Variance Of Fluctuations Research Articles

Solar Scintillation Effect for Optical Waves Propagating Through Gamma–Gamma Coronal Turbulence Channels

Optical communication is a promising strategy for deep space exploration but it is susceptible to coronal solar wind turbulence impairments during superior solar conjunction. The variance of amplitude fluctuations caused by coronal turbulence on optical waves propagation is proposed in this paper. Both the generalized non-Kolmogorov coronal turbulence spectrum and the aperture averaging effect are taken into account. The analytic expression of the bit error rate (BER) for free-space optical (FSO) link is then derived based on Gamma–Gamma distribution model under the weak-to-moderate coronal turbulence channels. Numerical evaluations results demonstrate that coronal turbulence with small non-Kolmogorov spectral index, large outer scale, and inner scale has more potential to deduce amplitude fluctuations. With the increment of antenna radius, the amplitude fluctuations decrease obviously. In addition, the variation tendencies of these parameters can further result in small BER. Therefore, the link performance will be improved by decreasing the optical wavelength and enlarging the antenna radius. Our proposed amplitude fluctuations model with aperture averaging effect has potential application for the future deep space FSO communication.

Noise-induced limitations to the scalability of distributed integral control

We study performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of how the performance of distributed integral control is affected by measurement noise. We consider second-order consensus-like problems modeled over a toric lattice network, and study asymptotic scalings (in network size) of H2 performance metrics that quantify the variance of nodal state fluctuations. While previous studies have shown that distributed integral control fundamentally improves these performance scalings compared to distributed proportional feedback control, our results show that an explicit inclusion of measurement noise leads to the opposite conclusion. The noise’s impact on performance is shown to decrease with an increased inter-nodal alignment of the local integral states. However, even though the controller can be tuned for acceptable performance for any given network size, performance will degrade as the network grows, limiting the scalability of any such controller tuning. In particular, the requirement for inter-nodal alignment increases with network size. We show that this may in practice imply that very large and sparse networks will require any integral control to be centralized, rather than distributed. In this case, the best-achievable performance scaling, which is shown to be that of proportional feedback control, is retrieved.

How do ecological resilience metrics relate to community stability and collapse?

The concept of ecological resilience (the amount of disturbance a system can absorb before collapsing and reorganizing) holds potential for predicting community change and collapse—increasingly common issues in the Anthropocene. Yet neither the predictions nor metrics of resilience have received rigorous testing. The cross-scale resilience model, a leading operationalization of resilience, proposes resilience can be quantified by the combination of diversity and redundancy of functions performed by species operating at different scales. Here, we use 48 years of sub-continental avian community data aggregated at multiple spatial scales to calculate resilience metrics derived from the cross-scale resilience model (i.e., cross-scale diversity, cross-scale redundancy, within-scale redundancy, and number of body mass aggregations) and test core predictions inherent to community persistence and change. Specifically, we ask how cross-scale resilience metrics relate community stability and collapse. We found low mean cross-correlation between species richness and cross-scale resilience metrics. Resilience metrics constrained the magnitude of community fluctuations over time (mean species turnover), but resilience metrics but did not influence variability of community fluctuations (variance in turnover). We show shifts in resilience metrics closely predict community collapse: shifts in cross-scale redundancy preceded abrupt changes in community composition, and shifts in cross-scale diversity synchronized with abrupt changes in community composition. However, we found resilience metrics only weakly relate to maintenance of particular species assemblages over time. Our results distinguish ecological resilience from ecological stability and allied concepts such as elasticity and resistance: we show communities may fluctuate widely yet still be resilient. Our findings also differentiate the roles of functional redundancy and diversity as metrics of resilience and reemphasize the importance of considering resilience metrics from a multivariate perspective. Finally, we support the contention that ecological stability is nested within ecological resilience: stability predicts the behavior of systems within an ecological regime, and resilience predicts the maintenance of regimes and behavior of systems collapsing into alternative regimes.

Stock price fluctuation and the business cycle in the BRICS countries: A nonparametric quantiles causality approach

Using the newly developed nonparametric quantile causality method, we investigate the causal relationships in the mean and variance between stock price fluctuation and the business cycle for the BRICS countries. The empirical results reveal that the causality in the mean between stock price fluctuation and the business cycle is insignificant across all distributions, apart from Russia; however, the bidirectional causality in the variance covers virtually all quantiles, with some exceptions in the tails for all BRICS countries. Therefore, the investors and economic policy makers could consider the variance of stock price fluctuation and the business cycle and pay special attention to the tail quantiles to improve the efficiency of investment and policy.

Non-Markov character of the phase fluctuations for sound propagation over relatively small ranges in the turbulent atmosphere

The Markov approximation significantly simplifies formulations for the statistical moments of a wave propagating in a random medium. For the phase fluctuations, the Markov approximation is expected to be valid if the propagation range is much greater than the scale of largest inhomogeneities in a medium. In the atmospheric boundary layer, this scale can be several hundred meters, indicating that the Markov approximation might be inapplicable for relatively small ranges. In this paper, using geometrical acoustics, the correlation function and variance of the phase fluctuations of a plane sound wave are calculated without the Markov approximation and compared to previous results based on this approximation. The mean sound field and the spatial mutual coherence function (MCF) are also analyzed by expressing them in terms of the phase fluctuations. It is shown that for ranges smaller than the scale of largest inhomogeneities, the variance of the phase fluctuations is significantly smaller than that found with the Markov approximation. For large ranges, the relative difference between the two results tends to zero, while the absolute difference remains constant and can be much greater than unity. For the MCF, the Markov approximation is valid for both small and large ranges.

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise.

It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from the interaction of unknown molecular components with the network and from the cell's changing environment. While there are many methods to study the effect of intrinsic noise on the system dynamics, few exist to study the influence of both types of noise. Here we show how one can extend the conventional linear-noise approximation to allow for the rapid evaluation of the molecule numbers statistics of a biochemical network influenced by intrinsic noise and by slow lognormally distributed extrinsic noise. The theory is applied to simple models of gene regulatory networks and its validity confirmed by comparison with exact stochastic simulations. In particular, we consider three important biological examples. First, we investigate how extrinsic noise modifies the dependence of the variance of the molecule number fluctuations on the rate constants. Second, we show how the mutual information between input and output of a network motif is affected by extrinsic noise. And third, we study the robustness of the ubiquitously found feed-forward loop motifs when subjected to extrinsic noise.

Propagation of wind-power-induced fluctuations in power grids.

Renewable generators perturb the electric power grid with heavily non-Gaussian and time correlated fluctuations. While changes in generated power on timescales of minutes and hours are compensated by frequency control measures, we report subsecond distribution grid frequency measurements with local non-Gaussian fluctuations which depend on the magnitude of wind power generation in the grid. Motivated by such experimental findings, we simulate the subsecond grid frequency dynamics by perturbing the power grid, as modeled by a network of phase coupled nonlinear oscillators, with synthetically generated wind power feed-in time series. We derive a linear response theory and obtain analytical results for the variance of frequency increment distributions. We find that the variance of short-term fluctuations decays, for large inertia, exponentially with distance to the feed-in node, in agreement with numerical results both for a linear chain of nodes and the German transmission grid topology. In sharp contrast, the kurtosis of frequency increments is numerically found to decay only slowly, not exponentially, in both systems, indicating that the non-Gaussian shape of frequency fluctuations persists over long ranges.

Ionospheric Clutter Model for HF Sky-Wave Path Propagation with an FMCW Source

A theoretical model of the sky-wave path propagation with frequency modulated continuous wave (FMCW) source for high frequency (HF) radar is proposed in this paper. Based on the modeling of pulsed source, the expression of the received electric field with an FMCW source is derived for the reflection case from the ionospheric irregularities. Subsequently, the ionospheric reflection coefficient with different phase power spectrums for vertical and oblique backscattering propagation paths is incorporated into the ionospheric clutter model. Simulation results show that the peak power of FMCW in average is lower than that of pulsed waveform. Furthermore, different incident angles and magnetic field in mid-latitude can also influence the power density of the backscattering ionospheric clutter. Finally, the data analysis results from the high frequency surface wave radar (HFSWR) and Ionosonde collected in Yellow Sea preliminarily verify the inversion of the variance of the electron density fluctuation and the vertical drift velocity of the irregularities within ionosphere.

