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- Synaptic boutons sizes are tuned to best fit their physiological performances (2013)
- Poster presentation: Twenty Second Annual Computational Neuroscience Meeting: CNS*2013. Paris, France. 13-18 July 2013. To truly appreciate the myriad of events which relate synaptic function and vesicle dynamics, simulations should be done in a spatially realistic environment. This holds true in particular in order to explain as well the rather astonishing motor patterns which we observed within in vivo recordings which underlie peristaltic contractionsas well as the shape of the EPSPs at different forms of long-term stimulation, presented both here, at a well characterized synapse, the neuromuscular junction (NMJ) of the Drosophila larva (c.f. Figure 1). To this end, we have employed a reductionist approach and generated three dimensional models of single presynaptic boutons at the Drosophila larval NMJ. Vesicle dynamics are described by diffusion-like partial differential equations which are solved numerically on unstructured grids using the uG platform. In our model we varied parameters such as bouton-size, vesicle output probability (Po), stimulation frequency and number of synapses, to observe how altering these parameters effected bouton function. Hence we demonstrate that the morphologic and physiologic specialization maybe a convergent evolutionary adaptation to regulate the trade off between sustained, low output, and short term, high output, synaptic signals. There seems to be a biologically meaningful explanation for the co-existence of the two different bouton types as previously observed at the NMJ (characterized especially by the relation between size and Po), the assigning of two different tasks with respect to short- and long-time behaviour could allow for an optimized interplay of different synapse types. We can present astonishing similar results of experimental and simulation data which could be gained in particular without any data fitting, however based only on biophysical values which could be taken from different experimental results. As a side product, we demonstrate how advanced methods from numerical mathematics could help in future to resolve also other difficult experimental neurobiological issues.

- Long-term potentiation through calcium-mediated N-Cadherin interaction is tightly controlled by the three-dimensional architecture of the synapse (2013)
- Poster presentation: Twenty Second Annual Computational Neuroscience Meeting: CNS*2013. Paris, France. 13-18 July 2013. The synaptic cleft is an extracellular domain that is capable of relaying a presynaptically received electrical signal by diffusive neurotransmitters to the postsynaptic membrane. The cleft is trans-synaptically bridged by ring-like shaped clusters of pre- and postsynaptically localized calcium-dependent adhesion proteins of the N-Cadherin type and is possibly the smallest intercircuit in nervous systems [1]. The strength of association between the pre- and postsynaptic membranes can account for synaptic plasticity such as long-term potentiation [2]. Through neuronal activity the intra- and extracellular calcium levels are modulated through calcium exchangers embedded in the pre- and postsynaptic membrane. Variations of the concentration of cleft calcium induces changes in the N-Cadherin-zipper, that in synaptic resting states is rigid and tightly connects the pre- and postsynaptic domain. During synaptic activity calcium concentrations are hypothesized to drop below critical thresholds which leads to loosening of the N-Cadherin connections and subsequently "unzips" the Cadherin-mediated connection. These processes may result in changes in synaptic strength [2]. In order to investigate the calcium-mediated N-Cadherin dynamics at the synaptic cleft, we developed a three-dimensional model including the cleft morphology and all prominent calcium exchangers and corresponding density distributions [3-6]. The necessity for a fully three-dimensional model becomes apparent, when investigating the effects of the spatial architecture of the synapse [7], [8]. Our data show, that the localization of calcium channels with respect to the N-Cadherin ring has substantial effects on the time-scales on which the Cadherin-zipper switches between states, ranging from seconds to minutes. This will have significant effects on synaptic signaling. Furthermore we see, that high-frequency action potential firing can only be relayed to the Calcium/N-Cadherin-system at a synapse under precise spatial synaptic reorganization.

- Lower bounds for multi-pass processing of multiple data streams (2009)
- This paper gives a brief overview of computation models for data stream processing, and it introduces a new model for multi-pass processing of multiple streams, the so-called mp2s-automata. Two algorithms for solving the set disjointness problem with these automata are presented. The main technical contribution of this paper is the proof of a lower bound on the size of memory and the number of heads that are required for solving the set disjointness problem with mp2s-automata.

- Ambiguity and communication (2009)
- The ambiguity of a nondeterministic finite automaton (NFA) N for input size n is the maximal number of accepting computations of N for an input of size n. For all k, r 2 N we construct languages Lr,k which can be recognized by NFA's with size k poly(r) and ambiguity O(nk), but Lr,k has only NFA's with exponential size, if ambiguity o(nk) is required. In particular, a hierarchy for polynomial ambiguity is obtained, solving a long standing open problem (Ravikumar and Ibarra, 1989, Leung, 1998).

- 12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria (2012)
- This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto.

- Encoding induction in correctness proofs of program transformations as a termination problem (2012)
- The diagram-based method to prove correctness of program transformations consists of computing complete set of (forking and commuting) diagrams, acting on sequences of standard reductions and program transformations. In many cases, the only missing step for proving correctness of a program transformation is to show the termination of the rearrangement of the sequences. Therefore we encode complete sets of diagrams as term rewriting systems and use an automated tool to show termination, which provides a further step in the automation of the inductive step in correctness proofs.

- Advances and applications of automata on words and trees : abstracts collection (2011)
- From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

- Advances and applications of automata on words and trees : executive summary (2011)
- Seminar: 10501 - Advances and Applications of Automata on Words and Trees. The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail.