One: Mathematics is the language of nature.
Two: Everything around us can be represented and understood through numbers.
Three: If you graph the numbers of any system, patterns emerge.
Therefore, there are patterns everywhere in nature.
Max Cohen, Pi
Two: Everything around us can be represented and understood through numbers.
Three: If you graph the numbers of any system, patterns emerge.
Therefore, there are patterns everywhere in nature.
Max Cohen, Pi
BOOKS AND MONOGRAPHS
Neuronal Noise and Beyond
Habilitation Thesis, 2016
Neuronal Noise
Springer, New York: 2012
PEER-REVIEWED ARTICLES
38.
ChessY:
A Mathematica toolbox for the generation, visualization and analysis of positional chess graphs
A Mathematica toolbox for the generation, visualization and analysis of positional chess graphs
SoftwareX, 2019, in press
37.
A discrete algebraic framework for stochastic systems which yield unique and exact solutions
Heliyon 4: e00691, 2018
36.
On a recursive construction of circular paths and the search for $\pi$ on the integer lattice $\mathbb{Z}^2$
Discrete Comput. Geom. 59: 643-662, 2018
35.
On the product representation of number sequences, with applications
to the family of generalized Fibonacci numbers
to the family of generalized Fibonacci numbers
J. Integer Sequences 19: 16.3.6, 2016
34.
On a link between Dirichlet kernels and central multinomial coefficients
Discrete Math. 338: 1567-1572, 2015
33.
Brain networks: small-worlds, after all?
New J. Phys. 16: 105004, 2014
32.
Aspects of randomness in neural graph structures
Biol. Cybern. 108: 381-396, 2014
31.
On a representation of the Verhulst logistic map
Discrete Math. 324: 19-27, 2014
30.
Algebraic approach to small-world network models
Phys. Rev. E 89: 012812, 2014
29.
Analytical integrate-and-fire neuron models with conductance-based dynamics and
realistic postsynaptic potential time course for event-driven simulation strategies
realistic postsynaptic potential time course for event-driven simulation strategies
Neural Comput. 24: 1426-1461, 2012
28.
PAX: A mixed hardware/software simulation platform for spiking neural networks
Neural Networks 23: 905-916, 2010
27.
Frequency-selectivity of a thalamocortical relay neuron during Parkinson's disease and
deep brain stimulation: a computational study
deep brain stimulation: a computational study
Eur. J. Neurosci. 30: 1306-1317, 2009
26.
High-resolution intracellular recordings using a real-time computational model of the electrode
Neuron 59: 379-391, 2008
25.
Calculating event-triggered average synaptic conductances from the membrane potential
J. Neurophysiol. 97: 2544-2552, 2007
24.
Inhibition determines membrane potential dynamics and controls action potential generation
in awake and sleeping cat cortex
in awake and sleeping cat cortex
J. Neurosci. 27: 5280-5290, 2007
23.
Activated cortical states: experiments, analyses and models
J. Physiol. (Paris) 101: 99-109, 2007
22.
Biophysical and phenomenological models of multiple spike interactions in
spike-timing dependent plasticity
spike-timing dependent plasticity
Int. J. of Neural Systems 16: 79-97, 2006
21.
A multichannel shot noise approach to describe synaptic background activity in neurons
Eur. Phys. J. B 52: 125-132, 2006
20.
Analytical Integrate-and-fire neurons with high-conductance state dynamics
for event-driven simulation strategies
for event-driven simulation strategies
Neural Comput. 18: 2146-2210, 2006
19.
On the use of analytic expressions for the voltage distribution to analyze intracellular recordings
Neural Comput. 18: 2917-2922, 2006
18.
An extended analytic expression for the membrane potential distribution of
conductance-based synaptic noise
conductance-based synaptic noise
Neural Comput. 17: 2301-2315, 2005
17.
Characterization of synaptic conductances and integrative properties during
electrically-induced EEG-activated states in neocortical neurons in vivo
electrically-induced EEG-activated states in neocortical neurons in vivo
J. Neurophysiol. 94: 2805-2821, 2005
16.
A method to estimate synaptic conductances from membrane potential fluctuations
J. Neurophysiol. 91: 2884-2896, 2004
15.
Extracting information from the power spectrum of synaptic noise
J. Comput. Neurosci. 17: 327-345, 2004
14.
A fast conducting, stochastic integrative mode for neocortical neurons in vivo
J. Neurosci. 23: 2466-2476, 2003
13.
Tuning neocortical pyramidal neurons between integrators and coincidence detectors
J. Comput. Neurosci. 14: 239-251, 2003
12.
The discharge variability of neocortical neurons during high-conductance states
Neurosci. 119: 855-873, 2003
11.
Characterization of subthreshold voltage fluctuations in neuronal membranes
Neural Comput. 15: 2577-2618, 2003
10.
Synaptic background noise controls the input/output characteristics of single cells
in an in vitro model of in-vivo activity
in an in vitro model of in-vivo activity
Neurosci. 122: 811-829, 2003
9.
Spike generating dynamics and the conditions for spike-time precision in cortical neurons
J. Comput. Neurosci. 15: 91-105, 2003
8.
Correlation detection and resonance in neural systems with distributed noise sources
Phys. Rev. Lett. 86: 3662-3665, 2001
7.
Do neocortical pyramidal neurons display stochastic resonance?
J. Comput. Neurosci. 11: 19-42, 2001
6.
Fluctuating synaptic conductances recreate in-vivo-like activity in neocortical neurons
Neurosci. 107: 13-24, 2001
5.
Towards an effective field theory of QED
Acta Phys. Polon. B31: 847-861, 2000
4.
Effective bosonic degrees of freedom for one-flavour chromodynamics
Ann. Inst. Henri Poincare 68: 285-313, 1998
3.
Gauge invariant formulation and bosonisation of the Schwinger model
Phys. Lett. B 419: 285-290, 1998
2.
On the algebra of gauge invariants for one-flavour chromodynamics
Rep. Math. Phys. 40: 131-142, 1997
1.
Functional integral of QED in terms of gauge-invariant quantities
Lett. Math. Phys. 33: 139-146, 1995
REVIEW ARTICLES
5.
Characterizing synaptic conductance fluctuations in cortical neurons
and their influence on spike generation
and their influence on spike generation
J. Neurosci. Meth. 169: 302-322, 2008
4.
Are corticothalamic 'up' states fragments of wakefulness?
Trends Neurosci. 30: 334-342, 2007
3.
Simulation of networks of spiking neurons: A review of tools and strategies
J. Comput. Neurosci. 23: 349-398, 2007
2.
Inferring network activity from synaptic noise
J. Physiol. (Paris) 98: 452-466, 2004
1.
The high-conductance state of neocortical neurons in vivo
Nature Rev. Neurosci. 4: 739-751, 2003
BOOK CHAPTERS
5.
Noisy dendrites: Models of dendritic integration in vivo
In: The Computing Dendrite: From Structure to Function, H. Cuntz, M.W.H. Remme, B. Torben-Nielsen (Eds.),
Springer Series in Computational Neuroscience, Vol. 11: 173-190, 2014
Springer Series in Computational Neuroscience, Vol. 11: 173-190, 2014
4.
Convergence in an adaptive neural network: The influence of noise inputs correlation
In: Bio-Inspired Systems: Computational and Ambient Intelligence, J. Cabestany et al. (Eds.),
Lecture Notes in Computer Science, Vol. 5517: 140-148, 2009
Lecture Notes in Computer Science, Vol. 5517: 140-148, 2009
3.
Testing methods for synaptic conductance analysis using controlled conductance
injection with dynamic clamp
injection with dynamic clamp
In: Dynamic-Clamp, A. Destexhe, T. Bal (Eds.),
Springer Series in Computational Neuroscience, Vol. 1: 115-140, 2009
Springer Series in Computational Neuroscience, Vol. 1: 115-140, 2009
2.
Synaptic 'noise': Experiments, computational consequences and methods to analyze experimental data
In: Stochastic Processes in Neuroscience, C. Laing, G.J. Lord (Eds.), Clarendon Press: 242-271, 2008
1.
Complexity in neuronal networks
In: Biological Networks, F. Kepes (Ed.), World Scientific: 291-340, 2007
CONFERENCE PAPERS
19.
How much can we trust neural simulation strategies?
Neurocomput. 70: 1966-1969, 2007
18.
