Computing of Extremal Characteristic Values of Symmetric Matrices by Individual Homotopy Algorithm

2011 ◽  
Author(s):  
Ran Baik
Keyword(s):  
Symmetric Matrices ◽  
Homotopy Algorithm ◽  
Extremal Characteristic ◽  
Characteristic Values

REMARKS ON THE KIELANOWSKI PARAMETRIZATION OF THE KOBAYASHI-MASKAWA MATRIX

1996 ◽  
Vol 11 (31) ◽  
pp. 2531-2537 ◽  
Author(s):  
TATSUO KOBAYASHI ◽  
ZHI-ZHONG XING
Keyword(s):  
Symmetric Matrices

We study the Kielanowski parametrization of the Kobayashi-Maskawa (KM) matrix V. A new two-angle parametrization is investigated explicitly and compared with the Kielanowski ansatz. Both of them are symmetric matrices and lead to |V13/V23|=0.129. Necessary corrections to the off-diagonal symmetry of V are also discussed.

scholarly journals Code Calibration of the Eurocodes

2021 ◽  
Vol 11 (12) ◽  
pp. 5474
Author(s):  
Tuomo Poutanen
Keyword(s):  
High Reliability ◽  
High Accuracy ◽  
Variable Load ◽  
Reliability Model ◽  
Safety Factors ◽  
Rounding Errors ◽  
Code Calibration ◽  
Load Factors ◽  
Characteristic Values

This article addresses the process to optimally select safety factors and characteristic values for the Eurocodes. Five amendments to the present codes are proposed: (1) The load factors are fixed, γG = γQ, by making the characteristic load of the variable load changeable, it simplifies the codes and lessens the calculation work. (2) Currently, the characteristic load of the variable load is the same for all variable loads. It creates excess safety and material waste for the variable loads with low variation. This deficiency can be avoided by applying the same amendment as above. (3) Various materials fit with different accuracy in the reliability model. This article explains two options to reduce this difficulty. (4) A method to avoid rounding errors in the safety factors is explained. (5) The current safety factors are usually set by minimizing the reliability indexes regarding the target when the obtained codes include considerable safe and unsafe design cases with the variability ratio (high reliability/low) of about 1.4. The proposed three code models match the target β50 = 3.2 with high accuracy, no unsafe design cases and insignificant safe design cases with the variability ratio 1.07, 1.03 and 1.04.

scholarly journals Early prognostication of COVID-19 to guide hospitalisation versus outpatient monitoring using a point-of-test risk prediction score

Thorax ◽  
2021 ◽  
pp. thoraxjnl-2020-216425
Author(s):  
Felix Chua ◽  
Rama Vancheeswaran ◽  
Adrian Draper ◽  
Tejal Vaghela ◽  
Matthew Knight ◽  
...  
Keyword(s):  
Operating Characteristic ◽  
Predictive Accuracy ◽  
Fatal Outcome ◽  
Individual Characteristics ◽  
Adverse Outcomes ◽  
Hospital Death ◽  
Outpatient Monitoring ◽  
Characteristic Values ◽  
Large Random Sample ◽  
Mortality Predictors

IntroductionRisk factors of adverse outcomes in COVID-19 are defined but stratification of mortality using non-laboratory measured scores, particularly at the time of prehospital SARS-CoV-2 testing, is lacking.MethodsMultivariate regression with bootstrapping was used to identify independent mortality predictors in patients admitted to an acute hospital with a confirmed diagnosis of COVID-19. Predictions were externally validated in a large random sample of the ISARIC cohort (N=14 231) and a smaller cohort from Aintree (N=290).Results983 patients (median age 70, IQR 53–83; in-hospital mortality 29.9%) were recruited over an 11-week study period. Through sequential modelling, a five-predictor score termed SOARS (SpO2, Obesity, Age, Respiratory rate, Stroke history) was developed to correlate COVID-19 severity across low, moderate and high strata of mortality risk. The score discriminated well for in-hospital death, with area under the receiver operating characteristic values of 0.82, 0.80 and 0.74 in the derivation, Aintree and ISARIC validation cohorts, respectively. Its predictive accuracy (calibration) in both external cohorts was consistently higher in patients with milder disease (SOARS 0–1), the same individuals who could be identified for safe outpatient monitoring. Prediction of a non-fatal outcome in this group was accompanied by high score sensitivity (99.2%) and negative predictive value (95.9%).ConclusionThe SOARS score uses constitutive and readily assessed individual characteristics to predict the risk of COVID-19 death. Deployment of the score could potentially inform clinical triage in preadmission settings where expedient and reliable decision-making is key. The resurgence of SARS-CoV-2 transmission provides an opportunity to further validate and update its performance.

Converting immanants on skew-symmetric matrices

2021 ◽  
Vol 618 ◽  
pp. 76-96
Author(s):  
M.A. Duffner ◽  
A.E. Guterman ◽  
I.A. Spiridonov
Keyword(s):  
Symmetric Matrices

scholarly journals The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree

2019 ◽  
Vol 7 (1) ◽  
pp. 257-262
Author(s):  
Kenji Toyonaga
Keyword(s):  
Symmetric Matrix ◽  
Symmetric Matrices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Multiplicity ◽  
Necessary And Sufficient ◽  
Multiplicity Of An Eigenvalue

Abstract Given a combinatorially symmetric matrix A whose graph is a tree T and its eigenvalues, edges in T can be classified in four categories, based upon the change in geometric multiplicity of a particular eigenvalue, when the edge is removed. We investigate a necessary and sufficient condition for each classification of edges. We have similar results as the case for real symmetric matrices whose graph is a tree. We show that a g-2-Parter edge, a g-Parter edge and a g-downer edge are located separately from each other in a tree, and there is a g-neutral edge between them. Furthermore, we show that the distance between a g-downer edge and a g-2-Parter edge or a g-Parter edge is at least 2 in a tree. Lastly we give a combinatorially symmetric matrix whose graph contains all types of edges.

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