We present a lattice model for a two-dimensional network of self-activated biological structures ... more We present a lattice model for a two-dimensional network of self-activated biological structures with a diffusive activating agent. The model retains basic and simple properties shared by biological systems at various observation scales, so that the structures can consist of individuals, tissues, cells, or enzymes. Upon activation, a structure emits a new mobile activator and remains in a transient refractory state before it can be activated again. Varying the activation probability, the system undergoes a nonequilibrium second-order phase transition from an active state, where activators are present, to an absorbing, activator-free state, where each structure remains in the deactivated state. We study the phase transition using Monte Carlo simulations and evaluate the critical exponents. As they do not seem to correspond to known values, the results suggest the possibility of a separate universality class.
Soybean lipoxygenase-1 kinetics are known to show product and substrate inhibition. With linoleic... more Soybean lipoxygenase-1 kinetics are known to show product and substrate inhibition. With linoleic acid as the substrate and using a simple Michaelis-Menten formulation, we have shown that K sii , the substrate inhibition constant was increased by more than five-fold when initial oxygen concentration was increased from 228 to 1140 μΜ. Excess substrate inhibition is in fact almost avoided at high initial oxygen concentration. This modification seems correlated with enzyme saturation with oxygen relative to linoleic acid, as reflected by alterations of the substrate conversion rate. Possible implications for the enzyme kinetics are discussed.
We investigated the epidemiology of antibiotic resistance and virulence properties among Pseudomo... more We investigated the epidemiology of antibiotic resistance and virulence properties among Pseudomonas aeruginosa clinical isolates collected in 1999 from patients hospitalized in the intensive care units of the centre hospitalier d'Orléans, in France. We compared the totality of the strains from mechanically ventilated patients with pneumonia (33 non-duplicate isolates, group 1) to 15 randomly chosen, imipenemresistant, extra-respiratory tract isolates, collected from non-infected patients hospitalized in the same units (group 2). The isolates were serotyped, typed by random amplified polymorphic DNA (RAPD), and screened for their pneumocyte cell adherence, cytotoxicity, and antibiotic resistance. A total of 35 RAPD profiles were found, and only two profiles were encountered in both groups, demonstrating a high genetic diversity. 84.8% of the group 1 and 93.3% of the group 2 isolates adhered to A549 cells. Three non-exclusive adhesive patterns were observed: a diffuse adhesion in 38 isolates, a localized adhesion in 14 isolates, and an aggregative adhesion in seven isolates. 78.8% of the group 1 and 93.3% of the group 2 isolates were cytotoxic. Considering all 48 isolates, there was a strong and statistically significant correlation between cytotoxicity and adherence. Among the three dominant serotypes, O:12 isolates were in majority avirulent, but the great majority of O:1 and all the O:11 isolates were found adherent and cytotoxic. Gentamicin was the least active antibiotic for both groups, and ceftazidime was the most active antibiotic for group 1 and amikacin for group 2. The penicillinase production phenotype was significantly correlated with a decrease in P. aeruginosa virulence.
We monitored the cell-free solubilization of extracellular matrix and fibronectin gels, catalyzed... more We monitored the cell-free solubilization of extracellular matrix and fibronectin gels, catalyzed by exogenous proteinases. The corresponding measurements could not be interpreted according to usual proteinase kinetics. The observation that this experimental system did not consist in surface but in bulk degradation and appeared specific to gel substrates, incited us to use gelation-related approaches to describe these kinetics. We show that the gel^sol transition theory adequately describes the enzyme reactions. This allowed formulation and experimental confirmation of a power law relating macroscopic changes of the gel to enzyme kinetics. This approach could also be used for other power laws predicted by the gel^sol transition theory, allowing a better understanding of macroscopic modification of the extracellular matrix during proteolysis, which is implied in many biological situations, especially tumor dissemination. ß
Journal of colloid and interface science, Jan 1, 2006
Fibronectin (Fn), a high molecular weight glycoprotein, is a central element of extracellular mat... more Fibronectin (Fn), a high molecular weight glycoprotein, is a central element of extracellular matrix architecture that is involved in several fundamental cell processes. In the context of bone biology, little is known about the influence of the mineral surface on fibronectin supramolecular assembly. We investigate fibronectin morphological properties induced by its adsorption onto a model mineral matrix of hydroxyapatite (HA). Fibronectin adsorption onto HA spontaneously induces its aggregation and fibrillation. In some cases, fibronectin fibrils are even found connected into a dense network that is close to the matrix synthesized by cultured cells. Fibronectin adsorption-induced self-assembly is a time-dependant process that is sensitive to bulk concentration. The N-terminal domain of the protein, known to be implicated in its self-association, does not significantly inhibit the protein self-assembly while increasing ionic strength in the bulk alters both aggregation and fibrillation. The addition of a non-ionic surfactant during adsorption tends to promote aggregation with respect to fibrillation. Ultimately, fibronectin fibrils appear to be partially structured like amyloid fibrils as shown by thioflavine T staining. Taken together, our results suggest that there might be more than one single organization route involved in fibronectin self-assembly onto hydroxyapatite. The underlying mechanisms are discussed with respect to Fn conformation, Fn/surface and Fn/Fn interactions, and a model of fibronectin fibrillogenesis onto hydroxyapatite is proposed.
