Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process?

To address the issue of whether the luminance-dependent (linear) and contrast-dependent (nonlinear) processes in stereo and motion have a common computational basis, we compare both carrier-dependent and envelope-dependent performance for these two modalities by using the same stimulus and task: two-flash apparent motion/depth for a wide range of displacements. We do this for different densities, bandwidths, contrasts, spatial frequencies, and exposure durations. The results suggest that there is concordance not only between the luminance-dependent (linear) processes of motion and stereo but also between the envelope-dependent (nonlinear) processes of both modalities. Only one exception was found, but we show this to be amenable to an explanation based on a different contrast dependence for the nonlinear mechanisms of stereo and motion. This suggests that the computational basis of linear and nonlinear processes may be similar for stereopsis and motion.

The classical surrogate data tests, which are used to differentiate linear noise processes from nonlinear processes, are not suitable for nonstationary time series. In this paper, we propose a surrogate data test that can be applied on both stationary time series as well as nonstationary time series with short-term fluctuations. The method is based on the idea of constructing a network from the time series, employing a generalized symbolic dynamics method introduced in this work, and using any one of the several easily computable network parameters as discriminating statistics. The construction of the network is designed to remove the long-term trends in the data automatically. The network-based test statistics pick up only the short-term variations, unlike the discriminating statistics of the traditional methods, which are influenced by nonstationary trends in the data. The method is tested on several systems generated by linear or nonlinear processes and with deterministic or stochastic trends, and in all cases it is found to be able to differentiate between linear stochastic processes and nonlinear processes quite accurately, especially in cases where the common methods would lead to false rejections of the null hypothesis due to nonstationarity being interpreted as nonlinearity. The method is also found to be robust to the presence of experimental or dynamical noise of a moderate level in an otherwise nonlinear system.

There are many stressful environments which deteriorate the performance of speech recognition systems. Examples include aircraft cockpits, 911 emergency telephone response, high workload task stress, or emotional situations. To address this, we investigate a number of linear and nonlinear features and processing methods for stressed speech classi cation. The linear features include properties of pitch, duration, intensity, glottal source, and the vocal tract spectrum. Nonlinear processing is based on our newly proposed Teager Energy Operator (TEO) speech feature which incorporates frequency domain critical band lters and properties of the resulting TEO autocorrelation envelope. In this study, we employ a Bayesian hypothesis testing approach and a hidden Markov model (HMM) processor as classi cation methods. Evaluations focused on speech under loud, angry, and the Lombard e ect1 from the SUSAS database. Results using receiver operating characteristic (ROC) curves and EER (equal error rate) based detection show that pitch is the best of the ve linear features for stress classi cation; while the new nonlinear TEO-based feature outperforms the best linear feature by +5.2%, with a reduction in classi cation rate variability from 8.66 to 3.90.

The linear and nonlinear processes in ferromagnetic films at low temperatures $(T\ensuremath{\ll}{T}_{c})$ are studied in a microscopic theory. Both the long-range magnetic dipole-dipole and the Heisenberg exchange interactions to nearest and next-nearest neighbors are included. The results obtained for the linearized spin-wave spectrum are compared with previous macroscopic theories. For ultrathin films (or for large wave vectors) the microscopic theory provides important corrections. The nonlinear dynamics of the spin waves are studied through a finite-temperature perturbation theory based on Feynman diagrams. We obtain explicit results for the energy shift and damping (or reciprocal lifetime) of the dipole-exchange spin waves due to all possible three-magnon and four-magnon processes involving combinations of the surface and quantized bulk spin waves at low temperatures. To investigate different dipole interaction strengths (relative to the exchange) numerical results are presented using parameters for Fe, EuO, and ${\mathrm{GdCl}}_{3}.$

This paper proposes a new algorithm to estimate the minimal value of the parameter number defining the model developed in Reproducing Kernel Hilbert Space (RKHS) and describing non linear processes. The estimated value which corresponds to the model order is equal to the number of input / output measurements contained in a learning set used to develop the model. The proposed algorithm consists on characterising the nonlinear process by an mth order model, incrementing this order and computing for each value a given criterion. The seaked value is obtained when the computed criterion jumps suddenly.

Non-orthogonal multiple access (NOMA) is an inter-esting technology that enables massive connectivity as required in future 5G and 6G networks. While purely linear processing already achieves good performance in NOMA systems, in certain scenarios, non-linear processing is mandatory to ensure accept-able performance. In this paper, we propose a neural network architecture that combines the advantages of both linear and non-linear processing. Its real-time detection performance is demonstrated by a highly efficient implementation on a graphics processing unit (GPU). Using real measurements in a laboratory environment, we show the superiority of our approach over conventional methods.

In this article, we consider a state estimation problem for large‐scale nonlinear processes in the absence of first‐principles process models. By exploiting process operation data, both process modeling and state estimation design are addressed within a distributed framework. By leveraging the Koopman operator concept, a parallel subsystem modeling approach is proposed to establish interactive linear subsystem process models in higher‐dimensional subspaces, each of which correlates with the original nonlinear subspace of the corresponding process subsystem via a nonlinear mapping. The data‐driven linear subsystem models can be used to collaboratively characterize and predict the dynamical behaviors of the entire nonlinear process. Based on the established subsystem models, local state estimators that can explicitly handle process operation constraints are designed using moving horizon estimation. The local estimators are integrated via information exchange to form a distributed estimation scheme, which provides estimates of the unmeasured/unmeasurable state variables of the original nonlinear process in a linear manner. The proposed framework is applied to a chemical process and an agro‐hydrological process to illustrate its effectiveness and applicability. Good open‐loop predictability of the linear subsystem models is confirmed, and accurate estimates of the process states are obtained without requiring a first‐principles process model.

Quantum techniques are used to treat the linear and nonlinear collisional processes in a uniform weakly interacting plasma near equilibrium in the absence of external magnetic field. The nonlinear collisional process consists of coupling of two particles to two waves whereas in linear collisional case only one wave is coupled to two particles. It is found that if the plasmon mode energy is below its equilibrium level, the nonlinear collisions give rise to growth and above, it contributes to damping.

A vibronic coupling model based on time-dependent wavepacket approach is applied to simulate linear optical processes, such as one-photon absorbance and resonance Raman scattering, and nonlinear optical processes, such as two-photon absorbance and resonance hyper-Raman scattering, on a series of small molecules. Simulations employing both the long-range corrected approach in density functional theory and coupled cluster are compared and also examined based on available experimental data. Although many of the small molecules are prone to anharmonicity in their potential energy surfaces, the harmonic approach performs adequately. A detailed discussion of the non-Condon effects is illustrated by the molecules presented in this work. Linear and nonlinear Raman scattering simulations allow for the quantification of interference between the Franck-Condon and Herzberg-Teller terms for different molecules.

The point-location-scale conservation equations of hydrologic processes, when viewed at the scale of computational grid areas, become stochastic partial differential equations (PDEs). For the upscaling of the point-location-scale conservation equations to the scale of computational grid areas, a common approach is to develop the ensemble averages of these equations. Accordingly, in this study general ensemble average conservation equations for determining the probabilistic and mean behavior of nonlinear and linear hydrologic processes are developed to exact second order. From the derived equations it is seen that the evolution equation for the probabilistic behavior of a generally nonlinear hydrologic system becomes a FokkerPlanck equation (FPE). As such, the determination of the probabilistic behavior of a hydrologic system of processes reduces to the solution of a linear, deterministic PDE, the FPE, under appropriate initial and boundary conditions. The solution of the FPE yields the probability density function of the hydrologic system which can then be used to obtain the means of the state variables of the system by the expectation operation. One can also determine the mean behavior of nonlinear stochastic hydrologic processes by means of master key ensemble average conservation equations developed in this study. Upon examination of these generic deterministic equations, one may note that they are implicit integro-differential nonlinear equations in the mixed EulerianLagrangian form. Meanwhile, the master key equations which were developed also for linear hydrologic processes, are explicit, linear PDEs.

The paper is concerned with the application of multivariate regression analysis to the reduction of multivariable control problems and to the identification of linear and nonlinear time-varying processes. Reduction is performed by grouping the input and output variables of a many variable process into a small number of groups. Control is exercised in terms of a few variables, each representing such a group. Regression is further applied to the dynamic identification of reduced or unreduced linear and nonlinear multivariable processes where no a priori information of the dynamic characteristics is available. Both reduction and identification may be performed on-line. The resulting techniques are conveniently incorporated in control procedures based on dynamic programming and on predictive adaptation.

