Self-regulating neurons: a model for synaptic plasticity in artificial recurrent neural networks

Robustness and adaptivity are important behavioural properties observed in biological systems, which are still widely absent in artificial intelligence applications. Such static or nonplastic artificial systems are limited to their very specific problem domain. This work introduces a general model for synaptic plasticity in embedded artificial recurrent neural networks, which is related to short-term plasticity by synaptic scaling in biological systems. The model is general in the sense that is does not require trigger mechanisms or artificial limitations and it operates on recurrent neural networks of arbitrary structure. A Self-Regulation Neuron is defined as a homeostatic unit which regulates its activity against external disturbances towards a target value by modulation of its incoming and outgoing synapses. Embedded and situated in the sensori-motor loop, a network of these neurons is permanently driven by external stimuli and will generally not settle at its asymptotically stable state. The system’s behaviour is determined by the local interactions of the Self-Regulating Neurons. The neuron model is analysed as a dynamical system with respect to its attractor landscape and its transient dynamics. The latter is conducted based on different control structures for obstacle avoidance with increasing structural complexity derived from literature. The result is a controller that shows first traces of adaptivity. Next, two controllers for different tasks are evolved and their transient dynamics are fully analysed. The first is a controller solving the standard benchmark problem of pole balancing. The second is a controller performing lightseeking under varying ambient light conditions. In the second experiment, a light source cannot be distinguished from ambient light in the raw sensor data. The task is solved by the homeostatic property of the neuron model and the interaction of the robot with its environment. The results of this work not only show that the proposed neuron model enhances the behavioural properties, but also points out the limitations of short-term plasticity which does not account for learning and memory.

[1]  Marieke Rohde,et al.  Adaptive Behaviour Control by Self-regulating Neurons , 2004 .

[2]  D. McCandless Fundamental neuroscience , 1997, Metabolic Brain Disease.

[3]  L. Cooper Neuron learning to brain organization , 1986, Cell Biophysics.

[4]  Frank Pasemann,et al.  (Co)Evolution of (De)Centralized Neural Control for a Gravitationally Driven Machine , 2005, ECAL.

[5]  Karl J. Friston,et al.  The Neural Structures Expressing Perceptual Hysteresis in Visual Letter Recognition , 2002, Neuron.

[6]  J. Yorke,et al.  Chaos: An Introduction to Dynamical Systems , 1997 .

[7]  F. Valverde,et al.  Rate and extent of recovery from dark rearing in the visual cortex of the mouse. , 1971, Brain research.

[8]  L. Abbott,et al.  Competitive Hebbian learning through spike-timing-dependent synaptic plasticity , 2000, Nature Neuroscience.

[9]  R. Hanneman Introduction to Social Network Methods , 2001 .

[10]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[11]  J. Neumann The General and Logical Theory of Au-tomata , 1963 .

[12]  B. Kendall Nonlinear Dynamics and Chaos , 2001 .

[13]  Inman Harvey,et al.  Evolutionary Robotics: A New Scientific Tool for Studying Cognition , 2005, Artificial Life.

[14]  Eric A Sobie,et al.  An Introduction to Dynamical Systems , 2011, Science Signaling.

[15]  J. Zukas Introduction to the Modern Theory of Dynamical Systems , 1998 .

[16]  Frank Pasemann,et al.  Adaptive Behavior Control with Self-regulating Neurons , 2006, 50 Years of Artificial Intelligence.

[17]  Francis Heylighen,et al.  Cybernetics and Second-Order Cybernetics , 2001 .

[18]  U. Brandes Faster Evaluation of Shortest-Path Based Centrality Indices , 2000 .

[19]  K. Kuypers,et al.  Effects of differential environments on plasticity of dendrites of cortical pyramidal neurons in adult rats , 1978, Experimental Neurology.

[20]  John Raymond Smythies The Dynamic Neuron , 2002 .

[21]  Nancy Forbes Imitation of Life , 2004 .

[22]  Keyan Zahedi,et al.  ISEE - A framework for the evolution and analysis of recurrent neural networks for embodied agents , 2006 .

[23]  C. Stevens Memory: From Mind to Molecules , 1999, Nature Medicine.

