Null Method Research Articles

Probing gravitational wave polarizations with Advanced LIGO, Advanced Virgo, and KAGRA

Assuming that, for a given source of gravitational waves (GWs), we know its sky position, as is the case of GW events with an electromagnetic counterpart such as GW170817, we discuss a null stream method to probe GW polarizations including spin-0 (scalar) GW modes and spin-1 (vector) modes, especially with an expected network of Advanced LIGO, Advanced Virgo and KAGRA. For two independent null streams for four non-co-aligned GW detectors, we study a location on the sky, exactly at which the spin-0 modes of GWs vanish in any null stream for the GW detector network, though the strain output at a detector may contain the spin-0 modes. Our numerical calculations show that there exist seventy sky positions that satisfy this condition of killing the spin-0 modes in the null streams. If a GW source with an electromagnetic counterpart is found in one of the seventy sky positions, the spin-1 modes will be testable separately from the spin-0 modes by the null stream method. In addition, we study a superposition of the two null streams to show that any one of the three modes (one combined spin-0 and two spin-1 modes) can be eliminated by suitably adjusting a weighted superposition of the null streams and thereby a set of the remaining polarization modes can be experimentally tested.

A new estimation of protein-level false discovery rate

BackgroundIn mass spectrometry-based proteomics, protein identification is an essential task. Evaluating the statistical significance of the protein identification result is critical to the success of proteomics studies. Controlling the false discovery rate (FDR) is the most common method for assuring the overall quality of the set of identifications. Existing FDR estimation methods either rely on specific assumptions or rely on the two-stage calculation process of first estimating the error rates at the peptide-level, and then combining them somehow at the protein-level. We propose to estimate the FDR in a non-parametric way with less assumptions and to avoid the two-stage calculation process.ResultsWe propose a new protein-level FDR estimation framework. The framework contains two major components: the Permutation+BH (Benjamini–Hochberg) FDR estimation method and the logistic regression-based null inference method. In Permutation+BH, the null distribution of a sample is generated by searching data against a large number of permuted random protein database and therefore does not rely on specific assumptions. Then, p-values of proteins are calculated from the null distribution and the BH procedure is applied to the p-values to achieve the relationship of the FDR and the number of protein identifications. The Permutation+BH method generates the null distribution by the permutation method, which is inefficient for online identification. The logistic regression model is proposed to infer the null distribution of a new sample based on existing null distributions obtained from the Permutation+BH method.ConclusionsIn our experiment based on three public available datasets, our Permutation+BH method achieves consistently better performance than MAYU, which is chosen as the benchmark FDR calculation method for this study. The null distribution inference result shows that the logistic regression model achieves a reasonable result both in the shape of the null distribution and the corresponding FDR estimation result.

Iterative null space projection method with adaptive thresholding in sparse signal recovery

Adaptive thresholding methods have proved to yield a high signal-to-noise ratio (SNR) and fast convergence in sparse signal recovery. The robustness of a class of iterative sparse recovery algorithms, such as the iterative method with adaptive thresholding, has been found to outperform the state-of-art methods in respect of reconstruction quality, convergence speed, and sensitivity to noise. In this study, the authors introduce a new method for compressed sensing, using the sensing matrix and measurements. In our method, they iteratively threshold the signal and project the thresholded signal onto the translated null space of the sensing matrix. The threshold level is assigned adaptively. The results of the simulations reveal that the authors’ proposed method outperforms other methods in the signal reconstruction (in terms of the SNR). This performance advantage is noticeable when the number of available measurements approaches twice the sparsity number.

Rapid B1 field mapping at 3 T using the 180° signal null method with extended flip angle

PurposeTo extend the null signal method (NSM) for B1 mapping to 3 T magnetic resonance imaging (MRI). BackgroundThe NSM operates in the steady state regime and exploits the linearity of the spoiled gradient recalled echo (SPGR) signal around the 180° flip angle (FA). Using linear regression, B1 maps are derived from three SPGR images acquired at different FAs with a short repetition time. While the conventional NSM allows accurate mapping of B1 for moderate B1 variation, we observed that this method fails for the larger B1 variations typical of high-field MRI. MethodsWe analyzed the effect of the FA range of the acquired SPGR images on B1 determination using the NSM for 3 T MRI through extensive numerical and in vivo analyses. B1 maps derived from the extended angle-range NSM (EA-NSM) were calculated and compared to those derived from the conventional, more restricted angle range, NSM, and to those derived from the reference, but much more time-consuming, double angle method (DAM). Furthermore, we investigated the compatibility of EA-NSM B1 mapping and the half-scan and SENSE reconstruction methods for accelerating acquisition time. ResultsOur results show that the use of the conventional FA range leads to substantial inaccuracies in B1 determination. Both numerical and in vivo analyses demonstrate that expanding the FA range of the acquired SPGR images substantially improves the accuracy of B1 maps. Furthermore, B1 maps derived from EA-NSM were demonstrated to be quantitatively comparable to those derived from the lengthy DAM protocol. We also found that B1 maps derived from SPGR images using the EA-NSM and imaging acceleration methods were comparable to those derived from images acquired without acceleration. Finally, the use of half scanning combined with SENSE reconstruction permits whole-brain B1 mapping in ~1 min. ConclusionsThe EA-NSM permits accurate, fast, and practical B1 mapping in a 3 T clinical setting.

Null function classification using NFR matrix and decision tree

This research work is based on the classification of the functions which are required and which is not required for the efficient development of the software. The motivation of this work is to identify non required functions to reduce development cost and efforts. The classification is the technique which can classify data into certain number of classes. The NFR matrix is the existing technique which can classify the Null functions. To classify the null functions NFR use clustering method which can modify to increase accuracy of classification. In the existing method NFR matrix is used for the null function classification, it use the clustering for the classification. In this work, decision tree will based with the clustering. It take input result of clustering and generate classified result.

Null space method for tap value initialization in constant modulus algorithm for mode division multiplexing systems

In this paper, we propose a constant modulus algorithm (CMA) for mode division multiplexing (MDM) systems with improved convergence performance. In order to adapt to sparse channels with large differential mode group delay (DMGD) in MDM systems, the CMA adopts a variable step size similar to the improved proportionate normalized least-mean-square (IPNLMS) algorithm. In additional to that, when a singularity problem is encountered or the tap values fail to converge, it reinitializes the tap coefficients according to the tap vectors of the successfully de-multiplexed data tributaries. The proposed initialization approach is based on the fact that the channel matrix is unitary in the frequency domain in the absence of mode dependent loss (MDL), which means the channel coefficient vectors for each data tributary should be orthogonal to each other. By limiting the initial values of the taps within the null space of the complex conjugate vectors of the successfully de-multiplexed channels, singularity can be effectively avoided and the convergence of the taps is guaranteed. When the number of modes is two, the proposed algorithm becomes the constrained CMA, which has been commonly implemented in polarization division multiplexing (PDM) systems. Although the algorithm has been derived under zero MDL assumption, it is found that the proposed CMA can be quite resilient to MDL. No singularity/tap convergence failure problem occurs when the MDL is below 4 dB at both the input and the output ports.

Probabilistic assessment of the impact of coal seam gas development on groundwater: Surat Basin, Australia

Modelling cumulative impacts of basin-scale coal seam gas (CSG) extraction is challenging due to the long time frames and spatial extent over which impacts occur combined with the need to consider local-scale processes. The computational burden of such models limits the ability to undertake calibration and sensitivity and uncertainty analyses. A framework is presented that integrates recently developed methods and tools to address the computational burdens of an assessment of drawdown impacts associated with rapid CSG development in the Surat Basin, Australia. The null space Monte Carlo method combined with singular value decomposition (SVD)-assisted regularisation was used to analyse the uncertainty of simulated drawdown impacts. The study also describes how the computational burden of assessing local-scale impacts was mitigated by adopting a novel combination of a nested modelling framework which incorporated a model emulator of drawdown in dual-phase flow conditions, and a methodology for representing local faulting. This combination provides a mechanism to support more reliable estimates of regional CSG-related drawdown predictions. The study indicates that uncertainties associated with boundary conditions are reduced significantly when expressing differences between scenarios. The results are analysed and distilled to enable the easy identification of areas where the simulated maximum drawdown impacts could exceed trigger points associated with legislative ‘make good’ requirements; trigger points require that either an adjustment in the development scheme or other measures are implemented to remediate the impact. This report contributes to the currently small body of work that describes modelling and uncertainty analyses of CSG extraction impacts on groundwater.

Thermodynamics phase transition and Hawking radiation of the Schwarzschild black hole with quintessence-like matter and a deficit solid angle

In this paper, we investigate the thermodynamics and Hawking radiation of Schwarzschild black hole with quintessence-like matter and deficit solid angle. From the metric of the black hole, we derive the expressions of temperature and specific heat using the laws of black hole thermodynamics. Using the null geodesics method and Parikh–Wilczeck tunneling method, we derive the expressions of Boltzmann factor and the change of Bekenstein–Hawking entropy for the black hole. The behaviors of the temperature, specific heat, Boltzmann factor and the change of Bekenstein entropy versus the deficit solid angle ( $$\epsilon ^{2}$$ ) and the density of static spherically symmetric quintessence-like matter ( $$\rho _{0}$$ ) were explicitly plotted. The results show that, when the deficit solid angle ( $$\epsilon ^{2}$$ ) and the density of static spherically symmetric quintessence-like matter at $$r=1$$ ( $$\rho _{0}$$ ) vanish $$(\rho _{0}=\epsilon =0)$$ , these four thermodynamics quantities are reduced to those obtained for the simple case of Schwarzschild black hole. For low entropies, the presence of quintessence-like matter induces a first order phase transition of the black hole and for the higher values of the entropies, we observe the second order phase transition. When increasing $$\rho _{0}$$ , the transition points are shifted to lower entropies. The same thing is observed when increasing $$\epsilon ^{2}$$ . In the absence of quintessence-like matter ( $$\rho _{0}=0$$ ), these transition phenomena disappear. Moreover the rate of radiation decreases when increasing $$\rho _{0}$$ or $$(\epsilon ^2)$$ .

