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In this article, a complete set of real-valued entire-domain vector basis functions is developed on a circular domain. The basis functions are constructed based on the orthogonal Zernike polynomials, and they satisfy the boundary conditions of vanishing normal components at the rim of the domain. This study discovers a number of new mathematical relations of the radial Zernike polynomials, which allows the method of moments (MoM) impedance matrix to be obtained in a completely analytical manner without the need of meshing or numerical integrations. An empirical, sufficient condition for the convergence of an MoM solution with the proposed basis is presented. As an example, the developed theories are applied to the determination of the characteristic modes of circular conducting plates, and their effectiveness and efficiency are demonstrated by comparing to results in the literature and those obtained by using the Rao–Wilton–Glisson (RWG) subdomain basis functions. The validity of the empirical convergence condition is also verified. [ABSTRACT FROM AUTHOR]

An increasing trend for reducing cost, space, and weight leads to modern embedded systems that execute multiple tasks with different criticality levels on a common hardware platform while guaranteeing a safe operation. In such mixed-criticality (MC) systems, multiple worst case execution times (WCETs) are defined for each task, corresponding to the system operation mode to improve the MC system’s timing behavior at runtime. Determining the appropriate WCETs for lower criticality (LC) modes is nontrivial. On the one hand, considering a very low WCET for tasks can improve the processor utilization by scheduling more tasks in that mode, on the other hand, using a larger WCET ensures that the mode switches (which causes by task overrunning) are minimized, thereby improving the quality of service for all tasks, albeit at the cost of processor utilization. Hitherto, no analytical solutions are proposed to determine WCETs in LC modes. In this regard, we propose a scheme to determine WCETs by the Chebyshev theorem, to make a tradeoff between the number of scheduled tasks at design-time and the number of dropped low-criticality tasks at runtime as a result of frequent mode switches. To have a tight bound of execution times and mode switching probability, we also propose a distribution analytics-based scheme, in which the mode switching probability is obtained based on the cumulative distribution function. Our experimental results show that our scheme improves the utilization of state-of-the-art MC systems by up to 72.27%, while maintaining 24.28% mode switching probability in the worst case scenario. Besides, the results of running embedded real-time benchmarks on a real platform show that the distribution-based scheme can improve the utilization by 7.30% while bounding the mode switching probability by 4.85% more, compared to the Chebyshev-based scheme. [ABSTRACT FROM AUTHOR]

Proximity testing technologies have been of increasing importance in vehicular ad-hoc networks (VANETs), especially in location-based services. However, there exist several known challenges in most existing proximity testing methods. For instance, during proximity testing, how to protect the location privacy of users, guarantee the fairness trait of both communication parties, and reduce computational costs is challenging. In this article, we present an efficient privacy-preserving proximity testing scheme using private set intersection (PSI) and differential privacy. In our design, a Chebyshev-based PSI is constructed to achieve location privacy with low energy consumption during the proximity testing process. Furthermore, geo-indistinguishability is employed in our scheme to generate virtual points as inputs set of PSI, which further protects the location privacy from exposure and provides resistance to collusion attacks. Fairness requirement is alsosatisfied in our scheme. The performance evaluation shows that the proposed scheme achieves good efficiency and is suitable for VANETs. [ABSTRACT FROM AUTHOR]

Due to the explosive increase of electric vehicles (EVs) and universal charging stations (CS), achieving fast authentication is an important topic in the vehicle-to-grid (V2G) network at present. Fast authentication cannot only forcefully defend potential adversaries but also can greatly speed up the charging process between EVs and CSs. Although many researchers have realized this problem and proposed some lightweight cryptographic protocols for fast EV charging, desired security features are not entirely satisfied, such as man-in-the-middle attacks, replay attacks, and impersonation attacks. In this article, we propose an ultra super fast authentication protocol for EV charging by utilizing the characteristics of extended chaotic maps. Furthermore, in view of the unsolved security issues mentioned previously, our proposed protocol can provide elaborate solutions to eliminate these possible attacks in a provable manner. Finally, compared with the relevant authentication protocols for V2G network, the communication and computation costs of our protocol are decreased a lot. [ABSTRACT FROM AUTHOR]

We propose a minimax design method for finite impulse response (FIR) graph filters in this brief. We first convert the graph filter design problem into a numerically stable equivalent problem using a shifted monomial basis. Then, we convert the minimax graph filter design problem into a semidefinite programming problem. Furthermore, we propose a computationally-efficient structure to implement the FIR graph filters designed using the proposed method. Design examples confirm that the proposed method can be used to design FIR graph filters having reasonably high orders, and the proposed implementation structure substantially saves additions required to process a graph signal compared to graph filters designed using a previously proposed Chebyshev polynomial approximation method. [ABSTRACT FROM AUTHOR]

The Fuzzy transform is applied mainly to 1-D signals and 2-D data organized as a regular grid (e.g., 2-D images), thus, limiting its potential application to arbitrary data in terms of dimensionality and structure. This article defines and analyzes the properties of the data-driven F-transform, with a focus on the construction of the class of data-driven membership functions, which are multiscale, local, linearly independent, intrinsic, and robust to data discretization. Data-driven membership functions are defined by applying a 1-D filter to the Laplace–Beltrami operator, which encodes the geometric and topological properties of the input data. Then, we address the efficient computation of the data-driven F-transform through a polynomial or a rational polynomial approximation of the input filter. In this way, the computation of the data-driven F-transform is independent of the evaluation of the membership functions at any point of the input domain and reduces to the solution of a small set of sparse and symmetric linear systems. Finally, the data-driven F-transform is efficiently evaluated on large and arbitrary data, in terms of dimensionality, structure, and size. [ABSTRACT FROM AUTHOR]

An efficient hybrid method based on subdomain adaptive integral method (SAIM) and Chebyshev approximation technology (CAT) is proposed for analyzing the wideband radar cross section (RCS) of complex multiscale objects in this letter. The SAIM cannot only be used to effectively deal with the difficulty of slow convergence caused by the mutiscale problems, but also greatly reducing the computational memory. By introducing the CAT into SAIM, we can use the currents at a few frequency sampling points to predict the currents at any frequency point over the entire band. In addition, the application of the Maehly approximation can obtain a better accuracy. Numerical examples show that the proposed SAIM-CAT can significantly improve the calculation efficiency without loss of accuracy. [ABSTRACT FROM AUTHOR]

We study the problem of off-policy evaluation in the multi-armed bandit model with bounded rewards, and develop minimax rate-optimal procedures under three settings. First, when the behavior policy is known, we show that the Switch estimator, a method that alternates between the plug-in and importance sampling estimators, is minimax rate-optimal for all sample sizes. Second, when the behavior policy is unknown, we analyze performance in terms of the competitive ratio, thereby revealing a fundamental gap between the settings of known and unknown behavior policies. When the behavior policy is unknown, any estimator must have mean-squared error larger—relative to the oracle estimator equipped with the knowledge of the behavior policy— by a multiplicative factor proportional to the support size of the target policy. Moreover, we demonstrate that the plug-in approach achieves this worst-case competitive ratio up to a logarithmic factor. Third, we initiate the study of the partial knowledge setting in which it is assumed that the minimum probability taken by the behavior policy is known. We show that the plug-in estimator is optimal for relatively large values of the minimum probability, but is sub-optimal when the minimum probability is low. In order to remedy this gap, we propose a new estimator based on approximation by Chebyshev polynomials that provably achieves the optimal estimation error. Numerical experiments on both simulated and real data corroborate our theoretical findings. [ABSTRACT FROM AUTHOR]

A wideband bandpass filter (BPF) with in-band Chebyshev equal-ripple responses and extended upper stopband is proposed, which is composed of composite microstrip, slotline, and coplanar waveguide (CPW) structure. According to the odd-mode and even-mode equivalent circuits, there are four in-band transmission poles constructing the ultrabroad bandwidth can be directly deduced. In addition, there are two sets of lowpass filter (LPF) embedding in the CPW connecting line to greatly widen the upper stopband without increasing circuit size. In order not to affect original passband Chebyshev equal-ripple responses, the LPFs are synthesized using the low-pass prototype network. Furthermore, there are two finite frequency transmission zeros (TZs) which generated by cross-coupling effects located at lower and upper side of passband to effectively improve the shirt selectivity. Finally, for experimental verification, the proposed BPF prototype is manufactured and tested. Experimental results are consistent with predicted theoretical responses, which verify the validity and feasibility of proposed approach. [ABSTRACT FROM AUTHOR]

A technique for trading off the main lobe width against sidelobe magnitude for any arbitrary window was reported in Lim et al. and subsequently, a fast convergence method for its implementation was proposed by the same authors. These methods require the computation of derivatives involving the evaluation of trigonometric and hyperbolic functions. In this paper, we show that the derivatives can be computed without evaluating trigonometric and hyperbolic functions if the window function is a sum of exponentials such as a Fourier series. [ABSTRACT FROM AUTHOR]

Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more robust to noise, and better captures the global graph structure. We propose a graph neural network implementation of the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, localized in the node space, and can be transferred to new graphs at test time. We perform a spectral analysis to study the filtering effect of the proposed ARMA layer and report experiments on four downstream tasks: semi-supervised node classification, graph signal classification, graph classification, and graph regression. Results show that the proposed ARMA layer brings significant improvements over graph neural networks based on polynomial filters. [ABSTRACT FROM AUTHOR]

To maintain the vibrations of the gyroscope proof mass, a trajectory tracking control system using a neural network estimator is proposed. The proposed control system incorporates a fractional controller based on the terminal sliding-mode and a recurrent Chebyshev fuzzy neural network using a self-evolving mechanism. The fractional-order terminal sliding-mode control can guarantee the tracking error exponential stable, and a self-evolving recurrent Chebyshev fuzzy neural network (SERCFNN) is introduced to relax the requirement of nonlinear functional certainty. In addition, the SERCFNN develops the advantages of the self-evolving fuzzy neural network (SEFNN), recurrent fuzzy neural network (RFNN), and Chebyshev function network (CFN). The SEFNN can adaptively update the dynamic structure through generating and adjusting fuzzy logic rules. The RFNN improves the performance for coping with a temporal problem with the capability to store prior information. The CFN is capable to enlarge the dimensionality of the input variables. Moreover, the asymptotic stability of the proposed control system can be proved by the Lyapunov stability theory. The effectiveness and superiority of the performance are exhibited with simulation studies and comprehensive comparisons. [ABSTRACT FROM AUTHOR]

