Normal Distribution
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2022 ◽  
Vol 64 (1) ◽  
pp. 85
Author(s):  
Ю.М. Бойко ◽  
В.А. Марихин ◽  
О.А. Москалюк ◽  
Л.П. Мясникова

Regularities of statistical distributions of a complex of mechanical properties, including the module of elasticity (E), strength () and strain at break (b), high-strength industrial oriented polypropylene (PP) fibers have been analyzed using the Weibull and Gauss models based on large a wide array of measurements (50 identical samples in each series). The values of the statistical Weibull modulus (m) - a parameter characterizing the scatter of the measured values of the data arrays of E,  and b – have been estimated for the PP samples of two types: single fibers (monofilaments) and multifilament fibers consisting from several hundred single fibers. For the PP multifilament fibers, a more correct description of the distributions of E,  and b has been received both in the framework of the normal distribution (Gaussian distribution) and in the framework of the Weibull distribution in comparison with the description of such distributions for the PP monofilaments. The influence of the polymer chain conformation on the regularities of the statistical distributions of E,  and b for the high-strength oriented polymeric materials with different chemical chain structures and the correctness of their descriptions in the framework of the Gauss and Weibull models have been analyzed. For this purpose, the values of m calculated in this work for PP with a helical chain conformation have been compared with the values of m determined by us earlier for ultra-high molecular weight polyethylene and polyamide-6 with the chain conformations in the form of an in-plane trans-zigzag.


2021 ◽  
Author(s):  
Abdullahi Mohammad ◽  
Christos Masouros ◽  
Yiannis Andreopoulos

We consider a downlink situation where the BS is equipped with four antennas (M = 4) that serve single users; and assume a single cell. We obtain the dataset from the channel realizations randomly generated from a normal distribution with zero mean and unit variance. The dataset is reshaped and converted to real number domain.<div>The input dataset is normalized by the transmit data symbol so that data entries are within the nominal range, potentially aiding the training. We generate 50,000 training samples and 2000 test samples, respectively. The transmit data symbols are modulated using a QPSK modulation scheme. The training SINR is obtained randomly from uniform distribution Γtrain∼U(Γlow, Γhigh). Stochastic gradient descent is used with the Lagrangian function as a loss metric. A parametric rectified linear unit (PReLu) activation function is used for convolutional and fully connected layers in a full-precision model and the low-bit activation function for the quantized model. After every iteration, the learning rate is reduced by a factor α= 0.65 to help the learning algorithm converge faster. <br></div>


2021 ◽  
Vol 29 (1) ◽  
Author(s):  
O. M. Hollah

AbstractDepending on a field study for one of the largest iron and paints warehouses in Egypt, this paper presents a new multi-item periodic review inventory model considering the refunding quantity cost. Through this field study, we found that the inventory level is monitored periodically at equal time intervals. Returning a part of the goods that were previously ordered is permitted. Also, a shortage is permissible to occur despite having orders, and it is a combination of the backorder and lost sales. This model has been applied in both crisp and fuzzy environments since the fuzzy case is more suitable for real-life than crisp. The Lagrange multiplier technique is used for solving the restricted mathematical model. Here, the demand is a random variable that follows the normal distribution with zero lead-time. Finally, the model is followed by a real application to clarify the model and prove its efficiency.


2021 ◽  
Author(s):  
Abdullahi Mohammad ◽  
Christos Masouros ◽  
Yiannis Andreopoulos

We consider a downlink situation where the BS is equipped with four antennas (M = 4) that serve single users; and assume a single cell. We obtain the dataset from the channel realizations randomly generated from a normal distribution with zero mean and unit variance. The dataset is reshaped and converted to real number domain.<div>The input dataset is normalized by the transmit data symbol so that data entries are within the nominal range, potentially aiding the training. We generate 50,000 training samples and 2000 test samples, respectively. The transmit data symbols are modulated using a QPSK modulation scheme. The training SINR is obtained randomly from uniform distribution Γtrain∼U(Γlow, Γhigh). Stochastic gradient descent is used with the Lagrangian function as a loss metric. A parametric rectified linear unit (PReLu) activation function is used for convolutional and fully connected layers in a full-precision model and the low-bit activation function for the quantized model. After every iteration, the learning rate is reduced by a factor α= 0.65 to help the learning algorithm converge faster. <br></div>


Algorithms ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 296
Author(s):  
Lucy Blondell ◽  
Mark Z. Kos ◽  
John Blangero ◽  
Harald H. H. Göring

Statistical analysis of multinomial data in complex datasets often requires estimation of the multivariate normal (mvn) distribution for models in which the dimensionality can easily reach 10–1000 and higher. Few algorithms for estimating the mvn distribution can offer robust and efficient performance over such a range of dimensions. We report a simulation-based comparison of two algorithms for the mvn that are widely used in statistical genetic applications. The venerable Mendell-Elston approximation is fast but execution time increases rapidly with the number of dimensions, estimates are generally biased, and an error bound is lacking. The correlation between variables significantly affects absolute error but not overall execution time. The Monte Carlo-based approach described by Genz returns unbiased and error-bounded estimates, but execution time is more sensitive to the correlation between variables. For ultra-high-dimensional problems, however, the Genz algorithm exhibits better scale characteristics and greater time-weighted efficiency of estimation.


