Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models

This research proposes a mortality model with an age shift to project future mortality using principal component analysis (PCA). Comparisons of the proposed PCA model with the well-known models—the Lee-Carter model, the age-period-cohort model (Renshaw and Haberman, 2006), and the Cairns, Blake, and Dowd model—employ empirical studies of mortality data from six countries, two each from Asia, Europe, and North America. The mortality data come from the human mortality database and span the period 1970-2005. The proposed PCA model produces smaller prediction errors for almost all illustrated countries in its mean absolute percentage error. To demonstrate longevity risk in annuity pricing, we use the proposed PCA model to project future mortality rates and analyze the underestimated ratio of annuity price for whole life annuity and deferred whole life annuity product respectively. The effect of model risk on annuity pricing is also investigated by comparing the results from the proposed PCA model with those from the LC model. The findings can benefit actuaries in their efforts to deal with longevity risk in pricing and valuation.     

Boundary integral equation method in micropolar elasticity

This paper presents the integral representations of the displacement and rotation fields of the micropolar continuum, and the regularized integral representations of the traction and couple vector. Thus the boundary integral equations and the boundary integro-differential equations are derived. In addition, the formulation for crack problems is given by both the boundary integral equations and the boundary integro-differential equations.     

Application of multivariate analysis of TOF-SIMS spectra for studying the effect of high glucose intake on aortic lipid profile

Aim

To study the effect of long-term glucose feeding on aortic lipid composition by using the time of flight-secondary ion mass spectrometry (TOF-SIMS).

Method

Rats were divided into two groups, drinking water with or without 10% glucose from birth to 6 months of age. The aortic wall was dissected out, high-pressure frozen, freeze-fractured, freeze-dried and analyzed by TOF-SIMS using a Bismuth cluster ion source. Surface spectra were taken from standardized regions of the vessel wall.

Results

Different peaks, such as cholesterol, fatty acids (FAs) and diacylglycerols (DAGs), were identified by the principal component analysis as carries of variance between two groups. These peaks were then compared by conventional t-test. Our data showed that the intensity of cholesterol, but not FAs and DAGs, was significantly decreased in the glucose-drinking rat. Moreover, the long-term glucose intake changed ratios between different FAs in the aorta.

Conclusion

The long-term glucose intake led to decreased cholesterol intensity in the aortic wall and this effect was revealed through a global analytical approach with objective selection of significant variables.     

Iron‐Catalyzed Aerobic Oxidation of Aldehydes: Single Component Catalyst and Mechanistic Studies

An aerobic oxidation of aldehydes towards carboxylic acids in MeCN using 1 atm of pure oxygen or oxygen in air as the oxidant and a catalytic amount of single component catalyst, Fe(NO₃)₃ · 9H₂O, has been developed. Carboxylic acids with different synthetically useful functional groups were obtained at room temperature. Two mechanistic pathways have been proposed based on isotopic labeling, NMR monitoring, and control experiments. The practicality of this reaction has been demonstrated by conducting several 50 mmol‐scale reactions using pure oxygen or an air‐flow of ~30 mL/min.     

Study of a high-dimensional chaotic attractor

The nature of a very high-dimensional chaotic attractor in an infinite-dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high-dimensional attractor in the phase space. We introduce two complementary bases from which the attractor is observed, one the Lyapunov basis composed of the Lyapunov vectors and the another the Fourier basis composed of the Fourier modes. We introduce the exterior subspaces on the basis of the Lyapunov vectors and observe the chaotic motion projected onto these exteriors. It is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor. The origin of such a phenomenon is attributed to more fundamental features of our attractor, which become manifest when the attractor is observed from the Lyapunov basis. A counterpart of the phenomenon can be observed also on the Fourier basis because there is a statistical one-to-one correspondence between the Lyapunov vectors and the Fourier modes. In particular, a statistical property of the high-pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor.     

Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions

We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely near-monotonicity, and show that there always exists a solution to the risk-sensitive Hamilton–Jacobi–Bellman (HJB) equation, and that any minimizer in the Hamiltonian is optimal in the class of stationary Markov controls. Under the additional hypothesis that the coefficients of the diffusion are bounded, and satisfy a condition that limits (even though it still allows) transient behavior, we show that any minimizer in the Hamiltonian is optimal in the class of all admissible controls. In addition, we present a sufficient condition, under which the solution of the HJB is unique (up to a multiplicative constant), and establish the usual verification result. We also present some new results concerning the multiplicative Poisson equation for elliptic operators in ${\mathbb{R}}^d$.     

The size of the giant high‐order component in random hypergraphs

The phase transition in the size of the giant component in random graphs is one of the most well‐studied phenomena in random graph theory. For hypergraphs, there are many possible generalizations of the notion of a connected component. We consider the following: two j‐sets (sets of j vertices) are j‐connected if there is a walk of edges between them such that two consecutive edges intersect in at least j vertices. A hypergraph is j‐connected if all j‐sets are pairwise j‐connected. In this paper, we determine the asymptotic size of the unique giant j‐connected component in random k‐uniform hypergraphs for any and .     

Biharmonic hypersurfaces with three distinct principal curvatures in spheres

We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmu?‐Montaldo‐Oniciuc, we prove that compact orientable proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces are either the hypersphere or the Clifford hypersurface with and . Moreover, we also show that there does not exist proper biharmonic hypersurface with at most three distinct principal curvatures in hyperbolic spaces .     

A Penalized Likelihood Approach to Rotation of Principal Components

A new paradigm for enhancing the interpretability of principal components through rotation is presented within the framework of penalized likelihood. The rotated components are computed as the maximizers of a Gaussian-based profile log-likelihood function plus a penalty term defined by a standard rotation criterion. This method enjoys a number of advantages over other methods for principal component rotation, notably (1) the rotation specifically targets ill-defined principal components, which may benefit the most from rotation, and (2) the connection with likelihood allows assessment of the fidelity of the rotated components to the data, thereby guiding the choice of penalty parameter. The method is illustrated with an application to a small functional dataset. Efficient computation of the penalized likelihood solution is possible using recently developed algorithms for optimization under orthogonality constraints.     

基于小波高频分量的浮游植物活体荧光识别技术研究

提出了一种基于小波高频分量的浮游植物活体荧光识别技术。通过测量近海常见52种浮游植物的三维荧光光谱,利用小波函数将光谱分解6层后得到系列正交高频分量cd1～cd6,通过标准偏差选择稳定而特异性强的分量特征点及其组合作为浮游植物荧光识别特征谱,并对其稳定性和判别能力进行贝叶斯判别分析,以判别正确率为基准选择分量组合cd3～cd6作为最佳荧光识别特征谱构建浮游植物荧光标准特征谱库,结合非负最小二乘法实现了浮游植物群落组成门、属水平上的识别测定:单种浮游植物在门、属水平上的识别正确率分别为95.5%和85.7%;浮游植物混合样品(混合比例分别为100%,75%,25%)在门水平上的识别正确率分别为100%,90.9%,53.3%,平均识别相对含量分别为79.7%,68.3%,17.5%;优势藻(单种优势度达75%)在属水平上的识别正确率为81.2%。将该技术用于围隔实验和现场调查采集水样,有效实现了浮游植物在门水平上的定性定量识别测定。