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This paper presents a new approach to speed up the operation of time delay neural networks. The entire data are collected together in a long vector and then tested as a one input pattern. The proposed fast time delay neural networks (FTDNNs) use cross correlation in the frequency domain between the tested data and the input weights of neural networks. It is proved mathematically and practically that the number of computation steps required for the presented time delay neural networks is less than that needed by conventional time delay neural networks (CTDNNs). Simulation results using MATLAB confirm the theoretical computations.

We report a room temperature 570-630 GHz frequency domain terahertz (THz) spectroscopy system developed on the basis of a broadband quasi-optical zero bias Schottky diode detector. The detector is designed to cover the frequency range of 100 GHz to nearly 900 GHz. A responsivity of 300-1000 V/W has been measured, and the noise equivalent power (NEP) is estimated to be 5-20 pW/√Hz based on the measurements of similar detectors. For a prototype demonstration, the frequency domain THz spectroscopy system was operated within the region of 570-630 GHz using a VDI (Virginia Diodes, Inc.) frequency extension module (FEM) to provide the THz radiation. Mylar thin films with different thicknesses and THz metal mesh filters have been measured using this system, demonstrating a measurement accuracy of ~2%. This system has been applied to measure biomolecules in liquid-phase, and nano-material samples in solid-phase. Initial results and discussion are presented.

This paper proposes new perspective on the nexus between transportation and urbanization in China to test the search-matching theory. We find that the linkage between transportation and urbanization has both frequency and time-varying features. We find that transportation improves urbanization in the short term, while urbanization plays the importation role in transportation during the period 1969–1996. This result obviously supports search-matching theory that in the subsample periods, the transportation infrastructure exerts positive effects on urbanization in the short term but not in the long term. In the long term, urbanization will promote the development of transportation, while short-term traffic infrastructure investment can effectively improve the transfer of population to urban regions. It would be beneficial for the government to formulate the scientific traffic planning policy and adjust the transport structure to improve urbanization.

This study analyzes the dynamic connectedness (i.e., spillovers and spillbacks) of financial stress across advanced and emerging economies. As proxy for financial stress, we reconstruct the financial stress index (FSI) for 16 advanced economies and 15 emerging economies from January 1997 to August 2020. The constructed FSIs reflect combined stress level in banking sectors, equity markets, capital markets and exchange rate markets. Using frameworks proposed by Diebold and Yilmaz (Better to give than to receive: Predictive directional measurement of volatility spillovers. International Journal of Forecasting, 28(1), 57–66) and Baruník and Křehlík (Measuring the frequency dynamics of financial connectedness and systemic risk. Journal of Financial Econometrics, 16(2), 271–296), we find that there is strong connectedness of financial stress across economies. Moreover, the connectedness of the financial stress is stronger after the global financial crisis and during the COVID-19 pandemic. Although the spillover of shocks is strongest in the short-term horizon, the spillovers in the longer-term horizons are not trivial. Our results also show that the US is the largest shock transmitter as well as one of the largest shock receivers. Our results also suggest that shocks originating in advanced economies have strong effects on other economies, but shocks originating in emerging economies also play an increasing role. Global factors such as global economic policy uncertainty and geopolitical risks influence the magnitude of the spillover of financial stress.

In outdoor scenes, haze limits the visibility of images, and degrades people’s judgement of the objects. In this paper, based on an assumption of human visual perception in frequency domain, a novel image haze removal filtering is proposed. Combining this assumption with the theory of frequency domain filtering, we first estimate the cut-off frequency to divide the frequency domain of the hazy image into three components — low-frequency domain, intermediate-frequency domain and high-frequency domain. Then, by introducing the weighting factors, the three components are recombined together. After the theoretical deduction of frequency domain, the establishment of the actual model and adjusting the cut-off frequency and weighting factors, we finally acquire a global and adaptive filtering. This filtering can restore the details and the contours of the images, which have less noise, and improve the visibility of the objects in hazy images. Moreover, our method is simple in structure and strongly applicable, and rarely affected by parameters. Our algorithm is stable and performs well in heavy fog and the scene changes.

The multiplicity problem of limit cycles arising from a weak focus is addressed. The proposed methodology is a combination of the frequency domain method to handle some degenerate Hopf bifurcations with the powerful tools of the singularity theory. The frequency domain approach uses the harmonic balance method to study the existence of periodic solutions. On the other hand, the singularity theory provides the conditions and formulas for the classification problem of the unfolding of the singularity in terms of the distinguished and auxiliary parameters. A classical example introduced by Bautin is shown in which the multiplicity of limit cycles is recovered by using this type of hybrid methodology and standard software in the continuation of periodic solutions (LOCBIF and XPPAUT). For small amplitude limit cycles, the proposed methodology gives accurate results.

