Zero Frequency Research Articles

Detective efficiency of photon counting detectors with spectral degradation and crosstalk.

Charge sharing and migration of scattered and fluorescence photons in an energy discriminating photon counting detector (PCD) degrade the detector's energy response and can cause a single incident photon to be registered as multiple events at different energies among neighboring pixels, leading to spatio-energetic correlation. Such a correlation in conventional linear, space-invariant imaging system can be usefully characterized by the frequency dependent detective quantum efficiency DQE(f). Defining and estimating DQE(f) for PCDs in a manner consistent with that of conventional detectors is complicated because the traditional definition of DQE(f) does not address spectral information. We introduce the concept of presampling spectroscopic detective quantum efficiency, DQEs (f), and present an analysis of it for CdTe PCDs using a spatial domain method that starts from a previously described analytic computation of spatio-energetic crosstalk. DQEs (f) is estimated as the squared signal-to-noise ratio of the amplitude of a small-signal sinusoidal modulation of the object (cortical bone) thickness at frequency f estimated using data from the detector under consideration compared that obtained from the photon distribution incident on the detector. DQEs for material decomposition (spectral) and effective monoenergetic imaging tasks for different pixel pitch is studied based on the multipixel Cramér-Rao lower bound (CRLB) that accounts for inter pixel basis material correlation. Effective monoenergetic DQEs is estimated from the CRLB of a linear weighted combination of basis materials, and its energy dependence is also studied. Zero frequency DQEs for the spectral task was ~18%, 25%, and 34% for 250μm, 500μm, and 1mm detector pixels respectively. Inter pixel signal correlation results in positive noise correlation between same basis material estimates of neighboring pixels, resulting in least impact on DQEs at the detector's Nyquist frequency. Effective monoenergetic DQEs (0) at the optimal energy is relatively tolerant of spectral degradation (85-91% depending on pixel size), but is highly dependent on the selected effective energy, with maximum variation (in 250μm pixels) of 17% to 85% for effective energy between 30 to 120keV. Our results show that spatio-energetic correlations degrade DQEs (f) beyond what is lost by poor spectral response in a single detector element. The positive correlation between computed single basis material values in neighboring pixels results in the penalty to DQEs (f) to be the least at the Nyquist frequency of the detector. It is desirable to reduce spectral degradation and crosstalk to minimize the impact on system performance. Larger pixels sizes have better spatio-energetic response due to lower charge sharing and escape of scatter and K-fluorescence photons, and therefore higher DQEs (0). Effective monoenergetic DQEs (0) at the optimal energy is much less affected by spectral degradation and crosstalk compared to DQEs for spectral tasks.

A Bayesian mixture model for the analysis of allelic expression in single cells

Allele-specific expression (ASE) at single-cell resolution is a critical tool for understanding the stochastic and dynamic features of gene expression. However, low read coverage and high biological variability present challenges for analyzing ASE. We demonstrate that discarding multi-mapping reads leads to higher variability in estimates of allelic proportions, an increased frequency of sampling zeros, and can lead to spurious findings of dynamic and monoallelic gene expression. Here, we report a method for ASE analysis from single-cell RNA-Seq data that accurately classifies allelic expression states and improves estimation of allelic proportions by pooling information across cells. We further demonstrate that combining information across cells using a hierarchical mixture model reduces sampling variability without sacrificing cell-to-cell heterogeneity. We applied our approach to re-evaluate the statistical independence of allelic bursting and track changes in the allele-specific expression patterns of cells sampled over a developmental time course.

Stable Implementation of Zero Frequency Filtering of Speech Signals for Efficient Epoch Extraction

Epochs are the abrupt-closure events in vocal fold vibration during the production of voiced speech. Zero frequency filtering is a simple and effective technique used to estimate the glottal closure instants accurately from the speech signal. However, the zero frequency filter is an unstable system. Hence, it may not be suitable for practical implementation due to the requirements of high precision computation. In this letter, zero-phase zero frequency resonator is proposed as an alternative to zero frequency filter. The proposed approach provides a stable zero-phase response. The experimental results indicate that the performance of the proposed method outperformed the state-of-the-art methods in terms of identification rate 99.17% and provides comparable performance in terms of false alarm rate (0.41%), and identification accuracy (0.28 ms).

