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... to the family of Doob-Gillespie algorithms (also in the following simply called stochastic simulation algorithm (SSA)). These algorithms, first applied to biochemical reaction networks by Gillespie (=-=Gillespie 1977-=-), essentially model a chemical reaction network as a continuous-time Markov chain and generate a sample trajectory. Since then, many variants have been developed to improve the efficiency of the orig...

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...distribution (i.e., the ’histogram’) generated by the given configuration with the reference data, by using the paired Wilcoxon rank-sum test (Sheskin 2007, p. 513) and the Jensen-Shannon divergence (=-=Lin 1991-=-). 4.2 Exploration of Accuracy Data As introduced above, our visualization approach has to handle 2,200 different configurations each with 500 accuracy values along the simulation output. In the follo...

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...ald, Schwarze, Schumann, and Uhrmacher number of trajectories, one is able to approximate the underlying chemical master equation arbitrarily close (e.g., see Gillespie 2007). Others, like τ-leaping (=-=Gillespie 2001-=-), are non-exact. They typically outperform the exact methods, sometimes by several orders of magnitude (Jeschke and Ewald 2008). Since τ-leaping variants trade speed for accuracy, this raises another...

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...stems whose semantics is predominantly rooted in continuous-time Markov chains, and thus rely on an efficient SSA for execution. To those belong stochastic process algebras for systems biology (e.g., =-=Priami 1995-=-) or rule-based modeling languages (e.g., Maus et al. 2011). Hence, all these developments may profit from insights into SSA performance. While we focus on a single, parameterizable variant of τ-leapi...

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...-established kind of model. As mentioned in Section 1, we regard this problem as future work. 4 APPLICATION 4.1 Accuracy Experiments We generated accuracy data for the linear chain system (LCS) from (=-=Cao et al. 2004-=-), a benchmark model that consists of a single chain of unary reactions, S0→ S1, . . . ,Sn−1→ Sn, each with a reaction rate constant Luboschik, Rybacki, Ewald, Schwarze, Schumann, and Uhrmacher Figure...

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...ld of uncertainty visualization in terms of visual analytics: Several investigations on the definition and characteristics of uncertainties for example identify accuracy as one aspect of uncertainty (=-=MacEachren et al. 2005-=-, Griethe and Schumann 2006, Skeels et al. 2010). Thereby, the visualization of uncertainties depends on the underlying data (e.g., volume data, architectural data, abstract data. . . ) and differs ac...

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...). To support accepting or rejecting a certain configuration, the record view, the accuracy view, the accuracy map as well as the parameter map are closely interconnected. Using brushing and linking (=-=Buja et al. 1991-=-), a changed selection in the accuracy view automatically updates all other views to show the current record. In return, the slider-equipped parameter map can be used to determine a specific parametri...

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... simulator falls back to an exact SSA variant), and nc, which controls what reactions are considered critical and hence are treated differently. We vary the parameters around the values suggested in (=-=Cao et al. 2006-=-), where ε = 0.03, γ = 10, and nc = 10: ε ∈ {0.01,0.012, . . . ,0.048}, γ ∈ {5,6, . . . ,15}, and nc ∈ {0,5, . . . ,45}, amounting to 20 · 11 · 10 = 2.200 τ-leaping setups altogether. To generate the ...

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...isualize confidence information along and closely related to the data. To differentiate both — data and uncertainties — it is a common approach to use a fuzzy visual representation for uncertainties (=-=MacEachren 1992-=-, Luboschik et al. 2010). But there are also explicit representations especially for stochastic measures. In (Potter et al. 2010) classical box plots are extended to communicate accuracy measures alon...

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...tion of a configuration with a desired accuracy and the transfer of that configuration to the current experiment for subsequent usage (Sect. 3.4). We use this procedure within the JAMES II framework (=-=Himmelspach and Uhrmacher 2007-=-) to configure subsequent simulation experiments. Section 4 demonstrates our approach and Section 5 concludes the paper. 2 BACKGROUND & RELATED WORK By introducing visual analytics to the selection of...

