Stochastic volatility models with leverage and heavy-tailed distributions: A Bayesian approach using scale mixtures

This paper studies a heavy-tailed stochastic volatility (SV) model with leverage effect, where a bivariate Student-t distribution is used to model the error innovations of the return and volatility equations. Choy et al. (2008) studied this model by expressing the bivariate Student-t distribution as a scale mixture of bivariate normal distributions. We propose an alternative formulation by first deriving a conditional Student-t distribution for the return and a marginal Student-t distribution for the log-volatility and then express these two Student-t distributions as a scale mixture of normal (SMN) distributions. Our approach separates the sources of outliers and allows for distinguishing between outliers generated by the return process or by the volatility process, and hence is an improvement over the approach of Choy et al. (2008). In addition, it allows an efficient model implementation using the WinBUGS software. A simulation study is conducted to assess the performance of the proposed approach and its comparison with the approach by Choy et al. (2008). In the empirical study, daily exchange rate returns of the Australian dollar to various currencies and daily stock market index returns of various international stock markets are analysed. Model comparison relies on the Deviance Information Criterion and convergence diagnostic is monitored by Geweke’s convergence test.     

On Word Equations in One Variable

For a word equation E of length n in one variable x occurring # _x times in E a resolution algorithm of O(n+# _x log n) time complexity is presented here. This is the best result known and for the equations that feature #_x < \fracnlogn\#_{x}<\frac{n}{\log n} it yields time complexity of O(n) which is optimal. Additionally it is proven here that the set of solutions of any one-variable word equation is either of the form F or of the form F∪(uv)⁺ u where F is a set of O(log n) words and u, v are some words such that uv is a primitive word.     

Sterol and steryl ester regulation of phospholipase A2 from the mosquito parasiteLagenidium giganteum

Lagenidium giganteum, a facultative parasite of mosquito larvae, cannot synthesize sterols, and requires an exogenous source of these lipids in order to enter its reproductive cycle. This parasite grows vegetatively in the absence of sterols, but requires cholesterol or structurally related compounds to produce motile zoospores, which are the only stage capable of infecting mosquitoes. Sterols structurally related to cholesterol and some steryl esters inhibited the activity ofL. giganteum phospholipase A₂ (PLA₂), an enzyme that hydrolyzes fatty acids from thesn-2 position of glycerophospholipids. Sterols that induce reproduction inhibitedL. giganteum PLA₂ activity, while sterols and steroids that do not support sporulation had minimal effect. Most steryl esters had no effect on enzyme activity, but cholesteryl arachidonate (CA) was a potent inhibitor of parasite PLA₂. Not all enzymes partly purified using a DEAE-Sephacel column were affected by these lipids, demonstrating selective inhibition of specific enzymes. Potency was enhanced by up to several orders of magnitude if epoxy fatty acids were esterified to the cholesterol nucleus. The steryl ester pool was dynamic during morphogenesis, and the fatty acid composition of the steryl esters did not mimic total cell or membrane (glycerophospholipid) fatty acid composition asL. giganteum proceeded through its growth cycle. Synthesis of CA and monoepoxy CA by the parasite was confirmed using electrospray mass spectrometry and collision-induced dissociation. Steryl derivatives selectively inhibited PLA₂ enzymes from bovine pancreas, snake venom, and human cytoplasmic 85-kDa PLA₂.     

Methods of Image Compression by PHL Transform

In this paper an image data compression scheme based on Periodic Haar Piecewise-Linear (PHL) transform and quantization tables is proposed. Effectiveness of the compression for different classes of images is evaluated. The comparison of the compression quality using PHL and DCT transforms is given.     

Static and Dynamic Slider Air-Bearing Behavior in Heat-Assisted Magnetic Recording Under Thermal Flying Height Control and Laser System-Induced Protrusion

The air bearing’s response to regions of elevated temperature on its bounding surfaces (the slider and disk) may be an important consideration in the head–disk interface design of heat-assisted magnetic recording (HAMR) systems. We implement the general non-isothermal molecular gas lubrication equation into an iterative static solver and dynamic air-bearing solver to evaluate the effect of localized heating of the air-bearing surface (ABS) due to the near-field transducer (NFT). The heat-dissipating components in our simplified HAMR design are the NFT, laser diode, and thermal flying height control (TFC) heater. We investigate the effect of each HAMR slider component on ABS temperature and thermal deformation and the slider’s flying height. The NFT induces a localized thermal spot and protrusion on the larger TFC bulge, and it is the location of maximum temperature. This ABS temperature profile alters the air-bearing pressure distribution, increasing the pressure at the hot NFT location compared with predictions of an isothermal air-bearing solver, so that the center of the pressure acting on the ABS is slightly closer to the trailing edge, thereby decreasing the pitch angle and increasing the minimum flying height. Other researchers have shown that the NFT’s thermal response time may be much faster than its protrusion response time (Xu et al. in IEEE Trans Magn 48:3280–3283, 2012). The slider’s dynamic response to a time-varying NFT thermal spot on the ABS while the combined TFC and NFT induced thermal protrusion remains constant is investigated with our dynamic air-bearing solver. We simulate the slider’s step response to a suddenly applied ABS temperature profile and a pulsed temperature profile that represents laser-on over data zones and laser-off over servo zones. The sudden (step) or rapid (pulse) increase in ABS temperature induces a sudden or rapid increase in pressure at the NFT location, thereby exciting the air bearing’s first pitch mode. For the slider design and simulation conditions used here, the result of the pitch mode excitation is to alter the position of the center of pressure in the slider’s length direction, thereby changing the pitch moment. In response, the pitch angle and minimum flying height change. The step response decays after approximately 0.15 ms. Because the laser duty cycle is much shorter than this response time, a periodic disturbance is predicted for the center of pressure coordinate, pitch angle, and minimum flying height. The peak-to-peak minimum flying height modulations are relatively small (only up to 0.126 nm); more significantly, the time-averaged minimum flying height increases 0.5 nm for the NFT that reached 208 °C compared to simulations of the isothermal ABS at ambient temperature.