2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Md. Shadhin ◽  
Mashiur Rahman ◽  
Raghavan Jayaraman ◽  
Danny Mann

AbstractVacuum-assisted resin transfer molding (VARTM), used in manufacturing medium to large-sized composites for transportation industries, requires non-woven mats. While non-woven glass mats used in these applications are optimized for resin impregnation and properties, such optimized mats for natural fibers are not available. In the current research, cattail fibers were extracted from plants (18–30% yield) using alkali retting and non-woven cattail fiber mat was manufactured. The extracted fibers exhibited a normal distribution in diameter (davg. = 32.1 µm); the modulus and strength varied inversely with diameter, and their average values were 19.1 GPa and 172.3 MPa, respectively. The cattail fiber composites were manufactured using non-woven mats, Stypol polyester resin, VARTM pressure (101 kPa) and compression molding pressures (260 and 560 kPa) and tested. Out-of-plane permeability changed with the fiber volume fraction (Vf) of the mats, which was influenced by areal density, thickness, and fiber packing in the mat. The cattail fibers reinforced the Stypol resin significantly. The modulus and the strength increased with consolidation pressures due to the increase in Vf, with maximum values of 7.4 GPa and 48 MPa, respectively, demonstrating the utility of cattail fibers from waste biomass as reinforcements.


2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Nadine Haddad ◽  
Hannah Eleanor Clapham ◽  
Hala Abou Naja ◽  
Majd Saleh ◽  
Zeina Farah ◽  
...  

Abstract Introduction The first detected case in Lebanon on 21 February 2020 engendered implementation of a nationwide lockdown alongside timely contact-tracing and testing. Objectives Our study aims to calculate the serial interval of SARS-CoV-2 using contact tracing data collected 21 February to 30 June 2020 in Lebanon to guide testing strategies. Methods rRT-PCR positive COVID-19 cases reported to the Ministry of Public Health Epidemiological Surveillance Program (ESU-MOH) are rapidly investigated and identified contacts tested. Positive cases and contacts assigned into chains of transmission during the study time-period were verified to identify those symptomatic, with non-missing date-of-onset and reported source of exposure. Selected cases were classified in infector–infectee pairs. We calculated mean and standard deviation for the serial interval and best distribution fit using AIC criterion. Results Of a total 1788 positive cases reported, we included 103 pairs belonging to 24 chains of transmissions. Most cases were Lebanese (98%) and male (63%). All infectees acquired infection locally. Mean serial interval was 5.24 days, with a standard deviation of 3.96 and a range of − 4 to 16 days. Normal distribution was an acceptable fit for our non-truncated data. Conclusion Timely investigation and social restriction measures limited recall and reporting biases. Pre-symptomatic transmission up to 4 days prior to symptoms onset was documented among close contacts. Our SI estimates, in line with international literature, provided crucial information that fed into national contact tracing measures. Our study, demonstrating the value of contact-tracing data for evidence-based response planning, can help inform national responses in other countries.


2021 ◽  
Author(s):  
Tobias Raphael Spiller ◽  
Or Duek ◽  
Markus Helmer ◽  
John D. Murray ◽  
Roland von Känel ◽  
...  

The heterogeneity of symptoms among individuals diagnosed with the same mental disorder complicates the identification of biomarkers and the development of targeted treatments. Yet, the characteristics of this heterogeneity remain largely unknown. We investigated the frequency of disorder-specific symptom combinations, a marker of symptom heterogeneity, in five samples, each assessed for symptoms of a specific disorder (posttraumatic stress disorder, depression, anxiety, schizophrenia and burnout). The frequency of symptom combinations was heavily skewed in all samples, with most symptom combinations being reported only by few individuals. Moreover, the distribution of the symptom combination frequency could be approximated by a power-law and a log-normal distribution. This demonstrates similarities in the structure of symptom heterogeneity among mental disorders. Furthermore, we show that studies with sample sizes typical for research in mental health preclude many rare symptom combinations, limiting the validity of the obtained evidence by such studies for individuals with rare symptom combinations.


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