Language dynamics in finite populations

Any mechanism of language acquisition can only learn a restricted set of grammars. The human brain contains a mechanism for language acquisition which can learn a restricted set of grammars. The theory of this restricted set is universal grammar (UG). UG has to be sufficiently specific to induce linguistic coherence in a population. This phenomenon is known as "coherence threshold". Previously, we have calculated the coherence threshold for deterministic dynamics and infinitely large populations. Here, we extend the framework to stochastic processes and finite populations. If there is selection for communicative function (selective language dynamics), then the analytic results for infinite populations are excellent approximations for finite populations; as expected, finite populations need a slightly higher accuracy of language acquisition to maintain coherence. If there is no selection for communicative function (neutral language dynamics), then linguistic coherence is only possible for finite populations.     

The evolutionary dynamics of grammar acquisition

Grammar is the computational system of language. It is a set of rules that specifies how to construct sentences out of words. Grammar is the basis of the unlimited expressibility of human language. Children acquire the grammar of their native language without formal education simply by hearing a number of sample sentences. Children could not solve this learning task if they did not have some pre-formed expectations. In other words, children have to evaluate the sample sentences and choose one grammar out of a limited set of candidate grammars. The restricted search space and the mechanism which allows to evaluate the sample sentences is called universal grammar. Universal grammar cannot be learned; it must be in place when the learning process starts. In this paper, we design a mathematical theory that places the problem of language acquisition into an evolutionary context. We formulate equations for the population dynamics of communication and grammar learning. We ask how accurate children have to learn the grammar of their parents' language for a population of individuals to evolve and maintain a coherent grammatical system. It turns out that there is a maximum error tolerance for which a predominant grammar is stable. We calculate the maximum size of the search space that is compatible with coherent communication in a population. Thus, we specify the conditions for the evolution of universal grammar.     

New approaches to the problem of generating coherent,reproducible phenotypes

Fundamental, unresolved questions in biology include how a bacterium generates coherent phenotypes, how a population of bacteria generates a coherent set of such phenotypes, how the cell cycle is regulated and how life arose. To try to help answer these questions, we have developed the concepts of hyperstructures, competitive coherence and life on the scales of equilibria. Hyperstructures are large assemblies of macromolecules that perform functions. Competitive coherence describes the way in which organisations such as cells select a subset of their constituents to be active in determining their behaviour; this selection results from a competition between a process that is responsible for a historical coherence and another process responsible for coherence with the current environment. Life on the scales of equilibria describes how bacteria depend on the cell cycle to negotiate phenotype space and, in particular, to satisfy the conflicting constraints of having to grow in favourable conditions so as to reproduce yet not grow in hostile conditions so as to survive. Both competitive coherence and life on the scales deal with the problem of reconciling conflicting constraints. Here, we bring together these concepts in the common framework of hyperstructures and make predictions that may be tested using a learning program, Coco, and secondary ion mass spectrometry.     

Statistical-mechanical measure of stochastic spiking coherence in a population of inhibitory subthreshold neurons

By varying the noise intensity, we study stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). This stochastic spiking coherence may be well visualized in the raster plot of neural spikes. For a coherent case, partially-occupied "stripes" (composed of spikes and indicating collective coherence) are formed in the raster plot. This partial occupation occurs due to "stochastic spike skipping" which is well shown in the multi-peaked interspike interval histogram. The main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot. We introduce a new spike-based coherence measure M ( s ) by considering the occupation pattern and the pacing pattern of spikes in the stripes. In particular, the pacing degree between spikes is determined in a statistical-mechanical way by quantifying the average contribution of (microscopic) individual spikes to the (macroscopic) ensemble-averaged global potential. This "statistical-mechanical" measure M ( s ) is in contrast to the conventional measures such as the "thermodynamic" order parameter (which concerns the time-averaged fluctuations of the macroscopic global potential), the "microscopic" correlation-based measure (based on the cross-correlation between the microscopic individual potentials), and the measures of precise spike timing (based on the peri-stimulus time histogram). In terms of M ( s ), we quantitatively characterize the stochastic spiking coherence, and find that M ( s ) reflects the degree of collective spiking coherence seen in the raster plot very well. Hence, the "statistical-mechanical" spike-based measure M ( s ) may be used usefully to quantify the degree of stochastic spiking coherence in a statistical-mechanical way.     

