Fähigkeiten eines assoziativen Speichersystems im Vergleich zu Gehirnfunktionen

Zusammenfassung Assoziative Informationsspeicherung und assoziativer Informationsaufruf stellen ein Prinzip der Funktion des menschlichen Gehirns dar. Auf der UNIVAC 1106 wurde ein Neuronennetzwerk aus 100 erregenden Bausteinen simuliert. Die Bausteine bestanden aus Verzögerungsglied, Kennlinienglied mit Schwellenwert und PD-Glied; sie entsprachen in ihrem Verhalten weitgehend dem von realen Neuronen mit verzögertem Anstieg und Adaptation des Ausgangssignals. Die Systemerregung wurde durch einen hemmenden Baustein konstant gehalten. Information wurde als Muster erregter Einzelbausteine codiert. Die Speicherung der Muster und ebenso der zeitlichen Reihenfolge der Muster erfolgte durch Kopplungskoeffizienten (Maß für die Signaldurchlässigkeit der Verbindungen zwischen den erregenden Bausteinen).—In stark vereinfachter Weise vermag das beschriebene System Leistungen des menschlichen Gehirns nachzuahmen: parallele Assoziation (vollständiger Aufruf eines Musters durch Eingabe eines Teils des Musters), serielle Assoziation (Aufruf einer zeitlichen Mustersequenz durch Eingabe des Anfangsmusters), Auswahl zwischen beiden Assoziationsarten durch ein Steuersignal, Zuordnung eines unbekannten (nicht gespeicherten) Musters, Zuordnung von Mustern aus zwei Systembereichen, Assoziation einer wahrscheinlicheren Musterfolge, Störung des Assoziationsvorganges Eselsbrücke, Abstraktion des Gemeinsamen, Umlernen und produktiver Einfall.—Das Prinzip der wechselseitigen bedingten Verknüpfung kann als Hypothese für den Lernvorgang d.h. die Abbildung von Informationsmustern bzw. zeitlichen Mustersequenzen durch Kopplungskoeffizienten angesehen werden.—Einzelbaustein, Systemstruktur und Funktionsprinzipien des beschriebenen Systems werden mit Strukturprinzipien des Gehirns verglichen.

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Associative information storage and associative information recall are fundamental principles of the human brain. A neuron network consisting of 100 excitatory elements was simulated on the UNIVAC 1106. The network elements consisted of a delay element, a characteristic with a threshold value and a PD-element. The element's behaviour was to a great extent analogues to that of real neurons with delayed increase and adaptation of the output signal. The total excitation of the system was controlled by an inhibitory component. Information was coded as a pattern of excitated elements. The information patterns and also the temporal sequence of patterns were stored in the coupling coefficients (measure of the signal transfer between the excitatory elements).—In a very simplified manner the system described above is able to imitate effects of the human brain, including parallel association (complete recall of the stored information pattern when a part of the pattern is offered at the system's input), serial association (recall of a temporal sequence of information patterns by input of the first pattern of the sequence), selection between the two association modes by means of an external signal, classification of an unknown (not stored) information pattern, coordination of patterns from two fields of the system, association of a more probable pattern sequence, disturbance of the association process, memory aids, abstraction of common characteristics, reversal learning and productive ideas.—The principle of the mutually conditioned connection may be regarded as a hypothesis for the learning act, that is for the representation of information patterns or temporal sequences of patterns through coupling coefficients.—The network elements, the structure and the function of the system are compared with structure and principles of the brain.

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Die Arbeit wurde durchgeführt mit finanzieller Unterstützung durch die Deutsche Forschungsgemeinschaft

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Prof. Dr. B. Hassenstein danke ich für die Überlassung des Themas und für die Betreuung der Arbeit     

A Signature of Attractor Dynamics in the CA3 Region of the Hippocampus

The notion of attractor networks is the leading hypothesis for how associative memories are stored and recalled. A defining anatomical feature of such networks is excitatory recurrent connections. These “attract” the firing pattern of the network to a stored pattern, even when the external input is incomplete (pattern completion). The CA3 region of the hippocampus has been postulated to be such an attractor network; however, the experimental evidence has been ambiguous, leading to the suggestion that CA3 is not an attractor network. In order to resolve this controversy and to better understand how CA3 functions, we simulated CA3 and its input structures. In our simulation, we could reproduce critical experimental results and establish the criteria for identifying attractor properties. Notably, under conditions in which there is continuous input, the output should be “attracted” to a stored pattern. However, contrary to previous expectations, as a pattern is gradually “morphed” from one stored pattern to another, a sharp transition between output patterns is not expected. The observed firing patterns of CA3 meet these criteria and can be quantitatively accounted for by our model. Notably, as morphing proceeds, the activity pattern in the dentate gyrus changes; in contrast, the activity pattern in the downstream CA3 network is attracted to a stored pattern and thus undergoes little change. We furthermore show that other aspects of the observed firing patterns can be explained by learning that occurs during behavioral testing. The CA3 thus displays both the learning and recall signatures of an attractor network. These observations, taken together with existing anatomical and behavioral evidence, make the strong case that CA3 constructs associative memories based on attractor dynamics.     

Mode dynamics of interacting neural populations by bi-orthogonal spectral decomposition

A system of coupled bistable Hopf oscillators with an external periodic input source was used to model the ability of interacting neural populations to synchronize and desynchronize in response to variations of the input signal. We propose that, in biological systems, the settings of internal and external coupling strengths will affect the behaviour of the system to a greater degree than the input frequency. While input frequency and coupling strength were varied, the spatio-temporal dynamics of the network was examined by the bi-orthogonal decomposition technique. Within this method, effects of variation of input frequency and coupling strength were analyzed in terms of global, spatial and temporal mode entropy and energy, using the spatio-temporal data of the system. We observed a discontinuous evolution of spatio-temporal patterns depending sensitively on both the input frequency and the internal and external coupling strengths of the network. Received: 10 June 1998 / Accepted in revised form: 9 August 1999     

Cluster associative memory formation in a three-layer network of phase oscillators

A three-layer network model of oscillatory associative memory is proposed. The network is capable of storing binary images, which can be retrieved upon presenting an appropriate stimulus. Binary images are encoded in the form of the spatial distribution of oscillatory phase clusters in-phase and anti-phase relative to a reference periodic signal. The information is loaded into the network using a set of interlayer connection weights. A condition for error-free pattern retrieval is formulated, delimiting the maximal number of patterns to be stored in the memory (storage capacity). It is shown that the capacity can be significantly increased by generating an optimal alphabet (basis pattern set). The number of stored patterns can reach values of the network size (the number of oscillators in each layer), which is significantly higher than the capacity of conventional oscillatory memory models. The dynamical and information characteristics of the retrieval process based on the optimal alphabet, including the size of “attraction basins“ and the input pattern distortion admissible for error-free retrieval, are investigated.     

The sheep genome contributes to localization of control elements in a human gene with complex regulatory mechanisms

Genes that show complex tissue-specific and temporal control by regulatory elements located outside their promoters present a considerable challenge to identify the sequences involved. The rapid accumulation of genomic sequence information for a number of species has enabled a comparative phylogenetic approach to find important regulatory elements. For some genes, which show a similar pattern of expression in humans and rodents, genomic sequence information for these two species may be sufficient. Others, such as the cystic fibrosis transmembrane conductance regulator (CFTR) gene, show significant divergence in expression patterns between mouse and human, necessitating phylogenetic approaches involving additional species. The ovine CFTR gene has a temporal and spatial expression pattern that is very similar to that of human CFTR. Comparative genomic sequence analysis of ovine and human CFTR identified high levels of homology between the core elements in several potential regulatory elements defined as DNase I hypersensitive sites in human CFTR. These data provide a case for the power of an artiodactyl genome to contribute to the understanding of human genetic disease.     

Hard-wired central pattern generators for quadrupedal locomotion

Animal locomotion is generated and controlled, in part, by a central pattern generator (CPG), which is an intraspinal network of neurons capable of producing rhythmic output. In the present work, it is demonstrated that a hard-wired CPG model, made up of four coupled nonlinear oscillators, can produce multiple phase-locked oscillation patterns that correspond to three common quadrupedal gaits — the walk, trot, and bound. Transitions between the different gaits are generated by varying the network's driving signal and/or by altering internal oscillator parameters. The above in numero results are obtained without changing the relative strengths or the polarities of the system's synaptic interconnections, i.e., the network maintains an invariant coupling architecture. It is also shown that the ability of the hard-wired CPG network to produce and switch between multiple gait patterns is a model-independent phenomenon, i.e., it does not depend upon the detailed dynamics of the component oscillators and/or the nature of the inter-oscillator coupling. Three different neuronal oscillator models — the Stein neuronal model, the Van der Pol oscillator, and the FitzHugh-Nagumo model -and two different coupling schemes are incorporated into the network without impeding its ability to produce the three quadrupedal gaits and the aforementioned gait transitions.     

Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape

In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical temporal pattern in gene expression during flower development. We modeled the regulatory network of organ identity genes in the Arabidopsis thaliana flower as a stochastic system. This network has previously been shown to converge to ten fixed-point attractors, each with gene expression arrays that characterize inflorescence cells and primordial cells of sepals, petals, stamens, and carpels. The network used is binary, and the logical rules that govern its dynamics are grounded in experimental evidence. We introduced different levels of uncertainty in the updating rules of the network. Interestingly, for a level of noise of around 0.5-10%, the system exhibited a sequence of transitions among attractors that mimics the sequence of gene activation configurations observed in real flowers. We also implemented the gene regulatory network as a continuous system using the Glass model of differential equations, that can be considered as a first approximation of kinetic-reaction equations, but which are not necessarily equivalent to the Boolean model. Interestingly, the Glass dynamics recover a temporal sequence of attractors, that is qualitatively similar, although not identical, to that obtained using the Boolean model. Thus, time ordering in the emergence of cell-fate patterns is not an artifact of synchronous updating in the Boolean model. Therefore, our model provides a novel explanation for the emergence and robustness of the ubiquitous temporal pattern of floral organ specification. It also constitutes a new approach to understanding morphogenesis, providing predictions on the population dynamics of cells with different genetic configurations during development.     

A neural network model for trace conditioning

We studied the dynamics of a neural network that has both recurrent excitatory and random inhibitory connections. Neurons started to become active when a relatively weak transient excitatory signal was presented and the activity was sustained due to the recurrent excitatory connections. The sustained activity stopped when a strong transient signal was presented or when neurons were disinhibited. The random inhibitory connections modulated the activity patterns of neurons so that the patterns evolved without recurrence with time. Hence, a time passage between the onsets of the two transient signals was represented by the sequence of activity patterns. We then applied this model to represent the trace eye blink conditioning, which is mediated by the hippocampus. We assumed this model as CA3 of the hippocampus and considered an output neuron corresponding to a neuron in CA1. The activity pattern of the output neuron was similar to that of CA1 neurons during trace eye blink conditioning, which was experimentally observed.     

STORE working memory networks for storage and recall of arbitrary temporal sequences

Neural network models of working memory, called “sustained temporal order recurrent” (STORE) models, are described. They encode the invariant temporal order of sequential events in short-term memory (STM) in a way that mimics cognitive data about working memory, including primacy, recency, and bowed order and error gradients. As new items are presented, the pattern of previously stored items remains invariant in the sense that relative activations remain constant through time. This invariant temporal order code enables all possible groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system. Such competence is needed to design self-organizing temporal recognition and planning systems in which any subsequence of events may need to be categorized in order to control and predict future behavior or external events. STORE models show how arbitrary event sequences may be invariantly stored, including repeated events. A preprocessor interacts with the working memory to represent event repeats in spatially separate locations. It is shown why at least two processing levels are needed to invariantly store events presented with variable durations and interstimulus intervals. It is also shown how network parameters control the type and shape of primacy, recency, or bowed temporal order gradients that will be stored. Received: 3 November 1992/Accepted in revised form: 2 May 1994     

Elements for a general memory structure: properties of recurrent neural networks used to form situation models

We study how individual memory items are stored assuming that situations given in the environment can be represented in the form of synaptic-like couplings in recurrent neural networks. Previous numerical investigations have shown that specific architectures based on suppression or max units can successfully learn static or dynamic stimuli (situations). Here we provide a theoretical basis concerning the learning process convergence and the network response to a novel stimulus. We show that, besides learning “simple” static situations, a nD network can learn and replicate a sequence of up to n different vectors or frames. We find limits on the learning rate and show coupling matrices developing during training in different cases including expansion of the network into the case of nonlinear interunit coupling. Furthermore, we show that a specific coupling matrix provides low-pass-filter properties to the units, thus connecting networks constructed by static summation units with continuous-time networks. We also show under which conditions such networks can be used to perform arithmetic calculations by means of pattern completion.     

Computer simulation of inhibition-dependent binding in a neural network

Reverberating dynamics of neural network is modeled on PC in order to illustrate possible role of inhibition as binding controller in the network. The network is composed of binding neurons. In the binding neuron model [BioSystems 48 (1998) 263], the degree of temporal coherence between synaptic inputs is decisive for triggering, and slow inhibition is expressed in terms of the degree, which is necessary for triggering. Two learning mechanisms are implemented in the network, namely, adjusting synaptic strength and/or propagation delays. By means of forced playing of external pattern, the network is taught to support dynamics with disconnected and bound patterns of activity. By choosing either high, or low inhibition, one can switch between the disconnected and bound patterns, respectively. This is interpreted as inhibition-controlled binding in the network.     

EEG analysis gives model of neuronal template-matching mechanism for sensory search with olfactory bulb

The spatial pattern of EEG activity at the surface of the olfactory bulb tends to be invariant with respect to input and to change to a new pattern whenever an animal is trained to expect or search for a particular odor. It is postulated here that the spatial EEG pattern is dependent on a neural template for that odor that is formed during training. This hypothesis is expressed in the form of a model consisting of an array of interconnected elements (1x10 or 6x6). Each element represents 2 excitatory and 2 inhibitory subsets of neurons with 3 types of internal feedback: negative, mutually excitatory, and mutually inhibitory. The elements are interconnected only by mutual excitation and mutual inhibition. Each neural subset is represented by a nonlinear differential equation; the connections are represented by modifiable coupling coefficients. With appropriate values of the time, coupling, and gain coefficients, and with input that is modelled on olfactory input, the set of 40 or 144 equations gives output that simulates the time and space patterns of the EEG.In the naive state the coefficients are uniform. A template is formed by giving input to selected elements, cross-correlating the outputs, and weighting the mutually excitatory coupling coefficient between each pair of elements by the corresponding correlation coefficient. When a template has been formed, input to nontemplate elements is treated as noise. Optionally a matched filter is made to simulate habituation by reducing the synaptic gain coefficients of those excitatory subsets that receive the noise. The model is tested by giving input to nontemplate elements and to none, part or all of the template elements.There are two outputs of the model. One is the spatial pattern V _j of the root mean square (rms) amplitudes of the individual outputs v(j,t) of the elements. The other output is the rms amplitude E _rms of the ensemble average E(t) over v(j, t).The results show that V _j depends on the template and is relatively insensitive to input, whether or not input is given to template elements. However, E _rms increases in proportion to the number of hits on the template. If the number of elements receiving noise does not exceed the number of elements in a template, or if the noise is matched with a habituation filter, then E _rms rises above the noise level for a hit on any one or more template elements irrespective of location or combination. V _j conforms to the performance of the surface EEG. E _rms is not yet accessible to physiological measurement.Supported by a grant MH 06686 from the National Institute of Mental Health and by a Research Professorship from the Miller Institute, Berkeley.     

Functional interactions in hierarchically organized neural networks studied with spatiotemporal firing patterns and phase-coupling frequencies

A scalable hardware/software hybrid module--called Ubidule--endowed with bio-inspired ontogenetic and epigenetic features is configured to run a neural networks simulation with developmental and evolvable capabilities. We simulated the activity of hierarchically organized spiking neural networks characterized by an initial developmental phase featuring cell death followed by spike timing dependent synaptic plasticity in presence of background noise. An upstream 'sensory' network received a spatiotemporally organized external input and downstream networks were activated only via the upstream network. Precise firing sequences, formed by recurrent patterns of spikes intervals above chance levels, were observed in all recording conditions, thus suggesting the build-up of a connectivity able to sustain temporal information processing. The activity of a Ubinet--a network of Ubidules--is analyzed by means of virtual electrodes that recorded neural signals similar to EEG. The analysis of these signals was compared with a small set of human recordings and revealed common patterns of shift in quadratic phase coupling. The results suggest some interpretations of changes and plasticity of functional interactions between cortical areas driven by external stimuli and by learning/cognitive     

Associative search network: A reinforcement learning associative memory

An associative memory system is presented which does not require a teacher to provide the desired associations. For each input key it conducts a search for the output pattern which optimizes an external payoff or reinforcement signal. The associative search network (ASN) combines pattern recognition and function optimization capabilities in a simple and effective way. We define the associative search problem, discuss conditions under which the associative search network is capable of solving it, and present results from computer simulations. The synthesis of sensory-motor control surfaces is discussed as an example of the associative search problem.     

Computational dynamics of gradient bistable networks

We describe a neural-like, homogeneous network consisting of coupled bistable elements and we study its abilities of learning, pattern recognition and computation. The technique allows new possibilities of pattern recognition, including the memorization and perfect recall of several memory patterns, without interference from spurious states. When the coupling strength between elements exceeds a critical value, the network readily converges to a unique attractor. Below this critical value one could perfectly recall all memorized patterns.     

Effects of Poisson noise in a IF model with STDP and spontaneous replay of periodic spatiotemporal patterns,in absence of cue stimulation

We consider a network of leaky integrate and fire neurons, whose learning mechanism is based on the Spike-Timing-Dependent Plasticity. The spontaneous temporal dynamic of the system is studied, including its storage and replay properties, when a Poissonian noise is added to the post-synaptic potential of the units. The temporal patterns stored in the network are periodic spatiotemporal patterns of spikes. We observe that, even in absence of a cue stimulation, the spontaneous dynamics induced by the noise is a sort of intermittent replay of the patterns stored in the connectivity and a phase transition between a replay and non-replay regime exists at a critical value of the spiking threshold. We characterize this transition by measuring the order parameter and its fluctuations.     

Cellular signaling: aspects for tumor diagnosis and therapy.

Cells are organic microsystems with functional compartments interconnected by complex signal chains. Intracellular signaling routes and signal reception from the extracellular environment are characterized by redundancy, i.e., parallel pathways exist. If a cell is exposed to an external "signal input", the signal processing elements within the cell provide a response that will be a pattern of reactions manifest as a metabolic, morphologic or electric "signal output". Cell-chip hybrid structures are miniaturized analytical systems with the capability to monitor such cell responses in real time and under continuous control of the environmental conditions. A system analysis approach gives an idea of how the biological component of these hybrid structures works. This is exemplified by the putative role of the microenvironmental pH as a parameter of the utmost importance for the malignant "mode" of tumor cells, which can be monitored and modeled on such hybrid structures.     

Two-category model of task allocation with application to ant societies

In many network models of interacting units such as cells or insects, the coupling coefficients between units are independent of the state of the units. Here we analyze the temporal behavior of units that can switch between two 'category' states according to rules that involve category-dependent coupling coefficients. The behaviors of the category populations resulting from the asynchronous random updating of units are first classified according to the signs of the coupling coefficients using numerical simulations. They range from isolated fixed points to lines of fixed points and stochastic attractors. These behaviors are then explained analytically using iterated function systems and birth-death jump processes. The main inspiration for our work comes from studies of non-hierarchical task allocation in, e.g., harvester ant colonies where temporal fluctuations in the numbers of ants engaged in various tasks occur as circumstances require and depend on interactions between ants. We identify interaction types that produce quick recovery from perturbations to an asymptotic behavior whose characteristics are function of the coupling coefficients between ants as well as between ants and their environment. We also compute analytically the probability density of the population numbers, and show that perturbations in our model decay twice as fast as in a model with random switching dynamics. A subset of the interaction types between ants yields intrinsic stochastic asymptotic behaviors which could account for some of the experimentally observed fluctuations. Such noisy trajectories are shown to be random walks with state-dependent biases in the 'category population' phase space. With an external stimulus, the parameters of the category-switching rules become time-dependent. Depending on the growth rate of the stimulus in comparison to its population-dependent decay rate, the dynamics may qualitatively differ from the case without stimulus. Our simple two-category model provides a framework for understanding the rich variety of behaviors in network dynamics with state-dependent coupling coefficients, and especially in task allocation processes with many tasks.     

Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns

Hebbian learning allows a network of spiking neurons to store and retrieve spatio-temporal patterns with a time resolution of 1 ms, despite the long postsynaptic and dendritic integration times. To show this, we introduce and analyze a model of spiking neurons, the spike response model, with a realistic distribution of axonal delays and with realistic postsynaptic potentials. Learning is performed by a local Hebbian rule which is based on the synchronism of presynaptic neurotransmitter release and some short-acting postsynaptic process. The time window of this synchronism determines the temporal resolution of pattern retrieval, which can be initiated by applying a short external stimulus pattern. Furthermore, a rate quantization is found in dependence upon the threshold value of the neurons, i.e., in a given time a pattern runsn times as often as learned, wheren is a positive integer (n 0). We show that all information about the spike pattern is lost if only mean firing rates (temporal average) or ensemble activities (spatial average) are considered. An average over several retrieval runs in order to generate a post-stimulus time histogram may also deteriorate the signal. The full information on a pattern is contained in the spike raster of a single run. Our results stress the importance, and advantage, of coding by spatio-temporal spike patterns instead of firing rates and average ensemble activity. The implications regarding modelling and experimental data analysis are discussed.