Gamma Approximation Based Multi-Antenna Covert Communication Detection

Covert communication technology makes wireless communication more secure,but it also provides more opportunities for illegal users to transmit harmful information.In order to detect the illegal covert communication of the lawbreakers in real time for subsequent processing,this paper proposes a Gamma approximation-based detection method for multi-antenna covert communication systems.Specifically,the Gamma approximation property is used to calculate the miss detection rate and false alarm rate of the monitor firstly.Then the optimization problem to minimize the sum of the missed detection rate and the false alarm rate is proposed.The optimal detection threshold and the minimum error detection probability are solved according to the properties of the Lambert W function.Finally,simulation results are given to demonstrate the effectiveness of the proposed method.

Nonlinear Filtering With Sample-Based Approximation Under Constrained Communication:Progress, Insights and Trends

The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance.The main objective of nonlinear filtering is to infer the states of a nonlinear dynamical system of interest based on the available noisy measurements. In recent years, the advance of network communication technology has not only popularized the networked systems with apparent advantages in terms of installation,cost and maintenance, but also brought about a series of challenges to the design of nonlinear filtering algorithms, among which the communication constraint has been recognized as a dominating concern. In this context, a great number of investigations have been launched towards the networked nonlinear filtering problem with communication constraints, and many samplebased nonlinear filters have been developed to deal with the highly nonlinear and/or non-Gaussian scenarios. The aim of this paper is to provide a timely survey about the recent advances on the sample-based networked nonlinear filtering problem from the perspective of communication constraints. More specifically, we first review three important families of sample-based filtering methods known as the unscented Kalman filter, particle filter,and maximum correntropy filter. Then, the latest developments are surveyed with stress on the topics regarding incomplete/imperfect information, limited resources and cyber security.Finally, several challenges and open problems are highlighted to shed some lights on the possible trends of future research in this realm.

Determining Hubbard U of VO_(2) by the quasi-harmonic approximation

Vanadium dioxide VO_(2) is a strongly correlated material that undergoes a metal-to-insulator transition around 340 K.In order to describe the electron correlation effects in VO_(2), the DFT+U method is commonly employed in calculations.However, the choice of the Hubbard U parameter has been a subject of debate and its value has been reported over a wide range. In this paper, taking focus on the phase transition behavior of VO_(2), the Hubbard U parameter for vanadium oxide is determined by using the quasi-harmonic approximation(QHA). First-principles calculations demonstrate that the phase transition temperature can be modulated by varying the U values. The phase transition temperature can be well reproduced by the calculations using the Perdew–Burke–Ernzerhof functional combined with the U parameter of 1.5eV. Additionally,the calculated band structure, insulating or metallic properties, and phonon dispersion with this U value are in line with experimental observations. By employing the QHA to determine the Hubbard U parameter, this study provides valuable insights into the phase transition behavior of VO_(2). The findings highlight the importance of electron correlation effects in accurately describing the properties of this material. The agreement between the calculated results and experimental observations further validates the chosen U value and supports the use of the DFT+U method in studying VO_(2).

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Evolutionary Safe Padé Approximation Scheme for Dynamical Study of Nonlinear Cervical Human Papilloma Virus Infection Model

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic(CCE)model.The underlying CCE model lacks a closed-form exact solution.Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model’s necessary properties,such as positivity,boundedness,and feasibility.Therefore,the development of structure-preserving semi-analytical approaches is always necessary.This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model’s physical properties by formulating an equivalent unconstrained optimization problem.Singularity-free safe Padérational functions approximate the mathematical shape of state variables,while the model’s physical requirements are treated as problem constraints.The primary model of the governing differential equations is imposed to minimize the error between approximate solutions.An evolutionary algorithm,the Genetic Algorithm with Multi-Parent Crossover(GA-MPC),executes the optimization task.The resulting method is the Evolutionary Safe PadéApproximation(ESPA)scheme.The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations.The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padéapproximants.

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Strong Uniqueness of Best Approximations from RS-sets in Banach Spaces

The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.

Modeling of bistatic scattering from an underwater non-penetrable target using a Kirchhoff approximation method

A numerical triangulation and transformation into the time domain of a Kirchhoff approximation(KA)method is proposed for the modeling of bistatic scattering from an underwater non-penetrable target.The time domain solution in this approximation can be split up into two parts:the solution of reflected field,contributing around the specular direction,and the solution of shadow radiation,contributing around the forward direction.An average solution in the time domain satisfying the reciprocity principle is presented.The solution is expressed in terms of non-singular functions.The proposed method is validated against a normal mode method for bistatic scattering from a rigid sphere.Moreover,the reflected and shadow highlights on the surface of the sphere are shown to verify the integration surface of the reflected field and shadow radiation.It is also tested against a finite element method and an experiment involving a scaled Benchmark Target Strength Simulation Submarine model.The time-angle bistatic spectra for the model are evaluated by the direct and transformed average solutions of KA,and the former accelerates its speed of calculation.The results are good,and show that this method can be used to predict the bistatic scattered field of a non-penetrable target.

