Reiner Kree - Academia.edu (original) (raw)
Papers by Reiner Kree
Verhandlungen der Deutschen Physikalischen Gesellschaft, 2005
European Physical Journal E, Feb 1, 2022
We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spheric... more We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spherical liquid drop at general position rs. The squirmer is subject to an external force and torque in addition to the slip velocity on its surface. We have derived exact analytical expressions for the linear and rotational velocity of the squirmer as well as the linear velocity of the drop for general, non-axisymmetric configurations. The mobilities of both, squirmer and drop, are in general anisotropic, depending on the orientation of rs, relative to squirmer axis, external force or torque. We discuss their dependence on the size of the squirmer, its distance from the center of the drop and the viscosities. Our results provide a framework for the discussion of the trajectories of the composite system of drop and enclosed squirmer.
Physical review, Dec 1, 1995
We describe a stochastic dynamics of tissue cells with special emphasis on epithelial cells and f... more We describe a stochastic dynamics of tissue cells with special emphasis on epithelial cells and fibroblasts and fibrocytes of the connective tissue. Pattern formation and growth characteristics of such cell populations in culture are investigated numerically by Monte Carlo simulations for quasitwo-dimensional systems of cells. A number of quantitative predictions are obtained which may be confronted with experimental results. Furthermore we introduce several biologically motivated variants of our basic model and briefly discuss the simulation of two-dimensional analogs of two complex processes in tissues: the growth of a sarcoma across an epithelial boundary and the wound healing of a skin cut. As compared to other approaches, we find the Monte Carlo approach to tissue growth and structure to be particularly simple and Hexible. It allows for a hierarchy of models reaching from global description of birth-death processes to very specific features of intracellular dynamics.
EPL, Aug 10, 1996
ABSTRACT We discuss the critical dynamics of dipolar glasses as observed in the dynamic dielectri... more ABSTRACT We discuss the critical dynamics of dipolar glasses as observed in the dynamic dielectric response and the dynamic structure factor. Our analysis is based on a hydrodynamic model, generalized to include slow (dipolar) fluctuations near the glass transition. The critical slowing-down of the dipoles gives rise to anomalies in the dynamic dielectric response, the appearance of a central peak and a divergent sound damping. All three phenomena are interrelated and determined by the critical exponents of an Ising spin glass. We work out the consequences of a dynamic scaling hypothesis for the dipolar autocorrelation and discuss two examples of such a scaling function. One is calculated within mean-field theory and the other is taken from numerical simulations. We compare our results to recent experiments on (NH4I)x(KI)1 − x.
Journal of Fluid Mechanics, May 25, 2017
We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming ... more We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming microorganisms or artificial microswimmers. In contrast to approaches, which start from active velocity fields produced by the system, we consider active surface force or body force densities or active stresses as the origin of autonomous swimming. For negligible Reynolds number and given activity we first calculate the external and the internal flow fields as well as the center of mass velocity and an angular velocity of the droplet at fixed time. To construct trajectories from single time snapshots, the evolution of active forces or stresses must be determined in the laboratory frame. Here, we consider the case of active matter, which is carried by a continuously distributed, rigid but sparse (cyto)-sceleton that is immersed in the droplet's interior. We calculate examples of trajectories of a droplet and its sceleton from force densities or stresses, which may be explicitely time dependent in a frame fixed within the sceleton.
Studies in classification, data analysis, and knowledge organization, 1993
A rapidly growing body of literature is devoted to applications of neural networks in classificat... more A rapidly growing body of literature is devoted to applications of neural networks in classification tasks. Most of the authors working in this field consider feed-forward architectures with hidden units, which can be trained via standard algorithms. In the present contribution we discuss possible applications of feedback attractor neural networks to multi-censoring classification problems. We study cooperating networks with self-organizing inter-network connections. In our model, information is transferred from one network to another only if the transmitting node is sufficiently sure (according to some semi-empiric criterion) that it will be able to solve its subtask. In this way it is possible to design networks for multi-censoring tasks which consist of subtasks of widly varying complexity. Furthermore it can be shown that the improved performance of such nets —as compared to fully connected networks— is due to a drastic reduction of connections. This may be a considerable advantage in applications on large data sets.
NATO advanced study institutes series, 1990
Networks of interacting two-state variables have been proposed as models for a variety of systems... more Networks of interacting two-state variables have been proposed as models for a variety of systems, e.g.,neuronal circuits and associative memory devices(1)of population dynamics and magnetic systems.We will concentrate in the following on neural network models though some of the results can be applied to other systems as well.
Journal of physics, Aug 21, 1988
The authors extend the architecture of the Hopfield network, such that it can recognise transform... more The authors extend the architecture of the Hopfield network, such that it can recognise transformed versions of a set of learnt prototypes. As an example they construct a network which can generalise over all topologically equivalent representations of graphs or images. The construction is based on two coupled networks: a Hopfield network to store and retrieve patterns and a preprocessor
Network: Computation In Neural Systems, 1994
We investigate the effect of non-local synaptic enhancement within the framework of networks of f... more We investigate the effect of non-local synaptic enhancement within the framework of networks of formal neurons. Enhancement of nearby synapses on a common axon without simultaneous post- and presynaptic stimulation is modelled by a generalized Hebbian rule. The imprinted patterns of activity are no longer attractors of the network dynamics, but are processed instead. The network acts as a low band-pass filter for spatially uncorrelated patterns and can discriminate spatially correlated patterns, according to their degree and range of correlation. While the network is processing information, it still maintains some of the error-correcting properties of attractor neural networks.
Verhandlungen der Deutschen Physikalischen Gesellschaft, 2005
European Physical Journal E, Feb 1, 2022
We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spheric... more We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spherical liquid drop at general position rs. The squirmer is subject to an external force and torque in addition to the slip velocity on its surface. We have derived exact analytical expressions for the linear and rotational velocity of the squirmer as well as the linear velocity of the drop for general, non-axisymmetric configurations. The mobilities of both, squirmer and drop, are in general anisotropic, depending on the orientation of rs, relative to squirmer axis, external force or torque. We discuss their dependence on the size of the squirmer, its distance from the center of the drop and the viscosities. Our results provide a framework for the discussion of the trajectories of the composite system of drop and enclosed squirmer.
Physical review, Dec 1, 1995
We describe a stochastic dynamics of tissue cells with special emphasis on epithelial cells and f... more We describe a stochastic dynamics of tissue cells with special emphasis on epithelial cells and fibroblasts and fibrocytes of the connective tissue. Pattern formation and growth characteristics of such cell populations in culture are investigated numerically by Monte Carlo simulations for quasitwo-dimensional systems of cells. A number of quantitative predictions are obtained which may be confronted with experimental results. Furthermore we introduce several biologically motivated variants of our basic model and briefly discuss the simulation of two-dimensional analogs of two complex processes in tissues: the growth of a sarcoma across an epithelial boundary and the wound healing of a skin cut. As compared to other approaches, we find the Monte Carlo approach to tissue growth and structure to be particularly simple and Hexible. It allows for a hierarchy of models reaching from global description of birth-death processes to very specific features of intracellular dynamics.
EPL, Aug 10, 1996
ABSTRACT We discuss the critical dynamics of dipolar glasses as observed in the dynamic dielectri... more ABSTRACT We discuss the critical dynamics of dipolar glasses as observed in the dynamic dielectric response and the dynamic structure factor. Our analysis is based on a hydrodynamic model, generalized to include slow (dipolar) fluctuations near the glass transition. The critical slowing-down of the dipoles gives rise to anomalies in the dynamic dielectric response, the appearance of a central peak and a divergent sound damping. All three phenomena are interrelated and determined by the critical exponents of an Ising spin glass. We work out the consequences of a dynamic scaling hypothesis for the dipolar autocorrelation and discuss two examples of such a scaling function. One is calculated within mean-field theory and the other is taken from numerical simulations. We compare our results to recent experiments on (NH4I)x(KI)1 − x.
Journal of Fluid Mechanics, May 25, 2017
We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming ... more We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming microorganisms or artificial microswimmers. In contrast to approaches, which start from active velocity fields produced by the system, we consider active surface force or body force densities or active stresses as the origin of autonomous swimming. For negligible Reynolds number and given activity we first calculate the external and the internal flow fields as well as the center of mass velocity and an angular velocity of the droplet at fixed time. To construct trajectories from single time snapshots, the evolution of active forces or stresses must be determined in the laboratory frame. Here, we consider the case of active matter, which is carried by a continuously distributed, rigid but sparse (cyto)-sceleton that is immersed in the droplet's interior. We calculate examples of trajectories of a droplet and its sceleton from force densities or stresses, which may be explicitely time dependent in a frame fixed within the sceleton.
Studies in classification, data analysis, and knowledge organization, 1993
A rapidly growing body of literature is devoted to applications of neural networks in classificat... more A rapidly growing body of literature is devoted to applications of neural networks in classification tasks. Most of the authors working in this field consider feed-forward architectures with hidden units, which can be trained via standard algorithms. In the present contribution we discuss possible applications of feedback attractor neural networks to multi-censoring classification problems. We study cooperating networks with self-organizing inter-network connections. In our model, information is transferred from one network to another only if the transmitting node is sufficiently sure (according to some semi-empiric criterion) that it will be able to solve its subtask. In this way it is possible to design networks for multi-censoring tasks which consist of subtasks of widly varying complexity. Furthermore it can be shown that the improved performance of such nets —as compared to fully connected networks— is due to a drastic reduction of connections. This may be a considerable advantage in applications on large data sets.
NATO advanced study institutes series, 1990
Networks of interacting two-state variables have been proposed as models for a variety of systems... more Networks of interacting two-state variables have been proposed as models for a variety of systems, e.g.,neuronal circuits and associative memory devices(1)of population dynamics and magnetic systems.We will concentrate in the following on neural network models though some of the results can be applied to other systems as well.
Journal of physics, Aug 21, 1988
The authors extend the architecture of the Hopfield network, such that it can recognise transform... more The authors extend the architecture of the Hopfield network, such that it can recognise transformed versions of a set of learnt prototypes. As an example they construct a network which can generalise over all topologically equivalent representations of graphs or images. The construction is based on two coupled networks: a Hopfield network to store and retrieve patterns and a preprocessor
Network: Computation In Neural Systems, 1994
We investigate the effect of non-local synaptic enhancement within the framework of networks of f... more We investigate the effect of non-local synaptic enhancement within the framework of networks of formal neurons. Enhancement of nearby synapses on a common axon without simultaneous post- and presynaptic stimulation is modelled by a generalized Hebbian rule. The imprinted patterns of activity are no longer attractors of the network dynamics, but are processed instead. The network acts as a low band-pass filter for spatially uncorrelated patterns and can discriminate spatially correlated patterns, according to their degree and range of correlation. While the network is processing information, it still maintains some of the error-correcting properties of attractor neural networks.