Emergence of symmetric, modular, and reciprocal connections in recurrent networks with Hebbian learning

While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs. Received: 27 April 1998 / Accepted in revised form: 16 March 1999     

Entrainment ranges of forced phase oscillators

In the vertebrate spinal cord, a neural circuit called the central pattern generator produces the basic locomotory rhythm. Short and long distance intersegmental connections serve to maintain coordination along the length of the body. As a way of examining the influence of such connections, we consider a model of a chain of coupled phase oscillators in which one oscillator receives a periodic forcing stimulus. For a certain range of forcing frequencies, the chain will match the stimulus frequency, a phenomenon called entrainment. Motivated by recent experiments in lampreys, we derive analytical expressions for the range of forcing frequencies that entrain the chain, and how that range depends on the forcing location. For short intersegmental connections, in which an oscillator is connected only to its nearest neighbors, we describe two ways in which entrainment is lost: internally, in which oscillators within the chain no longer oscillate at the same frequency; and externally, in which the the chain no longer has the same frequency as the forcing. By analyzing chains in which every oscillator is connected to every other oscillator (i.e., all-to-all connections), we show that the presence of connections with lengths greater than one do not necessarily change the entrainment ranges based on the nearest–neighbor model. We derive a criterion for the ratio of connection strengths under which the connections of length greater than one do not change the entrainment ranges produced in the nearest–neighbor model, provided entrainment is lost externally. However, when this criterion holds, the range of entrained frequencies is a monotonic function of forcing location, unlike experimental results, in which entrainment ranges are larger near the middle of the chain than at the ends. Numerically, we show that similar non-monotonic entrainment ranges are possible if the ratio criterion does not hold, suggesting that in the lamprey central pattern generator, intersegmental connection strengths are not a simple function of the connection length.     

Dynamic updating of distributed neural representations using forward models

In this paper, we present a continuous attractor network model that we hypothesize will give some suggestion of the mechanisms underlying several neural processes such as velocity tuning to visual stimulus, sensory discrimination, sensorimotor transformations, motor control, motor imagery, and imitation. All of these processes share the fundamental characteristic of having to deal with the dynamic integration of motor and sensory variables in order to achieve accurate sensory prediction and/or discrimination. Such principles have already been described in the literature by other high-level modeling studies (Decety and Sommerville in Trends Cogn Sci 7:527–533, 2003; Oztop et al. in Neural Netw 19(3):254–271, 2006; Wolpert et al. in Philos Trans R Soc 358:593–602, 2003). With respect to these studies, our work is more concerned with biologically plausible neural dynamics at a population level. Indeed, we show that a relatively simple extension of the classical neural field models can endow these networks with additional dynamic properties for updating their internal representation using external commands. Moreover, an analysis of the interactions between our model and external inputs also shows interesting properties, which we argue are relevant for a better understanding of the neural processes of the brain.     

A dynamic neural network with temporal coding and functional connectivity

A neural network model capable of altering its pattern classifying properties by program input is proposed. Here the “program input” is another source of input besides the pattern input. Unlike most neural network models, this model runs as a deterministic point process of spikes in continuous time; connections among neurons have finite delays, which are set randomly according to a normal distribution. Furthermore, this model utilizes functional connectivity which is dynamic connectivity among neurons peculiar to temporal-coding neural networks with short neuronal decay time constants. Computer simulation of the proposed network has been performed, and the results are considered in light of experimental results shown recently for correlated firings of neurons. Received: 6 December 1996 / Accepted in revised form: 15 September 1997     

Neural computations underlying the exertion of force: a model

We have developed a model that simulates possible mechanisms by which supraspinal neuronal signals coding forces could converge in the spinal cord and provide an ongoing integrated signal to the motoneuronal pools whose activation results in the exertion of force. The model consists of a three-layered neural network connected to a two-joint-six-muscle model of the arm. The network layers represent supraspinal populations, spinal cord interneurons, and motoneuronal pools. We propose an approach to train the network so that, after the synaptic connections between the layers are adjusted, the performance of the model is consistent with experimental data obtained on different organisms using different experimental paradigms: the stiffness characteristics of human arm; the structure of force fields generated by the stimulation of the frog's spinal cord; and a correlation between motor cortical activity and force exerted by monkey against an immovable object. The model predicts a specific pattern of connections between supraspinal populations coding forces and spinal cord interneurons: the weight of connection should be correlated with directional preference of interconnected units. Finally, our simulations demonstrate that the force generated by the sum of neural signals can be nearly equal to the vector sum of forces generated by each signal independently, in spite of the complex nonlinearities intervening between supraspinal commands and forces exerted by the arm in response to these commands.     