[24]  John R. Searle,et al.  Chinese room argument , 2006, Scholarpedia.

[25]  P. Manoonpong Neural Processing of Auditory-tactile Sensor Data to Perform Reactive Behavior of Walking Machines , 2004 .

[26]  Rodney A. Brooks,et al.  Intelligence Without Reason , 1991, IJCAI.

[27]  F. Pasemann Evolving neurocontrollers for balancing an inverted pendulum. , 1998, Network.

[28]  T. Morrison,et al.  Dynamical Systems , 2021, Nature.

[29]  Inman Harvey,et al.  Noise and the Reality Gap: The Use of Simulation in Evolutionary Robotics , 1995, ECAL.

[30]  Karl Sims,et al.  Evolving 3D Morphology and Behavior by Competition , 1994, Artificial Life.

[31]  Bernd Porr,et al.  Sequence-learning in a self-referential closed-loop behavioural system , 2003 .

[32]  Howard Kaufman,et al.  An Experimental Investigation of Process Identification by Competitive Evolution , 1967, IEEE Trans. Syst. Sci. Cybern..

[33]  James Clark,et al.  XSL Transformations (XSLT) Version 1.0 , 1999 .

[34]  W. Greenough,et al.  Persistence of visual cortex dendritic alterations induced by postweaning exposure to a "superenriched" environment in rats. , 1986, Behavioral neuroscience.

[35]  Frank Pasemann,et al.  Evolving Neurocontrollers in the RoboCup Domain , 2006 .

[36]  Shanmuganathan Rajasekar,et al.  Nonlinear dynamics : integrability, chaos, and patterns , 2003 .

[37]  F. Pasemann A simple chaotic neuron , 1997 .

[38]  John McCarthy,et al.  What Computers Still Can't Do , 1996, Artif. Intell..

[39]  V. Kilman,et al.  Increases in dendritic length in occipital cortex after 4 days of differential housing in weanling rats. , 1992, Behavioral and neural biology.

[40]  R. Eckmiller Hysteresis in the static characteristics of eye position coded neurons in the alert monkey , 2004, Pflügers Archiv.

[41]  Christoph von der Malsburg,et al.  The Correlation Theory of Brain Function , 1994 .

[42]  F. Volkmar,et al.  Rearing Complexity Affects Branching of Dendrites in the Visual Cortex of the Rat , 1972, Science.

[43]  Frank Pasemann,et al.  SO(2)-Networks as Neural Oscillators , 2003, IWANN.

[44]  Inman Harvey,et al.  Evolutionary robotics: the Sussex approach , 1997, Robotics Auton. Syst..

[45]  Randall D. Beer,et al.  The brain has a body: adaptive behavior emerges from interactions of nervous system, body and environment , 1997, Trends in Neurosciences.

[46]  Francesco Mondada,et al.  Mobile Robot Miniaturisation: A Tool for Investigation in Control Algorithms , 1993, ISER.

[47]  Richard S. Sutton,et al.  Neuronlike adaptive elements that can solve difficult learning control problems , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[48]  G. Turrigiano Homeostatic plasticity in neuronal networks: the more things change, the more they stay the same , 1999, Trends in Neurosciences.

[49]  H. Korn,et al.  Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation. , 2001, Comptes rendus de l'Academie des sciences. Serie III, Sciences de la vie.

[50]  Frank Pasemann,et al.  Characterization of periodic attractors in neural ring networks , 1995, Neural Networks.

[51]  Wulfram Gerstner,et al.  Mathematical formulations of Hebbian learning , 2002, Biological Cybernetics.

[52]  Ralph Johnson,et al.  design patterns elements of reusable object oriented software , 2019 .

[53]  Y. Dan,et al.  Spike-timing-dependent synaptic plasticity depends on dendritic location , 2005, Nature.

[54]  John R. Searle,et al.  Minds, brains, and programs , 1980, Behavioral and Brain Sciences.

[55]  Niraj S. Desai,et al.  Activity-dependent scaling of quantal amplitude in neocortical neurons , 1998, Nature.

