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- The performance of approximating ordinary differential equations by neural nets (2008)
- The dynamics of many systems are described by ordinary differential equations (ODE). Solving ODEs with standard methods (i.e. numerical integration) needs a high amount of computing time but only a small amount of storage memory. For some applications, e.g. short time weather forecast or real time robot control, long computation times are prohibitive. Is there a method which uses less computing time (but has drawbacks in other aspects, e.g. memory), so that the computation of ODEs gets faster? We will try to discuss this question for the assumption that the alternative computation method is a neural network which was trained on ODE dynamics and compare both methods using the same approximation error. This comparison is done with two different errors. First, we use the standard error that measures the difference between the approximation and the solution of the ODE which is hard to characterize. But in many cases, as for physics engines used in computer games, the shape of the approximation curve is important and not the exact values of the approximation. Therefore, we introduce a subjective error based on the Total Least Square Error (TLSE) which gives more consistent results. For the final performance comparison, we calculate the optimal resource usage for the neural network and evaluate it depending on the resolution of the interpolation points and the inter-point distance. Our conclusion gives a method to evaluate where neural nets are advantageous over numerical ODE integration and where this is not the case. Index Terms—ODE, neural nets, Euler method, approximation complexity, storage optimization.

- Mutual information based clustering of market basket data for profiling users (2007)
- Attraction and commercial success of web sites depend heavily on the additional values visitors may find. Here, individual, automatically obtained and maintained user profiles are the key for user satisfaction. This contribution shows for the example of a cooking information site how user profiles might be obtained using category information provided by cooking recipes. It is shown that metrical distance functions and standard clustering procedures lead to erroneous results. Instead, we propose a new mutual information based clustering approach and outline its implications for the example of user profiling.

- Handwriting analysis for diagnosis and prognosis of Parkinson’s disease (2006)
- At present, there are no quantitative, objective methods for diagnosing the Parkinson disease. Existing methods of quantitative analysis by myograms suffer by inaccuracy and patient strain; electronic tablet analysis is limited to the visible drawing, not including the writing forces and hand movements. In our paper we show how handwriting analysis can be obtained by a new electronic pen and new features of the recorded signals. This gives good results for diagnostics. Keywords: Parkinson diagnosis, electronic pen, automatic handwriting analysis

- Adaptive modeling of biochemical pathways (2004)
- In bioinformatics, biochemical pathways can be modeled by many differential equations. It is still an open problem how to fit the huge amount of parameters of the equations to the available data. Here, the approach of systematically learning the parameters is necessary. In this paper, for the small, important example of inflammation modeling a network is constructed and different learning algorithms are proposed. It turned out that due to the nonlinear dynamics evolutionary approaches are necessary to fit the parameters for sparse, given data. Keywords: model parameter adaption, septic shock. coupled differential equations, genetic algorithm.

- Model selection and adaptation for biochemical pathways (2004)
- In bioinformatics, biochemical signal pathways can be modeled by many differential equations. It is still an open problem how to fit the huge amount of parameters of the equations to the available data. Here, the approach of systematically obtaining the most appropriate model and learning its parameters is extremely interesting. One of the most often used approaches for model selection is to choose the least complex model which “fits the needs”. For noisy measurements, the model which has the smallest mean squared error of the observed data results in a model which fits too accurately to the data – it is overfitting. Such a model will perform good on the training data, but worse on unknown data. This paper propose as model selection criterion the least complex description of the observed data by the model, the minimum description length. For the small, but important example of inflammation modeling the performance of the approach is evaluated. Keywords: biochemical pathways, differential equations, septic shock, parameter estimation, overfitting, minimum description length.

- Data driven automatic model selection and parameter adaptation – a case study for septic shock (2004)
- In bioinformatics, biochemical pathways can be modeled by many differential equations. It is still an open problem how to fit the huge amount of parameters of the equations to the available data. Here, the approach of systematically learning the parameters is necessary. This paper propose as model selection criterion the least complex description of the observed data by the model, the minimum description length. For the small, but important example of inflammation modeling the performance of the approach is evaluated.

- Neuronal networks for sepsis prediction - the MEDAN project (2004)
- Since the description of sepsis by Schottmüller in 1914, the amount on knowledge available on sepsis and its underlying pathophysiology has substantially increased. Epidemiologic examinations of abdominal septic shock patients show the potential for high risk posed by and the extensive therapy situation in the intensive care unit (ICU) (5). Unfortunately, until now it has not been possible to significantly reduce the mortality rate of septic shock, which is as high as 50-60% worldwide, although PROWESS' results (1) are encouraging. This paper summarizes the main results of the MEDAN project and their medical impacts. Several aspects are already published, see the references. The heterogeneity of patient groups and the variations in therapy strategies is seen as one of the main problems for sepsis trials. In the MEDAN multi-center study of 71 intensive care units in Germany, a group of 382 patients made up exclusively of abdominal septic shock patients who met the consensus criteria for septic shock (3) was analysed. For use within scores or stand-alone experiments variables are often studied as isolated variables, not as a multidimensional whole, e.g. a recent study takes a look at the role thrombocytes play (15). To avoid this limitation, our study compares several established scores (SOFA, APACHE II, SAPS II, MODS) by a multi-dimensional neuronal network analysis. For outcome prediction the data of 382 patients was analysed by using most of the commonly documented vital parameters and doses of medicine (metric variables). Data was collected in German hospitals from 1998 to 2001. The 382 handwritten patient records were transferred to an electronic database giving the amount of 2.5 million data entries. The metric data contained in the database is composed of daily measurements and doses of medicine. We used range and plausibility checks to allow no faulty data in the electronic database. 187 of the 382 patients are deceased (49 %).

- Adaptive modeling of biochemical pathways (2003)
- In bioinformatics, biochemical pathways can be modeled by many differential equations. It is still an open problem how to fit the huge amount of parameters of the equations to the available data. Here, the approach of systematically learning the parameters is necessary. In this paper, for the small, important example of inflammation modeling a network is constructed and different learning algorithms are proposed. It turned out that due to the nonlinear dynamics evolutionary approaches are necessary to fit the parameters for sparse, given data. Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence - ICTAI 2003