scholarly journals On Minimal Copulas under the Concordance Order

2019 ◽  
Vol 184 (3) ◽  
pp. 762-780 ◽  
Author(s):  
Jae Youn Ahn ◽  
Sebastian Fuchs
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Negative Dependence ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Minimal Elements ◽  
Measures Of Concordance ◽  
Concordance Order

AbstractIn the present paper, we study extreme negative dependence focussing on the concordance order for copulas. With the absence of a least element for dimensions $$d\ge 3$$d≥3, the set of all minimal elements in the collection of all copulas turns out to be a natural and quite important extreme negative dependence concept. We investigate several sufficient conditions, and we provide a necessary condition for a copula to be minimal. The sufficient conditions are related to the extreme negative dependence concept of d-countermonotonicity and the necessary condition is related to the collection of all copulas minimizing multivariate Kendall’s tau. The concept of minimal copulas has already been proved to be useful in various continuous and concordance order preserving optimization problems including variance minimization and the detection of lower bounds for certain measures of concordance. We substantiate this key role of minimal copulas by showing that every continuous and concordance order preserving functional on copulas is minimized by some minimal copula, and, in the case the continuous functional is even strictly concordance order preserving, it is minimized by minimal copulas only. Applying the above results, we may conclude that every minimizer of Spearman’s rho is also a minimizer of Kendall’s tau.

scholarly journals Muscle Activation Sequence in Flywheel Squats

2021 ◽  
Vol 18 (6) ◽  
pp. 3168
Author(s):  
Darjan Spudić ◽  
Darjan Smajla ◽  
Michael David Burnard ◽  
Nejc Šarabon
Keyword(s):  
Muscle Activation ◽  
Coordination Pattern ◽  
Muscle Coordination ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Exercise Interventions ◽  
Leg Muscles ◽  
Sequential Rank ◽  
Functional Movements

Background: Muscle coordination is important for rational and effective planning of therapeutic and exercise interventions using equipment that mimics functional movements. Our study was the first to assess muscle coordination during flywheel (FW) squats. Methods: Time-of-peak electromyographic activation order was assessed separately for 8, 4, and 3 leg muscles under four FW loads. A sequential rank agreement permutations tests (SRA) were conducted to assess activation order and Kendall’s tau was used to assess the concordance of activation order across subjects, loads and expected order of activation. Results: SRA revealed a latent muscle activation order at loads 0.05, 0.075, and 0.1, but not at 0.025 kg·m2. Kendall’s tau showed moderate-to-strong concordance between the expected (proximal-to-distal) and the observed muscle activation order only at a load 0.025 kg·m2, regardless of the number of muscles analyzed. Muscle activation order was highly concordant between loads 0.05, 0.075, and 0.1 kg·m2. Conclusions: The results show a specific role of each muscle during the FW squat that is load-dependent. While the lowest load follows the proximal-to-distal principle of muscle activation, higher loads lead to a reorganization of the underlying muscle coordination mechanisms. They require a specific and stable muscle coordination pattern that is not proximal-to-distal.

scholarly journals New families of bivariate copulas via unit weibull distortion

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Fadal A.A. Aldhufairi ◽  
Jungsywan H. Sepanski
Keyword(s):  
Tail Dependence ◽  
Copula Function ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Density Distributions ◽  
New Family ◽  
Upper Tail Dependence ◽  
Bivariate Copula

Abstract This paper introduces a new family of bivariate copulas constructed using a unit Weibull distortion. Existing copulas play the role of the base or initial copulas that are transformed or distorted into a new family of copulas with additional parameters, allowing more flexibility and better fit to data. We present a general form for the new bivariate copula function and its conditional and density distributions. The tail behaviors are investigated and indicate the unit Weibull distortion may result in new copulas with upper tail dependence when the base copula has no upper tail dependence. The concordance ordering and Kendall’s tau are derived for the cases when the base copulas are Archimedean, such as the Clayton and Frank copulas. The Loss-ALEA data are analyzed to evaluate the performance of the proposed new families of copulas.

scholarly journals A Biconvex Form for Copulas

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Sebastian Fuchs
Keyword(s):  
Probability Measure ◽  
Probability Measures ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Spearman's Rho ◽  
Spearman’S Rho ◽  
Measures Of Concordance

AbstractWe study the integration of a copula with respect to the probability measure generated by another copula. To this end, we consider the map [. , .] : C × C → R given bywhere C denotes the collection of all d–dimensional copulas and QD denotes the probability measures associated with the copula D. Specifically, this is of interest since several measures of concordance such as Kendall’s tau, Spearman’s rho and Gini’s gamma can be expressed in terms of the map [. , .]. Quite generally, the map [. , .] can be applied to construct and investigate measures of concordance.

The Temptations of Christ and Other Stories

2018 ◽  
Author(s):  
Eleonore Stump
Keyword(s):  
Human Person ◽  
Necessary Condition ◽  
Biblical Narratives ◽  
God's Love ◽  
The Way

This chapter examines biblical narratives to illuminate the role of Christ’s passion and death in bringing a person to a life in grace. Reflection on the narratives shows that Christ’s passion and death are a most promising way for God to help a human person to the surrender which is the necessary condition for spiritual and moral regeneration. The stories of the temptations of Christ show the way in which Christ’s suffering and death are connected to justification and sanctification. A person’s ceasing to resist the grace of God and surrendering to God’s love is the pinnacle on which her salvation has to stand. If we focus on this necessary condition for salvation, we can see the reason for Christ’s suffering. What can be gained by weakness that could not be gotten through power is the melting of a heart accustomed to willed loneliness and hardened against joy.

Some new results on the subexponential class

1989 ◽  
Vol 26 (4) ◽  
pp. 892-897 ◽  
Author(s):  
Emily S. Murphree
Keyword(s):  
Distribution Function ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Subexponential Class ◽  
Class Of Functions

A distribution function F on (0,∞) belongs to the subexponential class if the ratio of 1 – F(2)(x) to 1 – F(x) converges to 2 as x →∞. A necessary condition for membership in is used to prove that a certain class of functions previously thought to be contained in has members outside of . Sufficient conditions on the tail of F are found which ensure F belongs to ; these conditions generalize previously published conditions.

scholarly journals R-Regularity of Set-Valued Mappings Under the Relaxed Constant Positive Linear Dependence Constraint Qualification with Applications to Parametric and Bilevel Optimization

2021 ◽  
Author(s):  
Patrick Mehlitz ◽  
Leonid I. Minchenko
Keyword(s):  
Linear Dependence ◽  
Constraint Qualification ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Bilevel Optimization ◽  
Regularity Property ◽  
Constant Rank Constraint Qualification ◽  
Existence Criterion ◽  
Set Valued Mappings

AbstractThe presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of, e.g., stability analysis or bilevel optimization. An example of such a Lipschitzian property for set-valued mappings, whose graph is the solution set of a system of nonlinear inequalities and equations, is R-regularity. Based on the so-called relaxed constant positive linear dependence constraint qualification, we provide a criterion ensuring the presence of the R-regularity property. In this regard, our analysis generalizes earlier results of that type which exploited the stronger Mangasarian–Fromovitz or constant rank constraint qualification. Afterwards, we apply our findings in order to derive new sufficient conditions which guarantee the presence of R-regularity for solution mappings in parametric optimization. Finally, our results are used to derive an existence criterion for solutions in pessimistic bilevel optimization and a sufficient condition for the presence of the so-called partial calmness property in optimistic bilevel optimization.

scholarly journals Workload for radiologists during on-call hours: dramatic increase in the past 15 years

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
R. J. M. Bruls ◽  
R. M. Kwee
Keyword(s):  
Western Europe ◽  
Kendall Test ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
X Ray ◽  
The Past ◽  
Relative Value ◽  
Burn Out ◽  
Picture Archiving And Communication ◽  
Ct Studies

