Organization of excitable dynamics in hierarchical biological networks

This study investigates the contributions of network topology features to the dynamic behavior of hierarchically organized excitable networks. Representatives of different types of hierarchical networks as well as two biological neural networks are explored with a three-state model of node activation for systematically varying levels of random background network stimulation. The results demonstrate that two principal topological aspects of hierarchical networks, node centrality and network modularity, correlate with the network activity patterns at different levels of spontaneous network activation. The approach also shows that the dynamic behavior of the cerebral cortical systems network in the cat is dominated by the network's modular organization, while the activation behavior of the cellular neuronal network of Caenorhabditis elegans is strongly influenced by hub nodes. These findings indicate the interaction of multiple topological features and dynamic states in the function of complex biological networks.     

The dynamics of hierarchical age-structured populations

An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.     

How songbirds deal with large amounts of serial information: retrieval rules suggest a hierarchical song memory

Many songbirds develop remarkably large vocal repertoires, and this has prompted questions about how birds are able to successfully learn and use the often enormous amounts of information encoded in their various signal patterns. We have studied these questions in nightingales (Luscinia megarhynchos), a species that performs more than 200 different types of songs (strophen), or more than 1000 phonetically different elements composing the songs. In particular, we investigated whether and how both song repertoires and song performance rules of nightingales were coded by auditory stimuli presented in serial learning experiments. Evaluation of singing episodes produced by our trained birds revealed that nightingales cope well with an exposure to even long strings of master song-types. They can readily acquire information encoded within and between the different master songs, and they memorize, for example, which master song-types they have experienced in the same learning context. Imitations of such song-types form distinct sequential associations that are termed “context groups”. Additionally, nightingales develop other song-type associations that are smaller in size and termed “package groups”. Package formation results from constraints of the acquisition mechanisms which obviously lead to a segmentation of auditorily perceived master song sequences. Further experimentation validated that the song memory of nightingales is organized in a hierarchical manner and holding information about “context groups” composed of packages, “package groups” composed of songs, and songs composed of song elements. The evidence suggests that implementation of such a hierarchical organization facilitates a quick retrieval of particular songs, and thereby provides an essential prerequisite for a functionally appropriate use of large vocal repertoire is in songbirds. Received: 4 October 1997 / Accepted in revised form: 26 August 1998     

Molecular mechanisms of memory retrieval

Memory retrieval is a fundamental component or stage of memory processing. In fact, retrieval is the only possible measure of memory. The ability to recall past events is a major determinant of survival strategies in all species and is of paramount importance in determining our uniqueness as individuals. Most biological studies of memory using brain lesion and/or gene manipulation techniques cannot distinguish between effects on the molecular mechanisms of the encoding or consolidation of memories and those responsible for their retrieval from storage. Here we examine recent findings indicating the major molecular steps involved in memory retrieval in selected brain regions of the mammalian brain. Together the findings strongly suggest that memory formation and retrieval may share some molecular mechanisms in the hippocampus and that retrieval initiates extinction requiring activation of several signaling cascades and protein synthesis.     

The long-term memory retrieval following kainic acid administration

Effect of the neurotoxin kainic acid to the food-procuring task were studied in Wistar rats. A single injection of the acid in subconvulsive dose (8 mg/kg) impaired the task performance within some weeks but not immediately after the treatment. Higher doses of kainic acid (10 mg/kg) impaired the task performance within a few hours after treatment for up to 10 days. The treatment did not prevent rat's learning of a new task in the same experimental chamber. The revealed deficit in the long-term memory retrieval might be explained by specific effects of kainic acid upon the hippocampal system.     

The dynamics of sparse random networks

Recurrent neural networks with full symmetric connectivity have been extensively studied as associative memories and pattern recognition devices. However, there is considerable evidence that sparse, asymmetrically connected, mainly excitatory networks with broadly directed inhibition are more consistent with biological reality. In this paper, we use the technique of return maps to study the dynamics of random networks with sparse, asymmetric connectivity and nonspecific inhibition. These networks show three qualitatively different kinds of behavior: fixed points, cycles of low period, and extremely long cycles verging on aperiodicity. Using statistical arguments, we relate these behaviors to network parameters and present empirical evidence for the accuracy of this statistical model. The model, in turn, leads to methods for controlling the level of activity in networks. Studying random, untrained networks provides an understanding of the intrinsic dynamics of these systems. Such dynamics could provide a substrate for the much more complex behavior shown when synaptic modification is allowed.     

Stochastic resonance in the speed of memory retrieval

The stochastic resonance (SR) phenomenon in human cognition (memory retrieval speed for arithmetical multiplication rules) is addressed in a behavioral and neurocomputational study. The results of an experiment in which performance was monitored for various magnitudes of acoustic noise are presented. The average response time was found to be minimal for some optimal noise level. Moreover, it was shown that the optimal noise level and the magnitude of the SR effect depend on the difficulty of the task. A computational framework based on leaky accumulators that integrate noisy information and provide the output upon reaching a threshold criterion is used to illustrate the observed phenomena.     

Entropy bounds for hierarchical molecular networks

In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of non-hierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entropy of a single hierarchical graph, we see that the derived bounds can also be used for characterizing graph classes. Our contribution is an important extension to previous results about the entropy of non-hierarchical networks because for practical applications hierarchical networks are playing an important role in chemistry and biology. In addition to the derivation of the entropy bounds, we provide a numerical analysis for two special graph classes, rooted trees and generalized trees, and demonstrate hereby not only the computational feasibility of our method but also learn about its characteristics and interpretability with respect to data analysis.     

The global dynamics of a discrete nonlinear hierarchical population system

This paper is concerned with the global dynamics of a hierarchical population model,in which the fertility of an individual depends on the total number of higher-ranking members.We investigate the stability of equilibria,nonexistence of periodic orbits and the persistence of the population by means of eigenvalues,Lyapunov function,and several results in discrete dynamical systems.Our work demonstrates that the reproductive number governs the evolution of the population.Besides the theoretical results,some numerical experiments are also presented.     

Striatal contributions to declarative memory retrieval

Declarative memory is known to depend on the medial temporal lobe memory system. Recently, there has been renewed focus on the relationship between the basal ganglia and declarative memory, including the involvement of striatum. However, the contribution of striatum to declarative memory retrieval remains unknown. Here, we review neuroimaging and neuropsychological evidence for the involvement of the striatum in declarative memory retrieval. From this review, we propose that, along with the prefrontal cortex (PFC), the striatum primarily supports cognitive control of memory retrieval. We conclude by proposing three hypotheses for the specific role of striatum in retrieval: (1) striatum modulates the re-encoding of retrieved items in accord with their expected utility (adaptive encoding), (2) striatum selectively admits information into working memory that is expected to increase the likelihood of successful retrieval (adaptive gating), and (3) striatum enacts adjustments in cognitive control based on the outcome of retrieval (reinforcement learning).     

A distinct role for norepinephrine in memory retrieval

A role for norepinephrine in learning and memory has been elusive and controversial. A longstanding hypothesis states that the adrenergic nervous system mediates enhanced memory consolidation of emotional events. We tested this hypothesis in several learning tasks using mutant mice conditionally lacking norepinephrine and epinephrine, as well as control mice and rats treated with adrenergic receptor agonists and antagonists. We find that adrenergic signaling is critical for the retrieval of intermediate-term contextual and spatial memories, but is not necessary for the retrieval or consolidation of emotional memories in general. The role of norepinephrine in retrieval requires signaling through the beta(1)-adrenergic receptor in the hippocampus. The results demonstrate that mechanisms of memory retrieval can vary over time and can be different from those required for acquisition or consolidation. These findings may be relevant to symptoms in several neuropsychiatric disorders as well as the treatment of cardiac failure with beta blockers.     

