Kernel-based Joint Independence Tests for Multivariate Stationary and Non-stationary Time Series

Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the accurate statistical modelling and analysis of such systems. Here, we introduce kernel-based statistical tests of joint independence in multivariate time series by extending the $d$-variable Hilbert-Schmidt independence criterion (dHSIC) to encompass both stationary and non-stationary processes, thus allowing broader real-world applications. By leveraging resampling techniques tailored for both single- and multiple-realisation time series, we show how the method robustly uncovers significant higher-order dependencies in synthetic examples, including frequency mixing data and logic gates, as well as real-world climate and socioeconomic data. Our method adds to the mathematical toolbox for the analysis of multivariate time series and can aid in uncovering high-order interactions in data.Comment: 15 pages, 7 figure

Research on high-speed railway construction and the change of economic gravitation

The construction of high-speed railway(HSR) can not only improve the quality of transportation infrastructure in China, but also has a significant impact on regional economy. The influence of HSR construction on economic connection intensity in the context of the coordinated development of cities in Beijing-Tianjin-Hebei region is investigated. Based on the improved Gravity Model(GM), the research shows that HSR has a positive effect on the economic gravitation, while the influence of spatial distance on economic connections of cities is negative. According to empirical analysis, it represents an obvious Coreperiphery structure after HSR is opened. It also reveals that the regional economic development is unbalanced, which is caused by the poor transportation infrastructure. In addition, the paper further offers a perspective of how to promote regional economy

Gain-Assisted Giant Third-Order Nonlinearity of Epsilon-Near-Zero Multilayered Metamaterials

We investigate the third-order nonlinear optical properties of epsilon-near-zero (ENZ) Au/dye-doped fused silica multilayered metamaterials in the visible spectral range for TM incident by using nonlocal effective medium theory at different incidence angles. The nonlocal response affects the permittivity of anisotropic metamaterials when the thickness of the layer cannot be much smaller than the incident wavelength. By doping pump dye gain material within the dielectric layer to compensate for the metal loss, the imaginary part of the effective permittivity is reduced to 10−4, and the optical nonlinear refractive index and nonlinear absorption coefficient are enhanced. The real and imaginary parts of the permittivity are simultaneously minimized when the central emission wavelength of the gain material is close to the ENZ wavelength, and the nonlinear refraction coefficient reaches the order of 10−5 cm2/W, which is five orders of magnitude larger than that of the nonlinear response of the metamaterial without the gain medium. Our results demonstrate that a smaller imaginary part of the permittivity can be obtained by doping gain materials within the dielectric layer; it offers the promise of designing metamaterials with large nonlinearity at arbitrary wavelengths

The Coupled Nonlinear Schrodinger Equations Describing Power and Phase for Modeling Phase-Sensitive Parametric Amplification in Silicon Waveguides

The coupled nonlinear Schrodinger (NLS) equations describing power and phase of the optical waves are used to model phase-sensitive (PS) parametric amplification in a width-modulated silicon-on-insulator (SOI) channel waveguide. Through solving the coupled NLS equations by the split-step Fourier and Runge-Kutta integration methods, the numerical results show that the coupled NLS equations can perfectly describe and character the PS amplification process in silicon waveguides

Polarization-Independent Large Third-Order-Nonlinearity of Orthogonal Nanoantennas Coupled to an Epsilon-Near-Zero Material

The nonlinear optical response of common materials is limited by bandwidth and energy consumption, which impedes practical application in all-optical signal processing, light detection, harmonic generation, etc. Additionally, the nonlinear performance is typically sensitive to polarization. To circumvent this constraint, we propose that orthogonal nanoantennas coupled to Al-doped zinc oxide (AZO) epsilon-near-zero (ENZ) material show a broadband (~1000 nm bandwidth) large optical nonlinearity simultaneously for two orthogonal polarization states. The absolute maximum value of the nonlinear refractive index n2 is 7.65 cm2∙GW−1, which is 4 orders of magnitude larger than that of the bare AZO film and 7 orders of magnitude larger than that of silica. The coupled structure not only realizes polarization independence and strong nonlinearity, but also allows the sign of the nonlinear response to be flexibly tailored. It provides a promising platform for the realization of ultracompact, low-power, and highly nonlinear all-optical devices on the nanoscale

