Approximately Bi-Similar Symbolic Model for Discretetime Interconnected Switched System

Dear Editor,This letter concerns the development of approximately bi-similar symbolic models for a discrete-time interconnected switched system(DT-ISS).The DT-ISS under consideration is formed by connecting multiple switched systems known as component switched systems(CSSs).Although the problem of constructing approximately bi-similar symbolic models for DT-ISS has been addressed in some literature,the previous works have relied on the assumption that all the subsystems of CSSs are incrementally input-state stable.

Detection of Turbulence Anomalies Using a Symbolic Classifier Algorithm in Airborne Quick Access Record(QAR)Data Analysis

As the risks associated with air turbulence are intensified by climate change and the growth of the aviation industry,it has become imperative to monitor and mitigate these threats to ensure civil aviation safety.The eddy dissipation rate(EDR)has been established as the standard metric for quantifying turbulence in civil aviation.This study aims to explore a universally applicable symbolic classification approach based on genetic programming to detect turbulence anomalies using quick access recorder(QAR)data.The detection of atmospheric turbulence is approached as an anomaly detection problem.Comparative evaluations demonstrate that this approach performs on par with direct EDR calculation methods in identifying turbulence events.Moreover,comparisons with alternative machine learning techniques indicate that the proposed technique is the optimal methodology currently available.In summary,the use of symbolic classification via genetic programming enables accurate turbulence detection from QAR data,comparable to that with established EDR approaches and surpassing that achieved with machine learning algorithms.This finding highlights the potential of integrating symbolic classifiers into turbulence monitoring systems to enhance civil aviation safety amidst rising environmental and operational hazards.

State-Based Opacity Verification of Networked Discrete Event Systems Using Labeled Petri Nets

The opaque property plays an important role in the operation of a security-critical system,implying that pre-defined secret information of the system is not able to be inferred through partially observing its behavior.This paper addresses the verification of current-state,initial-state,infinite-step,and K-step opacity of networked discrete event systems modeled by labeled Petri nets,where communication losses and delays are considered.Based on the symbolic technique for the representation of states in Petri nets,an observer and an estimator are designed for the verification of current-state and initial-state opacity,respectively.Then,we propose a structure called an I-observer that is combined with secret states to verify whether a networked discrete event system is infinite-step opaque or K-step opaque.Due to the utilization of symbolic approaches for the state-based opacity verification,the computation of the reachability graphs of labeled Petri nets is avoided,which dramatically reduces the computational overheads stemming from networked discrete event systems.

Distributional Chaos Occurring on the Set of Proper Positive Upper Banach Density Recurrent Points of One-sided Symbolic Systems

The purpose of this paper is to show that for one-sided symbolic systems,there exists an uncountable distributionally scrambled set contained in the set of proper positive upper Banach density recurrent points.

PERIODIC WINDOWS OF NONLINEAR GEAR SYSTEM BASED ON SYMBOLIC DYNAMICS

The periodic window is researched by means of the symbolic dynamics and formal language. Firstly, the proper sampling period is taken and the orbital points of periodic motion are obtained through Poincar6 mapping. Secondly, according to the method of symbolic dynamics of one-dimensional discrete mapping, the symbolic sequence describing the periodic orbit is obtained. Finally, based on the symbolic sequence, the corresponding model of minimal finite automation is constructed and the entropy is obtained by calculating the maximal eigenvalue of Stefan matrix. The results show that the orbits in periodic windows can be strictly marked by using the method of symbolic dynamics, thus a foundation for control of switching between target orbits is provided.

Finding Symbolic and All Numerical Solutions for Design Optimization Based on Monotonicity Analysis and Solving Polynomial Systems

A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equivalent to the subproblem of the design optimization is taken as the symbolic (analytical) expression of the optimum solution for the symbolic optimization, i.e. the problem with symbolic coefficients. A method based on substituting and eliminating for determining Groebner Bases is also proposed, and method for finding all numerical optimum solutions is discussed. Finally an example is given, demonstrating the strategy and efficiency of the method.

Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression

Machine learning(ML)has powerful nonlinear processing and multivariate learning capabilities,so it has been widely utilised in the fatigue field.However,most ML methods are inexplicable black-box models that are difficult to apply in engineering practice.Symbolic regression(SR)is an interpretable machine learning method for determining the optimal fitting equation for datasets.In this study,domain knowledge-guided SR was used to determine a new fatigue crack growth(FCG)rate model.Three terms of the variable subtree ofΔK,R-ratio,andΔK_(th)were obtained by analysing eight traditional semi-empirical FCG rate models.Based on the FCG rate test data from other literature,the SR model was constructed using Al-7055-T7511.It was subsequently extended to other alloys(Ti-10V-2Fe-3Al,Ti-6Al-4V,Cr-Mo-V,LC9cs,Al-6013-T651,and Al-2324-T3)using multiple linear regression.Compared with the three semi-empirical FCG rate models,the SR model yielded higher prediction accuracy.This result demonstrates the potential of domain knowledge-guided SR for building the FCG rate model.

