Temporally precise sequences of neuronal spikes that span hundreds of milliseconds are observed in many brain areas, including songbird premotor nucleus, cat visual cortex, and primary motor cortex. Synfire chains—networks in which groups of neurons are connected via excitatory synapses into a unidirectional chain—are thought to underlie the generation of such sequences. It is unknown, however, how synfire chains can form in local neural circuits, especially for long chains. Here, we show through computer simulation that long synfire chains can develop through spike-time dependent synaptic plasticity and axon remodeling—the pruning of prolific weak connections that follows the emergence of a finite number of strong connections. The formation process begins with a random network. A subset of neurons, called training neurons, intermittently receive superthreshold external input. Gradually, a synfire chain emerges through a recruiting process, in which neurons within the network connect to the tail of the chain started by the training neurons. The model is robust to varying parameters, as well as natural events like neuronal turnover and massive lesions. Our model suggests that long synfire chain can form during the development through self-organization, and axon remodeling, ubiquitous in developing neural circuits, is essential in the process.

We examined neural spike recordings from prefrontal cortex (PFC) while monkeys performed a delayed somatosensory discrimination task. In general, PFC neurons displayed great heterogeneity in response to the task. That is, although individual cells spiked reliably in response to task variables from trial-to-trial, each cell had idiosyncratic combinations of response properties. Despite the great variety in response types, some general patterns held. We used linear regression analysis on the spike data to both display the full heterogeneity of the data and classify cells into categories. We compared different categories of cells and found little difference in their ability to carry information about task variables or their correlation to behavior. This suggests a distributed neural code for the task rather than a highly modularized one. Along this line, we compared the predictions of two theoretical models to the data. We found that cell types predicted by both models were not represented significantly in the population. Our study points to a different class of models that should embrace the inherent heterogeneity of the data, but should also account for the nonrandom features of the population.

We present findings in an experiment where we obtain stationary ramified transportation networks in a macroscopic nonbiological system. Our purpose here is to introduce the phenomenology of the experiment. We describe the dynamical formation of the network which consists of three growth stages: (I) strand formation, (II) boundary formation, and (III) geometric expansion. We find that the system forms statistically robust network features, like the number of termini and the number of branch points. We also find that the networks are usually trees, meaning that they lack closed loops; indeed, we find that loops are unstable in the network. Finally, we find that the final topology of the network is sensitive to the initial conditions of the particles, in particular to its geometry.pattern formation ͉ self-organization P attern formation, loosely speaking, is the study of order in open dissipative systems (1); this includes dynamic selforganization, characteristic of fluid and chemical systems (2), and inhomogeneous growth, characteristic in some physical (3-6) and biological (7-9) systems. Of more recent interest, not generally categorized under pattern formation, is the evolution of complex networks (10). Although this latter study has so far focused on abstract topological issues, it may soon bear important connections with the former studies, especially as it pertains to branched (what we shall refer to as ramified) patterns used for transportation throughout nature. Indeed, several researchers have attempted to include either spatial (11, §) or flow (12) constraints to the study of complex networks. Meanwhile, efficient transportation of resources through real fractal networks was already an important insight into understanding the allometric scaling of all organisms (13,14).Another example of a transportation network, this time nonbiological, was studied in experiments on an electromechanical system (15-17), where conducting particles selforganize into dendritic patterns under the inf luence of an electric field for the purpose of collecting and transporting charge. The authors were concerned with formulating a variational principle concerning the stability of patterns in open dissipative systems. In those studies, the authors concluded that in order for the patterns to be stable, they must be (locally) minimal in dissipation. The experiment has also been studied in simulation with the idea that fractals are generated by a dynamical rule: Particles always move to regions of higher gradient in potential until they stick next to a boundary point (18). All studies simplified the system by dealing only with the two-dimensional Poisson equation, and by assuming the source of charge was independent of both space and time: ٌ 2 ϭ S(r ជ, t)͞ oil Ϸ S 0 ͞ oil , where is the electric potential, S is the source term, and oil is the conductivity of the oil medium. The limitations of these approximations are unknown. Moreover, the proof showing that the dissipation is minimal relies on showing that the potential energy is al...