An EXPERIMENT on acquisition of information through non conventional channel
 


M. Bruschi
Phys. Dept.-University "La Sapienza"
Ple A. Moro 2- 00185 Roma - Italy
Phone: **39-6-49914303
Fax: **39-6-4957697
E-Mail:
bruschi@roma1.infn.it
bruma@pcg.telpress.it
Home-page:
http://www.roma1.infn.it/~ragnisco/bruma.htm
 


Abstract

The results obtained in an experiment on extrasensory perception result highly non - casual: the possible existence of a phenomenon of acquisition of knowledge through non conventional channels is suggested.
 


Introduction

In this experiment tests of clairvoyance and telepathy were done (the meaning of this terms will be defined more explicitly later on). The experiment was done, in more sittings, in the center of the 'Gruppo Ricerche Futuro - Dimensione Y' . For the tests a group of 50 people (who followed for a year a course held by Umberto Di Grazia to develop ESP) were used; apart from this common denominator the group is quite heterogeneous in terms of age, education, sex, profession etc. The tests (not quite innovative in concept) where projected and carried out by the author himself.
In the Section 2 of this work the PROTOCOLS used for the various TESTS, will be described in detail, in Section 3 the results will be reported, statistically evaluated and discussed and in Section 4 the conclusions of the author will be exposed
 


2 - Protocols

PIn order to describe in detail the protocol adopted, it is useful to divide the tests into the following categories:

Tests of clairvoyance (CT)
Tests of telepathy (TT)
CT tests are then subdivided in:
CT with present target (CT - P)
CT with remote target (CT - R)
CT of mathematical type (CT - M)
TT tests have the following subdivision:
TT with present transmitter (TT - P)
TT with remote transmitter (TT - R)
TT nocturnal (TT - N)
 


_______ PROTOCOL CT-P _________

a) Ten small object are chosen and taken by the author in his home.
b) A list is then given to the computer that orders the items by a random procedure.
c) Still with random procedure, an object on the list is chosen by the computer.
d) The object is then wrapped in news papers ( to avoid movements and sounds ) and put in a cardboard box (usually a shoe box) and sealed with parcel tape.
e) The printed list is closed in a non - transparent envelope, and the envelope is closed. These operations are done in the house of the author at least 2 hours before the test is done and with nobody present; for a better visualization of the procedure (see A1 where there is one of lists used for the tests).
f) The box is taken by the author to the Center and put within view of the subjects that are sitting in a single room.
g) The subject are given five minutes to "visualize" the object contained in the box (Target); the author remains in the room, sitting near the box.
h) The subject are told to fill the first part of the module PVK1 (see A2) describing what they "saw" and the personal mental associations. NOTE 1 These data, although not directly usable and in fact not used in the statistical elaboration of the results, could give useful indications/clues to better understanding of the phenomena (if any) and for a better project of future experiments (if any). Only a small recognition of this material has been done. NOTE 2 We chose to give subjects the privilege of anonymity: the modules are signed with a personal nickname -using letters and numbers (e.g. Minnie465), for a future identification.
i) The closed envelope, with the list of the ten objects, is then given to Umberto Di Grazia (UdG),while the author goes away from the sight of the subjects, as not to give unconscious subtle clues on the target (please remembers that the author is the only one to know the content of the box).
l) Umberto Di Grazia writes on a blackboard the list of possible targets and gives voice to a small description of them (see A2)
m) Subjects are invited to write in the slot at the and of module PVK1 (see A2) the name of the target.
n) The modules are collected by the author.
o) The author, after having checked integrity, opens the box and show the target (in order to satisfy the curiosity of participants).


__________ PROTOCOL CT-R __________
 

a) As before.
b) As before.
c) The computer is programmed to randomly choose an object from the list, to visualize the name on the screen and then to print it; all of this is programmed to happen after the author has left the house (that is empty and locked) and just before the test is under way: in other words as the test is being done, the target has been (just) chosen , but no one knows what it is.
d) The objects are put in place on the table in front of the computer.
e) As before.
f)g) The subjects are invited to visualize the objects on the table in the author's house (above 15 Km. from the Center) and to 'read' the name of the target on the computer screen.
h) As before.
i)l) Operations previously described in CT-P are now performed by the author, as this time he does not have knowledge of the target and can give, if asked, a more detailed description of the objects on the list.
m) As before.
n) As before.
o) The name of the target, as seen by the author on his return home, will be communicated to the subjects during the next session.
 


__________ PROTOCOL CT-M _________

a) The author decides on a code of association between 10 numbers (to choose between 0 - 100, extremes excluded) and the transcendent number ?. The code adopted is the following: if the kth number is <ji> then i should be the j + 1 figure of ? to the power of k (example: if 35 is the 7th of the 10 numbers, then 5 should be the third digit of ? to the 7th power). If the numbers has only one digit then comparison had be taken with the 10th digit of the corresponding power (example: if thesecond number is 5, 5 should be the 10th digit of ? to the second power).
b) The subject are asked to write in sequence 10 numbers between 1 and 99, extremes included, while thinking of the transcendent number??.
c) The modules are collected and the test repeated as in a) and b) with the transcendent Nepernumber e.
d) The results (total number of successes compared to the expected number) are communicated in the following session. The code is still not revealed. NOTE 3
The code indicated above is de facto used in only one test, variations of the same have been used for the other three CT - M test.
It is worthwhile to note that a greater maturity of subjects, even if they vaguely remembered ? , did not know the Neper number e nor the concept itself of transcendent number.


__________ PROTOCOL TT-P __________

a) Ten 'names' are selected by the author; the names can be that of concrete object (eg. apple, Venice) and of abstract qualities (eg: beauty, harmony): the only criterion held is that of avoiding as much as possible couples/doubles that can be connected by associative bonds (eg: sun - light, water - rain, snow - white, etc.) (see the lists A1 and A3).
b) The names are put in a random sequence by the computer.
c) The list is printed and closed in an opaque envelope, which is sealed.
d) The preceding steps are done by the author on his own and in his house, about two hours before the test is done.
e) The subjects are gathered in a room waiting for the transmitter. - The transmitters used are two: he author (TT - P - M) and Umberto Di Grazia (TT - P - U).
f) The transmitter, before entering the room where the receiving subjects are already gathered, open the envelope with the list and chooses the target to be transmitted using a random procedure (in fact, either extracting slits of paper with the names or throwing a dice with 20 faces and associating the second figure that appears with the name on that position on the list (e.g. if appear the number 13, then the target is the number 3 on the list); the list is then sealed again in an opaque envelope.
g) The transmitter enters the room and sits in front of the receivers and mentally transmits the target for about 3 minutes.
h) The receivers are told if they want to draw their impressions in the special space in the module MTK 1 (see A4 and NOTE 1 )
i) The (active) transmitter (t1) gives in the envelope with the list to the other transmitter (t2- the one that in this occasion had not transmitted and therefore ignores the target), then leaves the room .
l) t2 opens the envelope and writes the possible targets on a blackboard.
m) The receivers are told to write in the appointed space on the MTK 1 module the name of the target that, in their opinion, has been transmitted.
n) The name of the target effectively transmitted is communicated only after the modules have been taken into custody by the author (see later).
 


__________ PROTOCOL TT-R __________

 

a)b)c)d) as in preceding protocol
c) A computer program is set up so that at the time appointed for the test, a target among ten is chosen with a random procedure and visualized iteratively on the screen and printed simultaneously on the printer (with a procedure lasting 5 minutes). These operations happen at the author's house, while he is at the Center with the receiving subjects; the house is closed and empty; all, including the author, are unaware of the target.
f) The subjects are asked to receive a target transmitted by a friend of the author that is being transmitting from 15 Km away; the receivers ignore that it is but the computer that is transmitting (!)
NOTE 4
In fact still now the subjects ignore that the remote transmitter was in fact a computer.
g) 3 minutes are allowed to receive (the target).
h) as in the proceeding protocol.
i)l) The author writes on the blackboard the list of the possible targets.
n) The name of the target is communicated during the next session (Sec. also NOTE 4).
The TT - P - M, TT - P - U and TT - R tests are generally done in succession during the same session, hence the module MTK 1 has three targets.


_________ PROTOCOL TT-N ___________

a)b) as in protocol TT - P
c) The list is given to the subject.
d) It is explained to them that the author will transmit to them every night a target randomly chosen from the list.
e) The subjects are asked to write every morning on awakening, as concluded from their dreams and/or on their impressions, the target received .
 


3 - Result and valuations

The results for the CT-P, CT- R, TT- P-M, TT-P-U, TT - R tests are shown on figs. B 1 - 16, where it has been chosen to show not only the exact answers but also to show the spread of all the answers on all possible targets.
In Table C the results are summarized for quick reading, while in Table D the global results of tests CT-M, TT - N are shown.
Before going on to the evaluations, two comments are necessary regarding tests TT - N and CT-R in (B 15) and (B-16).
The author decided to include for the sake of completeness, even if, although for different reasons, they are indeed anomalous. With regard to the TT-N, even though they were scheduled for 21 consecutive days, on a selection of 39 people, only 181 answer were given to the author (compared to the 813 predicted) and none of these are to be trusted as many subjects have declared that they did not stick to the procedure described in Protocol TT-N; many of the subjects that, forgetting to write down the target each morning, did so later, retrospectively, at times after several days (some actually filled in the answers at the end of the test period, at the end of the 21 days!). With regards to CT-R (B 15 -16) the author has to specify that the protocol CT-R in these 2 cases was not entirely followed; the essential differences are:
i) The author and the selected objects were 250 Km. away from the Center.
ii) The list was revealed by telephone before the test, to Umberto Di Grazia who then put into act the procedures f) and n) of the protocol (these are then the only tests done without direct super-vision of the author).
iii) because of an unpredictable event, the author did not chose the target at the appointed hour of the test (B16) but an hour after the test was done; also because for another unpredictable situation the usual random section of target operated by computer was substituted, at the last minutes, by throwing a 20 faced dice:
iiii) Anyway the name of the target was communicated to the subjects only after the test modules where taken by the author.
 


VALUATION

Obviously, after having taken all reasonable precautions so that the subjects could not know beforehand (at least by normal means) the right answers (see Protocols), one should expect that the successes obtained (the right answers) be due only to chance; so now we will try to evaluate if this has actually happened.
Having made sure that for each test there are 10 objects to be chosen from, the probability for guessing (by chance) the real target is p = 1/10; the probability of guessing (by chance) n times every N tries is obviously given by the binomial distribution, therefore:(1)



you have M successes is:(2a)



with: (2b)



NOTE 5 - In the following, we will refer to the probability pc as "probability of chance" while the complementary pnc will be spoken of as "probability of non chance"
The results are shown in TAB. E

NOTA 6 - Two other useful indicators are: the number of successes expected



and the "standard deviation"



the first one can be easily recovered in each fig. B, the latter is reported in Table C and in Table D. Are they or are they not casual results? A look at Tab. E should leave no doubts, the subjects have guessed more then could be rationally predicted with the hypothesis that only chance is at work. More in detail, it is worthwhile to notice that the worst results are obtained in tests TT-N and CT-R of B - 16, for which the before - hand considerations are valid; for the rest, the global results that of 'clairvoyance' tests (CT) and 'telepathy' tests (TT) are comparable; it is also interesting to notice that the (a lot ) more significative tests are those in which a remote target is used (even including doubt B-16), therefore the very tests whose protocol seems the most irreprehensible (at least to the author).

Even not being able or wanting to try here a Parapsychological evaluation and interpretation of the obtained results, some considerations however can be made:

a) · in the field of parapsychology, events with a probability of chance (see Note 5 ) in the order of 1 percent are already considered significative (i.e. 'proof' of extra-sensory activity, see [1] [2] [3]) : our results are much over this threshold , they are indeed far beyond the best results obtained in single experiments (pc <1/10000, see [3] [4]): of course Umberto Di Grazia attributes this to the specialties of the subjects that, we remind you, had been trained to develop ESP;

b) · the results of CT-R, CT-M and TT-R seem to indicate that the traditional divisions between clairvoyance and telepathy need to be reviewed, what seems to be happening seems to be the capability to get information in a non - standard way, or, as already noted by other researches [5] the capacity to have success in a way that is independent from experimental conditions (this should justify A POSTERIORI the little care taken in the protocols to distinguish phenomena of pure telepathy from those of pure clairvoyance).

c) l· the exceptionality of the results obtained, has brought the author to postpone a possibly useful study of ways to optimize the experimental modalities (e.g.: are 10 targets too dispersive ? what is the optimal time of transmission? Is there an optimal distance between receiver - transmitter? etc.).

Apart from the considerations reported in the next Section, all alternative explanations of the obtained results are well accepted.
 