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

We propose a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing. The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we implement a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work suggest a more efficient scaling of computational cost with molecular size as compared to other methods.

Transport Barrier Triggered by Resonant Three-Wave Processes Between Trapped-Particle-Modes and Zonal Flow

We address the mechanisms underlying low-frequency zonal flow generation in a turbulent system through the parametric decay of collisionless trapped particle modes and its feedback on the stabilization of the system. This model is in connection with the observation of barrier transport in reduced gyrokinetic simulations (A. Ghizzo et al., Euro. Phys. Lett. 119(1), 15003 (2017)). Here the analysis is extended with a detailed description of the resonant mechanism. A key role is also played by an initial polarisation source that allows the emergence of strong initial shear flow. The parametric decay leads to the growth of a zonal flow which differs from the standard zero frequency zonal flow usually triggered by the Reynolds stress in fluid drift-wave turbulence. The resulting zonal flow can oscillate at low frequency close to the ion precession frequency, making it sensitive to strong amplification by resonant kinetic processes. The system becomes then intermittent. These new findings, obtained from numerical experiments based on reduced semi-Lagrangian gyrokinetic simulations, shed light on the underlying physics coming from resonant wave-particle interactions for the formation of transport barriers. Numerical simulations are based on a Hamiltonian reduction technique, including magnetic curvature and interchange turbulence, where both fastest scales (cyclotron and bounce motions) are gyro-averaged.

Overall Effects of Risk Factors Associated with Dental Caries Indices Using the Marginalized Zero-Inflated Negative Binomial Model

The purpose of this paper is to identify risk factors for decayed, missing, and filled permanent teeth (DMFT) in a population of 12–15-year-old schoolchildren and to apply the marginalized zero-inflated negative binomial (MZINB) model for determination and estimation of the overall effects of the risk factors. A cross-sectional survey comprising 764 students aged between 12 and 15 years was used to analyze the association between caries in children and some background characteristics in children and their parents. Information on the samples’ social, behavioral, and demographic status was obtained through a series of closed questions. The incidence rate ratios (IRR) were used to associate some risk factors with caries. In the entire sample, the frequency of zero was 194 (25.4%). The result of the shared-parameter marginalized zero-inflated negative binomial (SP-MZINB) model showed that being a girl (IRR = 1.18; p value = 0.021), higher dental visits frequency (IRR = 1.20; p value <0.001), lower tooth brushing frequency (IRR = 0.91; p value = 0.019), higher flossing frequency (IRR = 1.11; p value = 0.001), and lower mothers’ education (IRR = 0.89; p value = 0.042) are associated with DMFT. Our results may provide better insights of the factors associated with DMFT, and health programs should focus their efforts on healthcare services, for both preventive and curative purposes. This regression model provides an appropriate fit and meaningful interpretation to handling zero-inflated count outcomes. Also, it provides direct estimates of the effects of risk factors on the overall mean that does not require postmodeling computations.

An Optimized Third Harmonic Injection Method for Reducing DC-Link Voltage Fluctuation and Alleviating Power Imbalance of Three-Phase Cascaded H-Bridge Photovoltaic Inverter

Due to different solar radiation, temperature, and other reasons of modules in the three-phase cascaded H-bridge (CHB) photovoltaic (PV) inverter, the output power among PV modules will be unequal and lead to unbalanced grid currents, which cannot meet the requirements of grid codes. On the other hand, the second-order voltage ripple is aroused in the dc-link capacitor since each phase-leg of the CHB inverter is made up of a single-phase inverter. Concerning these two issues, this paper proposes an optimized third harmonic injection method based on fundamental frequency zero sequence injection (FFZSI), which is a conventional method to handle the slight power imbalance problem. In this paper, the FFZSI is adopted to redistribute the power among three phases, and then the third harmonic is injected into the three-phase combined reference waveforms according to the two requirements: all modules are free from overmodulation and the dc-link voltage fluctuation is mostly reduced. Therefore, the proposed method can reduce the dc-link voltage fluctuation and extend the power balance range of FFZSI at the same time. The validity and effectiveness of the proposed method are verified by simulation and experimental results.

Performance and Evaluation of Five-Phase Dual Random SVPWM Strategy With Optimized Probability Density Function

This paper presents a five-phase dual random space vector pulsewidth modulation (FPDR-SVPWM) strategy with an optimized probability density function (PDF) for a five-phase voltage-source inverter, and its performance and evaluation are also analyzed. Based on the nearest four vectors modulation method, the FPDR-SVPWM strategy, combined with random switching frequency and random zero vector, is investigated to significantly reduce the amplitude of high-order harmonics near the switching frequency and its integer multiples. For the nonsinusoidal power supply, third harmonic injection is introduced in this modulation strategy as well. Considering the effect of random numbers on the performance, an optimized Beta distribution is studied in detail. In order to analyze harmonic dispersion degree qualitatively and quantitatively, the power spectral density and the harmonic spread factor are both employed to assess the performance of the FPDR-SVPWM strategy. A series of results of simulation in MATLAB and experiments based on field programmable gate array demonstrate that the proposed modulation strategy is correct and valid, and it distributes high-order harmonics into a wide range without affecting the fundamental wave and third harmonic.

On spectra of upper Sergeev frequencies of linear differential equations

It is known that the spectra (ranges) of upper and lower Sergeev frequencies of zeros, signs, and roots of a linear differential equation of order greater than two with continuous coefficients belong to the class of Suslin sets on the nonnegative half-line of the extended real line. Moreover, for the spectra of upper frequencies of third-order equations this result was inverted under the assumption that the spectra contain zero. In the present paper we obtain an inversion of the above statement for equations of the fourth order and higher. Namely, for an arbitrary zero-containing Suslin subset S on the non-negative half-line of the extended real line and a positive integer number n greater than three a n order linear differential equation is constructed, which spectra of the upper Sergeev frequencies of zeros, signs, and roots coincide with the set S.

Hybrid modular multilevel converter with cascaded full bridges for medium-voltage motor drives

Modular multilevel converter (MMC) is especially appropriate in high-voltage constant-frequency systems due to its modularity and scalability. But, so far MMC has not been widely used in motor drives applications. Since the capacitor voltage fluctuation is proportional to the output current amplitude and inversely proportional to the output frequency under constant torque load, at the low-speed, the excessive sub-module (SM) capacitor voltage fluctuation is one of the major obstacles for MMC applied in motor drives. To suppress the SM capacitor voltage fluctuation, an effective solution is to inject a high frequency zero sequence voltage to the three-phase output voltages of MMC and control the circulating current per phase reasonably. However, the introduced high frequency and high amplitude common voltage at the motor side is harmful. In this paper, a hybrid MMC with cascaded full-bridge SMs (HMMC-CFB) topology is used in the medium-voltage motor drives. The high frequency and high amplitude common mode voltage is absorbed by the cascaded full-bridge SMs. Besides, the capacitor voltage fluctuations of each arm and the cascaded full-bridge SMs is easily limited within a reasonable range. Finally, the state space model of HMMC-CFB system is established and a stable state-error feedback control law is given. By the passive theory, the necessary and sufficient condition for the globally uniformly asymptotical stability of the HMMC-CFB closed-loop system is deduced. Simulation results confirm the superiority of this novel topology and the validity of the proposed control strategy.

A new ordinary differential equation for the evaluation of the frequency-domain Green function

Clément (2013) derived a second order ordinary differential equation (ODE) satisfied by the free-surface Green function in the frequency domain. Since then, similar ODEs for the gradient of the Green function have been developed. Unfortunately, all these ODEs degenerate at zero frequency. Therefore, it is not possible to initialize the numerical solution of these ODEs from this zero frequency. Alternative methods based on the shifting of the initial condition to frequencies strictly greater than zero have then been developed.The present paper describes an alternative approach to address this issue. It involves a new function which is the solution of a modified ODE which can be solved from the zero frequency.Finally, comparisons with evaluations of the Green function using the classical direct integration method are provided. They show that the new ODE can provide accurate estimates of the Green function.

Temporal Aggregation of Seasonally Near‐Integrated Processes

We investigate the implications that temporally aggregating, either by average sampling or systematic (skip) sampling, a seasonal process has on the integration properties of the resulting series at both the zero and seasonal frequencies. Our results extend the existing literature in three ways. First, they demonstrate the implications of temporal aggregation for a general seasonally integrated process with S seasons. Second, rather than only considering the aggregation of seasonal processes with exact unit roots at some or all of the zero and seasonal frequencies, we consider the case where these roots are local‐to‐unity such that the original series is near‐integrated at some or all of the zero and seasonal frequencies. These results show, among other things, that systematic sampling, although not average sampling, can impact on the non‐seasonal unit root properties of the data; for example, even where an exact zero frequency unit root holds in the original data it need not necessarily hold in the systematically sampled data. Moreover, the systematically sampled data could be near‐integrated at the zero frequency even where the original data is not. Third, the implications of aggregation on the deterministic kernel of the series are explored.‐142

Spectral characteristics of MTF in turbid atmosphere and its application for imaging band selection.

The formalized modulation transfer function (MTF) is used to describe the effects induced by turbid atmosphere on image quality. Spectral characteristics of formalized MTF are analyzed in detail. The zero and nonzero spatial frequency components of formalized MTF, which represent different image information, show strong wavelength dependence. Furthermore, both components vary sharply at some wavelengths, which is significantly correlated with molecule absorption. The formalized MTF spectral characteristics are obviously different from atmospheric transmittance. According to its spectral characteristics, turbid atmosphere effects on imaging can be predicted, and a waveband selection method for optimal imaging is proposed. Comparisons between the proposed method and other methods show good consistency at some wavebands. The simulated imaging results and actual imaging results both verify that the optimal imaging band analysis and selection method is effective.

Impact of Observability and Multi-objective Optimization on the Performance of Extended Kalman Filter for DTC of AC Machines

It is well known that the selection of extended Kalman filter (EKF) covariance elements has a considerable bearing on the effectiveness of EKF performance. The observability at very low frequency is also an essential property for the selection of EKF elements. This paper investigates the optimization of the EKF covariance elements when zero frequency is included in the training profile for direct torque control (DTC) of induction motor. In addition, the paper studies the optimization of EKF by speed and torque fitness functions using a non-dominated sorting genetic algorithm-II at zero and high speeds under stable flux regulation. For this purpose, DTC with constant switching frequency controller which has the capability of establishing continuous flux rotation regardless of speed variation is used. The optimized results of EKF for both DTC motor drives and speed and torque cost functions are verified experimentally.

Effect of Spectral Estimation on Ultrasonic Backscatter Parameters in Measurements of Cancellous Bones

Objective: the purpose of this paper was to investigate the effect of spectral computation methods on the estimation of the four ultrasonic backscatter parameters, namely, the apparent integrated backscatter (AIB), the zero frequency intercept of apparent backscatter (FIAB), the frequency slope of apparent backscatter (FSAB), and the backscatter spectral centroid shift (SCS) from the backscattered signal of interest (SOI), and their subsequent correlations with cancellous bone parameter [bone volume/total volume (BV/TV)]. Methods: ultrasonic backscatter measurements were performed on 26 bovine cancellous bone specimens using a 1.0-MHz focused transducer. Four spectral estimation algorithms, including the classical periodogram, the autoregressive (AR) Burg algorithm, the AR covariance algorithm, and the AR modified covariance algorithm, were used to calculate the ultrasonic parameters. Influence of the signal's delay time (T1) and its length (T2) on the strength of correlation between BV/TV and backscatter parameters was also studied. Results: the results have demonstrated that the AR-based estimators provide much more reliable and stronger correlations between the BV/TV and backscatter parameters than the classical periodogram. Recommendations for choosing SOI were also suggested. Conclusion: these results indicate that the AR-based method has a promising potential to enhance the performance of evaluation and diagnosis of the cancellous bone using the ultrasonic backscatter method. Significance: the enhancement of the correlation may provide a positive impact on the ultrasonic backscatter method to diagnose and monitor the bone quantity.

The Use of Telematics Devices to Improve Automobile Insurance Rates.

Most automobile insurance databases contain a large number of policyholders with zero claims. This high frequency of zeros may reflect the fact that some insureds make little use of their vehicle, or that they do not wish to make a claim for small accidents in order to avoid an increase in their premium, but it might also be because of good driving. We analyze information on exposure to risk and driving habits using telematics data from a pay-as-you-drive sample of insureds. We include distance traveled per year as part of an offset in a zero-inflated Poisson model to predict the excess of zeros. We show the existence of a learning effect for large values of distance traveled, so that longer driving should result in higher premiums, but there should be a discount for drivers who accumulate longer distances over time due to the increased proportion of zero claims. We confirm that speed limit violations and driving in urban areas increase the expected number of accident claims. We discuss how telematics information can be used to design better insurance and to improve traffic safety.

Digit frequencies and self-affine sets with non-empty interior

In this paper we study digit frequencies in the setting of expansions in non-integer bases, and self-affine sets with non-empty interior. Within expansions in non-integer bases we show that if $\unicode[STIX]{x1D6FD}\in (1,1.787\ldots )$ then every $x\in (0,1/(\unicode[STIX]{x1D6FD}-1))$ has a simply normal $\unicode[STIX]{x1D6FD}$-expansion. We also prove that if $\unicode[STIX]{x1D6FD}\in (1,(1+\sqrt{5})/2)$ then every $x\in (0,1/(\unicode[STIX]{x1D6FD}-1))$ has a $\unicode[STIX]{x1D6FD}$-expansion for which the digit frequency does not exist, and a $\unicode[STIX]{x1D6FD}$-expansion with limiting frequency of zeros $p$, where $p$ is any real number sufficiently close to $1/2$. For a class of planar self-affine sets we show that if the horizontal contraction lies in a certain parameter space and the vertical contractions are sufficiently close to $1$, then every non-trivial vertical fibre contains an interval. Our approach lends itself to explicit calculation and gives rise to new examples of self-affine sets with non-empty interior. One particular strength of our approach is that it allows for different rates of contraction in the vertical direction.

Helmholtz Decomposition and Boundary Element Method Applied to Dynamic Linear Elastic Problems

The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the longitudinal and transverse fields satisfy scalar Helmholtz equations that can be solved using a desingularized boundary element method (BEM) framework. The curl free longitudinal and divergence free transversal conditions can also be cast as additional scalar Helmholtz equations. When compared to other BEM implementations, the current framework leads to smaller matrix dimensions and a simpler conceptual approach. The numerical implementation of this approach is benchmarked against the 3D elastic wave field generated by a rigid vibrating sphere embedded in an infinite linear elastic medium for which the analytical solution has been derived. Examples of focussed 3D elastic waves generated by a vibrating bowl-shaped rigid object with convex and concave surfaces are also considered. In the static zero frequency limit, the Helmholtz decomposition becomes non-unique, and both the longitudinal and transverse components contain divergent terms that are proportional to the inverse square of the frequency. However, these divergences are equal and opposite so that their sum, that is the displacement field that reflects the physics of the problem, remains finite in the zero frequency limit.

Controlling the deformation of metamaterials: Corner modes via topology

Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously relied on the Maxwell condition, namely that the system has equal numbers of degrees of freedom and constraints. Here, we show that otherwise rigid periodic mechanical structures are described by a map with a nontrivial topological degree (a generalization of the winding number introduced by Kane and Lubensky) that creates, directs and protects modes on their boundaries. We introduce a model system consisting of rigid quadrilaterals connected via free hinges at their corners in a checkerboard pattern. This bulk structure generates a topological linear deformation mode exponentially localized in one corner, as investigated numerically and via experimental prototype. Unlike the Maxwell lattices, these structures select a single desired mode, which controls variable stiffness and mechanical amplification that can be incorporated into devices at any scale.

Holographic pump probe spectroscopy

We study the non-linear response of a 2+1 dimensional holographic model with weak momentum relaxation and finite charge density to an oscillatory electric field pump pulse. Following the time evolution of one point functions after the pumping has ended, we find that deviations from thermality are well captured within the linear response theory. For electric pulses with a negligible zero frequency component the response approaches the instantaneously thermalizing form typical of holographic Vaidya models. We link this to the suppression of the amplitude of the quasinormal mode that governs the approach to equilibrium. In the large frequency limit, we are also able to show analytically that the holographic geometry takes the Vaidya form. A simple toy model captures these features of our holographic setup. Computing the out-of-equilibrium probe optical conductivity after the pump pulse, we similarly find that for high-frequency pulses the optical conductivity reaches its final equilibrium value effectively instantaneously. Pulses with significant DC components show exponential relaxation governed by twice the frequency of the vector quasinormal mode that governs the approach to equilibrium for the background solution. We explain this numerical factor in terms of a simple symmetry argument.