[56]  Jürgen Branke,et al.  Evolutionary optimization in uncertain environments-a survey , 2005, IEEE Transactions on Evolutionary Computation.

[57]  U. Eco,et al.  The Island of the Day Before , 1994 .

[58]  Peter J. Angeline,et al.  An evolutionary algorithm that constructs recurrent neural networks , 1994, IEEE Trans. Neural Networks.

[59]  Stefano Nolfi,et al.  How to Evolve Autonomous Robots: Different Approaches in Evolutionary Robotics , 1994 .

[60]  L. Cooper,et al.  A biophysical model of bidirectional synaptic plasticity: Dependence on AMPA and NMDA receptors , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[61]  Guo-Qiang Bi,et al.  Spatiotemporal specificity of synaptic plasticity: cellular rules and mechanisms , 2002, Biological Cybernetics.

[62]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[63]  F. Pasemann,et al.  A Modular Approach to Construction and Control of Walking Robots , 2004 .

[64]  T. Christaller,et al.  Dual dynamics: Designing behavior systems for autonomous robots , 1998, Artificial Life and Robotics.

[65]  Keyan Zahedi,et al.  AN EVOLVED NEURAL NETWORK FOR FAST QUADRUPEDAL LOCOMOTION , 2007 .

[66]  On the rate of transmission of the nerve impulse, 1850. , 1948 .

[67]  Bjarne Stroustrup,et al.  C++ Programming Language , 1986, IEEE Softw..

[68]  S. Royer,et al.  Conservation of total synaptic weight through balanced synaptic depression and potentiation , 2003, Nature.

[69]  Rodney A. Brooks,et al.  A robot that walks; emergent behaviors from a carefully evolved network , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[70]  Bjarne Stroustrup,et al.  The C++ Programming Language: Special Edition , 2000 .

[71]  Martin Hülse Multifunktionalität rekurrenter neuronaler Netze: Synthese und Analyse nichtlinearer Kontrolle autonomer Roboter , 2007 .

[72]  John Haugeland,et al.  Artificial intelligence - the very idea , 1987 .

[73]  Marvin Minsky,et al.  Perceptrons: An Introduction to Computational Geometry , 1969 .

[74]  Mark W. Spong,et al.  Underactuated mechanical systems , 1998 .

[75]  A. Clark Being There: Putting Brain, Body, and World Together Again , 1996 .

[76]  Joshua E. S. Socolar,et al.  Nonlinear Dynamical Systems , 2006 .

[77]  Sandy Lovie How the mind works , 1980, Nature.

[78]  Y. Jan,et al.  Growing Dendrites and Axons Differ in Their Reliance on the Secretory Pathway , 2007, Cell.

[79]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[80]  Clifford A. Pickover,et al.  Does God Play Dice? (The Mathematics of Chaos) by Ian Stewart (review) , 2017 .

[81]  R B Welch,et al.  Research on Adaptation to Rearranged Vision: 1966–1974 , 1974, Perception.

[82]  H. Foerster,et al.  Wissen und Gewissen : Versuch einer Brücke , 1993 .

[83]  D. J. Felleman,et al.  Distributed hierarchical processing in the primate cerebral cortex. , 1991, Cerebral cortex.

[84]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[85]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[86]  Rolf Pfeifer,et al.  How the body shapes the way we think - a new view on intelligence , 2006 .

[87]  Phil Husbands,et al.  Evolutionary robotics , 2014, Evolutionary Intelligence.

[88]  Geoffrey Hunter What Computers Can't Do , 1988, Philosophy.

[89]  Jordan B. Pollack,et al.  Automatic design and manufacture of robotic lifeforms , 2000, Nature.

[90]  Joan Cabestany,et al.  Biological and Artificial Computation: From Neuroscience to Technology , 1997, Lecture Notes in Computer Science.

[91]  Frank Pasemann,et al.  Reflex-oscillations in evolved single leg neurocontrollers for walking machines , 2007, Natural Computing.

[92]  J. D. Farmer,et al.  Artificial life: The coming evolution , 1990 .

[93]  G. Zajicek,et al.  The Wisdom of the Body , 1934, Nature.

