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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.

- On functional module detection in metabolic networks (2013)
- Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models.

- An erasure-resilient and compute-efficient coding scheme for storage applications (2013)
- Driven by rapid technological advancements, the amount of data that is created, captured, communicated, and stored worldwide has grown exponentially over the past decades. Along with this development it has become critical for many disciplines of science and business to being able to gather and analyze large amounts of data. The sheer volume of the data often exceeds the capabilities of classical storage systems, with the result that current large-scale storage systems are highly distributed and are comprised of a high number of individual storage components. As with any other electronic device, the reliability of storage hardware is governed by certain probability distributions, which in turn are influenced by the physical processes utilized to store the information. The traditional way to deal with the inherent unreliability of combined storage systems is to replicate the data several times. Another popular approach to achieve failure tolerance is to calculate the block-wise parity in one or more dimensions. With better understanding of the different failure modes of storage components, it has become evident that sophisticated high-level error detection and correction techniques are indispensable for the ever-growing distributed systems. The utilization of powerful cyclic error-correcting codes, however, comes with a high computational penalty, since the required operations over finite fields do not map very well onto current commodity processors. This thesis introduces a versatile coding scheme with fully adjustable fault-tolerance that is tailored specifically to modern processor architectures. To reduce stress on the memory subsystem the conventional table-based algorithm for multiplication over finite fields has been replaced with a polynomial version. This arithmetically intense algorithm is better suited to the wide SIMD units of the currently available general purpose processors, but also displays significant benefits when used with modern many-core accelerator devices (for instance the popular general purpose graphics processing units). A CPU implementation using SSE and a GPU version using CUDA are presented. The performance of the multiplication depends on the distribution of the polynomial coefficients in the finite field elements. This property has been used to create suitable matrices that generate a linear systematic erasure-correcting code which shows a significantly increased multiplication performance for the relevant matrix elements. Several approaches to obtain the optimized generator matrices are elaborated and their implications are discussed. A Monte-Carlo-based construction method allows it to influence the specific shape of the generator matrices and thus to adapt them to special storage and archiving workloads. Extensive benchmarks on CPU and GPU demonstrate the superior performance and the future application scenarios of this novel erasure-resilient coding scheme.

- Virtual machine scheduling in dedicated computing clusters (2012)
- Time-critical applications process a continuous stream of input data and have to meet speciﬁc timing constraints. A common approach to ensure that such an application satisﬁes its constraints is over-provisioning: The application is deployed in a dedicated cluster environment with enough processing power to achieve the target performance for every speciﬁed data input rate. This approach comes with a drawback: At times of decreased data input rates, the cluster resources are not fully utilized. A typical use case is the HLT-Chain application that processes physics data at runtime of the ALICE experiment at CERN. From a perspective of cost and efficiency it is desirable to exploit temporarily unused cluster resources. Existing approaches aim for that goal by running additional applications. These approaches, however, a) lack in ﬂexibility to dynamically grant the time-critical application the resources it needs, b) are insufficient for isolating the time-critical application from harmful side-effects introduced by additional applications or c) are not general because application-speciﬁc interfaces are used. In this thesis, a software framework is presented that allows to exploit unused resources in a dedicated cluster without harming a time-critical application. Additional applications are hosted in Virtual Machines (VMs) and unused cluster resources are allocated to these VMs at runtime. In order to avoid resource bottlenecks, the resource usage of VMs is dynamically modiﬁed according to the needs of the time-critical application. For this purpose, a number of previously not combined methods is used. On a global level, appropriate VM manipulations like hot migration, suspend/resume and start/stop are determined by an informed search heuristic and applied at runtime. Locally on cluster nodes, a feedback-controlled adaption of VM resource usage is carried out in a decentralized manner. The employment of this framework allows to increase a cluster’s usage by running additional applications, while at the same time preventing negative impact towards a time-critical application. This capability of the framework is shown for the HLT-Chain application: In an empirical evaluation the cluster CPU usage is increased from 49% to 79%, additional results are computed and no negative effect towards the HLT-Chain application are observed.

- 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.

- Beschreibungskomplexität von Zellularautomaten (2004)
- Zellularautomaten sind ein massiv paralleles Berechnungsmodell, das aus sehr vielen identischen einfachen Prozessoren oder Zellen besteht, die homogen miteinander verbunden sind und parallel arbeiten. Es gibt Zellularautomaten in unterschiedlichen Ausprägungen. Beispielsweise unterscheidet man die Automaten nach der zur Verfügung stehenden Zeit, nach paralleler oder sequentieller Verarbeitung der Eingabe oder durch Beschränkungen der Kommunikation zwischen den einzelnen Zellen. Benutzt man Zellularautomaten zum Erkennen formaler Sprachen und betrachtet deren generative Mächtigkeit, dann kann bereits das einfachste zellulare Modell kontextsensitive Sprachen akzeptieren. In dieser Arbeit wird die Beschreibungskomplexität von Zellularautomaten betrachtet. Es wird untersucht, wie sich die Beschreibungsgröße einer formalen Sprache verändern kann, wenn die Sprache mit unterschiedlichen Typen von Zellularautomaten oder sequentiellen Modellen beschrieben wird. Ein wesentliches Ergebnis im ersten Teil der Arbeit ist, daß zwischen zwei Automatenklassen, deren entsprechende Sprachklassen echt ineinander enthalten oder unvergleichbar sind, nichtrekursive Tradeoffs existieren. Das heißt, der Größenzuwachs beim Wechsel von einem Automatenmodell in das andere läßt sich durch keine rekursive Funktion beschränken. Im zweiten Teil der Arbeit werden Zellularautomaten dahingehend beschränkt, daß nur eine feste Zellenzahl zugelassen ist. Zusätzlich werden Automaten mit unterschiedlichem Grad an bidirektionaler Kommunikation zwischen den einzelnen Zellen betrachtet, und es wird untersucht, welche Auswirkungen auf die Beschreibungsgröße unterschiedliche Grade an bidirektionaler Kommunikation haben können. Im Gegensatz zum unbeschränkten Modell können polynomielle und damit rekursive obere Schranken bei Umwandlungen zwischen den einzelnen Modellen bewiesen werden. Durch den Beweis unterer Schranken kann in fast allen Fällen auch die Optimalität der Konstruktionen belegt werden.

- Descriptional complexity of cellular automata and decidability questions (2001)
- We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata.

- Minimizing finite automata is computationally hard (2002)
- It is known that deterministic finite automata (DFAs) can be algorithmically minimized, i.e., a DFA M can be converted to an equivalent DFA M' which has a minimal number of states. The minimization can be done efficiently [6]. On the other hand, it is known that unambiguous finite automata (UFAs) and nondeterministic finite automata (NFAs) can be algorithmically minimized too, but their minimization problems turn out to be NP-complete and PSPACE-complete [8]. In this paper, the time complexity of the minimization problem for two restricted types of finite automata is investigated. These automata are nearly deterministic, since they only allow a small amount of non determinism to be used. On the one hand, NFAs with a fixed finite branching are studied, i.e., the number of nondeterministic moves within every accepting computation is bounded by a fixed finite number. On the other hand, finite automata are investigated which are essentially deterministic except that there is a fixed number of different initial states which can be chosen nondeterministically. The main result is that the minimization problems for these models are computationally hard, namely NP-complete. Hence, even the slightest extension of the deterministic model towards a nondeterministic one, e.g., allowing at most one nondeterministic move in every accepting computation or allowing two initial states instead of one, results in computationally intractable minimization problems.

- On one-way cellular automata with a fixed number of cells (2003)
- We investigate a restricted one-way cellular automaton (OCA) model where the number of cells is bounded by a constant number k, so-called kC-OCAs. In contrast to the general model, the generative capacity of the restricted model is reduced to the set of regular languages. A kC-OCA can be algorithmically converted to a deterministic finite automaton (DFA). The blow-up in the number of states is bounded by a polynomial of degree k. We can exhibit a family of unary languages which shows that this upper bound is tight in order of magnitude. We then study upper and lower bounds for the trade-off when converting DFAs to kC-OCAs. We show that there are regular languages where the use of kC-OCAs cannot reduce the number of states when compared to DFAs. We then investigate trade-offs between kC-OCAs with different numbers of cells and finally treat the problem of minimizing a given kC-OCA.

- On the descriptional complexity of iterative arrays (2003)
- The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable.