Small Random Errors Research Articles

“Oh Grandmother, what big teeth you have!” Incentives to spur scientific research at business schools have been treacherous

Scientific research was introduced in business schools in the mid-1950s to raise the quality of business education as well as to improve actual business practices. Schools expected scientific research to provide a benign and respected path toward improvements, and government support for research and students’ strong interest in studying business brought financial resources and hiring opportunities that made large changes possible. Consequently, hundreds of business schools began urging professors to publish scientific research. Sixty years later, plentiful evidence is showing that scientific research has not brought expected benefits for business operations; on the contrary, business-school research has generated a high percentage of untrustworthy “findings”. This disappointing outcome has six interacting causes: (1) Business schools have expanded by hiring professors who study fundamental topics of economics, psychology, and sociology rather than topics relevant for business practices, so few research findings have been adopted and tested by firms. (2) Instead of evaluating the quality or consequences of research, schools have relied on evaluations by journal editors and reviewers, whose overriding criteria emphasize theory at the expense of practical implications. (3) Editorial evaluations have high error rates because editors and reviewers only know what researchers choose to tell them, and because the complexity of manuscripts causes editors and reviewers to disagree frequently. (4) Schools have incentivized professors by making promotions and job security depend on publishing numerous papers in “prestigious” journals. (5) Many professors have responded to these incentives by engaging in covert practices that make studies unlikely to be supported in replications, and some professors have gone so far as to manufacture fake data. (6) Researchers, editors, and reviewers have largely relied on null-hypothesis statistical significance tests, which are prone to interpret small variations or random errors in data as “significant” findings. Although there are fresh efforts to make research findings more reliable and impactful, the need for further interventions to reform the present knowledge-production system is all too apparent.

Surface-guided radiotherapy systems in locoregional deep inspiration breath hold radiotherapy for breast cancer - a multicenter study on the setup accuracy.

Daily image-guided radiotherapy (IGRT) and deep inspiration breath hold (DIBH) technique are recommended for locoregional RT of breast cancer. The optimal workflow for a combination of surface-guided RT (SGRT) with DIBH technique is of current clinical interest. The setup accuracy at three hospitals was evaluated using different SGRT workflows. A total of 150 patients (2269 image pairs) were analyzed in three groups: patient setup with the AlignRT® SGRT system in Tampere (Site 1, n = 50), the Catalyst™ SGRT system in Turku (Site 2, n = 50) and the Catalyst™ SGRT system in Jönköping (Site 3, n = 50). Each site used their routine workflow with SGRT-based setup and IGRT positioning. Residual errors of the bony chest wall, thoracic vertebra (Th 1) and humeral head were evaluated using IGRT images. Systematic residual errors in the cranio-caudal (CC) direction and in pitch were generally larger at Site 2 than those at Sites 1 and 3 (p = 0.01-0.7). With daily IGRT, only a small difference (p = 0.01-0.9) was observed in residual random errors of bony structures in other directions between sites. The introduction of SGRT and the use of daily IGRT lead to small residual errors when combining the best workflow practices from different hospitals. Our multicenter evaluation led to improved workflow by tightening the SGRT tolerances on Site 2 and fixation modification. Because of mainly small random errors, systematic posture errors in the images need to be corrected after posture correction with new setup surfaces. We recommend tight SGRT tolerances, good fixation and correction of systematic errors.

Low-Data Deep Quantum Chemical Learning for Accurate MP2 and Coupled-Cluster Correlations.

Accurate ab initio prediction of electronic energies is very expensive for macromolecules by explicitly solving post-Hartree-Fock equations. We here exploit the physically justified local correlation feature in a compact basis of small molecules and construct an expressive low-data deep neural network (dNN) model to obtain machine-learned electron correlation energies on par with MP2 and CCSD levels of theory for more complex molecules and different datasets that are not represented in the training set. We show that our dNN-powered model is data efficient and makes highly transferable predictions across alkanes of various lengths, organic molecules with non-covalent and biomolecular interactions, as well as water clusters of different sizes and morphologies. In particular, by training 800 (H2O)8 clusters with the local correlation descriptors, accurate MP2/cc-pVTZ correlation energies up to (H2O)128 can be predicted with a small random error within chemical accuracy from exact values, while a majority of prediction deviations are attributed to an intrinsically systematic error. Our results reveal that an extremely compact local correlation feature set, which is poor for any direct post-Hartree-Fock calculations, has however a prominent advantage in reserving important electron correlation patterns for making accurate transferable predictions across distinct molecular compositions, bond types, and geometries.