Criticism

It is worthwhile to discuss here some objections given with regard to the protocol and/or the statistical treatment of the data.
The first criticism is the following:
· As the subjects are each time gathered in a single room, and they can communicate among themselves, is not plausible, even inevitable, that there should be a correlation between the given answers? Would this effect not be such that, lowering the degrees of freedom or number of possible answers effectively independent for a single test, the results would be back into the limits of casualness/randomness/chance (say within 2 standard deviations of the expected value)?
To answer to this abjection let us calculate how big the correlation coefficient should be so that this could be happened (i.e. we try to evaluate the average number of people that give a group rather that personal answers). Let us suppose that the correlation coefficient is r; then the total number of tries N, the number of successes (hits) n, the deviation ??from the expected number of successes (N*p), the standard deviation ??(see Note 6) needs to be corrected as follows

(3) N'=N/r

(4) n'=n/r

(5) D'= n'-N *p

(6)

then: (7)



Even considering only the data more subject to correlation distortion, therefore excluding CT-M and TT-N, we have:
7,16,6
Then, if we want '= 2, there should be a correlation coefficient of r = 9, it means that every 33-34 people participating (on average) to the test only 3 - 4 answers should emerge from each test: this is denied by figs. B 1 - 16. The obtained correlation coefficient r = 9 is illogical in any case: a level of communication such that a third of the group is involved, would not have been over-looked by the author.
Even supposing ?'= 3 ( but in this case the results would be again significative) the correlation coefficient would be r = 5; again this index, for the above mentioned reasons, is in our opinion too high. Indeed, putting together personal experience of the experimental conditions and psychology of the subjects (who used to distinguish themselves rather than hide in a crowd), the author thinks that the correlation coefficient should not be over 1.5; but even admitting r = 2, we would have ?'= 4.24 and the results would still be highly non-casual.
The second criticism [7] is in reality a multiplicity of objections:

 

i. the protocols are too many, needlessly complicated and not
precise: it would have been better to have just one, simple and such that
the results could be compared to extreme possibilities (such as fraud, strategies
put in action by the subjects doing the test, see later on);
ii. as the protocols and test modalities are so varied, it is not correct
to aggregate the results: each test should be treated statistically apart
from the other;
iii. the author has not considered the possibility that the subjects could
have agreed on some strategy that could bring up the significance of the eventual
(casual) successes. For example, if in each test the answers were premeditatively
distributed uniformly on half of the possible targets, the casual distribution
would still be a binomial one but with p = 1/2: then to evaluate the results
using p = 1/10 ( as above, in the hypothesis that, having the subjects no
information, the answers would be distributed with equal probability on all
possible targets) would be wrong and would bring to a heavy over-estimate
of the probability of non chance.

Lets try to answer point by point. With regards to

i) we can convene on the
usefulness of using a unique protocol in future experiments: however the choice
of varying as much as possible the tests, seemed reasonable for two reasons:

· this experiment was thought as a preliminary one, just to pick out the workplan for future experiments: hence the variety of procedures adopted;
· in all literature on paranormal [1,2,3] there is an empirical law (many times verified by the researchers in this field), that the answer curve, during the course of an experiments, after an initial peak tends to a rapidly decline (tiredness, boredom, less interest and attention ?) to then raise again toward the end of the experiment. It seemed opportune to try to avoid this fall by keeping the interest and motivation up by having a weekly interval between varied tests.
With regards to the safety of the protocols, the author thinks that a good standard has been adopted and maintained (not a paranoiac one!): if, as auspicable, the experiment shall be repeated, any suggestion to keep up the standard (presence of conjurers, etc.) will be well accepted.
Objection ii) does not seem founded; it would be valid only if we were measuring different quantities (telepathy, clairvoyance, etc.); as the purpose of the experiment is to see in what measure the results are given by chance, from this point of view the various tests are perfectly equivalent (save the diverse degree of safety of the protocols, see above).
The last objection seems to be the most relevant; expressed in other terms, it raises again the problem of the correlation of experimental data; should be there a voluntary correlation, the reasonings done before would loose good part of their value.
A problem is posed in how to evaluate the probability of chance correctly, not based on a priori hypothesis, but on the data themselves, whatever correlation is present: fortunately this can be done and the method that we will use is "standard" in experimental physics.