Spectra analysis and network coherence for weighted folded hypercube

Weighted folded hypercube is an charming variance of the famous hypercube and is superior to the weighted hypercube in many criteria. We mainly study the scaling of network coherence for the weighted folded hypercube that is controlled by a weight factor. Network coherence quantifies the steady-state variance of these fluctuations, and it can be regarded as a measure of robustness of the consensus process to the additive noise. If networks with small steady-state variance have better network coherence, it can be regarded as more robust to noise than networks with low coherence. We firstly calculate the spectra of weighted folded hypercube and obtain the leading terms of network coherence that are quantified as the sum and square sum of reciprocals of all nonzero Laplacian eigenvalues. Finally, the results show that network coherence depends on iterations and weight factor. Meanwhile, with larger order, the scatings of the first- and second-order network coherence of weighted folded hypercube decrease with the increasing of weight factor.

Small-scale resolving simulations of the turbulent mixing in confined planar jets using one-dimensional turbulence

Small-scale effects of turbulent mixing are numerically investigated by applying the map-based, stochastic, one-dimensional turbulence (ODT) model to confined planar jets. The model validation is carried out for the momentum transport by comparing ODT results to available reference data for the bulk Reynolds numbers Re=20,000 and 40,000. Various pointwise statistical quantities are computed and compared to the available reference data. We show that these quantities can be captured well, or at least to a reasonable extent, by the stand-alone model formulation and for fixed model parameters. Only the root-mean-square velocity fluctuations remain systematically underestimated in the ODT results (by an approximate factor of 1.5). Afterwards, the turbulent transport of a passive scalar is addressed for the Schmidt numbers Sc=1 and 1250. For the high Schmidt number and in contrast to the velocity fluctuations, it is shown that the scalar fluctuation variance is up to ten times larger in the ODT simulations resolving the Batchelor scale. The fluctuation variance is notably smaller for the lower Schmidt number, but exhibits better agreement with the references at a nominally higher Schmidt number. We suggest that this is due to implicit filtering in the references, which barely resolve the Kolmogorov scale. ODT turbulence spectra support this interpretation since a Batchelor-like scalar turbulence spectrum is only observed for the higher Schmidt number. With the aid of these spectra and the fluctuation statistics we conclude that implicit filtering has a similar effect as a reduction of the Schmidt number.

The problem of detrending when analysing potential indicators of disease elimination

As we strive towards the elimination of many burdensome diseases, the question of when intervention efforts may cease is increasingly important. It can be very difficult to know when prevalences are low enough that the disease will die out without further intervention, particularly for diseases that lack accurate tests. The consequences of stopping an intervention prematurely can put back elimination efforts by decades.Critical slowing down theory predicts that as a dynamical system moves through a critical transition, deviations from the steady state return increasingly slowly. We study two potential indicators of disease elimination predicted by this theory, and investigate their response using a simple stochastic model. We compare our dynamical predictions to simulations of the fluctuation variance and coefficient of variation as the system moves through the transition to elimination. These comparisons demonstrate that the primary challenge facing the analysis of early warning signs in timeseries data is that of accurately ‘detrending’ the signal, in order to preserve the statistical properties of the fluctuations. We show here that detrending using the mean of even just four realisations of the process can give a significant improvement when compared to using a moving window average.Taking this idea further, we consider a ‘metapopulation’ model of an endemic disease, in which infection spreads in various separated areas with some movement between the subpopulations. We successfully predict the behaviour of both variance and the coefficient of variation in a metapopulation by using information from the other subpopulations to detrend the system.

Deviation from the matching law reflects an optimal strategy involving learning over multiple timescales

Behavior deviating from our normative expectations often appears irrational. For example, even though behavior following the so-called matching law can maximize reward in a stationary foraging task, actual behavior commonly deviates from matching. Such behavioral deviations are interpreted as a failure of the subject; however, here we instead suggest that they reflect an adaptive strategy, suitable for uncertain, non-stationary environments. To prove it, we analyzed the behavior of primates that perform a dynamic foraging task. In such nonstationary environment, learning on both fast and slow timescales is beneficial: fast learning allows the animal to react to sudden changes, at the price of large fluctuations (variance) in the estimates of task relevant variables. Slow learning reduces the fluctuations but costs a bias that causes systematic behavioral deviations. Our behavioral analysis shows that the animals solved this bias-variance tradeoff by combining learning on both fast and slow timescales, suggesting that learning on multiple timescales can be a biologically plausible mechanism for optimizing decisions under uncertainty.

