Variance Of Fluctuations Research Articles

Characterization of noise in multistable genetic circuits reveals ways to modulate heterogeneity.

Random fluctuations in the amount of cellular components like mRNA and protein molecules are inevitable due to the stochastic and discrete nature of biochemical reactions. If large enough, this so-called “cellular noise” can lead to random transitions between the expression states of a multistable genetic circuit. That way, heterogeneity within isogenic populations is created. Our aim is to understand which dynamical features of a simple autoregulatory system determine its intrinsic noise level, and how they can be modified in order to regulate state-transitions. To that end, novel mathematical methods for the state-dependent characterization and prediction of noise in multistable systems are developed. First, we introduce the hybrid LNA, a modified version of the Linear Noise Approximation. It yields good predictions on variances of mRNA and protein fluctuations, even for reaction systems comprising low-copy-number components (e.g. mRNA) and highly nonlinear reaction rates. Furthermore, the temporal structure of fluctuations and the skewness of the protein distribution are characterized via state-dependent protein burst sizes and burst frequencies. Based on this mathematical framework, we develop graphical methods which support the intuitive design of regulatory circuits with a desired noise pattern. The methods are then used to predict how overall noise in the system can be adapted, and how state-specific noise modifications are possible that allow, e.g., the generation of unidirectional transitions. Our considerations are validated by stochastic simulations. This way, a design of genetic circuits is possible that takes population heterogeneity into account and is valuable in applications of synthetic biology and biotechnology. Moreover, natural phenomena like the bimodal development of genetic competence can be studied.

Stochastic Effects in Autoimmune Dynamics

Among various possible causes of autoimmune disease, an important role is played by infections that can result in a breakdown of immune tolerance, primarily through the mechanism of “molecular mimicry”. In this paper we propose and analyse a stochastic model of immune response to a viral infection and subsequent autoimmunity, with account for the populations of T cells with different activation thresholds, regulatory T cells, and cytokines. We show analytically and numerically how stochasticity can result in sustained oscillations around deterministically stable steady states, and we also investigate stochastic dynamics in the regime of bi-stability. These results provide a possible explanation for experimentally observed variations in the progression of autoimmune disease. Computations of the variance of stochastic fluctuations provide practically important insights into how the size of these fluctuations depends on various biological parameters, and this also gives a headway for comparison with experimental data on variation in the observed numbers of T cells and organ cells affected by infection.

A Comparison of Maps and Power Spectra Determined from South Pole Telescope and Planck Data

Abstract We study the consistency of 150 GHz data from the South Pole Telescope (SPT) and 143 GHz data from the Planck satellite over the patch of sky covered by the SPT-SZ survey. We first visually compare the maps and find that the residuals appear consistent with noise after accounting for differences in angular resolution and filtering. We then calculate (1) the cross-spectrum between two independent halves of SPT data, (2) the cross-spectrum between two independent halves of Planck data, and (3) the cross-spectrum between SPT and Planck data. We find that the three cross-spectra are well fit (PTE = 0.30) by the null hypothesis in which both experiments have measured the same sky map up to a single free calibration parameter—i.e., we find no evidence for systematic errors in either data set. As a by-product, we improve the precision of the SPT calibration by nearly an order of magnitude, from 2.6% to 0.3% in power. Finally, we compare all three cross-spectra to the full-sky Planck power spectrum and find marginal evidence for differences between the power spectra from the SPT-SZ footprint and the full sky. We model these differences as a power law in spherical harmonic multipole number. The best-fit value of this tilt is consistent among the three cross-spectra in the SPT-SZ footprint, implying that the source of this tilt is a sample variance fluctuation in the SPT-SZ region relative to the full sky. The consistency of cosmological parameters derived from these data sets is discussed in a companion paper.

What Drives Aggregate Investment?: Evidence from German Survey Data

The ifo Investment Survey asks firms in the German manufacturing sector about the importance of sales, technological factors, finance, return expectations, and macroeconomic policy for their investment activity in a given year. We show that these subjective investment determinants 1) capture economically what their labels suggest, and 2) have strong explanatory power for aggregate manufacturing investment growth fluctuations. In a second step, we use these determinants to identify aggregate demand and aggregate technology shocks and argue that the bulk of the variance of both aggregate manufacturing investment and output growth fluctuations (as much as approximately two thirds in both cases) is explained by aggregate demand shocks. Consistent with neoclassical views, however, technological factors are the most important investment determinant on average.

