Effect of nonlinear interactions on p-mode frequencies and line widths

One goal of personal genomics is to use information about genomic variation to predict who is at risk for various common diseases. Technological advances in genotyping have spawned several personal genetic testing services that market genotyping services directly to the consumer. An important goal of consumer genetic testing is to provide health information along with the genotyping results. This has the potential to integrate detailed personal genetic and genomic information into healthcare decision making. Despite the potential importance of these advances, there are some important limitations. One concern is that much of the literature that is used to formulate personal genetics reports is based on genetic association studies that consider each genetic variant independently of the others. It is our working hypothesis that the true value of personal genomics will only be realized when the complexity of the genotype-to-phenotype mapping relationship is embraced, rather than ignored. We focus here on complexity in genetic architecture due to epistasis or nonlinear gene-gene interaction. We have previously developed a multifactor dimensionality reduction (MDR) algorithm and software package for detecting nonlinear interactions in genetic association studies. In most prior MDR analyses, the permutation testing strategy used to assess statistical significance was unable to differentiate MDR models that captured only interaction effects from those that also detected independent main effects. Statistical interpretation of MDR models required post-hoc analysis using entropy-based measures of interaction information. We introduce here a novel permutation test that allows the effects of nonlinear interactions between multiple genetic variants to be specifically tested in a manner that is not confounded by linear additive effects. We show using simulated nonlinear interactions that the power using the explicit test of epistasis is no different than a standard permutation test. We also show that the test has the appropriate size or type I error rate of approximately 0.05. We then apply MDR with the new explicit test of epistasis to a large genetic study of bladder cancer and show that a previously reported nonlinear interaction between is indeed significant, even after considering the strong additive effect of smoking in the model. Finally, we evaluated the power of the explicit test of epistasis to detect the nonlinear interaction between two XPD gene polymorphisms by simulating data from the MDR model of bladder cancer susceptibility. The results of this study provide for the first time a simple method for explicitly testing epistasis or gene-gene interaction effects in genetic association studies. Although we demonstrated the method with MDR, an important advantage is that it can be combined with any modeling approach. The explicit test of epistasis brings us a step closer to the type of routine gene-gene interaction analysis that is needed if we are to enable personal genomics.

In this paper the nonlinear pulsed acoustic pressure fields from the focused square and rectangular apertures are considered. Experimental results in water of the 4D nonlinear sound field radiated from a 2.8 MHz focused (focal distance F = 80 mm) transducer of a square (20 x 20 mm) and rectangular (10 x 25 mm) geometry for various excitation levels (producing the average pressure P0 at the source equal to 0.045, 0.225 and 0.45 MPa) are presented. The measurement results are compared with the numerical calculations obtained for the same boundary conditions. The novel, developed by the second author, numerical algorithm was used to simulate the 4D nonlinear pressure field propagation from nonaxisymmetric focused acoustic sources radiating pulsed waves in the attenuating media. Our theoretical model is based on the Time-Averaged Pressure Envelope (TAPE) method, recently developed in our lab. This method employs the representation of the propagated pulsed pressure waveform as a quasi-Fourier series, i.e. as a superposition of sinusoidal wavelet- like packets with carrier frequencies equal to harmonics of the initial tone burst, and with envelopes (being functions of space coordinates and time) determined by the TAPE method. The spectrum of the propagating pressure waveform is considered to be a sum of contributions of each wavelet spectrum. Our model uses the second-order operator splitting approach with an incremental propagation scheme whereby the effects of combined diffraction and absorption are computed separately from the effects of nonlinear harmonic interactions over incremental steps. The proposed model is free from paraxial approximation, is computationally efficient and capable of predicting the 4D ultrasound field in nonlinear and attenuating media with the arbitrary absorption from pulsed, arbitrary shaped, plane and focused sources (including phased arrays with an angular beam deflection). Using a computational power of a standard PC a computation time required for the full 4D nonlinear field simulation depends on the source dimensions, radiated frequency and excitation level as well as on the medium absorption and nonlinearity strength and can vary from few minutes to few hours. Comparison between experimental and simulation results clearly show that our numerical model predicts well the structure of the nonlinear ultrasound field for all boundary conditions considered. I. INTRODUCTION The theoretical and experimental studies of the finite amplitude acoustic waves propagation in attenuating media from nonaxisymmetric sources rather rarely can be found in literature in spite of the fact that probes of the rectangular geometry (such as linear phased arrays) are commonly used in clinical practice for medical ultrasonic imaging purposes. The main reason of such situation is a lack in simpler theoretical models and in computationally efficient numerical algorithms that are able to predict accurately the nonlinear effects in 4D ultrasound fields from pulsed, arbitrarily shaped sources (plane and focused) in biological media with arbitrary frequency- dependent absorption. In recent years the only study describing the computationally efficient numerical model that is able to simulate accurately the 4D nonlinear ultrasound field in water and in biological tissues from pulsed nonaxisymmetric sources was developed by Zemp et al. (1). Their model is based on the second order operator-splitting method, proposed by Tavakkoli et al., with the modified fractional step scheme whereby the combined effects of diffraction and absorption are accounted for over half-steps and the effects of nonlinear harmonic interactions over full incremental steps. The computation of diffraction and absorption sub-steps was based on the angular spectrum technique with modified sampling method (to obtain computational savings due to larger axial propagation steps) while the computation of nonlinear steps was based on the time-domain solution to Burgers' equation. There are not reports yet describing an experimental confirmation of an agreement between the simulated nonlinear acoustic pulsed fields in water or in soft tissues from nonaxisymmetric focused sources (obtained by using the numerical model proposed) and nonlinear field from realistic probes. In this work the experimental measurement results of the 4D nonlinear field from the both square and rectangular ultrasonic focused transducer radiating the pulsed pressure wave in water are presented. The realistic beam patterns are compared with the simulation results obtained by using our novel numerical algorithm.

Computational model of an inclined aerial ropeway and numerical method for analyzing nonlinear cable-car interaction

Nonlinear frequency shift behavior of graphene–elastic–piezoelectric laminated films as a nano-mass detector

The mechanisms of freak wave generation in 3D island-reef topography are investigated. Four types of freak waves are investigated, based on the wavelet transform for examining the characteristics of freak waves and their mechanism. The freak waves come from a three-dimensional experimental terrain model in a random wave. The wavelet energy spectrum, scale-averaged and time-averaged wavelet spectrum are considered. A new parameter (scale-centroid wavelet spectrum) is defined, based on the wavelet transform algorithm, to quantitatively analyze and further estimate the energy transfer process. The results suggest that the occurrence of freak waves is associated with the gradual alignment of the phases of wave components. The nonlinear interaction in terms of wavelet cross-bispectrum implies that wave–wave interaction, especially with high-frequency components, is obviously enhanced during a freak wave occurrence. The energy transforms to a high frequency during a freak wave occurrence. The current result forms a definite indication that the occurrence of freak waves is caused by the combined effects of linear superposition and nonlinear interactions. Linear superposition begins to take effect long before the freak wave occurs, whereas nonlinear interactions primarily occur during the shorter period just before the freak wave forms. It provides an important reference for the prediction of abnormal waves.

A mechanical analysis model for tunnels under strike-slip faulting considering the fault zone width and nonlinear tunnel-stratum interaction

Investigation on aerodynamic stability of long-span suspension bridges under erection

Propeller load fluctuation in rough sea conditions is caused by two components: one is the fluctuating inflow velocity and the other is the emergence of the propeller disk from the water. Such disturbances cause large fluctuations in engine power and revolutions, and can lead to the failure of the propulsion plant, which is unacceptable in extreme seas. However, due to strong nonlinearity in the effect of propeller emergence and nonlinear interactions with the inflow velocity in the propeller torque fluctuation, the procedure for obtaining the statistical properties of the propeller torque in extreme sea conditions is not clear. If the statistical properties of propeller torque fluctuation—such as the variance and the probability density function—are known, the corresponding statistics of the response of the engine can be obtained, allowing the safe operation of ship propulsion plants in extreme irregular seas to be assessed.

Is total laparoscopic hysterectomy with longer operative time associated with a decreased benefit compared with total abdominal hysterectomy?

The resonance of stationary waves forced by topography is examined using a quasi-geostrophic model on a beta-plane channel. It is shown analytically that among the factors favoring the resonance of large, rather than synoptic or small, scale waves is the fact that the sensitivity of the large resonant responses to a change of zonal wind decreases as the scale of the resonant wave increases. A numerical model is used to examine resonance in the presence of topography having zonal wavenumber 2 with zonal flows having horizontal and vertical shear and including the effects of damping and nonlinear interactions. Although the effects of resonance are found to be important even in the presence of damping mechanisms, linear experiments with topographical forcing of reasonable amplitude indicate that a period or several weeks is required for a resonant internal mode to achieve large amplitude in the troposphere. However, as the structure of the resonant mode is such that it has much larger amplitudes in ...

Effect on non-linear soil-structure interaction due to base slab uplift on the seismic response of a high-temperature gas-cooled reactor (HTGR)

Soliton formation at the upper hybrid frequency has been discussed recently on the basis of warm two-fluid theory. In this paper we report the results of a reductive perturbation theory analysis of the Vlasov equation describing the nonlinear modulation of electrostatic waves in a warm magnetized plasma. This approach allows a treatment of soliton formation with scale lengths of the order of, or less than, the electron Larmor radius rL for both upper hybrid and Bernstein waves. A three-dimensional generalized nonlinear Schrödinger equation has been found. Contributions to the nonlinear frequency shift derive from three distinct processes. One contribution describes the generation of the second harmonic governed by (ω + ω) → 2w where ω is the frequency of the electrostatic carrier; a second arises from the self-interaction between the high-frequency waves (ω + ω → ω + ω) while the third contribution describes the nonlinear coupling between the carrier and the slow background plasma motion.Propagation orthogonal to the magnetic field is studied and leads to a simplified nonlinear Schrodinger equation with cubic nonlinearity, predicting soliton formation at the upper hybrid and cyclotron harmonic frequencies. Expressions for the nonlinear frequency shift coefficient are presented for the upper hybrid and Bernstein modes in the low temperature limit and the relative strengths of the three competing nonlinear processes are compared. For krL ≥ 1·0, numerical analysis shows the dominant nonlinearity to be that arising from the nonlinear wave-particle interaction. The stability of the soliton solution is determined by the relative signs of the dispersion and the nonlinear frequency shift coefficient. Some properties of upper hybrid and Bernstein solitons are examined. In particular the variation of the normalized dispersion and nonlinear frequency shift coefficient with the basic plasma parameters (krL)2 and (ωpe/Ω, is presented, where (ope, fi are the electron plasma frequency and electron gyrofrequency respectively. Regions of instability are identified for both upper hybrid and Bernstein modes. The connection between reductive perturbation theory and previous warm fluid theories is also established.

Band excitation piezoresponse force microscopy enables local investigation of the nonlinear piezoelectric behavior of ferroelectric thin films. However, the presence of additional nonlinearity associated with the dynamic resonant response of the tip-surface junction can complicate the study of a material’s nonlinearity. Here, the relative importance of the two nonlinearity sources was examined as a function of the excitation function. It was found that in order to minimize the effects of nonlinear tip-surface interactions but achieve good signal to noise level, an optimal excitation function must be used.

A better understanding of fog and low stratus (FLS) life cycle processes can help traffic safety, improve solar power planning and enhance the understanding of ecosystem processes in fog-prone regions. Nevertheless, large-scale analyses of FLS life cycle processes are challenging due to the high spatial variability of FLS and complex interactions between the land surface and the atmosphere. Here, we use a satellite-based FLS formation and dissipation time data set, as well as reanalysis data to investigate regional variations in the FLS life cycle in the Po valley region in northern Italy. With its large spatial extent, relatively low topographic variability and high FLS occurrence, the Po valley is an ideal area to study FLS life cycle processes in central Europe. In a case study approach, we analyze FLS life cycle processes pertaining to variations in land surface characteristics and atmospheric drivers. First results reveal the importance of the temporal development of temperature, specific humidity and boundary layer height for FLS formation during radiation-driven FLS events. These effects are further modified by the local topography and the synoptic situation. This analysis provides a basis to set up further process-oriented sensitivity studies using explainable machine learning, which has shown to be an ideal tool to gain a deeper understanding of the effect of non-linear land-atmosphere interactions on the FLS life cycle.

Very-high energy gamma-rays from extragalactic sources pair-produce off of the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the "oblique" instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here, we show with numerical calculations that the effective damping rate is $8\times 10^{-4}$ of the growth rate of the linear instability, which is sufficient for the "oblique" instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wavenumber and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to approximate equipartition with the beam by increasingly depositing energy into long wavelength modes. As we have not included the effect of nonlinear wave-wave interactions on these long wavelength modes, this scenario represents the "worst-case" scenario for the oblique instability. As it continues to drain energy from the beam at a faster rate than other processes, we conclude that the "oblique" instability is sufficiently strong to make it the physically dominant cooling mechanism for high-energy pair beams in the intergalactic medium.