This article investigates the $\eta$ -exponential stabilization and positivity of the controlled discrete-time polynomial fuzzy model (DPFM) system with time delay. $\eta$ -exponential polynomial copositive Lyapunov candidate is proposed to detect the system stability under the convergence (decay) rate. Static output feedback fuzzy controller is then synthesized to assure the DPFM closed-loop system with time delay. We propose Chebyshev membership functions (CMFs) to approach the primary membership function and attenuate the conservativeness of $\eta$ -exponential stability formulation and positivity analysis. Chebyshev norm approximation error is utilized to introduce the error between CMFs and primary membership functions using slack matrices. A numerical example is presented to validate the proposed methods. [ABSTRACT FROM AUTHOR]

This brief proposes a wideband interdigital bandpass filter (IBPF), exploiting the through-silicon via (TSV)-based 3-D integrated circuit (3-D IC) technology. IBPF is a structure composed of multiple groups of parallel-coupled line resonators, which can increase the bandwidth and out-band suppression (OBS) characteristics of a bandpass filter. Through the transformation of the Chebyshev low-pass circuit model, a seventh-order IBPF centered at 85 GHz is obtained. By combining TSV technology with the coupling coefficient method, the design process from the Chebyshev low-pass circuit model to the final optimization of IBPF is given. The fractional bandwidth (FBW) of IBPF based on TSV is 63%, the out-of-band suppression is greater than 80 dB, the insertion loss is 1.3 dB, the return loss is 20 dB, and the size of the compact IBPF is only $0.50\times0.34$ mm2 ($0.48\times 0.33\,\,\lambda \text{g}^{2}$). [ABSTRACT FROM AUTHOR]

The deceptive jamming technique can threaten a synthetic aperture radar (SAR) imaging system by repeatedly transmitting copied radar signals back to the radar. A conventional phased array can generate only an angle-dependent beam and cannot distinguish the jammer from other targets. Instead, a frequency diverse array (FDA) can offer a range-angle-dependent beampattern by introducing small frequency offsets to array elements, which can be adopted to distinguish signals from different range cells. Thus, considering that the position of the jammer is unknown, it is necessary to suppress the range peak sidelobe as much as possible. To lower this value, this communication proposes a weighted FDA to achieve the optimal solution at the expense of raising other range sidelobes. [ABSTRACT FROM AUTHOR]

This paper aims to build a supervised classifier for dealing with imbalanced datasets, uncertain class proportions, dependencies between features, the presence of both numeric and categorical features, and arbitrary loss functions. The Bayes classifier suffers when prior probability shifts occur between the training and testing sets. A solution is to look for an equalizer decision rule whose class-conditional risks are equal. Such a classifier corresponds to a minimax classifier when it maximizes the Bayes risk. We develop a novel box-constrained minimax classifier which takes into account some constraints on the priors to control the risk maximization. We analyze the empirical Bayes risk with respect to the box-constrained priors for discrete inputs. We show that this risk is a concave non-differentiable multivariate piecewise affine function. A projected subgradient algorithm is derived to maximize this empirical Bayes risk over the box-constrained simplex. Its convergence is established and its speed is bounded. The optimization algorithm is scalable when the number of classes is large. The robustness of our classifier is studied on diverse databases. Our classifier, jointly applied with a clustering algorithm to process mixed attributes, tends to equalize the class-conditional risks while being not too pessimistic. [ABSTRACT FROM AUTHOR]

Signal and power integrity design in the time domain requires equivalent circuit models for interconnects and packages, whose descriptions may only be available as tabulated impedance or admittance parameters. Accurate models for these components should maintain their physical properties including causality, stability, and passivity. Even though a heuristic approach, pole flipping (i.e., changing the sign of the real part of an unstable pole) has proven to be sufficiently accurate for many applications, resulting in models with ensured causality and stability. In this article, we address the problem of generating passive scalar models, such as driving point impedances or admittances, based on an existing causal, stable, but nonpassive model. Our approach is based on using sum-of-squares (SOS) polynomials and results in a convex optimization problem, hence a global optimum is obtained. We obtain approximations through two distinct SOS algorithms: a coefficient and a sampling-based method. We also present a simple passivity test for such functions based on calculating the roots of numerator and denominator polynomials, which provides an intuitive link among existing approaches based on solving an eigenvalue problem. [ABSTRACT FROM AUTHOR]

A wideband planar multilayer filtering magic-T is proposed and developed. The proposed magic-T uses coupled microstrip slotlines (CMSs) and microstrip-slot transitions. With the orthogonality of even and odd modes of the CMS, the Chebyshev filtering responses of both the in-phase divider part (H-T) and out-of-phase divider part (E-T) are independent of each other. The microstrip-slot transitions act as a part of filtering structures to realize vertical transmission of energy. With equivalent impedance transformer models, the synthesis processes of a four-pole Chebyshev filtering H-T and a three-pole Chebyshev filtering E-T are derived and analyzed. To verify the proposed concept, a prototype with an operating center frequency of 3 GHz, a 100% equal ripple fractional bandwidth, and a different H-T and E-T in-band ripple are synthesized and implemented on a three-layer printed circuit board. The synthesized, simulated, and measured results show good agreements among them, verifying the feasibility of the proposed planar magic-T. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) is a commonly used pattern analysis method that maps high-dimensional data into a lower-dimensional space maximizing the data variance, that results in the promotion of separability of data. Inspired by the principle of PCA, a novel type of learning discriminative matrix information geometry (MIG) detectors in the unsupervised scenario are developed, and applied to signal detection in nonhomogeneous environments. Hermitian positive-definite (HPD) matrices can be used to model the sample data, while the clutter covariance matrix is estimated by the geometric mean of a set of secondary HPD matrices. We define a projection that maps the HPD matrices in a high-dimensional manifold to a low-dimensional and more discriminative one to increase the degree of separation of HPD matrices by maximizing the data variance. Learning a mapping can be formulated as a two-step mini-max optimization problem in Riemannian manifolds, which can be solved by the Riemannian gradient descent algorithm. Three discriminative MIG detectors are illustrated with respect to different geometric measures, i.e., the Log-Euclidean metric, the Jensen–Bregman LogDet divergence and the symmetrized Kullback–Leibler divergence. Simulation results show that performance improvements of the novel MIG detectors can be achieved compared with the conventional detectors and their state-of-the-art counterparts within nonhomogeneous environments. [ABSTRACT FROM AUTHOR]

In this letter, a behavior model, namely CP- LSTM, composed of Chebyshev polynomials (CP) and a long short-term memory (LSTM) network is built to linearize the wideband millimeter-wave power amplifier (mmW PA) in the fifth-generation (5G) mobile communication system. In order to verify the linearization performance of the CP- LSTM predistorter, a 100-MHz bandwidth 5G new radio (5G NR) signal is employed to test the 28-GHz mmW PA under the text. Experimental results show that the adjacent channel power ratio (ACPR) of the mmW PA with the CP- LSTM can be improved by 20 dB which is 5-dB better than with the LSTM and 3-dB better than with the generalized memory polynomial (GMP). Therefore, the proposed CP- LSTM model is very effective to linearize 5G mmW PAs. [ABSTRACT FROM AUTHOR]

In this letter, the modified elliptic low-pass filtering (LPF) matching network (MN) is proposed for harmonic suppression of a wideband gallium nitride (GaN) microwave monolithic integrated circuit (MMIC) power amplifier (PA) at millimeter-wave (mm-wave). To investigate the effectiveness of the method at mm-wave, a three-stage 25–31-GHz GaN MMIC PA is designed using a commercial 150-nm GaN HEMT foundry process, with a mask area of $4.5\times2.6$ mm2. Simulated results show that the second harmonic of the PA can be effectively suppressed by using the elliptic LPF MN. Experimental results show that the realized MMIC PA achieves a saturated power-added efficiency (PAE) higher than 26.1% from 25 to 31 GHz, with a peak PAE of 31.5% at 29 GHz. The saturated gain and output power are more than 20 and 34 dBm within the band, respectively. [ABSTRACT FROM AUTHOR]

Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the gyroscope signal but is subject to a fundamentally numerical stability problem due to the Runge effect on equispaced samples. This article reviews the theoretical results of Runge phenomenon in related areas and proposes a straightforward borrowing-and-cutting (BAC) strategy to depress it. It employs the neighboring samples for higher order polynomial interpolation but only uses the middle polynomial segment in the actual time interval. The BAC strategy has been incorporated into attitude computation by functional iteration, leading to accuracy benefit of several orders of magnitude under the classical coning motion. It would potentially bring significant benefits to the inertial navigation computation under sustained dynamic motions. [ABSTRACT FROM AUTHOR]

One of the major considerations for a short- or intermediate-distance wireless power transfer (WPT) system is its robustness against variations of the distance, displacement, misalignment between the transmitting and receiving coils, and variations of the loads. Designing such a robust system has not been easy since most methods require some forms of trial-and-errors or optimization that present different degrees of uncertainty. In this article, we propose a design method to overcome the above issue: we make the power transfer efficiency (PTE) function of the WPT equivalent to that of a modified filter. Then, we apply a well-established filter theory to develop a systematic WPT design method; it can keep the PTE stable within the specified ranges of the distance changes, displacements, misalignments, and load variations. We take the Chebyshev filter as an example to verify the proposed method and build and test the prototype. Experiments show that when distance and misalignments occur, the prototype can maintain the efficiency of around 90% with less than 5% in variations as predicted by the theoretical design. In comparison, the conventional magnetically coupled resonant WPT system can only maintain the efficiency of 82% with more than 20% in variations. Therefore, the proposed design method presents a new efficient and optimized way to develop a robust WPT system for practical applications. [ABSTRACT FROM AUTHOR]

In order to increase the nonlinear fitting performance of functional link neural network (FLNN), a novel chebyshev functional link spline neural filter (CFLSNF) to apply in system identification is proposed. Compared with the weak nonlinearity and boundedness of the fixed activation function (e.g., $sigmoid$ and $tanh$), CFLSNF has stronger nonlinear approximation ability than FLNN due to the flexible interpolation ability of spline activation function. At the same time, the proposed CFLSNF eliminates the hidden layers by using Chebyshev polynomial to extend the input space into high dimensions, which shows certain computational advantages compared with the artificial neural network (ANN) structures. Moreover, to update the weights of the CFLSNF, the CFLSNF-LMS is also developed. The stability conditions and computational complexity are studied. Besides, in order to make CFLSNF structure suitable for impulsive noise interference environment, a robust algorithm based on maximum versoria criterion is also proposed. Finally, the validity of the proposed architecture and algorithm are verified by experiments. [ABSTRACT FROM AUTHOR]

