decompose the spectrum into different intrinsic mode functions (IMFs). According to different characteristics of the IMFs, an adaptive and adjustable parameter based on MFE, which reflects the intrinsic characteristics, is introduced into the threshold function to improve the performance of noise cleaning. Finally, this hybrid data cleaning method is designed to filter the high-frequency noise on the IMFs. Results show that our proposed method not only has great potential to improve the noise-cleaning performance but also does not distort noise-free data. [ABSTRACT FROM AUTHOR]

Reaction networks are commonly used within the mathematical biology and mathematical chemistry communities to model the dynamics of interacting species. These models differ from the typical graphs found in random graph theory since their vertices are constructed from elementary building blocks, i.e. the species. We consider these networks in an Erdös–Rényi framework and, under suitable assumptions, derive a threshold function for the network to have a deficiency of zero, which is a property of great interest in the reaction network community. Specifically, if the number of species is denoted by n and the edge probability by $p_n$ , then we prove that the probability of a random binary network being deficiency zero converges to 1 if $p_n\ll r(n)$ as $n \to \infty$ , and converges to 0 if $p_n \gg r(n)$ as $n \to \infty$ , where $r(n)=\frac{1}{n^3}$. [ABSTRACT FROM AUTHOR]