[94]  Florentin Wörgötter,et al.  Isotropic Sequence Order Learning , 2003, Neural Computation.

[95]  T. Poggio,et al.  Adaptation of Inputs in the Somatosensory System , 2002 .

[96]  Bruno Lara,et al.  Evolving Neural Behaviour Control for Autonomous Robots , 2001, ICANN.

[97]  John Barrett,et al.  Book Reviews , 1821, Heredity.

[98]  E. A. Dipaolo,et al.  Homeostatic adaptation to inversion of the visual field and other sensorimotor disruptions , 2000 .

[99]  T. Bliss,et al.  Long‐lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path , 1973, The Journal of physiology.

[100]  Leif Kobbelt,et al.  Graphische Datenverarbeitung , 2005, GI Jahrestagung.

[101]  Nicholas T. Carnevale,et al.  Simulation of networks of spiking neurons: A review of tools and strategies , 2006, Journal of Computational Neuroscience.

[102]  Bernardo L Sabatini,et al.  Anatomical and physiological plasticity of dendritic spines. , 2007, Annual review of neuroscience.

[103]  W. Greenough,et al.  Plasticity in adult rat visual cortex: an examination of several cell populations after differential rearing. , 1980, Behavioral and neural biology.

[104]  R. A. Brooks,et al.  Intelligence without Representation , 1991, Artif. Intell..

[105]  A. Hobson Dynamic Approaches to Cognition , 1998 .

[106]  C. Büchel,et al.  Dissociable Retrosplenial and Hippocampal Contributions to Successful Formation of Survey Representations , 2005, The Journal of Neuroscience.

[107]  F. Pasemann Complex dynamics and the structure of small neural networks , 2002, Network.

[108]  Florentin Wörgötter,et al.  Chained learning architectures in a simple closed-loop behavioural context , 2007, Biological Cybernetics.

[109]  Rolf Pfeifer,et al.  Understanding intelligence , 2020, Inequality by Design.

[110]  George E. P. Box,et al.  Evolutionary Operation: a Method for Increasing Industrial Productivity , 1957 .

[111]  E. Kandel,et al.  Is Heterosynaptic modulation essential for stabilizing hebbian plasiticity and memory , 2000, Nature Reviews Neuroscience.

[112]  Shlomo Geva,et al.  The Cart-Pole Experiment as a Benchmark for Trainable Controllers , 1992 .

[113]  Stefano Nolfi,et al.  Evolving Mobile Robots in Simulated and Real Environments , 1995, Artificial Life.

[114]  C. C. Law,et al.  Formation of receptive fields in realistic visual environments according to the Bienenstock, Cooper, and Munro (BCM) theory. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[115]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[116]  Simone Santini,et al.  The cell-centered database , 2007, Neuroinformatics.

[117]  Pattie Maes,et al.  Toward the Evolution of Dynamical Neural Networks for Minimally Cognitive Behavior , 1996 .

[118]  Stefano Nolfi,et al.  Co-evolving predator and prey robots , 1998, Artificial Life.

[119]  G. Ermentrout Dynamic patterns: The self-organization of brain and behavior , 1997 .

[120]  S. Levy Artificial life: the quest for a new creation , 1992 .

[121]  A. Selverston,et al.  Dynamical principles in neuroscience , 2006 .

[122]  Hywel T. P. Williams,et al.  Homeostatic plasticity in recurrent neural networks , 2004 .

[123]  Bruno Lara,et al.  Robot control and the evolution of modular neurodynamics , 2001, Theory in Biosciences.

[124]  Jörn Fischer A modulatory learning rule for neural learning and metalearning in real world robots with many degrees of freedom , 2003 .

[125]  Tad McGeer,et al.  Passive Dynamic Walking , 1990, Int. J. Robotics Res..

[126]  A. Hodgkin,et al.  The frequency of nerve action potentials generated by applied currents , 1967, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[127]  Frank Pasemann,et al.  Balancing rotators with evolved neurocontrollers , 1997 .

[128]  H. Foerster Understanding Understanding , 2002, Springer New York.

[129]  John H. Holland,et al.  Genetic Algorithms and the Optimal Allocation of Trials , 1973, SIAM J. Comput..