In this brief, we investigate the cluster synchronization of multi-weighted complex networks with pinning control. We assume that the network contains multiple coupling matrices, and they can be all asymmetric (including the symmetric case), which is more practical in the real world. For multiple asymmetric coupling matrices, the Lyapunov function is hard to design. We firstly define a candidate region for every matrix. Then if these regions are not too far, we can find (at least) a common vector lying in each region. This method has geometrical meaning, so it is different from previous LMI method. That is to say, we can design a new Lyapunov function with a vector combining all normalized left eigenvectors (NLEVec) corresponding to the zero eigenvalue of coupling matrices. With some sufficient conditions presented accordingly, the realization of the cluster synchronization is guaranteed. Especially, we carefully discuss the case with three coupling matrices. The adaptive rule for cluster synchronization is also designed. Finally, numerical simulations are given to demonstrate our results’ effectiveness. [ABSTRACT FROM AUTHOR]

Inference of disease-gene associations helps unravel the pathogenesis of diseases and contributes to the treatment. Although many machine learning-based methods have been developed to predict causative genes, accurate association inference remains challenging. One major reason is the inaccurate feature selection and accumulation of error brought by commonly used multi-stage training architecture. In addition, the existing methods do not incorporate cell-type-specific information, thus fail to study gene functions at a higher resolution. Therefore, we introduce single-cell transcriptome data and construct a context-aware network to unbiasedly integrate all data sources. Then we develop a graph convolution-based approach named CIPHER-SC to realize a complete end-to-end learning architecture. Our approach outperforms four state-of-the-art approaches in five-fold cross-validations on three distinct test sets with the best AUC of 0.9501, demonstrating its stable ability either to predict the novel genes or to predict with genetic basis. The ablation study shows that our complete end-to-end design and unbiased data integration boost the performance from 0.8727 to 0.9443 in AUC. The addition of single-cell data further improves the prediction accuracy and makes our results be enriched for cell-type-specific genes. These results confirm the ability of CIPHER-SC to discover reliable disease genes. Our implementation is available at http://github.com/YidingZhang117/CIPHER-SC. [ABSTRACT FROM AUTHOR]

In this article, we present a comprehensive discussion of a new class of inline microwave filters with transmission zeros in the response, namely, the path filters. The main features of this filters class are highlighted, and an original (synthesis-based) design approach is presented, relying on the derivation of suitable characteristic polynomials. In addition to the classical generalized Chebyshev characteristic, two new characteristics are introduced (namely, the bounded Chebyshev and the reduced Chebyshev), which allows improving the flexibility in the requirements assignment of path filters. A new method for the synthesis of the low-pass prototype is also introduced, which overcomes the limitation in the classical synthesis based on the manipulation of the transversal prototype (whose synthesis may fail in case of path filters). Finally, the proposed approach for designing the class of considered filters has been validated by several examples that include the evaluation of the characteristic polynomials, the prototype synthesis, and the dimensioning of the physical structures in waveguide technology. [ABSTRACT FROM AUTHOR]

In RF/microwave circuits, parametric uncertainty can take two forms—epistemic and aleatory uncertainty. Epistemic uncertainty arises from the instrumentation, human, and approximation errors when measuring the value of a circuit parameter. This uncertainty is modeled using variables whose values lie within fixed intervals of support. On the other hand, aleatory uncertainty arises from random fabrication process variations and manufacturing tolerances. This uncertainty is modeled using random variables of known probability density functions. Standard polynomial chaos (PC) metamodels suffer from the aggravated curse of dimensionality when tackling both these forms of uncertainty. To address this issue, in this article, a new polymorphic PC (PPC) formulation is developed for cases where both epistemic and aleatory uncertainty reside in the same circuit parameter. This PPC formulation uses a new type of variable called a polymorphic variable. Polymorphic variables can capture the combined effects of both epistemic and aleatory uncertainty embedded in a circuit parameter, thus leading to a compression in the number of dimensions without any loss in information. This leads to significantly faster training of the PC metamodel as illustrated by multiple numerical examples in this article. [ABSTRACT FROM AUTHOR]

Ground-based differential absorption lidar (DIAL) can measure vertical CO2 concentration profiles in the troposphere. Here, we propose a method of improving the accuracy and precision of CO2concentration profiles measurements. This method combines a conditional adjustment with Chebyshev fitting to reduce the error of the retrieved results in view of the received signal around the atmospheric boundary layer (ABL) with a high signal-to-noise ratio (SNR). Simulation experiments verified the effectiveness of this method. The accuracy of CO2 concentration profiles can be improved larger than 83.4% when compared with that via traditional methods, and the standard deviation of the measured CO2 concentration profiles calculated by our method was reduced by approximately 0.43–22.51 ppm when compared with the results calculated by traditional methods. Two real cases in different locations were also examined with the proposed technique. The results indicated the applicability of our method in measuring other trace gases by using DIAL. [ABSTRACT FROM AUTHOR]

