Dynamic Bivariate Mortality Modelling

The dependence structure of the life statuses plays an important role in the valuation of life insurance products involving multiple lives. Although the mortality of individuals is well studied in the literature, their dependence remains a challenging field. In this paper, the main objective is to introduce a new approach for analyzing the mortality dependence between two individuals in a couple. It is intended to describe in a dynamic framework the joint mortality of married couples in terms of marginal mortality rates. The proposed framework is general and aims to capture, by adjusting some parametric form, the desired effect such as the “broken-heart syndrome”. To this end, we use a well-suited multiplicative decomposition, which will serve as a building block for the framework to relate the dependence structure and the marginals, and we make the link with existing practice of affine mortality models. Finally, given that the framework is general, we propose some illustrative examples and show how the underlying model captures the main stylized facts of bivariate mortality dynamics.

     

Similarities Between Rotation and Stratification Effects on Homogeneous Shear Flow

Linear theory is applied to examine rotation and buoyancy effects on homogeneous turbulent shear flows with given vertical velocity shear, S=d/dx ₃. In the rotating shear case (where the rotation vector is perpendicular to the plane of the mean flow, Ω _i =Ωδ _{i 2}), general solutions for the Fourier components of the fluctuating velocity are proposed. These solutions are compared with those proposed in the literature for the Fourier components of the fluctuating velocity and density in the case of a homogeneous stratified shear flow with vertical density gradient, S _ρ=d/dx ₃. It is shown that from the normal mode stability stand point the Bradshaw parameter B=2Ω/S(1+2Ω/S) (in the rotating shear case) and the Richardson number R _i (in the statified shear case) play similar roles in identifying the stability for all the wave components except in the case where Ω·k=0, for which rotation has no effects on the flow. Analysis of the long-time behavior of the non-dimensional spectral density of energy, e ^g , is carried out. In the stable case, e ^g has decaying oscillations or undergoes a power law decay in time. Analytical solutions for the streamwise two-dimensional energy ℰ _ii ¹/2 (i.e. the limit at k ₁=0 of the one-dimensional energy spectra) are proposed. At large time, ℰ _ii ¹(t)/ℰ _ii ¹(0) oscillates around the value (3R _i +1)/(4R _i ) except at R _i =1 it stays constant in time. Similar behavior for ℰ _ii ¹(t)/ℰ _ii ¹(0) is also observed in the rotating shear case (ℰ _ii ¹(t)/ℰ _ii ¹(0) oscillates around the value (1+4B)/(4B)). Due to the behavior of the dimensionless spectral density of energy in both flow cases, the turbulent kinetic energy, /2, the production rate, ?, and the rate due to the buoyancy forces, ℬ, are split into two parts, , ?=?₁+?₂, ℬ=ℬ₁+ℬ₂ (in the stratified shear case, both ?₁ and ℬ₁ vanish when R _i >?, while in the rotating shear case one has ℬ=0). It is shown that when rotation is “cyclonic” (i.e. Ω/S>0), part reaches maximum magnitudes at St ≈2, independent of the B value, and the first time to a zero crossing of ?₂ occurs at this particular value. When rotation is “anticyclonic” (i.e. Ω/S<0) one finds St ≈1.6 instead of St ≈2. In the stratified shear case, both ?₂ and ℬ₂ cross zero at Nt=St ≈2, and part reaches maximum magnitudes at this particular value. These results and in particular those for the turbulent kinetic energy are compared with previous direct numerical simulation (DNS) results in homogeneous stratified shear flows. Received 30 July 2001 and accepted 19 February 2002     

Equilibrium states in homogeneous turbulence with baroclinic instability

The evolution of energies and fluxes in homogeneous turbulence with baroclinic instability is analyzed using the linear theory. The mean flow corresponds to a vertical shear having a uniform mean velocity gradient, ?U _i /?x _j  = S δ _i1 δ _j3, a system rotation about the vertical axis with rate Ω, Ω _i  = Ωδ _i3, and uniform buoyancy gradients in the spanwise ${(\partial B{/}\partial x_2\,{=}\, N_h^2\,{=}\,-2\Omega S)}The evolution of energies and fluxes in homogeneous turbulence with baroclinic instability is analyzed using the linear theory. The mean flow corresponds to a vertical shear having a uniform mean velocity gradient, ∂U _i /∂x _j  = S δ _i1 δ _j3, a system rotation about the vertical axis with rate Ω, Ω _i  = Ωδ _i3, and uniform buoyancy gradients in the spanwise (?B/?x₂ = N_h² = -2WS){(\partial B{/}\partial x_2\,{=}\, N_h^2\,{=}\,-2\Omega S)} and vertical (?B/?x₃ = N_v²){(\partial B{/}\partial x_3\,{=}\,N_v^2)} directions. Computations based on the rapid distortion theory (RDT) are performed for several values of the rotation number R = 2Ω/S and the Richardson number R_i = N_v²/S² < 1{R_i\,{=}\,N_v^2/S^2 <1 }. It is shown that, during an initial phase, the energies and the buoyancy fluxes are sensitive to the effects of pressure and viscosity. At large time, the ratios of energies, as well as the normalized fluxes, evolve to an asymptotically constant value, while the pressure–strain correlation scaled with the product of the turbulent kinetic energy by the shear rate approaches zero. Accordingly, an analytical parametric study based on the “pressure-less” approach (PLA) is also presented. The analytical study indicates that, when R _i  < 1, there is an exponential instability and equilibrium states of turbulence, in agreement with RDT. The energies and the buoyancy fluxes grow exponentially for large times with the same rate (γ in St units). The asymptotic value of the ratios of energies yielded by RDT is well described by its PLA counterpart derived analytically. At R _i  = 0, the asymptotic value of γ increases with increasing R approaching 2 for high rotation rates. At low rotation rates, an important contribution to the kinetic energy comes from the streamwise kinetic energy, whereas, at high rotation rates, the contribution of the vertical kinetic energy is dominant. When 0 < R _i  < 1 and R 1 0{R\ne 0}, the asymptotic value of γ decreases as R _i increases so as it becomes zero at R _i  = 1.     

On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

Hybrid Materials Based on Conducting Polymers for Nitrite Sensing: A Mini Review

Well-known as a hazardous compound, nitrite constitute a real threat to the public health. So, there is a pressing need to detect and quantify them in different matrix. Even though conventional analytical methods can be used to address this issue, electrochemistry allows a fast, sensitive, and efficient analysis. Conducting polymers continue to raise great interest among scientific communities due to their properties. Moreover, their combination with carbon nanomaterials, or metallic nanoparticles improves their properties, and provides great results. In this paper, we will focus on some revealing works devoted to the electrochemical detection of nitrite using this kind of materials.     

Rains of solitons in a figure-of-eight passively mode-locked fiber laser

We report experimental observation of rains of solitons in figure-of-eight fiber laser passively mode-locked through nonlinear optical loop mirror. Soliton pulses are created from an extended noisy background and drift until they reach a condensed phase comprising several tens of aggregated solitons. The observation of this dynamics tends to strengthen the idea of the universality of the collective behavior of solitons.     

Influence of deposition conditions on the optical properties of erbium-doped yttrium oxide films grown by aerosol-UV assisted MOCVD

Erbium-doped Y₂O₃ films were prepared by aerosol-UV assisted metal-organic chemical vapour deposition (MOCVD) at 410 °C. The effects of humidity of carrier gas and UV-assistance on their structure and optical properties were investigated on the as-deposited and thermal annealed films using infrared spectroscopy, X-ray diffraction and transmission electron microscopy. It was found that the as-deposited Er:Y₂O₃ films crystallise in the Y₂O₃ cubic structure and present a very low organic contamination when the deposition takes place under high air humidity and, even better, with UV-assistance. After annealing, two different structural phases are observed corresponding to the cubic and the monoclinic structures of Y₂O₃. The Er³⁺ luminescence analysed in the visible and IR regions, shows the classical green transitions. The best optical properties were obtained with as-deposited and annealed Er:Y₂O₃ films grown under high air humidity with UV-assistance. Under such deposition conditions, ⁴I_13/2 lifetimes was found to be 3.07 and 6.1 ms for films annealed at 800 and 1000 °C, respectively, and up-conversion phenomena were underlined. This indicates that the deposition conditions, in particular air humidity, play an important role in the luminescent properties even after annealing.     

High-Q factor single mode circular photonic crystal nano-resonator

In this work, the analysis, fabrication and optical characterization of a two-dimensional circular photonic crystal (2D-CPC) nano-resonator based on an air/GaAs/air slab waveguide are presented. Four InAs/InGaAs quantum dots (QDs) stacked layers emitting around 1300 nm at room temperature were embedded in a GaAs waveguide layer grown on an Al_0.7Ga_0.3As layer and GaAs substrate. The patterning of the structure and the membrane release were achieved by using electron beam lithography, ICP plasma etching and selective wet etching of the AlGaAs sacrificial layer. The micro-luminescence spectrum recorded from the fabricated nano-cavity shows a narrow optical transition at the resonance wavelength of about 1282 nm with a FWHM and Q-factor of 6.2 Å and more than 2000, respectively.     

Location-routing: Issues,models and methods

This paper is a survey of location-routing: a relatively new branch of locational analysis that takes into account vehicle routing aspects. We propose a classification scheme and look at a number of problem variants. Both exact and heuristic algorithms are investigated. Finally, some suggestions for future research are presented.