The Effect of Nonstationarity on Models Inferred from Neural Data

Neurons subject to a common non-stationary input may exhibit a correlated firing behavior. Correlations in the statistics of neural spike trains also arise as the effect of interaction between neurons. Here we show that these two situations can be distinguished, with machine learning techniques, provided the data are rich enough. In order to do this, we study the problem of inferring a kinetic Ising model, stationary or nonstationary, from the available data. We apply the inference procedure to two data sets: one from salamander retinal ganglion cells and the other from a realistic computational cortical network model. We show that many aspects of the concerted activity of the salamander retinal neurons can be traced simply to the external input. A model of non-interacting neurons subject to a non-stationary external field outperforms a model with stationary input with couplings between neurons, even accounting for the differences in the number of model parameters. When couplings are added to the non-stationary model, for the retinal data, little is gained: the inferred couplings are generally not significant. Likewise, the distribution of the sizes of sets of neurons that spike simultaneously and the frequency of spike patterns as function of their rank (Zipf plots) are well-explained by an independent-neuron model with time-dependent external input, and adding connections to such a model does not offer significant improvement. For the cortical model data, robust couplings, well correlated with the real connections, can be inferred using the non-stationary model. Adding connections to this model slightly improves the agreement with the data for the probability of synchronous spikes but hardly affects the Zipf plot.Comment: version in press in J Stat Mec

Inferring network connectivity using kinetic Ising models

Poster presentation</p

Mixture models for analysis of melting temperature data

<p>Abstract</p> <p>Background</p> <p>In addition to their use in detecting undesired real-time PCR products, melting temperatures are useful for detecting variations in the desired target sequences. Methodological improvements in recent years allow the generation of high-resolution melting-temperature (T_m) data. However, there is currently no convention on how to statistically analyze such high-resolution T_mdata.</p> <p>Results</p> <p>Mixture model analysis was applied to T_mdata. Models were selected based on Akaike's information criterion. Mixture model analysis correctly identified categories in T_mdata obtained for known plasmid targets. Using simulated data, we investigated the number of observations required for model construction. The precision of the reported mixing proportions from data fitted to a preconstructed model was also evaluated.</p> <p>Conclusion</p> <p>Mixture model analysis of T_mdata allows the minimum number of different sequences in a set of amplicons and their relative frequencies to be determined. This approach allows T_mdata to be analyzed, classified, and compared in an unbiased manner.</p

The Central Limit Theorem for Random Dynamical Systems

We consider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. The Central Limit Theorem for random dynamical systems is established

Statistical modelling and saddle-point approximation of tail probabilities for accumulated splice loss in fibre-optic networks

Tail probabilities are calculated by saddle-point approximation in a probabilistic-statistical model for the accumulated splice loss that results from a number of fusion splices in the installation of fibre-optic networks. When these probabilities, representing the risk of exceeding a specified total loss, can be controlled and kept low, the requirements on the individual losses can be substantially relaxed from their customary settings. As a consequence, it should be possible to save considerable installation time and cost. The probabilistic model, which can be theoretically motivated, states that the individual loss is basically exponentially distributed, but with a Gaussian contribution added and truncated at a set value, and that the loss is additive over splices. An extensive set of installation data fitted well with this model, except for occasional high losses. Therefore, the model described was extended to allow for a frequency of unspecified high losses of this sort. It is also indicated how the model parameters can be estimated from data.

Expression profiling of repetitive elements by melting temperature analysis: variation in HERV-W gag expression across human individuals and tissues.

BACKGROUND: Human endogenous retroviruses (HERV) constitute approximately 8% of the human genome and have long been considered "junk". The sheer number and repetitive nature of these elements make studies of their expression methodologically challenging. Hence, little is known of transcription of genomic regions harboring such elements. RESULTS: Applying a recently developed technique for obtaining high resolution melting temperature data, we examined the frequency distributions of HERV-W gag element into 13 Tm categories in human tissues. Transcripts containing HERV-W gag sequences were expressed in non-random patterns with extensive variations in the expression between both tissues, including different brain regions, and individuals. Furthermore, the patterns of such transcripts varied more between individuals in brain regions than other tissues. CONCLUSION: Thus, regulated expression of non-coding regions of the human genome appears to include the HERV-W family of repetitive elements. Although it remains to be established whether such expression patterns represent leakage from transcription of functional regions or specific transcription, the current approach proves itself useful for studying detailed expression patterns of repetitive regions