Leader neurons in leaky integrate and fire neural network simulations

In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465–8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311–345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063–1070, 2004; Gerstner and Naud, Science 326:379–380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neurons.     

Gene Duplication and the Properties of Biological Networks

Patterns of network connection of members of multigene families were examined for two biological networks: a genetic network from the yeast Saccharomyces cerevisiae and a protein–protein interaction network from Caenorhabditis elegans. In both networks, genes belonging to gene families represented by a single member in the genome (“singletons”) were disproportionately represented among the nodes having large numbers of connections. Of 68 single-member yeast families with 25 or more network connections, 28 (44.4%) were located in duplicated genomic segments believed to have originated from an ancient polyploidization event; thus, each of these 28 loci was thus presumably duplicated along with the genomic segment to which it belongs, but one of the two duplicates has subsequently been deleted. Nodes connected to major “hubs” with a large number of connections, tended to be relatively sparsely interconnected among themselves. Furthermore, duplicated genes, even those arising from recent duplication, rarely shared many network connections, suggesting that network connections are remarkably labile over evolutionary time. These factors serve to explain well-known general properties of biological networks, including their scale-free and modular nature. [Reviewing Editor : Dr. Manyuan Long]     

Neural field model of binocular rivalry waves

We present a neural field model of binocular rivalry waves in visual cortex. For each eye we consider a one-dimensional network of neurons that respond maximally to a particular feature of the corresponding image such as the orientation of a grating stimulus. Recurrent connections within each one-dimensional network are assumed to be excitatory, whereas connections between the two networks are inhibitory (cross-inhibition). Slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We derive an analytical expression for the speed of a binocular rivalry wave as a function of various neurophysiological parameters, and show how properties of the wave are consistent with the wave-like propagation of perceptual dominance observed in recent psychophysical experiments. In addition to providing an analytical framework for studying binocular rivalry waves, we show how neural field methods provide insights into the mechanisms underlying the generation of the waves. In particular, we highlight the important role of slow adaptation in providing a “symmetry breaking mechanism” that allows waves to propagate.     

Regeneration of central and peripheral synaptic connections in the locomotor system of the pteropod molluscClione limacina

The neural network underlying rhythmic wing movements in the molluscClione limacina is well-studied. Two different groups of motoneurons innervate two distinct groups of wing muscles. The locomotor rhythm generated in the left and right pedal ganglia is synchronized by interneurons. When the axons of the locomotor motoneurons are crushed, numerous fine neurites sprout towards the denervated muscles and reach them in 8–15 days. At this stage motoneurons project to and synapse on not only correct but equally incorrect muscle targets. After 2 weeks of regeneration the number of incorrect neurites and synaptic connections begins to decrease and following 1.5–2 months all incorrect connections are eliminated, incorrect axons are withdrawn and the behavioral deficit is compensated. In this study the regeneration of interneurons and the growth profiles of inter- and motoneurons were also studiedin vitro. Two individually isolated pedal ganglia were co-cultured in three different configurations: a) the wing nerve stump from one ganglion was fixed against the commissural stump from another ganglion; b) the wing nerve stumps were fixed against each other; c) the commissural stumps were fixed against each other. Under the above experimental conditions we found that the interneurons were able to cross only the contact between two commissural stumps, and in this case found their original targets, restored correct connections and synchronized the rhythm in two pedal ganglia. In contrast, motoneurons were able to cross all types of contacts.     

