Recent advances in the analysis of neuronal activities suggest that the instantaneous activity patterns can be mostly explained by considering only first-order and pairwise interactions between recorded elements, i. activity patterns than the pairwise model when applied to ensembles of 10 electrodes. Furthermore, the hierarchical model was successfully applied to a larger-scale data of ~60 electrodes. Electrode activities within clusters were highly correlated and spatially contiguous. In contrast, long-range interactions were diffuse, suggesting the presence of higher-than-pairwise-order interactions involved in the LFP peak activities. Thus, the identification of appropriate models of conversation may allow for the successful characterization of neuronal activities in large-scale networks. Introduction Multineuron firing patterns constitute a basis of neural coding, and different proposals have been made concerning their functions (Abeles et al., 1993; Aertsen and Arndt, 1993; Singer and Gray, 1995; Richmond and Gawne, 1998; Salinas and Sejnowski, 2001; Pillow et al., 2008). Recent studies in the retina (Schneidman et al., 2006; Shlens et al., 2006) and in cortical cultures (Tang et al., 2008) suggested that the probabilities of multineuron spike activities [or multielectrode local field potential (LFP) peaks] can be mostly predicted by pairwise interactions between binary activities of elements (neurons or electrodes) and, consequently, that higher-than-pairwise neuronal interactions can be effectively ignored. In theory, a network with elements can have multiple orders of interactions, from second-order (pairwise), third-order, up to (DIV), when neuronal avalanches were found (Gireesh and Plenz, 2008; Stewart and Plenz, 2008). Spontaneous extracellular activity (LFP) was sampled at 4 kHz per channel for an average of 3C5 h per condition (MC-Rack; BAY 1000394 manufacture Multi Channel Systems) against the ground electrode incorporated in the MEA, which acted as the common signal ground for all those BAY 1000394 manufacture electrodes. Light microscopic BAY 1000394 manufacture pictures taken at 1 DIV and during the first and second weeks of cultivation enabled reconstruction of the electrode locations in the cortical culture. Data from 12 cultures HNPCC1 (10C16 DIV) were used in this study. Extracting nLFP peak activity Recordings were low-pass filtered at 200 Hz with a second-order Butterworth filter for the extraction of LFPs, which exhibited sharp unfavorable peaks indicative of populace spikes (Beggs and Plenz, 2003). The threshold was set at ?8 SDs of the signal to detect significant negative peaks, and the time of the maximum excursion below the threshold was recorded as the time of the nLFP peak activity (see Fig. 1= (has BAY 1000394 manufacture a value of 1 1 or 0, indicating the presence or absence of an nLFP peak, respectively. The underlying true probability of an activity pattern is usually denoted as BAY 1000394 manufacture = (with the linear functions for the first-order and for the second-order terms), and the corresponding expected values [i.e., first-order contains electrodes, then = (has log activity level is usually given by and is given by = (clusters spanning a given electrode array. There are advantages and disadvantages associated with each type of cluster activity. The linear cluster activity most faithfully reflects the overall number of active electrodes in a cluster, but is usually computationally the most expensive. The hierarchical model with linear cluster activity has a number of parameters comparable to that of the pairwise model, which for electrodes is usually given by clusters, each of which has electrodes > 2 discrete-alphabet sizes (Amari, 2001; Ince et al., 2009). The basic framework remains the same, except that this constraints now depend on the probabilities of cluster activities taking multiple values. The set of first- and second-order probabilities must include combinations of all nonzero levels of cluster activity. For example, given two clusters should be applied. The maximum entropy problem still follows the general form of Equation 3, but includes the indicate the values of cluster activity in each cluster and is the observed probability of linear cluster activity, the parentheses on the right indicate the binomial coefficient (or the choose function), and all electrode patterns of a given cluster activity are equally likely to occur. To quantify the level of homogeneity in a cluster relative to its estimated distribution and in Equation 5; the coefficient indicates the level of conversation between the two clusters. For log cluster activity, there is one coefficient for each combination.