Chaos: An Interdisciplinary Journal of …, Jan 1, 2006
Modern computer microprocessors are composed of hundreds of millions of transistors that interact... more Modern computer microprocessors are composed of hundreds of millions of transistors that interact through intricate protocols. Their performance during program execution may be highly variable and present aperiodic oscillations. In this paper, we apply current nonlinear time series analysis techniques to the performances of modern microprocessors during the execution of prototypical programs. Our results present pieces of evidence strongly supporting that the high variability of the performance dynamics during the execution of several programs display low-dimensional deterministic chaos, with sensitivity to initial conditions comparable to textbook models. Taken together, these results show that the instantaneous performances of modern microprocessors constitute a complex (or at least complicated) system and would benefit from analysis with modern tools of nonlinear and complexity science. PACS numbers: 05.45.Ac,05.45.Tp, 89.20.Ff, 89.75.-k * Electronic address: hugues.berry@inria.fr
The aim of the present paper is to study the effects of Hebbian learning in random recurrent neur... more The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore consider that the neuron dynamics may occur at a (shorter) time scale than synaptic plasticity and consider the possibility of learning rules with passive forgetting. We show that the application of such Hebbian learning leads to drastic changes in the network dynamics and structure. In particular, the learning rule contracts the norm of the weight matrix and yields a rapid decay of the dynamics complexity and entropy. In other words, the network is rewired by Hebbian learning into a new synaptic structure that emerges with learning on the basis of the correlations that progressively build up between neurons. We also observe that, within this emerging structure, the strongest synapses organize as a small-world network. The second effect of the decay of the weight matrix spectral radius consists in a rapid contraction of the spectral radius of the Jacobian matrix. This drives the system through the "edge of chaos" where sensitivity to the input pattern is maximal. Taken together, this scenario is remarkably predicted by theoretical arguments derived from dynamical systems and graph theory.
Extracellular matrix mass balance is implied in many physiological and pathological events, such ... more Extracellular matrix mass balance is implied in many physiological and pathological events, such as metastasis dissemination. Widely studied, its destructive part is mainly catalysed by extracellular proteinases. Conversely, the properties of the constructive part are less obvious, cellular neo-synthesis being usually considered as its only element. In this paper, we introduce the action of transglutaminase in a mathematical model for extracellular matrix remodeling. This extracellular enzyme, catalysing intermolecular protein cross-linking, is considered here as a reverse proteinase as far as the extracellular matrix physical state is concerned. The model is based on a proteinase/transglutaminase cycle interconverting insoluble matrix and soluble proteolysis fragments, with regulation of cellular proteinase expression by the fragments. Under "closed" (batch) conditions, i.e. neglecting matrix influx and fragment efflux from the system, the model is bistable, with reversible hysteresis. Extracellular matrix proteins concentration abruptly switches from low to high levels when transglutaminase activity exceeds a threshold value. Proteinase concentration usually follows the reverse complementary kinetics, but can become apparently uncoupled from extracellular matrix concentration for some parameter values. When matrix production by the cells and fragment degradation are taken into account, the dynamics change to sustained oscillations because of the emergence of a stable limit cycle. Transitions out of and into oscillation areas are controlled by the model parameters. Biological interpretation indicates that these oscillations could represent the normal homeostatic situation, whereas the other exhibited dynamics can be related to pathologies such as tumor invasion or fibrosis. These results allow to discuss the insights that the model could contribute to the comprehension of these complex biological events.