Adjusting Noise in the Genetic Toggle Switch through Stochastic Circuit Design

Bistable genetic circuits are important regulatory elements that can serve as biological switches. However, for a switch to function correctly, the noise inherent to the circuit needs to be taken into account, as it affects the robustness of the system. Using the example of a genetic toggle switch, we analyse the dependence of its intrinsic noise on the biochemical properties of the circuit. To that end, the circuit is described stochastically, and the variances of mRNA and protein fluctuations in each stable expression state are formulated as functions of relevant circuit parameters. This is done with the help of the linear noise approximation. As the obtained dependence is highly complex and difficult to interpret, simplified models with increasing complexity are analyzed successively. First, mRNA levels are eliminated assuming infinitely fast mRNA dynamics. Based on this model, influences of mutual inhibition dynamics and of the distribution of time-scales between the two gene expression systems are evaluated. By introducing translational bursts into the model, the interplay between mRNA and protein dynamics can be studied for quickly degrading mRNAs. Finally, special cases of the full stochastic model are discussed. Our results are verified by stochastic simulations and interpreted from a biological point of view. This enables to suggest genetic modifications for the targeted modulation of transition probabilities between distinct expression states.

The Coordinated Control of Wind-Diesel Hybrid Micro-Grid Based on Sliding Mode Method and Load Estimation

In order to reduce the frequency deviation resulting from renewable energy fluctuation and load variance, the coordination control strategy for isolated wind-diesel hybrid micro-grid is proposed by taking advantage of smart neural network observer and sliding mode method. For diesel generator system side, the sliding mode load frequency control including load variance is designed to regulate the output power. For the wind turbine generator system side, the sliding mode pitch angle control considering load variance is constructed to smooth the wind turbine generator output power fluctuation. Furthermore, the different coordinated strategies are proposed to realize the plug and play for the hybrid micro-grid, it is easy to see that the control accuracy can be improved by the designed neural network adaptive observer and considering the load variation. The effectiveness of the proposed control strategy is validated through real time digital simulator platform under different operation condition.

Effect of imperfect experimental condition on generation of Schrödinger cat state

Schrödinger cat state is an important non-classical state, and it can be used in quantum teleportation, quantum computation and quantum repeater. Schrödinger cat state is usually obtained experimentally by subtracting one photon from a squeezed-vacuum state. The fidelity between a photon-subtracted squeezed state and a cat state can be very high under suitable parameters. However, the quality of the generated state will be affected by the imperfect experimental conditions. In this paper, the effect of imperfect experimental conditions on the generation of cat state is theoretically calculated and analyzed.<br/>The input squeezed-vacuum field is represented by Weyl characteristic function, which contains the fluctuation variance of the squeezed and amplified noises. The characteristic function of generated state is obtained by using the transmission matrix of beam splitter and the measurement operator of single-photon detector. We acquire the expression of Wigner function of generated state by the Fourier transform of the Weyl characteristic function. The fidelity is calculated by using the formula <i>F</i>=1/π∫d<sup>2</sup>ζ<sup>C</sup><sub>1</sub>(ζ)<i>C</i><sub>|cat-></sub>(ζ), where <i>C</i><sub>1</sub>(ζ) and <i>C</i><sub>|cat-></sub>(ζ) represent Weyl characteristic function of the generated state and the Schrodinger cat state, respectively. The imperfection of the input squeezed state, the imperfection of the single-photon detector and the loss of the balanced homodyne detection are included in our theoretical model. We calculate the Wigner function at the phase-space origin <i>W</i>(0) and the fidelity in terms of different experimental parameters.<br/>The results show that the fidelity and negativity of <i>W</i>(0) decrease with squeezing purity decreasing. A pure squeezed-vacuum state is composed of even photon number states. In the case of impure squeezing, some odd photon number states appear in the photon number distribution. After subtracting one photon from the impure squeezing state, the generated state consists of not only odd photon number state but also even photon states, which degrades the fidelity of the generated state. The lower squeezing purity is required to meet the demand for <i>W</i>(0)<0 under the condition of higher squeezing degree. There is an optimal squeezing degree to maximize the fidelity of generated state with impure squeezing. The use of inefficient on-ff single-photon detector and the loss of the balanced homodyne detection will further reduce the fidelity of the generated state. Under the practical experimental condition:squeezing degree <i>s</i>=-3 dB, the squeezing purity <i>μ</i>=99% and the quantum efficiency of balanced homodyne detection <i>η</i>=98%, the fidelity of generated state can reach 0.88 with using a commercially available on-off single-photon detector. This work can provide theoretical guidance for generating a high-quality Schrödinger cat state.

Solar‐Driven Variation in the Atmosphere of Uranus

AbstractLong‐term measurements (1972–2015) of the reflectivity of Uranus at 472 and 551 nm display variability that is incompletely explained by seasonal effects. Spectral analysis shows that this nonseasonal variability tracks the 11 year solar cycle. Two mechanisms could cause solar modulation: (a) nucleation onto ions or electrons created by galactic cosmic rays (GCR) or (b) UV‐induced aerosol color changes. Ion‐aerosol theory is used to identify expected relationships between reflectivity fluctuations and GCR flux, tested with multiple regression and compared to the linear response predicted between reflectivity and solar UV flux. The statistics show that 24% of the variance in reflectivity fluctuations at 472 nm is explained by GCR ion‐induced nucleation, compared to 22% for a UV‐only mechanism. Similar GCR‐related variability exists in Neptune's atmosphere; hence, the effects found at Uranus provide the first example of common variability in two planetary atmospheres driven through energetic particle modulation by their host star.

Logarithmic scaling for fluctuations of a scalar concentration in wall turbulence.

Within wall turbulence, there is a sublayer where the mean velocity and the variance of velocity fluctuations vary logarithmically with the height from the wall. This logarithmic scaling is also known for the mean concentration of a passive scalar. By using heat as such a scalar in a laboratory experiment of a turbulent boundary layer, the existence of the logarithmic scaling is shown here for the variance of fluctuations of the scalar concentration. It is reproduced by a model of energy-containing eddies that are attached to the wall.

Sensitivity of the Hydrogen Epoch of Reionization Array and its build-out stages to one-point statistics from redshifted 21 cm observations

We present a baseline sensitivity analysis of the Hydrogen Epoch of Reionization Array (HERA) and its build-out stages to one-point statistics (variance, skewness, and kurtosis) of redshifted 21 cm intensity fluctuation from the Epoch of Reionization (EoR) based on realistic mock observations. By developing a full-sky 21 cm lightcone model, taking into account the proper field of view and frequency bandwidth, utilising a realistic measurement scheme, and assuming perfect foreground removal, we show that HERA will be able to recover statistics of the sky model with high sensitivity by averaging over measurements from multiple fields. All build-out stages will be able to detect variance, while skewness and kurtosis should be detectable for HERA128 and larger. We identify sample variance as the limiting constraint of the variance measurement while skewness and kurtosis measurements will be primarily limited by thermal noise. The sensitivity can be improved by performing frequency binning and windowing. In addition, we find that strong sample variance fluctuation in the kurtosis measured from an individual field of observation indicates the present of outlying cold or hot regions in the underlying fluctuations, a feature that can potentially be used as an EoR bubble indicator. This manuscript is altered from the originally published paper to reflect corrections in the erratum.

Role of Zakat as Social Finance Catalyst to Islamic Banking and Economic Growth

This paper is aimed to assess the contribution of Zakat in boosting Islamic banks’ financing and economic growth for the period 2011-2015, in 10 district/city of West Java Province, Indonesia. Through Vector Autoregressive (VAR) panel co-integration analysis, variance decompositions (VD) and impulse response functions (IRF), this study investigates Zakat, Islamic Banking, and economic growth nexus. Findings in this research highlight that Zakat has a significant impact on Islamic banking, so this institution would contribute to economic growth both in the short and the long run, with fluctuation in variance from the first year. The results lend support to the view that Zakat not only leads to social benefits but also has a positive impact on the economy through increasing Islamic banks’ financing. Therefore, this research will serve as a motivation for the industry players and regulators to continuously promote Zakat as a strategic policy. The originality of this research is to assess Zakat-led growth and finance by analyzing the impact of Zakat on the Islamic banking and regional economic outcome. Another novel aspect of this study is in the methodology as it employs VAR panel co-integration analysis, VDs and IRFs on the set of annual data.
 Keywords: Zakat, Islamic Banking Financing, Economic Growth, West Java

Categorisation of polyphonic musical signals by using modularity community detection in audio-associated visibility network

This article proposes a method to numerically characterise the homogeneity of polyphonic musical signals through community detection in audio-associated visibility networks and to detect patterns that allow the categorisation of these signals into two types of grouping based on this numerical characterization. To implement this methodology, we first calculate the variance fluctuation series in fixed-size windows of an audio stretch. Next we map this series onto a visibility graph, where the nodes are the points of the series, and the edges are defined by the visibility between each pair of points. Then, we measure the quality of the partitions of the network using the modularity and Louvain optimisation. We observed that a greater or lesser homogeneity of the magnitudes of the signal transients is related to a higher or lower modularity of the audio-associated visibility network. We also note that these differences are related to musical choices that can establish important differences between musical styles. In this article, we show that the modularity is able to give relevant information to allow the categorisation of 120 musical signs labelled in percussive and symphonic music.

Characterizing pixel and point patterns with a hyperuniformity disorder length.

We introduce the concept of a "hyperuniformity disorder length" h that controls the variance of volume fraction fluctuations for randomly placed windows of fixed size. In particular, fluctuations are determined by the average number of particles within a distance h from the boundary of the window. We first compute special expectations and bounds in d dimensions, and then illustrate the range of behavior of h versus window size L by analyzing several different types of simulated two-dimensional pixel patterns-where particle positions are stored as a binary digital image in which pixels have value zero if empty and one if they contain a particle. The first are random binomial patterns, where pixels are randomly flipped from zero to one with probability equal to area fraction. These have long-ranged density fluctuations, and simulations confirm the exact result h=L/2. Next we consider vacancy patterns, where a fraction f of particles on a lattice are randomly removed. These also display long-range density fluctuations, but with h=(L/2)(f/d) for small f, and h=L/2 for f→1. And finally, for a hyperuniform system with no long-range density fluctuations, we consider "Einstein patterns," where each particle is independently displaced from a lattice site by a Gaussian-distributed amount. For these, at large L,h approaches a constant equal to about half the root-mean-square displacement in each dimension. Then we turn to gray-scale pixel patterns that represent simulated arrangements of polydisperse particles, where the volume of a particle is encoded in the value of its central pixel. And we discuss the continuum limit of point patterns, where pixel size vanishes. In general, we thus propose to quantify particle configurations not just by the scaling of the density fluctuation spectrum but rather by the real-space spectrum of h(L) versus L. We call this approach "hyperuniformity disorder length spectroscopy".

Application of third-order correlation between intensity fluctuations to determination of scattering potential of quasi-homogeneous medium.

Within the first-order Born approximation, we introduce the third-order correlation between intensity fluctuation (CIF) of light scattered from a quasi-homogeneous (QH) medium. By utilizing the Gaussian moment theorem for describing the scattering potential statistics, analytic forms are derived for the third-order, normalized CIF and variance of intensity fluctuations (VIF) of the far-zone scattered field. It is found that the normalized CIF of the scattered field is proportional to the product of Fourier transforms of the strengths of the scattering potential, while the variance of intensity fluctuations (VIF) of the scattered field is the cube of the Fourier transform of the normalized correlation coefficient (NCC) of the scattering potential. Based on the derived formulas, we show that the correlation function of the scattering potential of the medium can be determined from the scattering equations where the third-order CIF properties of the scattered field must be known in advance.

Power Spectrum of Refractive-Index Fluctuation in Hypersonic Plasma Turbulence

Anisotropic spatial distribution data of refractive-index fluctuation in hypersonic turbulence are obtained based on the experimental images of hypersonic turbulence. Furthermore, taking re-entry turbulent plasma fluctuation into consideration, the variance of the refractive-index fluctuation in hypersonic plasma is calculated based on the Saha equation and the expression of refractive index in hypersonic plasma. On this basic, the anisotropic power-spectral model of hypersonic plasma turbulence is established by introducing the orientation factor to the modified von Karman spectrum. Finally, the mutual coherence function (MCF) and the angle-of-arrival fluctuations of electromagnetic (EM) waves propagation in hypersonic plasma turbulence are calculated. Results show that the angle-of-arrival fluctuations have obvious differences between the directions of vertical to turbulent plasma flow field and parallel to it. The various gradients of the electron density along the direction of vertical to turbulent plasma flow field are far greater than the parallel to it, which causes the horizontal scale is larger than perpendicular scale of plasma eddies. Therefore, when EM waves propagating through plasma turbulence, the refractive effect of plasma eddies show obvious anisotropy. The results of this paper can be used to analyze the EM waves propagation characteristics in hypersonic plasma turbulence.

Primordial anisotropies from cosmic strings during inflation

In this work we study the imprints of a primordial cosmic string on inflationary power spectrum. Cosmic string induces two distinct contributions on curvature perturbations power spectrum. The first type of correction respects the translation invariance while violating isotropy. This generates quadrupolar statistical anisotropy in CMB maps which is constrained by the Planck data. The second contribution breaks both homogeneity and isotropy, generating a dipolar power asymmetry in variance of temperature fluctuations with its amplitude falling on small scales. We show that the strongest constraint on the tension of string is obtained from the quadrupolar anisotropy and argue that the mass scale of underlying theory responsible for the formation of string can not be much higher than the GUT scale. The predictions of string for the diagonal and off-diagonal components of CMB angular power spectrum are presented.

Stiffening thermal membranes by cutting.

Two-dimensional crystalline membranes have recently been realized experimentally in systems such as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly affect the effective mechanical properties of properly thermalized membranes, renormalizing both bending rigidity and elastic moduli so that in particular they become stiffer to bending than their bare bending rigidity would suggest. We use molecular dynamics simulations to examine how the mechanical behavior of thermalized two-dimensional clamped ribbons (cantilevers) depends on their precise topology and geometry. We find that a simple slit smooths roughness as measured by the variance of height fluctuations. This counterintuitive effect may be due to the counterposed coupling of the lips of the slit to twist in the intact regions of the ribbon.

Relation between Vibrational Dephasing Time and Energy Gap Fluctuations.

Dephasing processes are present in basically all applications in which quantum mechanics plays a role. These applications certainly include excitation energy and charge transfer in biological systems. In a previous study, we have analyzed the vibrational dephasing time as a function of energy gap fluctuation for a large set of molecular simulations. In that investigation, individual molecular subunits were the focus of the calculations. The set of studied molecules included bacteriochlorophylls in Fenna-Matthews-Olson and light-harvesting system 2 complexes as well as bilins in PE545 aggregates. The present work extends this study to entire complexes, including the respective intermolecular couplings. Again, it can be concluded that a universal and inverse proportionality exists between dephasing time and variance of the excitonic energy gap fluctuations, whereas the respective proportionality constants can be rationalized using the energy gap autocorrelation functions. Furthermore, these findings can be extended to the gaps between higher-lying neighboring excitonic states.

Spatial synchrony and harvesting in fluctuating populations:Relaxing the small noise assumption

In spatio-temporal population dynamic models, the most important concept, in addition to mean and variance of local density fluctuations, is the spatial scale of fluctuations in density expressed by studying the spatial autocovariance function. Analytical formulas for this scale in models with local density regulation, dispersal and spatially autocorrelated noise, are rather simple when based on asymptotic theory giving linear models in the limit as the environmental variance approaches zero. The accuracy of these analytical small noise approximations has, however, not been investigated theoretically. Here, we work out improved approximations for the scale as well the spatial autocorrelation function using non-linear logistic local dynamics and going to the next order of approximation with respect to the environmental variance. Generally, it turns out that the asymptotic results are remarkably accurate under moderate fluctuations in density but may be inaccurate for very large fluctuations. For populations with small dispersal capacity, the main error comes from the fact that the logistic dynamics is non-linear, and this error is partly wiped out as dispersal increases. Proportional harvesting has a large effect on the dynamics in spatial as well as non-spatial models, increasing population fluctuations and their spatial scale. The optimal harvesting rate with respect to expected yield per time unit, however, is only to a small extent affected by the magnitude of population fluctuations unless these are very large, so that asymptotic results are applicable over a large range of population fluctuations.

A value transfer GERT network model for carbon fiber industry chain based on input–output table

This paper builds an input–output table for carbon fiber industry chain in accordance with input–output theory. In order to get a clear picture of the dynamic input–output process between a variety of sectors involved in the carbon fiber industry chain and the increment of value hereinto, a Graphical Evaluation and Review Technique (GERT) network model is constructed on the basis of value flow, and an analytical algorithm for the GERT network model is proposed to get the value transfer probability, the amount of value increment, and the fluctuation variance, from which the equivalence value transfer process and results between sectors are obtained. Finally, in the case study part, this paper finds out the value transfer relationship within the carbon fiber industry chain in Jiangsu Province, China based on the empirical data gotten from field investigations, and then some constructive policy-making and investment suggestions are put forward in view of the results and analyses.