Search

Breast cancer (BC) is a prominent cause of female mortality on a global scale. Recently, there has been growing interest in utilizing blood and tissue-based biomarkers to detect and diagnose BC, as this method offers a non-invasive approach. To improve the classification and prediction of BC using large biomarker datasets, several machine-learning techniques have been proposed. In this paper, we present a multi-stage approach that consists of computing new features and then sorting them into an input image for the ResNet50 neural network. The method involves transforming the original values into normalized values based on their membership in the Gaussian distribution of healthy and BC samples of each feature. To test the effectiveness of our proposed approach, we employed the Coimbra and Wisconsin datasets. The results demonstrate efficient performance improvement, with an accuracy of 100% and 100% using the Coimbra and Wisconsin datasets, respectively. Furthermore, the comparison with existing literature validates the reliability and effectiveness of our methodology, where the normalized value can reduce the misclassified samples of ML techniques because of its generality., (© 2024. The Author(s).)

We introduce a groundbreaking approach: the minimum free energy-based Gaussian Self-Benchmarking (MFE-GSB) framework, designed to combat the myriad of biases inherent in RNA-seq data. Central to our methodology is the MFE concept, facilitating the adoption of a Gaussian distribution model tailored to effectively mitigate all co-existing biases within a k-mer counting scheme. The MFE-GSB framework operates on a sophisticated dual-model system, juxtaposing modeling data of uniform k-mer distribution against the real, observed sequencing data characterized by nonuniform k-mer distributions. The framework applies a Gaussian function, guided by the predetermined parameters-mean and SD-derived from modeling data, to fit unknown sequencing data. This dual comparison allows for the accurate prediction of k-mer abundances across MFE categories, enabling simultaneous correction of biases at the single k-mer level. Through validation with both engineered RNA constructs and human tissue RNA samples, its wide-ranging efficacy and applicability are demonstrated., (© The Author(s) 2024. Published by Oxford University Press.)

Background: Some voxels may alter the tractography results due to unintentional alteration of noises and other unwanted factors., Objective: This study aimed to investigate the effect of local phase features on tractography results providing data are mixed by a Gaussian or random distribution noise., Material and Methods: In this simulation study, a mask was firstly designed based on the local phase features to decrease false-negative and -positive tractography results. The local phase features are calculated according to the local structures of images, which can be zero-dimensional, meaning just one point (equivalent to noise in tractography algorithm), a line (equivalent to a simple fiber), or an edge (equivalent to structures more complex than a simple fiber). A digital phantom evaluated the feasibility current model with the maximum complexities of configurations in fibers, including crossing fibers. In this paper, the diffusion images were mixed separately by a Gaussian or random distribution noise in 2 forms a zero-mean noise and a noise with a mean of data., Results: The local mask eliminates the pixels of unfitted values with the main structures of images, due to noise or other interferer factors., Conclusion: The local phase features of diffusion images are an innovative solution to determine principal diffusion directions., Competing Interests: None, (Copyright: © Journal of Biomedical Physics and Engineering.)

Equilibrium density fluctuations at the molecular level produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these probabilities should follow a Gaussian distribution. Computer simulations confirmed this prediction across various liquid models if the size of the observation volume is not large. The reversible work required to create a cavity and the chance of finding no molecules in a fixed observation volume are directly correlated. The Gaussian formula for the latter probability is scrutinized to derive the changes in enthalpy and entropy, which arise from the cavity creation. The reversible work of cavity creation has a purely entropic origin as a consequence of the solvent-excluded volume effect produced by the inaccessibility of a region of the configurational space. The consequent structural reorganization leads to a perfect compensation of enthalpy and entropy changes. Such results are coherent with those obtained from Lee in his direct statistical mechanical study.

Addressing the challenges posed by the complexity of the structure and the multitude of sensor types installed in space application fluid loop systems, this paper proposes a fault diagnosis method based on an improved D-S evidence theory. The method first employs the Gaussian affiliation function to convert the information acquired by sensors into BPA functions. Subsequently, it utilizes a pignistic probability transformation to convert the multiple subset focal elements into single subset focal elements. Finally, it comprehensively evaluates the credibility and uncertainty factors between evidences, introducing Bray-Curtis dissimilarity and belief entropy to achieve the fusion of conflicting evidence. The proposed method is initially validated on the classic Iris dataset, demonstrating its reliability. Furthermore, when applied to fault diagnosis in space application fluid circuit loop pumps, the results indicate that the method can effectively fuse multiple sensors and accurately identify faults.

Linear regression is one of the most used statistical techniques in neuroscience, including the study of the neuropathology of Alzheimer's disease (AD) dementia. However, the practical utility of this approach is often limited because dependent variables are often highly skewed and fail to meet the assumption of normality. Applying linear regression analyses to highly skewed datasets can generate imprecise results, which lead to erroneous estimates derived from statistical models. Furthermore, the presence of outliers can introduce unwanted bias, which affect estimates derived from linear regression models. Although a variety of data transformations can be utilized to mitigate these problems, these approaches are also associated with various caveats. By contrast, a robust regression approach does not impose distributional assumptions on data allowing for results to be interpreted in a similar manner to that derived using a linear regression analysis. Here, we demonstrate the utility of applying robust regression to the analysis of data derived from studies of human brain neurodegeneration where the error distribution of a dependent variable does not meet the assumption of normality. We show that the application of a robust regression approach to two independent published human clinical neuropathologic data sets provides reliable estimates of associations. We also demonstrate that results from a linear regression analysis can be biased if the dependent variable is significantly skewed, further indicating robust regression as a suitable alternate approach., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision., (Copyright © 2024 Malek-Ahmadi, Ginsberg, Alldred, Counts, Ikonomovic, Abrahamson, Perez and Mufson.)

Tiny objects in remote sensing images only have a few pixels, and the detection difficulty is much higher than that of regular objects. General object detectors lack effective extraction of tiny object features, and are sensitive to the Intersection-over-Union (IoU) calculation and the threshold setting in the prediction stage. Therefore, it is particularly important to design a tiny-object-specific detector that can avoid the above problems. This article proposes the network JSDNet by learning the geometric Jensen-Shannon (JS) divergence representation between Gaussian distributions. First, the Swin Transformer model is integrated into the feature extraction stage as the backbone to improve the feature extraction capability of JSDNet for tiny objects. Second, the anchor box and ground-truth are modeled as two two-dimensional (2D) Gaussian distributions, so that the tiny object is represented as a statistical distribution model. Then, in view of the sensitivity problem faced by the IoU calculation for tiny objects, the JSDM module is designed as a regression sub-network, and the geometric JS divergence between two Gaussian distributions is derived from the perspective of information geometry to guide the regression prediction of anchor boxes. Experiments on the AI-TOD and DOTA datasets show that JSDNet can achieve superior detection performance for tiny objects compared to state-of-the-art general object detectors., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Ni, Lin, Wang, Li, Liao and Li.)