Electromagnetic scattering from two-layer rough interfaces in the Kirchhoff approximation

Electromagnetic wave scattering from multilayers consisting of two two-layer Caussian rough surfaces with lossless media is investigated in the Kirchhoff approximation （KA）, with consideration of the shadowing effects. The tapered incident wave is introduced into the classic KA, and the bistatic scattering coefficient is redetermined. The advantage of this method is that it is faster in computation than the exact numerical methods. The numerical results show that the bistatic scattering coefficient calculated in the KA is in good agreement with that obtained by using the method of moment （MOM） over a most angular range, which indicates the validity of the KA proposed in our paper. Finally, the effects of the relative permittivity, the root-mean-square （RMS） height, the correlative length, and the average height between the two interfaces on the bistatic scattering coefficient are discussed in detail.

Extended Quark Potential Model from Random Phase Approximation

The quark potential model is extended to include the sea quark excitation using the random phase approx-imation. The effective quark interaction preserves the important QCD properties - chiral symmetry and confinementsimultaneously. A primary qualitative analysis shows that the π meson as a well-known typical Goldstone boson andthe other mesons made up of valence qq quark pair such as the ρ meson can also be described in this extended quarkpotential model.

Integrating a novel irrigation approximation method with a process-based remote sensing model to estimate multi-years'winter wheat yield over the North China Plain

Accurate estimation of regional winter wheat yields is essential for understanding the food production status and ensuring national food security.However,using the existing remote sensing-based crop yield models to accurately reproduce the inter-annual and spatial variations in winter wheat yields remains challenging due to the limited ability to acquire irrigation information in water-limited regions.Thus,we proposed a new approach to approximating irrigations of winter wheat over the North China Plain(NCP),where irrigation occurs extensively during the winter wheat growing season.This approach used irrigation pattern parameters(IPPs)to define the irrigation frequency and timing.Then,they were incorporated into a newly-developed process-based and remote sensing-driven crop yield model for winter wheat(PRYM–Wheat),to improve the regional estimates of winter wheat over the NCP.The IPPs were determined using statistical yield data of reference years(2010–2015)over the NCP.Our findings showed that PRYM–Wheat with the optimal IPPs could improve the regional estimate of winter wheat yield,with an increase and decrease in the correlation coefficient(R)and root mean square error(RMSE)of 0.15(about 37%)and 0.90 t ha–1(about 41%),respectively.The data in validation years(2001–2009 and 2016–2019)were used to validate PRYM–Wheat.In addition,our findings also showed R(RMSE)of 0.80(0.62 t ha–1)on a site level,0.61(0.91 t ha–1)for Hebei Province on a county level,0.73(0.97 t ha–1)for Henan Province on a county level,and 0.55(0.75 t ha–1)for Shandong Province on a city level.Overall,PRYM–Wheat can offer a stable and robust approach to estimating regional winter wheat yield across multiple years,providing a scientific basis for ensuring regional food security.

Study of scattering from time-varying Gerstners sea surface using second-order small slope approximation

Backscattered fields from one-dimensional time-varying Gerstners sea surface are calculated utilising the secondorder small slope approximation. It is well known that spectral properties of the backscattered echoes relate to the velocity of the small elementary scatterers on sea surface profiles. Therefore, modeling Doppler spectra from the ocean requires an accurate description of the sea surface motion. The profile of nonlinear Gerstners sea surface shows verticalskewness of sea waves, it is sharper at the crest and flatter at the trough than linear waves, and its maximum slope position is closer to the crest than to the trough. Furthermore, the horizontal component of the small elementary scatterers orbit velocity on the sea surface, which yields noticeable influence on Doppler spectra, can be obtained conveniently by Gerstners sea surface model. In this study the characteristics of Doppler spectra of backscattered fields from time-varying Gerstners sea surface are investigated and the dependences of the Doppler frequency and the Doppler bandwidth on the parameters, such as the wind speed, the radar frequency, the incident angle, etc. are discussed. It is shown that the Doppler bandwidth of microwave scattered fields from Gerstners sea surface is considerably broadened. For the case of high frequency backscattered fields, the values of the higher-order spectrum peaks are larger than those obtained by linear sea surface.

Extended Quark Potential Model From Random Phase Approximation

The quark potential model is extended to include the sea quark excitation using the random phase approximation. The effective quark interaction preserves the important QCD properties — chiral symmetry and confinement simultaneously. A primary qualitative analysis shows that the π meson as a well-known typical Goldstone boson and the other mesons made up of valence quark pair such as the ρ meson can also be described in this extended quark potential model.