The paper deals with mathematical model of linear and nonlinear processes occurring at the propagation of femtosecond laser pulses in the vitreous of the human eye. Methods of computing modeling are applied for the nonlinear spectral equation solution describing the dynamics of a two-dimensional TE-polarized radiation in a homogeneous isotropic medium with cubic fast-response nonlinearity without the u retina when passing through the vitreous body of the eye. Dependence between the pulse duration on the retina has been revealed and the duration of the input pulse and the values of power density at which there is self-focusing have been found. It is shown that the main mechanism of radiation damage with the use of titanium-sapphire laser is photoionization. The results coincide with those obtained by the other scientists, and are usable for creation Russian laser safety standards for femtosecond laser systems.sage of slowly varying envelope approximation. Environments close to the optical media parameters of the eye were used for the simulation. The model of femtosecond radiation propagation takes into account the process dynamics for dispersion broadening of pulses in time and the occurence of the self-focusing near the

This work introduces an adaptive model predictive control (MPC) scheme for nonlinear processes. It is well-known that the conventional MPC uses linear model to represent local dynamics of a nonlinear process and resulting optimization problem is convex. However, the model mismatch between linear model and nonlinear process may significantly degrade the performance of MPC and thereby the closed-loop stability may not be guaranteed. To address this issue, the model used in MPC should be accurate enough for different operating conditions. The contribution of this paper is the development of a steady state constrained autoregressive with exogenous terms model (SSARX) that is still linear and adaptive to the variation of operating conditions. This new model then can be integrated with a linear MPC to achieve a trade-off between computational complexity and model accuracy. The proposed controller is applied in a continuous fermentation process and compared to an MPC with unconstrained ARX model (non-adaptive). The simulation shows that the MPC with ARX model leads to an offset during setpoint tracking while the MPC with SSARX model is offset free.

The various aspects of the propagation of long waves onto a shelf (i.e., reflection, transmission and propagation on the shelf) are examined experimentally and theoretically. The results are applied to tsunamis propagating onto the continental shelf. A numerical method of solving the one-dimensional Boussinesq equations for constant depth using finite element techniques is presented. The method is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth) in the direction of wave propagation. The scheme is applied to the propagation of solitary waves over a slope onto a shelf and is confirmed by experiments. A theory is developed for the generation in the laboratory of long waves of permanent form, i.e., solitary and cnoidal waves. The theory, which incorporates the nonlinear aspects of the problem, applies to wave generators which consist of a vertical plate which moves horizontally. Experiments have been conducted and the results agree well with the generation theory. In addition, these results are used to compare the shape, celerity and damping characteristics of the generated waves with the long wave theories. The solution of the linear nondispersive theory for harmonic waves of a single frequency propagating over a slope onto a shelf is extended to the case of solitary waves. Comparisons of this analysis with the nonlinear dispersive theory and experiments are presented. Comparisons of experiments with solitary and cnoidal waves with the predictions of the various theories indicate that, apart from propagation, the reflection of waves from a change in depth is a linear process except in extreme cases. However, the transmission and the propagation of both the transmitted and the reflected waves in general are nonlinear processes. Exceptions are waves with heights which are very small compared to the depth. For these waves, the entire process of propagation onto a shelf in the vicinity of the shelf is linear . Tsunamis propagating from the deep ocean onto the continental shelf probably fall in this class.

EEG correlates of two main effects of long-term hyperventilation (cyclic breathing similar to rebirthing), namely, psychotic manifestations and sensations in internal organs, are considered. Standard EEGs of 44 subjects were recorded and subsequently treated by multiparametric methods. It was shown that, in the case of psychotic phenomena (hallucinations, visual and auditory images, different scenes, virtual travels, out-of-body experiences, etc.), the changes in the spatial organization of bioelectric potentials as compared with the baseline have different patterns than in the case of sensations in internal organs. The changes are observed in the frontal regions of the cortex: a decrease in spatial synchronization (linear processes) during an increase in spatial disarray (nonlinear processes) of bioelectric potentials and the intensifying of high-frequency β activity. If sensations in internal organs appear, a decrease in the above parameters was observed in the right hemisphere and in posterior cortical areas. The data are discussed from the viewpoint of qualitative specificity of changes in functional states during an altered state of consciousness with manifestations of different psychovisceral phenomena.