Consider the data from the 16 tests in fig. [ B 1-16 ] and build with these the matrix T which contains in the element T(j,k) the number of answers given in the jth test on the kth target (eg. T(2,5) = 12 means that in the second test the target 5 was chosen 12 times).

Then build all the possible sums S:: (10)



where is a certain element in the column k( j ) of the row j: in other words for every row (test) of T we choose an element and we sum these 16 chosen elements to obtain S, this is done in all possible ways. The total number of possible S is obviously: :

(11) N(S) = 10**16

The values of S theoretically run from 0 to M(S), with : (12)



where m( j ) is the number of people that have participated to the jth test; in our case, as we can see from Table C, we have M( S ) = 570
Let us now call S(T) the particular value of S obtained choosing the elements in T corresponding to the real targets( from Table C, it is seen that in our case S( T ) = 99), then the probability of chance is estimated as

(13) Pc= n (ST)/ N(S)

where n(ST) is the number of the sums S having a value greater than (or equal to) the total number of successes S(T); N(S) is the total number of the S (see above).
Its easy to convince oneself that this way of calculating pc directly from the data keeps track automatically of each eventual correlation between the data themselves (the effect of this correlation is to enlarge the curve of distribution of the number of S versus the interval [ 0 - M(S)] of the values taken by S, making less the estimated value of pc as the correlation becomes bigger).
Unfortunately the value N(S) in our case is so high as to make it impossible to obtain, in reasonable time, the exact computation of pc even using the fastest (available) computers. It is necessary then to obtain an estimate of pc using a sample that represents sufficiently well the totality of the S's; therefore 10.000.000 randomly chosen sums S have been calculated; the stability controls, done every 500.000 S, and the good matching up of the mean value calculated from the sample with the real one (vm = 570/10), have convinced us that the sample is sufficiently representative for our purposes.
In Figure C1 the histogram of the sample is reported with the values of S on the abscissa and the number of the thousands of S that have taken these values on the ordinate (the value of S(T) is also given); in Figure C2 the same graph is shown in logarithmic scale to emphasize the tail of the distribution: finally from the sample itself the values of the mean value vm have been calculated, as well as the standard deviation and obviously pc (according to the above formula (*)).
Results are :

(14)vm = 57,00

(15) s = 9,84

(16) Pc = 5,42 . 10-5

The first thing to stress is that the above probability of chance pc , although it is 3 orders over that which had been calculated according to the binomial distribution with p=1/10 ( see Table E, tot. 1+ 2), is still very small. (moreover the deviation of the number of successes S(T) from the mean value vm goes over 4.26 standard deviations): so the results obtained are still significatively non casual.
It is interesting to note that the correlation coefficient r estimated from the sample, i.e. the value of r that allows to obtain from binomial distribution the actual pc (see above), results as r ~ 1.8, therefore a bit higher than that predicted in the previous discussion. This could be partly due to a kind of paranormal correlation; in fact admitting for a moment the existence of the phenomenon, it's clear that although we have done our best to choose targets the more possible different, some resonance's are inevitable [consider f.i. the test, TT-P-M, whose targets are listed in A3 and the results in fig. ( B1 ); the target transmitted was 'stars', but let us admit that one of the receivers perceived it not as 'luminous ray' (as for ALFA 333, see A4) but as 'space', 'sky', 'high over the earth', then a natural correlation raises with the target 'to fly' (see Fig. B-1; certainly it would be more difficult to explain the 'resonance' with the target 'tree' that also is there...).
However, admitting the existence of a measurable phenomenon, another more important consideration needs to be made: the method used above to estimate the value of pc, is certainly correct whatever correlation is present, nevertheless there one supposes that the results are due only to chance and within this hypothesis the possibility of obtaining the result S(T) by chance is evaluated. But, admitting the existence of a non casual 'signal', (and the smallness of pc itself authorizes this hypothesis), then the method used above is essentially wrong and substantially pessimistic. In fact with that, the non casual signal is mixed with the casual background noise, raising this last in a exaggerated way and producing an over-evaluation of this last pc itself. For a correct treatment of the data, it is necessary to take out the 'signal' and measure only against the casual background noise the probability of obtaining ( by chance) the result which was obtained: therefore it necessary to cancel from the matrix T the elements corresponding to the real targets. That done, the above described procedure is again applied, this time calculating a random sample of 250.000.000 S; the results are plotted in D1 and D2 (that are the corresponding of C1 and C2).
The new values vm, ? and pc are:

