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Concept: Autocorrelation


Advances in the development of micro-electromechanical systems (MEMS) have made possible the fabrication of cheap and small dimension accelerometers and gyroscopes, which are being used in many applications where the global positioning system (GPS) and the inertial navigation system (INS) integration is carried out, i.e., identifying track defects, terrestrial and pedestrian navigation, unmanned aerial vehicles (UAVs), stabilization of many platforms, etc. Although these MEMS sensors are low-cost, they present different errors, which degrade the accuracy of the navigation systems in a short period of time. Therefore, a suitable modeling of these errors is necessary in order to minimize them and, consequently, improve the system performance. In this work, the most used techniques currently to analyze the stochastic errors that affect these sensors are shown and compared: we examine in detail the autocorrelation, the Allan variance (AV) and the power spectral density (PSD) techniques. Subsequently, an analysis and modeling of the inertial sensors, which combines autoregressive (AR) filters and wavelet de-noising, is also achieved. Since a low-cost INS (MEMS grade) presents error sources with short-term (high-frequency) and long-term (low-frequency) components, we introduce a method that compensates for these error terms by doing a complete analysis of Allan variance, wavelet de-nosing and the selection of the level of decomposition for a suitable combination between these techniques. Eventually, in order to assess the stochastic models obtained with these techniques, the Extended Kalman Filter (EKF) of a loosely-coupled GPS/INS integration strategy is augmented with different states. Results show a comparison between the proposed method and the traditional sensor error models under GPS signal blockages using real data collected in urban roadways.

Concepts: Estimation theory, Signal processing, Inertial navigation system, Accelerometer, Global Positioning System, Dead reckoning, Autocorrelation, Unmanned aerial vehicle


Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent application in electrophysiological research, including the short-time Fourier transform, continuous wavelets, band-pass filtering and multitaper-based approaches, each carries certain drawbacks related to computational efficiency and spectral leakage. This work surveys the advantages of a WFD not previously applied in electrophysiological settings.

Concepts: Psychometrics, Fourier transform, Fourier analysis, Short-time Fourier transform, Autocorrelation, Fractional Fourier transform, Chirplet transform, Window function


In this work, we study the timing instability of a scalar twin-pulse soliton molecule generated by a passively mode-locked Er-fiber laser. Subfemtosecond precision relative timing jitter characterization between the two solitons composing the molecule is enabled by the balanced optical cross-correlation (BOC) method. Jitter spectral density reveals a short-term (on the microsecond to millisecond timescale) random fluctuation of the pulse separation even in the robust stationary soliton molecules. The root-mean-square (rms) timing jitter is on the order of femtoseconds depending on the pulse separation and the mode-locking regime. The lowest rms timing jitter is 0.83 fs, which is observed in the dispersion managed mode-locking regime. Moreover, the BOC method has proved to be capable of resolving the soliton interaction dynamics in various vibrating soliton molecules.

Concepts: Scientific method, Fundamental physics concepts, Fluid dynamics, Orders of magnitude, Dispersion, Autocorrelation, Soliton


Cathodoluminescence (CL) imaging spectroscopy provides two-dimensional optical excitation images of photonic nanostructures with deep-subwavelength spatial resolution. So far, CL imaging was unable to provide a direct measurement of the excitation and emission probabilities of photonic nanostructures in a spatially resolved manner. Here, we demonstrate that by mapping the cathodoluminescence autocorrelation function g(2)together with the CL spectral distribution the excitation and emission rates can be disentangled at every excitation position. We use InGaN/GaN quantum wells in GaN nanowires with diameters in the range 200 - 500 nm as a model system to test our new g(2)mapping methodology, and find characteristic differences in excitation and emission rate both between wires and within wires. Strong differences in average CL intensity between the wires are the result of differences in the emission efficiencies. At the highest spatial resolution, intensity variations observed within wires are the result of excitation rates that vary with the nanoscale geometry of the structures. The fact that strong spatial variations observed in CL intensity are not uniquely linked to variations in emission efficiency but also to excitation efficiency has profound implications for the interpretation of CL data for nanostructured geometries in general.

Concepts: Quantum mechanics, Optics, Light, Geometry, Solar cell, Angular diameter, Autocorrelation, Nanostructure


EEG signals have weak intensity, low signal-to-noise ratio, non-stationary, non-linear, time-frequency-spatial characteristics. Therefore, it is important to extract adaptive and robust features that reflect time, frequency and spatial characteristics. This paper proposes an effective feature extraction method WDPSD (feature extraction from the Weighted Difference of Power Spectral Density in an optimal channel couple) that can reflect time, frequency and spatial characteristics for 2-class motor imagery-based BCI system. In the WDPSD method, firstly, Power Spectral Density (PSD) matrices of EEG signals are calculated in all channels, and an optimal channel couple is selected from all possible channel couples by checking non-stationary and class separability, and then a weight matrix which reflects non-stationary of PSD difference matrix in selected channel couple is calculated; finally, the robust and adaptive features are extracted from the PSD difference matrix weighted by the weight matrix. The proposed method is evaluated from EEG signals of BCI Competition IV Dataset 2a and Dataset 2b. The experimental results show a good classification accuracy in single session, session-to-session, and the different types of 2-class motor imagery for different subjects.