Abstract Background The objective of this study is to investigate the workload for radiologists during on-call hours and to quantify the 15-year trend in a large general hospital in Western Europe. Methods Data regarding the number of X-ray, ultrasound and computed tomography (CT) studies during on-call hours (weekdays between 6.00 p.m. and 7.00 a.m., weekends, and national holidays) between 2006 and 2020 were extracted from the picture archiving and communication system. All studies were converted into relative value units (RVUs) to estimate the on-call workload. The Mann–Kendall test was performed to assess the temporal trend. Results The total RVUs during on-call hours showed a significant increase between 2006 and 2020 (Kendall's tau-b = 0.657, p = 0.001). The overall workload in terms of RVUs during on-call hours has quadrupled. The number of X-ray studies significantly decreased (Kendall's tau-b = − 0.433, p = 0.026), whereas the number of CT studies significantly increased (Kendall's tau-b = 0.875, p < 0.001) between 2006 and 2020. CT studies which increased by more than 500% between 2006 and 2020 are CT for head trauma, brain CTA, brain CTV, chest CT (for suspected pulmonary embolism), spinal CT, neck CT, pelvic CT, and CT for suspected aortic dissection. The number of ultrasound studies did not change significantly (Kendall's tau-b = 0.202, p = 0.298). Conclusions The workload for radiologists during on-call hours increased dramatically in the past 15 years. The growing amount of CT studies is responsible for this increase. Radiologist and technician workforce should be matched to this ongoing increasing trend to avoid potential burn-out and to maintain quality and safety of radiological care.

scholarly journals Sufficient conditions for hyperbolicity and consistency of the dynamic equations for fluid-saturated solids

2021 ◽  
Author(s):  
Vladimir A. Osinov
Keyword(s):  
Boundary Value Problem ◽  
Wave Speed ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Positive Definiteness ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Systems Of Equations ◽  
Acoustic Tensor ◽  
Ill Posed

AbstractPrevious studies showed that the dynamic equations for a porous fluid-saturated solid may lose hyperbolicity and thus render the boundary-value problem ill-posed while the equations for the same but dry solid remain hyperbolic. This paper presents sufficient conditions for hyperbolicity in both dry and saturated states. Fluid-saturated solids are described by two different systems of equations depending on whether the permeability is zero or nonzero (locally undrained and drained conditions, respectively). The paper also introduces a notion of wave speed consistency between the two systems as a necessary condition which must be satisfied in order for the solution in the locally drained case to tend to the undrained solution as the permeability tends to zero. It is shown that the symmetry and positive definiteness of the acoustic tensor of the skeleton guarantee both hyperbolicity and the wave speed consistency of the equations.

Some generalized characters associated to a transitive permutation group

2020 ◽  
Vol 23 (3) ◽  
pp. 393-397
Author(s):  
Wolfgang Knapp ◽  
Peter Schmid
Keyword(s):  
Positive Integer ◽  
Permutation Group ◽  
Frobenius Group ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Transitive Permutation Group ◽  
Point Stabilizer ◽  
Necessary And Sufficient ◽  
Regular Character ◽  
Permutation Character

AbstractLet G be a finite transitive permutation group of degree n, with point stabilizer {H\neq 1} and permutation character π. For every positive integer t, we consider the generalized character {\psi_{t}=\rho_{G}-t(\pi-1_{G})}, where {\rho_{G}} is the regular character of G and {1_{G}} the 1-character. We give necessary and sufficient conditions on t (and G) which guarantee that {\psi_{t}} is a character of G. A necessary condition is that {t\leq\min\{n-1,\lvert H\rvert\}}, and it turns out that {\psi_{t}} is a character of G for {t=n-1} resp. {t=\lvert H\rvert} precisely when G is 2-transitive resp. a Frobenius group.

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