Strong experimental evidence indicates that protein kinase and phosphatase (KP) cycles are critic... more Strong experimental evidence indicates that protein kinase and phosphatase (KP) cycles are critical to both the induction and maintenance of activity-dependent modifications in neurons. However, their contribution to information storage remains controversial, despite impressive modeling efforts. For instance, plasticity models based on KP cycles do not account for the maintenance of plastic modifications. Moreover, bistable KP cycle models that display memory fail to capture essential features of information storage: rapid onset, bidirectional control, graded amplitude, and finite lifetimes. Here, we show in a biophysical model that upstream activation of KP cycles, a ubiquitous mechanism, is sufficient to provide information storage with realistic induction and maintenance properties: plastic modifications are rapid, bidirectional, and graded, with finite lifetimes that are compatible with animal and human memory. The maintenance of plastic modifications relies on negligible reaction rates in basal conditions and thus depends on enzyme nonlinearity and activation properties of the activity-dependent KP cycle. Moreover, we show that information coding and memory maintenance are robust to stochastic fluctuations inherent to the molecular nature of activitydependent KP cycle operation. This model provides a new principle for information storage where plasticity and memory emerge from a single dynamic process whose rate is controlled by neuronal activity. This principle strongly departs from the long-standing view that memory reflects stable steady states in biological systems, and offers a new perspective on memory in animals and humans. Citation: Delord B, Berry H, Guigon E, Genet S (2007) A new principle for information storage in an enzymatic pathway model. PLoS Comput Biol 3(6): e124.
A possible alternative to topology fine-tuning for Neural Network (NN) optimization is to use Ech... more A possible alternative to topology fine-tuning for Neural Network (NN) optimization is to use Echo State Networks (ESNs), recurrent NNs built upon a large reservoir of sparsely randomly connected neurons. The promises of ESNs have been fulfilled for supervised learning tasks, but unsupervised ones, e.g. control problems, require more flexible optimization methods -such as Evolutionary Algorithms. This paper proposes to apply CMA-ES, the state-of-the-art method in evolutionary continuous parameter optimization, to the evolutionary learning of ESN parameters. First, a standard supervised learning problem is used to validate the approach and compare it to the standard one. But the flexibility of Evolutionary optimization allows us to optimize not only the outgoing weights but also, or alternatively, other ESN parameters, sometimes leading to improved results. The classical double pole balancing control problem is then used to demonstrate the feasibility of evolutionary (i.e. reinforcement) learning of ESNs. We show that the evolutionary ESN obtain results that are comparable with those of the best topology-learning methods.
We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural ... more We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning dynamics.
Extracellular proteolysis during cell invasion is thought to be tightly organized, both temporall... more Extracellular proteolysis during cell invasion is thought to be tightly organized, both temporally and spatially. This work presents a simple kinetic model that describes the interactions between extracellular matrix (ECM) proteins, proteinases, proteolytic fragments, and integrins. Nonmonotonous behavior arises from enzyme de novo synthesis consecutive to integrin binding to fragments or entire proteins. The model has been simulated using realistic values for kinetic constants and protein concentrations, with fibronectin as the ECM protein. The simulations show damped oscillations of integrin-complex concentrations, indicating alternation of maximal adhesion periods with maximal mobility periods. Comparisons with experimental data from the literature confirm the similarity between this system behavior and cell invasion. The influences on the system of cryptic functions of ECM proteins, proteinase inhibitors, and soluble antiadhesive peptides were examined. The first critical parameter for oscillation is the discrepancy between integrin affinity for intact ECM proteins and the respective proteolytic fragments, thus emphasizing the importance of cryptic functions of ECM proteins in cell invasion. Another critical parameter is the ratio between proteinase and the initial ECM protein concentration. These results suggest new insights into the organization of the ECM degradation during cell invasion.