Tracking financial cycles in ten transitional economies 2005?2018 using singular spectrum analysis (SSA) techniques

Research background: Financial cycles are behind many deep financial crises and it closely connects them with the business cycles, showing long memory properties and effects. Being closely connected with the business cycles, we must first explore the true nature of the financial cycles to understand the nature of the business cycles. Financial cycles are real, they have long memory properties and long-lasting effects on the economy.
 Purpose of the article: This study investigates the use of (SSA) in tracking and monitoring financial cycles focusing on ten (10) transitional economies 2005?2018.
 Methods: Singular spectrum analysis isolate significant oscillatory patterns (cycles) on housing markets with an average 4-years length. We isolate credit cycles just for Bulgaria, implying long memory properties of the cycles since this study investigated medium term (2?5 years) oscillations.
 Findings & Value added: The results prove the importance and advantages of using (SSA) in the study of financial cycles attempting to reveal the true nature of financial cycles as the principal component behind business cycles. Financial cycles show longer oscillations in the credit and property price series, which can explain 37.7%?49.9% of the variance of the total financial cycle fluctuations. Study results are of practical importance, particularly to policy-makers and practitioners in former transitional economies being vulnerable to adverse shocks on the financial markets. The results should assist policy-makers and financial practitioners in building and maintaining a sound financial policy needed to avoid future financial ?bubbles?.

A note on Stein’s overreaction puzzle

Recently, Christoffersen et al. (Rev Financ Stud 26(8):1963–2006, 2013) argue that the overreaction puzzle of Stein (J Finance 44(4):1011–1023, 1989) can be explained by a variance-dependent pricing kernel. In this note, we challenge this view. Our theoretical results are in line with their argument that the variance under risk-neutral measure is more persistent than the variance under physical measure due to a negative variance risk premium. But our results do not support their argument that the more persistent variance is able to qualitatively explain Stein’s findings. We show theoretically that the persistence of the volatility cannot amplify the movements of long-term variance to short-term fluctuations in variance and, therefore, conclude that Stein’s overreaction puzzle is still unsolved.

Effect of imaging geometry and noise model on polarimetric contrast optimization.

We study the effect of the noise model and imaging geometry on contrast optimization with an active polarimetric imager. Considering scenes with various polarization contrast sources and fluctuation statistics of polarimetric properties, we show that to maximize the range of scene orientation angles for which contrast is sufficient, one has to take into account not only the polarization difference between the target and background but also the variance of fluctuations in the image. In particular, for scenes exhibiting depolarization contrast, the best strategy is often to set the illumination and analysis polarization states orthogonal to each other in order to reduce the variance of the image. These results are important for designing and optimizing remote sensing or robotics-oriented polarization imagers.

Primordial black holes and local non-Gaussianity in canonical inflation

Primordial black holes (PBHs) cannot be produced abundantly enough to be the dark matter in canonical single-field inflation under slow roll. This conclusion is robust to local non-Gaussian correlations between long- and short-wavelength curvature modes, which we show have no effect in slow roll on local primordial black hole abundances. For the prototypical model which evades this no go, ultra-slow roll (USR), these squeezed non-Gaussian correlations have at most an order unity effect on the variance of PBH-producing curvature fluctuations for models that would otherwise fail to form sufficient PBHs. Moreover, the transition out of USR, which is necessary for a successful model, suppresses even this small enhancement unless it causes a large increase in the inflaton kinetic energy in a fraction of an e-fold, which we call a large and fast transition. Along the way we apply the in-in formalism, the delta N formalism, and gauge transformations to compute non-Gaussianities and illuminate different aspects of the physical origin of these results. Local non-Gaussianity in the squeezed limit does not weaken the Gaussian conclusion that PBHs as dark matter in canonical single-field inflation require a complicated and fine-tuned potential shape with an epoch where slow roll is transiently violated.

Spacecraft Radio Frequency Fluctuations in the Solar Corona: A MESSENGER–HELIOS Composite Study

Abstract Fluctuations in plasma electron density may play a role in solar coronal energy transport and the dissipation of wave energy. Transcoronal spacecraft radio sounding observations reveal frequency fluctuations (FFs) that encode the electron number density disturbances, allowing an exploration of the coronal compressive wave and advected inhomogeneity models. Primary FF observations from MESSENGER 2009 and published FF residuals from HELIOS 1975–1976 superior conjunctions were combined to produce a composite view of equatorial region FF near solar minimum over solar offset range 1.4–25R ⊙. Methods to estimate the electron number density fluctuation variance from the observed FF were developed. We created a simple stacked, magnetically structured slab model that incorporated both propagating slow density waves and advected spatial density variations to explain the observed FF. Slow density waves accounted for most of the FF at low solar offset, while spatial density inhomogeneities advected at solar wind speed dominated above the sonic point at 6R ⊙. Corresponding spatial scales ranged 1–38 Mm, with scales above 10 Mm contributing most to FF variance. Magnetic structuring of the model introduced radial elongation anistropy at lower solar offsets, but geometric conditions for isotropy were achieved as the slab correlation scales increased further out in the corona. The model produced agreement with the FF observations up to 12R ⊙. FF analysis provides information on electron density fluctuations in the solar corona, and should take into account the background compressive slow waves and solar wind-related advection of quasi-static spatial density variations.

