Method for detecting synchronicity between several digital measurement series with the aid of a computer

Abstract

The method makes it possible to determine synchronicity of several measurement series which consist of binary frequency data, in order to detect redundancy between several neurons. In this case, every possible combination of synchronicity has its own occurrence probability.The synchronicity is detected by measuring a discriminating significance, which tests a null hypothesis with a surrogate method.One possible application is the detection of neuronal coding patterns in the brain.

Description

BACKGROUND OF THE INVENTION

The invention relates to a method for detecting synchronicity between several digital measurement series with the aid of a computer.

When presented with measurement data given by time series, which for example originate from different neurons, then it is of great interest to know with what probability synchronicity occurs between the various possible combinations of the binary signals of the time series.

FIG. 1 serves as an illustration. It shows three time series ZR1, ZR2 and ZR3 by way of example. These time series may for example originate from different neurons or, in general, represent arbitrary binary frequency data. The order O is defined as being how many times series are taken into account for the synchronicity. In FIG. 1, the order O is equal to 3. For all possible combinations of the 3.sup.rd order binary groupings occurring in the example, a probability of synchronicity should thus in each case be given. Thus, FIG. 1 indicates by way of example a combination Pat1 (011) which occurs two times.

The reference by T. M. Cover, "Elements of Information Theory, John Wiley & Sons, 1976, pp. 18-23, ISBN 0-471-06259-6, discloses a method for determining a discriminating statistic.

SUMMARY OF THE INVENTION

The object of the invention is to provide a method for detecting synchronicity between several digital measurement series, the method being suitable in particular for detecting neuronal coding patterns in the brain.

The method formulates a nonparametric statistical approach for detecting redundancy between several digital measurement series. A relevant concrete example involves the synchronous firing of several neurons. The synchronicity is detected by measuring a discriminating significance, which tests a null hypothesis of independent firing with a surrogate method. The surrogate data used correspond to the null hypothesis of a noncausal relation between the firing or the nonfiring of several neuron groups. Rejection of the null hypothesis is based on the calculation of the discriminating statistic .LAMBDA. of the original data record and of the discriminating statistic D.sub.si of the i-th surrogate data record which has been produced by making the null hypothesis.

As mentioned above, one refinement example of the method according to the invention may be the firing of several neurons, the number of which determines the order O, lying at the basis of the measurement series. The method according to the invention can therefore be used to solve the difficult problem of detecting neuronal coding patterns in the brain.

BRIEF DESCRIPTION OF THE DRAWINGS

The features of the present invention which are believed to be novel, are set forth with particularity in the appended claims. The invention, together with further objects and advantages, may best be understood by reference to the following description taken in conjunction with the accompanying drawings, in the several Figures of which like reference numerals identify like elements, and in which:

FIG. 1 shows illustrative measurement data of various time series;

FIG. 2 shows a block diagram which represents the steps of the method according to the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 indicates three different time series ZR1, ZR2 and ZR3 by way of example.

Generally, the order O is determined by the maximum number of "1s" occurring. In relation to an application example, the "1s" may be interpreted as the firing of a neuron. There are generally 2.sup.O different combinations in the case of O binary measurement series. In the example, the order is equal to three and there are eight different binary combinations. This example which is represented in FIG. 1 is continued in FIG. 2 in order to explain the method according to the invention.

FIG. 2 represents a block diagram which contains the individual steps of the method according to the invention. With the aid of different measurement series, which may originate from neurons, a real occurrence probability for each different binary combination is calculated (see step 2a). This probability P is given as ##EQU1##

In relation to the example represented in FIG. 1, this means calculating the probability P for all possible binary combinations of the corresponding order, that is to say for the triple

{(000), (001), (010), (011), (100), (101), (110), (111)} (3)

A discriminating statistic .LAMBDA. is given by the T. M. Cover reference as (see FIG. 2, step 2b):

.LAMBDA.=R(x,z.vertline.y)-R(x,z), (4) R(. . . ) denoting a redundancy, x,y,z denoting an i-th order tuple consisting of the values of the measurement series.

The formula (4) indicated here can be logically extended for higher-order discriminating statistics.

The null hypothesis P* is determined in step 2c according to ##EQU2##

To explain formula (4) above, it may be mentioned that when there is an odd number of "1s" in the tuple, the sign is negative, otherwise it is positive.

The pertubation variable w will be determined below such that the discriminating statistic .LAMBDA. gives a null result from the null hypothesis, i.e.

.LAMBDA.(P*)=0 (6),

With the condition that the pertubation variable w lies in a range

W.sub.min <w<w.sub.max (7a) it being in this case necessary to respect the condition 0<P* (1.sub.A)<1.A-inverted.A (7b) 1.sub.A denotes all possible permutations of "1s" in a tuple with power .vertline.A.vertline.. Additionally, a constraint is imposed according to the sum of all occurrence probabilities of the null hypothesis: ##EQU3##

Using the null hypothesis P*, surrogate data records, i.e. arbitrary instances of the null hypothesis condition, are determined by random generator (step 2d). Expressed a different way, "dice are thrown" for the measurement series, the "die" having the occurrence probability fixed by the null hypothesis for each possible combination.

The decision as to whether or not there is synchronicity, is determined by a significance S (step 2e): ##EQU4##

An advantageous application of the method according to the invention consists, as mentioned above in the use of measurement series which are based on the firing of real neurons. The method can equally be applied to any binary frequency data.

The invention is not limited to the particular details of the method depicted and other modifications and applications are contemplated. Certain other changes may be made in the above described method without departing from the true spirit and scope of the invention herein involved. It is intended, therefore, that the subject matter in the above depiction shall be interpreted as illustrative and not in a limiting sense.

Claims

1. A method for detecting synchronicity between several digital measurement series using a computer, comprising the steps of:

a) using an order to indicate a number of measurement series taken into account which are to be examined for synchronicity;

b) calculating an occurrence probability P.sub.j for different binary combination K.sub.j such that ##EQU5## c) determining a discriminating statistic .LAMBDA. depending on the order given in step a);

d) forming a null hypothesis, P*, such that ##EQU6## e) looking up a perturbation variable w such that

.LAMBDA.(P*)=0

W.sub.min and W.sub.max being defined such that

0<P* (1.sub.A)<1.A-inverted.A

with the constraint ##EQU7## f) determining surrogate data records, which are arbitrary instances of a condition of the null hypothesis P*:

g) determining, for establishing existence of synchronicity, a significance S such that ##EQU8##

2. The method as claimed in claim 1, wherein time series of different neurons are used as the digital measurement series.