Spatial-area selective retrieval of multiple object–place associations in a hierarchical cognitive map formed by theta phase coding

The human cognitive map is known to be hierarchically organized consisting of a set of perceptually clustered landmarks. Patient studies have demonstrated that these cognitive maps are maintained by the hippocampus, while the neural dynamics are still poorly understood. The authors have shown that the neural dynamic “theta phase precession” observed in the rodent hippocampus may be capable of forming hierarchical cognitive maps in humans. In the model, a visual input sequence consisting of object and scene features in the central and peripheral visual fields, respectively, results in the formation of a hierarchical cognitive map for object–place associations. Surprisingly, it is possible for such a complex memory structure to be formed in a few seconds. In this paper, we evaluate the memory retrieval of object–place associations in the hierarchical network formed by theta phase precession. The results show that multiple object–place associations can be retrieved with the initial cue of a scene input. Importantly, according to the wide-to-narrow unidirectional connections among scene units, the spatial area for object–place retrieval can be controlled by the spatial area of the initial cue input. These results indicate that the hierarchical cognitive maps have computational advantages on a spatial-area selective retrieval of multiple object–place associations. Theta phase precession dynamics is suggested as a fundamental neural mechanism of the human cognitive map.     

Mechanisms of spontaneous activity in developing spinal networks

Developing networks of the chick spinal cord become spontaneously active early in development and remain so until hatching. Experiments using an isolated preparation of the spinal cord have begun to reveal the mechanisms responsible for this activity. Whole-cell and optical recordings have shown that spinal neurons receive a rhythmic, depolarizing synaptic drive and experience rhythmic elevations of intracellular calcium during spontaneous episodes. Activity is expressed throughout the neuraxis and can be produced by different parts of the cord and by the isolated brain stem, suggesting that it does not depend upon the details of network architecture. Two factors appear to be particularly important for the production of endogenous activity. The first is the predominantly excitatory nature of developing synaptic connections, and the second is the presence of prolonged activity-dependent depression of network excitability. The interaction between high excitability and depression results in an equilibrium in which episodes are expressed periodically by the network. The mechanism of the rhythmic bursting within an episode is not understood, but it may be due to a “fast” form of network depression. Spontaneous embryonic activity has been shown to play a role in neuron and muscle development, but is probably not involved in the initial formation of connections between spinal neurons. It may be important in refining the initial connections, but this possibility remains to be explored. © 1998 John Wiley & Sons, Inc. J Neurobiol 37: 131–145, 1998

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Dynamics and bifurcations of two coupled neural oscillators with different connection types

In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodicin-phase oscillations, while the connection of populations of the same type lead to periodicanti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central “top level” subcortical circuit (e.g. the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus.     

Estradiol interacts with an opioidergic network to achieve rapid modulation of a vocal pattern generator

Estrogens rapidly regulate neuronal activity within seconds-to-minutes, yet it is unclear how estrogens interact with neural circuits to rapidly coordinate behavior. This study examines whether 17-beta-estradiol interacts with an opioidergic network to achieve rapid modulation of a vocal control circuit. Adult plainfin midshipman fish emit vocalizations that mainly differ in duration, and rhythmic activity of a hindbrain–spinal vocal pattern generator (VPG) directly establishes the temporal features of midshipman vocalizations. VPG activity is therefore predictive of natural calls, and ‘fictive calls’ can be elicited by electrical microstimulation of the VPG. Prior studies show that intramuscular estradiol injection rapidly (within 5 min) increases fictive call duration in midshipman. Here, we delivered opioid antagonists near the VPG prior to estradiol injection. Rapid estradiol actions on fictive calling were completely suppressed by the broad-spectrum opioid antagonist naloxone and the mu-opioid antagonist beta-funaltrexamine, but were unaffected by the kappa-opioid antagonist nor-binaltorphimine. Unexpectedly, prior to estradiol administration, all three opioid antagonists caused immediate, transient reductions in fictive call duration. Together, our results indicate that: (1) vocal activity is modulated by opioidergic networks, confirming hypotheses from birds and mammals, and (2) the rapid actions of estradiol on vocal patterning depend on interactions with a mu-opioid modulatory network.     

