69 citations · 304 across the 20 of their papers we have counts for
20 papers
Self-tolerance and autoimmunity in a minimal model of the idiotypic network
Stefan Landmann, Nicolas Preuss, Ulrich Behn
We consider self-tolerance and its failure -autoimmunity- in a minimal mathematical model of the idiotypic network. A node in the network represents a clone of B-lymphocytes and it…
Discontinuous transitions in globally coupled potential systems with additive noise
Rüdiger Kürsten, Ulrich Behn
An infinite array of globally coupled overdamped constituents moving in a double-well potential with -th order saturation term under the influence of additive Gaussian white noi…
Patchwork Sampling of Stochastic Differential Equations
Rüdiger Kürsten, Ulrich Behn
We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare t…
Self tolerance in a minimal model of the idiotypic network
Robert Schulz, Benjamin Werner, Ulrich Behn
We consider the problem of self tolerance in the frame of a minimalistic model of the idiotypic network. A node of this network represents a population of B lymphocytes of the same…
Critical manifold of globally coupled overdamped anharmonic oscillators driven by additive Gaussian white noise
Rüdiger Kürsten, Susanne Gütter, Ulrich Behn
We prove for an infinite array of globally coupled overdamped anharmonic oscillators subject to additive Gaussian white noise the existence of a well-behaved critical manifold in t…
Randomly Evolving Idiotypic Networks: Structural Properties and Architecture
Holger Schmidtchen, Mario Thüne, Ulrich Behn
We consider a minimalistic dynamic model of the idiotypic network of B-lymphocytes. A network node represents a population of B-lymphocytes of the same specificity (idiotype), whic…
Randomly Evolving Idiotypic Networks: Modular Mean Field Theory
Holger Schmidtchen, Ulrich Behn
We develop a modular mean field theory for a minimalistic model of the idiotypic network. The model comprises the random influx of new idiotypes and a deterministic selection. It d…
First-passage and first-exit times of a Bessel-like stochastic process
Edgar Martin, Ulrich Behn, Guido Germano
We study a stochastic process related to the Bessel and the Rayleigh processes, with various applications in physics, chemistry, biology, economics, finance and other fields.…
Mathematical Modelling of Allergy and Specific Immunotherapy: Th1-Th2-Treg Interactions
Fridolin Gross, Gerhard Metzner, Ulrich Behn
Regulatory T cells (Treg) have recently been identified as playing a central role in allergy and during allergen-specific immunotherapy. We have extended our previous mathematical…
Nonequilibrium phase transitions in finite arrays of globally coupled Stratonovich models: Strong coupling limit
Fabian Senf, Philipp M. Altrock, Ulrich Behn
A finite array of globally coupled Stratonovich models exhibits a continuous nonequilibrium phase transition. In the limit of strong coupling there is a clear separation of tim…
Generation of spatiotemporal correlated noise in 1+1 dimensions
Arne Traulsen, Karen Lippert, Ulrich Behn
We propose a generalization of the Ornstein-Uhlenbeck process in 1+1 dimensions which is the product of a temporal Ornstein-Uhlenbeck process with a spatial one and has exponential…
Laser diffraction by periodic dynamic patterns in anisotropic fluids
Th. John, U. Behn, R. Stannarius
This paper describes the application of a laser diffraction technique to the study of electroconvection in nematic liquid crystal cells. It allows a real-time quantitative access t…
Patterns in randomly evolving networks: Idiotypic networks
M. Brede, U. Behn
We present a model for the evolution of networks of occupied sites on undirected regular graphs. At every iteration step in a parallel update I randomly chosen empty sites are occu…
Fundamental scaling laws of on-off intermittency in a stochastically driven dissipative pattern forming system
Th. John, U. Behn, R. Stannarius
Noise driven electroconvection in sandwich cells of nematic liquid crystals exhibits on-off intermittent behaviour at the onset of the instability. We study laser scattering of con…
Critical Behaviour of Non-Equilibrium Phase Transitions to Magnetically Ordered States
Thomas Birner, Karen Lippert, Reinhard Müller +2
We describe non-equilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spa…
Phase diagram of the random field Ising model on the Bethe lattice
Thomas Nowotny, Heiko Patzlaff, Ulrich Behn
The phase diagram of the random field Ising model on the Bethe lattice with a symmetric dichotomous random field is closely investigated with respect to the transition between the…
Convolution of multifractals and the local magnetization in a random field Ising chain
Thomas Nowotny, Ulrich Behn
The local magnetization in the one-dimensional random-field Ising model is essentially the sum of two effective fields with multifractal probability measure. The probability measur…
The Architecture of Idiotypic Networks: Percolation and Scaling Behaviour
Markus Brede, Ulrich Behn
We investigate a model where idiotypes (characterizing B-lymphocytes and antibodies of an immune system) and anti-idiotypes are represented by complementary bitstrings of a given l…
Orbits and phase transitions in the multifractal spectrum
Thomas Nowotny, Heiko Patzlaff, Ulrich Behn
We consider the one dimensional classical Ising model in a symmetric dichotomous random field. The problem is reduced to a random iterated function system for an effective field. T…
On-off Intermittency in Stochastically Driven Electrohydrodynamic Convection in Nematics
Thomas John, Ralf Stannarius, Ulrich Behn
We report on-off intermittency in electroconvection of nematic liquid crystals driven by a dichotomous stochastic electric voltage. With increasing voltage amplitude we observe lam…