Design of high-performance ion-doped CoP systems for hydrogen evolution:From multi-level screening calculations to experiment

Rational design of high-performance electrocatalysts for hydrogen evolution reaction(HER)is vital for future renewable energy systems.The incorporation of foreign metal ions into catalysts can be an effective approach to optimize its performance.However,there is a lack of systematic theoretical studies to reveal the quantitative relationships at the electronic level.Here,we develop a multi-level screening methodology to search for highly stable and active dopants for CoP catalysts.The density functional theory(DFT)calculations and symbolic regression(SR)were performed to investigate the relationship between the adsorption free energy(ΔG_(H^(*)))and 10 electronic parameters.The mathematic formulas derived from SR indicate that the difference of work function(ΔΦ)between doped metal and the acceptor plays the most important role in regulatingΔG_(H^(*)),followed by the d-band center(d-BC)of doped system.The descriptor of HER can be expressed asΔG_(H^(*))=1.59×√|0.188ΔΦ+d BC+0.120|1/2-0.166 with a high determination coefficient(R^(2)=0.807).Consistent with the theoretical prediction,experimental results show that the Al-CoP delivers superior electrocatalytic HER activity with a low overpotential of75 m V to drive a current density of 10 mA cm^(-2),while the overpotentials for undoped CoP,Mo-CoP,and V-CoP are 206,134,and 83 m V,respectively.The current work proves that theΔΦis the most significant regulatory parameter ofΔG_(H^(*))for ion-doped electrocatalysts.This finding can drive the discovery of high-performance ion-doped electrocatalysts,which is crucial for electrocatalytic water splitting.

Painlevé Analysis and Darboux Transformation for a Variable-Coefficient Boussinesq System in Fluid Dynamics with Symbolic Computation

The new soliton solutions for the variable-coefficient Boussinesq system, whose applications are seen influid dynamics, are studied in this paper with symbolic computation. First, the Painleve analysis is used to investigateits integrability properties. For the identified case we give, the Lax pair of the system is found, and then the Darbouxtransformation is constructed. At last, some new soliton solutions are presented via the Darboux method. Those solutionsmight be of some value in fluid dynamics.

Symbolic generation of the kinematics of multibody systems in EasyDyn: From MuPAD to Xcas/Giac

In the EasyDyn multibody open source project, computer algebra has been used from the beginning to generate the expressions of velocities and accelerations of the bodies, by symbolic differentiation of their position. Originally, the MuPAD computer algebra system had been retained because it was freely available for non commercial purposes and showed very good technical features.Unfortunately, MuPAD is nowadays only available through commercial channels and needs to be replaced to keep EasyDyn publicly available. This paper presents why Xcas/Giac is finally selected,among other long-term promising projects like Axiom, Maxima, Sage or Yacas. Among the choice criteria, the accessibility, the portability, the ease of use, the automatic export to C language, and the similarity with the -MuPAD language are all considered. The performances of the MuPAD and Xcas/Giac implementations are also compared on some examples.C 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.13013012]

A SYMBOLIC COMPUTATION METHOD TO DECIDE THE COMPLETENESS OF THE SOLUTIONS TO THE SYSTEM OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS

A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method, and it can be carried out on the computer in the Maple environment.

A robust symbol timing strategy for cellular systems

In cellular systems,establishing the initial symbol timing of potential preambles is the first step of a cell search.The envelope fluctuation of the downlink signal hinders the successful timing of conventional symbol timing methods.To solve this problem,a hybrid timing strategy is proposed with two novel detectors,namely the normalized replica-based detector and normalized differential detector.The strategy first detects all potential preambles via the normalized replica-based detector and then employs the normalized differential detector to verify the target preamble,which comes from the target cell and has the highest power.The strategy is unaffected by envelope fluctuation and has computational complexity comparable to that of conventional methods.Simu-lations and real-data tests show that the hybrid timing strategy is robust and practical for initial symbol timing.

Training-based symbol detection with temporal convolutional neural network in single-polarized optical communication system

In order to reduce the physical impairment caused by signal distortion,in this paper,we investigate symbol detection with Deep Learning(DL)methods to improve bit-error performance in the optical communication system.Many DL-based methods have been applied to such systems to improve bit-error performance.Referring to the speech-to-text method of automatic speech recognition,this paper proposes a signal-to-symbol method based on DL and designs a receiver for symbol detection on single-polarized optical communications modes.To realize this detection method,we propose a non-causal temporal convolutional network-assisted receiver to detect symbols directly from the baseband signal,which specifically integrates most modules of the receiver.Meanwhile,we adopt three training approaches for different signal-to-noise ratios.We also apply a parametric rectified linear unit to enhance the noise robustness of the proposed network.According to the simulation experiments,the biterror-rate performance of the proposed method is close to or even superior to that of the conventional receiver and better than the recurrent neural network-based receiver.

Evolution Performance of Symbolic Radial Basis Function Neural Network by Using Evolutionary Algorithms

Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.

Analysis of the Symbolic Meaning of James Joyce’s Araby

Araby is a short story by the famous Irish stream-of-consciousness writer James Joyce.Through a series of images,the novel expresses the theme of the story:the“mental paralysis”of Dubliners and the“spiritual Epiphany”of the little boy,which reflects the spiritual barren of Dubliners at that time.Through the analysis of the symbolic meaning of many images in the work,this paper reveals the social background and religious significance hidden behind the images.

The Symbolic Expression in the Material Form in Public Spaces

The article explores the topic of symbolic expression in the physical elements that form urban public spaces.It is done by giving an overview and analysing spaces that hold a widely-recognised symbolic value.The author discusses the means of encoding and perceiving meanings in the spacial composition,physical form and materials of its elements,and other aspects that influence the sensory or psychological perception of the observer.At the same time,different theoretical approaches to the perception of space are discussed,addressing not only architectural theory but also the ideas proposed in the fields of philosophy,fenomenology and cultural studies.

The Problems and Upgrade Strategies for City Symbolic Image of Yibin in Sichuan Province

The connotation of city symbolic image was redefined in this study.Based on this,the main shortages of Yibin City symbolic image were listed and analyzed with an emphasis.And then the specific strategies to improve intrinsic image and symbolic image of the city were proposed with a pertinence,so as to provide reference for establishment of Yibin City symbolic image and development of export-oriented economy.

Inverse kinematic deriving and actuator control of Delta robot using symbolic computation technology

In order to effectively derive the inverse kinematic solution of the Delta robot and realize actuator control a description of the linear graph principle for automatically generating kinematic equations in a mechanical system as well as the symbolic computation implementation of this procedure is reviewed and projected into the Delta robot. Based on the established linear graph representation the explicit symbolic expression of constraint equations and inverse kinematic solutions are obtained successfully using a symbolic computation engine Maple so that actuator control and trajectory tracking can be directly realized.Two practical motions the circular path and Adept motion are simulated for the validation of symbolic solutions respectively.Results indicate that the simulation satisfies the requirement of the quick motion within an acceptable threshold. Thus the precision of kinematic response can be confirmed and the correctness of inverse solution is verified.

Binary Program Vulnerability Mining Based on Neural Network

Software security analysts typically only have access to the executable program and cannot directly access the source code of the program.This poses significant challenges to security analysis.While it is crucial to identify vulnerabilities in such non-source code programs,there exists a limited set of generalized tools due to the low versatility of current vulnerability mining methods.However,these tools suffer from some shortcomings.In terms of targeted fuzzing,the path searching for target points is not streamlined enough,and the completely random testing leads to an excessively large search space.Additionally,when it comes to code similarity analysis,there are issues with incomplete code feature extraction,which may result in information loss.In this paper,we propose a cross-platform and cross-architecture approach to exploit vulnerabilities using neural network obfuscation techniques.By leveraging the Angr framework,a deobfuscation technique is introduced,along with the adoption of a VEX-IR-based intermediate language conversion method.This combination allows for the unified handling of binary programs across various architectures,compilers,and compilation options.Subsequently,binary programs are processed to extract multi-level spatial features using a combination of a skip-gram model with self-attention mechanism and a bidirectional Long Short-Term Memory(LSTM)network.Finally,the graph embedding network is utilized to evaluate the similarity of program functionalities.Based on these similarity scores,a target function is determined,and symbolic execution is applied to solve the target function.The solved content serves as the initial seed for targeted fuzzing.The binary program is processed by using the de-obfuscation technique and intermediate language transformation method,and then the similarity of program functions is evaluated by using a graph embedding network,and symbolic execution is performed based on these similarity scores.This approach facilitates cross-architecture analysis of executable programs without their source codes and concurrently reduces the risk of symbolic execution path explosion.

SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES

We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.