Contrary to Hopfield-like networks, random recurrent neural networks (RRNN), where the couplings ... more Contrary to Hopfield-like networks, random recurrent neural networks (RRNN), where the couplings are random, exhibit complex dynamics (limit cycles, chaos). It is possible to store information in these networks through Hebbian learning. Eventually, learning "destroys" the dynamics and leads to a fixed point attractor. We investigate here the structural changes occurring in the network through learning. We show that a simple Hebbian learning rule organizes synaptic weight redistribution on the network from an initial homogeneous and random distribution to a heterogeneous one, where strong synaptic weights preferentially assemble in triangles. Hence learning organizes the network of the large synaptic weights as a "small-world" one.
We study the steady states of a reaction-diffusion medium modelled by a stochastic 2D cellular au... more We study the steady states of a reaction-diffusion medium modelled by a stochastic 2D cellular automaton. We consider the Greenberg-Hastings model where noise and topological irregularities of the grid are taken into account. The decrease of the probability of excitation changes qualitatively the behaviour of the system from an "active" to an "extinct" steady state. Simulations show that this change occurs near a critical threshold ; it is identified as a nonequilibrium phase transition which belongs to the directed percolation universality class. We test the robustness of the phenomenon by introducing persistent defects in the topology : directed percolation behaviour is conserved. Using experimental and analytical tools, we suggest that the critical threshold varies as the inverse of the average number of neighbours per cell.
A possible alternative to fine topology tuning for Neural Network (NN) optimization is to use Ech... more A possible alternative to fine topology tuning for Neural Network (NN) optimization is to use Echo State Networks (ESNs), recurrent NNs built upon a large reservoir of sparsely randomly connected neurons. The promises of ESNs have been fulfilled for supervised learning tasks, but unsupervised learning tasks, such as control problems, require more flexible optimization methods. We propose here to apply stateof-the-art methods in evolutionary continuous parameter optimization, to the evolutionary learning of ESN. First, a standard supervised learning problem is used to validate our approach and compare it to the standard quadratic one. The classical double pole balancing control problem is then used to demonstrate that unsupervised evolutionary learning of ESNs yields results that compete with the best topologylearning methods.
We present a lattice model for a two-dimensional network of self-activated biological structures ... more We present a lattice model for a two-dimensional network of self-activated biological structures with a diffusive activating agent. The model retains basic and simple properties shared by biological systems at various observation scales, so that the structures can consist of individuals, tissues, cells, or enzymes. Upon activation, a structure emits a new mobile activator and remains in a transient refractory state before it can be activated again. Varying the activation probability, the system undergoes a nonequilibrium second-order phase transition from an active state, where activators are present, to an absorbing, activator-free state, where each structure remains in the deactivated state. We study the phase transition using Monte Carlo simulations and evaluate the critical exponents. As they do not seem to correspond to known values, the results suggest the possibility of a separate universality class.
Soybean lipoxygenase-1 kinetics are known to show product and substrate inhibition. With linoleic... more Soybean lipoxygenase-1 kinetics are known to show product and substrate inhibition. With linoleic acid as the substrate and using a simple Michaelis-Menten formulation, we have shown that K sii , the substrate inhibition constant was increased by more than five-fold when initial oxygen concentration was increased from 228 to 1140 μΜ. Excess substrate inhibition is in fact almost avoided at high initial oxygen concentration. This modification seems correlated with enzyme saturation with oxygen relative to linoleic acid, as reflected by alterations of the substrate conversion rate. Possible implications for the enzyme kinetics are discussed.
