A morpho-density approach to estimating neural connectivity.

Neuronal signal integration and information processing in cortical neuronal networks critically depend on the organization of synaptic connectivity. Because of the challenges involved in measuring a large number of neurons, synaptic connectivity is difficult to determine experimentally. Current computational methods for estimating connectivity typically rely on the juxtaposition of experimentally available neurons and applying mathematical techniques to compute estimates of neural connectivity. However, since the number of available neurons is very limited, these connectivity estimates may be subject to large uncertainties. We use a morpho-density field approach applied to a vast ensemble of model-generated neurons. A morpho-density field (MDF) describes the distribution of neural mass in the space around the neural soma. The estimated axonal and dendritic MDFs are derived from 100,000 model neurons that are generated by a stochastic phenomenological model of neurite outgrowth. These MDFs are then used to estimate the connectivity between pairs of neurons as a function of their inter-soma displacement. Compared with other density-field methods, our approach to estimating synaptic connectivity uses fewer restricting assumptions and produces connectivity estimates with a lower standard deviation. An important requirement is that the model-generated neurons reflect accurately the morphology and variation in morphology of the experimental neurons used for optimizing the model parameters. As such, the method remains subject to the uncertainties caused by the limited number of neurons in the experimental data set and by the quality of the model and the assumptions used in creating the MDFs and in calculating estimating connectivity. In summary, MDFs are a powerful tool for visualizing the spatial distribution of axonal and dendritic densities, for estimating the number of potential synapses between neurons with low standard deviation, and for obtaining a greater understanding of the relationship between neural morphology and network connectivity.

Ranking network of a captive rhesus macaque society: a sophisticated corporative kingdom.

We develop a three-step computing approach to explore a hierarchical ranking network for a society of captive rhesus macaques. The computed network is sufficiently informative to address the question: Is the ranking network for a rhesus macaque society more like a kingdom or a corporation? Our computations are based on a three-step approach. These steps are devised to deal with the tremendous challenges stemming from the transitivity of dominance as a necessary constraint on the ranking relations among all individual macaques, and the very high sampling heterogeneity in the behavioral conflict data. The first step simultaneously infers the ranking potentials among all network members, which requires accommodation of heterogeneous measurement error inherent in behavioral data. Our second step estimates the social rank for all individuals by minimizing the network-wide errors in the ranking potentials. The third step provides a way to compute confidence bounds for selected empirical features in the social ranking. We apply this approach to two sets of conflict data pertaining to two captive societies of adult rhesus macaques. The resultant ranking network for each society is found to be a sophisticated mixture of both a kingdom and a corporation. Also, for validation purposes, we reanalyze conflict data from twenty longhorn sheep and demonstrate that our three-step approach is capable of correctly computing a ranking network by eliminating all ranking error.

Computing a ranking network with confidence bounds from a graph-based Beta random field.

We address two largely overlooked, fundamental issues in computing a ranking hierarchy within a society: which information in the network is relevant, and what effect chance has on the hierarchy. To properly account for uncertainty from limited data, we construct a random field in a matrix form having entry-wise posterior Beta distributions based on a graph of pairwise conflict outcomes. To evaluate relevant network information using information transitivity, another random matrix of synthesized transitive dominance odds is computed collectively along observed dominance paths. These two matrices are coupled together to fuse both direct and indirect dominance information. An ensemble of realizations of this fused random matrix facilitates an ensemble of optimal ranking networks by means of simulated annealing. Conditional statistical inferences regarding network features are derived, manifesting the effect of uncertainty. Our computational approach is suitable for large graphs of pairwise conflict outcomes, and can accommodate tremendous data heterogeneity-a typical feature in such studies. We also demonstrate the infeasibility of the classical maximum-likelihood approach, and expose the mechanistic flaws that stem from completely ignoring relevant information residing in the graph. We analyse two real datasets of decisive conflict outcomes, the first involving college football teams, and the second involving an adult rhesus macaque society in captivity.

Coupling among electroencephalogram gamma signals on a short time scale.

An important goal in neuroscience is to identify instances when EEG signals are coupled. We employ a method to measure the coupling strength between gamma signals (40-100 Hz) on a short time scale as the maximum cross-correlation over a range of time lags within a sliding variable-width window. Instances of coupling states among several signals are also identified, using a mixed multivariate beta distribution to model coupling strength across multiple gamma signals with reference to a common base signal. We first apply our variable-window method to simulated signals and compare its performance to a fixed-window approach. We then focus on gamma signals recorded in two regions of the rat hippocampus. Our results indicate that this may be a useful method for mapping coupling patterns among signals in EEG datasets.

Slope estimation in structural line-segment heteroscedastic measurement error models.

This paper extends the line-segment parametrization of the structural measurement error (ME) model to situations in which the error variance on both variables is not constant over all observations. Under these conditions, we develop a method-of-moments estimate of the slope, and derive its asymptotic variance. We further derive an accurate estimator of the variability of the slope estimate based on sample data in a rather general setting. We perform simulations that validate our results and demonstrate that our estimates are more precise than estimates under a different model when the ME variance is not small. Finally, we illustrate our estimation approach using real data involving heteroscedastic ME, and compare its performance with that of earlier models.

Time, temperature, and data cloud geometry.

We demonstrate that the geometry of a data cloud is computable on multiple scales without prior knowledge about its structure. We show that the concepts of "time" and "temperature" are beneficial for constructing a hierarchical geometry based on local information provided by a similarity measure. We design two devices for construction of this hierarchy. Along the time axis, a regulated random walk incorporated with recurrence-time dynamics detects information about the number of clusters and the corresponding cluster membership of individual data nodes. Along the temperature axis we build the geometric hierarchy of a data cloud, which consists of only a few phase transitions. The base level of the hierarchy especially exhibits the intrinsic data structure. At each chosen temperature, we form an ensemble matrix that summarizes information extracted from many regulated random walks. This device constitutes the basis for constructing one corresponding level of the hierarchy by means of spectral clustering. We illustrate the construction of such geometric hierarchies using simulated and real data.