The Hopf bifurcation in a calcium oscillation model is theoretically analyzed by Hopf bifurcation theory in frequency domain. Approximation expressions for frequencies and amplitudes of periodic orbits arising from Hopf bifurcation are provided by using second-order harmonic balance method. In addition, a new method is proposed to control the amplitudes of the periodic orbits. Numerical simulations show the effectiveness of the method for suppressing periodic oscillations.

We investigate the bifurcation phenomena in a Belousov–Zhabotinsky reaction model by applying Hopf bifurcation theory in frequency domain and harmonic balance method. The high accurate predictions, i.e. fourth-order harmonic balance approximation, on frequencies, amplitudes, and approximation expressions for periodic solutions emerging from Hopf bifurcation are provided. We also detect the stability and location of these periodic solutions. Numerical simulations not only confirm the theoretical analysis results but also illustrate some complex oscillations such as a cascade of period-doubling bifurcation, quasi-periodic solution, and period-doubling route to chaos. All these results improve the understanding of the dynamics of the model.

The bifurcation phenomena in a power system with three machines and four buses are investigated by applying bifurcation theory and harmonic balance method. The existence of saddle-node bifurcation and Hopf bifurcation is analyzed in time domain and in frequency domain, respectively. The approach of the fourth-order harmonic balance is then applied to derive the approximate expressions of periodic solutions bifurcated from Hopf bifurcations and predict their frequencies and amplitudes. Since the approach is valid only in some neighborhood of a bifurcation point, numerical simulations and the software Auto2007 are utilized to verify the predictions and further study bifurcations of these periodic solutions. It is shown that the power system may have various types of bifurcations, including period-doubling bifurcation, torus bifurcation, cyclic fold bifurcation, and complex dynamical behaviors, including quasi-periodic oscillations and chaotic behavior. These findings help to better understand the dynamics of the power system and may provide insight into the instability of power systems.

A mathematical model describing interactions among tumor cells, healthy host cells and immune cells is extensively investigated through bifurcation analysis with all parameters fixed except one bifurcation parameter. Transcritical bifurcation and saddle-node bifurcation are studied in the vector fields restricted to the corresponding center manifolds. Hopf bifurcation is analyzed in the frequency domain. In particular, the sixth-order harmonic balance approximations to the frequency and the amplitude of the periodic solutions, and the analytical expressions for these solutions are given. Numerical simulation study demonstrates various types of bifurcations and the complex solution behaviors, such as cyclic fold bifurcation, period-doubling bifurcation, period-doubling cascade and chaotic orbits. All these results complement previous theoretical studies on the model, and contribute to a better understanding of the qualitative dynamics of the cancer model.

This paper is concerned with a version of photoacoustic tomography, that uses line shaped detectors (instead of point-like ones) for the recording of acoustic data. The three-dimensional image reconstruction problem is reduced to a series of two-dimensional ones. First, the initial data of the two-dimensional wave equation is recovered from boundary data, and second, the classical two-dimensional Radon transform is inverted. We discuss uniqueness and stability of reconstruction, and compare frequency domain reconstruction formulas for various geometries.

An efficient and accurate numerical frequency domain formulation is proposed to investigate the 2D acoustic wave propagation within a shallow water region with a rigid bottom and a free surface. The proposed configuration combines different regions that have either a sloping or a flat rigid bottom.

The numerical approach used here is based on the method of fundamental solutions (MFS). In this model only the vertical interface between different regions is discretized, as the model incorporates Green's functions that take into account the free water surface and the presence of either a horizontal or sloping rigid bottom.

The importance of soil–structure interaction analysis has been proven by many researchers. It is obvious that soil media should be considered as an infinite domain to represent the radiation of waves into infinity. Perfectly matched discrete layer (PMDL) is one of the most promising methods to describe properly the infinite domain in soil media in frequency and time domains. In this research, a modified version of PMDLs that has a different strategy to determine their parameters is proposed. The method is named perfectly matched discrete layers with analytical wavelengths (AW-PMDLs). For verification of the proposed method, the dynamic compliances of strip foundations are analyzed and validated in the frequency domain. In the analyses, frequency-dependent system properties and hysteretic (material) damping are considered. The results show that the proposed procedure, AW-PMDL method, is effective for soil–structure interaction analysis in the frequency domain.

The torsional dynamic response of a pile embedded in transversely isotropic saturated soil is investigated while allowing for the construction of disturbance effect. The dynamic governing equations of soil are established based on Biot’s poroelastic theory. By virtue of the continuous conditions of stress and displacement of adjacent disturbance circle and the boundary conditions of pile-soil coupling system, the circumferential displacement of soil and the shear stress on pile-soil contact surface are derived. Subsequently, a closed-form solution for the torsional dynamic response of a pile is derived in the frequency domain. By using inverse Fourier transform and the convolution theorem, a quasi-analytical solution for the velocity response of the pile head subjected to a semi-sine excitation torque is derived in the time domain. The proposed analytical solution is verified by comparing with the two existing solutions available in literature. Following the present solution, a parameter study is undertaken to portray the influence on the complex impedance, twist angle and torque of pile.