High-efficiency Terahertz-wave generation in silicon membrane waveguides

Terahertz (THz) wave generation via four-wave mixing (FWM) in silicon membrane waveguides is investigated with mid-infrared pump. The silicon membrane waveguides with width of 12 μm and heights varied from 14 μm to 17 μm, which can confine the THz-wave ranging from 7.5 THz to 10 THz due to the large refractive index contrast of the waveguide core and cladding, are designed to realize the collinear phase matching for THz-wave generation via FWM. Compared with the conventional parametric amplification or wavelength conversion based on FWM in silicon waveguides, which needs a pump wavelength located in the anomalous group-velocity dispersion (GVD) regime to realize broad phase matching, the pump wavelength located in the normal GVD regime is required to realize phase matching because of the large signal-pump frequency detuning. Phase matching for a tunable THz-wave ranging from 8.57 THz to 10 THz can be realized by tuning the pump wavelength from 4.2 μm to 4.4 μm in the silicon waveguide with rib height of 15 μm. Whilst, the phase matching bandwidth of THz-wave ranging from 7.7 THz to 10 THz can be achieved by tailoring the waveguide height from 14 μm to 17 μm when the pump wavelength is 4.3μm. Moreover, the conversion efficiency of the THz-wave generation is studied with different pump wavelengths and waveguide heights, the maximum conversion efficiency of 1.25 % at 9.2 THz can be obtained in a 6-mm long silicon waveguide when the pump wavelength is 4.3 μm and the waveguide height is 15 μm

Enhancement of quantum-enhanced LADAR receiver in nonideal phase-sensitive amplification

The phase-sensitive amplification (PSA) with an injected squeezed vacuum field is theoretically investigated in quantum-enhanced laser detection and ranging (LADAR) receiver. The theoretical model of the amplified process is derived to investigate the quantum fluctuations in detail. A new method of mitigating the unflat gain of nonideal PSA is proposed by adjusting the squeezed angle of the squeezed vacuum field. The simulation results indicate that signal-noise ratio (SNR) of system can be efficiently improved and close to the ideal case by this method. This research will provide an important potential in the applications of quantum-enhanced LADAR receiver

Random scattering of images and visibility enhancement via stochastic resonance

We investigate numerically the random scattering of two-dimensional (2-D) images and the visibility enhancement via stochastic resonance both in intensity and momentum spaces. The multiple scattering destroys the direct transmission of photons, but some ballistic photons carrying the image information still penetrate the scattering media. The underlying ballistic image signals exhibit an instability and are enhanced at the expense of scattering noise under self-focusing nonlinearity, which is described as a stochastic resonance. It is found that the higher ratio of ballistic signals to scattering noise triggers a stronger instability. The effect of visibility enhancement in different scattering conditions is discussed, and the 2-D quasiparticle motion model is designed to analyze the nonlinear dynamic evolution. Our results provide potential guidance for noisy image detection. (C) 2019 Society of Photo-Optical Instrumentation Engineers (SPIE)

Reconstruction of noisy images via stochastic resonance in nematic liquid crystals

Abstract We employ nematic liquid crystals as the nonlinear medium to recover noisy images via stochastic resonance, in which nonlinear coupling allows signals to grow at the expense of noise. The process is theoretically analyzed and the cross-correlation is numerically calculated. It is found that the quality of output images is affected by the input noise intensity, the applied voltage and the correlation length of noise light. Noise-hidden images can be effectively recovered by optimizing these parameters. The results suggest that nematic liquid crystals can be used for reconstruction of noisy images via stochastic resonance based on modulation instability with molecule reorientation nonlinearity