The evolutionary dynamics of the lexical matrix

The lexical matrix is an integral part of the human language system. It provides the link between word form and word meaning. A simple lexical matrix is also at the center of any animal communication system, where it defines the associations between form and meaning of animal signals. We study the evolution and population dynamics of the lexical matrix. We assume that children learn the lexical matrix of their parents. This learning process is subject to mistakes: (i) children may not acquire all lexical items of their parents (incomplete learning); and (ii) children might acquire associations between word forms and word meanings that differ from their parents’ lexical items (incorrect learning). We derive an analytic framework that deals with incomplete learning. We calculate the maximum error rate that is compatible with a population maintaining a coherent lexical matrix of a given size. We calculate the equilibrium distribution of the number of lexical items known to individuals. Our analytic investigations are supplemented by numerical simulations that describe both incomplete and incorrect learning, and other extensions.     

IMGT-Kaleidoscope, the formal IMGT-ONTOLOGY paradigm

IMGT, the international ImMunoGeneTics information system (http://imgt.cines.fr), is the reference in immunogenetics and immunoinformatics. IMGT standardizes and manages the complex immunogenetic data which include the immunoglobulins (IG) or antibodies, the T cell receptors (TR), the major histocompatibility complex (MHC) and the related proteins of the immune system (RPI) which belong to the immunoglobulin superfamily (IgSF) and the MHC superfamily (MhcSF). The accuracy and consistency of IMGT data and the coherence between the different IMGT components (databases, tools and Web resources) are based on IMGT-ONTOLOGY, the first ontology for immunogenetics and immunoinformatics. IMGT-ONTOLOGY manages the immunogenetics knowledge through diverse facets relying on seven axioms, "IDENTIFICATION", "DESCRIPTION", "CLASSIFICATION", "NUMEROTATION", "LOCALIZATION", "ORIENTATION" and "OBTENTION", that postulate that objects, processes and relations have to be identified, described, classified, numerotated, localized, orientated, and that the way they are obtained has to be determined. These axioms constitute the Formal IMGT-ONTOLOGY, also designated as IMGT-Kaleidoscope. Through the example of the IG molecular synthesis, the concepts generated from the "IDENTIFICATION", "DESCRIPTION", "CLASSIFICATION" and "NUMEROTATION" axioms are detailed with their main instances and semantic relations. The axioms have been essential for the conceptualization of the molecular immunogenetics knowledge and can be used to generate concepts for multi scale approaches at the molecule, cell, tissue, organ, organism or population level, emphasizing the generalization of the application domain. In that way the Formal IMGT-ONTOLOGY represents a paradigm for the elaboration of ontologies in system biology.     

Natural selection of the critical period for language acquisition

The language acquisition period in humans lasts about 13 years. After puberty it becomes increasingly difficult to learn a language. We explain this phenomenon by using an evolutionary framework. We present a dynamical system describing competition between language acquisition devices, which differ in the length of the learning period. There are two selective forces that play a role in determining the critical learning period: (i) having a longer learning period increases the accuracy of language acquisition; (ii) learning is associated with certain costs that affect fitness. As a result, there exists a limited learning period which is evolutionarily stable. This result is obtained analytically by means of a Nash equilibrium analysis of language acquisition devices. Interestingly, the evolutionarily stable learning period does not maximize the average fitness of the population.     

The locked-in patient and the characteristics of the electrical activity of his brain

"Locked-in" state differs from the known states characterized by the motor activity blockade, preservation of conscience of speech contact, despite the fact that connection with outer world during this state is limited only by vertical movements of eyes and eyelids in response to speech signals. Three "locked-in" men were studied at different stages of development of this state. Spectral-coherent analysis of the EEG was conducted. The most typical for the developed state of the "locked-in" man is a uniform change of the intercentral EEG relations. In the motor areas of the cortex alpha-activity and its links are not formed (coherence in alpha-range is zero) while high and low frequencies are coherent. In the visual areas, in contrast, the alpha-rhythm is coherent. Distinct interhemispheric asymmetry of coherent connections appears. In the right hemisphere a decrease of coherence level is sharp and even, in the left one--in occipito-temporal parts the level remains close to norm, while in the frontal parts of the cortex it decreases.     

Regional coherence of climatic and lake thermal variables of four lake districts in the Upper Great Lakes Region of North America