We investigated the epidemiology of antibiotic resistance and virulence properties among Pseudomo... more We investigated the epidemiology of antibiotic resistance and virulence properties among Pseudomonas aeruginosa clinical isolates collected in 1999 from patients hospitalized in the intensive care units of the centre hospitalier d'Orléans, in France. We compared the totality of the strains from mechanically ventilated patients with pneumonia (33 non-duplicate isolates, group 1) to 15 randomly chosen, imipenemresistant, extra-respiratory tract isolates, collected from non-infected patients hospitalized in the same units (group 2). The isolates were serotyped, typed by random amplified polymorphic DNA (RAPD), and screened for their pneumocyte cell adherence, cytotoxicity, and antibiotic resistance. A total of 35 RAPD profiles were found, and only two profiles were encountered in both groups, demonstrating a high genetic diversity. 84.8% of the group 1 and 93.3% of the group 2 isolates adhered to A549 cells. Three non-exclusive adhesive patterns were observed: a diffuse adhesion in 38 isolates, a localized adhesion in 14 isolates, and an aggregative adhesion in seven isolates. 78.8% of the group 1 and 93.3% of the group 2 isolates were cytotoxic. Considering all 48 isolates, there was a strong and statistically significant correlation between cytotoxicity and adherence. Among the three dominant serotypes, O:12 isolates were in majority avirulent, but the great majority of O:1 and all the O:11 isolates were found adherent and cytotoxic. Gentamicin was the least active antibiotic for both groups, and ceftazidime was the most active antibiotic for group 1 and amikacin for group 2. The penicillinase production phenotype was significantly correlated with a decrease in P. aeruginosa virulence.
We monitored the cell-free solubilization of extracellular matrix and fibronectin gels, catalyzed... more We monitored the cell-free solubilization of extracellular matrix and fibronectin gels, catalyzed by exogenous proteinases. The corresponding measurements could not be interpreted according to usual proteinase kinetics. The observation that this experimental system did not consist in surface but in bulk degradation and appeared specific to gel substrates, incited us to use gelation-related approaches to describe these kinetics. We show that the gel^sol transition theory adequately describes the enzyme reactions. This allowed formulation and experimental confirmation of a power law relating macroscopic changes of the gel to enzyme kinetics. This approach could also be used for other power laws predicted by the gel^sol transition theory, allowing a better understanding of macroscopic modification of the extracellular matrix during proteolysis, which is implied in many biological situations, especially tumor dissemination. ß
Journal of colloid and interface science, Jan 1, 2006
Fibronectin (Fn), a high molecular weight glycoprotein, is a central element of extracellular mat... more Fibronectin (Fn), a high molecular weight glycoprotein, is a central element of extracellular matrix architecture that is involved in several fundamental cell processes. In the context of bone biology, little is known about the influence of the mineral surface on fibronectin supramolecular assembly. We investigate fibronectin morphological properties induced by its adsorption onto a model mineral matrix of hydroxyapatite (HA). Fibronectin adsorption onto HA spontaneously induces its aggregation and fibrillation. In some cases, fibronectin fibrils are even found connected into a dense network that is close to the matrix synthesized by cultured cells. Fibronectin adsorption-induced self-assembly is a time-dependant process that is sensitive to bulk concentration. The N-terminal domain of the protein, known to be implicated in its self-association, does not significantly inhibit the protein self-assembly while increasing ionic strength in the bulk alters both aggregation and fibrillation. The addition of a non-ionic surfactant during adsorption tends to promote aggregation with respect to fibrillation. Ultimately, fibronectin fibrils appear to be partially structured like amyloid fibrils as shown by thioflavine T staining. Taken together, our results suggest that there might be more than one single organization route involved in fibronectin self-assembly onto hydroxyapatite. The underlying mechanisms are discussed with respect to Fn conformation, Fn/surface and Fn/Fn interactions, and a model of fibronectin fibrillogenesis onto hydroxyapatite is proposed.
Chaos: An Interdisciplinary Journal of …, Jan 1, 2006
Modern computer microprocessors are composed of hundreds of millions of transistors that interact... more Modern computer microprocessors are composed of hundreds of millions of transistors that interact through intricate protocols. Their performance during program execution may be highly variable and present aperiodic oscillations. In this paper, we apply current nonlinear time series analysis techniques to the performances of modern microprocessors during the execution of prototypical programs. Our results present pieces of evidence strongly supporting that the high variability of the performance dynamics during the execution of several programs display low-dimensional deterministic chaos, with sensitivity to initial conditions comparable to textbook models. Taken together, these results show that the instantaneous performances of modern microprocessors constitute a complex (or at least complicated) system and would benefit from analysis with modern tools of nonlinear and complexity science. PACS numbers: 05.45.Ac,05.45.Tp, 89.20.Ff, 89.75.-k * Electronic address: hugues.berry@inria.fr
The aim of the present paper is to study the effects of Hebbian learning in random recurrent neur... more The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore consider that the neuron dynamics may occur at a (shorter) time scale than synaptic plasticity and consider the possibility of learning rules with passive forgetting. We show that the application of such Hebbian learning leads to drastic changes in the network dynamics and structure. In particular, the learning rule contracts the norm of the weight matrix and yields a rapid decay of the dynamics complexity and entropy. In other words, the network is rewired by Hebbian learning into a new synaptic structure that emerges with learning on the basis of the correlations that progressively build up between neurons. We also observe that, within this emerging structure, the strongest synapses organize as a small-world network. The second effect of the decay of the weight matrix spectral radius consists in a rapid contraction of the spectral radius of the Jacobian matrix. This drives the system through the "edge of chaos" where sensitivity to the input pattern is maximal. Taken together, this scenario is remarkably predicted by theoretical arguments derived from dynamical systems and graph theory.
Extracellular matrix mass balance is implied in many physiological and pathological events, such ... more Extracellular matrix mass balance is implied in many physiological and pathological events, such as metastasis dissemination. Widely studied, its destructive part is mainly catalysed by extracellular proteinases. Conversely, the properties of the constructive part are less obvious, cellular neo-synthesis being usually considered as its only element. In this paper, we introduce the action of transglutaminase in a mathematical model for extracellular matrix remodeling. This extracellular enzyme, catalysing intermolecular protein cross-linking, is considered here as a reverse proteinase as far as the extracellular matrix physical state is concerned. The model is based on a proteinase/transglutaminase cycle interconverting insoluble matrix and soluble proteolysis fragments, with regulation of cellular proteinase expression by the fragments. Under "closed" (batch) conditions, i.e. neglecting matrix influx and fragment efflux from the system, the model is bistable, with reversible hysteresis. Extracellular matrix proteins concentration abruptly switches from low to high levels when transglutaminase activity exceeds a threshold value. Proteinase concentration usually follows the reverse complementary kinetics, but can become apparently uncoupled from extracellular matrix concentration for some parameter values. When matrix production by the cells and fragment degradation are taken into account, the dynamics change to sustained oscillations because of the emergence of a stable limit cycle. Transitions out of and into oscillation areas are controlled by the model parameters. Biological interpretation indicates that these oscillations could represent the normal homeostatic situation, whereas the other exhibited dynamics can be related to pathologies such as tumor invasion or fibrosis. These results allow to discuss the insights that the model could contribute to the comprehension of these complex biological events.
Strong experimental evidence indicates that protein kinase and phosphatase (KP) cycles are critic... more Strong experimental evidence indicates that protein kinase and phosphatase (KP) cycles are critical to both the induction and maintenance of activity-dependent modifications in neurons. However, their contribution to information storage remains controversial, despite impressive modeling efforts. For instance, plasticity models based on KP cycles do not account for the maintenance of plastic modifications. Moreover, bistable KP cycle models that display memory fail to capture essential features of information storage: rapid onset, bidirectional control, graded amplitude, and finite lifetimes. Here, we show in a biophysical model that upstream activation of KP cycles, a ubiquitous mechanism, is sufficient to provide information storage with realistic induction and maintenance properties: plastic modifications are rapid, bidirectional, and graded, with finite lifetimes that are compatible with animal and human memory. The maintenance of plastic modifications relies on negligible reaction rates in basal conditions and thus depends on enzyme nonlinearity and activation properties of the activity-dependent KP cycle. Moreover, we show that information coding and memory maintenance are robust to stochastic fluctuations inherent to the molecular nature of activitydependent KP cycle operation. This model provides a new principle for information storage where plasticity and memory emerge from a single dynamic process whose rate is controlled by neuronal activity. This principle strongly departs from the long-standing view that memory reflects stable steady states in biological systems, and offers a new perspective on memory in animals and humans. Citation: Delord B, Berry H, Guigon E, Genet S (2007) A new principle for information storage in an enzymatic pathway model. PLoS Comput Biol 3(6): e124.
A possible alternative to topology fine-tuning for Neural Network (NN) optimization is to use Ech... more A possible alternative to topology fine-tuning for Neural Network (NN) optimization is to use Echo State Networks (ESNs), recurrent NNs built upon a large reservoir of sparsely randomly connected neurons. The promises of ESNs have been fulfilled for supervised learning tasks, but unsupervised ones, e.g. control problems, require more flexible optimization methods -such as Evolutionary Algorithms. This paper proposes to apply CMA-ES, the state-of-the-art method in evolutionary continuous parameter optimization, to the evolutionary learning of ESN parameters. First, a standard supervised learning problem is used to validate the approach and compare it to the standard one. But the flexibility of Evolutionary optimization allows us to optimize not only the outgoing weights but also, or alternatively, other ESN parameters, sometimes leading to improved results. The classical double pole balancing control problem is then used to demonstrate the feasibility of evolutionary (i.e. reinforcement) learning of ESNs. We show that the evolutionary ESN obtain results that are comparable with those of the best topology-learning methods.
We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural ... more We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning dynamics.
Extracellular proteolysis during cell invasion is thought to be tightly organized, both temporall... more Extracellular proteolysis during cell invasion is thought to be tightly organized, both temporally and spatially. This work presents a simple kinetic model that describes the interactions between extracellular matrix (ECM) proteins, proteinases, proteolytic fragments, and integrins. Nonmonotonous behavior arises from enzyme de novo synthesis consecutive to integrin binding to fragments or entire proteins. The model has been simulated using realistic values for kinetic constants and protein concentrations, with fibronectin as the ECM protein. The simulations show damped oscillations of integrin-complex concentrations, indicating alternation of maximal adhesion periods with maximal mobility periods. Comparisons with experimental data from the literature confirm the similarity between this system behavior and cell invasion. The influences on the system of cryptic functions of ECM proteins, proteinase inhibitors, and soluble antiadhesive peptides were examined. The first critical parameter for oscillation is the discrepancy between integrin affinity for intact ECM proteins and the respective proteolytic fragments, thus emphasizing the importance of cryptic functions of ECM proteins in cell invasion. Another critical parameter is the ratio between proteinase and the initial ECM protein concentration. These results suggest new insights into the organization of the ECM degradation during cell invasion.
Contrary to Hopfield-like networks, random recurrent neural networks (RRNN), where the couplings ... more Contrary to Hopfield-like networks, random recurrent neural networks (RRNN), where the couplings are random, exhibit complex dynamics (limit cycles, chaos). It is possible to store information in these networks through Hebbian learning. Eventually, learning "destroys" the dynamics and leads to a fixed point attractor. We investigate here the structural changes occurring in the network through learning. We show that a simple Hebbian learning rule organizes synaptic weight redistribution on the network from an initial homogeneous and random distribution to a heterogeneous one, where strong synaptic weights preferentially assemble in triangles. Hence learning organizes the network of the large synaptic weights as a "small-world" one.
We study the steady states of a reaction-diffusion medium modelled by a stochastic 2D cellular au... more We study the steady states of a reaction-diffusion medium modelled by a stochastic 2D cellular automaton. We consider the Greenberg-Hastings model where noise and topological irregularities of the grid are taken into account. The decrease of the probability of excitation changes qualitatively the behaviour of the system from an "active" to an "extinct" steady state. Simulations show that this change occurs near a critical threshold ; it is identified as a nonequilibrium phase transition which belongs to the directed percolation universality class. We test the robustness of the phenomenon by introducing persistent defects in the topology : directed percolation behaviour is conserved. Using experimental and analytical tools, we suggest that the critical threshold varies as the inverse of the average number of neighbours per cell.
A possible alternative to fine topology tuning for Neural Network (NN) optimization is to use Ech... more A possible alternative to fine topology tuning for Neural Network (NN) optimization is to use Echo State Networks (ESNs), recurrent NNs built upon a large reservoir of sparsely randomly connected neurons. The promises of ESNs have been fulfilled for supervised learning tasks, but unsupervised learning tasks, such as control problems, require more flexible optimization methods. We propose here to apply stateof-the-art methods in evolutionary continuous parameter optimization, to the evolutionary learning of ESN. First, a standard supervised learning problem is used to validate our approach and compare it to the standard quadratic one. The classical double pole balancing control problem is then used to demonstrate that unsupervised evolutionary learning of ESNs yields results that compete with the best topologylearning methods.
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Papers by Hugues Berry