Test–Retest Reliability and Responsiveness of the Computerized Adaptive Test of Social Functioning in Persons With Stroke

ObjectiveTo examine the test–retest reliability, minimal detectable change (MDC), responsiveness, and efficiency of the Computerized Adaptive Test of Social Functioning (Social-CAT) in patients with stroke. DesignRepeated-assessments design. SettingA department of rehabilitation of a medical center. ParticipantsIn total, 31 patients with chronic stroke and 65 patients with subacute stroke were recruited. InterventionNot available. Main Outcome MeasureSocial-CAT. ResultsThe Social-CAT showed acceptable test–retest reliability (intraclass correlation coefficient, 0.80) and small random measurement error (MDC%: 18.0%). However, heteroscedasticity was found (r between the means and the absolute change scores: 0.32), so the MDC% adjusted cut-off score is recommended for determining real improvement. Regarding responsiveness, the Social-CAT showed large differences (Kazis’ effect size and standardized mean response: 1.15 and 1.09, respectively) in subacute patients. Regarding efficiency, the Social-CAT required an average of 5 items and less than 2 minutes for completion. ConclusionsOur findings indicate that the Social-CAT is a reliable and efficient measure with good test–retest reliability, small random measurement error, and good responsiveness. Thus, the Social-CAT is a useful outcome measure for routine monitoring of the changes in social function of patients with stroke.

Factory quality assurance of passive radiotherapy intensity modulators for electrons using kilovoltage x-ray imaging.

This work developed an x-ray-based method for performing factory quality assurance (QA) of Passive Radiotherapy Intensity Modulators for Electrons (PRIME) device fabrication. This method measures errors in position, diameter, and orientation of cylindrical island blocks on a hexagonal grid that comprises PRIME devices and the impact of such errors on the underlying intensity distribution. X-ray images were acquired of six PRIME devices, which modeled three error cases (small random, large random, and systematic errors) for two island block diameters (0.158 and 0.352cm). Island blocks in each device, 0.6cm long tungsten cylinders of constant diameter, were spaced 0.6cm on a hexagonal grid over approximately 8cm square. Using a 50 kVp x-ray image, each island block projected a racetrack, whose perimeter was fit to a function that allowed determination of its position, diameter, and angular orientation (θ, ϕ). These measured parameters were input into a pencil beam algorithm (PBA) dose calculation performed in water (16 MeV, SSD=103cm) for each device. PBA calculated intensity distributions using measured and planned (exact) island block parameters were compared. Θ distributions for the 0.158 and 0.352cm devices were nearly identical for each error case, with θ values for most island blocks being within 3.2°, 8.5°, and 7.5° for the small random, large random, and systematic error PRIME devices, respectively. Corresponding intensity differences between using measured and planned island block parameters were within 1.0% and 2.8% (small random), 2.2% and 4.8% (large random), and 3.2% and 6.7% (systematic) for the 0.158 and 0.352cm devices, respectively. This approach provides a viable and economical method for factory QA of fabricated PRIME devices by determining errors in their planned intensity distribution from which their quality can be assessed prior to releasing to the customer.