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... a common approach to use a fuzzy visual representation for uncertainties (MacEachren 1992, Luboschik et al. 2010). But there are also explicit representations especially for stochastic measures. In (=-=Potter et al. 2010-=-) classical box plots are extended to communicate accuracy measures along a single line plot. An application to several line plots would result in visual clutter. Other approaches like (Holzhüter et ...

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...inuous-time Markov chains, and thus rely on an efficient SSA for execution. To those belong stochastic process algebras for systems biology (e.g., Priami 1995) or rule-based modeling languages (e.g., =-=Maus et al. 2011-=-). Hence, all these developments may profit from insights into SSA performance. While we focus on a single, parameterizable variant of τ-leaping in this paper, i.e., the one presented by Cao et al. (2...

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...analytics: Several investigations on the definition and characteristics of uncertainties for example identify accuracy as one aspect of uncertainty (MacEachren et al. 2005, Griethe and Schumann 2006, =-=Skeels et al. 2010-=-). Thereby, the visualization of uncertainties depends on the underlying data (e.g., volume data, architectural data, abstract data. . . ) and differs accordingly. Nevertheless, those visualizations h...

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...2006, Waser et al. 2010, Matkovic et al. 2010). Other work focuses on complex parameterizations and thus facilitates the visual exploration of large parameter spaces and the clustering of parameters (=-=Pretorius et al. 2011-=-) as well as the interaction with such spaces (van Wijk and van Overveld 2003). The approaches in (Marks et al. 1997, Bruckner and Möller 2010) also relate parameter settings to output data, but thei...

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...ects concerning parameters and their relation to the output data, whereas a major aspect addressed in this domain is to understand the influence of parameters or parameter changes to the output data (=-=Tweedie et al. 1994-=-, Tweedie et al. 1996, Kerren 2006, Waser et al. 2010, Matkovic et al. 2010). Other work focuses on complex parameterizations and thus facilitates the visual exploration of large parameter spaces and ...

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...ating an arbitrary Luboschik, Rybacki, Ewald, Schwarze, Schumann, and Uhrmacher number of trajectories, one is able to approximate the underlying chemical master equation arbitrarily close (e.g., see =-=Gillespie 2007-=-). Others, like τ-leaping (Gillespie 2001), are non-exact. They typically outperform the exact methods, sometimes by several orders of magnitude (Jeschke and Ewald 2008). Since τ-leaping variants trad...

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...a major aspect addressed in this domain is to understand the influence of parameters or parameter changes to the output data (Tweedie et al. 1994, Tweedie et al. 1996, Kerren 2006, Waser et al. 2010, =-=Matkovic et al. 2010-=-). Other work focuses on complex parameterizations and thus facilitates the visual exploration of large parameter spaces and the clustering of parameters (Pretorius et al. 2011) as well as the interac...

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...eters and their relation to the output data, whereas a major aspect addressed in this domain is to understand the influence of parameters or parameter changes to the output data (Tweedie et al. 1994, =-=Tweedie et al. 1996-=-, Kerren 2006, Waser et al. 2010, Matkovic et al. 2010). Other work focuses on complex parameterizations and thus facilitates the visual exploration of large parameter spaces and the clustering of par...

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...ce information along and closely related to the data. To differentiate both — data and uncertainties — it is a common approach to use a fuzzy visual representation for uncertainties (MacEachren 1992, =-=Luboschik et al. 2010-=-). But there are also explicit representations especially for stochastic measures. In (Potter et al. 2010) classical box plots are extended to communicate accuracy measures along a single line plot. A...

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... visual exploration of large parameter spaces and the clustering of parameters (Pretorius et al. 2011) as well as the interaction with such spaces (van Wijk and van Overveld 2003). The approaches in (=-=Marks et al. 1997-=-, Bruckner and Möller 2010) also relate parameter settings to output data, but their main focus is on the exploration of the resulting output data to set parameters accordingly. The latter also makes...