Element Selection for Optimized Multiwide Nulls in Almost Uniformly Excited Arrays

In this letter, a novel multiwide null steering method for uniformly excited large arrays by only adjusting the amplitude and phase of a relatively small number of elements on the extremes of the array is presented. These adjustable elements are optimized by means of genetic algorithm (GA) to construct a specific cancellation pattern that can be used to produce multiple wide nulls in the radiation patterns of the uniformly excited linear arrays. To simplify the feeding network as well as to increase the convergence speed of the optimization algorithm, the excitations of the majority of the array elements are kept constant. Results of applying the GA to optimize 10 out of 100 elements are shown.

A Novel Fully Analog Null Instrument for Resistive Wheatstone Bridge With a Single Resistive Sensor

When high-speed measurements are not necessary, the Wheatstone bridge-based null measurement instruments surpass the Wheatstone Bridge-based instruments using deflection technique, due to the fact that the null method has some intrinsic advantages over the deflection method. In this particle, a fully analog method has been introduced in order to implement a null measurement instrument for a resistive Wheatstone bridge with a single resistive sensor. In order to implement the proposed circuit, only two operational amplifiers and some passive elements have been used. The proposed method can be constructed and implemented by discrete components without any special limitation. Since the suggested scheme has linear output, the required computation in order to measure and display the measurand is reduced dramatically. Finally, in order to evaluate the performance and usefulness of the proposed method, it has been tested experimentally as well as by using computer aided design software.

Measurement of Cotton Transpiration

There are a few field methods available to directly measure water evapotranspiration (ET) along with its two components, evaporation from the soil (E) and from the crop (T). One such technique that measures T, uses sensors to calculate the sap flow (F) of water through the plant stem and is based on the conservation of mass and energy, i.e., the stem heat balance method. This instrument consists of a flexible heater that is wrapped around the plant stem with temperature sensors to measure the difference in temperature of F below and above the heater. This is a null method, where all inputs and outputs are known and the calculated F is a direct measure of T. This method has been used to measure T in a variety of crops, including cotton, grapes, olive trees, soybean, ornamental and horticultural crops. A new version of the EXO-SkinTM is the Stem Gauge Dual Channel Design (SGDCTM), which was commercially introduced and had a radically new design resulting in a different energy balance, compared to the original design, which needed experimental verification. An initial evaluation was done with potted cotton (Gossypium hirsutum, L.) plants in a greenhouse experiment showing that values of cotton-T measured with the new sensor were accurate; however, this comparison was limited to daily T T in the 2 - 7 mm/d range, representative of the semiarid Texas High Plains. For this purpose, cotton was planted on 12 June 2017 on a 1000 m2 plot in a soil classified in the Amarillo series at the facilities of the USDA-ARS, Lubbock, TX. For a period of 15 days, 2 to 16 Sep 2017, we measured hourly cotton-T with the new sensors and with portable growth chambers (0.75 m × 1 m cross-section, and 1 m height) where water vapor flux was measured at a 10 Hz frequency using an infrared gas analyzer. We used three chambers and, in each chamber, the new sensors were installed on four cotton plants. We used linear regression analysis to compare hourly and daily values of cotton-T measured with the sap flow gauges against T measured by the chambers. Using a t-test (p T for a wide range of environmental conditions.

Motion Analysis of Multibody Systems by Null Space Matrix Method of Differential Equation Type

Motion Analysis of Multibody Systems by Null Space Matrix Method of Differential Equation Type

Derivation of Constrain Forces of Multibody System by Null Space Matrix Method

Derivation of Constrain Forces of Multibody System by Null Space Matrix Method

Prestructuring sparse matrices with dense rows and columns via null space methods

SummarySeveral applied problems may produce large sparse matrices with a small number of dense rows and/or columns, which can adversely affect the performance of commonly used direct solvers. By posing the problem as a saddle point system, an unconventional application of a null space method can be employed to eliminate dense rows and columns. The choice of null space basis is critical in retaining the overall sparse structure of the matrix. A new one‐sided application of the null space method is also presented to eliminate either dense rows or columns. These methods can be considered techniques that modify the nonzero structure of the matrix before employing a direct solver and may result in improved direct solver performance.