In the field of intelligent vehicle technology, there is a high dependence on images captured under challenging conditions to develop robust perception algorithms. However, acquiring these images can be both time-consuming and dangerous. To address this issue, unpaired image-to-image translation models offer a solution by synthesizing samples of the desired domain, thus eliminating the reliance on ground truth supervision. However, the current methods predominantly focus on single projections rather than multiple solutions, not to mention controlling the direction of generation, which creates a scope for enhancement. In this study, we propose a generative adversarial network (GAN)-based model, which incorporates both a style encoder and a content encoder, specifically designed to extract relevant information from an image. Further, we employ a decoder to reconstruct an image using these encoded features, while ensuring that the generated output remains within a permissible range by applying a self-regression module to constrain the style latent space. By modifying the hyperparameters, we can generate controllable outputs with specific style codes. We evaluate the performance of our model by generating snow scenes on the Cityscapes and the EuroCity Persons datasets. The results reveal the effectiveness of our proposed methodology, thereby reinforcing the benefits of our approach in the ongoing evolution of intelligent vehicle technology.

Cavitation damage on a mercury target vessel for a pulsed spallation neutron source is induced by a proton beam injection in mercury. Cavitation damage is one of factors affecting the allowable beam power and the life time of a mercury target vessel. The prediction method of the cavitation damage using Monte Carlo simulations was proposed taking into account the uncertainties of the core position of cavitation bubbles and impact pressure distributions. The distribution of impact pressure attributed to individual cavitation bubble collapsing was assumed to be Gaussian distribution and the probability distribution of the maximum value of impact pressures was assumed to be three kinds of distributions: the delta function and Gaussian and Weibull distributions. Two parameters in equations describing the distribution of impact pressure were estimated using Bayesian optimization by comparing the distribution of the cavitation damage obtained from the experiment with the distribution of the accumulated plastic strain obtained from the simulation. Regardless of the distribution type, the estimated maximum impact pressure was 1.2-2.9 GPa and existed in the range of values predicted by the ratio of the diameter and depth of the pit. The estimated dispersion of the impact pressure distribution was 1.0-1.7 μm and corresponded to the diameter of major pits. In the distribution of the pits described by the accumulated plastic strain, which was assumed in three cases, the delta function and Gaussian and Weibull distributions, the Weibull distribution agreed well with the experimental results, particularly including relatively large pit size. Furthermore, the Weibull distribution reproduced the depth profile, i.e., pit shape, better than that using the delta function or Gaussian distribution. It can be said that the cavitation erosion phenomenon is predictable by adopting the Weibull distribution. This prediction method is expected to be applied to predict the cavitation damage in fluid equipment such as pumps and fluid parts.

Background and Aims: All fields have seen an increase in machine-learning techniques. To accurately evaluate the efficacy of novel modeling methods, it is necessary to conduct a critical evaluation of the utilized model metrics, such as sensitivity, specificity, and area under the receiver operator characteristic curve (AUROC). For commonly used model metrics, we proposed the use of analytically derived distributions (ADDs) and compared it with simulation-based approaches., Methods: A retrospective cohort study was conducted using the England National Health Services Heart Disease Prediction Cohort. Four machine learning models (XGBoost, Random Forest, Artificial Neural Network, and Adaptive Boost) were used. The distribution of the model metrics and covariate gain statistics were empirically derived using boot-strap simulation ( N  = 10,000). The ADDs were created from analytic formulas from the covariates to describe the distribution of the model metrics and compared with those of bootstrap simulation., Results: XGBoost had the most optimal model having the highest AUROC and the highest aggregate score considering six other model metrics. Based on the Anderson-Darling test, the distribution of the model metrics created from bootstrap did not significantly deviate from a normal distribution. The variance created from the ADD led to smaller SDs than those derived from bootstrap simulation, whereas the rest of the distribution remained not statistically significantly different., Conclusions: ADD allows for cross study comparison of model metrics, which is usually done with bootstrapping that rely on simulations, which cannot be replicated by the reader., Competing Interests: The authors declare no conflict of interest., (© 2023 The Authors. Health Science Reports published by Wiley Periodicals LLC.)

The purpose of this work was to investigate by Monte Carlo method the adjustment of photon beams delivered by the medical LINear ACcelerator (LINAC) Elekta Synergy MLCi2. This study presents an optimization of the Gaussian distribution parameters of the accelerated electrons before the target simulated by two Monte Carlo codes and for three beams. The photon (x-ray) beam is produced by the interaction of accelerated electrons with the LINAC target. The electrons are accelerated by a potential difference created between the anode and the cathode of the gun and directed towards the target. In the Monte Carlo simulation, it is necessary to setup the spectrum parameters of the generated electrons to simulate the x-ray dose distribution. In this study, we modeled the LINAC geometry for photon beams 18MV and 6MV in cases Flattened (FF) and Flattening-Filter-Free (FFF). The Monte Carlo simulations are based on G4Linac_MT and GATE codes. The results of the optimized configurations determined after more than 20 tests for each beam energy show a very good agreement with the experimental measurements for different irradiation fields for the depth (PDD) and lateral (Profile) dose distribution. In all Monte Carlo calculations performed in this study, the statistical uncertainty is less than 2%. The results were also in very good agreement in terms of γ -index analysis, for the 3%/3 mm and 2%/2 mm criteria., (© 2023 IOP Publishing Ltd.)

Evolutionary multitasking algorithms aim to solve several optimization tasks simultaneously, and they can improve the efficiency of various tasks evolution through the knowledge transfer between different optimization tasks. Evolutionary multitasking algorithms have been applied to various applications and achieved certain results. However, how to transfer knowledge between tasks is still a problem worthy of research. Aiming to improve the positive transfer between tasks and reduce the negative transfer, we propose a single-objective multitask optimization algorithm based on elite individual transfer, namely MSOET. In this paper, whether to execute knowledge transfer between tasks depends on a certain probability. Meanwhile, in order to enhance the effectiveness and the global search ability of the algorithm, the current population and the elite individual in the transfer population are further utilized as the learning sources to construct a Gaussian distribution model, and the offspring is generated by the Gaussian distribution model to achieve knowledge transfer between tasks. We compared the proposed MSOET with ten multitask optimization algorithms, and the experimental results verify the algorithm's excellent performance and strong robustness.

This paper designs a texture-hidden QR code to prevent the illegal copying of a QR code due to its lack of anti-counterfeiting ability. Combining random texture patterns and a refined QR code, the code is not only capable of regular coding but also has a strong anti-copying capability. Based on the proposed code, a quality assessment algorithm (MAF) and a dual feature detection algorithm (DFDA) are also proposed. The MAF is compared with several current algorithms without reference and achieves a 95% and 96% accuracy for blur type and blur degree, respectively. The DFDA is compared with various texture and corner methods and achieves an accuracy, precision, and recall of up to 100%, and also performs well on attacked datasets with reduction and cut. Experiments on self-built datasets show that the code designed in this paper has excellent feasibility and anti-counterfeiting performance.

To investigate the mechanisms of the adhesion (self-bonding) strength ( σ ) development during the early stages of self-healing of polymer-polymer interfaces and fracture thereof, it is useful to operate not only with the average σ value but with the σ distribution as well. The latter has been shown to obey Weibull's statistics for such interfaces. However, whether it can also follow the most widely used normal (Gaussian) distribution is currently unclear. Moreover, a more complicated self-healing case, when the σ development at an initially amorphous interface is accompanied by its crystallization, has not been investigated yet in this respect. In order to address these two important issues, 10 pairs of amorphous poly(ethylene terephthalate) (PET) samples were kept in contact for various periods of time from 5 min to 15 h at a temperature ( T ) of 94 °C (preserving the amorphous state) or T = 150 °C (giving rise to cold crystallization), or both T s. Thereafter, the as-formed amorphous and semi-crystalline PET-PET auto-adhesive joints were shear fractured in tension at ambient temperature. For the first time, the statistical distributions of a number of the measured σ data sets were analyzed and discussed using both Weibull's and the Gaussian model, including several normality tests.

Multi-source information fusion is widely used because of its similarity to practical engineering situations. With the development of science and technology, the sources of information collected under engineering projects and scientific research are more diverse. To extract helpful information from multi-source information, in this paper, we propose a multi-source information fusion method based on the Dempster-Shafer (DS) evidence theory with the negation of reconstructed basic probability assignments (nrBPA). To determine the initial basic probability assignment (BPA), the Gaussian distribution BPA functions with padding terms are used. After that, nrBPAs are determined by two processes, reassigning the high blur degree BPA and transforming them into the form of negation. In addition, evidence of preliminary fusion is obtained using the entropy weight method based on the improved belief entropy of nrBPAs. The final fusion results are calculated from the preliminary fused evidence through the Dempster's combination rule. In the experimental section, the UCI iris data set and the wine data set are used for validating the arithmetic processes of the proposed method. In the comparative analysis, the effectiveness of the BPA determination using a padded Gaussian function is verified by discussing the classification task with the iris data set. Subsequently, the comparison with other methods using the cross-validation method proves that the proposed method is robust. Notably, the classification accuracy of the iris data set using the proposed method can reach an accuracy of 97.04%, which is higher than many other methods.

Polymer nanocomposites have found wide acceptance in research applications as pressure sensors under the designation of force-sensing resistors (FSRs). However, given the random dispersion of conductive nanoparticles in the polymer matrix, the sensitivity of FSRs notably differs from one specimen to another; this condition has precluded the use of FSRs in industrial applications that require large part-to-part repeatability. Six Sigma methodology provides a standard framework to reduce the process variability regarding a critical variable. The Six Sigma core is the DMAIC cycle (Define, Measure, Analyze, Improve, and Control). In this study, we have deployed the DMAIC cycle to reduce the process variability of sensor sensitivity, where sensitivity was defined by the rate of change in the output voltage in response to the applied force. It was found that sensor sensitivity could be trimmed by changing their input (driving) voltage. The whole process comprised: characterization of FSR sensitivity, followed by physical modeling that let us identify the underlying physics of FSR variability, and ultimately, a mechanism to reduce it; this process let us enhance the sensors' part-to-part repeatability from an industrial standpoint. Two mechanisms were explored to reduce the variability in FSR sensitivity. (i) It was found that the output voltage at null force can be used to discard noncompliant sensors that exhibit either too high or too low sensitivity; this observation is a novel contribution from this research. (ii) An alternative method was also proposed and validated that let us trim the sensitivity of FSRs by means of changing the input voltage. This study was carried out from 64 specimens of Interlink FSR402 sensors.

The pyrolite model, which can reproduce the upper-mantle seismic velocity and density profiles, was suggested to have significantly lower velocities and density than seismic models in the lower mantle transition zone (MTZ). This argument has been taken as mineral-physics evidence for a compositionally distinct lower MTZ. However, previous studies only estimated the pyrolite velocities and density along a one-dimension (1D) geotherm and never considered the effect of lateral temperature heterogeneity. Because the majorite-perovskite-akimotoite triple point is close to the normal mantle geotherm in the lower MTZ, the lateral low-temperature anomaly can result in the presence of a significant fraction of akimotoite in pyrolitic lower MTZ. In this study, we reported the elastic properties of Fe-bearing akimotoite based on first-principles calculations. Combining with literature data, we found that the seismic velocities and density of the pyrolite model can match well those in the lower MTZ when the lateral temperature heterogeneity is modeled by a Gaussian distribution with a standard deviation of ∼100 K and an average temperature of dozens of K higher than the triple point of MgSiO 3 . We suggest that a harzburgite-rich lower MTZ is not required and the whole mantle convection is expected to be more favorable globally., Competing Interests: The authors declare that they have no conflicts of interest in this work., (© 2022 The Authors.)

Background: Inaccuracy in estimating reference intervals (RIs) is a problem with small sample sizes., Objectives: This study aimed to identify the most accurate statistical methods to estimate RIs based on sample size and population distribution shape. We also studied the accuracy of sample frequency distribution histograms to retrieve the original population distribution and compared strategies based on the histogram and goodness-of-fit test., Methods: The statistical methods that best enhanced accuracy were determined for various sample sizes (n = 20-60) and population distributions (Gaussian, log-normal, and left-skewed) were determined by repeated-measures ANOVA and posthoc analyses. Frequency distribution histograms were built from 900 samples of five different sizes randomly extracted from six simulated populations. Three reviewers classified the population distributions from visual assessments of a sample histogram, and the classification error rate was calculated. RI accuracy was compared among the strategies based on the histograms and goodness-of-fit tests., Results: The parametric, nonparametric, and robust methods enhanced lower reference limit estimation accuracy for Gaussian, log-normal, and left-skewed distributions, respectively. The parametric, nonparametric bootstrap, and nonparametric methods enhanced the upper limit estimation accuracy for Gaussian, log-normal, and left-skewed distributions, respectively. Regardless of sample size, sample histogram assessments properly classified the original population distribution 71% to 93.9% of the time, depending on the reviewers. In this study, the strategy based on histograms assessed by the statistician was significantly more precise and accurate than the strategy based on the goodness-of-fit test (P < 0.001)., Conclusions: A strategy based on histograms might enhance the accuracy of RI estimations. However, relevant inter-reviewer variations in histogram interpretation were detected. Factors affecting inter-reviewer variations should be further explored., (© 2021 American Society for Veterinary Clinical Pathology.)

Purpose: A high-precision rotated elliptical beam profiling method based on pixel ion chamber is proposed in this paper. This method aims to improve the accuracy by modeling the transverse profile of rotated beam as an ellipse with additional correlation coefficient and eliminating the fitting error due to the volume averaging effect of pixel ion chamber., Methods: In pencil beam scanning (PBS) proton therapy systems, the transverse beam profile model is generally represented as a standard Gaussian distribution. Considering the elliptical spots, two-dimensional (2D) joint Gaussian distribution characterized with the correlation coefficient ρ is adopted in this study. Gaussian-type particle distribution with white noise was generated and processed in MATLAB to simulate the secondary particle collection in the pixel ion chamber. The simulated pixel ion chamber is a commercially available ion chamber which consists of 12 × 12 small square pixels (3.75 × 3.75 mm 2 ) with a 0.05 mm interval. The simulated signals were preprocessed by filtering with the noise threshold and extracting the maximum simply connected domain (MSCD) of the signal. Then, five geometric parameters that identify the transverse beam profiles were fitted under different signal-to-noise ratio (SNR) conditions: the center of the beam (x 0 , y 0 ), the spot size (σ major , σ minor ), and the rotation angle θ formed between the major axes of elliptical spot and the x axes of the ion chamber. First, the simulated signals were preprocessed by filtering with the noise threshold and extracting the MSCD of the signal. Second, a rectification curve of systematic error in fitted spot size versus the prescribed spot size was used to predict the systematic error due to the volume averaging effect. Finally, the effects of fitting errors on therapeutic dose were evaluated in terms of gamma index and relative dose difference., Results: When the SNR is not less than 20 dB, the relative fitting error of spot size and the absolute fitting error of angle θ are less than 1% and 6.1°, respectively. The fitting error of beam center increases with spot size and will not exceed 0.22 mm when spot size reaches up to 12 mm. At a SNR equal to 20 dB, neither cold nor hot spots were presented in dose distribution calculated with the fitted spot parameters., Conclusion: The improved Gaussian fitting algorithm performs well when SNR is not less than 20 dB. This method can effectively distinguish the nominal beam and rotated elliptical beam. An ideal systematic error curve can be predicted and used to correct the fitted spot size, thus eliminating the systematic error due to the volume averaging effect of the pixel ion chamber. The fitting error of spot size cannot be fully corrected, but it is negligible and shows little effect on the overall therapeutic dose., (© 2021 American Association of Physicists in Medicine.)

