Rao-Blackwellized particle smoothers for mixed linear/nonlinear state-space models

We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction. © 2013 IEEE.

Interannual horizontal heat advection in the surface mixed layer over the equatorial Pacific Ocean: assimilation versus TAO analysis

The interannual anomalies of horizontal heat advection in the surface mixed layer over the equatorial Pacific Ocean in an assimilation experiment are studied and compared with existing observational analyses. The assimilation builds upon a hindcast study that has produced a good simulation of the observed equatorial currents and optimizes the simulation of the Reynolds sea surface temperature (SST) data. The comparison suggests that the assimilation has improved the simulation of the interannual horizontal heat advection of the surface mixed layer significantly. During periods of interrupted current measurements, the assimilation is shown to produce more meaningful anomalies of the heat advection than the interpolation of the observational data does. The assimilation also shows that the eddy heat flux due to the correlation between high-frequency current and SST variations, which is largely overlooked by the existing observational analyses, is important for the interannual SST balance over the equatorial Pacific. The interannual horizontal heat advection anomalies are found to be sensitive to SST errors where oceanic currents are strong, which is a challenge for ENSO prediction. The study further suggests that the observational analyses of the tropical SST balance based on the TAO and the Reynolds SST data contain significant errors due to the large gradient errors in the Reynolds SST data, which are amplified into the advection anomalies by the large equatorial currents.

Simulation of the ocean surface mixed layer under the wave breaking

A one-dimensional mixed-layer model, including a Mellor-Yamada level 2.5 turbulence closure scheme, was implemented to investigate the dynamical and thermal structures of the ocean surface mixed layer in the northern South China Sea. The turbulent kinetic energy released through wave breaking was incorporated into the model as a source of energy at the ocean surface, and the influence of the breaking waves on the mixed layer was studied. The numerical simulations show that the simulated SST is overestimated in summer without the breaking waves. However, the cooler SST is simulated when the effect of the breaking waves is considered, the corresponding discrepancy with the observed data decreases up to 20% and the MLD calculated averagely deepens 3.8 m. Owing to the wave-enhanced turbulence mixing in the summertime, the stratification at the bottom of the mixed layer was modified and the temperature gradient spread throughout the whole thermocline compared with the concentrated distribution without wave breaking.

Annual cycle of stratification and tidal fronts in the Bohai Sea: A model study

In general, competition between buoyancy mechanisms and mixing dynamics largely determines the water column structure in a shelf sea. A three dimensional baroclinic ocean model forced by surface heat fluxes and the 2.5 order Mellor-Yamada turbulence scheme is used to simulate the annual cycle of the temperature in the Bohai Sea. The difference between the sea surface temperature (SST) and sea bottom temperature (SBT) is used to examine the evolution of its vertical stratification. It is found that the water column is well-mixed from October to March and that the seasonal thermocline appears in April, peaks in July and then weakens afterwards, closely following the heat budget. In addition, the Loder parameter based on the topography and tidal current amplitude is also computed in order to examine tidal fronts in the BS, which are evident in summer months when the wind stirring mechanism is weak.

Wave breaking on turbulent energy budget in the ocean surface mixed layer

As an important physical process at the air-sea interface, wave movement and breaking have a significant effect on the ocean surface mixed layer (OSML). When breaking waves occur at the ocean surface, turbulent kinetic energy (TKE) is input downwards, and a sublayer is formed near the surface and turbulence vertical mixing is intensively enhanced. A one-dimensional ocean model including the Mellor-Yamada level 2.5 turbulence closure equations was employed in our research on variations in turbulent energy budget within OSML. The influence of wave breaking could be introduced into the model by modifying an existing surface boundary condition of the TKE equation and specifying its input. The vertical diffusion and dissipation of TKE were effectively enhanced in the sublayer when wave breaking was considered. Turbulent energy dissipated in the sublayer was about 92.0% of the total depth-integrated dissipated TKE, which is twice higher than that of non-wave breaking. The shear production of TKE decreased by 3.5% because the mean flow fields tended to be uniform due to wave-enhanced turbulent mixing. As a result, a new local equilibrium between diffusion and dissipation of TKE was reached in the wave-enhanced layer. Below the sublayer, the local equilibrium between shear production and dissipation of TKE agreed with the conclusion drawn from the classical law-of-the-wall (Craig and Banner, 1994).

Factors influencing the climatological mixed layer depth in the South China Sea: numerical simulations

The mixed layer depth (MLD) in the upper ocean is an important physical parameter for describing the upper ocean mixed layer. We analyzed several major factors influencing the climatological mixed layer depth (CMLD), and established a numerical simulation in the South China Sea (SCS) using the Regional Ocean Model System (ROMS) with a high-resolution (1/12A degrees x1/12A degrees) grid nesting method and 50 vertical layers. Several ideal numerical experiments were tested by modifying the existing sea surface boundary conditions. Especially, we analyzed the sensitivity of the results simulated for the CMLD with factors of sea surface wind stress (SSWS), sea surface net heat flux (SSNHF), and the difference between evaporation and precipitation (DEP). The result shows that of the three factors that change the depth of the CMLD, SSWS is in the first place, when ignoring the impact of SSWS, CMLD will change by 26% on average, and its effect is always to deepen the CMLD; the next comes SSNHF (13%) for deepening the CMLD in October to January and shallowing the CMLD in February to September; and the DEP comes in the third (only 2%). Moreover, we analyzed the temporal and spatial characteristics of CMLD and compared the simulation result with the ARGO observational data. The results indicate that ROMS is applicable for studying CMLD in the SCS area.

Submesoscale activity over the shelf of the northern South China Sea in summer: simulation with an embedded model

We applied a primitive equation ocean model to simulate submesoscale activities and processes over the shelf of the northern South China Sea (NSCS) with a one-way nesting technology for downscaling. The temperature and density fields showed that submesoscale activities were ubiquitous in the NSCS shelf. The vertical velocity was considerably enhanced in submesoscale processes and could reach an average of 58 m per day in the subsurface. At this point, the mixed layer depth also was deepened along the front, and the surface kinetic energy also increased with the intense vertical movement induced by submesoscale activity. Thus, submesoscale stirring/mixing is important for tracers, such as temperature, salinity, nutrients, dissolved organic, and inorganic carbon. This result may have implication for climate and biogeochemical investigations.

Mixed-layer water oscillations in tropical Pacific for ENSO cycle

The main modes of interannal variabilities of thermocline and sea surface wind stress in the tropical Pacific and their interactions are investigated, which show the following results. (1) The thermocline anomalies in the tropical Pacific have a zonal dipole pattern with 160 W as its axis and a meridional seesaw pattern with 6-8 degrees N as its transverse axis. The meridional oscillation has a phase lag of about 90 to the zonal oscillation, both oscillations get together to form the El Nino/La Nina cycle, which behaves as a mixed layer water oscillates anticlockwise within the tropical Pacific basin between equator and 12 degrees N. (2) There are two main patterns of wind stress anomalies in the tropical Pacific, of which the first component caused by trade wind anomaly is characterized by the zonal wind stress anomalies and its corresponding divergences field in the equatorial Pacific, and the abnormal cross- equatorial flow wind stress and its corresponding divergence field, which has a sign opposite to that of the equatorial region, in the off-equator of the tropical North Pacific, and the second component represents the wind stress anomalies and corresponding divergences caused by the ITCZ anomaly. (3) The trade winds anomaly plays a decisive role in the strength and phase transition of the ENSO cycle, which results in the sea level tilting, provides an initial potential energy to the mixed layer water oscillation, and causes the opposite thermocline displacement between the west side and east side of the equator and also between the equator and 12 degrees N of the North Pacific basin, therefore determines the amplitude and route for ENSO cycle. The ITCZ anomaly has some effects on the phase transition. (4) The thermal anomaly of the tropical western Pacific causes the wind stress anomaly and extends eastward along the equator accompanied with the mixed layer water oscillation in the equatorial Pacific, which causes the trade winds anomaly and produces the anomalous wind stress and the corresponding divergence in favor to conduce the oscillation, which in turn intensifies the oscillation. The coupled system of ocean-atmosphere interactions and the inertia gravity of the mixed layer water oscillation provide together a phase-switching mechanism and interannual memory for the ENSO cycle. In conclusion, the ENSO cycle essentially is an inertial oscillation of the mixed layer water induced by both the trade winds anomaly and the coupled ocean-atmosphere interaction in the tropical Pacific basin between the equator and 12 degrees N. When the force produced by the coupled ocean-atmosphere interaction is larger than or equal to the resistance caused by the mixed layer water oscillation, the oscillation will be stronger or maintain as it is, while when the force is less than the resistance, the oscillation will be weaker, even break.

Inclusive education policy, the general allocation model and dilemmas of practice in primary schools

Background: Inclusive education is central to contemporary discourse internationally reflecting societies’ wider commitment to social inclusion. Education has witnessed transforming approaches that have created differing distributions of power, resource allocation and accountability. Multiple actors are being forced to consider changes to how key services and supports are organised. This research constitutes a case study situated within this broader social service dilemma of how to distribute finite resources equitably to meet individual need, while advancing inclusion. It focuses on the national directive with regard to inclusive educational practice for primary schools, Department of Education and Science Special Education Circular 02/05, which introduced the General Allocation Model (GAM) within the legislative context of the Education of Persons with Special Educational Needs (EPSEN) Act (Government of Ireland, 2004). This research could help to inform policy with ‘facts about what is happening on the ground’ (Quinn, 2013). Research Aims: The research set out to unearth the assumptions and definitions embedded within the policy document, to analyse how those who are at the coalface of policy, and who interface with multiple interests in primary schools, understand the GAM and respond to it, and to investigate its effects on students and their education. It examines student outcomes in the primary schools where the GAM was investigated. Methods and Sample The post-structural study acknowledges the importance of policy analysis which explicitly links the ‘bigger worlds’ of global and national policy contexts to the ‘smaller worlds’ of policies and practices within schools and classrooms. This study insists upon taking the detail seriously (Ozga, 1990). A mixed methods approach to data collection and analysis is applied. In order to secure the perspectives of key stakeholders, semi-structured interviews were conducted with primary school principals, class teachers and learning support/resource teachers (n=14) in three distinct mainstream, non-DEIS schools. Data from the schools and their environs provided a profile of students. The researcher then used the Pobal Maps Facility (available at www.pobal.ie) to identify the Small Area (SA) in which each student resides, and to assign values to each address based on the Pobal HP Deprivation Index (Haase and Pratschke, 2012). Analysis of the datasets, guided by the conceptual framework of the policy cycle (Ball, 1994), revealed a number of significant themes. Results: Data illustrate that the main model to support student need is withdrawal from the classroom under policy that espouses inclusion. Quantitative data, in particular, highlighted an association between segregated practice and lower socioeconomic status (LSES) backgrounds of students. Up to 83% of the students in special education programmes are from lower socio-economic status (LSES) backgrounds. In some schools 94% of students from LSES backgrounds are withdrawn from classrooms daily for special education. While the internal processes of schooling are not solely to blame for class inequalities, this study reveals the power of professionals to order children in school, which has implications for segregated special education practice. Such agency on the part of key actors in the context of practice relates to ‘local constructions of dis/ability’, which is influenced by teacher habitus (Bourdieu, 1984). The researcher contends that inclusive education has not resulted in positive outcomes for students from LSES backgrounds because it is built on faulty assumptions that focus on a psycho-medical perspective of dis/ability, that is, placement decisions do not consider the intersectionality of dis/ability with class or culture. This study argues that the student need for support is better understood as ‘home/school discontinuity’ not ‘disability’. Moreover, the study unearths the power of some parents to use social and cultural capital to ensure eligibility to enhanced resources. Therefore, a hierarchical system has developed in mainstream schools as a result of funding models to support need in inclusive settings. Furthermore, all schools in the study are ‘ordinary’ schools yet participants acknowledged that some schools are more ‘advantaged’, which may suggest that ‘ordinary’ schools serve to ‘bury class’ (Reay, 2010) as a key marker in allocating resources. The research suggests that general allocation models of funding to meet the needs of students demands a systematic approach grounded in reallocating funds from where they have less benefit to where they have more. The calculation of the composite Haase Value in respect of the student cohort in receipt of special education support adopted for this study could be usefully applied at a national level to ensure that the greatest level of support is targeted at greatest need. Conclusion: In summary, the study reveals that existing structures constrain and enable agents, whose interactions produce intended and unintended consequences. The study suggests that policy should be viewed as a continuous and evolving cycle (Ball, 1994) where actors in each of the social contexts have a shared responsibility in the evolution of education that is equitable, excellent and inclusive.

