Lattice structures for bisimilar Probabilistic Automata

The paper shows that there is a deep structure on certain sets of bisimilar Probabilistic Automata (PA). The key prerequisite for these structures is a notion of compactness of PA. It is shown that compact bisimilar PA form lattices. These results are then used in order to establish normal forms not only for finite automata, but also for infinite automata, as long as they are compact.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

On the Riesz Representation for Optimal Stopping Problems

In this thesis we summarize results about optimal stopping problems analyzed with the Riesz representation theorem. Furthermore we consider two examples: Firstly the optimal investment problem with an underlying d-dimensional geometric Brow- nian motion. We derive formulas for the optimal stopping boundaries for the one- and two-dimensional cases and we find a numerical approximation for the boundary in the two-dimensional problem. After this we change the focus to a space-time one-dimensional geometric Brownian motion with finite time horizon. We use the Riesz representation theorem to approximate the optimal stopping boundaries for three financial options: the American Put option, American Cash-or-Nothing option and the American Asset-or-Nothing option

Changes in first arrival dates of common migratory bird species in southwestern Germany

Der globale Klimawandel beeinflusst die Phänologie des Zugverhaltens von Vögeln. Es ist zu erwarten (und andernorts gezeigt worden), dass (1) die Zugvögel im Frühjahr früher im Brutgebiet ankommen und dass (2) dieser Effekt bei Kurzstreckenziehern stärker ist als bei Langstreckenziehern. Um dies zu überprüfen, wurden langfristige Beobachtungsreihen (1970-2003) analysiert, bei denen (1) mindestens acht Erstankünfte aus den Zeiträumen 1970-1986 und 1987-2003 vorlagen, (2) der Beobachter keinen Wohnortwechsel vorgenommen hatte und (3) mindestens drei unabhängige Beobachtungsreihen für eine Art vorhanden waren. Insgesamt wurden die Erstankunftszeiten von 17 Zugvogelarten an 13 verschiedenen Orten in Südwestdeutschland untersucht. Die Analyse der Ankunftszeiten erfolgte mit Hilfe der linearen Regression und durch den Vergleich der Mediane für die Perioden 1970-1986 und 1987-2003 (U-Test nach Mann-Whitney). Von 103 ausgewerteten Beobachtungsreihen wurde bei 96 ein Trend zur früheren Erstankunft festgestellt, während nur bei sieben Reihen das Gegenteil der Fall war. Betrachtet man die Steigung der Regressionsgeraden als Maß für die jährliche Veränderung der Ankunftszeiten, wurde bei 58 Beobachtungsreihen eine signifikant frühere Erstankunft festgestellt. Durchschnittlich verfrühte sich die Ankunft um 0,3 Tage (max. 2,9) pro Jahr. Hingegen konnte nur bei einer Art eine signifikant spätere Ankunft festgestellt werden. Der U-Test führte zu sehr ähnlichen Erkenntnissen. Eine Varianzanalyse ergab, dass die Effekte bei Kurzstreckenziehern stärker waren als bei Langstreckenziehern. Es wird vermutet, dass die frühere Ankunft überwiegend darauf zurückzuführen ist, dass sich die Überwinterungsgebiete vieler Arten nach Norden verschoben haben.Global change affects the timing of bird migration. It presumed (and has been shown) that, (1) species arrived earlier in spring and that (2) this response to climate change is stronger in short-distance than in long-distance migratory species. To confirm this pattern we analysed long-term observational data from field ornithologists under the condition that (1) at least eight arrival dates for the periods 1970-1986 and 1987-2003 were available, (2) observers had not changed their study area during these years, and (3) at least three time series were available for a species. In total, we examined the first arrival dates of 17 migratory species at 13 sites in southwestern Germany. To analyse changes in arrival times we used two statistical procedures: linear regression for the period 1970-2003 and Mann-Whitney U-test to compare median arrival dates of the periods 1970-1986 and 1987-2003. Out of 103 time series 96 showed a trend towards earlier spring arrival, whereas series only for seven time series the reverse was true. Using linear regression for 58 species time series we found a significantly earlier arrival date. On average, arrival date changed 0.3 (max. 2.9) days per year. Only one species showed a significant later arrival date. The U-test revealed similar results. An analyses of variance (ANOVA) showed that this effect was stronger in short-distance than in long-distance migrants. We suggest that earlier spring arrival could be due to a shift of wintering areas towards the North – even in some long-distance migratory species