Ultra-wideband (UWB) sensors have been widely applied to indoor positioning. The indoor positioning of UWB sensors usually refers to the positioning of the mobile node that interacts with the anchors through radio for calculating the distance between the mobile node and each of the surrounding anchors. The positioning accuracy of the mobile node is affected by the installation positions of surrounding anchors. A mathematical model was proposed in this paper to respectively analyze the mobile node's 2-dimensional (2D) and 3-dimensional (3D) positioning errors. The factors influencing the mobile node's positioning errors were explored through the mathematical models. The best installation positions of surrounding anchors were obtained based on the mathematical models. The mobile node's 2D and 3D positioning errors were reduced based on the anchor positions derived from the mathematical model. Both computer simulations and practical experiments were implemented to justify the results obtained in the mathematical models.

Dielectric spectroscopy of the human blood is a powerful and convenient non-invasive testing technique that can be used to diagnose diseases such as diabetes and leukemia. One needs to consider rigorous experimental procedures and mathematical models to make the results of this type of test comparable. The present paper will discuss previously published results to further investigate the statistical modeling of the dielectric properties of human blood. The analysis shows that previously published results were related to Modified Weibull (MW) distributions of relaxation times, not Gaussian distributions, as reported. This re-analysis prevents the ill definition of fitting parameters, making sure they present physically justifiable values. Besides, for fluids presenting a Modified Weibull distribution of relaxation times, novel exact and closed-form expressions for the real and imaginary parts of complex permittivities were obtained in terms of generalized hypergeometric functions. Also, a high accuracy approximation was built for the imaginary part of the complex permittivity, creating an easy-to-use alternative expression for practitioners. The new results are used to fit experimental results for human blood, showing that more robust estimators are built for the parameters involved, which can be used as thresholds to classify the dielectric behavior of blood as normal (healthy) or anomalous (sick)., Competing Interests: The authors declare no conflict of interest., (© 2021 The Authors.)

The highly infectious COVID-19 critically affected the world that has stuck millions of citizens in their homes to avoid possible spreading of the disease. Researchers in different fields are continually working to develop vaccines and prevention strategies. However, an accurate forecast of the outbreak can help control the pandemic until a vaccine is available. Several machine learning and deep learning-based approaches are available to forecast the confirmed cases, but they lack the optimized temporal component and nonlinearity. To enhance the current forecasting frameworks' capability, we proposed optimized long short-term memory networks (LSTM) to forecast COVID-19 cases and reduce mean absolute error. For the optimization of LSTM, we applied bat algorithm. Furthermore, to tackle the premature convergence and local minima problem of BA, we proposed an enhanced variant of BA. The proposed version utilized Gaussian adaptive inertia weight to control the individual velocity in the entire swarm. In addition, we substitute random walk with the Gaussian walk to observe the local search mechanism. The proposed LSTM examines the personal best solution with the swarm's local best and preserves the optimal solution by combining the Gaussian walk. To evaluate the optimized LSTM, we compared it with the non-optimal version of LSTM, recurrent neural network, gated recurrent units, and other recent state-of-the-art algorithms. The experimental results prove the superiority of the optimized LSTM over other recent algorithms by obtaining 99.52 % accuracy., Competing Interests: Conflict of interestThe authors declare that they have no conflict of interest., (© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021.)

The vote shares by party on a given subdivision of a territory form a vector called composition (mathematically, a vector belonging to a simplex). It is interesting to model these shares and study the impact of the characteristics of the territorial units on the outcome of the elections. In the political economy literature, few regression models are adapted to the case of more than two political parties. In the statistical literature, there are regression models adapted to share vectors including Compositional Data (CoDa) models, but also Dirichlet models, and others. Our goal is to discuss and illustrate the use CoDa regression models for political economy models for more than two parties. The models are fitted on French electoral data of the 2015 departmental elections., Competing Interests: No potential conflict of interest was reported by the authors., (© 2020 Informa UK Limited, trading as Taylor & Francis Group.)

A single-matrix hydrophobic ceramic membrane (HCM) was prepared via gel-casting and membrane grafting. Fly ash cenospheres and 1H,1H,2H,2H-perfluorooctyl trichlorosilane were used as the single-matrix material. The results showed that when the sintering temperature was 1300℃, the porosity was 75.56 %, and flexural strength was 11.1 MPa; this means that the material meets the requirements for mechanical properties. After grafting 1H,1H,2H,2H-perfluorooctane trichlorosilane, the Si-CH 3 peak increased and the Si-OH peak was weaker. Also, the contact angle of the droplet increased from 56° to 126°, and this indicates that the droplet was successfully chemically adsorbed to the surface of the ceramic membrane. The results of computational fluid dynamics simulation show that a gaussian spherical wall greatly improved the permeation flux of foamed ceramic membranes, and the permeation flux of the microchannel increased by 26.5 %∼76.2 % at the same transmembrane pressure. Pure water permeation flux and heavy metal adsorption experiments shows excellent high permeation flux and satisfactory heavy metal adsorption performance of HCM. From the perspective of membrane cost, HCM is suitable to be promoted. In summary, HCM has the potential for commercial application., (Copyright © 2020 Elsevier B.V. All rights reserved.)

A large variety of methods exist to estimate brain coupling in the frequency domain from electrophysiological data measured, e.g., by EEG and MEG. Those data are to reasonable approximation, though certainly not perfectly, Gaussian distributed. This work is based on the well-known fact that for Gaussian distributed data, the cross-spectrum completely determines all statistical properties. In particular, for an infinite number of data, all normalized coupling measures at a given frequency are a function of complex coherency. However, it is largely unknown what the functional relations are. We here present those functional relations for six different measures: the weighted phase lag index, the phase lag index, the absolute value and imaginary part of the phase locking value (PLV), power envelope correlation, and power envelope correlation with correction for artifacts of volume conduction. With the exception of PLV, the final results are simple closed form formulas. In an excursion we also discuss differences between short time Fourier transformation and Hilbert transformation for estimations in the frequency domain. We tested in simulations of linear and non-linear dynamical systems and for empirical resting state EEG on sensor level to what extent a model, namely the respective function of coherency, can explain the observed couplings. For empirical data we found that for measures of phase-phase coupling deviations from the model are in general minor, while power envelope correlations systematically deviate from the model for all frequencies. For power envelope correlation with correction for artifacts of volume conduction the model cannot explain the observed couplings at all. We also analyzed power envelope correlation as a function of time and frequency in an event related experiment using a stroop reaction task and found significant event related deviations mostly in the alpha range., (Copyright © 2020 Nolte, Galindo-Leon, Li, Liu and Engel.)

