The pinnacle set of a permutation

The peak set of a permutation records the indices of its peaks. These sets have been studied in a variety of contexts, including recent work by Billey, Burdzy, and Sagan, which enumerated permutations with prescribed peak sets. In this article, we look at a natural analogue of the peak set of a permutation, instead recording the values of the peaks. We define the “pinnacle set” of a permutation $w$ to be the set $\{w\left(i\right):i\text{ is a peak of}w\}$. Although peak sets and pinnacle sets mark the same phenomenon for a given permutation, the behaviors of these sets differ in notable ways as distributions over the symmetric group. In the work below, we characterize admissible pinnacle sets and study various enumerative questions related to these objects.     

On sufficient second order optimality conditions in multiobjective optimization

A second order sufficient optimality criterion is presented for a multiobjective problem subject to a constraint given just as a set. To this aim, we first refine known necessary conditions in such a way that the sufficient ones differ by the replacement of inequalities by strict inequalities. Furthermore, we show that no relationship holds between this criterion and a sufficient multipliers rule, when the constraint is described by inequalities and equalities. Finally, improvements of this criterion for the unconstrained case are presented, stressing the differences with single-objective optimization     

Asymptotic approximation for the probability density function of an arbitrary sequence of random variables

We establish a large deviation approximation for the density function of an arbitrary sequence of random variables. The results are analogous to those obtained by Chaganty and Sethuraman (1985). We apply our theorems to the sample variance and the Mann–Whitney two-sample statistic.     

保险企业偿付能力的监控

本讨论保险公司偿付能力监控指标的构成,并针对我国目前保险公司的现状提出用多元统计控制方法和指标加权平均法对保险公司偿付能力进行监控,最后,以一例说明其实际应用。     

Sufficient Dimension Reduction via Distance Covariance

We introduce a novel approach to sufficient dimension-reduction problems using distance covariance. Our method requires very mild conditions on the predictors. It estimates the central subspace effectively even when many predictors are categorical or discrete. Our method keeps the model-free advantage without estimating link function. Under regularity conditions, root-n consistency and asymptotic normality are established for our estimator. We compare the performance of our method with some existing dimension-reduction methods by simulations and find that our method is very competitive and robust across a number of models. We also analyze the Auto MPG data to demonstrate the efficacy of our method. Supplemental materials for this article are available online.     

Adsorption of adamantanol isomers on graphitized thermal carbon black

The thermodynamic characteristics of adsorption of some adamantanol isomers on graphitized thermal carbon black were calculated and determined experimentally. The parameters of the potential function for the intermolecular interaction between hydroxyl oxygen and carbon of the graphite basis plane were determined for the first time. The adsorption properties of adamantanols are largely determined by electron density distribution in the adamantane cage, which are related to the cage effect.     

Fields of extremals and sufficient conditions for the simplest problem of the calculus of variations

In this paper we present an elementary proof of a classical sufficient condition for free problems in the calculus of variations using an extension of the direct sufficiency method, originating in the work of G. Leitmann (Int. J. NonLin. Mech. 2, 55–59 (1967)), found in D.A. Carlson (J. Optim. Theory Appl. 114, 345–362 (2002)).     

Susceptibility of the rectangular Ising ferromagnet

The critical index values= 7/4 for the susceptibility and=15 for the critical isotherm are derived rigorously for the rectangular Ising ferromagnet with nearest neighbor interactions. The critical indices associated with the Fisher moment definition of the correlation length are obtained asTT _c+. The index of the fluctuation sum definition of critical correlations is obtained.Partially supported by grant PHY 76 17191.     

Fuzzy集的退化锥和关于闭性的几个充分条件

本文对Fuzzy集引进退化锥、后退锥、投影锥等概念,并利用它们建立了关于Fuzzy集闭性的几个充分性条件。这些结果对于讨论具有控制锥的Fuzzy多目标规划是有用的。     

Machine Learning Models and Statistical Complexity to Analyze the Effects of Posture on Cerebral Hemodynamics

The mechanism of cerebral blood flow autoregulation can be of great importance in diagnosing and controlling a diversity of cerebrovascular pathologies such as vascular dementia, brain injury, and neurodegenerative diseases. To assess it, there are several methods that use changing postures, such as sit-stand or squat-stand maneuvers. However, the evaluation of the dynamic cerebral blood flow autoregulation (dCA) in these postures has not been adequately studied using more complex models, such as non-linear ones. Moreover, dCA can be considered part of a more complex mechanism called cerebral hemodynamics, where others (CO₂ reactivity and neurovascular-coupling) that affect cerebral blood flow (BF) are included. In this work, we analyzed postural influences using non-linear machine learning models of dCA and studied characteristics of cerebral hemodynamics under statistical complexity using eighteen young adult subjects, aged 27 ± 6.29 years, who took the systemic or arterial blood pressure (BP) and cerebral blood flow velocity (BFV) for five minutes in three different postures: stand, sit, and lay. With models of a Support Vector Machine (SVM) through time, we used an AutoRegulatory Index (ARI) to compare the dCA in different postures. Using wavelet entropy, we estimated the statistical complexity of BFV for three postures. Repeated measures ANOVA showed that only the complexity of lay-sit had significant differences.