A rectangular-window sidelobe magnitude reduction method by widening the main lobe width was proposed by Saramäki. A technique for trading off main lobe width against sidelobe magnitude for any arbitrary window was reported by Lim et al.; a fast convergence algorithm for its implementation was proposed by the same authors in another article, where the derivatives of the window function are expressed in Chebyshev polynomials which have high arithmetic complexity. All the coefficients of a rectangular-window are equal; this special property is exploited, in this paper, for deriving the window function’s derivatives without the use of Chebyshev polynomials resulting in a great reduction in the arithmetic complexity. [ABSTRACT FROM AUTHOR]

Deep learning (DL) based methods have swept the field of mechanical fault diagnosis, because of the powerful ability of feature representation. However, many of existing DL methods fail in relationship mining between signals explicitly. Unlike those deep neural networks, graph convolutional networks (GCNs) taking graph data with topological structure as input is more efficient for data relationship mining, making GCN to be powerful for feature representation from graph data in non-Euclidean space. Nevertheless, existing GCNs have two limitations. First, most GCNs are constructed on unweighted graphs, considering importance of neighbors as the same, which is not in line with reality. Second, the receptive field of GCNs is fixed, which limits the effectiveness of GCNs for feature representation. To address these issues, a multireceptive field graph convolutional network (MRF-GCN) is proposed for effective intelligent fault diagnosis. In MRF-GCN, data samples are converted into weighted graphs to indicate differences in relationship of data samples. Moreover, MRF-GCN learns not only features from different receptive field, but also fuses learned features as an enhanced feature representation. To verify the efficacy of MRF-GCN for machine fault diagnosis, case studies are implemented, and the results show that MRF-GCN can achieve superior performance even under imbalanced dataset. [ABSTRACT FROM AUTHOR]

We study the phase synchronization problem with measurements ${Y}= {z}^{\ast} {z}^{\ast{\mathrm {H}}}+\sigma {W}\in \mathbb {C}^{n}\times {n}$ , where ${z}^{\ast}$ is an ${n}$ -dimensional complex unit-modulus vector and ${W}$ is a complex-valued Gaussian random matrix. It is assumed that each entry ${Y}_{jk}$ is observed with probability ${p}$. We prove that the minimax lower bound of estimating ${z}^{\ast}$ under the squared $\ell _{2}$ loss is $(1- {o}(1))\frac {\sigma ^{2}}{2p}$. We also show that both generalized power method and maximum likelihood estimator achieve the error bound $(1+ {o}(1))\frac {\sigma ^{2}}{2p}$. Thus, $\frac {\sigma ^{2}}{2p}$ is the exact asymptotic minimax error of the problem. Our upper bound analysis involves a precise characterization of the statistical property of the power iteration. The lower bound is derived through an application of van Trees’ inequality. [ABSTRACT FROM AUTHOR]

We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes an estimate of a desired parameter. We develop lower bounds for the minimax risk of estimating the underlying parameter for a large class of losses and distributions. Our results show that under mild regularity conditions, the communication constraint reduces the effective sample size by a factor of $d$ when $k$ is small, where $d$ is the dimension of the estimated parameter. Furthermore, this penalty reduces at most exponentially with increasing $k$ , which is the case for some models, e.g., estimating high-dimensional distributions. For other models however, we show that the sample size reduction is re-mediated only linearly with increasing $k$ , e.g. when some sub-Gaussian structure is available. We apply our results to the distributed setting with product Bernoulli model, multinomial model, Gaussian location models, and logistic regression which recover or strengthen existing results. Our approach significantly deviates from existing approaches for developing information-theoretic lower bounds for communication-efficient estimation. We circumvent the need for strong data processing inequalities used in prior work and develop a geometric approach which builds on a new representation of the communication constraint. This approach allows us to strengthen and generalize existing results with simpler and more transparent proofs. [ABSTRACT FROM AUTHOR]

Internet of Things (IoT) consists of numerous smart devices for sharing sensed data through the availability of online services. Direct communication by smart devices with people to identify parameters of healthcare and send them to a central repository is crucial. There is a need to secure messages among the sender and recipient during data exchange in order to tackle the malicious attacks by human. To provide secure communication, various signature-based schemes are presented in the literature. However, smart devices require lightweight tasks by guaranteeing essential security strengths. The main difficulty in signature-based methods is more computational cost incurred for signature and verification stages involving large numbers. This article introduces a lightweight provably secure short digital signature technique for safe communication amongst smart devices in human-centered IoT (HCIoT), the security of which is closely related to an extended chaotic maps assumption in a random oracle model (ROM). Moreover, we used less comprehensive operations to accomplish processes of verification and signing, similar to human signing on legitimate documents and then check as per witness. The proposed technique provides a stronger guarantee of protection than existing signature techniques. The key advantage of the presented technique over the DSA techniques is that it takes less computation in the verification stage and signing length; it retains the degree of protection. The presented short signature takes less bandwidth for communication, storage, and computing resources. [ABSTRACT FROM AUTHOR]