The effects of an epitaxial layer on the rectifying behavior of n -GaAs/Ti/Au/Si:Al 0.33 Ga 0.67 As diodes have been examined through the inhomogeneity model on n -GaAs substrate with orientation. The electrical properties and conduction mechanism of these materials were understood through theoretical models. The inhomogeneity model was used to electrical behavior of these diodes was explained. The barrier height inhomogeneity model reveals a 13% and 15% barrier height inhomogeneity in N1 and N2 Schottky diodes, respectively. The ideal thermionic emission behavior increases the ideality factors and reduces barrier heights. Within the entire temperature range, the effective Schottky barrier for a thin epitaxial layer was higher. Such results depicted the presence of defects in the thick layer, which decreased the barrier height and ultimately degraded diode performance. The thermionic emission theory along with Gaussian distribution of barrier heights is explained by the temperature dependence of the forward bias current-voltage-temperature (I-V-T) features.+ -GaAs substrate with orientation. The electrical properties and conduction mechanism of these materials were understood through theoretical models. The inhomogeneity model was used to electrical behavior of these diodes was explained. The barrier height inhomogeneity model reveals a 13% and 15% barrier height inhomogeneity in N1 and N2 Schottky diodes, respectively. The ideal thermionic emission behavior increases the ideality factors and reduces barrier heights. Within the entire temperature range, the effective Schottky barrier for a thin epitaxial layer was higher. Such results depicted the presence of defects in the thick layer, which decreased the barrier height and ultimately degraded diode performance. The thermionic emission theory along with Gaussian distribution of barrier heights is explained by the temperature dependence of the forward bias current-voltage-temperature (I-V-T) features., (© 2020 The Author.)

Among all the methods of extracting randomness, quantum random number generators are promising for their genuine randomness. However, existing quantum random number generator schemes aim at generating sequences with a uniform distribution, which may not meet the requirements of specific applications such as a continuous-variable quantum key distribution system. In this paper, we demonstrate a practical quantum random number generation scheme directly generating Gaussian distributed random sequences based on measuring vacuum shot noise. Particularly, the impact of the sampling device in the practical system is analyzed. Furthermore, a related post-processing method, which maintains the fine distribution and autocorrelation properties of raw data, is exploited to extend the precision of generated Gaussian distributed random numbers to over 20 bits, making the sequences possible to be utilized by the following system with requiring high precision numbers. Finally, the results of normality and randomness tests prove that the generated sequences satisfy Gaussian distribution and can pass the randomness testing well.

This paper presents a new proposal to generate optimal pseudorandom numbers with Gaussian distribution. The generator is especially designed for low-cost hardware implementation, although the software version is also considered. For this reason, Linear Feedback Shift Registers in conjunction with cyclic rotations are employed. The proposal presents a low implementation cost and overcomes the limitations of the previous Gaussian generators based on linear feedback shift registers by means of a less complex algorithm to find optimal configurations. As a consequence, it turns into a really usable generator. Moreover, a further improvement, based on the simulated annealing algorithm, is applied in order for the random values to be better adjusted to the normal distribution.

Birthweight is strongly associated with infant mortality and is a major determinant of infant survival. Several factors such as maternal, environmental, clinical, and social factors influence birthweight, and these vary geographically, including across low, middle, and economically advanced countries. The aim of the study was to investigate the geographical modification of the effect of oxides of nitrogen exposure on birthweight adjusted for clinical and socio-demographic factors. Data for the study was obtained from the Mother and Child in the Environment birth cohort study in Durban, South Africa. Pregnant females were selected from public sector antenatal clinics in low socioeconomic neighborhoods. Land use regression models were used to determine household level antenatal exposure to oxides of nitrogen (NOx). Six hundred and seventy-seven births were analysed, using the geoadditive model with Gaussian distribution and identity link function. The newborns in the cohort had a mean birthweight of 3106.5 g (standard deviation (SD): 538.2 g and the maternal mean age was 26.1 years (SD: 5.7). A spatially modified NOx exposure-related effect on birthweight was found across two geographic regions in Durban. Prenatal exposure to NOx was also found to have a non-linear effect on the birthweight of infants. The study suggested that incorporating spatial variability is important to understand and design appropriate policies to reduce air pollution in order to prevent risks associated with birthweight., (Copyright © 2020 Elsevier Inc. All rights reserved.)

Identifying stable gene markers at an individual level can help to understand the genetic mechanisms of each individual patient and accomplish personalized medicine. In this paper, we propose an efficient framework to identify sample-specific markers. Gene expression data first is transformed to a corresponding likelihood matrix to alleviate inherent noise besides adding population information to each sample. Then those significantly differential genes or gene pairs are further mapped to a STRING network for analysis by assuming that the likelihood of each gene or gene pairs in the control group follows a Gaussian distribution. The proposed method is applied to three benchmark datasets including lung adenocarcinoma, kidney renal clear cell carcinoma, and uterine corpus endometrial carcinoma. It is found that disease gene markers identified by the proposed methods outperform the previous sample-specific network (SSN) method in both subtyping and survival analysis. Furthermore, we exploit the application of the subtype markers in following drug selection. The difference of the enriched drug set may reflect some underlying mechanisms of the subtypes and shed light on selecting appropriate drugs for each cancer subtype., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

Dark target detection is important for engineering applications but the existing methods do not consider the imaging environment of dark targets, such as the adjacency effect. The adjacency effect will affect the quantitative applications of remote sensing, especially for high contrast images and images with ever-increasing resolution. Further, most studies have focused on how to eliminate the adjacency effect and there is almost no research about the application of the adjacency effect. However, the adjacency effect leads to some unique characteristics for the dark target surrounded by a bright background. This paper utilizes these characteristics to assist in the detection of the dark object, and the low-high threshold detection strategy and the adaptive threshold selection method under the assumption of Gaussian distribution are designed. Meanwhile, preliminary case experiments are carried out on the crack detection of concrete slope protection. Finally, the experiment results show that it is feasible to utilize the adjacency effect for dark target detection.

Background: According to the ASVCP and other guidelines, samples should comprise at least 120 individuals for reference interval (RI) estimation. Unfortunately, this minimum sample size is difficult to achieve in veterinary medicine. Several statistical methods are described to determine RIs from small sample sizes, but it is unclear which method provides the best accuracy., Objectives: This study aimed to compare statistical strategies for estimating RIs and determine which strategy best enhances accuracy when the sample size is between 20 and 120., Methods: Different sample size groups (n = 120, 100, 80, 60, 40, and 20) were randomly selected 50 times from simulated Gaussian, log-normal, and left-skewed populations of 5000 total values. RIs were calculated using seven different statistical strategies comprising robust, parametric, nonparametric, and bootstrap methods, alone or in combination. RI accuracy was compared among these strategies at each sample size. The strategy that was significantly more accurate than others in the largest number of comparisons was considered as the one that best-enhanced RI accuracy., Results: The strategies that best-enhanced RI accuracy included using the parametric method when the Shapiro-Wilk P > 0.2 and, otherwise, using the nonparametric method to determine the upper and lower RI limits when there were between 60 and 100 reference individuals, and finding the lower RI limit when there were 40 reference individuals. The Box-Cox transformation parametric method best-enhanced RI accuracy of the upper RI limit when there were 40 reference individuals, and the nonparametric method best-enhanced RI accuracy of both RI limits when there were 20 reference individuals., Conclusions: Using the parametric method when the Shapiro-Wilk P > 0.2, and the nonparametric method in other instances, will likely enhance RI accuracy when there are between 40 and 100 reference individuals. For smaller samples, the nonparametric method might be preferred., (© 2019 American Society for Veterinary Clinical Pathology.)

