Gradient free parameter estimation for hidden Markov models with intractable likelihoods

In this article we focus on Maximum Likelihood estimation (MLE) for the static model parameters of hidden Markov models (HMMs). We will consider the case where one cannot or does not want to compute the conditional likelihood density of the observation given the hidden state because of increased computational complexity or analytical intractability. Instead we will assume that one may obtain samples from this conditional likelihood and hence use approximate Bayesian computation (ABC) approximations of the original HMM. Although these ABC approximations will induce a bias, this can be controlled to arbitrary precision via a positive parameter , so that the bias decreases with decreasing . We first establish that when using an ABC approximation of the HMM for a fixed batch of data, then the bias of the resulting log- marginal likelihood and its gradient is no worse than O(n), where n is the total number of data-points. Therefore, when using gradient methods to perform MLE for the ABC approximation of the HMM, one may expect parameter estimates of reasonable accuracy. To compute an estimate of the unknown and fixed model parameters, we propose a gradient approach based on simultaneous perturbation stochastic approximation (SPSA) and Sequential Monte Carlo (SMC) for the ABC approximation of the HMM. The performance of this method is illustrated using two numerical examples

An equivariant quantum Pieri rule for the Grassmannian on cylindric shapes

The quantum cohomology ring of the Grassmannian is determined by the quantum Pieri rule for multiplying by Schubert classes indexed by row or column-shaped partitions. We provide a direct equivariant generalization of Postnikov's quantum Pieri rule for the Grassmannian in terms of cylindric shapes, complementing related work of Gorbounov and Korff in quantum integrable systems. The equivariant terms in our Graham-positive rule simply encode the positions of all possible addable boxes within one cylindric skew diagram. As such, unlike the earlier equivariant quantum Pieri rule of Huang and Li and known equivariant quantum Littlewood-Richardson rules, our formula does not require any calculations in a different Grassmannian or two-step flag variety

Characterization of Rotating Cavitation in a Four Bladed Inducer

This work aims to characterize the dynamic behavior of a four bladed inducer and clarify the physical mechanism that leads to the onset of rotating cavitation. The inducer under consideration is representative of a low-pressure liquid oxygen pump (LPOP) inducer of modern design and incorporates several standard design features used in rocket turbopumps to suppress rotating cavitation. The mechanism is characterized based on a combination of two-phase numerical simulations and inducer experiments. Experimental measurements demonstrate a supersynchronous rotating cavity in the periphery of the inducer inlet at frequencies between 1.2 and 1.6 times rotor frequency and a synchronous 2nd spatial harmonic pattern associated with alternate blade cavitation. The analysis indicates a causal link between alternate blade cavitation and rotating cavitation, with a distinct cut-on cut-off behavior. Numerical calculations and high-speed videos elucidate the mechanism of breakdown of alternate blade cavitation and the formation of rotating cavitation. The present work suggests that rotating cavitation is caused by the coupling of the cavities on adjacent blades during alternate blade cavitation. Due to the nearly tangential flow, the vortex lines from one of the non-cavitating blades wrap around the blade leading edge of the adjacent blade, which yields a drop in static pressure and cavity formation. The tip vortex cavity interaction with the leading edge of the blade leads to sheet cavity breakdown with periodic growth and collapse of cavities, creating the apparent super-synchronous rotation of the cavitating region.United States. National Aeronautics and Space Administration (NASA Marshall Space Flight Center

Numerical test of the damping time of layer-by-layer growth on stochastic models

We perform Monte Carlo simulations on stochastic models such as the Wolf-Villain (WV) model and the Family model in a modified version to measure mean separation $\ell$ between islands in submonolayer regime and damping time $\tilde t$ of layer-by-layer growth oscillations on one dimension. The stochastic models are modified, allowing diffusion within interval $r$ upon deposited. It is found numerically that the mean separation and the damping time depend on the diffusion interval $r$, leading to that the damping time is related to the mean separation as ${\tilde t} \sim \ell^{4/3}$ for the WV model and ${\tilde t} \sim \ell^2$ for the Family model. The numerical results are in excellent agreement with recent theoretical predictions.Comment: 4 pages, source LaTeX file and 5 PS figure

