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1、21 May 1998 On the temporal resolution of neural activity Akira Date, Elie Bienenstock and Stuart Geman Division of Applied Mathematics Brown University Providence, RI 02912 An important issue regarding brain function is the existence and role of fi ne temporal structure in neural activity. Multi-ne
2、uronal recording techniques are now available to study this issue. We present a simple statistical method devised to detect fi ne temporal structure in simultaneously recorded spike processes.We apply this method to data recorded from monkey Supplementary Motor Area, and show a preliminary result wh
3、ich suggests that the nervous system may indeed use a temporal resolution of about 6 ms (or higher). Address for correspondence:Akira Date Division of Applied Mathematics Brown University Providence, RI 02912, USA Email:datedam.brown,edu Phone:401-863-2830 Fax:401-863-1355 INTRODUCTION There is an o
4、n-going debate about neural coding:according to some, information is carried only in the average spike frequency, while others hold that the brain may actually use the fi ne temporal structure of neural discharges. This may include various temporal relationships between spikes emitted by different n
5、eurons. Such a view stems in particular from the consideration that the brain needs to somehow bind entities and events represented hierarchically in different cortical areas (Damasio, 1989; Livingstone, 1996; von der Malsburg, 1995). If there exists a mechanism for rapidly and reversibly binding ot
6、herwise uncorrelated spatio-temporal patterns of neural activities, one could look for evidence of this binding mechanism in the fi ne temporal structure of single- and multi-neuronal spiking processes. A related, albeit more general, question is: What is the time scale used by the nervous system?By
7、 this we mean the following.Suppose we could randomly and independently perturb the time of occurrence of each spike of each neuron by a small amount; would this affect the behavior of the subject? If the perturbation is smaller than “the time scale of the brain,” nothing would change. If on the oth
8、er hand the perturbation is large enough, we expect that the subjects behavior will be affected. Since there is no way to move spikes randomly in real brains, we address this issue indirectly. We ask simply whether there is any reliably reproducible fi ne temporal structure in brains. The alternativ
9、e, which will be our null hypothesis?0, is that brain activity is completely random when looked at on a fi ne resolution. That is, the multi- dimensional spiking process of any collection of neurons cannot be distinguished from a randomly generated process which has the same properties as the origin
10、al one on a coarse time scale. Under the null hypothesis, a small perturbation couldnt possibly affect the functioning of the brain in any way. To formulate?0, we use the following model.Suppose the multidimensional 2 spiking process is an inhomogeneous Poisson process in which all fi ring rates rem
11、ain constant in time intervals of length?. (We use a fi xed, arbitrary, partition of the time axis into intervals of length? .) Other than that, the fi ring rates are themselves a multi-dimensional stochastic process, with any possible joint probability distribution. Depending on?, this model can be
12、 made completely general: if?1 ms, then the model includes all possible multi-dimensional spiking processes defi ned on the 1-ms time scale. If however, say,?10 ms, then the model makes a statement about the randomness of spiking on the fi ne, i.e., 1-ms, time scale. To reject the null with?10, we d
13、evise an appropriate statistical test. Based on an observed spike sequence from a multi-unit recording, we randomly generate many spike sequences with the same spike count, for each neuron and in each interval of length ?, as the corresponding spike count in the original sequence. We then ask whethe
14、r the originalobservation differs,in anystatisticallysignifi cant way, fromthejittered ones. The null hypothesis,?0, says that the original multi-dimensional point process actually comes from the random distribution we use to generate all these jittered processes. To reject this null, we use a stati
15、stic?, which can be any function of the process. If?computed on the original sequence is signifi cantly different from?computed on the jittered data, i.e., from the sample statistic, we reject the null and conclude that there is fi ne temporal structure in the brain on a time scale that is at least
16、as fi ne as?. Of course such a conclusion doesnt imply that the fi ne time structure is actually used by the brain or that this structure is important in any way. Such structure could be an epiphenomenon of the dynamics of interconnected neurons. Also, the mere existence of a refractory period will in some cases allow us to reject?0for the spiking activity of a single neuron. Alternatively, we may reject the null because the activities of the recorded neurons are all time-locked to an ext