Inhibitory conductance dynamics in cortical neurons during activated states
Neurocomput. 70: 1602-1604, 2007
17.
A nonparametric electrode model for intracellular recording
Neurocomput. 70: 1597-1601, 2007
16.
Event-based simulation strategy for conductance-based synaptic interactions and plasticity
Neurocomput. 69: 1130-1133, 2006
15.
High discharge variability in neurons driven by current noise
Neurocomput. 65: 493-498, 2005
14.
Recreating active states in vitro with a dynamic clamp protocol
Neurocomput. 65: 55-60, 2005
13.
Reconstructing synaptic background activity from conductance measurements in vivo
Neurocomput. 65: 673-678, 2005
12.
Multi-channel shot noise and characterization of cortical network activity
Neurocomput. 65: 641-646, 2005
11.
Extracting information from the power spectrum of voltage noise
Neurocomput. 65: 901-906, 2005
10.
A novel method for characterizing synaptic noise in cortical neurons
Neurocomput. 58: 191-196, 2004
9.
Estimation of synaptic conductances and their variances from intracellular recordings
of neocortical neurons in vivo
of neocortical neurons in vivo
Neurocomput. 58: 387-392, 2004
8.
Location independence and fast conduction of synaptic inputs in neocortical neurons in vivo
Neurocomput. 52: 233-238, 2003
7.
Gain modulation and frequency locking under conductance noise
Neurocomput. 52: 907-912, 2003
6.
Point-conductance models of cortical neurons with high discharge variability
Neurocomput. 44: 147-152, 2002
5.
Novel dynamics of dendritic integration in the high conductance state of cortical neurons
Neurocomput. 44: 141-146, 2002
4.
Synaptic background activity affects the dynamics of dendritic integration
in model neocortical pyramidal neurons
in model neocortical pyramidal neurons
Neurocomput. 38: 327-333, 2001
3.
Gauge invariants and bosonization
In: AIP Conference Proceedings 453, Woodbury: 382-393, 1998
2.
Gauge theories with fermions in terms of gauge invariants
In: Proc. XXI Int. Coll. on Group Theoretical Meth. Phys. II: 639-643,1997
1.
Gauge theories in terms of invariants
Rep. Math. Phys. 40: 565-578, 1997
PREPRINTS
14.
Pi visits Manhattan
arXiv:1708.00766 [math.HO], 2017
13.
On a recursive construction of circular paths and the search for $\pi$ on the integer lattice $\mathbb{Z}^2$
1602.06239 [cs.GR], 2016
12.
On the product representation of number sequences, with applications
to the family of generalized Fibonacci numbers
to the family of generalized Fibonacci numbers
arXiv:1508.07894 [math.NT], 2015
11.
On an explicit representation of central $(2k+1)$-nomial coefficients
arXiv:1403.5942v1 [math.CO], 2014
10.
Percolation in random graphs: a finite approach
arXiv:1405.2233v1 [cond-mat.stat-mech], 2014
9.
Aspects of randomness in neural graph structures
arXiv:1310.5062v1 [physics.soc-ph], 2013
8.
Structual vulnerability of the nematode worm neural graph
arXiv:1208.3383v1 [cond-mat.dis-nn], 2012
7.
High-resolution intracellular recordings using a real-time computational model of the electrode
arXiv:0711.2075v1 [q-bio.NC], 2007
6.
On the use of analytic expressions for the voltage distribution to analyze intracellular recordings
arXiv:q-bio/0602010v1 [q-bio.NC], 2006
5.
Towards an effective field theory of QED
NTZ Preprint 21/1999, University of Leipzig, 1999
arXiv:hep-th/9909113v1, 1999
arXiv:hep-th/9909113v1, 1999
4.
String theory and beyond
arXiv:hep-th/9812201v1, 1998
3.
Gauge invariant formulation and bosonisation of the Schwinger model
arXiv:hep-th/9710003v1, 1997
2.
Effective bosonic degrees of freedom for one-flavour chromodynamics
NTZ Preprint 22/1996, University of Leipzig, 1996
arXiv:hep-th/9606020v1, 1996
arXiv:hep-th/9606020v1, 1996
1.
Functional integral of QED in terms of gauge-invariant quantities
University of Leipzig, NTZ Preprint-Nr. 4/94