Background: Head movement interferences are a common problem during prolonged dynamic brain electrical impedance tomography (EIT) clinical monitoring. Head movement interferences mainly originate from body movements of patients and nursing procedures performed by medical staff, etc. These body movements will lead to variation in boundary voltage signals, which affects image reconstruction., Methods: This study employed a data preprocessing method based on wavelet decomposition to inhibit head movement interferences in brain EIT data. Mixed Gaussian models were applied to describe the distribution characteristics of brain EIT data. We identified head movement signal through the differences in distribution characteristics of corresponding wavelet decomposition coefficients between head movement artifacts and normal signals, and then managed the contaminated data with improved on-line wavelet processing methods., Results: To validate the efficacy of the method, simulated signal experiments and human data experiments were performed. In the simulation experiment, the simulated movement artifact was significantly reduced and data quality was improved with indicators' increase in PRD and correlation coefficient. Human data experiments demonstrated that this method effectively suppressed head movement in signals and reduce artifacts resulting from head movement artifacts in images., Conclusion: In this paper, we proposed an on-line strategy to manage the head movement interferences from the brain EIT data based on the distribution characteristics of wavelet coefficients. Our strategy is capable of reducing the movement interference in the data and improving the reconstructed images. This work would improve the clinical practicability of brain EIT and contribute to its further promotion.

Developing a holistic understanding of the ecosystem impacts of global change requires methods that can quantify the interactions among multiple response variables. One approach is to generate high dimensional spaces, or hypervolumes, to answer ecological questions in a multivariate context. A range of statistical methods has been applied to construct hypervolumes but have not yet been applied in the context of ecological data sets with spatial or temporal structure, for example, where the data are nested or demonstrate temporal autocorrelation. We outline an approach to account for data structure in quantifying hypervolumes based on the multivariate normal distribution by including random effects. Using simulated data, we show that failing to account for structure in data can lead to biased estimates of hypervolume properties in certain contexts. We then illustrate the utility of these "model-based hypervolumes" in providing new insights into a case study of afforestation effects on ecosystem properties where the data has a nested structure. We demonstrate that the model-based generalization allows hypervolumes to be applied to a wide range of ecological data sets and questions., (© 2019 The Authors. Ecology published by Wiley Periodicals, Inc. on behalf of Ecological Society of America.)

While membrane bioreactor (MBR) technology is generally considered as one of the most promising technologies for wastewater treatment and recovery, membrane fouling remains the major obstacle limiting its applications. Interfacial interactions, which critically determine adhesion process and membrane fouling, were investigated in this study. It was found that, natural membrane surface was of a Gaussian surface obeying Gaussian distribution. A Gaussian approach integrating Fourier transform technique, Gaussian distribution and spectrum method was deduced to simulate rough surface topography of membrane. Thereafter, surface element integral (SEI) method, together with composite Simpson rule and triangulation of Gaussian surface was proposed to calculate interfacial interactions. By using the unified method, quantification of interfacial interactions with a Gaussian membrane surface was realized for the first time to date. It was further found that, membrane surface topography had profound impacts on interfacial interactions and adhesive fouling in the MBR. The deduced method can be used to address impacts of various factors on interfacial interactions and adhesive fouling, posing in-depth thermodynamic insights into membrane fouling and pointing towards its widespread potential in fouling research in MBRs., (Copyright © 2018 Elsevier Inc. All rights reserved.)

The problem of the correlation of indolic molecules with special regard to melatonin and immune processes has been widely investigated. However, there are only few studies focusing on circadian variation of peripheral blood leukocytes. The purpose of this study is thus to understand the influence of MLT on leukocyte populations and its correlation with leukocyte distribution. This is accomplished by administrating placebo and melatonin to different groups of individuals and by performing a biophysical Gaussian analysis on the number of leukocytes by means of a comparison of their p.m. vs. a.m. variations under the effect of placebo and of melatonin and via a comparison in the morning between leukocytes population of untreated group and MLT group. It is shown that: (a) melatonin has the effect of narrowing the normal distribution concentrating most of the individuals towards the mean value of the observed variation of leukocytes population and (b) the individuals who have not received either placebo or supplement have a leukocyte population that follows a normal distribution. These results confirm the crucial role played by melatonin, as the most representative of indolic amide in biological systems, in the circadian peripheral variations of leukocyte numbers because counts of white blood cells are essential in medical urgency and differential diagnosis situations. Hence, further studies are suggested to account for these physiological variations and for the evaluation of the full involvement of the action of MLT on leukocytes distribution.

Representative elementary volume (REV) is important to characterize dense nonaqueous phase liquids (DNAPLs) during surfactant-Enhanced aquifer remediation (SEAR) period. To investigate the REVs of DNAPL in remediation, a perchloroethylene (PCE) SEAR experiment is conducted in a two dimensional (2D) heterogeneous translucent porous media. Light transmission techniques are used to quantify PCE saturation (S oil ) and PCE-water interfacial area (A OW ). Afterward, corresponding REVs are estimated using a criterion of relative gradient error (ε g i -REV size closely follows a Gaussian distribution in 0.0mm-11.0mm. Simultaneously, the frequency of minimum A oil -REV size is close to a Gaussian distribution in 2.0mm-9.0mm and appears a peak value in 13.0mm-14.0mm. As SEAR experiment proceeds, both the shapes of frequency and cumulative frequency of REV sizes are changed. At the end of SEAR experiment, the frequency of minimum S OW -REV size is close to a Gaussian distribution in 2.0mm-9.0mm and appears a peak value in 13.0mm-14.0mm. As SEAR experiment proceeds, both the shapes of frequency and cumulative frequency of REV sizes are changed. At the end of SEAR experiment, the frequency of minimum S oil -REV and minimum A OW -REV size tend to Gaussian distributions in 0.0mm-6.0mm and 0.0mm-9.0mm, respectively, which suggest both minimum S oil -REV size and minimum A OW -REV size show decreasing tendency. Continuous quantification of the REVs of DNAPL is realized in this study to reveal the change of REVs influenced by surface active agent. The finding has important significance on improving our understanding of the characteristics of DNAPL in SEAR process, simulating DNAPL remediation and designing appropriate remediation scheme with high-resolution., (Copyright © 2018 Elsevier B.V. All rights reserved.)

Imitation learning through self-exploration is essential in developing sensorimotor skills. Most developmental theories emphasize that social interactions, especially understanding of observed actions, could be first achieved through imitation, yet the discussion on the origin of primitive imitative abilities is often neglected, referring instead to the possibility of its innateness. This paper presents a developmental model of imitation learning based on the hypothesis that humanoid robot acquires imitative abilities as induced by sensorimotor associative learning through self-exploration. In designing such learning system, several key issues will be addressed: automatic segmentation of the observed actions into motion primitives using raw images acquired from the camera without requiring any kinematic model; incremental learning of spatio-temporal motion sequences to dynamically generates a topological structure in a self-stabilizing manner; organization of the learned data for easy and efficient retrieval using a dynamic associative memory; and utilizing segmented motion primitives to generate complex behavior by the combining these motion primitives. In our experiment, the self-posture is acquired through observing the image of its own body posture while performing the action in front of a mirror through body babbling. The complete architecture was evaluated by simulation and real robot experiments performed on DARwIn-OP humanoid robot.

Background: The equine m. gluteus medius (GM) is the largest muscle of the horse, its main movement function is the extension of the hip joint. The objective of the present study was to measure equine GM activity in three adjacent locations on GM during walk and trot on a treadmill, in order to document potential differences. Fourteen Haflinger mares were measured using surface electromyography and kinematic markers to identify the motion cycles on three occasions over 16 weeks. The electrodes were placed on left and right gluteus medius muscle over the middle of its widest part and 5 cm lateral and medial of it. For data processing, electrical activity was normalised to its maximum value and timing was normalised to the motion cycle. A Gaussian distribution approach was used to determine up to 10 modes of focussed activity, and results were analysed separately for stance and swing phase of the ipsilateral hindlimb., Results: Fair reliability was found for mean mode values (Cronbach's alpha = 0.66) and good reliability was found for mean mode locations (Cronbach's alpha = 0.71) over the three data collection days. The magnitude of muscle activity identified as mean mode value was much larger at trot than at walk, and mean mode value was significantly different between stance phases of walk and trot for all electrode positions (p < 0.01). The pattern of muscle activity identified as mean mode location was significantly different for walk and trot at all electrode positions, both during stance and swing phases (p < 0.001). This indicates the different timing pattern between the gaits. Results of the three electrode positions on the same muscle during each gait were not significantly different when comparing the same measurement., Conclusions: The middle of the equine GM does not show any indication of functional differentiation during walk and trot on a treadmill; this might be due to lack of segmentation as such, or due to lack of need for segmented use for these very basic main tasks of the muscle. The reliability of the sEMG measurements over several weeks was fair to good, an indication for the robustness of the methodology.

To address the problem of face recognition with image sets, we aim to capture the underlying data distribution in each set and thus facilitate more robust classification. To this end, we represent image set as the Gaussian mixture model (GMM) comprising a number of Gaussian components with prior probabilities and seek to discriminate Gaussian components from different classes. Since in the light of information geometry, the Gaussians lie on a specific Riemannian manifold, this paper presents a method named discriminant analysis on Riemannian manifold of Gaussian distributions (DARG). We investigate several distance metrics between Gaussians and accordingly two discriminative learning frameworks are presented to meet the geometric and statistical characteristics of the specific manifold. The first framework derives a series of provably positive definite probabilistic kernels to embed the manifold to a high-dimensional Hilbert space, where conventional discriminant analysis methods developed in Euclidean space can be applied, and a weighted Kernel discriminant analysis is devised which learns discriminative representation of the Gaussian components in GMMs with their prior probabilities as sample weights. Alternatively, the other framework extends the classical graph embedding method to the manifold by utilizing the distance metrics between Gaussians to construct the adjacency graph, and hence the original manifold is embedded to a lower-dimensional and discriminative target manifold with the geometric structure preserved and the interclass separability maximized. The proposed method is evaluated by face identification and verification tasks on four most challenging and largest databases, YouTube Celebrities, COX, YouTube Face DB, and Point-and-Shoot Challenge, to demonstrate its superiority over the state-of-the-art.To address the problem of face recognition with image sets, we aim to capture the underlying data distribution in each set and thus facilitate more robust classification. To this end, we represent image set as the Gaussian mixture model (GMM) comprising a number of Gaussian components with prior probabilities and seek to discriminate Gaussian components from different classes. Since in the light of information geometry, the Gaussians lie on a specific Riemannian manifold, this paper presents a method named discriminant analysis on Riemannian manifold of Gaussian distributions (DARG). We investigate several distance metrics between Gaussians and accordingly two discriminative learning frameworks are presented to meet the geometric and statistical characteristics of the specific manifold. The first framework derives a series of provably positive definite probabilistic kernels to embed the manifold to a high-dimensional Hilbert space, where conventional discriminant analysis methods developed in Euclidean space can be applied, and a weighted Kernel discriminant analysis is devised which learns discriminative representation of the Gaussian components in GMMs with their prior probabilities as sample weights. Alternatively, the other framework extends the classical graph embedding method to the manifold by utilizing the distance metrics between Gaussians to construct the adjacency graph, and hence the original manifold is embedded to a lower-dimensional and discriminative target manifold with the geometric structure preserved and the interclass separability maximized. The proposed method is evaluated by face identification and verification tasks on four most challenging and largest databases, YouTube Celebrities, COX, YouTube Face DB, and Point-and-Shoot Challenge, to demonstrate its superiority over the state-of-the-art.

A new primary model has been developed, using Gaussian distributed populations and Eyrings rate constant for the transition state, to describe inactivation kinetics of enzymes and micro-organisms subjected to heat and chemical treatment. The inactivation of both enzymes and micro-organisms could be associated with the irreversible transition to an inactivated state, as suggested by the Lumry-Eyring model for protein denaturation and enzyme inactivation. The characteristic inactivation model parameters, standard activation enthalpy and entropy, are directly related to the reference temperature and Z-value commonly used for kinetic analysis in food microbiology. An essential feature of the kinetic model is that its parameters, and hence the transition temperature, are treated as stochastic variables. The characteristic line shape of the primary model is the log-normal distribution. The performance of the model was validated, using literature data for enzyme and microbial inactivation over a wide range of temperature and pH., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

18 F-DMFP-PET is an emerging neuroimaging modality used to diagnose Parkinson's disease (PD) that allows us to examine postsynaptic dopamine D 2/3 receptors. Like other neuroimaging modalities used for PD diagnosis, most of the total intensity of 18 F-DMFP-PET images is concentrated in the striatum. However, other regions can also be useful for diagnostic purposes. An appropriate delimitation of the regions of interest contained in 18 F-DMFP-PET data that improves the accuracy of computer aided diagnosis systems for PD. First, the data were segmented using an algorithm based on Hidden Markov Random Field. As a result, each neuroimage was divided into 4 maps according to the intensity and the neighborhood of the voxels. The maps were then individually normalized so that the shape of their histograms could be modeled by a Gaussian distribution with equal parameters for all the neuroimages. This approach was evaluated using a dataset with neuroimaging data from 87 parkinsonian patients. After these preprocessing steps, a Support Vector Machine classifier was used to separate idiopathic and non-idiopathic PD. Data preprocessed by the proposed method provided higher accuracy results than the ones preprocessed with previous approaches.18 F-DMFP-PET data that improves the accuracy of computer aided diagnosis systems for PD. First, the data were segmented using an algorithm based on Hidden Markov Random Field. As a result, each neuroimage was divided into 4 maps according to the intensity and the neighborhood of the voxels. The maps were then individually normalized so that the shape of their histograms could be modeled by a Gaussian distribution with equal parameters for all the neuroimages. This approach was evaluated using a dataset with neuroimaging data from 87 parkinsonian patients. After these preprocessing steps, a Support Vector Machine classifier was used to separate idiopathic and non-idiopathic PD. Data preprocessed by the proposed method provided higher accuracy results than the ones preprocessed with previous approaches.

Multi-sensor data fusion technology based on Dempster-Shafer evidence theory is widely applied in many fields. However, how to determine basic belief assignment (BBA) is still an open issue. The existing BBA methods pay more attention to the uncertainty of information, but do not simultaneously consider the reliability of information sources. Real-world information is not only uncertain, but also partially reliable. Thus, uncertainty and partial reliability are strongly associated with each other. To take into account this fact, a new method to represent BBAs along with their associated reliabilities is proposed in this paper, which is named reliability-based BBA. Several examples are carried out to show the validity of the proposed method., Competing Interests: The authors declare that they have no competing interests.

The multitarget version of the traditional target theory based on the Poisson distribution is still used to describe the dose-survival curves of cells after ionizing radiation in radiobiology and radiotherapy. However, noting that the usual ionizing radiation damage is the result of two sequential stochastic processes, the probability distribution of the damage number per cell should follow a compound Poisson distribution, like e.g. Neyman's distribution of type A (N. A.). In consideration of that the Gaussian distribution can be considered as the approximation of the N. A. in the case of high flux, a multitarget model based on the Gaussian distribution is proposed to describe the cell inactivation effects in low linear energy transfer (LET) radiation with high dose-rate. Theoretical analysis and experimental data fitting indicate that the present theory is superior to the traditional multitarget model and similar to the Linear - Quadratic (LQ) model in describing the biological effects of low-LET radiation with high dose-rate, and the parameter ratio in the present model can be used as an alternative indicator to reflect the radiation damage and radiosensitivity of the cells., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

Dempster-Shafer evidence theory is widely used in many soft sensors data fusion systems on account of its good performance for handling the uncertainty information of soft sensors. However, how to determine basic belief assignment (BBA) is still an open issue. The existing methods to determine BBA do not consider the reliability of each attribute; at the same time, they cannot effectively determine BBA in the open world. In this paper, based on attribute weights, a novel method to determine BBA is proposed not only in the closed world, but also in the open world. The Gaussian model of each attribute is built using the training samples firstly. Second, the similarity between the test sample and the attribute model is measured based on the Gaussian membership functions. Then, the attribute weights are generated using the overlap degree among the classes. Finally, BBA is determined according to the sensed attribute weights. Several examples with small datasets show the validity of the proposed method.

Model-based measurement techniques use experimental data and simulations of the underlying physics to extract quantitative estimates of the measurands of a specimen based upon a parametric model of that specimen. The uncertainties of these estimates are based upon not only the uncertainties in the experimental data, but also the sensitivity of that data to the model parameters, and parametric correlations among those parameters. The combination of two or more model-based techniques as well as the Bayesian approach are shown to be optimal for obtaining the lowest possible uncertainties. As an example, using this form of hybrid metrology, state-of-the-art sub-14 nm-wide lines from semiconductor manufacturing are measured using a combined regression from critical-dimension small-angle x-ray scattering and scanning electron microscopy that leads to lower uncertainties.

Background: According to international guidelines, parametric methods must be chosen for RI construction when the sample size is small and the distribution is Gaussian. However, normality tests may not be accurate at small sample size., Objectives: The purpose of the study was to evaluate normality test performance to properly identify samples extracted from a Gaussian population at small sample sizes, and assess the consequences on RI accuracy of applying parametric methods to samples that falsely identified the parent population as Gaussian., Methods: Samples of n = 60 and n = 30 values were randomly selected 100 times from simulated Gaussian, lognormal, and asymmetric populations of 10,000 values. The sensitivity and specificity of 4 normality tests were compared. Reference intervals were calculated using 6 different statistical methods from samples that falsely identified the parent population as Gaussian, and their accuracy was compared., Results: Shapiro-Wilk and D'Agostino-Pearson tests were the best performing normality tests. However, their specificity was poor at sample size n = 30 (specificity for P < .05: .51 and .50, respectively). The best significance levels identified when n = 30 were 0.19 for Shapiro-Wilk test and 0.18 for D'Agostino-Pearson test. Using parametric methods on samples extracted from a lognormal population but falsely identified as Gaussian led to clinically relevant inaccuracies., Conclusions: At small sample size, normality tests may lead to erroneous use of parametric methods to build RI. Using nonparametric methods (or alternatively Box-Cox transformation) on all samples regardless of their distribution or adjusting, the significance level of normality tests depending on sample size would limit the risk of constructing inaccurate RI., (© 2016 American Society for Veterinary Clinical Pathology.)

Our purpose in this study was to reduce the noise in order to improve the SNR of Dw images with high b-value by using two correction schemes. This study was performed with use of phantoms made from water and sucrose at different concentrations, which were 10, 30, and 50 weight percent (wt%). In noise reduction for Dw imaging of the phantoms, we compared two correction schemes that are based on the Rician distribution and the Gaussian distribution. The highest error values for each concentration with use of the Rician distribution scheme were 7.3 % for 10 wt%, 2.4 % for 30 wt%, and 0.1 % for 50 wt%. The highest error values for each concentration with use of the Gaussian distribution scheme were 20.3 % for 10 wt%, 11.6 % for 30 wt%, and 3.4 % for 50 wt%. In Dw imaging, the noise reduction makes it possible to apply the correction scheme of Rician distribution.

A method using wavelength dispersive X-ray spectroscopy (WDS) is applied to the measurement of grain boundary segregation of Sn in silicon steel. The quantification of monolayer concentration of Sn is acquired, which demonstrates an obvious segregation of Sn at grain boundaries. In consideration of the fact that segregated impurities (Sn or other species) distribute in multilayer and not just monolayer segregation can be characterized by WDS, the Gaussian distribution is applied to formulate the multilayer concentration depth distribution according to the measured total concentration. A correction factor is then put forward to improve the quantification. Based on the measured segregation of Sn and the derived formula of multilayer concentration depth distribution, the grain boundary concentrations of Sn are calculated for different thicknesses of segregated layer. From the experimental measurement, theoretical analyses and calculated results, an effective approach for the research of grain boundary segregation is provided., (Copyright © 2015 Elsevier B.V. All rights reserved.)

The stochastic Eigen model proposed by Feng et al. (2007) (Journal of Theoretical Biology, 246, 28) showed that error threshold is no longer a phase transition point but a crossover region whose width depends on the strength of the random fluctuation in an environment. The underlying cause of this phenomenon has not yet been well examined. In this article, we adopt a single peak Gaussian distributed fitness landscape instead of a constant one to investigate and analyze the change of the error threshold and the statistical property of the quasi-species population. We find a roughly linear relation between the width of the error threshold and the fitness fluctuation strength. For a given quasi-species, the fluctuation of the relative concentration has a minimum with a normal distribution of the relative concentration at the maximum of the averaged relative concentration, it has however a largest value with a bimodal distribution of the relative concentration near the error threshold. The above results deepen our understanding of the quasispecies and error threshold and are heuristic for exploring practicable antiviral strategies., (Copyright © 2015 Elsevier Ltd. All rights reserved.)