The impact of the loss of first permanent molars on the duration of treatment in patients treated with orthodontic space closure and without skeletal anchorage

BackgroundThis study aims to evaluate the impact of the loss of permanent molars on the duration of orthodontic treatment for space closure and without skeletal anchorage.MethodsRecords at the beginning (T0) and the end (T1) of orthodontic treatment were selected retrospectively. Patients were divided into two groups: loss of molar (n = 19) and control, without loss (n = 24). The impact of loss on treatment time was assessed using multiple linear regression adjusted for the number of absences, bonding failures, age, sex, PAR index at T0 and T1 at p<0.05. Treatment time was also evaluated by the number of losses and which arches were involved (upper, lower). The systematic and random errors for the PAR index were verified using the intraclass correlation coefficient (ICC) and the Dahlberg formula, respectively.ResultsA small random error (1.51) and excellent replicability (ICC = 99.6) were observed. Overall average treatment time was 22.5 months (± 7.95) for the group without loss and 44.7 months (± 17.3) with a loss. Treatment time was longer in cases where there was a higher number of missing molars and when both arches were involved. In addition to the loss (β = 4.25, p < 0.001), the number of missed appointments (β = 2.88, p < 0.001) had a significant effect and increased treatment time. Bonding failures, gender, age, and PAR index at T0 and T1 were not significantly associated with treatment time in the multivariate model (p > 0.05).ConclusionLoss of the first permanent molar has a negative impact on orthodontic treatment time in cases of space closure. The treatment time is longer when there are more tooth losses and arches involved. Treatment time also increases with greater numbers of missed clinical appointments.

Consistency and Reliability Analyses of a Comprehensive Index for the Evaluation of Teeth Alignment Performance.

(1) Introduction: The purpose of this work was to describe a method and propose a novel accuracy index to assess orthodontic alignment performance. (2) Methods: Fifteen patients who underwent orthodontic treatment using directly printed clear aligners were recruited. The study sample included 12 maxillary and 10 mandibular arches, whose pre-treatment, predicted and post-treatment digital models were superimposed on the untreated posterior teeth by means of a best-fit surface-based registration, which was also used to transfer three anatomical landmarks, digitally labeled on the crown of each anterior moving tooth, from the pre-treatment to the predicted and post-treatment models. The Teeth Alignment Performance (TAP) index, quantifying how close the final landmarks were to their expected final position, was proposed as an accuracy index of both individual tooth and group of teeth movement, and its inter-examiner repeatability was tested. (3) Results: No systematic inter-rater discrepancy associated with TAP was observed (p > 0.05), not even when a slight systematic inter-rater difference in landmark labelling was detected (for the upper central incisors, p < 0.001). In addition, all Intra-class Correlation Coefficient (ICC) values showed excellent inter-rater agreement (>0.95), and the small Random Error of Measurement (REM), ranging from 1% for the arch TAP to 3% for the lower canine TAP, indicated that this accuracy index is highly repeatable. (4) Conclusions: The TAP index was proven to be comprehensive, consistent and reliable in assessing the performance of teeth alignment according to a digital plan. The proposed method is also suitable to be implemented in the clinical digital workflow.

On the proper use of structural similarity for the robust evaluation of medical image synthesis models

To propose good practices for using the structural similarity metric (SSIM) and reporting its value. SSIM is one of the most popular image quality metrics in use in the medical image synthesis community because of its alleged superiority over voxel-by-voxel measurements like the average error or the peak signal noise ratio (PSNR). It has seen massive adoption since its introduction, but its limitations are often overlooked. Notably, SSIM is designed to work on a strictly positive intensity scale, which is generally not the case in medical imaging. Common intensity scales such as the Houndsfield units (HU) contain negative numbers, and they can also be introduced by image normalization techniques such as thez-normalization. We created a series of experiments to quantify the impact of negative values in the SSIM computation. Specifically, we trained a three-dimensional (3D) U-Net to synthesize T2-weighted MRI from T1-weighted MRI using the BRATS 2018 dataset. SSIM was computed on the synthetic images with a shifted dynamic range. Next, to evaluate the suitability of SSIM as a loss function on images with negative values, it was used as a loss function to synthesize z-normalized images. Finally, the difference between two-dimensional (2D) SSIM and 3D SSIM was investigated using multiple 2D U-Nets trained on different planes of theimages. The impact of the misuse of the SSIM was quantified; it was established that it introduces a large downward bias in the computed SSIM. It also introduces a small random error that can change the relative ranking of models. The exact values for this bias and error depend on the quality and the intensity histogram of the synthetic images. Although small, the reported error is significant considering the small SSIM difference between state-of-the-art models. It was shown therefore that SSIM cannot be used as a loss function when images contain negative values due to major errors in the gradient calculation, resulting in under-performing models. 2D SSIM was also found to be overestimated in 2D image synthesis models when computed along the plane of synthesis, due to the discontinuities between slices that is typical of 2D synthesismethods. Various types of misuse of the SSIM were identified, and their impact was quantified. Based on the findings, this paper proposes good practices when using SSIM, such as reporting the average over the volume of the image containing tissue and appropriately defining the dynamicrange.

Estimation of Ion Temperature in the Upper Ionosphere Along the Swarm Satellite Orbits

AbstractIon temperature is one of the key parameters that provides insight into the thermal balance of the coupled ionosphere‐thermosphere system. Together with the temperatures of neutral and electron gases, it affects physical and chemical processes and parameters in the upper atmosphere. These include the ion‐neutral collision frequencies, chemical reaction rates and plasma scale height, all of which influence the variation and distribution of ionospheric plasma. The European Space Agency's three, nearly polar‐orbiting Swarm satellites at about 500 km altitude measure ionospheric electron temperature, density, and ion drifts using electric field instrument (EFI) Langmuir probes and Thermal Ion Imagers. Measurements of the ion temperature, though initially planned, are not available due to technical problems with the ion imagers. This paper describes a model that estimates the ion temperature along the orbits of Swarm satellites and evaluates the validity of the corresponding data. This data‐driven, physics‐based model combines an ion heat balance equation of the upper ionosphere, the Swarm EFI measurements, and empirical models for neutral composition, winds, and electric field. The validity of this approach was investigated using a physics‐based ionosphere model (SAMI3) for different geophysical conditions. We have studied the effects of various assumptions and input data limitations to the model accuracy, and have validated the estimated ion temperature against independent measurements from low, middle, and high‐latitude incoherent scatter radars (ISRs). When compared with the ISR data, the obtained Swarm‐based ion temperature shows small systematic errors (1%–2%), high correlations (Swarm A/C 0.8, Swarm B 0.6), and random errors of 10%–20%.

Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions.

Aiming at conservative Maxwell equations with periodic oscillatory solutions, we adopt exponentially fitted trapezoidal scheme to approximate the temporal and spatial derivatives. The scheme is a multisymplectic scheme. Under periodic boundary condition, the scheme satisfies two discrete energy conservation laws. The scheme also preserves two discrete divergences. To reduce computation cost, we split the original Maxwell equations into three local one-dimension (LOD) Maxwell equations. Then exponentially fitted trapezoidal scheme, applied to the resulted LOD equations, generates LOD multisymplectic scheme. We prove the unconditional stability and convergence of the LOD multisymplectic scheme. Convergence of numerical dispersion relation is also analyzed. At last, we present two numerical examples with periodic oscillatory solutions to confirm the theoretical analysis. Numerical results indicate that the LOD multisymplectic scheme is efficient, stable and conservative in solving conservative Maxwell equations with oscillatory solutions. In addition, to one-dimension Maxwell equations, we apply least square method and LOD multisymplectic scheme to fit the electric permittivity by using exact solution disturbed with small random errors as measured data. Numerical results of parameter inversion fit well with measured data, which shows that least square method combined with LOD multisymplectic scheme is efficient to estimate the model parameter under small random disturbance.

Balancing of metal resonators of wave solid-state gyroscopes of general use

Wave solid-state gyroscopes (WSG) are among the most modern navigation devices. Based on the phenomenon of precession of elastic waves in thin-walled axisymmetric bodies, WSGs have a simple design, including 2-3 fixed parts, and have a number of advantages over other types of gyroscopes: great resource of work; small random error; resistance to severe operating conditions (overload, vibration, gamma radiation); relatively small overall dimensions, weight and power consumption; preservation of inertial information during short-term power outages. From the point of view of practical application and technologies used, three main groups of WSG can be distinguished. Wave solid-state gyroscopes of high precision. In such devices, high-quality (with a Q-factor of over 1·107) quartz resonators, contactless sensors and actuators, as well as complex electronic control systems are used. The field of application today, for various reasons, is limited to space technology, which requires, along with high precision, a long working life. Micromechanical devices of low accuracy for mass use (laptop computers, toys, industrial equipment, etc.) Integration of micromechanical WSGs with satellite systems makes it possible to create small-sized inexpensive navigation systems for widespread use. This market segment is developing very quickly, but production of such devices requires a very high the level of development of the microelectronic industry. An intermediate group consists of sensors of general use with metal resonators. Although these devices are larger than micromechanical devices, their production technology is much simpler. Metal resonators with a quality factor of (3 ... 5)∙104 can be manufactured using universal metal-cutting equipment; such devices have a simple design, do not require the creation of a high vacuum in their housing, and widespread radioelements can be used in control units. As a result, devices of this group, possessing insignificant power consumption and long working life, have a low cost price. On the other hand, the comparatively large dimensions of the resonator allow their precise tuning, which makes it possible to sharply increase the accuracy of the gyro instruments. From these points of view, a general-purpose WSG with a metal resonator is the most promising device that should replace the rotary-type electromechanical gyroscopes used today, and the production of which can be quickly mastered by the domestic industry. The development of such sensors requires solving a number of scientific and technical problems. Since all the main characteristics of such a device are determined by the properties of the resonator, special attention should be paid to its design and production technology. One of the most difficult and expensive operations in the WSG technology is the balancing of the resonator, carried out to eliminate the mass imbalance that arises during its manufacture due to inevitable deviations from the ideal axisymmetric shape (inhomogeneity of the wall thickness, displacement of the centers of the outer and inner surfaces, etc.). At a nonzero value of the 4th harmonics of the mass imbalance, a splitting of the natural frequency of the resonator occurs, leading to random errors in the WSG. A number of technologies are described in the literature to eliminate this mass defect [3-5]. The resonator balancing according to the first three forms of mass defect is much more difficult. Here, oscillations of the center of mass of the resonator occur during operation of the gyroscope and additional dissipation of the energy of oscillations of the resonator in the nodes of its attachment. This leads to a dependence of the Q-factor of the resonator on the orientation of the standing wave and, consequently, to a systematic error of the device. Thus, the aim of this work is to develop a technique and equipment for balancing metal resonators according to the first three forms of mass defect, suitable for use in the production of general-purpose WSGs.

Memory-assisted decoder for approximate Gottesman-Kitaev-Preskill codes

We propose a quantum error correction protocol for continuous-variable finite-energy, approximate Gottesman-Kitaev-Preskill (GKP) states undergoing small Gaussian random displacement errors, based on the scheme of Glancy and Knill [Phys. Rev. A {\bf 73}, 012325 (2006)]. We show that combining multiple rounds of error-syndrome extraction with Bayesian estimation offers enhanced protection of GKP-encoded qubits over comparible single-round approaches. Furthermore, we show that the expected total displacement error incurred in multiple rounds of error followed by syndrome extraction is bounded by $2\sqrt{\pi}$. By recompiling the syndrome-extraction circuits, we show that all squeezing operations can be subsumed into auxiliary state preparation, reducing them to beamsplitter transformations and quadrature measurements.

