Regularization techniques for ill-posed inverse problems in data assimilation

Optimal state estimation from given observations of a dynamical system by data assimilation is generally an ill-posed inverse problem. In order to solve the problem, a standard Tikhonov, or L2, regularization is used, based on certain statistical assumptions on the errors in the data. The regularization term constrains the estimate of the state to remain close to a prior estimate. In the presence of model error, this approach does not capture the initial state of the system accurately, as the initial state estimate is derived by minimizing the average error between the model predictions and the observations over a time window. Here we examine an alternative L1 regularization technique that has proved valuable in image processing. We show that for examples of flow with sharp fronts and shocks, the L1 regularization technique performs more accurately than standard L2 regularization.

L1-regularisation for ill-posed problems in variational data assimilation

We consider four-dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2-regularisation, a widely used method for solving ill-posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1-norm regularisation, recovers sharp edges better than L2-norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1-norm regularisation performs much better than the standard L2-norm regularisation in 4DVar.

On discrimination algorithms for ill-posed problems with an application to magnetic tomography

In this paper we explore classification techniques for ill-posed problems. Two classes are linearly separable in some Hilbert space X if they can be separated by a hyperplane. We investigate stable separability, i.e. the case where we have a positive distance between two separating hyperplanes. When the data in the space Y is generated by a compact operator A applied to the system states ∈ X, we will show that in general we do not obtain stable separability in Y even if the problem in X is stably separable. In particular, we show this for the case where a nonlinear classification is generated from a non-convergent family of linear classes in X. We apply our results to the problem of quality control of fuel cells where we classify fuel cells according to their efficiency. We can potentially classify a fuel cell using either some external measured magnetic field or some internal current. However we cannot measure the current directly since we cannot access the fuel cell in operation. The first possibility is to apply discrimination techniques directly to the measured magnetic fields. The second approach first reconstructs currents and then carries out the classification on the current distributions. We show that both approaches need regularization and that the regularized classifications are not equivalent in general. Finally, we investigate a widely used linear classification algorithm Fisher's linear discriminant with respect to its ill-posedness when applied to data generated via a compact integral operator. We show that the method cannot stay stable when the number of measurement points becomes large.

Does managerial turnover affect football club share prices?

This paper analyses the 53 managerial sackings and resignations from 16 stock exchange listed English football clubs during the nine seasons between 2000/01 and 2008/09. The results demonstrate that, on average, a managerial sacking results in a post-announcement day market-adjusted share price rise of 0.3%, whilst a resignation leads to a drop in share price of 1% that continues for a trading month thereafter, cumulating in a negative abnormal return of over 8% from a trading day before the event. These findings are intuitive, and suggest that sacking a poorly performing manager may be welcomed by the markets as a possible route to better future match performance, while losing a capable manager through resignation, who typically progresses to a superior job, will result in a drop in a club’s share price. The paper also reveals that while the impact of managerial departures on stock price volatilities is less clear-cut, speculation in the newspapers is rife in the build-up to such an event.

Modified section method for laser-welding of ill-fitting cp Ti and Ni-Cr alloy one-piece cast implant-supported frameworks

P>This study aimed to verify the effect of modified section method and laser-welding on the accuracy of fit of ill-fitting commercially pure titanium (cp Ti) and Ni-Cr alloy one-piece cast frameworks. Two sets of similar implant-supported frameworks were constructed. Both groups of six 3-unit implant-supported fixed partial dentures were cast as one-piece [I: Ni-Cr (control) and II: cp Ti] and evaluated for passive fitting in an optical microscope with both screws tightened and with only one screw tightened. All frameworks were then sectioned in the diagonal axis at the pontic region (III: Ni-Cr and IV: cp Ti). Sectioned frameworks were positioned in the matrix (10-Ncm torque) and laser-welded. Passive fitting was evaluated for the second time. Data were submitted to anova and Tukey-Kramer honestly significant difference tests (P < 0 center dot 05). With both screws tightened, one-piece cp Ti group II showed significantly higher misfit values (27 center dot 57 +/- 5 center dot 06 mu m) than other groups (I: 11 center dot 19 +/- 2 center dot 54 mu m, III: 12 center dot 88 +/- 2 center dot 93 mu m, IV: 13 center dot 77 +/- 1 center dot 51 mu m) (P < 0 center dot 05). In the single-screw-tightened test, with readings on the opposite side to the tightened side, Ni-Cr cast as one-piece (I: 58 center dot 66 +/- 14 center dot 30 mu m) was significantly different from cp Ti group after diagonal section (IV: 27 center dot 51 +/- 8 center dot 28 mu m) (P < 0 center dot 05). On the tightened side, no significant differences were found between groups (P > 0 center dot 05). Results showed that diagonally sectioning ill-fitting cp Ti frameworks lowers misfit levels of prosthetic implant-supported frameworks and also improves passivity levels of the same frameworks when compared to one-piece cast structures.

Recurrent sores by ill-fitting dentures and intra-oral squamous cell carcinoma in smokers

Objectives: To examine whether denture use and recurrent sores caused by ill-fitting dentures are associated with intra-oral squamous cell carcinoma (IO-SCC) in individuals exposed to tobacco. Methods: We conducted a hospital-based case-control study. The study population comprised 124 patients with IO-SCC and the same number of controls (individually paired according to gender and age) recruited from outpatient units of the same hospital. Conditional logistic regression analysis assessed the effect of denture use and recurrent oral sores by ill-fitting dentures, adjusted by covariates on the lifetime exposure to alcohol and tobacco, socioeconomic standings, and dietary patterns. Results: The use of dentures showed no association with IO-SCC [adjusted odds ratio (OR) 1.40, 95 percent confidence interval 0.51-3.87, P = 0.513] in an assessment controlled by socioeconomic position, lifetime exposure to alcohol and tobacco, and dietary patterns. However, the report of recurrent sores caused by ill-fitting dentures showed significant association with the disease (adjusted OR 4.58, 95 percent confidence interval 1.52-13.76, P = 0.007). Conclusions: The association between recurrent oral sores caused by ill-fitting dentures and squamous cell carcinoma of the mouth in smokers is in agreement with the hypothesis that the chronic physical irritation of oral mucosa contributes to the topical carcinogenic effect of tobacco, which must be taken into careful consideration in the planning of dental services for adults and the elderly.

"Dare to share!" : Bikt, moderskap och motstånd i Den stora mammabikten

”Dare to share!”: Confession, motherhood and resistance in The great mother confession This article explore the meaning of confession in a commercial, secular event – The great mother confession (TGM). The event is understood as imbedded in a therapeutic culture where emotional disclosure, in the form of confessions, is a highly valued practice. In a web-based confession-blog that constitutes part of the TGM-concept, confessions serve to free mothers from supressing norms. The blog becomes an arena for a volatile community where burdening and ”forbidden” thoughts and emotions becomes generalised and disarmed, releasing mothers from guilt. When this function of the blog is questioned from a competing sub-discourse of the therapeutic, emphasising the disclosure of happiness, a struggle emerges over the authority to define the meanings of confession. TGM can be understood as having potential for serving as an arena for challenging norms, but even as norms are implicitly addressed the practice makes a halt at that point. Norms that are seemingly dissolved in responses to confessions are not questioned, only recognised, normalised and de-politicised.

Commitment of the Mentally Ill in Maine: a History of Public Policy

This paper traces the historical development in the State of Maine of the procedures by which persons found to be mentally unsound can be committed to institutional care against their will. Beginning in 1820 and continuing to the present, specific changes in the statutes governing this area are noted. Both the criminal and civil commitment procedures are dealt with. Following the historical trace, pending legislation relating to the criminal commitment process is examined in detail. Finally, consideration is given to the need for a complete reexamination of the practice of involuntary commitment involving ethical and constitutional issues.

Using Interlibrary Loan Data as a Section Tool: ILL Trails Provide Collection Clues

This article describes analyzing Interlibrary Loan data to help inform collection management decision and offers guidance for formulating policies for discerning borrowed titles indicative of gaps in the library from special-interest pursuits beyond the scope of the university curriculum.

Are CGE Models still useful in economic policy making?

This paper develops background considerations to help better framing the results of a CGE exercise. Three main criticisms are usually addressed to CGE efforts. First, they are too aggregate, their conclusions failing to shed light on relevant sectors or issues. Second, they imply huge data requirements. Timeliness is frequently jeopardised by out-dated sources, benchmarks referring to realities gone by. Finally, results are meaningless, as they answer wrong or ill-posed questions. Modelling demands end up by creating a rather artificial context, where the original questions lose content. In spite of a positive outlook on the first two, crucial questions lie in the third point. After elaborating such questions, and trying to answer some, the text argues that CGE models can come closer to reality. If their use is still scarce to give way to a fruitful symbiosis between negotiations and simulation results, they remain the only available technique providing a global, inter-related way of capturing economy-wide effects of several different policies. International organisations can play a major role supporting and encouraging improvements. They are also uniquely positioned to enhance information and data sharing, as well as putting people from various origins together, to share their experiences. A serious and complex homework is however required, to correct, at least, the most dangerous present shortcomings of the technique.

Entrepreneurial risk and labour's share in output

This paper presents a theoretical model which discusses the role played by the entrepreneurial risk on the distribution of the national income. In a two-period general equilibrium framework with competitive risk-averse entrepreneurs it is shown that the highest the risk borne by firms, the lower will be real wages, employment and the labour's share in output. The model helps explain the fall of the labour's share in the Brazilian output during the 1980s.