Influence of local surface albedo variability and ice crystal shape on passive remote sensing of thin cirrus

Airborne measurements of solar spectral radiance reflected by cirrus are performed with the HALO-Solar Radiation (HALO-SR) instrument onboard the High Altitude and Long Range Research Aircraft (HALO) in November 2010. The data are used to quantify the influence of surface albedo variability on the retrieval of cirrus optical thickness and crystal effective radius. The applied retrieval of cirrus optical properties is based on a standard two-wavelength approach utilizing measured and simulated reflected radiance in the visible and near-infrared spectral region. Frequency distributions of the surface albedos from Moderate resolution Imaging Spectroradiometer (MODIS) satellite observations are used to compile surface-albedo-dependent lookup tables of reflected radiance. For each assumed surface albedo the cirrus optical thickness and effective crystal radius are retrieved as a function of the assumed surface albedo. The results for the cirrus optical thickness are compared to measurements from the High Spectral Resolution Lidar (HSRL). The uncertainty in cirrus optical thickness due to local variability of surface albedo in the specific case study investigated here is below 0.1 and thus less than that caused by the measurement uncertainty of both instruments. It is concluded that for the retrieval of cirrus optical thickness the surface albedo variability is negligible. However, for the retrieval of crystal effective radius, the surface albedo variability is of major importance, introducing uncertainties up to 50%. Furthermore, the influence of the bidirectional reflectance distribution function (BRDF) on the retrieval of crystal effective radius was investigated and quantified with uncertainties below 10%, which ranges below the uncertainty caused by the surface albedo variability. The comparison with the independent lidar data allowed for investigation of the role of the crystal shape in the retrieval. It is found that if assuming aggregate ice crystals, the HSRL observations fit best with the retrieved optical thickness from HALO-SR

Growth of Patterned Surfaces

During epitaxial crystal growth a pattern that has initially been imprinted on a surface approximately reproduces itself after the deposition of an integer number of monolayers. Computer simulations of the one-dimensional case show that the quality of reproduction decays exponentially with a characteristic time which is linear in the activation energy of surface diffusion. We argue that this life time of a pattern is optimized, if the characteristic feature size of the pattern is larger than $(D/F)^{1/(d+2)}$, where $D$ is the surface diffusion constant, $F$ the deposition rate and $d$ the surface dimension.Comment: 4 pages, 4 figures, uses psfig; to appear in Phys. Rev. Let

Underrecognition and undertreatment of asthma in Cape Town primary school children

Background. In view of the high local prevalence of asthma, the extent of recognition and appropriate managementof childhood asthma was studied in a large suburban area of Cape Town.Design. Cross-sectional study based on random community sample of schools.Method. 1955 parents of sub B pupils from 16 schools completed a questionnaire, followed by: (f) an interview of parents of 348 symptomatic children; and (if) bronchial responsiveness testing on 254 children. the final case group consisted of 242 children with reported asthma or multiple asthma symptoms on both questionnaires. Children in whom asthma was acknowledged were compared with those in whom it was not.Results. Overall, any past or current ('ever') asthma was acknowledged by respondents in only 53% of the children, and current asthma in only 37.1%. While most children had received treatment in the previous 12 months, 66.1% of therecognised group were on current treatment (23.2% on daily treatment), compared with 37% of the unrecognised group (3% daily). Salbutamol and theophylline syrups were the most common types of medication, while inhalers and antiinflammatory medications were underused. Only a minority of parents reported the child ever having used a peak flow meter, or volunteered knowledge of preventive measures. Current treatment, and to a lesser degree recognition of asthma by parents, were more common among children on medical aid and of higher socio-eonomic status.Conclusions. These findings suggest that ways need to be found: (i) to increase the use of current asthma treatment guidelines by practitioners; (ii) to provide access to comprehensive care by children not on medical aid; and (iii) to improve education of parents in home management measures such as severity assessment and avoidance of smoking, allergen and dietary triggers