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.     

MRI of hepatic lymphoma

Thirteen patients with biopsy proven hepatic lymphoma (2 Hodgkin, 11 Non-Hodgkin) and a control group of 15 patients with hepatic metastases were analyzed quantitatively and qualitatively by MRI. Focal hepatic lymphoma was most reliably detected (eight of eight patients) and appeared hypointense relative to liver on T₁ weighted (CNR − 7.4 ± 2.3) and hyperintense on T₂ weighted (CNR + 8.4 ± 2.9) images. The mean T₁ and T₂ relaxation times of focal hepatic lymphoma (T₁ = 832 ± 234 msec, T₂ = 84 ± 16 ms) differed significantly from adjacent non-tumorous liver (T₁ = 420 ± 121 ms, T₂ = 51 ± 9 ms; p < 0.05), however CNR values and relaxation times were similar to those of hepatic metastases. Diffuse hepatic lymphoma (microscopic periportal infiltration) was undetectable by MRI in three patients by either morphologic features or quantitative criteria. A mixed pattern of hepatic lymphoma (focal lesions and diffuse infiltration) showed focal areas of slightly decreased signal intensity on T₁ weighted images (CNR = −1.7 ± 0.4) while T₂ weighted images revealed multiple regions of focal hyperintensity (CNR = +13.3 ± 8.4) superimposed on a diffusely hyperintense liver. Our experience demonstrates that either T₁ or T₂ weighted techniques are useful in detecting focal and that T₂ weighted techniques are useful in detecting mixed hepatic lymphoma. Conventional image derived relaxation time measurements and quantitative parameters were of no additional diagnostic value.     

Stability and instability properties of rotating Bose–Einstein condensates

We consider the mean-field dynamics of Bose–Einstein condensates in rotating harmonic traps and establish several stability and instability properties for the corresponding solution. We particularly emphasize the difference between the situation in which the trap is symmetric with respect to the rotation axis and the one where this is not the case.

     

Constrained modeling for spectroscopic measurement of bi-exponential spin-lattice relaxation of water in vivo

The (1)H NMR water signal from spectroscopic voxels localized in gray matter contains contributions from tissue and cerebral spinal fluid (CSF). A typically weak CSF signal at short echo times makes separating the tissue and CSF spin-lattice relaxation times (T(1)) difficult, often yielding poor precision in a bi-exponential relaxation model. Simulations show that reducing the variables in the T(1) model by using known signal intensity values significantly improves the precision of the T(1) measurement. The method was validated on studies on eight healthy subjects (four males and four females, mean age 21 +/- 2 years) through a total of twenty-four spectroscopic relaxation studies. Each study included both T(1) and spin-spin relaxation (T(2)) experiments. All volumes were localized along the Sylvian fissure using a stimulated echo localization technique with a mixing time of 10 ms. The T(2) experiment consisted of 16 stimulated echo acquisitions ranging from a minimum echo time (TE) of 20 ms to a maximum of 1000 ms, with a repetition time of 12 s. All T(1) experiments consisted of 16 stimulated echo acquisition, using a homospoil saturation recovery technique with a minimum recovery time of 50 ms and a maximum 12 s. The results of the T(2) measurements provided the signal intensity values used in the bi-exponential T(1) model. The mean T(1) values when the signal intensities were constrained by the T(2) results were 1055.4 ms +/- 7.4% for tissue and 5393.5 ms +/- 59% for CSF. When the signal intensities remained free variables in the model, the mean T(1) values were 1085 ms +/- 19.4% and 5038.8 ms +/- 113.0% for tissue and CSF, respectively. The resulting improvement in precision allows the water tissue T(1) value to be included in the spectroscopic characterization of brain tissue.     

Laser beacon wave-front sensing without focal anisoplanatism

Wave-front sensing from artificial beacons is normally performed by formation of a focused spot in the atmosphere and sensing of the wave-front distortions produced during the beam's return passage. We propose an alternative method that senses the distortions produced during the outgoing path by forming an intensity pattern in the atmosphere that is then viewed from the ground. A key advantage of this method is that a parallel beam is used, and therefore the wave-front measurements will not suffer from the effects of focal anisoplanatism. We also envisage other geometries, all based on the concept of projecting a pupil pattern onto the atmosphere.     

Variational Quantum Chemistry Programs in JaqalPaq

We present example quantum chemistry programs written with JaqalPaq, a python meta-programming language used to code in Jaqal (Just Another Quantum Assembly Language). These JaqalPaq algorithms are intended to be run on the Quantum Scientific Computing Open User Testbed (QSCOUT) platform at Sandia National Laboratories. Our exemplars use the variational quantum eigensolver (VQE) quantum algorithm to compute the ground state energies of the H2, HeH+, and LiH molecules. Since the exemplars focus on how to program in JaqalPaq, the calculations of the second-quantized Hamiltonians are performed with the PySCF python package, and the mappings of the fermions to qubits are obtained from the OpenFermion python package. Using the emulator functionality of JaqalPaq, we emulate how these exemplars would be executed on an error-free QSCOUT platform and compare the emulated computation of the bond-dissociation curves for these molecules with their exact forms within the relevant basis.