An improved TROPOMI tropospheric HCHO retrieval over China

Abstract. We present an improved TROPOspheric Monitoring Instrument (TROPOMI) retrieval of formaldehyde (HCHO) over China. The new retrieval optimizes the slant column density (SCD) retrieval and air mass factor (AMF) calculation for TROPOMI observations of HCHO over China. Retrieval of HCHO differential SCDs (DSCDs) is improved using the basic optical differential spectroscopy (BOAS) technique resulting in lower noise and smaller random error, while AMFs are improved with a priori HCHO profiles from a higher resolution regional chemistry transport model. Compared to the operational product, the new TROPOMI HCHO retrieval shows better agreement with ground-based Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) measurements in Beijing. The improvements are mainly related to the AMF calculation with more precise a priori profiles in winter. Using more precise a priori profiles in general reduces HCHO vertical column densities (VCDs) by 52.37 % (± 27.09 %) in winter. Considering the aerosol effect in AMF calculation reduces the operational product by 11.46 % (± 1.48 %) and our retrieval by 17.61 % (± 1.92 %) in winter. The improved and operational HCHO are also used to investigate the spatial–temporal characteristics of HCHO over China. The result shows that both improved and operational HCHO VCDs reach maximum in summer and minimum in winter. High HCHO VCDs mainly located over populated areas, i.e., Sichuan Basin and central and eastern China, indicate a significant contribution of anthropogenic emissions. The hotspots are more obvious on the map of the improved HCHO retrieval than the operational product. The result indicates that the improved TROPOMI HCHO retrieval is more suitable for the analysis of regional- and city-scale pollution in China.

Analysis of Accuracy and Measuring Range of Dual Absolute Encoder System

As small-sized absolute encoders are currently being installed in small and high-power motors, a dual absolute encoder (DAE) system comprising two absolute encoders can now be constructed. The two absolute encoders in the DAE system are installed on a motor shaft and an output shaft; further, the two shafts are connected by a reduction mechanism. The DAE system will replace an ordinary dual encoder system in the future, because of its high accuracy and extended measurement range. In this paper, an analysis of the accuracy and measuring range of DAE system is presented. Index numbers that are calculated from readings of absolute encoders have a one-to-one correspondence with the number of rotations of the two shafts. Their positions are calculated based on the index number and extended greatest common factor ( EGCF ) of 1 and the inverse of reduction ratio. The error in the index number is investigated and maximum error tolerance of an absolute encoder that guarantees correct position estimation is proposed. Experiments are conducted separately in narrow and wide measurement ranges. Each range exhibits different types of errors, small random and large periodic errors. The large periodic errors are compensated using harmonic function model. The small random errors are utilized to calculate the maximum error tolerance and minimum resolution of the absolute encoder at the output shaft. The experimental results demonstrate that the final error decreases and the measurement range is extended to 1/ EGCF in the DAE system compared with the ordinary dual encoder system.

Apportionment of liability by the stochastic Shapley value

If multiple defendants are jointly liable for a plaintiff's harm, the court must determine the apportionments of the damages among them. Recently, in a series of papers, Dehez and Ferey (2013) and Ferey and Dehez (2016a,b) took a cooperative game theory approach, and used the Shapley value and the weighted Shapley value to determine the shares especially in the case of sequential acts. In this paper, we argue that their allocation rule is not strictly fair if we take even a small random error into account. We alternatively propose the stochastic Shapley value which extends the definition of the Shapley value to stochastic cooperative games and show that it satisfies ex post efficiency, symmetry, dummy, feasibility and fairness.

Positioning deviations in frameless and frame-based intracranial stereotactic radiosurgery

Intracranial stereotactic radiosurgery (SRS) is a well established therapeutic modality for the treatment of small brain lesions. Currently, two immobilization methods for that therapeutic modality are widely used: frame-based and frameless. The literature states that both methods are very accurate, but there is no consensus on the equivalence between them. In order to add information about those methods, residual positioning deviations of frame-based and frameless SRS were evaluated and compared. We randomly selected 50 cases of SRS performed in a radiotherapy clinic. That sample represents two groups depending on the clinical indication and lesion volume: 25 frame-based SRS and 25 frameless SRS. Data were collected of each case according to the planning with 6 degrees of freedom. The conventional protocol for frame-based SRS does not make use of IGRT. Therefore, for measures relating to the frame-based SRS a reflective spheres holder was used as an extra accessory. The systematic and random errors of those methods were calculated, assuming a Gaussian distribution confirmed by the Shapiro-Wilk normality test (p < 0.01). The difference between frame-based and frameless SRS systematic errors does not exceed 0.2 mm for translational displacements and 0.2° for rotational displacements. The frameless method has smaller random errors than frame-based in the lateral and vertical translations. The difference in the random errors is smaller than 0.45 mm (translational displacements) and 0.3° (rotational displacements). The Student’s t-test did not identify significant difference for any of the samples in question (p > 0.05), therefore, for this study, the methods of immobilization can be considered equivalent.

