Spectral Law Research Articles

Comparative analysis of statistical methods used for detecting differential expression in label-free mass spectrometry proteomics

Label-free LC-MS/MS proteomics has proven itself to be a powerful method for evaluating protein identification and quantification from complex samples. For comparative proteomics, several methods have been used to detect the differential expression of proteins from such data. We have assessed seven methods used across the literature for detecting differential expression from spectral count quantification: Student's t-test, significance analysis of microarrays (SAM), normalised spectral abundance factor (NSAF), normalised spectral abundance factor-power law global error model (NSAF-PLGEM), spectral index (SpI), DESeq and QSpec. We used 2000 simulated datasets as well as publicly available data from a proteomic standards study to assess the ability of these methods to detect differential expression in varying effect sizes and proportions of differentially expressed proteins. At two false discovery rate (FDR) levels, we find that several of the methods detect differential expression within the data with reasonable precision, others detect differential expression at the expense of low precision, and finally, others which fail to identify any differentially expressed proteins. The inability of these seven methods to fully capture the differential landscape, even at the largest effect size, illustrates some of the limitations of the existing technologies and the statistical methodologies. SignificanceIn label-free mass spectrometry experiments, protein identification and quantification have always been important, but there is now a growing focus on comparative proteomics. Detecting differential expression in protein levels can inform on important biological mechanisms and provide direction for further study. Given the high cost and labour intensive nature of validation experiments, statistical methods are important for prioritising proteins of interest. Here, we have performed a comparative analysis to investigate the statistical methodologies for detecting differential expression and provide a reference for future experimental designs.This article is part of a Special Issue entitled: Computational Proteomics.

Anomalous spectral laws in differential models of turbulence

Differential models for hydrodynamic, passive-scalar and wave turbulence given by nonlinear first- and second-order evolution equations for the energy spectrum in the k-space were analysed. Both types of models predict formation an anomalous transient power-law spectra. The second-order models were analysed in terms of self-similar solutions of the second kind, and a phenomenological formula for the anomalous spectrum exponent was constructed using numerics for a broad range of parameters covering all known physical examples. The first-order models were examined analytically, including finding an analytical prediction for the anomalous exponent of the transient spectrum and description of formation of the Kolmogorov-type spectrum as a reflection wave from the dissipative scale back into the inertial range. The latter behaviour was linked to pre-shock/shock singularities similar to the ones arising in the Burgers equation. Existence of the transient anomalous scaling and the reflection-wave scenario are argued to be a robust feature common to the finite-capacity turbulence systems. The anomalous exponent is independent of the initial conditions but varies for for different models of the same physical system.

Estimation of the maximum credible hazard in Kuala Lumpur and Singapore due to gigantic Sumatran megathrust earthquakes: based on a comparative study on attenuation laws

This paper has classified nine attenuation laws derived for subduction interface earthquakes through a comparative study based on the peak ground accelerations (PGAs) recorded in Peninsular Malaysia and Singapore. The goal of classification was to identify the attenuation laws that were the most compatible with the region. The PGAs predicted by the relations provided by Nabilah and Balendra (Earthq Eng 16:1076–1094, 2012) and Zhao et al. (Bull Seismol Soc Am 96:898–913, 2006) were found to correlate well with the recorded PGAs. The maximum credible hazard in Kuala Lumpur and Singapore was obtained by calculating the acceleration response spectra caused by three great Sumatran megathrust earthquakes (the worst possible earthquake scenarios) using Zhao et al. spectral attenuation law. Current building code in the region requires that buildings should be capable of resisting a notional ultimate lateral design load equals to 1.5 % of the characteristic dead weight, simultaneously applied at each floor (i.e., the minimum design level of buildings equals to ~0.15 m/s2). The results show that the risk level for structures of the two cities with natural period Tn = 1–1.5 s corresponding to 10- and 15-story buildings located on hard soil sites [National Earthquake Hazards Reduction Program (NEHRP) site class C] is high as the demand spectrum due to a worst possible earthquake scenario with moment magnitude (MW) 9.5 and an epicentral distance (Repi) of 600 km from Singapore was noticeably higher than their design level. The results of the present study are applicable in seismic hazard assessment projects in Peninsular Malaysia and Singapore. The most interesting conclusion from the earthquake engineering perspective, however, is that the design spectral shapes specified in IBC 2012 and Eurocode 8 (type 2) codes may not be particularly appropriate for sites that could be affected by large-magnitude, distant earthquakes.

Power and Spectral Efficiency of Multi-Pair Massive Antenna Relaying Systems With Zero-Forcing Relay Beamforming

We consider a multi-pair multi-antenna relay system, delivering data from multi-sources to their destinations simultaneously with the help of a massive antenna relay. We analyze the spectral efficiency and power scaling laws under perfect and imperfect channel state information (CSI) for zero-forcing relay beamforming. The analysis shows that the transmit power can be scaled down by $1/M^{\alpha}$ at the users and by $1/M^{\beta}$ at the relay as the number $M$ of relay antennas increases, where $(\alpha,\beta)=(t,1)$ or $(1,t)$ for $0\leq t\leq 1$ in the case of perfect CSI and $(\alpha,\beta)=(t,1-t)$ or $(1/2,t)$ for $0\leq t\leq 1/2$ in the case of imperfect CSI.

Spectral behavior of gravel dunes

Spectral behavior of gravel dunes formed under different flow discharges is analyzed with an attempt to verify the ‘−3’ spectral law that has been confirmed extensively for sand dunes. A schematic spectrum of gravel dunes is proposed based on the spectral analysis as well as results from the literature. The results of spectral analysis show a significant deviation from the ‘−3’ spectral law for gravel dunes, and the magnitude of deviation correlates with flow discharge. Possible explanations for the deviation from the ‘−3’ spectral law, being associated with kinetic and geometrical characteristics, have been explored. To investigate the kinetic characteristics of gravel dunes, a wavelet-based method that calculates the celerity of dunes based on a pair of elevational time series is quantitatively tested. Our results suggest that (1) the kinetic explanation based on the relationship between dune celerity and dune length cannot fully explain the spectral behavior of gravel dunes; (2) the geometrical explanation based on the self-similarity hypothesis is confirmed by the relationship between dune length and dune height; and (3) the development of gravel sheets accounts for the differences in kinetic and geometrical characteristics between gravel dunes and sand dunes.

Kerov's interlacing sequences and random matrices

To a N × N real symmetric matrix Kerov assigns a piecewise linear function whose local minima are the eigenvalues of this matrix and whose local maxima are the eigenvalues of its (N − 1) × (N − 1) submatrix. We study the scaling limit of Kerov's piecewise linear functions for Wigner and Wishart matrices. For Wigner matrices the scaling limit is given by the Verhik-Kerov-Logan-Shepp curve which is known from asymptotic representation theory. For Wishart matrices the scaling limit is also explicitly found, and we explain its relation to the Marchenko-Pastur limit spectral law.

Small-scale and lateral intermittency of oceanic microstructure in the pycnocline

The intermittency correction factor μc for the Obukhov–Corrsin ‘ − 5/3’ inertial-convective subrange spectral law is estimated using conductivity (temperature) fluctuation measurements conducted within the microstructure patches of oceanic pycnocline in Monterey Bay. The value of μc was found to be in the range of 0.46–0.51, depending on the accuracy of calculation, which is applicable to stratified, low-Reynolds-number oceanic turbulence. The intermittency factor μ Mc for mesoscale (up to 1 km) lateral variations of scalar dissipation is estimated as 0.43 ± 0.02. The breakdown mechanisms of small-scale locally isotropic and mesoscale non-isotropic (lateral) turbulent temperature fluctuations in oceanic turbulence are discussed in the light of the above observations.

Inverse cascades in rotating stratified turbulence: Fast growth of large scales

We examine the inverse cascade of kinetic energy to large scales in rotating stratified turbulence as occurs in the oceans and in the atmosphere, while varying the relative frequency of gravity to inertial waves, N/f. Using direct numerical simulations with grid resolutions up to 10243 points, we find that the transfer of energy from three-dimensional to two-dimensional modes is most efficient in the range 1/2 ⩽ N/f ⩽ 2, in which resonances disappear. In this range, the cascade is faster than in the purely rotating case, and thus the interplay between rotation and stratification helps creating large-scale structures. The ensuing inverse cascade follows a −5/3 spectral law with an approximately constant flux. This inverse cascade becomes negligible when stratification is dominant.

Experimental cross-correlation nitrogen Q-branch CARS thermometry in a spark ignition engine

A purely experimental technique was employed to derive temperatures from nitrogen Q-branch Coherent Anti-Stokes Raman Scattering (CARS) spectra, obtained in a high pressure, high temperature environment (spark ignition Otto engine). This was in order to obviate any errors arising from deficiencies in the spectral scaling laws which are commonly used to represent nitrogen Q-branch CARS spectra at high pressure. The spectra obtained in the engine were compared with spectra obtained in a calibrated high pressure, high temperature cell, using direct cross-correlation in place of the minimisation of sums of squares of residuals.The technique is demonstrated through the measurement of air temperature as a function of crankshaft angle inside the cylinder of a motored single-cylinder Ricardo E6 research engine, followed by the measurement of fuel–air mixture temperatures obtained during the compression stroke in a knocking Ricardo E6 engine. A standard CARS programme (SANDIA's CARSFIT) was employed to calibrate the altered non-resonant background contribution to the CARS spectra that was caused by the alteration to the mole fraction of nitrogen in the unburned fuel–air mixture. The compression temperature profiles were extrapolated in order to predict the auto-ignition temperatures.

Far field spectrum in surface plasmon-assisted Young's double-slit interferometer

We derive an expression for the resultant spectral density (spectrum) at a point in the far zone for the surface plasmons modulated Young's double-slit interference setup. The resultant spectral interference law has the same form as the standard spectral interference law for the scalar fields. This resemblance in turn provides a means for determination of the modified spectral degree of coherence at the two slits. The mathematical results also show that in an interesting situation when the field is incident at one slit only, the interference can still be observed at the observation plane. These findings are verified theoretically using a wide-band source, i.e. a black-body, having a spectrum following Planck's radiation law.

Thermalization and free decay in surface quasigeostrophic flows

We derive statistical equilibrium solutions of the truncated inviscid surface quasigeostrophic (SQG) equations, and verify the validity of these solutions at late times in numerical simulations. The results indicate the pseudoenstrophy thermalizes while the pseudoenergy can condense at the gravest modes, in agreement with previous indications of a direct cascade of pseudoenstrophy and an inverse cascade of pseudoenergy in forced-dissipative SQG systems. At early times, the truncated inviscid SQG simulations show a behavior reminiscent of forced-dissipative SQG turbulence, and we identify spectral scaling laws for the pseudoenergy and pseudoenstrophy spectra. More importantly, a comparison between viscous and inviscid simulations allows us to identify free-decay laws for the pseudoenstrophy in SQG turbulence at very large Reynolds number.

Propagation in a Decoupled Twin-Core Waveguide: A Frequency-Domain Analysis

The behavior of two waveguides, which are decoupled at a single frequency when a broadband pulse is launched into one of them, was studied recently in the time domain. We reinvestigate it in the frequency domain. This contributes to the clarification of the scope of the validity of previous results and allows extending them to dispersive waveguides. New results include a power spectral density conservation law and a revised calculation of the pulse breakup distance.

Von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

AbstractWe argue that the hypothesis of preservation of shape of dimensionless second- and third-order correlations during decay of incompressible homogeneous magnetohydrodynamic (MHD) turbulence requires, in general, at least two independent similarity length scales. These are associated with the two Elsässer energies. The existence of similarity solutions for the decay of turbulence with varying cross-helicity implies that these length scales cannot remain in proportion, opening the possibility for a wide variety of decay behaviour, in contrast to the simpler classic hydrodynamics case. Although the evolution equations for the second-order correlations lack explicit dependence on either the mean magnetic field or the magnetic helicity, there is inherent implicit dependence on these (and other) quantities through the third-order correlations. The self-similar inertial range, a subclass of the general similarity case, inherits this complexity so that a single universal energy spectral law cannot be anticipated, even though the same pair of third-order laws holds for arbitrary cross-helicity and magnetic helicity. The straightforward notion of universality associated with Kolmogorov theory in hydrodynamics therefore requires careful generalization and reformulation in MHD.

Kinetic cascade beyond magnetohydrodynamics of solar wind turbulence in two-dimensional hybrid simulations

The nature of solar wind turbulence in the dissipation range at scales much smaller than the large magnetohydrodynamic (MHD) scales remains under debate. Here, a two-dimensional model based on the hybrid code abbreviated as A.I.K.E.F. is presented, which treats massive ions as particles obeying the kinetic Vlasov equation and massless electrons as a neutralizing fluid. Up to a certain wavenumber in the MHD regime, the numerical system is initialized by assuming a superposition of isotropic Alfvén waves with amplitudes that follow the empirically confirmed spectral law of Kolmogorov. Then, turbulence develops and energy cascades into the dispersive spectral range, where also dissipative effects occur. Under typical solar wind conditions, weak turbulence develops as a superposition of normal modes in the kinetic regime. Spectral analysis in the direction parallel to the background magnetic field reveals a cascade of left-handed Alfvén/ion-cyclotron waves up to wave vectors where their resonant absorption sets in, as well as a continuing cascade of right-handed fast-mode and whistler waves. Perpendicular to the background field, a broad turbulent spectrum is found to be built up of fluctuations having a strong compressive component. Ion-Bernstein waves seem to be possible normal modes in this propagation direction for lower driving amplitudes. Also, signatures of short-scale pressure-balanced structures (very oblique slow-mode waves) are found.

Synthetic turbulence prediction in non-Kolmogorov turbulence

We use Kinematic Simulation to assess the role of sweeping in the theory of Richardson for particle pair dispersion. We use different spectral laws to show the particular case of Kolmogorov spectrum. KS shows good consistency with Richardson's locality assumption for a large range of spectral laws (1.15 ≤ p ≤ 1.96).

Helical Turbulence Prevails over Inertial Waves in Forced Rotating Flows at High Reynolds and Low Rossby Numbers

Abstract A study of spectral laws for helical turbulence in the presence of solid body rotation up to Reynolds numbers Re ~ 1 × 105 and down to Rossby numbers Ro ~ 3 × 10−3 is presented. The forcing function is a fully helical flow that can also be viewed as mimicking the effect of atmospheric convective motions. Variants of a model developed previously by Baerenzung et al. are tested in the helical case against direct numerical simulation (DNS), using data from a run on a grid of 15363 points; its efficiency is also contrasted against a spectral large-eddy simulation (LES) by Chollet and Lesieur, as well as an underresolved DNS. The model including the contribution of helicity to the spectral eddy dissipation and eddy noise behaves best, allowing the recovery of statistical features of the flow. Even if the model is based on isotropic assumptions, the authors demonstrated in a previous study that the small scales of flows at moderate Rossby number can be considered to be isotropic in the range of parameters considered here and that therefore their model is appropriate to treat this kind of flow. An exploration of parameter space is then performed beyond what is feasible today using DNS. At a fixed Reynolds number, lowering the Rossby number leads to a regime of wave-mediated inertial helicity cascades to small scales. However, at a fixed Rossby number, increasing the Reynolds number leads the system to be dominated by turbulent energy exchanges where the role of inertial waves is to weaken the direct cascade of energy while strengthening the large scales. It is found that a useful parameter for partitioning the data is , with Urms, ν, and Ω being the rms velocity, the viscosity, and the rotation rate, respectively. The parameter that determines how much the energy cascade is direct or inverse—in which case the cascade to small scales is predominantly that of helicity—is linked to Ro.

Anomalous scaling of passive scalars in rotating flows

We present results of direct numerical simulations of passive scalar advection and diffusion in turbulent rotating flows. Scaling laws and the development of anisotropy are studied in spectral space, and in real space using an axisymmetric decomposition of velocity and passive scalar structure functions. The passive scalar is more anisotropic than the velocity field, and its power spectrum follows a spectral law consistent with ~ k[Please see text](-3/2). This scaling is explained with phenomenological arguments that consider the effect of rotation. Intermittency is characterized using scaling exponents and probability density functions of velocity and passive scalar increments. In the presence of rotation, intermittency in the velocity field decreases more noticeably than in the passive scalar. The scaling exponents show good agreement with Kraichnan's prediction for passive scalar intermittency in two dimensions, after correcting for the observed scaling of the second-order exponent.

Wave-Number Spectral Characteristics of Drift Wave Micro-Turbulence with Large-Scale Structures

Wave-number spectral characteristics of drift wave micro-turbulence with large-scale structures (LSSs) including zonal flows (ZFs) and Kelvin-Holmheltz (KH) mode are investigated based on three dimensional gyrofluid simulations in a slab geometry. The focus is on the property of the wave-number spectral scaling law of the ambient turbulence under the back reaction of the self-generated LSSs. A comparison of the spectral scaling laws between ion/electron temperature gradient (ITG/ETG) driven turbulences is presented. It is shown that the spectral scaling of the ITG turbulence with robust ZFs is fitted well by an exponential-law function 〈φ2/2〉E ∝ e−λkx in kx and a power-law one in 〈φ2/2〉P ∝ ky−β in ky. However, the ETG turbulence is characterized by a mixing Kolmogorov-like power-law and exponential-law 〈φ2/2〉E ∝ e−λkx,ykx,y−3/(1 + kx,y2)2 scaling for both kx and ky spectra due to the ZFs and KH mode dynamics, with λ and β the slope index factors. The underlying physical mechanism is understood as the spectral scattering caused by the back-reaction of the LSSs on the ambient turbulence. These findings may provide helpful guideline to diagnose the plasma fluctuations and flow structures in experiments.

THE DEPENDENCE OF SUSPENDED SAND CONCENTRATION ON THE DEGREE OF STORM DEVELOPMENT

The basic purpose of the present research is the establishment of connections between surface waves' spectral characteristics and laws of the bottom material suspension. The basic method is the laboratory experiment that allows controlling the interconnected dynamic parameters of the water environment and processes of bottom deposits transport. It is shown, that observed suspension laws physical preconditions are the nonlinear intrawave interactions and hence the redistribution of waves spectral energy in frequency area.

Optical extinction by upper tropospheric/stratospheric aerosols and clouds: GOMOS observations for the period 2002–2008

Abstract. Although the retrieval of aerosol extinction coefficients from satellite remote measurements is notoriously difficult (in comparison with gaseous species) due to the lack of typical spectral signatures, important information can be obtained. In this paper we present an overview of the current operational nighttime UV/Vis aerosol extinction profile results for the GOMOS star occultation instrument, spanning the period from August 2002 to May 2008. Some problems still remain, such as the ones associated with incomplete scintillation correction and the aerosol spectral law implementation, but good quality extinction values are obtained at a wavelength of 500 nm. Typical phenomena associated with atmospheric particulate matter in the Upper Troposphere/Lower Stratosphere (UTLS) are easily identified: Polar Stratospheric Clouds, tropical subvisual cirrus clouds, background stratospheric aerosols, and post-eruption volcanic aerosols (with their subsequent dispersion around the globe). For the first time, we show comparisons of GOMOS 500 nm particle extinction profiles with the ones of other satellite occultation instruments (SAGE II, SAGE III and POAM III), of which the good agreement lends credibility to the GOMOS data set. Yearly zonal statistics are presented for the entire period considered. Time series furthermore convincingly show an important new finding: the sensitivity of GOMOS to the sulfate input by moderate volcanic eruptions such as Manam (2005) and Soufrière Hills (2006). Finally, PSCs are well observed by GOMOS and a first qualitative analysis of the data agrees well with the theoretical PSC formation temperature. Therefore, the importance of the GOMOS aerosol/cloud extinction profile data set is clear: a long-term data record of PSCs, subvisual cirrus, and background and volcanic aerosols in the UTLS region, consisting of hundreds of thousands of altitude profiles with near-global coverage, with the potential to fill the aerosol/cloud extinction data gap left behind after the discontinuation of occultation instruments such as SAGE II, SAGE III and POAM III.