Vicinity Of Zero Research Articles

Wide-angle and simultaneously wideband blazing (deflection) enabling multifunctionality in metagratings comprising epsilon-near-zero materials

This paper investigates diffractions by gratings made of a dispersive material in an epsilon-near-zero (ENZ) regime and having one-side corrugations, and those by two-component dielectric-ENZ gratings with the inner corrugations and flat outer interfaces. The goal is to achieve wideband and simultaneously wide-angle −1st order blazing (deflection) that may enable wideband spatial filtering and demultiplexing in reflection mode. Several typical scenarios are discussed, which differ in the maximum magnitude of the blazed wave and size of the blazing area observed on the frequency-incidence angle plane, as well as the contribution of the ranges of positive and negative permittivity in the vicinity of zero. The high capability of ENZ and dielectric-ENZ gratings in asymmetric reflection is demonstrated for three different levels of losses for the dispersive material.

Search for clusters among co-occurring objects and detection of protein complexes

The method of statistically based search for structures in data of different natures, previously proposed by the authors, is applied to the problem of searching for clusters of objects in sets of co-occurring objects. In bioinformatics, a similar problem arises when identifying protein complexes. A method for identifying significant interactions between proteins is proposed, based on the use of a statistical model in which the corresponding p-values are calculated. The algorithm for searching for clusters in one-dimensional data allows us to identify a cluster of small p-values located in the vicinity of zero. Next, we consider protein complexes that are formed only taking into account these significant interactions. Among the resulting complexes, as a rule, a giant component appears which in turn can be clustered. The proposed method for identifying significant deviations from the null hypothesis, based on searching for clusters of p-values in the vicinity of zero, is general.

The Calculation of the Probability Density and Distribution Function of a Strictly Stable Law in the Vicinity of Zero

The problem of calculating the probability density and distribution function of a strictly stable law is considered at x→0. The expansions of these values into power series were obtained to solve this problem. It was shown that in the case α<1, the obtained series were asymptotic at x→0; in the case α>1, they were convergent; and in the case α=1 in the domain |x|<1, these series converged to an asymmetric Cauchy distribution. It has been shown that at x→0 the obtained expansions can be successfully used to calculate the probability density and distribution function of strictly stable laws.

High Excursions of a Quadratic form for a Gaussian Stationary Vector Process

Exact asymptotic behavior is given for high excursion probabilities of a quadratic form for a zero-mean Gaussian stationary vector process with Pickands’ type covariance matrix in the vicinity of zero. The case of a quadratic form with a positive maximum eigenvalue of order 1 is considered.

Secure platooning control of automated vehicles under cyber attacks

This paper studies the problem of secure control of automated vehicles in a platoon-based driving pattern over a vehicular ad-hoc network (VANET) subject to various cyber attacks. The platoon under consideration is a convoy of a leader vehicle whose control input is unknown to its following vehicles and some follower vehicles with uncertain heterogeneous engine time constants, bounded disturbance and noise. First, a local estimator is developed for each follower vehicle so as to construct some confidence ellipsoidal estimation region always enclosing vehicular true state regardless of uncertain heterogenous engine time constants, bounded disturbance and noise. A convex optimization algorithm is proposed to find some optimal ellipsoidal sets and recursively solve out gain matrices of the local estimators. Then, a scalable control protocol employing the state estimates from its local and underlying neighboring estimators is designed to accomplish secure platooning control. Under the derived design technique, the resulting closed-loop platooning tracking errors are proven to remain in the vicinity of zero. Comparative studies are conducted to validate the efficacy of the proposed control method on achieving the satisfactory platooning performance by handling different attack strategies.

Composite synchronization on two pairs of vibrators in a far super-resonant vibrating system with the single rigid frame

In the present work, a new dynamical model with a single rigid frame driven by two pairs of vibrators, of which each pair of vibrators is engaged with each other by gear mechanism, is proposed to explore the composite synchronization of the system. The motion differential equations and vibration responses of the system are given first. The theory condition for achieving composite synchronization of the system is obtained, by using the average method to deduce the average torque balance equations of the two pairs of vibrators. According to the Hamilton’s theory, the system stability condition is presented, and it is mainly determined by the structural parameters of the system. The synchronous stable regions and stability ability versus the key parameters of the system are qualitatively discussed in numeric, and further quantitatively verified by simulations. It is shown that, in engineering, the reasonable working points of the system, should be selected in the region where the stable phase difference of the two pairs of vibrators is stabilized in the vicinity of zero. Only in this way, can the exciting forces of the two pairs of vibrators be positively superposed, and the linear motion of the system in the vertical direction be realized.