A Bipartition Model with Single-Scattering Approximation for the Calculations of Reflection of Energetic Ions from Surfaces

A bipartition model for ion transport in solids has been presented.Unlike the earlier bipartition model,a single-scattering approximation has been adopted and angular correlation of energy transfer has been partly taken into account.By the present bipartition model,the reflection coefficients and energy spectrum of reflected ions have been calculated.The results show that the present bipartition model gives better descriptions of reflection although it is simpler in calculation than the earlier bipartition model.

A population-level model from the microscopic dynamics in Escherichia coli chemotaxis via Langevin approximation

Recent extensive studies of Escherichia coli （E. coli） chemotaxis have achieved a deep understanding of its mi- croscopic control dynamics. As a result, various quantitatively predictive models have been developed to describe the chemotactic behavior of E. coli motion. However, a population-level partial differential equation （PDE） that rationally incorporates such microscopic dynamics is still insufficient. Apart from the traditional Keller-Segel （K-S） equation, many existing population-level models developed from the microscopic dynamics are integro-PDEs. The difficulty comes mainly from cell tumbles which yield a velocity jumping process. Here, we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision. The resulting model not only quantitatively repro- duces the results of pathway-based single-cell simulators, but also provides new inside information on the mechanism of E. coli chemotaxis. Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.

Electronic and Optical Properties of TiS2 Determined from Generalized Gradient Approximation Study

The electronic and optical properties of TiS2 are studied of density functional theory. A linearized and augmented by using an ab-initio calculation within the frame plane wave basis set with the generalized gradient approximation as proposed by Perdew et al. is used for the energy exchange-correlation determination. The results show a metallic character of TiS2, and the plots of total and partial densities of states of TiS2 show the metallic character of the bonds and a strong hybridization between the states d of Ti and p of S below the Fermi energy. The optical properties of the material such as real and imaginary parts of dielectric constant （ε（w） = ε1（w） ＋ iε2（w））, refractive index n（w）, optical reflectivity R（w）, for E / /x and E / /z are performed for the energy range of 0-.14 eV.

ON APPROXIMATION OF SMOOTH FUNCTIONS FROM NULL SPACES OF OPTIMAL LINEAR DIFFERENTIAL OPERATORS WITH CONSTANT COEFFICIENTS

For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients ak C R may be adapted to f.

Modelling of High-Frequency Roughness Scattering from Various Rough Surfaces through the Small Slope Approximation of First Order

The first-order small slope approximation is applied to model the scattering strength from a rough surface in underwater acoustics to account for seafloor for high frequencies from 10 kHz to hundreds of kilohertz. Emphasis is placed on simulating the response from two-dimensional anisotropic rough surfaces. Several rough surfaces are described based on structure functions such as the particular sandy ripples shape. The scattering strength is predicted by the small slope approximation and is first compared to a well known bistatic method, interpolating the Kirchhoff approximation and the small perturbations model, assuming that the rough interface is isotropic. Results obtained from the two different models are similar and show a higher level in the specular direction than in the other directions. For an isotropic surface, changing the propagation plane gives similar results. Then, SSA, which lets us adapt the structure function of the roughness straight away, is tested trough several anisotropic surfaces. In a longitudinal direction of ripples, the scattering strength is mostly in the specular direction, whereas in the transversal direction of ripples, the scattering strength prediction shows high values for different angular directions. Thus the scattering strength is spread in a very different way strictly related to the particular features of the ripples. Combine our results, indicates the importance of taking into account the anisotropy of a surface in a scattering prediction process, taking into account the positions of the emitter and of the receiver which are naturally significant when predicting scattering strength.

Methods of Approximation in hpk Framework for ODEs in Time Resulting from Decoupling of Space and Time in IVPs

The present study considers mathematical classification of the time differential operators and then applies methods of approximation in time such as Galerkin method (GM ), Galerkin method with weak form (GM / WF ), Petrov-Galerkin method ( PGM), weighted residual method (WRY ), and least squares method or process ( LSM or LSP ) to construct finite element approximations in time. A correspondence is established between these integral forms and the elements of the calculus of variations: 1) to determine which methods of approximation yield unconditionally stable (variationally consistent integral forms, VC ) computational processes for which types of operators and, 2) to establish which integral forms do not yield unconditionally stable computations (variationally inconsistent integral forms, VIC ). It is shown that variationally consistent time integral forms in hpk framework yield computational processes for ODEs in time that are unconditionally stable, provide a mechanism of higher order global differentiability approximations as well as higher degree local approximations in time, provide control over approximation error when used as a time marching process and can indeed yield time accurate solutions of the evolution. Numerical studies are presented using standard model problems from the literature and the results are compared with Wilson’s θ method as well as Newmark method to demonstrate highly meritorious features of the proposed methodology.