Mathematical modeling of the Drosophila neuromuscular junction

Poster presentation: An important challenge in neuroscience is understanding how networks of neurons go about processing information. Synapses are thought to play an essential role in cellular information processing however quantitative and mathematical models of the underlying physiologic processes that occur at synaptic active zones are lacking. We are generating mathematical models of synaptic vesicle dynamics at a well-characterized model synapse, the Drosophila larval neuromuscular junction. This synapse's simplicity, accessibility to various electrophysiological recording and imaging techniques, and the genetic malleability intrinsic to Drosophila system make it ideal for computational and mathematical studies. We have employed a reductionist approach and started by modeling single presynaptic boutons. Synaptic vesicles can be divided into different pools; however, a quantitative understanding of their dynamics at the Drosophila neuromuscular junction is lacking [4]. We performed biologically realistic simulations of high and low release probability boutons [3] using partial differential equations (PDE) taking into account not only the evolution in time but also the spatial structure in two dimensions (the extension to three dimensions will be implemented soon). PDEs are solved using UG, a program library for the calculation of multi-dimensional PDEs solved using a finite volume approach and implicit time stepping methods leading to extended linear equation systems be solvedwith multi-grid methods [3,4]. Numerical calculations are done on multi-processor computers for fast calculations using different parameters in order to asses the biological feasibility of different models. In preliminary simulations, we modeled vesicle dynamics as a diffusion process describing exocytosis as Neumann streams at synaptic active zones. The initial results obtained with these models are consistent with experimental data. However, this should be regarded as a work in progress. Further refinements will be implemented, including simulations using morphologically realistic geometries which were generated from confocal scans of the neuromuscular junction using NeuRA (a Neuron Reconstruction Algorithm). Other parameters such as glutamate diffusion and reuptake dynamics, as well as postsynaptic receptor kinetics will be incorporated as well

Synaptic boutons sizes are tuned to best fit their physiological performances

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

Synaptic bouton sizes are tuned to best fit their physiological performances : poster presentation from Twentieth Annual Computational Neuroscience Meeting: CNS*2011, Stockholm, Sweden, 23 - 28 July 2011

Poster presentation from Twentieth Annual Computational Neuroscience Meeting: CNS*2011 Stockholm, Sweden. 23-28 July 2011. 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 the rather astonishing motor patterns presented here which we observed within in vivo recordings which underlie peristaltic contractions at a well characterized synapse, the neuromuscular junction (NMJ) of the Drosophila larva. 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. As a side product, we demonstrate how advanced methods from numerical mathematics could help in future to resolve also other difficult experimental neurobiological issues

Site-Specific Assembly of DNA-Based Photonic Wires by Using Programmable Polyamides**

The first example of a programmable DNA photonic wire is reported utilizing fluorophore-tethered pyrrole-imidazole polyamides for site-directed fluorophore assembly along a pre-formed DNA duplex (see scheme; PB=Pacific Blue, Cy3=Cyanine 3; orange rectangles=fluorophore). The importance of such control is revealed by efficient energy transport over distances in excess of 27 nm

A Raman technique applicable for the analysis of the working principle of promoters and inhibitors of gas hydrate formation

We report a Raman technique applicable for the in situ analysis of the development of hydrogen bonds in the liquid water‐rich phase just before the onset of gas hydrate formation. Herewith, the phase transition as well as the working principle of hydrate formation inhibitors and promoters can be analyzed