Lognormal and gamma mixed negative binomial regression

In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior information, such as sparsity in the regression coefficients. By placing a gamma distribution prior on the NB dispersion parameter r, and connecting a log-normal distribution prior with the logit of the NB probability parameter p, efficient Gibbs sampling and variational Bayes inference are both developed. The closed-form updates are obtained by exploiting conditional conjugacy via both a compound Poisson representation and a Polya-Gamma distribution based data augmentation approach. The proposed Bayesian inference can be implemented routinely, while being easily generalizable to more complex settings involving multivariate dependence structures. The algorithms are illustrated using real examples. Copyright 2012 by the author(s)/owner(s).

Explanatory Model for the Use of Traditional Medicines in Kilimanjaro, Tanzania

Introduction: Traditional medicines are one of the most important means of achieving total health care coverage globally, and their importance in Tanzania extends beyond the impoverished rural areas. Their use remains high even in urban settings among the educated middle and upper classes. They are a critical component healthcare in Tanzania, but they also can have harmful side effects. Therefore we sought to understand the decision-making and reasoning processes by building an explanatory model for the use of traditional medicines in Tanzania.

Methods: We conducted a mixed-methods study between December 2013 and June 2014 in the Kilimanjaro Region of Tanzania. Using purposive sampling methods, we conducted focus group discussions (FGDs) and in-depth interviews of key informants, and the qualitative data were analyzed using an inductive Framework Method. A structured survey was created, piloted, and then administered it to a random sample of adults. We reported upon the reliability and validity of the structured survey, and we used triangulation from multiple sources to synthesize the qualitative and quantitative data.

Results: A total of five FGDs composed of 59 participants and 27 in-depth interviews were conducted in total. 16 of the in-depth interviews were with self-described traditional practitioners or herbal vendors. We identified five major thematic categories that relate to the decision to use traditional medicines in Kilimanjaro: healthcare delivery, disease understanding, credibility of the traditional practices, health status, and strong cultural beliefs.

A total of 473 participants (24.1% male) completed the structured survey. The most common reasons for taking traditional medicines were that they are more affordable (14%, 12.0-16.0), failure of hospital medicines (13%, 11.1-15.0), they work better (12%, 10.7-14.4), they are easier

to obtain (11%, 9.48-13.1), they are found naturally or free (8%, 6.56-9.68), hospital medicines have too many chemical (8%, 6.33-9.40), and they have fewer side effects (8%, 6.25-9.30). The most common uses of traditional medicines were for symptomatic conditions (42%), chronic diseases (14%), reproductive problems (11%), and malaria and febrile illnesses (10%). Participants currently taking hospital medicines for chronic conditions were nearly twice as likely to report traditional medicines usage in the past year (RR 1.97, p=0.05).

Conclusions: We built broad explanatory model for the use of traditional medicines in Kilimanjaro. The use of traditional medicines is not limited to rural or low socioeconomic populations and concurrent use of traditional medicines and biomedicine is high with frequent ethnomedical doctor shopping. Our model provides a working framework for understanding the complex interactions between biomedicine and traditional medicine. Future disease management and treatment programs will benefit from this understanding, and it can lead to synergistic policies with more effective implementation.

Hydrocarbon field size distributions: a case study in mixed integer nonlinear programming

Of key importance to oil and gas companies is the size distribution of fields in the areas that they are drilling. Recent arguments suggest that there are many more fields yet to be discovered in mature provinces than had previously been thought because the underlying distribution is monotonic not peaked. According to this view the peaked nature of the distribution for discovered fields reflects not the underlying distribution but the effect of economic truncation. This paper contributes to the discussion by analysing up-to-date exploration and discovery data for two mature provinces using the discovery-process model, based on sampling without replacement and implicitly including economic truncation effects. The maximum likelihood estimation involved generates a high-dimensional mixed-integer nonlinear optimization problem. A highly efficient solution strategy is tested, exploiting the separable structure and handling the integer constraints by treating the problem as a masked allocation problem in dynamic programming.

A mixed Eulerian-Lagrangian approach for metal extrusion

In this paper a mixed Eulerian-Lagrangian approach for the modelling metal extrusion processes is presented. The approach involves the solution of non-Newtonian fluid flow equations in an Eulerian context, using a free-surface algorithm to track the behaviour of the workpiece and its extrusion. The solid mechanics equations associated with the tools are solved in Lagangrian context. Thermal interactions between the workpiece are modelled and a fluid-structure interaction technique is employed to model the effect of the fluid traction load imposed by the workpiece on the tools. Two extrusion test cases are investigated and the results obtained show the potential of the model with regard to representing the physics of the process and the simulation time.