Windows such as Dolph-Chebyshev window and Kaiser window are adjustable, whereas windows such as Hamming window and Blackman window are traditionally not adjustable. In [1], a technique for trading off main lobe width against sidelobe magnitude for any arbitrary window, including the traditionally non-adjustable windows, was presented. However, the method in [1] requires a large number of iterations if the specification is very tight. Developed based on a new perspective on the window adjustment principle, a new method to achieve the same adjustment capability as in [1], but at a very much fewer iterations is presented in this letter. Our new method is particular useful if the specification is very tight. [ABSTRACT FROM AUTHOR]

In this article, we investigate the stability analysis of a polynomial-fuzzy-model-based control system by employing a new form of approximate membership functions called Chebyshev membership functions (CMFs) based on the Lyapunov stability theory. The membership-function-dependent method shows that the approximate functions can introduce useful information to relax the conservativeness of stability analysis. Therefore, in the case of the same order and operating domain, how to design the approximate functions to introduce more information to relax stability is a concern. In this article, given the Chebyshev norm relationship between the approximate membership functions and the original ones, CMFs can be obtained by the Chebyshev approximation theory and the Remez/Remez-type iterative algorithm, which own the minimum of the maximum absolute approximation error. Together with CMFs, the boundary information of premise variables on the overall operating domain is considered to reduce the conservativeness of stability analysis. Furthermore, to further relax the stability analysis without increasing the order of CMFs, the operating domain is divided into subdomains, and piecewise Chebyshev membership functions (PCMFs) are proposed to facilitate the stability analysis. Together with PCMFs, the subdomain boundary information of premise variables is introduced into stability conditions. A simulation example is given to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The generalized Chebyshev (pseudoelliptical) filter functions may not be optimal for certain applications due to physical constrains. With redundancy in filter polynomials, this article breaks down the “mental barrier” in conventional synthesis and directly synthesizes the “Chebyshev-like” functions to achieve desired filter performance under physical limitations. By exploiting the redundant restrictions on exact equal-ripple response, the reflection zeros can be moved to the complex plane, thus forming the “Chebyshev-like functions.” A class of inline filters with a block of second-order dangling resonators is synthesized, which can generate a pair of symmetric transmission zeros (Tzs) but is considered unrealizable using standard Chebyshev functions. With the proposed theories, an accurate and much improved filter prototype is directly derived from the “Chebyshev-like” polynomials, avoiding additional optimization in the design process. For verification, a group of examples with synthesis results are elucidated. Eight ten-pole filters with four Tzs are synthesized and fabricated. The simulated and measured results demonstrate the effectiveness and application of the proposed theories. [ABSTRACT FROM AUTHOR]

This article presents a rigorous design method for a one-port-reflectionless filter with a Chebyshev response. In particular, we, for the first time, present inverter-coupled resonator filter topologies capable of having a Chebyshev response with zero reflection at all frequencies in theory. This work demonstrates a systematic approach for filter synthesis to find the normalized coupling (inverter) values without employing optimization methods or heuristic approaches. In addition, it provides closed-form design formulas in terms of a target frequency for the design of a one-port-reflectionless filter of coupled-line structure. We also present an exact approach to increase the reflectionless range of a distributed-element filter. Distributed-element bandpass filter structures formulated by this work are capable of producing a predefined canonical transmission response and a reflectionless feature over the entire frequency range at the same time, which has never been reported up to date. The presented topologies, synthesis results, and design methods have been applied to the design of second- and third-order filters for demonstration. [ABSTRACT FROM AUTHOR]

This article introduces a new method for discretizing and solving integral equation formulations of Maxwell’s equations, which achieves spectral accuracy for smooth surfaces. The approach is based on a hybrid Nyström-collocation method using Chebyshev polynomials to expand the unknown current densities over curvilinear quadrilateral surface patches. As an example, the proposed strategy is applied to the magnetic field integral equation (MFIE) and the N-Müller formulation for scattering from metallic and dielectric objects, respectively. The convergence is studied for several different geometries, including spheres, cubes, and complex NURBS geometries imported from CAD software, and the results are compared against a commercial Method-of-Moments solver using RWG basis functions. [ABSTRACT FROM AUTHOR]

We consider the distributional connection between the lossy compressed representation of a high-dimensional signal X using a random spherical code and the observation of X under an additive white Gaussian noise (AWGN). We show that the Wasserstein distance between a bitrate-R compressed version of X and its observation under an AWGN-channel of signal-to-noise ratio 22R−1 is bounded in the problem dimension. We utilize this fact to connect the risk of an estimator based on the compressed version of X to the risk attained by the same estimator when fed the AWGN-corrupted version of X. We demonstrate the usefulness of this connection by deriving various novel results for inference problems under compression constraints, including minimax estimation, sparse regression, compressed sensing, and universality of linear estimation in remote source coding. [ABSTRACT FROM AUTHOR]

Continued great efforts have been dedicated toward high-quality trajectory generation based on optimization methods; however, most of them do not suitably and effectively consider the situation with moving obstacles; and more particularly, the future position of these moving obstacles in the presence of uncertainty within some possible prescribed prediction horizon. To cater to this rather major shortcoming, this work shows how a variational Bayesian Gaussian mixture model (vBGMM) framework can be employed to predict the future trajectory of moving obstacles; and then with this methodology, a trajectory generation framework is proposed which will efficiently and effectively address trajectory generation in the presence of moving obstacles, and incorporate the presence of uncertainty within a prediction horizon. In this work, the full predictive conditional probability density function (PDF) with mean and covariance is obtained and, thus, a future trajectory with uncertainty is formulated as a collision region represented by a confidence ellipsoid. To avoid the collision region, chance constraints are imposed to restrict the collision probability, and subsequently, a nonlinear model predictive control problem is constructed with these chance constraints. It is shown that the proposed approach is able to predict the future position of the moving obstacles effectively; and, thus, based on the environmental information of the probabilistic prediction, it is also shown that the timing of collision avoidance can be earlier than the method without prediction. The tracking error and distance to obstacles of the trajectory with prediction are smaller compared with the method without prediction. [ABSTRACT FROM AUTHOR]

