Extreme Points of the Credal Sets Generated by Elementary Comparative Probabilities

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

Download Full-text

Extreme Points and Majorization: Economic Applications

SSRN Electronic Journal ◽

10.2139/ssrn.3551258 ◽

2020 ◽

Cited By ~ 4

Author(s):

Andreas Kleiner ◽

Benny Moldovanu ◽

Philipp Strack

Keyword(s):

Extreme Points ◽

Economic Applications

Download Full-text

A short note on extreme points of certain polytopes

Special Matrices ◽

10.1515/spma-2020-0005 ◽

2020 ◽

Vol 8 (1) ◽

pp. 36-39

Author(s):

Lei Cao ◽

Ariana Hall ◽

Selcuk Koyuncu

Keyword(s):

Short Proof ◽

Convex Polytopes ◽

Short Note ◽

Convex Polytope ◽

Extreme Points ◽

Alternative Proof ◽

Stochastic Matrices ◽

Doubly Stochastic ◽

Birkhoff's Theorem ◽

Birkhoff’S Theorem

AbstractWe give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

Download Full-text

Investigation of ancestral alleles in the Bovinae subfamily

BMC Genomics ◽

10.1186/s12864-021-07412-9 ◽

2021 ◽

Vol 22 (1) ◽

Author(s):

Maulana M. Naji ◽

Yuri T. Utsunomiya ◽

Johann Sölkner ◽

Benjamin D. Rosen ◽

Gábor Mészáros

Keyword(s):

Extreme Points ◽

Genetic Mutation ◽

Zebu Cattle ◽

Ancestral State ◽

Initial State ◽

High Count ◽

Environmental Pressures ◽

Ancestral States ◽

Productive Traits ◽

Species Specific

Abstract Background In evolutionary theory, divergence and speciation can arise from long periods of reproductive isolation, genetic mutation, selection and environmental adaptation. After divergence, alleles can either persist in their initial state (ancestral allele - AA), co-exist or be replaced by a mutated state (derived alleles -DA). In this study, we aligned whole genome sequences of individuals from the Bovinae subfamily to the cattle reference genome (ARS.UCD-1.2) for defining ancestral alleles necessary for selection signatures study. Results Accommodating independent divergent of each lineage from the initial ancestral state, AA were defined based on fixed alleles on at least two groups of yak, bison and gayal-gaur-banteng resulting in ~ 32.4 million variants. Using non-overlapping scanning windows of 10 Kb, we counted the AA observed within taurine and zebu cattle. We focused on the extreme points, regions with top 0. 1% (high count) and regions without any occurrence of AA (null count). High count regions preserved gene functions from ancestral states that are still beneficial in the current condition, while null counts regions were linked to mutated ones. For both cattle, high count regions were associated with basal lipid metabolism, essential for survival of various environmental pressures. Mutated regions were associated to productive traits in taurine, i.e. higher metabolism, cell development and behaviors and in immune response domain for zebu. Conclusions Our findings suggest that retaining and losing AA in some regions are varied and made it species-specific with possibility of overlapping as it depends on the selective pressure they had to experience.

Download Full-text

Risk Assessment of Circuit Breakers Using Influence Diagrams with Interval Probabilities

Symmetry ◽

10.3390/sym13050737 ◽

2021 ◽

Vol 13 (5) ◽

pp. 737

Author(s):

Jelena D. Velimirovic ◽

Aleksandar Janjic

Keyword(s):

Power System ◽

Predictive Modelling ◽

Optimal Time ◽

Influence Diagrams ◽

Circuit Breakers ◽

Interval Probability ◽

Complex Power ◽

Interval Width ◽

Credal Sets ◽

The One

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. More specifically, influence diagrams—as extended Bayesian network functions with interval probabilities represented through credal sets—were chosen for the predictive modelling scenario of replacing the most critical circuit breakers in optimal time. Namely, based on the available data on circuit breakers and other variables that affect the considered model of a complex power system, a group of experts was able to assess the situation using interval probabilities instead of crisp probabilities. Furthermore, the paper examines how the confidence interval width affects decision-making in this context and eliminates the information asymmetry of different experts. Based on the obtained results for each considered interval width separately on the action to be taken over the considered model in order to minimize the risk of the power system failure, it can be concluded that the proposed approach clearly indicates the advantages of using interval probability when making decisions in systems such as the one considered in this paper.

Download Full-text

Determination of catastrophic sets of a tubular chemical reactor by two-parameter continuation method

International Journal of Chemical Reactor Engineering ◽

10.1515/ijcre-2020-0135 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Marek Berezowski

Keyword(s):

Continuation Method ◽

Extreme Points ◽

Chemical Reactor ◽

Stationary States ◽

Parameter Continuation Method ◽

It Systems ◽

Parametric Continuation ◽

Parameter Continuation ◽

Two Parameter

AbstractThe work relates to development and presentation a two-parameter continuation method for determining catastrophic sets of stationary states of a tubular chemical reactor with mass recycle. The catastrophic set is a set of extreme points occurring in the bifurcation diagrams of the reactor. There are many large IT systems that use the parametric continuation method. The most popular is AUTO’97. However, its use is sometimes not convenient. The method developed in this work allows to eliminate the necessity to use huge IT systems from the calculations. Unlike these systems, it can be inserted into the program as a short subroutine. In addition, this method eliminates time-consuming iterations from the calculations.

Download Full-text

Extreme Points of Convex Sets in Infinite Dimensional Spaces

American Mathematical Monthly ◽

10.2307/2322725 ◽

1987 ◽

Vol 94 (5) ◽

pp. 409 ◽

Cited By ~ 7

Author(s):

Nina M. Roy

Keyword(s):

Convex Sets ◽

Extreme Points ◽

Infinite Dimensional

Download Full-text

Research of Zero Calibration in Conoscopic Holography Measurement Based on Image

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.303-306.386 ◽

2013 ◽

Vol 303-306 ◽

pp. 386-389

Author(s):

Shu Yan Ren ◽

Yong Gang Yang ◽

Hai Long Duan

Keyword(s):

Extreme Points ◽

B Splines ◽

Contact Measurement ◽

Measurement Result ◽

Common Path ◽

Repeatability Error ◽

Zero Position ◽

Conoscopic Holography ◽

Patch Image ◽

Method Of Adjustment

Non-contact measurement based on conoscopic holography is a kind of interferometry with common path, so it is not influenced much by other factors such as vibration. But the measurement result is affected by the uniformity of the crystal, which is analyzed in this paper, and corresponding method of adjustment based on image is discussed. And B-splines function is used to calculate zero position in measurement image, which is fitted over the patch image in the neighborhood of gray extreme points of the stripes, which is important to reduce the repeatability error, optimize design, and improve the accuracy of system.

Download Full-text