(17)vm = 47,01

(18)s = 9,21

(19)Pc = 1,16 . 10-7

Note the stability of s, the slight lowering of vm and especially the very evident lowering of pc (more then 2 orders with respect the previous evaluate value, this new value is very near to that that can be obtained by binomial distribution from data in Table C, pc = 0.5· 10-7 ).
All this suggests that:
1) The correlation of data (as a result of some strategy or casual) is in fact negligible (correlation coefficient <1.2)
2) An evident 'signal' above the background has been effectively detected and measured: translating (rather freely) into words the results of the above statistical treatment, we can say that even taking into account fluctuations of 2 standard deviations from the background, of 35 people that on average have participated to the single tests, on average from 2 to 4 people have guessed the right target not by chance.
 


4 - CONCLUSIONS

The personal position of the author with regards to ESP and/or the so-called paranormal is that if these phenomena of ESP (or anyway phenomena that are apparently unexplainable to the light of actual knowledge) exist, then it is task of Science and in particular of Physics to study them.
The fact that no serious try has been made in this sense but in fact the greater part of the scientific community is orientated towards an evident and at times aprioristic refusal to work in this field (and even to discuss) is caused by a widespread conviction that no evidence has ever emerged with regards to these phenomena; this in spite of the great quantity of experimental data accumulated in half century and the related statistical evidence of non-chance, emerging from their treatment, that even the more obstinate opposers cannot disavow (8).
This experiment was born from the curiosity of the author to verify by his own hand these statistical data , having the opportunity to use a group of subjects that, because of the training received, could be considered (hopefully) above norm, but that was far from the limits of 'psychic professionalism' ( with all that goes with it - see [ 8 ]).
The experiment itself, although carried out with maximum care, was conceived as a preliminary one, to further select the group of subjects, and sharpen the protocols and/or have suggestions for other tests and experiments.
However, the very (unexpected) amount of success obtained, suggests than one should repeat the experiment, maintaining the experimental conditions unaltered as much as possible, may be with supervision and control by others members of the scientific community (possibly more competent in this field than the author is). The intervention of the new - constituted Scientific Committee of Control on the Paranormal Claims would be desirable.
The author is well aware of the problem of the problem of repeatability in this field (see [1 - 3 ], [ 8 ]), but let us remark that even phenomena of 'a single event', with probability of non-chance smaller then the present, are actually considered in Physics (see f.i. the recent detection of gravitational waves generated by a Supernova); also even in Physics the concept of repeatability itself is now at the center of controversies and discussions (see the cosmological theories and the very recent events connected with Cold Fusion).
A critical analysis on what is Science and what is not, is here clearly unproposable and impracticable, still a few simple considerations do not seem out of place. We could define, according to Galileo, the scientific method as 'the art of asking questions to Nature and listening to the answers'. Certainly the existence of consolidated theories and scientific praxis helps to ask the 'right' questions and to interpret the answers 'correctly': but it is true at the same time that a strong conditioning is given on what type of questions need to be asked and what kind of answers should be expected. In fact, many of the great, sudden and unexpected progresses of science are given by the courage (often of outsiders) and to ask unusual questions and to accept unexpected answers.
The question formulated in this experiment is certainly unusual (as compared to the official science's criteria); the answer certainly should be confirmed but, if (actually) confirmed, the scientific community would have to find the courage to accept that the acquisition of information through unconventional channels is possible and that this phenomenon can be measured. Only proving and accepting once and for all the existence of these phenomena, one can stop the eternal and frustrating starting all over again (that seems to be going on in the field of the paranormal) and one can eventually start the fruitful scientific process of accumulation that will bring a more profound understanding and possibly a theoretical explanation of the phenomenon itself.
The author, conscious of his inexperience in a field in which sometimes in the past the normal procedures and precaution of the scientific praxis revealed themselves to be insufficient (see again (8)), is ready to accept criticism, comments, suggestions. The worst thing it could happen (and probably it'll happen!) is that the obtained results shall be a priori refused and rejected by the scientific community as due, if not to fraud, to circumvention of the author by the subjects, that anonymous and for nothing, kindly accepted to subject themselves to the tests.
 


Figures & Tables