Populations of cortical neurons exhibit shared fluctuations in spiking activity over time. When measured for a pair of neurons over multiple repetitions of an identical stimulus, this phenomenon emerges as correlated trial-to-trial response variability via spike count correlation (SCC). However, spike counts can be viewed as noisy versions of firing rates, which can vary from trial to trial. From this perspective, the SCC for a pair of neurons becomes a noisy version of the corresponding firing-rate correlation (FRC). Furthermore, the magnitude of the SCC is generally smaller than that of the FRC, and is likely to be less sensitive to experimental manipulation. We provide statistical methods for disambiguating time-averaged drive from within-trial noise, thereby separating FRC from SCC. We study these methods to document their reliability, and we apply them to neurons recorded in vivo from area V4, in an alert animal. We show how the various effects we describe are reflected in the data: within-trial effects are largely negligible, while attenuation due to trial-to-trial variation dominates, and frequently produces comparisons in SCC that, because of noise, do not accurately reflect those based on the underlying FRC.

We investigate the problem of conditional dependence graph estimation when several pairs of nodes have no joint observation. For these pairs even the simplest metric of covariability, the sample covariance, is unavailable. This problem arises, for instance, in calcium imaging recordings where the activities of a large population of neurons are typically observed by recording from smaller subsets of cells at once, and several pairs of cells are never recorded simultaneously. With no additional assumption, the unavailability of parts of the covariance matrix translates into the unidentifiability of the precision matrix that, in the Gaussian graphical model setting, specifies the graph. Recovering a conditional dependence graph in such settings is fundamentally an extremely hard challenge, because it requires to infer conditional dependences between network nodes with no empirical evidence of their covariability. We call this challenge the "graph quilting problem". We demonstrate that, under mild conditions, it is possible to correctly identify not only the edges connecting the observed pairs of nodes, but also a superset of those connecting the variables that are never observed jointly. We propose an 1 regularized graph estimator based on a partially observed sample covariance matrix and establish its rates of convergence in high-dimensions. We finally present a simulation study and the analysis of calcium imaging data of ten thousand neurons in mouse visual cortex.

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It is now common to record dozens to hundreds or more neurons simultaneously, and to ask how the network activity changes across experimental conditions. A natural framework for addressing questions of functional connectivity is to apply Gaussian graphical modeling to neural data, where each edge in the graph corresponds to a non-zero partial correlation between neurons. Because the number of possible edges is large, one strategy for estimating the graph has been to apply methods that aim to identify large sparse effects using an [Formula: see text] penalty. However, the partial correlations found in neural spike count data are neither large nor sparse, so techniques that perform well in sparse settings will typically perform poorly in the context of neural spike count data. Fortunately, the correlated firing for any pair of cortical neurons depends strongly on both their distance apart and the features for which they are tuned. We introduce a method that takes advantage of these known, strong effects by allowing the penalty to depend on them: thus, for example, the connection between pairs of neurons that are close together will be penalized less than pairs that are far apart. We show through simulations that this physiologically-motivated procedure performs substantially better than off-the-shelf generic tools, and we illustrate by applying the methodology to populations of neurons recorded with multielectrode arrays implanted in macaque visual cortex areas V1 and V4.

An integrative approach based on morphological and genetic analyses was undertaken for the first time to confirm the species identification of Mediterranean samples belonging to the genus Tremoctopus. Sequences of two mtDNA genes (cytochrome c oxidase subunit (COI) and 16S) were generated for the first time from Mediterranean samples. Both the similarity-based identifications and tree-based methods indicated that three females can be identified as Tremoctopus violaceus sensu stricto in agreement with their morphological classifications. All Mediterranean sequences clustered with the sequences of Tremoctopus violaceus from the Gulf of Mexico and were clearly differentiated from the sequences attributed to T. gracilis and T. robsoni. The chromatic pattern of the web and some features of gill filaments, arms formula, stylets, radulae, beaks, and stomach contents were given for all the samples; 105,758, 20,140, and 11,237 oocytes were estimated in the mature, immature, and developing samples, respectively. The presence of four spermatangia inside the cavity of the maturing female suggested the ability of this species to mate before reaching full maturity with more partners. Age investigation using beaks, performed for the first time in T. violaceus and within the genus gave results consistent with the different sizes and maturity conditions of the samples.