Mathematical Model of Embodied Symbols: Cognition and Perceptual Symbol System

A mathematical model of perceptual symbol system is developed. This development requires new mathematical methods of dynamic logic (DL), which have overcome limitations of classical artificial intelligence and connectionist approaches. The paper discusses these past limitations, relates them to combinatorial complexity (exponential explosion) of algorithms in the past, and relates it further to the static nature of classical logic. DL is a process-logic;its salient property is evolution of vague representations into crisp. We first consider one aspect of PSS: situation learning from object perceptions. Next DL is related to PSS mechanisms of concepts, simulators, grounding, embodiment, productiveity, binding, recursion, and to the mechanisms relating embodied-grounded and amodal symbols. We discuss DL capability for modeling cognition on multiple levels of abstraction. PSS is extended toward interaction between cognition and language. Experimental predictions of the theory are discussed. They might influence experimental psychology and impact future theoretical developments in cognitive science, including knowledge representation, and mechanisms of interaction between perception, cognition, and language. All mathematical equations are also discussed conceptually, so mathematical understanding is not required. Experimental evidence for DL and PSS in brain imaging is discussed as well as future research directions.

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.

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.

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.

A Study on the Symbol-Based Narrative in the International Communication of Cities

Cultural symbols,a manifestation of cities’cultural resources,are not only signs that frame concepts but also forms that express meanings.Exploring the international communication of cities from the perspective of symbols,this paper analyzes in depth how cities create their cultural symbols in the dynamic process of international communication in an era of symbol-based digital media,and how they develop their narratives and explain meanings through the dissemination of symbols when telling their stories to international audiences,thus enhancing the efficiency and effectiveness of their international communication efforts.

Symbols in The Magic Barrel

The article takes the famous modern American Jewish writer Bernard Malamud’s novel The Magic Barrel as the object of study,and uses symbolism to interpret it,analyzing it one by one in terms of the magic barrel,the colors,the seasons and the windows,respectively,so as to reveal the process of getting rid of the childishness within the novel’s male protagonist,Leo Finkel,who is maturing,as well as the novel’s Jewish theme of searching for the soul of the self.

Camilla Guerrieri’s Portrait of Guidobaldo II della Rovere:Symbols of Honor and Power

The Altomani&Sons Collection owns a remarkable newly discovered portrait of Guidobaldo II della Rovere,Duke of Urbino(1514-1574),a historical military figure who was a condottiere,ruler of Urbino,Commander-in-chief of the Papal Estate,and Perfect of Rome,as well as a collector and patron of the Fine Arts.Camilla Guerrieri Nati(1628-1694),a seventeenth-century Italian painter from Fossombrone(in the province of Pesaro and Urbino),portrayed this heroic personage surrounded by emblems associated with his military courage and leadership,including his plumed burgonet helmet,metal gilded armor,a necklace with the golden fleece,and batons of secular and religious dominions.This oil painting on copper-considered a precious metal at the time-emphasizes the importance of the commission.The material and technique also reveals a unique artistic achievement in that it provides the painting with a smooth,reflective surface and vibrant coloration,symbolizing precious imagery.

Low-Complexity Joint Channel Estimation and Symbol Detection for OFDMA Systems

In this paper,we propose a joint channel estimation and symbol detection(JCESD)algorithm relying on message-passing algorithms(MPA)for orthogonal frequency division multiple access(OFDMA)systems.The channel estimation and symbol detection leverage the framework of expectation propagation(EP)and belief propagation(BP)with the aid of Gaussian approximation,respectively.Furthermore,to reduce the computation complexity involved in channel estimation,the matrix inversion is transformed into a series of diagonal matrix inversions through the Sherman-Morrison formula.Simulation experiments show that the proposed algorithm can reduce the pilot overhead by about 50%,compared with the traditional linear minimum mean square error(LMMSE)algorithm,and can approach to the bit error rate(BER)performance bound of perfectly known channel state information within 0.1 dB.

Joint Estimation of Carrier Frequency and Phase Offset Based on Pilot Symbols in Quasi-Constant Envelope OFDM Satellite Systems

Spectral efficiency and energy efficiency are two important performance indicators of satellite systems. The Quasi-Constant Envelope Orthogonal Frequency Division Multiplexing(QCE-OFDM) technique can achieve both high spectral efficiency and low peak-to-average power ratio(PAPR). Therefore, the QCE-OFDM technique is considered as a promising candidate multi-carrier technique for satellite systems. However, the Doppler effect will cause the carrier frequency offset(CFO), and the non-ideal oscillator will cause the carrier phase offset(CPO) in satellite systems. The CFO and CPO will further result in the bit-error-rate(BER) performance degradation. Hence, it is important to estimate and compensate the CFO and CPO. This paper analyzes the effects of both CFO and CPO in QCE-OFDM satellite systems. Furthermore, we propose a joint CFO and CPO estimation method based on the pilot symbols in the frequency domain. In addition, the optimal pilot symbol structure with different pilot overheads is designed according to the minimum Cramer-Rao bound(CRB) criterion. Simulation results show that the estimation accuracy of the proposed method is close to the CRB.

Independent Component Analysis Based Blind Adaptive Interference Reduction and Symbol Recovery for OFDM Systems

To overcome the inter-carrier interference （ICI） of orthogonal frequency division multiplexing （OFDM） systems subject to unknown carrier frequency offset （CFO） and multipath, this paper develops a blind adaptive interference suppression scheme based on independent component analysis （ICA）. Taking into account statistical independence of subcarriers＇ signals of OFDM, the signal recovery mechanism is investigated to achieve the goal of blind equalization. The received OFDM signals can be considered as the mixed observation signals. The effect of CFO and multipath corresponds to the mixing matrix in the problem of blind source separation （BSS） framework. In this paper, the ICA- based OFDM system model is built, and the proposed ICA-based detector is exploited to extract source signals from the observation of a received mixture based on the assumption of statistical independence between the sources. The blind separation technique can increase spectral efficiency and provide robustness performance against erroneous parameter estimation problem. Theoretical analysis and simulation results show that compared with the conventional pilot-based scheme, the improved performance of OFDM systems is obtained by the proposed ICA-based detection technique.

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.

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]

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.

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.

Application of Heuristic (1-Opt local Search) and Metaheuristic (Ant Colony Optimization) Algorithms for Symbol Detection in MIMO Systems

Heuristic and metaheuristic techniques are used for solving computationally hard optimization problems. Local search is a heuristic technique while Ant colony optimization (ACO), inspired by the ants' foraging behavior, is one of the most recent metaheuristic technique. These techniques are used for solving optimization problems. Multiple-Input Multiple-Output (MIMO) detection problem is an NP-hard combinatorial optimization problem. We present heuristic and metaheuristic approaches for symbol detection in multi-input multi-output (MIMO) system. Since symbol detection is an NP-hard problem so ACO is particularly attractive as ACO algorithms are one of the most successful strands of swarm intelligence and are suitable for applications where low complexity and fast convergence is of absolute importance. Maximum Likelihood (ML) detector gives optimal results but it uses exhaustive search technique. We show that 1-Opt and ACO based detector can give near-optimal bit error rate (BER) at much lower complexity levels. Comparison of ACO with another nature inspired technique, Particle Swarm Optimization (PSO) is also discussed. The simulation results suggest that the proposed detectors give an acceptable performance complexity trade-off in comparison with ML and VBLAST detectors.