Спеціалізований програмний калькулятор для обчислення значень функції Ламберта W0(X) і споріднених з нею функцій

Запропоновано спеціалізований програмний калькулятор, призначений для обчислення значень функції Ламберта W0(х) і споріднених з нею функцій. Описана його програмна реалізація і наведено приклади обчислень. Калькулятор надає обчислювати значення верхньої гілки функції Ламберта, величину обернену до величини функції Ламберта, логарифм функції Ламберта, експоненту, показник ступеня якої містить функції Ламберта, значення першої і другої похідних, значення узагальненого логарифма, узагальненого тангенса, узагальненого котангенса, узагальненого синуса, узагальненого косинуса, гіперболічний узагальнений тангенс, гіперболічний узагальнений котангенс, гіперболічний узагальнений синус, гіперболічний узагальнений косинус. Калькулятор дозволяє обчислювати значення двох найбільш поширених видів визначених інтегралів, підінтегральна функція яких містить функцію Ламберта. Проведено порівняння різних засобів обчислення значень функції Ламберта і рекомендовані області їх застосування.

Infinite invariant density in a semi-Markov process with continuous state variables.

We report on a fundamental role of a non-normalized formal steady state, i.e., an infinite invariant density, in a semi-Markov process where the state is determined by the interevent time of successive renewals. The state describes certain observables found in models of anomalous diffusion, e.g., the velocity in the generalized Lévy walk model and the energy of a particle in the trap model. In our model, the interevent-time distribution follows a fat-tailed distribution, which makes the state value more likely to be zero because long interevent times imply small state values. We find two scaling laws describing the density for the state value, which accumulates in the vicinity of zero in the long-time limit. These laws provide universal behaviors in the accumulation process and give the exact expression of the infinite invariant density. Moreover, we provide two distributional limit theorems for time-averaged observables in these nonstationary processes. We show that the infinite invariant density plays an important role in determining the distribution of time averages.

On exponential decay of the variance of BLUE for the mean of a stationary sequence

Abstract In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of the variance of the best linear unbiased estimator (BLUE) for the unknown mean of a stationary sequence possessing a spectral density. In particular, we show that a necessary condition for variance of BLUE to decrease to zero exponentially is that the spectral density vanishes on a set of positive Lebesgue measure in any vicinity of zero.

Phase shift invariant imaging of coherent sources (PSIICOS) from MEG data

Increasing evidence suggests that neuronal communication is a defining property of functionally specialized brain networks and that it is implemented through synchronization between population activities of distinct brain areas. The detection of long-range coupling in electroencephalography (EEG) and magnetoencephalography (MEG) data using conventional metrics (such as coherence or phase-locking value) is by definition contaminated by spatial leakage. Methods such as imaginary coherence, phase-lag index or orthogonalized amplitude correlations tackle spatial leakage by ignoring zero-phase interactions. Although useful, these metrics will by construction lead to false negatives in cases where true zero-phase coupling exists in the data and will underestimate interactions with phase lags in the vicinity of zero. Yet, empirically observed neuronal synchrony in invasive recordings indicates that it is not uncommon to find zero or close-to-zero phase lag between the activity profiles of coupled neuronal assemblies.Here, we introduce a novel method that allows us to mitigate the undesired spatial leakage effects and detect zero and near zero phase interactions. To this end, we propose a projection operation that operates on sensor-space cross-spectrum and suppresses the spatial leakage contribution but retains the true zero-phase interaction component. We then solve the network estimation task as a source estimation problem defined in the product space of interacting source topographies. We show how this framework provides reliable interaction detection for all phase-lag values and we thus refer to the method as Phase Shift Invariant Imaging of Coherent Sources (PSIICOS).Realistic simulations demonstrate that PSIICOS has better detector characteristics than existing interaction metrics. Finally, we illustrate the performance of PSIICOS by applying it to real MEG dataset recorded during a standard mental rotation task. Taken together, using analytical derivations, data simulations and real brain data, this study presents a novel source-space MEG/EEG connectivity method that overcomes previous limitations and for the first time allows for the estimation of true zero-phase coupling via non-invasive electrophysiological recordings.

Comparison of two fractal interpolation methods

As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass–Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass–Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass–Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass–Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass–Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass–Mandelbrot fractal function method has strong periodicity, which is suitable for simulating periodic surface.

A Temperature-Insensitive Ba3.75Nd9.5Ti17.5(Cr0.5Nb0.5)0.5O54 Microwave Dielectric Ceramic by Bi3+ Substitution

In this study, effects of Bi3+ substitution upon microwave dielectric properties of the (Cr0.5Nb0.5)4+ replaced Ba3.75Nd9.5Ti18O54 (0 ≤ x ≤ 0.2) ceramic have been reported. The x-ray diffraction (XRD) result shows a single phase for all compositions with peak position fluctuation. Within the whole x range, while the quality factor (Q) is degraded, the dielectric constant (er) can be improved by as high as 32% and the temperature coefficient of resonant frequency (τf) is tailored from around +40 ppm/°C to the vicinity of zero. Considering practical requirements, we can obtain a series of temperature-insensitive ceramics (τf ∼ 0 ppm/°C) with relative permittivity about 95 and Qf (defined as Q times the resonant frequency f) higher than 6000 GHz. They have the potential of being utilized in wireless microwave communication applications.

Spectral approach to parameter-free unit root testing

A relatively simple frequency-type testing procedure for unit root potentially contaminated by an additive stationary noise is introduced, which encompasses general settings and allows for linear trends. The proposed test for unit root versus stationarity is based on a finite number of periodograms computed at low Fourier frequencies. It is not sensitive to the selection of tuning parameters defining the range of frequencies so long as they are in the vicinity of zero. The test does not require augmentation, has parameter-free non-standard asymptotic distribution and is correctly sized. The consistency rate under the alternative of stationarity reveals the relation between the power of the test and the long-run variance of the process. The finite sample performance of the test is explored in a Monte Carlo simulation study, and its empirical application suggests rejection of the unit root hypothesis for some of the Nelson–Plosser time series.

Design of a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems

This paper presents a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems. It is assumed that the systems are described by a discrete-time equation with nonlinear uncertainties to be viewed as the modelling errors and the unknown external disturbances, and the states are observed with measurement noises. To design the simplified adaptive fuzzy backstepping control, the modelling errors are approximated by using the fuzzy inference approach based on the extended single-input rule modules, and the estimates for the unmeasurable states and the adjustable parameters are derived by using the weighted and its simplified weighted least squares estimators. It is proved that the states are ultimately bounded, and the estimation errors remain in the vicinity of zero. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

Design of an adaptive fuzzy sliding mode control for uncertain discrete-time nonlinear systems based on noisy measurements

This paper presents the design of an adaptive fuzzy sliding mode control (AFSMC) for uncertain discrete-time nonlinear dynamic systems. The dynamic systems are described by a discrete-time state equation with nonlinear uncertainties, and the uncertainties include the modelling errors and the external disturbances to be unknown but nonlinear with the bounded properties. The states are measured by the restriction of measurement sensors and the contamination with independent measurement noises. The nonlinear uncertainties are approximated by using the fuzzy IF-THEN rules based on the universal approximation theorem, and the approximation error is compensated by adding an adaptive complementary term to the proposed AFSMC. The fuzzy inference approach based on the extended single input rule modules is proposed to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are obtained by using the weighted least squares estimator and its simplified one. It is proved that under some conditions the estimation errors will remain in the vicinity of zero as time increases, and the states are ultimately bounded subject to the proposed AFSMC. The effectiveness of the proposed method is indicated through the simulation experiment of a simple numerical system.

ON SEA LEVEL ALONG THE BRAZILIAN COAST

ABSTRACT . This is Part II of a contribution on Brazilian sea levels – Part I dealt with the seasonal variability. It examines the sea level changes along the Brazilian coast from series with less than 40 years of measurement, against the background of changes in series of all continents and islands around the world, considering data distributed by the Permanent Service for Mean Sea Level (PSMSL). The method of analysis follows the display of the data in a: 1) first plot of relative sea level trends (C), against the length of the series (L) expressed in years and a: 2) second plot showing the relative sea level regression coefficients (C), versus the corresponding correlation values (m). The first plot of all PSMSL data exhibited a cusped like shape of the distribution of (C), having maxima values about 10-20 cm/cty for the longest series (120-137 years), indicating the overall positive value of the global relative sea level trend. Similar first plot, a regional plot of African and South American data adjusted to the same global relative mean level, showed that the Brazilian trends (C), are mostly concentrated in the positive side of the cusped: (ports of Bel´em, Fortaleza. Recife, Canavieiras, Salvador, Ilha Fiscal, Rio de Janeiro, Ubatuba, Cananeia, and Imbituba) which have a mean value within 30 to 40 cm/cty. The second plot, with all set of PSMSL data, was necessary in order to display trend values of non simultaneous series of different continental borders and lengths in the same bin. The plot gave two different linear inclinations for trend values within ± 0.3 cm/y, in the positive and negative sides of the figure. The global ratio obtained for the trends was R = − 1.2, suggesting also, from the linearity of the plot, that the trends and correlation values are statistically dependent variables. The graph produced a different value for global balance of the value C obtained in the first plot. Similar regional second plot of the African Atlantic and South American borders, which include the Brazilian data, also gave rise to two new regression lines with trend C*1 0, with a ratio R = − 2.2, involving bins of m and C values that are also null in the vicinity of zero. This regionally plot confirmed the result of the second plot with PSMSL series that they (C and m), globally, should be dependent statistical variables. These findings, however, do not change the fact that the regional series with trends 0.2 cm/year have correlation values m 0 construidas a partir dos valores das tendencias C das series PSMSL, com inclinacoes dentro da faixa de 0,2 cm/ano na parte positiva e negativa da figura, sugerindo uma nao equivalencia entre essas inclinacoes, em favor de valor global negativo de C* para o Nivel Relativo do Mar. Figura semelhante produzida com as s´eries Africanas e Sul Americanas, que incluiram as series brasileiras, mostrou caracteristica similar, alem de indicar que series com tendencias ± 0,2 cm/ano tem valores de correlacao m < 0,3 qualquer que seja o comprimento da serie. Os resultados interessantes, mas contraditorios, que incluem a dependencia linear global entre correlacao e tendencias das series fornecidas pelo PSMSL, devem ser analisados em continuacao aos presentes estudos, que indicam que o nivel relativo do mar na costa brasileira esta aumentando a razao de 30 a 40 cm/seculo. Palavras-chave: nivel do mar, costa brasileira, series do PSMSL, nivel relativo do mar global, balanco do nivel relativo do mar.

Active disturbance rejection control and sliding mode control of one-dimensional unstable heat equation with boundary uncertainties

In this paper, we are concerned with the boundary stabilization of a one-dimensional unstable heat equation with the external disturbance flowing into the control end. The active disturbance rejection control (ADRC) and the sliding mode control (SMC) are adopted in investigation. By the ADRC approach, the disturbance is estimated through an external observer and cancelled online by the approximated one in the closed-loop. It is shown that the external disturbance can be attenuated in the sense that the resulting closed-loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity. In the second part, we use the SMC to reject the disturbance with the assumption in which the disturbance is supposed to be bounded. The reaching condition, and the existence and uniqueness of the solution for all states in the state space via SMC are established. Simulation examples are presented for both control strategies.

The active disturbance rejection and sliding mode control approach to the stabilization of the Euler–Bernoulli beam equation with boundary input disturbance

In this paper, we are concerned with the boundary feedback stabilization of a one-dimensional Euler–Bernoulli beam equation with the external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) are adopted in investigation. By the ADRC approach, the disturbance is estimated through an extended state observer and canceled online by the approximated one in the closed-loop. It is shown that the external disturbance can be attenuated in the sense that the resulting closed-loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity. In the second part, we use the SMC to reject the disturbance by removing the condition in ADRC that the derivative of the disturbance is supposed to be bounded. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the “reaching condition” is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system. The numerical simulations validate the effectiveness of both methods.

Sliding mode control and active disturbance rejection control to the stabilization of one-dimensional Schrödinger equation subject to boundary control matched disturbance

In this paper, we are concerned with the boundary stabilization of a one-dimensional anti-stable Schrödinger equation subject to boundary control matched disturbance. We apply both the sliding mode control (SMC) and the active disturbance rejection control (ADRC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop system is proved and the ‘reaching condition’ is obtained. Considering the SMC usually requires the large control gain and may exhibit chattering behavior, we develop the ADRC to attenuate the disturbance for which the derivative is also supposed to be bounded. Compared with the SMC, the advantage of the ADRC is not only using the continuous control but also giving an online estimation of the disturbance. It is shown that the resulting closed-loop system can reach any arbitrary given vicinity of zero as time goes to infinity and high gain tuning parameter goes to zero. Copyright © 2013 John Wiley & Sons, Ltd.

Synthesis of PID Tuning Rule Using the Desired Closed-Loop Response

Proportional−integral−derivative (PID) controllers are widely used in industry, because of their simple structure and ease in implementation. A tuning method based on the IMC−PID rule is synthesized for stable single-input−single-output systems. The controller transfer function is expanded, in the vicinity of zero in the complex plane, using a Laurent series, to derive analytical expressions for controller parameters. A tuning parameter is chosen to determine the stability of the response/closed-loop system. PID parameters are obtained for different types of processes, and related robustness issues are also discussed.