In the last two years I have continued my work in olfaction of insects
but also have become interested in the problem of accurate models of
identified cells/ identified cell types. In the process of developing novel
hybrid systems technology for online measurement and manipulation of
biological systems, in my case, the lobster stomatogastric system, I noticed
that conductance based models of cells with non-trivial dynamics often fail
to reproduce important aspects of the neuron dynamics. The direct assembly of
voltage clamp data to a Hodgkin-Huxley type neuron model seems to fail in
many cases. The reasons for this are manifold. A trivial but unresolvable
problem is that each current is characterized on a different
preparation. Even with the greatest care and using identified cells, there
will always be experimental and animal-specific variations in the
properties. Other more fundamental reasons might be redundancies of paramters
that lead to an appropriate paramter region which is non-convex, such that
averaging, as done in the voltage clamp experiments, is inappropriate to
determine adequate parameter values. On an even more principal level,
identified cells might not be identifiable based on similar parameters but
similar dynamics with possibly completely different underlying paramter sets
as suggested recently (Prinz et al., Nature Neurosci. (2004)).
I have adapted data fitting techniques to overcome these problems and fit conductance based models to large amounts of data. A manuscript on this work is in preparation.
In parallel I have continued Dynamic Clamp and other software development. The new package "NeurAnim" is - while rather simple and straightforward to implement - very powerful in visualizing the results of network simulations. For more details see the download pages for Dynamic Clamp and Neuron Animator .
I have also started an investigation of the possible functions of inhibitory plasticity in the entorhinal cortex in collaboration with Julie Haas. This is a puzzeling question as potentiation of inhibitory synapses occurs for post-after-presynaptic spike pairings which subsequently suppresses this type of events. The plasticity is removing the spike patterns it is caused by rather than imprinting them into the system as STDP of excitatory synapses does. We are able to demonstrate in models that this type of inhibitory spike-timing dependent plasticity can be a powerful while subtle control for run-away or seizure-like activity in the entorhinal cortex. A manuscript on this work is in preparation.
After my PhD I once more took a slight change in my field of work. Presently I investigate neural systems with several main questions in mind.
For one we try to understand the mechanisms of sequence learning in neural systems mediated by Spike Timing Dependent Plasticity (STDP). First encouraging results have been achieved and a manuscript is in preparation.
The second topic I'm presently working on is the information processing in the olfactory system in particular in the mushroom body of the locust. This information processing seems to have extremely interesting dynamical systems properties. The key question is how the spatio-temporal code produced by the winnerless competition principle believed to be implemented in the antennal lobe might be processed in the downstream areas (mushroom body, beta lobe).
The third topic arose in connection with recent work done by Valentin Zhigulin and Mish Rabinovich in our group. They showed that a synapse obeying an anti-Hebbian STDP learning rule can synchronize model neurons of various types in a very effective way which comes as a little bit of a surprise. As this inverse STDP is a rather rare effect in nature we decided to check whether the effect might be relevant for real biological neurons. To this end I adapted a dynamic clamp software of Reynaldo Pinto to include learning rules for the synapse emulated by the software. We now use this program to couple a simulated driving neuron with a real neuron from the abdominal ganglion of Aplysia.
For my PhD work I investigated properties of multifractals in general and the multifractal properties of the probability distributions of effective fields in random field Ising models in particular.
The one-dimensional random field Ising model with dichotomous quenched random field can be reformulated as a random iterated function system (RIFS) of two functions. This RIFS is contractive and therefore has by a result of Hutchinson 1984 a unique invariant measure. This invariant measure turns out to be a multifractal for a generic choice of the physical parameters. Its multifractal properties change drastically if the physical parameters temperature and random field strength are changed. We were able to find and understand the mechanism underlying these drastic changes often called phase transitions in the spirit of the thermodynamic formalism for multifractals. The results are published in the paper "Orbits and phase transitions in the multifractal spectrum" cited below.
During my investigations I noticed that while not being a physical observable itself the effective field under investigation leads in a simple way to the local magnetization. The local magnetization in the one-dimensional random field Ising model is essentially just the sum of two effective fields. Its probability distribution in the thermodynamic limit therefore is essentially the convolution of the invariant measure of the effective field with itself.
This leads directly to the question whether one can deduce information about the multifractal properties of the convolution of two multifractals from the multifractal properties of the two measures being convoluted. It turns out that on can give lower and upper bounds on the Dq-spectrum of the convolution in terms of the Dq-spectra of the convoluted measures. The results are published in the paper "Convolution of multifractals and the local magnetization in a random field Ising chain". This paper also contains the application of the bounds to and numerical results on the multifractal properties of the local magnetization in the one-dimensional random field Ising model.
In a third part of my PhD work I addressed the question of phase transitions, now in the proper physical sense, in the random field Ising model on the Bethe lattice. We developped several numerical criteria for such phase transitions based on our iterated functions approach. The numerical analysis revealed interesting discrepancies with an early work of Bruinsma. The results and a discussion are published in the paper "Phase diagram of the random field Ising model on the Bethe lattice".
All results obtained during my PhD work are summarized in my PhD thesis (naturally). As the University of Leipzig thankfully allows thesis submission in English the thesis is in this language and therfore hopefully accessible to everyone. It can be downloaded from the link below.
The first subject which rendered concrete results was dimension theory of graphs. We, i.e. M.Requardt and I, developed two notions of dimension on graphs and investigated their properties. The results are summarized in a paper about dimension theory of graphs and networks.
The second paper on pregeometric concepts follows a similar spirit.
My diploma thesis sums up most of what I did on this topic as well as a brief survey of different approaches to define geometric concepts on graphs. Regulations of the University of Göttingen require any diploma thesis to be in German.
unpublished notes sum up some of the results of numerical investigations
carried out throughout the two years of work on my diploma thesis. They are
slightly incomplete because of lack of time. I apologize that they are in
German because they originally were not intended for publication.
I have modified and improved the Dynamic Clamp software developed by R. D. Pinto et al. (DYNCLAMP2) to include spike timing dependent plasticity an many other features. The software is available free of charge for non-commercial applications from the StdpC Download Page
I have developed a tool to animate the results of neural systems simulations in a 3D environment. The software is based on the OpenGL extension of QT. It is available free of charge for non-commercial applications from the NeurAnim Download Page