Self-organized dynamics in plastic neural networks: bistability and coherence

 In this paper, we study the combined dynamics of the neural activity and the synaptic efficiency changes in a fully connected network of biologically realistic neurons with simple synaptic plasticity dynamics including both potentiation and depression. Using a mean-field of technique, we analyzed the equilibrium states of neural networks with dynamic synaptic connections and found a class of bistable networks. For this class of networks, one of the stable equilibrium states shows strong connectivity and coherent responses to external input. In the other stable equilibrium, the network is loosely connected and responds non coherently to external input. Transitions between the two states can be achieved by positively or negatively correlated external inputs. Such networks can therefore switch between their phases according to the statistical properties of the external input. Non-coherent input can only “rcad” the state of the network, while a correlated one can change its state. We speculate that this property, specific for plastic neural networks, can give a clue to understand fully unsupervised learning models. Received: 8 August 1999 / Accepted in revised form: 16 March 2000     

An artificial neural network model of the landscape pattern in Shanghai metropolitan region, China

To characterize the urbanization pattern quantitatively, a study on the mechanisms of the landscape pattern formation could facilitate the understanding on urban landscape patterns and processes, the ecological and socioeconomic consequences of urbanization, as well as the establishment of more effective strategies for landscape management. In this study, we integrated a Geographic Information System (GIS)-based analysis on landscape pattern with an artificial neural network (ANN) to quantitatively characterize the urbanization pattern of the metropolitan area of Shanghai, China, and to establish an ANN model that could preferably simulate the responses of urban landscape pattern to the natural and socioeconomic factors such as residence area, road density, population density, urban development history and the Huangpu River as an element of economic change. Our results showed that the ANN model seems appropriate for studying the nonlinear relationship among the forcing factors of urbanization and the urban landscape patterns, which provided an effective and practical approach for further understanding the mechanisms of the landscape formation pattern and the reciprocal relationship between landscape spatial pattern and ecological process. __________ Translated from Acta Ecologica Sinica, 2005, 25(5): 958–964 [译自: 生态学报, 2005, 25(5): 958–964]     

Synaptic connections in a dissociated mixed culture of rat dorsal root ganglion and spinal cord neurons

Postsynaptic currents and action potentials recorded from neurons in a mixed culture of rat dorsal root ganglion and spinal cord cells are described. The existence of mutual synaptic connections between the above two types of neurons is demonstrated. Neirofiziologiya/Neurophysiology, Vol. 38, No. 4, pp. 358–360, July–August, 2006.     

Schema design and implementation of the grasp-related mirror neuron system

 Mirror neurons within a monkey's premotor area F5 fire not only when the monkey performs a certain class of actions but also when the monkey observes another monkey (or the experimenter) perform a similar action. It has thus been argued that these neurons are crucial for understanding of actions by others. We offer the hand-state hypothesis as a new explanation of the evolution of this capability: the basic functionality of the F5 mirror system is to elaborate the appropriate feedback – what we call the hand state– for opposition-space based control of manual grasping of an object. Given this functionality, the social role of the F5 mirror system in understanding the actions of others may be seen as an exaptation gained by generalizing from one's own hand to an other's hand. In other words, mirror neurons first evolved to augment the “canonical” F5 neurons (active during self-movement based on observation of an object) by providing visual feedback on “hand state,” relating the shape of the hand to the shape of the object. We then introduce the MNS1 (mirror neuron system 1) model of F5 and related brain regions. The existing Fagg–Arbib–Rizzolatti–Sakata model represents circuitry for visually guided grasping of objects, linking the anterior intraparietal area (AIP) with F5 canonical neurons. The MNS1 model extends the AIP visual pathway by also modeling pathways, directed toward F5 mirror neurons, which match arm–hand trajectories to the affordances and location of a potential target object. We present the basic schemas for the MNS1 model, then aggregate them into three “grand schemas”– visual analysis of hand state, reach and grasp, and the core mirror circuit – for each of which we present a useful implementation (a non-neural visual processing system, a multijoint 3-D kinematics simulator, and a learning neural network, respectively). With this implementation we show how the mirror system may learnto recognize actions already in the repertoire of the F5 canonical neurons. We show that the connectivity pattern of mirror neuron circuitry can be established through training, and that the resultant network can exhibit a range of novel, physiologically interesting behaviors during the process of action recognition. We train the system on the basis of final grasp but then observe the whole time course of mirror neuron activity, yielding predictions for neurophysiological experiments under conditions of spatial perturbation, altered kinematics, and ambiguous grasp execution which highlight the importance of the timingof mirror neuron activity. Received: 6 August 2001 / Accepted in revised form: 5 February 2002     