The molecule-group schema of memory: storage, recognition and retrieval

A new schema, the molecule-group schema, explains memory storage, recognition and retrieval. The schema consists of three postulates about molecular specificity, grouping, and diffusion. In the schema, the physical memory trace consists of a stable group of different kinds of highly specific molecules. The schema is intended to provide an alternative to the widely known synaptic-change schema, in which it is assumed that changes of synaptic efficacies constitute the memory trace. The new schema is used to develop a particular model of memory. In the model, recognition occurs when specific intracellular "endotransmitters" react with complementary "endoreceptors" in the same cell. Retrieval, modelled as the process whereby memory causes the recurrence of a previously experienced pattern of neural activity, occurs when a group of pools of endotransmitters, located within an intracellular memory organelle, is released, allowing the endotransmitters to diffuse to the periphery of the cell body. The model suffices to explain long-term and short-term memory of events as well as innate memory.     

Population dynamics in migratory networks

Migratory animals are comprised of a complex series of interconnected breeding and nonbreeding populations. Because individuals in any given population can arrive from a variety of sites the previous season, predicting how different populations will respond to environmental change can be challenging. In this study, we develop a population model composed of a network of breeding and wintering sites to show how habitat loss affects patterns of connectivity and species abundance. When the costs of migration are evenly distributed, habitat loss at a single site can increase the degree of connectivity (mixing) within the entire network, which then acts to buffer global populations from declines. However, the degree to which populations are buffered depends on where habitat loss occurs within the network: a site that has the potential to receive individuals from multiple populations in the opposite season will lead to smaller declines than a site that is more isolated. In other cases when there are equal costs of migration to two or more sites in the opposite season, habitat loss can result in some populations becoming segregated (disconnected) from the rest of the network. The geographic structure of the network can have a significant influence on relative population sizes of sites in the same season and can also affect the overall degree of mixing in the network, even when sites are of equal intrinsic quality. When a migratory network is widely spaced and migration costs are high, an equivalent habitat loss will lead to a larger decline in global population size than will occur in a network where the overall costs of migration are low. Our model provides an important foundation to test predictions related to habitat loss in real-world migratory networks and demonstrates that migratory networks will likely produce different dynamics from traditional metapopulations. Our results provide strong evidence that estimating population connectivity is a prerequisite for successfully predicting changes in migratory populations.     

A hierarchical classification of first-order recurrent neural networks

We provide a decidable hierarchical classification of first-order recurrent neural networks made up of McCulloch and Pitts cells. This classification is achieved by proving an equivalence result between such neural networks and deterministic Büuchi automata, and then translating the Wadge classification theory from the abstract machine to the neural network context. The obtained hierarchy of neural networks is proved to have width 2 and height omega + 1, and a decidability procedure of this hierarchy is provided. Notably, this classification is shown to be intimately related to the attractive properties of the considered networks.     

Dynamics control of semantic processes in a hierarchical associative memory

A neural mechanism for control of dynamics and function of associative processes in a hierarchical memory system is demonstrated. For the representation and processing of abstract knowledge, the semantic declarative memory system of the human brain is considered. The dynamics control mechanism is based on the influence of neuronal adaptation on the complexity of neural network dynamics. Different dynamical modes correspond to different levels of the ultrametric structure of the hierarchical memory being invoked during an associative process. The mechanism is deterministic but may also underlie free associative thought processes. The formulation of an abstract neural network model of hierarchical associative memory utilizes a recent approach to incorporate neuronal adaptation. It includes a generalized neuronal activation function recently derived by a Hodgkin-Huxley-type model. It is shown that the extent to which a hierarchically organized memory structure is searched is controlled by the neuronal adaptability, i.e. the strength of coupling between neuronal activity and excitability. In the brain, the concentration of various neuromodulators in turn can regulate the adaptability. An autonomously controlled sequence of bifurcations, from an initial exploratory to a final retrieval phase, of an associative process is shown to result from an activity-dependent release of neuromodulators. The dynamics control mechanism may be important in the context of various disorders of the brain and may also extend the range of applications of artificial neural networks.