On the classification of plane graphs representing structurally stable rational Newton flows

We study certain plane graphs, called Newton graphs, representing a special class of dynamical systems which are closely related to Newton's iteration method for finding zeros of (rational) functions defined on the complex plane. These Newton graphs are defined in terms of nonvanishing angles between edges at the same vertex. We derive necessary and sufficient conditions -of purely combinatorial nature- for an arbitrary plane graph in order to be topologically equivalent with a Newton graph. Finally, we analyse the structure of Newton graphs and prove the existence of a polynomial algorithm to recognize such graphs

The Garbage Class Mixed Logit Model:Accounting for Low-Quality Response Patterns in Discrete Choice Experiments

Objectives: To introduce the garbage class mixed logit (MIXL) model as a convenient alternative to manually screening and accounting for respondents with low data quality in discrete choice experiments. Methods: Garbage classes are typically used in latent class logit analyses to designate or identify group(s) of respondents with low data quality. Yet, the same concept can be applied to MIXL models as well. Results: Based on a reanalysis of 4 discrete choice experiments that were originally analyzed using a standard MIXL model, it is shown that garbage class MIXL models can achieve the same effect as manually screening for (and excluding) respondents with low data quality based on the more commonly used root likelihood test, but with less effort and ambiguity. Conclusions: Including a garbage class in MIXL models removes the influence of respondents with a random choice pattern from the MIXL model estimates, provides an estimate of the number of low-quality respondents in the dataset, and avoids having to manually screen for respondents with low data quality based on internal or statistical validity tests. Although less versatile than the combination of standard MIXL estimates with separate assessments of data quality and sensitivity analyses, the proposed garbage class MIXL model provides an attractive alternative

A personal view on basic education in reproduction : Where are we now and where are we going?

This article explores the current and expected direction of education in reproduction at the Faculty of Veterinary Medicine of Utrecht University. The current reproductive course in the Bachelor's programme is described. Based on the yearly routine course evaluation, changes have been started and continue to be implemented, and the educational ideas behind it are defined. Interactive e-learning modules that combine knowledge clips, animations, and quizzes have been developed. For the practical classes, e-modules with instructional videos have been paired to the written material. Using these new tools during self-study, students have to prepare for the necessary face-to-face classes that contain more in-depth discussions and practical training. In the second part, the author describes his expectations for further educational development. The growth of effective self-study using e-learning, besides traditional textbooks, before more in-depth face-to-face classes is likely to occur. With the growth of modern possibilities, such as the haptic technique and virtual reality, a better preparation in laboratory skills before practical training with animals is expected. In the author's opinion, despite all new learning methods and material, small group, face-to-face lectures, and practical classes with animals or animal material remain absolutely necessary. This article concludes with some lessons learned during the current adaptation of the course

The impact of demographic change on value set validity and obsolescence

Purpose: To investigate the contribution of demographic trends in countries’ age and gender composition to value set validity and obsolescence. Methods: Time-trade off (TTO) valuation data from 3 EQ-5D-3L value sets of 20 years or older from the United Kingdom, Japan, and the United States were re-analyzed using Bayesian heteroskedastic Tobit models with sex and age group-specific scale parameters. Original value sets were obtained by weighting the original preference structures with the countries’ original demographic composition at the time of the data collection. Updated value sets were created using the original preference structure weighted using the countries’ most recent demographic composition. The differences between the original and updated value sets were monitored and compared based on 95% credible intervals. Results: The gender and age composition of the investigated countries changed in all 3 countries over time. The modelled health state preferences also depended on the respondents’ gender and age. However, the overall impact of this demographic change on the investigated value sets was negligeable in all 3 countries and this finding was robust to accounting for the impact of ethnicity trends in the United States.Conclusion: Value sets may become redundant and obsolete for various reasons, but demographic change was not identified as a contributing factor.</p

Image segmentation and feature extraction for recognizing strokes in tennis game videos

This paper addresses the problem of recognizing human actions from video. Particularly, the case of recognizing events in tennis game videos is analyzed. Driven by our domain knowledge, a robust player segmentation algorithm is developed real video data. Further, we introduce a number of novel features to be extracted for our particular application. Different feature combinations are investigated in order to find the optimal one. Finally, recognition results for different classes of tennis strokes using automatic learning capability of Hidden Markov Models (HMMs) are presented. The experimental results demonstrate that our method is close to realizing statistics of tennis games automatically using ordinary TV broadcast videos