Seismic action and wind excitation are the main sources of excitation to civil engineering structures. The analytical structural responses are similar for both cases, but the simplified formula in design codes on the displacement response under these excitations is quite different. This paper re-visits this difference from under stationary random excitation. The power spectrum density function of the above excitations contains several parameters which define the excitations in frequency domain. The simplified formulas of the displacement variance under different excitations are derived by adjusting these parameters. The responses from these formulas always include the resonance component of the response, whereas the presence of the background component depends on the ratio between the predominant frequency of excitation and the natural frequency of the structure. The influence of this ratio on the displacement covariance and the modal combination rules is then further discussed.

Dynamic force reconstruction theory has been developed for many years, generating numerous effective methods. However, the applications of engineering structures are relatively rare, owing to the difficult experiment, low accuracy and noise disturbance, among others. Aiming at the support platform structure commonly used in engineering, we propose the complete dynamic force reconstruction process based on the direct inversion method in frequency domain. The dynamic calibration methods of experiment and simulation are both analyzed in this case. In order to improve identification accuracy, the Tikhonov regularization is introduced. The results validate the reliability of our proposed method in real scenarios and the necessity of regularization method. Moreover, dynamic load identification method of structural variable stiffness is derived by the four-terminal parameter method. This work provides engineering application–a reference for the engineering of dynamic load identification technology.

As the supporting structure of the wind turbine, the tower is important for the safety of the wind turbine. The accurate estimation of tower response is critical for the wind turbine tower design. In the preliminary design, lots of calculations are necessary to determine design parameters. The traditional time domain calculation suffers its low efficiency and hinders the design progress. To overcome this difficulty, the frequency domain analysis should be developed, especially for the large wind turbine which may be significantly affected by the aerodynamic damping. In this study, a semi-analytical formula for the variance of the tower base bending moment is developed from the frequency domain analysis at parked condition. First, based on the quasi-steady theory and the three-component (mean, background and resonant components) method commonly used in the wind-resistant design of structure, the analytical formula of the variance for the tower base bending moment is presented considering the three components of the wind velocity. Second, the analytical formula is corrected based on the comparison with the calculation result by FAST. In the correction, the empirical aerodynamic damping is adopted. Finally, the applicability of the developed semi-analytical formula is verified by 5MW, 10MW and 15MW wind turbines.

Most of image compression methods are based on frequency domain transforms that are followed by a quantization and rounding approach to discard some coefficients. It is obvious that the quality of compressed images highly depends on the manner of discarding these coefficients. However, finding a good balance between image quality and compression ratio is an important issue in such manners. In this paper, a new lossy compression method called linear mapping image compression (LMIC) is proposed to compress images with high quality while the user-specified compression ratio is satisfied. This method is based on discrete cosine transform (DCT) and an adaptive zonal mask. The proposed method divides image to equal size blocks and the structure of zonal mask for each block is determined independently by considering its gray-level distance (GLD). The experimental results showed that the presented method had higher pick signal to noise ratio (PSNR) in comparison with some related works in a specified compression ratio. In addition, the results were comparable with JPEG2000.

The proper allocation of a therapy strategy and dosage is fundamentally associated with the quantified evaluation of gait quality. Wireless accelerometer systems for the evaluation of quantified hemiplegic gait characteristics has been successfully applied in inherently autonomous environments through the consideration of the temporal domain of the gait acceleration waveform. The frequency domain has notable potential for identifying the quantified disparity of the affected leg and unaffected leg through the application of a tandem-activated wireless accelerometer system mounted to the lateral malleolus of each lower leg through an elastic band. The quantification of disparity for hemiplegic gait via the application of wireless accelerometers was applied in an outdoor environment, while walking on a sidewalk. In addition, the wireless accelerometers were tandem activated while the subject had achieved steady-state gait status, which mitigated the need to subjectively remove starting acceleration and stopping deceleration aspects of the gait cycle. Four predominant frequencies within the 0–5 Hz bandwidth demonstrated a considerable degree of accuracy and reliability. The organization of the four predominant frequencies for both affected leg and unaffected leg were found to be disparate in a statistically significant manner, implicating a disparity of the rhythmicity respective of the affected leg in contrast to the unaffected leg in hemiplegic gait. These preliminary findings may advance gait quantification techniques, which may improve the efficacy of gait rehabilitation therapy. Enclosed are the initial test and evaluation of a tandem-activated wireless accelerometer system using the frequency domain for ascertaining a quantified disparity of hemiplegic gait.

We investigated the localization of current sources for spontaneous magnetoencephalographic (MEG) data in the frequency domain. MEGs were evaluated in three different states: (i) physiological condition; (ii) sweet taste, and (iii) salt taste. Low frequencies can be seen in the maps obtained with the sweet taste, whereas in the physiological and salt taste, the maps show higher frequencies in the majority of channels. A differentiation in the spatial distribution of the frequencies provides novel insights into the identification of taste quality with the MEG systems.