Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

[On quality of life after surgical therapy of oral cancer - a retrospective multi-center study: the connection between dedentition, denture, quality of life, and dysphagia, and the resulting rehabilitation schemes]

PURPOSE: The surgical treatment of oral cancer results in functional and aesthetical impairments. Patients' quality of life is considerably impaired by oral symptoms resulting from therapy of oral cancer. In many cases the inevitable resection of the tumor, as well as the adjuvant radiochemotherapy will cause the destruction of physiologically and anatomically important structures. One focus of research was the specific rehabilitation of dental loss by functional dentures. Another was the course of 19 impairments (comprehension of speech for unknown others, comprehension of speech for familiar others, eating/swallowing, mobility of the tongue, opening range of the mouth, mobility of lower jaw, mobility of neck, mobility of arms and shoulders, sense of taste, sense of smell, appearance, strength, appetite, respiration, pain, swelling, xerostomia, halitosis). METHODS: Commissioned by the German, Austrian and Swiss cooperative group on tumors of the maxillofacial region (DOSAK), data were collected in 3.894 questionnaires at 43 hospitals in Germany, Austria and Switzerland. The catalogue comprised 147 items in 9 chapters. At the end of the enquiry, 1.761 anonymous questionnaires were returned by 38 hospitals. 1.652 of these could be evaluated regarding the question. RESULTS: The sum score of the 19 impairments was highly increased immediately after the operation and recovered over the next 6 months, without, however, reaching the pre-surgery level. Of 1.652 patients, only 35% did not lose any teeth during therapy. 23% lost up to 5, 17% up to 10 teeth. A quarter of the patients lost more than 10 teeth. The more teeth were lost, the greater the decline of quality of life (p < or = 0.001), although this could be allayed by the functionality of the dentures (p < or = 0.001). There is a reciprocal dependence between the functionality of dental prosthetics and impairment by eating/swallowing (p < or = 0.001). CONCLUSIONS: Patients' quality of life after radical surgery of a carcinoma of the oral cavity depends not only on the functionality of dentures and the specificity of rehabilitation, but also from the initial findings, the extent and location of the resection, the chosen therapy, the general circumstances of the patient's life as well as their strategies of coping. These factors, however, unlike those of functionality of dental prosthesis and rehabilitation, are not modifiable.

Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Promoting research-user collaboration: an assessment of funding schemes: Fifth NCCR North-South Report on Effectiveness

Donors increasingly require that the research they fund be of benefit for society and the environment. To this end, researchers addressing complex and uncertain problems should work together with research users. This is not always easy: researchers are expected to collaborate with non-academic partners, but are not funded for the additional work. Collaborative research projects often cannot tap the full potential of user engagement. Therefore, specific institutional and organisational conditions are necessary that foresee or even foster research–user engagement; funding schemes are one possible solution. Right from the start, the NCCR North-South programme introduced Partnership Actions for Mitigating Syndromes of Global Change (PAMS). This evaluation assesses the types of collaboration supported by PAMS, as well as the value of PAMS as a funding scheme for collaboration. It compares PAMS with similar funding schemes of other universities, research programmes, or projects, and contains recommendations.

Influence of microphysical schemes on atmospheric water in the Weather Research and Forecasting model

This study examines how different microphysical parameterization schemes influence orographically induced precipitation and the distributions of hydrometeors and water vapour for midlatitude summer conditions in the Weather Research and Forecasting (WRF) model. A high-resolution two-dimensional idealized simulation is used to assess the differences between the schemes in which a moist air flow is interacting with a bell-shaped 2 km high mountain. Periodic lateral boundary conditions are chosen to recirculate atmospheric water in the domain. It is found that the 13 selected microphysical schemes conserve the water in the model domain. The gain or loss of water is less than 0.81% over a simulation time interval of 61 days. The differences of the microphysical schemes in terms of the distributions of water vapour, hydrometeors and accumulated precipitation are presented and discussed. The Kessler scheme, the only scheme without ice-phase processes, shows final values of cloud liquid water 14 times greater than the other schemes. The differences among the other schemes are not as extreme, but still they differ up to 79% in water vapour, up to 10 times in hydrometeors and up to 64% in accumulated precipitation at the end of the simulation. The microphysical schemes also differ in the surface evaporation rate. The WRF single-moment 3-class scheme has the highest surface evaporation rate compensated by the highest precipitation rate. The different distributions of hydrometeors and water vapour of the microphysical schemes induce differences up to 49 W m−2 in the downwelling shortwave radiation and up to 33 W m−2 in the downwelling longwave radiation.

Han Migration to Xinjiang Uyghur Autonomous Region: Between State Schemes and Migrants’ Strategies

Post-1949 Han migration to Xinjiang Uyghur Autonomous Region in northwest China is a hotly debated issue among the Xinjiang scholars and within the region itself. While it is often discussed using statistical data as a large-scale historical process, I argue in this article for a more differentiated view of Han migrants. I demonstrate that in the popular discourse migrants are distinguished into numerous categories like Bingtuaners , Profit-Driven Migrants, Border Supporters, Qualified Personnel, Educated Youth, and others. Accordingly, I argue that Han migrants to Xinjiang should not be understood as a homogeneous category of participants in a singular state project intended to establish state control over the region. High return rates demonstrate that state attempts to make Han settle in Xinjiang are only partly successful, and that migrants follow their own strategies when situation permits, rather than fulfill the government’s plans. Individuals who have migrated since the 1980s are especially careful in their assessment of the economic incentives of settlement, and many decide to remain mobile.