Hierarchical random additive model for wall-bounded flows at high Reynolds numbers

High Reynolds number wall-bounded flows involve dynamically important scales that cover many orders of magnitude in time and space. Fluid motions that dominate momentum transport also cover wide ranges of scales and all of these scales must be accounted for when modeling turbulence near walls. In this review, we summarize recent developments as related to the so-called hierarchical random additive process (HRAP), which models the near-wall momentum-carrying parts of turbulence by exploiting the self-similarity and the tree-like hierarchical organization of attached eddies. The HRAP model follows Townsend (1980 The Structure of Turbulent Shear Flow) and models boundary layer flows as collections of space-filling, self-similar, wall-attached eddies. However, instead of invoking specifically-shaped typical eddy, HRAP isolates the basic scaling properties of the phenomena by parameterizing contributions of near-wall eddies to generic flow quantities using random addends, a superposition of which leads to the real observable (fluid velocity, wall-shear stress, etc). This compact and relatively simple representation proves to be quite useful, leading to scaling predictions of many turbulence statistics. So far, the HRAP model has been used to provide estimates for scalings of single- and two-point velocity central moments, single- and two-point moment generating functions of velocity fluctuations, and variance of wall-shear stress fluctuations as a function of Reynolds number.

Performance Analysis of MPSK FSO Communication Based on the Balanced Detector in a Fiber-Coupling System

An average bit error ratio (ABER) performance model for multiple phase shift keying (MPSK) based on a balanced detector with a fiber is presented in the free-space link for the first time. The Johnson $S_{B} $ probability distribution function (pdf), to the best of our knowledge, is first experimentally explored, which can be used to describe the fading characteristics of an optical signal coupled into a single-mode fiber (SMF) in an atmospheric turbulence channel. Subsequently, an ABER expression is established by combining the photon characteristics of the balanced detector with the fiber. The numerical results show that the system has the most superior ABER performance when the splitting ratio is 0.5 and the quantum efficiency of the two photodetectors is equal. Moreover, the communication performances can be optimized by adjusting parameters, such as increasing the system bandwidth, selecting the appropriate modulation order, and improving the received optical power. Finally, the MPSK-signal-to-noise-ratio (SNR) model is also studied to evaluate system communication performance. Through our asymptotic analysis, if the required ABER falls below the 7% forward error correction (FEC) limit of $3.8 \times 10^{-3} $ , the SNR should maintain at least $38~dB $ or more, while the normalized fluctuation variance deteriorates to 5.2441. This paper provides a parameter reference for designing the MPSK free-space optical (FSO) communication system, especially the fiber-coupling receiver.

251 Extending directed brain connectivity beyond the mean: in-variance causality

Purpose Granger Causality (GC) approaches have recently been employed to estimate the directionality of the influence exerted by a brain region on another. Despite the fact that fluctuations in the BOLD signal at rest contain important information about the physiologic al processes that underlie neurovascular coupling, so far associations between brain signals have focused on central tendencies (i.e. mean or median) and have modeled this compounded variability as noise. A possible causative structure in the variability of brain activity remains completely unexplored. Methods and materials In this contribution, we develop a theoretical framework for simultaneous estimation of both in-mean and in-variance causality in complex networks. We validate our approach in synthetically–generated signals from complex networks of coupled nonlinear Kuramoto oscillators and employ it on fMRI Human Connectome Project (HCP) data in order to estimate of in-variance connectome of the human brain. Results Fig. 1 shows ROC curves obtained for both in-mean and in-variance causal network reconstruction in synthetic validation. Applying the framework to in vivo data, structured and distinct in-mean and in-variance causal connectomes emerge. Fig. 2 shows circular plots highlighting the top 1% connections belonging to the matrices derived from HCP data. Conclusion Our results serve as proof of principle for demonstrating the relevance of targeted experimental investigation about the origin of coupled fluctuations in variance in BOLD signals measured using fMRI.