1. Within a region with common climatic conditions, lake thermal variables should exhibit coherent variability patterns to the extent to which they are not influenced by lake specific features such as morphometry and water clarity. We tested the degree of temporal coherence in interannual variability for climatic variables (air temperature and solar radiation) among four lake districts in the Upper Great Lakes Region. We also tested the degree of coherence of lake thermal variables (near‐surface temperature, eplimnetic temperature, hypolimnetic temperature and thermocline depth) for lakes within these districts. 2. Our four lake districts included the Experimental Lakes Area in north‐western Ontario, the Dorset Research Centre area north of Toronto, Ontario, the Northern Highland Lake District in northern Wisconsin, and the Yahara Lakes near Madison in southern Wisconsin. Seventeen lakes were analyzed for lake thermal variables dependent on stratification. Another five lakes were added for the analysis of near‐surface temperature. 3. The analysis tested whether for monthly and summer means, the climate (air temperature and solar radiation) across the four lake districts was coherent interannually and whether variables which measure the thermal structure of the lakes were coherent interannually among lakes within each lake district and across the four lake districts. 4. Temporal coherence was estimated by the correlation between lake districts for meteorological variables and between lake pairs for lake thermal variables. Mean coherence and the percentage of correlations exceeding the 5% significance level were derived both within and between lake districts for lake thermal variables. 5. Across the four lake districts, summer mean air temperature was highly coherent while summer solar radiation was less coherent. Approximately 60–80% of the interannual variation in mean summer air temperature at a site occurred across the entire region. Less than 45% of the variation in solar radiation occurred across sites. 6. Epilimnetic temperature and the near‐surface temperature were highly coherent both within and between lake districts. The coherence of thermocline depth within and between lake districts was weaker. Hypolimnetic temperature was not coherent between lake districts for most lake pairs. It was coherent among lakes within some lake districts. 7. The influences of local weather and differences among lakes in water clarity are discussed in the context of differences in levels of coherence among lake thermal variables and among lake pairs for a given variable.     

Genomic ancestry, self-reported "color" and quantitative measures of skin pigmentation in Brazilian admixed siblings

A current concern in genetic epidemiology studies in admixed populations is that population stratification can lead to spurious results. The Brazilian census classifies individuals according to self-reported "color", but several studies have demonstrated that stratifying according to "color" is not a useful strategy to control for population structure, due to the dissociation between self-reported "color" and genomic ancestry. We report the results of a study in a group of Brazilian siblings in which we measured skin pigmentation using a reflectometer, and estimated genomic ancestry using 21 Ancestry Informative Markers (AIMs). Self-reported "color", according to the Brazilian census, was also available for each participant. This made it possible to evaluate the relationship between self-reported "color" and skin pigmentation, self-reported "color" and genomic ancestry, and skin pigmentation and genomic ancestry. We observed that, although there were significant differences between the three "color" groups in genomic ancestry and skin pigmentation, there was considerable dispersion within each group and substantial overlap between groups. We also saw that there was no good agreement between the "color" categories reported by each member of the sibling pair: 30 out of 86 sibling pairs reported different "color", and in some cases, the sibling reporting the darker "color" category had lighter skin pigmentation. Socioeconomic status was significantly associated with self-reported "color" and genomic ancestry in this sample. This and other studies show that subjective classifications based on self-reported "color", such as the one that is used in the Brazilian census, are inadequate to describe the population structure present in recently admixed populations. Finally, we observed that one of the AIMs included in the panel (rs1426654), which is located in the known pigmentation gene SLC24A5, was strongly associated with skin pigmentation in this sample.     

Threshold learning dynamics in social networks

Social learning is defined as the ability of a population to aggregate information, a process which must crucially depend on the mechanisms of social interaction. Consumers choosing which product to buy, or voters deciding which option to take with respect to an important issue, typically confront external signals to the information gathered from their contacts. Economic models typically predict that correct social learning occurs in large populations unless some individuals display unbounded influence. We challenge this conclusion by showing that an intuitive threshold process of individual adjustment does not always lead to such social learning. We find, specifically, that three generic regimes exist separated by sharp discontinuous transitions. And only in one of them, where the threshold is within a suitable intermediate range, the population learns the correct information. In the other two, where the threshold is either too high or too low, the system either freezes or enters into persistent flux, respectively. These regimes are generally observed in different social networks (both complex or regular), but limited interaction is found to promote correct learning by enlarging the parameter region where it occurs.     

Perceptual organization of local elements into global shapes in the human visual cortex

The question of how local image features on the retina are integrated into perceived global shapes is central to our understanding of human visual perception. Psychophysical investigations have suggested that the emergence of a coherent visual percept, or a "good-Gestalt", is mediated by the perceptual organization of local features based on their similarity. However, the neural mechanisms that mediate unified shape perception in the human brain remain largely unknown. Using human fMRI, we demonstrate that not only higher occipitotemporal but also early retinotopic areas are involved in the perceptual organization and detection of global shapes. Specifically, these areas showed stronger fMRI responses to global contours consisting of collinear elements than to patterns of randomly oriented local elements. More importantly, decreased detection performance and fMRI activations were observed when misalignment of the contour elements disturbed the perceptual coherence of the contours. However, grouping of the misaligned contour elements by disparity resulted in increased performance and fMRI activations, suggesting that similar neural mechanisms may underlie grouping of local elements to global shapes by different visual features (orientation or disparity). Thus, these findings provide novel evidence for the role of both early feature integration processes and higher stages of visual analysis in coherent visual perception.     