U.S. Geological Survey experience with the residual absolutes method

Abstract. The U.S. Geological Survey (USGS) Geomagnetism Program has developed and tested the residual method of absolutes, with the assistance of the Danish Technical University's (DTU) Geomagnetism Program. Three years of testing were performed at College Magnetic Observatory (CMO), Fairbanks, Alaska, to compare the residual method with the null method. Results show that the two methods compare very well with each other and both sets of baseline data were used to process the 2015 definitive data. The residual method will be implemented at the other USGS high-latitude geomagnetic observatories in the summer of 2017 and 2018.

Tunnelling Phenomenon near an Apparent Horizon in Two-Dimensional Dilaton Gravity**Supported by the National Natural Science Foundation of China under Grant Nos. 11622543 and 11235010, and by the Open Project Program of Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (No. Y5KF161CJ1)

Based on the definition of the apparent horizon in a general two-dimensional dilaton gravity theory, we analyze the tunnelling phenomenon near the apparent horizon. In this theory the definition of the horizon is very different from those in higher-dimensional gravity theories. By using the Hamilton–Jacobi method, the spectrum of the radiation is obtained and the temperature of the radiation is read out from this spectrum. The temperature is proportional to the surface gravity of the apparent horizon as usual. Besides, in stationary cases we calculate the spectrum by using Parikh and Wilczek’s null geodesic method and the result conforms to that obtained by using the Hamilton–Jacobi method. This is expected since the Hamilton–Jacobi method applies to generic spacetimes, including stationary ones.

A Novel Subspace Based Method for Compensation of Multiple CFOs in Uplink MIMO OFDM Systems

The tri-linear data model for an arbitrary multi-user uplink multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) system comprising orthogonal frequency division multiplexing access users and co-channel (CC) users is formulated in this letter. A novel subspace-based method for multi-access interference cancellation and CC data separation in multi-user MIMO OFDM systems, utilizing the independent manifolds spanned by user’s carrier frequency offset matrix, is proposed in this letter. The system constraints under which the proposed subspace nulling method works are derived, which includes the under-determined cases, where minimum mean square error/zero forcing methods fail.

Signal or noise? A null model method for evaluating the significance of turnover pulses

AbstractPatterns of turnover in the mammalian fossil record have been interpreted as reflecting “pulses” of originations and extinctions hypothesized to be driven by climate change. However, criteria for determining what constitutes a meaningful pulse have been idiosyncratic, and investigations of turnover patterns in mammals have yielded mixed results.This study presents simple simulations of fossil records in which origination and extinction probabilities for each lineage are held constant. Nonetheless, the total number of turnover events per time bin varies stochastically, producing statistical “noise.” Various simulation and analytical assumptions are examined to determine their impact on the type I error rate (i.e., how often “pulses” are detected in a purely stochastic process).Results suggest that simple analytical parameters (length of time bins and turnover-pulse criterion) have predictable and straightforward effects on false-positive rates. Furthermore, “pulses” of turnover of a magnitude similar to that observed in the terrestrial mammalian fossil record may be quite common under realistic analytical conditions.The null turnover model offers a practical way to evaluate the significance of observed turnover events in future empirical studies of the fossil record. In evaluating the significance of a “pulse” of fossil origination or extinction events, analytical parameters can be explored using this null model to determine the approximate type I error rate for a set of parameters. Because false-positive rates are shown to be quite high, functional trait-based approaches may offer more reliable indicators of the impact of climate change on turnover dynamics.

A anti-jamming method for satellite navigation system based on multi-objective optimization technique.

In this paper, an anti-jamming method, which turns the single objective optimization problem into a multi-objective optimization problem by utilizing 2-norm, is proposed. The proposed jamming suppression method can reduce the wide nulls and wrong nulls problems, which are generated by the common adaptive nulling methods. Therefore a better signal-noise-ratio (SNR) can be achieved, especially when the jammers are close to satellite signals. It can also improve the robustness of the algorithm. The effectiveness of the proposed method is evaluated by simulation and practical outdoor experiments with the GPS L1 band C/A signals. The experimental results show that with the dedicated method, the nulls targeting at the corresponding jammers become narrower and the wrong nulls can be eliminated.

Optimal null steering method in uniformly excited equally spaced linear arrays by optimising two edge elements

The implementation of the feeding network in the arrays that composed of a large number of elements and using non-uniform excitations is a real challenging issue. The complexity of the feeding network can be greatly simplified by using uniformly excited arrays. However, such arrays suffer from sidelobe limitation. An optimised approach for sector sidelobe nulling in the equally spaced linear array pattern with uniform excitations except for two edge elements is presented. The genetic algorithm and particle swarm optimisation are independently used to find the optimal values of the amplitude and phase excitations for those edge elements.