Not all respondents use a multiplicative utility function in choice experiments for health state valuations, which should be reflected in the elicitation format (or statistical analysis)

Discrete choice experiments (DCEs) that include health states and duration are becoming a common method for estimating quality‐adjusted life year (QALY) tariffs. These DCEs need to be analyzed under the assumption that respondents treat health and duration multiplicatively. However, in the most commonly used DCE duration format there is no guarantee that respondents actually do so; in fact, respondents can easily simplify the choice tasks by considering health and duration separately. This would result in valid DCE responses but preclude subsequent QALY tariff calculations. Using a Bayesian latent class model and data from two existing valuation studies, our analyses confirm that in both datasets the majority of respondents do not appear to have used a multiplicative utility function. Moreover, a statistical correction for respondents who used an incorrect function changes the range of the QALY weights. Hence our results imply that one can neither assume that respondents use the theoretically required multiplicative utility function nor assume that the type of utility function that respondents use does not affect the estimated QALY weights. As a solution, we advise researchers to use an alternative, more constrained DCE elicitation format that avoids these behavioral problems

A New and Improved Experimental Design for the Discrete Choice Experiment Module of the EuroQol Valuation Technology Protocol

Objectives: The EuroQol Valuation Technology (EQ-VT) protocol, which is used to value the EQ-5D-5L instrument, comprises a composite time trade-off and a discrete choice experiment (DCE) module. Despite significant limitations, the DCE module has not been updated since its inception in 2012. This study aimed to update the EQ-VT DCE design using state-of-the-art methods. Methods: DCE data from 19 EQ-5D-5L valuation studies were summarized using a Bayesian hierarchical meta-analysis model, which created the priors for our Bayesian efficient DCE design. This design comprised 20 subdesigns, each with 12 choice tasks, and included 2 levels that overlapped to reduce the complexity of the choice tasks. The relative efficiency and robustness of the new design were established by comparing the D-errors and minimal sample size requirements for the 19 within-sample and 7 out-of-sample countries with the previous DCE design. Results: The updated DCE design shows large reductions in the D-error: by 20% and 22% for the 19 within-sample and 7 out-of-sample countries, respectively. Sample size requirements were also reduced, resulting in an average reduction of 45% for both the within and out-of-sample countries. Conclusions: The updated DCE design outperforms the current EQ-VT design. Given its enhanced performance and reduced complexity, it is set to replace the existing DCE design in future EQ-5D-5L valuation studies using the EQ-VT protocol.</p

One-parameter families of optimization problems: equality constraints

In this paper, we introduce generalized critical points and discuss their relationship with other concepts of critical points [resp., stationary points]. Generalized critical points play an important role in parametric optimization. Under generic regularity conditions, we study the set of generalized critical points, in particular, the change of the Morse index. We focus our attention on problems with equality constraints only and provide an indication of how the present theory can be extended to problems with inequality constraints as well

Critical sets in parametric optimization

We deal with one-parameter families of optimization problems in finite dimensions. The constraints are both of equality and inequality type. The concept of a ‘generalized critical point’ (g.c. point) is introduced. In particular, every local minimum, Kuhn-Tucker point, and point of Fritz John type is a g.c. point. Under fairly weak (even generic) conditions we study the set∑ consisting of all g.c. points. Due to the parameter, the set∑ is pieced together from one-dimensional manifolds. The points of∑ can be divided into five (characteristic) types. The subset of ‘nondegenerate critical points’ (first type) is open and dense in∑ (nondegenerate means: strict complementarity, nondegeneracy of the corresponding quadratic form and linear independence of the gradients of binding constraints). A nondegenerate critical point is completely characterized by means of four indices. The change of these indices along∑ is presented. Finally, the Kuhn-Tucker subset of∑ is studied in more detail, in particular in connection with the (failure of the) Mangasarian-Fromowitz constraint qualification

On the stratification of a class of specially structured matrices

We consider specially structured matrices representing optimization problems with quadratic objective functions and (finitely many) affine linear equality constraints in an n-dimensional Euclidean space. The class of all such matrices will be subdivided into subsets ['strata'], reflecting the features of the underlying optimization problems. From a differential-topological point of view, this subdivision turns out to be very satisfactory: Our strata are smooth manifolds, constituting a so-called Whitney Regular Stratification, and their dimensions can be explicitly determined. We indicate how, due to Thom's Transversality Theory, this setting leads to some fundamental results on smooth one-parameter families of linear-quadratic optimization problems with ( finitely many) equality and inequality constraints