Reconstruction of space-dependent potential and/or damping coefficients in the wave equation

In this paper, nonlinear reconstructions of the space-dependent potential and/or damping coefficients in the wave equation from Cauchy data boundary measurements of the displacement and the flux tension are investigated. This is a very interesting and challenging nonlinear inverse coefficient problem with important applications in wave propagation phenomena. The uniqueness and stability results that are revised and in some cases proved demonstrate an advancement in understanding the stability of the inverse coefficient problems. However, in practice, the inverse coefficient identification problems under investigation are still ill-posed since small random errors in the input data cause large errors in the output solution. In order to stabilize the solution we employ the nonlinear Tikhonov regularization method. Numerical reconstructions performed for the first time are presented and discussed to illustrate the accuracy and stability of the numerical solutions under finite difference mesh refinement and noise in the measured data.

Design of robust high-order superdirectivity for circular arrays with sensor gain and phase errors

Though the high-order superdirectivity theory proposed in recent years is attractive, it is hard to implement in practice due to its poor robustness to small random array errors. Hence, in this paper, we present two robust designs of high-order superdirectivity for circular arrays with gain and phase errors. Firstly, we study on the sensitivity function of the high-order superdirectivity and give an alternative solution for a robust superdirective beamformer based on sensitivity function constraint. This method could achieve an arbitrary compromise between directivity and robustness, so it is more flexible and applicable than the existing higher-order truncation method. Although it does not improve on computational complexity or performance with respect to the second-order cone programming obviously, it could lay the foundation for the following robust design method. Then, considering the fact that different eigenbeams correspond to different eigenvalues, we study the method of diagonal loading with variable factors in detail, and further improve the performance of the former sensitivity function constrained method by loading variable factors to different eigenbeams, which results in better performance and greater flexibility in making a compromise. We also show that this proposed loading variable factors method can achieve an equivalent result to the higher-order truncation method by setting proper factors. Simulation results demonstrate the robustness and effectiveness of the above two methods, especially the performance improvement of the loading variable factors method.

Recommendations for diagnosing effective radiative forcing from climate models for CMIP6

AbstractThe usefulness of previous Coupled Model Intercomparison Project (CMIP) exercises has been hampered by a lack of radiative forcing information. This has made it difficult to understand reasons for differences between model responses. Effective radiative forcing (ERF) is easier to diagnose than traditional radiative forcing in global climate models (GCMs) and is more representative of the eventual temperature response. Here we examine the different methods of computing ERF in two GCMs. We find that ERF computed from a fixed sea surface temperature (SST) method (ERF_fSST) has much more certainty than regression based methods. Thirty year integrations are sufficient to reduce the 5–95% confidence interval in global ERF_fSST to 0.1 W m−2. For 2xCO2 ERF, 30 year integrations are needed to ensure that the signal is larger than the local confidence interval over more than 90% of the globe. Within the ERF_fSST method there are various options for prescribing SSTs and sea ice. We explore these and find that ERF is only weakly dependent on the methodological choices. Prescribing the monthly averaged seasonally varying model's preindustrial climatology is recommended for its smaller random error and easier implementation. As part of CMIP6, the Radiative Forcing Model Intercomparison Project (RFMIP) asks models to conduct 30 year ERF_fSST experiments using the model's own preindustrial climatology of SST and sea ice. The Aerosol and Chemistry Model Intercomparison Project (AerChemMIP) will also mainly use this approach. We propose this as a standard method for diagnosing ERF and recommend that it be used across the climate modeling community to aid future comparisons.

P value interpretations and considerations

Application and interpretation of statistical evaluation of relationships is a necessary element in biomedical research. Statistical analyses rely on P value to demonstrate relationships. The traditional level of significance, P<0.05, can be negatively impacted by small sample size, bias, and random error, and has evolved to include interpretation of statistical trends, correction factors for multiple analyses, and acceptance of statistical significance for P>0.05 for complex relationships such as effect modification.