Decoding of a motor command vector from distributed activity in superior colliculus

 Several alternative methods for decoding the desired motor command vector from neural networks containing distributed, place-coded information have been suggested. The two most widely discussed candidate mechanisms are vector summation (VS) and a center-of-mass (CM) computation. The latter mechanism has also been called vector averaging. The present paper compares the operation of these two methods in a model of an experimentally well-studied neural structure, the superior colliculus (SC). The SC is one structure that has been shown to be responsible for generating saccadic command vectors in the form of distributed neural activity that is topologically arranged across its surface. It has been suggested that the pattern of eye-movement errors obtained following the placement of a collicular lesion can distinguish between these two mechanisms. As a result of this suggestion, the pattern of saccadic errors produced by lesions in the SC have been widely cited to support the CM hypothesis. In the present paper the placement of a discrete lesion is simulated in a recurrent (dynamic) neural network model of the SC. These dynamic connections in the model SC network produce a systematic shift of the locus of distributed activity away from the site of the lesion. The spatiotemporal shift in the location of SC activity then produces a pattern of saccadic errors that appear to support the CM hypothesis, even though ensemble activity in our model colliculus is decoded by VS. This result demonstrates that, when ensemble activity on the SC motor map is dynamically modulated over space and time by intrinsic collicular circuitry, an explicit CM computation is not needed to reproduce the pattern of physiological results that follow focal SC lesions. Received: 19 December 2000 / Accepted in revised form: 27 September 2001     

Increased spinal expression of c-Fos following stimulation of the lower urinary tract in chronic spinal cord-injured rats

c-Fos expression was studied in the lumbar and sacral spinal cord regions involved in processing afferent input from the lower urinary tract and a comparison was made between spinal cord-injured (SCI) animals and control animals with intact neuraxes. Afferent pathways from the lower urinary tract were activated either by insertion of a catheter through the urethra into the urinary bladder or by catheterisation plus induction of reflex micturition contractions by intravesical saline infusion. Placement of a catheter alone elicited Fos expression in a similar number of neurones in SCI and control rats mainly in the medial dorsal horn (MDH) and dorsal commissure (DCM) in the segments L1–2 and L5–S1 with a maximum in L5. Additional saline infusion induced low-frequency, high-amplitude, rhythmic bladder contractions of long duration in the rats with intact spinal cords, whereas in SCI rats, bladder distension elicited reflex contractions at a higher frequency, smaller amplitude and shorter duration. However, the basal and mean bladder pressure, as well as the total contraction time relative to the whole recording time, was not significantly different. Distension-induced bladder contractions markedly increased Fos expression primarily in the spinal segments L5–S1 in the control rats, where the majority of bladder and urethral afferent fibres terminates. Fos-positive cells were located in the MDH, lateral dorsal horn (LDH), DCM and the lateral aspect of laminae V–VII. Compared to controls, Fos expression after spinal cord injury (SCI) occurred in a significantly greater number of neurones throughout the segments L3–S1 following induction of bladder reflexes. The greatest proportional increase in the number of Fos-positive cells occurred in L3–5 which normally receive only little afferent input from the urinary bladder. Cell numbers predominantly increased in the LDH and lateral lamina V–VII. The data are consistent with the concept of a neuroplastic reorganisation of spinal pathways after SCI. Unmasking of silent synapses or formation of new connections by afferent axonal sprouting caudal to the lesion, as evident from the increased numbers of cells expressing Fos after bladder distension, could be factors underlying the emergence of reflexogenic micturition in chronic SCI rats. Accepted: 27 May 1999