Excellent Potential of Geometric Brownian Motion (GBM) as

a Random Process Model for Level of Drowsiness Signals

Pouyan Ebrahimbabaie and Jacques G. Verly

Department of Electrical Engineering and Computer Science, University of Li

ege, Li

ege, Belgium

Keywords:

Drowsiness, Somnolence, Random Process, Geometric Brownian Motion, GBM, Driving, Psychomotor

Vigilance Test, PVT.

Abstract:

We show that Geometric Brownian Motion (GBM) appears to be an excellent choice of random process model

to describe mathematically the real-life signals that represent the evolution with time of the level of drowsiness

(LoD) of an individual, such as a driver. We collected data from thirty (30) healthy participants, who each

underwent three tests (either driving in a simulator or performing Psychomotor Vigilance Tests) at successive

levels of sleep deprivation. During each test, the LoD was produced by a photooculography (POG) based

device designed and built by our team. We so obtained a total of 90 LoD signals. For each, we applied

statistical methods to determine whether a GBM was a valid model for it. All 90 signals passed statistical tests

of normality and independency, meaning that each can be modeled by GBM, thereby showing the excellent

potential of GBM as a random process model for LoD signals. This ﬁnding could lead to the development

of a number of innovative means for predicting the evolution of the LoD and the occurrence of related events

beyond the present moment. The resulting technology should help reduce the number of accidents due to

drowsy driving.

1 INTRODUCTION

The drowsy state is an intermediate state between

alert wakefulness and sleep as deﬁned electro-

physiologically by the pattern of brain waves (EEG),

eye movements (EOG), and muscle activity (EMG)

(Johns, 2001, p. 5). Drowsiness is a major cause of

accidents in many areas of human activity (whether

personal or professional), and transportation is prob-

ably the single most important source of drowsiness-

related accidents. For example, one third (1/3) of fatal

accidents on highways in France are reported due to

the driver falling asleep at the wheel (Association des

Soci

es Franc¸aises d’Autoroutes, 2010).

It is thus paramount to monitor the level of drowsi-

ness (LoD) of a driver and to devise in-car safety sys-

tems that can help prevent accidents due to drowsi-

ness. This implies the development and use of drowsi-

ness monitoring systems. We focus here on systems

that monitor the physiological state of the subject, e.g.

by using images of an eye.

All systems that we know of can establish a

present LoD based on such data obtained up to the

present time. But, if the LoD at the present time

reaches a critical level, it may be too late to save a

driver’s life. Therefore, there is an imperative need

to estimate how the LoD will evolve past the present

time, and to make LoD-related predictions. To the

best of our knowledge, the ﬁeld of predicting the evo-

lution of drowsiness and of related parameters in the

future is essentially completely unexplored. The ﬁrst

investigations of this question appear to be (Ebrahim-

babaie and Verly, 2016a; Ebrahimbabaie and Verly,

2016b; Ebrahimbabaie and Verly, 2016c).

A conventional strategy for predicting future val-

ues of a signal is to describe this signal via a model.

Since the evolution of the LoD is inherently random,

one must treat each real-life ”LoD signal” as a real-

ization of a random process (RP).

The RP process models that often come to mind

in a wide variety of applications are AR, ARMA,

and ARIMA models, where ”AR” stands for ”autore-

gressive”, ”MA” for ”moving average”, and ”I” for

”integrated” (Manolakis et al., 2005; Hayes, 1996).

In (Ebrahimbabaie and Verly, 2016a; Ebrahimbabaie

and Verly, 2016b; Ebrahimbabaie and Verly, 2016c),

we examined the application of such models to a

PERCLOS signal and to an LoD signal, and we

found that these signals could be properly modeled

by AR(I)MA RP models. However, we also pointed

Ebrahimbabaie, P. and Verly, J.

Excellent Potential of Geometric Brownian Motion (GBM) as a Random Process Model for Level of Drowsiness Signals.

DOI: 10.5220/0006545101050112

In Proceedings of the 11th International Joint Conference on Biomedical Engineer ing Systems and Technologies (BIOSTEC 2018) - Volume 4: BIOSIGNALS, pages 105-112

ISBN: 978-989-758-279-0

105

out that these models are quite heavy to deal with, in

part because, for each, the order is unknown and the

parameters are unknown and numerous.

Our search for better RP models in the context of

drowsiness monitoring led us to examine the Geomet-

ric Brownian Motion (GBM) RP model (Jeanblanc

et al., 2009). A preliminary investigation indicated

that the GBM RP model could be very appropriate for

the signals found in the context of drowsiness moni-

toring, such as a PERCLOS signal and an LoD signal.

The main goal of the present paper is to describe

the work that we did with real subjects in several

states of sleep deprivation to establish that the GBM

RP model appears to be a good, promising choice of

RP model to describe the LoD signals produced by a

speciﬁc, validated, POG-based drowsiness quantiﬁca-

tion instrument, at least based on the data we had.

The GBM RP model lies at the heart of this paper.

We now give a brief deﬁnition of what a GBM RP is.

As one shall see, the notion of a GBM RP is rooted in

signiﬁcantly advanced mathematics (Jeanblanc et al.,

2009).

A continuous-time RP X(t) is said to be a GBM,

or GBM - i.e. to follow a GBM (RP) model - if it

satisﬁes the stochastic differential equation (SDE)

dX(t)

X(t)

= µdt + σdW (t), (1)

where µ is a ﬁxed, real-valued parameter, σ a ﬁxed,

real, positive parameter, and W (t) a Weiner (random)

process also called Brownian Motion (BM) (Jean-

blanc et al., 2009).

The left side of Equation 1 is the relative incre-

ment of X(t) in the period of time [t,t + dt], i.e.

(X(t + dt) − X(t))/X(t). The right side of this equa-

tion shows that this relative increment has a determin-

istic linear trend µdt that is disturbed by a random

noise term σdW (t). The constant µ is the so-called

“drift” (or “mean rate of return” in ﬁnancial mathe-

matics), and σ is the so-called “volatility”.

Recall that the goal of this paper is to show that

GBM is a good RP model for real-life LoD signals.

2 METHODS

We used data from two laboratory-based studies, re-

ferred to here as Study A and Study B. Both stud-

ies used the same overall (experimental) protocol,

and they differed only by (1) the groups of partici-

pants/subjects who took part in each study, and (2)

the nature of the tests/tasks that each participant was

asked to submit to in each study.

2.1 Participants

We recorded experimental data from N = 30 healthy

participants aged 19-33. Study A contributed 13 sub-

jects (mean age: 23.7; 7 men, 6 women), and Study B

17 subjects (mean age: 22.7; 8 men, 9 women).

2.2 Protocol

In each of the two studies (A and B), the correspond-

ing participants were each asked to submit to three

successive, time-separated test sessions in different

sleep-deprivation conditions over two days. During

each test session, the LoD signal of each participant

was produced using a drowsiness monitoring system

designed, built, and validated by our team.

In Study A, each test session consisted in driving

in a high-ﬁdelity driving simulator; the three succes-

sive sessions had durations of 45, 45, and 60 minutes.

In Study B, each test session consisted in performing

a Psychomotor Vigilance Test (PVT); the three suc-

cessive sessions all had durations of 10 minutes.

For ease of explanation, the overall two-day ex-

periment for each participant (for either type of test)

can be viewed as the succession of Night 1, Day 1,

Night 2, and Day 2, and as consisting of three succes-

sive test sessions. Figure 1 provides an illustration of

the overall protocol used for both studies. On Night

1, the participant slept at home and was asked to re-

port the number of hours of sleep using a sleep diary

(mean ± standard deviation for all participants is 7.57

± 0.8 h of sleep, range 6.5–9.0 h). Then, the partic-

ipant was not allowed to sleep from the time he/she

woke up on Day 1 until the end of the study (12:00

noon on Day 2). (All times are in 24 h notation.) At

8:00 on Day 1, the participant arrived at our labora-

tory and submitted to the ﬁrst test session, between

8:00 and 10:00. The participant was then free to leave

the laboratory to carry out his/her normal activities

but was equipped with an actigraph (either Actiwatch

2 or Philips Respironics) in order to check that he/she

had not slept while away. The participant came back

to our laboratory at 20:30 on Day 1. On Night 2,

the participant submitted to the second test session

between 2:00 and 4:00 and, after breakfast on Day

2, he/she submitted to the third test session between

11:00 and 13:00 (and after at least 28 hours of sleep

deprivation). At the end of the study, the participant

was sent back home. From noon on Day 1 until the

end of third test session, the participant was asked not

to consume any stimulant (coffee, tea, etc.). This pro-

tocol was approved by the Ethics Committee of the

University of Li

ege (Franc¸ois et al., 2016).

BIOSIGNALS 2018 - 11th International Conference on Bio-inspired Systems and Signal Processing

106

Figure 1: Graphical overview of overall protocol common to both studies, i.e. for Study A (driving in a simulator) and Study

B (PVT). The successive ﬁve lines show: (1) when each participant had to submit to a test; (2) the succession of nights and

days; (3) the presence at home or in our lab; (4) the period of sleep deprivation; (5) the period of stimulant deprivation.

2.3 Measurements

We setup our drowsiness monitoring system to pro-

duce one sample of the LoD every 20 sec in Study A

and every 5 sec in Study B. One reason for consid-

ering two distinct sampling intervals was to examine

whether the conclusion concerning the nature of the

underlying RP for LoD signals would dependent on

the value of the sampling interval. One other reason

for decreasing the sampling interval to 5 sec - thereby

producing LoD signals with 4 times as many samples

- was to provide more data for the statistical analysis.

2.4 Instruments

Our team designed, built, and validated (Franc¸ois

et al., 2016; Franc¸ois et al., 2014) a fully automatic

drowsiness monitoring system based on the physio-

logical state of a person. The system consists in a pair

of specially-made eyeglasses linked to a computer via

a cable. The eyeglasses contain a controlled source

of illumination in the infrared (IR) and a high-speed

camera sensitive in the IR.

The algorithms running on the computer use ocu-

lar parameters extracted from images of the eye (i.e.

POG) to determine, periodically in time, an LoD on

a numerical scale from 0 to 10, with 0 corresponding

to ”very awake” (or ”very vigilant”) and 10 to ”very

drowsy” (Franc¸ois et al., 2016).

2.5 Data Analysis

The sequence of LoD values produced by our drowsi-

ness monitoring system during each particular test

session is referred to here as a signal. The signals

recorded during Study A and Study B are further de-

scribed in the next section. In an actual operational

situation, the signal would be the sequence of samples

produced during the time the operator has the glasses

on, such as during a long drive.

Consider a given, real-life signal - such as the one

just described - that is considered to be one realiza-

tion of a RP. Here, we describe the methodology that

is typically used to determine whether the GBM RP

model is a valid model for this real-life signal.

Before describing this methodology, we introduce

some key concepts. For ease of explanation, it is use-

ful to treat a RP as a sequence of random variables

(RVs), thus ordered in time. However, rather than

considering these RVs, one works here with the re-

lated log-ratio (LR) RVs. The LR RV at some time

index n is deﬁned as the natural logarithm of the ratio

of the RV at n and the RV at n - 1. The collection of

LR RVs constitutes a new RP, called here the LR RP.

(Note that the number of RVs in the LR RP is neces-

sarily one unit less that in the original RP.) Of course,

in practice, we (only) have one realization of the orig-

inal RP, and thus one realization of the LR RP, and,

consequently, one realization of each original RV or

LR RV. While all theoretical developments must be

done in terms of RPs and RVs, the methodology only

uses the single available realization of the original RP

and that of the corresponding LR RP, as well as of

their corresponding RVs.

At the theoretical level, if the original RP is a

GBM RP, then one can show that the LR RP is char-

acterized by the following pair of properties: (1) all

LR RVs are individually characterized by a normal

(i.e. Gaussian) PDF, and the PDFs of all these RVs

are identical (thus with the same mean and standard

deviation); (2) any two distinct LR RVs are indepen-

Excellent Potential of Geometric Brownian Motion (GBM) as a Random Process Model for Level of Drowsiness Signals

107

dent in the usual statistical sense, meaning that their

joint (2D) PDF factorizes (Brandimarte, 2014).

At the methodology level, one must determine

whether both of the above properties (or conditions)

are veriﬁed. The difﬁculty - which is typical in the

type of approach used here - is that the theory deals

with all possible realizations, while the methodology

has only access to a single one, i.e. the observed sig-

nal. The methodology must thus do its best with a sin-

gle signal/realization to establish one or more proper-

ties that pertain to all possible realizations. In short,

the methodology must replace considerations across

a statistical ensemble by considerations across time.

Below, we simply describe the methodology, and we

do not attempt to justify it in terms of the theory.

In light of the above discussion, there are thus

two conditions to be veriﬁed on the signal/realization

available to establish whether this realization can be

modelled by a GBM RP. We refer to these condi-

tions as the ”normality condition” and the ”inde-

pendency condition”.

In order to verify normality condition, we applied,

to each signal, (1) two established graphical methods,

i.e. the quantile-quantile (QQ) plot and the histogram,

and (2) one numerical (non-graphical) method, i.e.

the Shapiro-Wilk (S-W) test.

To assess the independency condition, we looked

at the scatter plot of Log-Ratios versus time of each

signal to see whether there was any (time) correlation

between the logarithms of the ratios of successive val-

ues.

3 RESULTS

3.1 Data

Each participant in Study A and Study B contributed 3

LoD signals, with each signal corresponding to one of

the 3 tests at progressively increasing levels of sleep

deprivation. Thus, the 13 participants of Study A

(driving in a simulator) contributed 13 x 3 = 39 LoD

signals, and the 17 participants of Study B (perform-

ing PVTs) contributed 17 x 3 = 51 LoD signals.

As alluded to earlier, some characteristics of the

LoD signals produced are different for each study. In

Study A, each signal consists of 42 samples spaced by

20 seconds (for a total duration of 840 sec = 14 min),

and in Study B, each signal consists of 110 samples

spaced by 5 seconds (for a total duration of 550 sec =

9 min 10 sec). The time intervals of 20 and 5 sec are

those at which the drowsiness measurement system

was asked to produce its output samples. This should

be distinguished from the speed at which the images

of the eye were collected, i.e. 120 images/sec in both

Study A and Study B.

In summary, we have the following numbers of

LoD signals and samples:

• Study A: 13 x 3 = 39 signals; 39 x 42 = 1,638

samples;

• Study B: 17 x 3 = 51 signals; 51 x 110 = 5,610

samples

• Total for both studies: 90 signals; 7,248 samples.

Below, we illustrate the application of the methodol-

ogy (described in the Methods section) to one exam-

ple signal from Study A and to one from Study B.

These example signals, referred to as ”Signal A” and

”Signal B”, are shown in Figure 2.

3.2 Application of Methodology to

Signal A & Signal B

We present here the results of applying the methodol-

ogy to Signal A and Signal B. Speciﬁcally, we show

the results of applying the three techniques for check-

ing the normality condition (histogram, Q-Q plot, and

S-W test) and the one technique for checking the in-

dependency condition (linear regression).

3.2.1 Check of Normality Condition

Figure 3(a) shows the histogram of log-ratio sample

values - or, simply, log-ratios - for Signal A, and the

corresponding ”best-ﬁt” normal (i.e. Gaussian) PDF,

i.e. that with the mean and standard deviation of the

log-ratios. Figure 3(b) shows the corresponding sub-

ﬁgure for Signal B.

Figure 4(a) shows the Q-Q plot of log-ratios for

Signal A, and the corresponding ”best-ﬁt” straight

line, i.e. that minimizing the total least-square ﬁt er-

ror. Figure 4(b) shows the corresponding subﬁgure

for Signal B.

Since the histogram and Q-Q plot techniques are

graphical, it is by visual inspection of the plots that

one must decide whether the normality condition is

veriﬁed or not. Through our experience based on

looking at tens of such plots in the particular context

of LoD signals, as well as at many in the literature for

other applications, we conclude with conﬁdence that,

according to the histograms and Q-Q plots, Signal A

and Signal B both satisfy the normality condition.

The application of the S-W test with signiﬁcance

level α = 0.05 leads to the following conclusions.

For Signal A: The p-value of the S-W test is 0.10.

Since it is greater than 0.05, we cannot reject the H

hypothesis that the log-ratio RVs have a normal (i.e.

Gaussian) PDF. Recall that this does NOT allow us

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108

Figure 2: Example LoD signals from (a) Study A and (b) Study B, referred to as ”Signal A” and ”Signal B”, respectively.

Figure 3: Histograms of log-ratio sample values (or log-ratios) for (a) Signal A and (b) Signal B, and corresponding ”best-ﬁt”

normal PDFs.

to conclude that Signal A then veriﬁes the normality

condition.

For Signal B: The p-value of the S-W test is 0.01.

Since it is smaller than 0.05, we must reject the H

hypothesis. This allows us to conclude that Signal B

does not verify the normality condition according to

the present test.

The results of the three techniques (histogram, Q-

Q plot, and S-W test) lead us to the following conclu-

sions.

For Signal A: The pair of graphical tests indicates

that Signal A satisﬁes the normality condition, and

the S-W test does NOT allow us to say that it does

not satisfy this condition, which is the best one could

hope for in light of the two other tests.

For Signal B: The pair of graphical tests indi-

cates that Signal B satisﬁes the normality condition,

whereas the S-W test indicates that it does not.

While all three techniques allow us to conclude

with conﬁdence that Signal A veriﬁes the normality

Excellent Potential of Geometric Brownian Motion (GBM) as a Random Process Model for Level of Drowsiness Signals

109

Figure 4: Q-Q plots of log-ratio sample values (or log-ratios) for (a) Signal A and (b) Signal B, and corresponding ”best-ﬁt”

straight lines.

condition, one cannot so easily reach a conclusion

for Signal B. However, since the graphical techniques

both show in a convincing way that Signal B veriﬁes

the normality conditions, we made the decision to de-

clare that Signal B veriﬁes the normality condition.

3.2.2 Check of Independency Condition

Figure 5(a) shows the plot of log-ratio sample values

(or log-ratios) for Signal A as a function of time, and

the corresponding ”best-ﬁt”/regression straight line.

Figure 5(b) shows the corresponding subﬁgure for

Signal B.

Since the linear regression technique is graphical,

it is by visual inspection of the plots that one must de-

cide whether the independency condition is veriﬁed

or not. As for the histograms and Q-Q plots, through

our experience of looking at many such plots, we con-

clude with conﬁdence - from the regression lines - that

Signal A and Signal B both verify the independency

condition.

3.2.3 Conclusion for Signal A & Signal B

Since each of Signal A and Signal B can reasonably

be said to verify both the normality condition and the

independency condition, we conclude that GBM is a

valid choice of model for each of Signal A and Signal

3.3 Results for all 90 LoD Signals

We applied to all 90 LoD signals available the same

detailed analysis as the one applied above for Signal

A and Signal B.

3.3.1 Check of Normality Condition

According to the graphical techniques of histogram

and Q-Q plot, we concluded that all 90 LoD signals

from Study A and Study B verify the normality con-

dition.

According to the S-W test with signiﬁcance level

α = 0.05, we reached the following conclusions.

For Study A: for each LoD signal in this study,

the H

hypothesis cannot be rejected. Recall that this

does NOT allow us to conclude that such signal then

veriﬁes the normality condition.

For Study B: for each LoD signal in this study, the

hypothesis must be rejected. This allows us to con-

clude that such signal does NOT verify the normality

condition according to the present test.

Therefore, for Study A, all LoD signals verify the

normality condition according to all three techniques,

whereas, for Study B, they verify it only according to

the graphical techniques.

However, just as in the case of Signal B above,

the graphical techniques of histogram and Q-Q plot

allowed us to conclude that all LoD signals in Study

B can reasonably be said to verify the normality con-

dition.

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110

Figure 5: Plots of log-ratio sample values (or log-ratios) as a function of time and of the corresponding ”best-ﬁt” straight lines

for (a) Signal A and (b) Signal B.

In conclusion, all 90 LoD signals from Study A

and Study B can reasonably be said to verify the nor-

mality condition.

3.3.2 Check of Independency Condition

The linear regression technique allowed us to declare

that all LoD signals from Study A and Study B verify

the independency condition.

3.3.3 Conclusion for all LoD Signals from Study

A & Study B

Since each signal in Study A and in Study B can rea-

sonably be said to verify the normality condition and

the independency condition, we conclude that GBM

is a valid choice of model for each signal in Study A

and in Study B.

4 DISCUSSION

Using a carefully planned and executed protocol, and

a validated drowsiness monitoring system, we col-

lected discrete-time signals that represent the evolu-

tion of the level of drowsiness (LoD) of 30 individu-

als at three increasing levels of sleep deprivation over

three days, thus resulting in 90 validated LoD signals.

Given their nature, LoD signals must be viewed

as realizations of random processes (RPs). Predicting

the (unknown) future values of such signals, as well as

related events, based upon data available up to close

to the present time requires one to have a model of the

underlying RP.

Using appropriate statistical analysis, we have

shown that Geometric Brownian Motion (GBM) is a

valid choice of random process (RP) model for mod-

elling all 90 LoD signals, thus without a single excep-

tion.

Of course, before being sure that GBM is an ex-

cellent model for ”all” LoD signals to be encountered

in all real-life circumstances, it will be necessary to

conduct studies on more subjects and in actual opera-

tional conditions such as driving on a real road.

At the time of this writing, we are exploring the

avenues that open up in the ﬁeld of drowsiness moni-

toring if/when the LoD signals are GBM.

In addition, the work reported here can provide a

strong motivation for researchers interested in mod-

elling physiological and biological processes to ex-

amine whether - starting from the physiological and

biological mechanisms involved in the evolution of

drowsiness, and using appropriate mathematical mod-

els and tools - they can possibly show that an LoD

signal should in fact naturally be a realization of an

underlying GBM RP model.

ACKNOWLEDGMENTS

We wish to thank Mrs. Cl

ementine Franc¸ois, from our

research team, for providing the level-of-drowsiness

signals used in this paper. She played a signiﬁcant

role in their acquisition, as part of her PhD thesis

work.

Excellent Potential of Geometric Brownian Motion (GBM) as a Random Process Model for Level of Drowsiness Signals

111

REFERENCES

Association des Soci

es Franc¸aises d’Autoroutes

(2010). Somnolence au volant:

une

etude pour mieux comprendre.

http://www.autoroutes.fr/FCKeditor/UserFiles/File/

Publications/ASFA - Somnolence p-p2.pdf.

Acessed: November 19, 2016.

Brandimarte, P. (2014). Handbook in Monte Carlo Sim-

ulation: Applications in Financial Engineering, Risk

Management, and Economics. John Wiley & Sons,

New Jersey.

Ebrahimbabaie, P. and Verly, J. G. (2016a). ’Prediction of

future values of a level of drowsiness derived from im-

ages of an eye based on its past values, with applica-

tion to drowsy driving’. Paper presented to the Inter-

national Symposium on Somnolence, Vigilance, and

Safety (SomnoSafe). Brussels, Belgium. 21-23 Febru-

ary.

Ebrahimbabaie, P. and Verly, J. G. (2016b). ’Prediction

of future values of the eye PERCLOS based on its

past values, with application to drowsiness monitor-

ing’. Paper presented to the International Symposium

on Somnolence, Vigilance, and Safety (SomnoSafe).

Brussels, Belgium. 21-23 February.

Ebrahimbabaie, P. and Verly, J. G. (2016c). ’Random

process modeling of an optooculography-based level

of drowsiness, with application to drowsy driving’.

Poster presented to the Joint Meeting of the IEEE-

EMBS Benelux Chapter and the 14th Belgian Na-

tional Day on Biomedical Engineering. Brussels, Bel-

gium. 27 November.

Franc¸ois, C., Hoyoux, T., Wertz, J., and Verly, J. G. (2016).

Tests of a new drowsiness characterization and moni-

toring system based on ocular parameters. 13:174.

Franc¸ois, C., Wertz, J., and Verly, J. G. (2014). ’valida-

tion of a new automatic drowsiness quantiﬁcation sys-

tem for drivers’. Paper presented to the 5th Interna-

tional Conference on Applied Human Factors and Er-

gonomics (AHFE). Krakow, Poland. 19-23 July.

Hayes, M. H. (1996). Statistical Digital Signal Processing

and Modeling. John Wiley & Sons, New York, NY.

Jeanblanc, M., Yor, M., and Chesney, M. (2009). Math-

ematical Methods for Financial Markets. Springer,

London.

Johns, M. W. (2001). Assessing the drowsiness of drivers.

Melbourne: VicRoads.

Manolakis, D. G., Ingle, V. K., and Kogan, M. S. (2005).

Statistical and Adaptive Signal Processing: Spectral

Estimation, Signal Modeling, Adaptive Filtering, and

Array Processing. Artech House, Norwood, MA.

BIOSIGNALS 2018 - 11th International Conference on Bio-inspired Systems and Signal Processing

112