The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For testing in the simple normal location problem (that is, testing for the mean of multivariate Gaussians), we overcome the difficulty as follows. In this problem there exists a natural “hardness” order between parameters as for different parameters the error-probabilities curves (when the parameter is known) are either identical, or one dominates the other. We can thus define minimax performance as the worst-case among parameters which are below some hardness level. Fortunately, there exists a universal minimax test, in the sense that it is minimax for all hardness levels simultaneously. Under this criterion we also find the optimal test for composite hypothesis testing with training data. THIS criterion extends to the wide class of local asymptotic normal models, in an asymptotic sense where the approximation of the error probabilities is additive. Since we have the asymptotically optimal tests for composite hypothesis testing with and without training data, we quantify the loss of universality and gain of training data for these models. [ABSTRACT FROM AUTHOR]

2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important nonparametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to be nearly minimax rate optimal for the class of functions with bounded variation. In this paper, we complement these worst case guarantees by investigating the adaptivity of the TVD estimator to functions which are piecewise constant on axis aligned rectangles. We rigorously show that, when the truth is piecewise constant with few pieces, the ideally tuned TVD estimator performs better than in the worst case. We also study the issue of choosing the tuning parameter. In particular, we propose a fully data driven version of the TVD estimator which enjoys similar worst case risk guarantees as the ideally tuned TVD estimator. [ABSTRACT FROM AUTHOR]

The generation process of difference beam is analyzed from the perspective of beam superposition. By analyzing the continuous linear source, a differential beam synthesis method, which can control the sidelobes level, is proposed with a simple form. The sidelobes level of the difference pattern is determined by controlling the direction of the subbeam and applying the traditional synthesis method, such as Chebyshev method and Taylor method. The proposed synthesis method is theoretical and explicit. Examples are presented for assessing the capabilities of the synthesis of difference patterns. The general distribution function is given. [ABSTRACT FROM AUTHOR]

We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class of techniques for providing straggler and fault tolerance in the area of coded computing. Our contributions are as follows: 1)We construct new codes for matrix multiplication that achieve the same fault/straggler tolerance as the previously constructed MatDot Codes and Polynomial Codes. 2)We show that the condition number of every m × m sub-matrix of an m × n, n ≥ m Chebyshev-Vandermonde matrix, evaluated on the n-point Chebyshev grid, grows as O(n2(n-m) for n > m. 3)By specializing our orthogonal polynomial based constructions to Chebyshev polynomials, and using our condition number bound for Chebyshev-Vandermonde matrices, we construct new numerically stable techniques for coded matrix multiplication. We empirically demonstrate that our constructions have significantly lower numerical errors compared to previous approaches which involve inversion of Vandermonde matrices. We generalize our constructions to explore the trade-off between computation/communication and fault-tolerance. 4)We propose a numerically stable specialization of Lagrange coded computing. Our approach involves the choice of evaluation points and a suitable decoding procedure. Our approach is demonstrated empirically to have lower numerical errors as compared to standard methods. [ABSTRACT FROM AUTHOR]

In this brief, the minimax design problem of graph filter using Chebyshev polynomial approximation (CPA) is studied. First, conventional CPA graph filter design is investigated to show that it does not provide the minimax design, so the peak error of the spectral response of the designed filter is not minimized. Then, a spectral transformation is used to convert the minimax design problem of CPA graph filter into the one of the type-I linear-phase FIR digital filter such that the Parks-McClellan method can be employed to obtain the optimal filter coefficients of minimax design. Next, using the recurrence relation of Chebyshev polynomials, an implementation structure of CPA graph filter with low computational complexity is presented. Finally, a graph signal denoising application example is illustrated to show the usefulness of the proposed CPA graph filter. [ABSTRACT FROM AUTHOR]

Zeros, x[k,N],k = 1 . . . N, of orthogonal polynomials are useful for numerical applications, e.g., Gaussian quadrature were combined with quadrature weights, w[k,N], integrals with weight function ρ(x) are performed to high precision. For broad classes of OPs, the ratios w[k,N]/ρ(x[k,N])are independent of the OPs at hand if x[k,N] lie within a smooth part of ρ(x). This universality as N → ∞ suggests that these ratios may be evaluated as x'[k,N] = d(x[k,N])/dk. This Derivative Rule Conjecture, or DRC, then gives, even for small ρ(x[K,N]) = w[k,N]/x'[k,N], and Stieltjes imaging, or inversion, with exponential convergence. Similar methods apply to the numerics of Schrödinger resolvents. The example chosen to illustrate this latter indicates that the assumption of universality, while suggesting and validating the DRC, is not necessary. [ABSTRACT FROM AUTHOR]