Perceptual Grouping over Time within and across Auditory and Tactile Modalities

In auditory scene analysis, population separation and temporal coherence have been proposed to explain how auditory features are grouped together and streamed over time. The present study investigated whether these two theories can be applied to tactile streaming and whether temporal coherence theory can be applied to crossmodal streaming. The results show that synchrony detection between two tones/taps at different frequencies/locations became difficult when one of the tones/taps was embedded in a perceptual stream. While the taps applied to the same location were streamed over time, the taps applied to different locations were not. This observation suggests that tactile stream formation can be explained by population-separation theory. On the other hand, temporally coherent auditory stimuli at different frequencies were streamed over time, but temporally coherent tactile stimuli applied to different locations were not. When there was within-modality streaming, temporally coherent auditory stimuli and tactile stimuli were not streamed over time, either. This observation suggests the limitation of temporal coherence theory when it is applied to perceptual grouping over time.     

Dynamics of the spectral-coherent characteristics of the human EEG in healthy subjects and brain pathology

EEGs of 15 healthy subjects and 30 patients in early period after surgical ablation of tumours with basal localization, were investigated by means of monitor "Neuro-1" which allows to obtain in continuous regime characteristics of EEG dynamics according to power spectra and reveal the characteristics of intercentral relations of electrical brain processes by coherence and phase shifts. In healthy subjects in the period of transition from wakefulness to drowsiness highly coherent beta-rhythm (16-18 Hz) was revealed, preceeding typical picture of drowsiness and sleep. Study of the patients shows that certain characteristics of coherence and phasic shifts have an important prognostic value. Conclusion is made that for estimation of the functional state of healthy subjects during transition from wakefulness to drowsiness and of patients in early postoperative period the data on spectra of coherence are most informative.     

A parturition-associated nonsynaptic coherent activity pattern in the developing hippocampus

Correlated neuronal activity is instrumental in the formation of networks, but its emergence during maturation is poorly understood. We have used multibeam two-photon calcium microscopy combined with targeted electrophysiological recordings in order to determine the development of population coherence from embryonic to postnatal stages in the hippocampus. At embryonic stages (E16-E19), synchronized activity is absent, and neurons are intrinsically active and generate L-type channel-mediated calcium spikes. At birth, small cell assemblies coupled by gap junctions spontaneously generate synchronous nonsynaptic calcium plateaus associated to recurrent burst discharges. The emergence of coherent calcium plateaus at birth is controlled by oxytocin, a maternal hormone initiating labour, and progressively shut down a few days later by the synapse-driven giant depolarizing potentials (GDPs) that synchronize the entire network. Therefore, in the developing hippocampus, delivery is an important signal that triggers the first coherent activity pattern, which is silenced by the emergence of synaptic transmission.     

Attractivity of coherent manifolds in metapopulation models

The likelihood that coupled dynamical systems will completely synchronize, or become “coherent”, is often of great applied interest. Previous work has established conditions for local stability of coherent solutions and global attractivity of coherent manifolds in a variety of spatially explicit models. We consider models of communities coupled by dispersal and explore intermediate regimes in which it can be shown that states in phase space regions of positive measure are attracted to coherent solutions. Our methods yield rigorous and practically useful coherence criteria that facilitate useful analyses of ecological and epidemiological problems.     

Correlative coherence analysis: variation from intrinsic and extrinsic sources in competing populations

The concept of the correlation between two signals is generalized to the correlative coherence of a set of n signals by introducing a Shannon-Weaver-type measure of the entropy of the normalized eigenvalues of the n-dimensional correlation matrix associated with the set of signals. Properties of this measure are stated for canonical cases. The measure is then used to evaluate which subsets of a particular set of n signals are more or less coherent. This set of signals comprises extrinsic, stochastic resource inputs and the population trajectories obtained from simulations of a discrete time model of competing biological populations driven by these resource inputs. The analysis reveals that, at low levels of competition, the correlative coherence of the combined system of intrinsic population and extrinsic resource variables is relatively low, but increases with increasing variation in the resources. Further, at intermediate and high competition levels, the correlative coherence depends more strongly on competition than entrainment of stochasticity in the extrinsic resource variables. Density dependence has the effect of amplifying variation in noise only when this variation is relatively large. Also, chaotic systems appear to be entrained by sufficiently noisy environmental inputs.