Concepts: Fundamental physics concepts, Signal processing, English-language films, Physical quantities, Spectrum, Extraction, Signal-to-noise ratio, Autocorrelation


Self-initiated movements are reliably preceded by a gradual buildup of neuronal activity known as the readiness potential (RP). Recent evidence suggests that the RP may reflect subthreshold stochastic fluctuations in neural activity that can be modeled as a process of accumulation to bound. One element of accumulator models that has been largely overlooked in the literature is the stochastic term, which is traditionally modeled as Gaussian white noise. While there may be practical reasons for this choice, we have long known that noise in neural systems is not white - it is long-term correlated with spectral density of the form 1/fβ(with roughly 1 < β < 3) across a broad range of spatial scales. I explored the behavior of a leaky stochastic accumulator when the noise over which it accumulates is temporally autocorrelated. I also allowed for the possibility that the RP, as measured at the scalp, might reflect the input to the accumulator (i.e., its stochastic noise component) rather than its output. These two premises led to two novel predictions that I empirically confirmed on behavioral and electroencephalography data from human subjects performing a self-initiated movement task. In addition to generating these two predictions, the model also suggested biologically plausible levels of autocorrelation, consistent with the degree of autocorrelation in our empirical data and in prior reports. These results expose new perspectives for accumulator models by suggesting that the spectral properties of the stochastic input should be allowed to vary, consistent with the nature of biological neural noise.

Concepts: Scientific method, Science, Empiricism, Empirical, White noise, Autocorrelation, Stationary process, Wiener–Khinchin theorem


The aim of this paper is to revisit the quantum spectral density (SD) of weak H-bonds treated without taking into account the relaxation mechanism, as performed using the linear response theory. Within the framework of the strong anharmonic coupling theory, and in the adiabatic approximation, we assimilated that the simplified expression of the classical SD, in absence of damping, is considered to be I_{Cl}(ω)=Re[∫₀^{∞}G_{Cl}(t)e^{-iΩt}dt] in which the classical-like autocorrelation function (ACF) is given by G_{Cl}(t)=tr{ρ(β) {μ(0)}{μ(t)}^{†}}. With this consideration, we have shown that the classical SD is equivalent to the lineshape obtained by F(ω)=ΩI_{Cl}(ω), which in turn is equivalent to the quantum SD given by I_{Qu}(ω)=Re[∫₀^{∞}G_{Qu}(t)e^{-iΩt}dt] , where G_{Qu}(t) is the corresponding quantum ACF having for expression G_{Qu}(t)=(1/β)tr{ρ∫₀^{β}{μ(0)}{μ(t+iλℏ)}^{†}dλ}. Thus, we have shown that the quantum approaches are equivalent to the more general classical one in which the starting ACF is however of quantum nature and where the SD is the Fourier transform of the ACF times the angular frequency. It is further shown that the classical approach seems then to be more simple, complete, and lead identically to the quantum result found by Maréchal and Witkowski in their pioneering work, in which they ignored the linear response theory.

Concepts: Function, Fundamental physics concepts, Nuclear magnetic resonance, Hilbert space, Fourier transform, Fourier analysis, Autocorrelation, Wiener–Khinchin theorem


Random packings built of cubes are studied numerically using a random sequential adsorption algorithm. To compare the obtained results with previous reports, three different models of cube orientation sampling were used. Also, three different cube-cube intersection algorithms were tested to find the most efficient one. The study focuses on the mean saturated packing fraction as well as kinetics of packing growth. Microstructural properties of packings were analyzed using density autocorrelation function.

Concepts: Algorithm, Variance, Volume, Programming language, Numerical analysis, Autocorrelation, Analysis of algorithms, Discrete mathematics


In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble (“bundle”) of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.

Concepts: Function, Signal processing, Stochastic process, Functional analysis, White noise, Autocorrelation, Stationary process, Autocovariance


Biological populations are strongly influenced by random variations in their environment, which are often autocorrelated in time. For disturbance specialist plant populations, the frequency and intensity of environmental stochasticity (via disturbances) can drive the qualitative nature of their population dynamics. In this article, we extended our earlier model to explore the effect of temporally autocorrelated disturbances on population persistence. In our earlier work, we only assumed disturbances were independent and identically distributed in time. We proved that the plant seed bank population converges in distribution, and we showed that the mean and variance in seed bank population size were both increasing functions of the autocorrelation coefficient for all parameter values considered, but the interplay between increasing population size and increasing variability caused interesting relationships between quasi-extinction probability and autocorrelation. For example, for populations with low seed survival, fecundity, and disturbance frequency, increasingly positive autocorrelated disturbances decreased quasi-extinction probability. Higher disturbance frequency coupled with low seed survival and fecundity caused a nonmontone relationship between autocorrelation and quasi-extinction, where increasingly positive autocorrelations eventually caused an increase in quasi-extinction probability. For higher seed survival, fecundity, and/or disturbance frequency, quasi-extinction probability was generally a monotonically increasing function of the autocorrelation coefficient.

Concepts: Variance, Monotonic function, Function, Demography, Population, Population ecology, Probability theory, Autocorrelation