[130]  Rodney A. Brooks,et al.  A Robust Layered Control Syste For A Mobile Robot , 2022 .

[131]  Wulfram Gerstner,et al.  SPIKING NEURON MODELS Single Neurons , Populations , Plasticity , 2002 .

[132]  Marinus Maris,et al.  Exploiting physical constraints: heap formation through behavioral error in a group of robots , 1996, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS '96.

[133]  H. Dreyfus What Computers Can't Do: The Limits of Artificial Intelligence , 1978 .

[134]  Jeffrey L. Elman,et al.  Finding Structure in Time , 1990, Cogn. Sci..

[135]  Jeffrey L. Elman Connectionism , Artificial Life , and Dynamical Systems : New approaches to old questions , 1998 .

[136]  E. Capaldi,et al.  The organization of behavior. , 1992, Journal of applied behavior analysis.

[137]  Mw Hirsch,et al.  Chaos In Dynamical Systems , 2016 .

[138]  E. Bienenstock,et al.  Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex , 1982, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[139]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[140]  R. Pfeifer,et al.  Repeated structure and dissociation of genotypic and phenotypic complexity in artificial ontogeny , 2001 .

[141]  Michael Himsolt,et al.  GML: A portable Graph File Format , 2010 .

[142]  Charles J. Wilson,et al.  A model of reverse spike frequency adaptation and repetitive firing of subthalamic nucleus neurons. , 2004, Journal of neurophysiology.

[143]  Ralf Der,et al.  Learning to feel the physics of a body , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[144]  T. Gelder,et al.  Mind as Motion: Explorations in the Dynamics of Cognition , 1995 .

[145]  Ben J Hicks,et al.  World Multiconference on Systemics, Cybernetics and Informatics , 2000 .

[146]  P M Churchland,et al.  Could a machine think? , 1990, Scientific American.

[147]  K. Plunkett,et al.  Watching the Infant Brain Learn Words: Effects of Vocabulary Size and Experience. , 2005 .

[148]  Jordan B. Pollack,et al.  The GOLEM project: evolving hardware bodies and brains , 2000, Proceedings. The Second NASA/DoD Workshop on Evolvable Hardware.

[149]  F. Pasemann DYNAMICS OF A SINGLE MODEL NEURON , 1993 .

[150]  Joanne H. Walker,et al.  Evolving Controllers for Real Robots: A Survey of the Literature , 2003, Adapt. Behav..

[151]  Jordan B. Pollack,et al.  Coevolutionary robotics , 1999, Proceedings of the First NASA/DoD Workshop on Evolvable Hardware.

[152]  T. Gelder,et al.  The dynamical hypothesis in cognitive science , 1998, Behavioral and Brain Sciences.

[153]  S. Sarbadhikari,et al.  Chaos in the brain: a short review alluding to epilepsy, depression, exercise and lateralization. , 2001, Medical engineering & physics.

[154]  W. Greenough,et al.  Environmental complexity modulates growth of granule cell dendrites in developing but not adult hippocampus of rats , 1978, Experimental Neurology.

[155]  W. Walter A Machine that Learns , 1951 .

[156]  Stevan Harnad,et al.  What's Wrong and Right About Searle's Chinese Room Argument? , 2001 .

[157]  Lee G. Morris,et al.  Muscle Response to Changing Neuronal Input in the Lobster(Panulirus Interruptus) Stomatogastric System: Slow Muscle Properties Can Transform Rhythmic Input into Tonic Output , 1998, The Journal of Neuroscience.

[158]  Allen Newell,et al.  GPS, a program that simulates human thought , 1995 .

[159]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[160]  Francesco Mondada,et al.  Evolution of Plastic Neurocontrollers for Situated Agents , 1996 .

[161]  Poramate Manoonpong,et al.  Neural preprocessing and control of reactive walking machines - towards versatile artificial perception-action systems , 2006, Cognitive Technologies.

[162]  Christoph Adami,et al.  Evolving Virtual Creatures and Catapults , 2007, Artificial Life.

[163]  Pattie Maes,et al.  Designing autonomous agents: Theory and practice from biology to engineering and back , 1990, Robotics Auton. Syst..

[164]  W. Levy,et al.  Temporal contiguity requirements for long-term associative potentiation/depression in the hippocampus , 1983, Neuroscience.

[165]  ULF DIECKMANN COEVOLUTION AS AN AUTONOMOUS LEARNING STRATEGY FOR NEUROMODULES , 2003 .

[166]  Steffen Wischmann,et al.  Neural dynamics of social behavior: an evolutionary and mechanistic perspective on communication, cooperation, and competition among situated agents , 2008 .

[167]  Martijn Wisse,et al.  Essentials of dynamic walking; analysis and design of two-legged robots , 2004 .

[168]  A. Grinvald,et al.  Linking spontaneous activity of single cortical neurons and the underlying functional architecture. , 1999, Science.

[169]  Bob Welham What computers still can’t do: a critique of artificial reason , 1994 .

[170]  David Anderson,et al.  Artificial Life and the Chinese Room Argument , 2002, Artificial Life.

[171]  Norbert Wiener,et al.  The human use of human beings - cybernetics and society , 1988 .

[172]  Frank Pasemann Pole-Balancing with Different Evolved Neurocontrollers , 1997, ICANN.

[173]  E. D. Paolo,et al.  Organismically-inspired robotics: homeostatic adaptation and teleology beyond the closed sensorimotor loop , 2003 .

[174]  Bruno Lara,et al.  Evolving Brain Structures for Robot Control , 2001, IWANN.

[175]  S. Laughlin,et al.  Computational neuroethology: a provisional manifesto , 1991 .

[176]  T. Bliss Long-lasting potentiation of synaptic transmission , 2005 .

[177]  Dario Floreano,et al.  Evolutionary Robotics in Behavior Engineering and Artificial Life , 1998 .

[178]  Frank Pasemann,et al.  Evolved Neurocontrollers for Pole-Balancing , 1997, IWANN.

[179]  Frank Pasemann,et al.  Evolved Neurodynamics for Robot Control , 2003, ESANN.

[180]  G. Davis Homeostatic control of neural activity: from phenomenology to molecular design. , 2006, Annual review of neuroscience.

[181]  A. Andronov,et al.  Qualitative Theory of Second-order Dynamic Systems , 1973 .

[182]  Martin A. Riedmiller Learning to Control Dynamic Systems , 1996 .

[183]  Viktor Mikhaĭlovich Glushkov,et al.  An Introduction to Cybernetics , 1957, The Mathematical Gazette.

[184]  M. Bishop,et al.  Essays on Searle's Chinese Room Argument , 2001 .

[185]  Frank Pasemann,et al.  From Passive to Active Dynamic 3D Bipedal Walking — An Evolutionary Approach , 2004 .

[186]  Frank Pasemann,et al.  Dynamical Neural Schmitt Trigger for Robot Control , 2002, ICANN.

[187]  M. Mead,et al.  Cybernetics , 1953, The Yale Journal of Biology and Medicine.

[188]  R. Der,et al.  Emergent robot behavior from the principle ofhomeokinesis , 2000 .

[189]  L. Munari How the body shapes the way we think — a new view of intelligence , 2009 .

[190]  Rodney A. Brooks,et al.  Elephants don't play chess , 1990, Robotics Auton. Syst..

[191]  Eugene M. Izhikevich,et al.  Encyclopedia of dynamical systems , 2011, Scholarpedia.

[192]  D. Corey,et al.  Dynamic aspects of CNS synapse formation. , 2007, Annual review of neuroscience.

[193]  K. Miller,et al.  Synaptic Economics: Competition and Cooperation in Synaptic Plasticity , 1996, Neuron.

[194]  Michael I. Jordan Serial Order: A Parallel Distributed Processing Approach , 1997 .

[195]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[196]  John A. Miller,et al.  Java , 1977, Itinerario.

[197]  Frank Pasemann Repräsentation ohne Repräsentation - Überlegungen zu einer Neurodynamik modularer kognitiver Systeme * , 1996 .

[198]  Richard M. Friedberg,et al.  A Learning Machine: Part I , 1958, IBM J. Res. Dev..

[199]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .