Azza Ben Mosbah
email: azza.benmosbah@nist.gov

Timothy A Hall
email: tim.hall@nist.gov

Michael Souryal
email: michael.souryal@nist.gov

Hossam Afifi
email: hossam.afifi@telecom-sudparis.eu

Analysis of the Vulnerability of the Incumbent Frequency to Inference Attacks in Spectrum Sharing

Keywords: 3.5 GHz, channel assignment, Federal bands, inference attack, privacy protection, spectrum sharing

Sharing between commercial and Federal incumbent users, such as in the 3.5 GHz band, is expected to increase the availability of spectrum for wireless broadband use. However, the spectrum coordination needed between incumbent and commercial users gives rise to several privacy concerns. This paper analyzes the vulnerability of the incumbent's operational center frequency to disclosure from inference attacks. We evaluate the inherent protection provided by two channel assignment schemes in terms of the time required for an attacker to infer the incumbent's frequency. We account for the activity of secondary users in a dynamically-shared environment. This analysis allows the Spectrum Access System to quantify privacy for a given secondary load. It also provides an analytical framework to quantify the effectiveness of countermeasures such as limiting the query rate of secondaries.

I. INTRODUCTION

Recently, spectrum sharing has been proposed in order to make more efficient use of statically managed frequency bands. For example, in the U.S., the Federal Communications Commission (FCC) has selected a multi-tiered shared access model, managed by a Spectrum Access System (SAS), to assign spectrum resources in the 3.5 GHz band without causing interference to incumbent operations [START_REF]Amendment of the commission's rules with regard to commercial operations in the 3550-3650 mhz band[END_REF].

While the main concern in the scientific literature has been interference management, additional concerns have been raised. Incumbents such as military and public safety users require full protection of their operations, not only from harmful interference, but also from exposure of confidential information. Bahrak et al. [START_REF] Bahrak | Protecting the primary users' operational privacy in spectrum sharing[END_REF] define an inference attack, where knowledge acquired from the sharing environment can be used to infer sensitive information about the incumbent. The operational parameters of primary users, such as location, frequency, and time of operation are sensitive and should not be revealed. Specifically, protecting the operational frequency of an incumbent against inferences can be critical to mitigate intentional interference (a jamming attack).

Our contributions consist of modeling secondary activity as an Erlang queueing system, analyzing inference attacks on the incumbent's operational frequency to evaluate inherent obfuscation and the effectiveness of countermeasures. In Section II, we present our system modeling to quantify the privacy vulnerability. Section III demonstrates the analysis of simulation results. Finally, Section IV summarizes the findings and discusses future works.

II. VULNERABILITY ANALYSIS A. Channel Assignment Schemes

We consider two channel assignment schemes that can be used by the SAS:

• Random channel assignment assigns channels to secondaries randomly from the list of available channels. • Ordered channel assignment assigns channels to secondaries in an order-wise fashion, and any particular order can be employed.

B. Simulation Model

We divide the band into n equal channels. We consider a sample system including one incumbent, one SAS and one adversary within the same area. The incumbent is operating on a single channel. Secondaries share the use of the remaining n -1 channels. The SAS manages access to those channels. Secondaries query the SAS according to a Poisson process with aggregate rate λ, and the service time is exponentially distributed with rate µ. Once all channels are occupied, new access requests will be denied. This is known as an Erlang loss system [START_REF] Chaiken | An extension of Erlang's formulas which distinguishes individual servers[END_REF].

We assume that the attacker is one of the secondaries and is trying to infer the operational channel of the incumbent. We also assume that the channels available for use by secondaries do not change during the incumbent's active period. For each query, the SAS replies with one available channel. The attacker does not know a priori the channel assignment scheme used by the SAS. It only uses the information given by the SAS and does not have access to any external knowledge. Its initial knowledge is a list of all potential incumbent channels (i.e., all n channels). Once the SAS returns a channel in reply to a query, the attacker knows that channel is not used by the incumbent. Hence, the attacker updates its knowledge by removing the returned channel from the list of potential channels used by the incumbent.

C. Privacy Metrics 1) Distance of inference:

The inference process can be regarded as a discovery process of all channels available for use by secondaries. Therefore, we can evaluate privacy as a measure of "distance," that is, the number of channels remaining to be discovered.

2) Cost of inference: In spectrum sharing, the attacker invests effort to infer sensitive data. We measure the inference cost to the attacker in terms of how long the attacker takes to acquire the inferred knowledge and the number of queries to acquire that knowledge.

III. RESULTS AND DISCUSSION

We conducted this work to analyze the vulnerability of the incumbent's frequency to inference attacks and determine inherent privacy-preserving techniques to thwart them. We conclude that the values of system parameters have a significant effect on the privacy of incumbents.

Implementing an ordered channel assignment scheme is effective in all cases, regardless of the spectrum load ρ or the attacker's query rate λ a . Since randomness in the channel assignment scheme adds diversity to the query responses, it allows the attacker to infer the incumbent's channel in less time. Hence, the use of the ordered scheme raises both the distance (Fig. 1) and the cost (Fig. 2) of inference, i.e., an attacker will take more time to infer the same information. An attacker can fake different identities, get help from other secondaries or just flood the system with queries in order to speed up the inference process. Limiting the secondary users query rate can be an efficient way to mitigate the inference of the incumbent frequency during the operational period. For example, Fig. 3 suggests that if, in a system with ρ = 5, the incumbent needs 10 µ time units to use the channel and leave, the SAS should limit a user's query rate to 3µ when using random channel assignment and to 10µ when using ordered channel assignment, under moderate load. For ρ = 1, using an ordered channel assignment scheme is the best approach.

As a result, the SAS should implement effective privacypreserving techniques by calibrating some adjustable parameters (channel assignment scheme, query rate of secondaries) to the system load. IV. CONCLUSIONS Spectrum sharing in Federal bands can be productive yet challenging because of the privacy needs of the incumbents. This analysis sheds light on the impact of different system parameters on the privacy of the incumbent. Ordered channel assignment significantly enhances privacy as measured by an attacker's ability to infer the channel used by the incumbent. However, when the system load is high, the channel assignment scheme is irrelevant. One way to mitigate the inference risk is to limit the query rate (i.e., number of queries) per secondary user. This will prevent aggressive attackers from expediting the inference process.

2 ¡ ¢ £ ¤2 ¤ ¤¡ ¤¢ e v ¥ ¦ § ¨¥ © ¥ © v ¥ ¦ ) x!"#$%&'() 01("3 "$4( !5 46( $44$78(" e9 a /@) "$r)!#A B C ¤ !")("()A B C ¤ "$r)!#A B C D !")("()A B C D
In a real world scenario, an attacker may have other sources of information. So, it may be necessary to use additional obfuscation techniques to increase the cost of inference or the anonymity of the incumbent's channel.

= 1 Fig. 1 .

 11 Fig. 1. Effect of the time on the inherent obfuscation (n = 10)

Fig. 2 .

 2 Fig. 2. Effect of the spectrum load on the inherent obfuscation (n = 10)

Fig. 3 .

 3 Fig. 3. Effect of the attacker's query rate on the inherent obfuscation (n = 10)


Michel Valstar

Jonathan Gratch

Björn Schuller

Fabien Ringeval

Roddy Cowie

Maja Pantic

Summary for AVEC 2016 -Depression, Mood, and Emotion Recognition Workshop and Challenge

Keywords: A↵ective Computing, Social Signal Processing, Depression

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

This year's Audio-Visual Emotion Challenge and workshop (AVEC 2016) has been organised in conjunction with the 24th ACM International Conference on Multimedia, held in Amsterdam, The Netherlands, 15 -19 October 2016.

The AVEC 2016's theme is 'Depression, Mood, and Emotion Recognition' and it is the sixth competition event aimed at comparison of multimedia processing and machine learning methods for automatic audio, visual and audio-visual emotion analysis, with all of the participants competing under strictly the same conditions in this first of its kind series [START_REF] Ringeval | Av+ ec 2015: The first a↵ect recognition challenge bridging across audio, video, and physiological data[END_REF][START_REF] Schuller | AVEC 2012 -The Continuous Audio/Visual Emotion Challenge[END_REF][START_REF] Schuller | AVEC 2011 -The First International Audio/Visual Emotion Challenge[END_REF][START_REF] Valstar | Workshop summary for the 3rd international audio/visual emotion challenge and workshop (AVEC'13)[END_REF][START_REF] Valstar | Avec 2014: 3d dimensional a↵ect and depression recognition challenge[END_REF]. However, further similar endeavours that ⇤ The author is further a liated with Imperial College London, Department of Computing, London, U.K.

† The author is further a liated with Twente University, EEMCS, Twente, The Netherlands.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. have been undertaken since AVEC started in 2011 are to be noted, e. g., [START_REF] Dhall | Emotion Recognition In The Wild Challenge[END_REF].

The AVEC 2016 edition features besides true multimodal emotion recognition in its emotion recognition sub-challenge, where besides audio and video participants also have access to physiological data. In addition, we take emotion analysis to a higher-level behaviour understanding by looking at mood disorders, in particular the serious and important problem of automatic detection of depression. Adding objective measures to what is otherwise an entirely subjective process of diagnosing and monitoring depression promises to be an invaluable support to the mental health profession besides the usage in media retrieval systems.

As before, the goal of the Challenge is to provide a common benchmark test set for individual multimodal information processing and to bring together the audio and video emotion recognition communities (extended with the physiological analysis community for the emotion recognition sub-challenge), to compare the relative merits of these approaches to emotion and depression recognition under welldefined and strictly comparable conditions and to establish to what extent fusion of the approaches is possible and beneficial. A second motivation is the need to advance emotion recognition for multimedia retrieval to a level where behaviomedical systems [START_REF] Valstar | Automatic behaviour understanding in medicine[END_REF] are able to deal with large volumes of non-prototypical naturalistic behaviour in reaction to known stimuli, as this is exactly the type of data that diagnostic tools and other applications would have to face in the real world.

We called for participation in two Sub-Challenges: (i) fully-continuous emotion detection from audio, from video, and physiological data or from any combination thereof, and (ii) classification of depression. As benchmarking database an enhanced subset of the AVEC 2015 RECOLA database is used [START_REF] Ringeval | Introducing the RECOLA multimodal corpus of remote collaborative and a↵ective interactions[END_REF]. Emotion needed to be recognised in terms of continuous time, and continuous valued dimensional a↵ect in two dimensions: valence and arousal. For depression, the Distress Analysis Interview Corpus -Wizard of Oz (DAIC-WOZ) database was used. This is part of a larger corpus, the Distress Analysis Interview Corpus (DAIC) [START_REF] Gratch | The distress analysis interview corpus of human and computer interviews[END_REF], that contains clinical interviews designed to support the diagnosis of psychological distress conditions such as anxiety, depression, and post-traumatic stress disorder. Depression needed to be estimated in terms of binary classes depressed/nondepressed, based on a widely accepted clinical self-report questionnaire, PHQ8.

Besides participation in the Challenge we called for papers addressing the overall topics of this workshop, in particular works that address the di↵erences between audio and video processing of emotive data, and the issues concerning combined audio-visual emotion recognition.

In the following sections, we will describe the participation in this year and outline the conditions for participation in particular in the competitive challenge event. We further acknowledge those that helped realise AVEC 2016.

CHALLENGE CONDITIONS

A baseline paper explaining the dataset, the challenge evaluation procedure, baseline features and baseline results was made available while the challenge was ongoing [START_REF] Valstar | Avec 2016 -depression, mood, and emotion recognition workshop and challenge[END_REF]. Due to the sensitive nature of the data, a strict registration for access to the challenge data policy was followed. As in previous years, a web-based database was used, however, we required to sign a new end user license agreement and for the depression sub-challenge no raw video was made available, only video features. After downloading the data participants could directly start their own experiments with the train and development sets. Once they found their best method they should write a paper for the Workshop. At the same time they could compute their results per instance of the test set. Participants' results needed to be sent as a single packed file per Sub-Challenge to the organisers by email and scores were returned within 24 hours during typical working days.

Each participant had up to five submission attempts per Sub-Challenge. Badly formatted results were not counted towards one of these five submissions. The organisers provided for each a↵ective dimension the Concordance Correlation Coe cient (CCC), which is used to rank participants on the emotion sub-challenge. For the depression sub-challenge the F1 measure was used to rank participants. The RMS error of the actual PHQ8 scores was provided as well, which could be used by the authors to further discuss their results in the paper accompanying their submission.

PARTICIPATION

The call for participation and papers attracted registrations of 56 teams from all over the world. 13 teams submitted results for the A↵ect recognition Sub-Challenge, and 7 teams submitted results for the Depression recognition Sub-Challenge. Finally, 12 paper submissions were received, which were assigned three reviewers, each, and reviewed independently. AVEC 2016 reviewing was double blind, and acceptance was based on relevance to the workshop, novelty, and technical quality. The programme committee accepted

papers in addition to the baseline paper as oral presentation. Again, we hope that these proceedings will serve as a valuable reference for researchers and developers in the area of audio-visual emotion recognition and depression analysis.

Acknowledgments

The challenge in general has been generously supported by the Association for the Advancement of A↵ective Computing (AAAC). The research leading to these results has received funding from the EC's 7th Framework Programme through the ERC Starting Grant No. 338164 (iHEARu), and the European Union's Horizon 2020 Programme through the Innovative Action No. 645094 (SEWA), and the Research Innovative Action No. 645378 (ARIA-VALUSPA), and No. 688835 (DE-ENIGMA).


Azza Ben Mosbah
email: azza.benmosbah@nist.gov

Timothy A Hall
email: tim.hall@nist.gov

Michael Souryal
email: michael.souryal@nist.gov

Hossam Afifi
email: hossam.afifi@telecom-sudparis.eu

An Analytical Model for Inference Attacks on the Incumbent's Frequency in Spectrum Sharing

Keywords: 3.5 GHz band, analytical evaluation, incumbent vulnerability, inference attack, privacy, spectrum sharing

In spectrum sharing, incumbents with sensitive parameters require full protection of their operations. The incumbent's protection includes the protection of its privacy (e.g., operational frequency) against inference attacks carried out by malicious authorized secondary users. In this paper, we develop an analytical model to analyze the vulnerability of the incumbent's frequency to inference attacks and validate it by simulation. Specifically, we study random and ordered channel assignment schemes and compare results for both schemes.

I. INTRODUCTION

The 3550 MHz to 3700 MHz band in the United States has a three tier access model managed by a spectrum access system (SAS) with the assistance of an environmental sensing capability (ESC). Tier 1 users includes authorized Federal users. Tier 2 and tier 3 users are collectively referred to here as secondary users (SUs). The ESC determines channel availability while the SAS manages access of SUs to the spectrum. Introducing these SUs into the band affects the privacy of the Federal incumbent. Specifically, a malicious SU may gain authorized access to the spectrum and carry out attacks to infer sensitive information about the incumbent by just fusing information given by the SAS. Such an attack is referred to as an inference attack.

In a previous work [START_REF] Ben Mosbah | Analysis of the vulnerability of the incumbent frequency to inference attacks in spectrum sharing[END_REF], we used simulations to model inference attacks and demonstrated that the privacy of the incumbent can be improved by adjusting the system parameters (i.e., inherent obfuscation). In this paper, we mathematically model attacks that attempt to infer the incumbent's operational frequency through repeated requests for spectrum and validate our analytical model with simulations.

II. SYSTEM MODEL A. Network Model

The SAS manages n channels within a given area. Only l channels are available for use by SUs. We model the SU activity using an M/M/l/l queue [START_REF] Ben Mosbah | Analysis of the vulnerability of the incumbent frequency to inference attacks in spectrum sharing[END_REF]. When a SU requests spectrum resources, the SAS replies with an available channel. If no channel is available, the request is denied. * This paper was written in partial fulfillment of Mrs. Ben Mosbah's doctoral program at Télécom SudParis (France) while working as a guest researcher at NIST.

B. Attack Model

The attacker is a legitimate SU sending queries requesting access to the spectrum. Its initial knowledge is a list of all channels in the band. Once the SAS returns an available channel, the attacker knows that the given channel is not used by the incumbent. Hence, the attacker updates its knowledge by removing it from the list of potential incumbent channels. Let X be the random variable representing the number of queries needed to discover all channels available to secondaries and, hence, the channels used by the incumbents.

III. ANALYTICAL EVALUATION

In this Section, we show how to compute the expected number of queries needed to infer the incumbent's channel E[X] for two SAS channel assignment schemes: one where the SAS assigns an idle channel at random, and the other where the SAS assigns the lowest-numbered idle channel [START_REF] Ben Mosbah | Analysis of the vulnerability of the incumbent frequency to inference attacks in spectrum sharing[END_REF]. In order to calculate this, we use the M/M/l/l queue model and assume the system is in equilibrium.

A. Analysis of the Random Channel Assignment

In the case of the random assignment scheme, the SAS returns a channel at random in reply to an attacker's request. The blocking probability P B is the probability that all channels are busy at the time of a request and is calculated as follows

P B = ρ l l! l k=0 ρ k k! -1 , (1)
where ρ = λ/µ is the system load, λ is the aggregate arrival rate, and 1/µ is the individual service time. In the above system, when the attacker makes a request, the SAS will either return one of the available idle channels or, if all the channels are busy, will respond saying no channel is available. In this case we can express E[X] as

E[X] = E[X b ] + E[X r ] , (2)
where X b is the number of queries made when all channels were busy, i.e., the request was blocked, and X r is the number of queries for which an available idle channel was returned by the SAS. We know that All that remains is to calculate E[X r ]. When 1 ≤ k ≤ l channels are idle, then each channel is idle with probability k/l, and if idle will be returned by the SAS with probability 1/k. Thus each channel has probability 1/l of being returned. E[X r ] can then be calculated using the solution to the coupon collector's problem with equal probabilities.

E[X b ] = P B E[X] . (3
E[X r ] = l l k=1 1 k = lH l , (4)
where H l is the l th harmonic number [START_REF] Ferrante | The coupon collector's problem[END_REF]. Thus, we have

E[X] = lH l 1 -P B . (5)

B. Analysis of the Ordered Channel Assignment

In the case of the ordered assignment scheme, channels are assigned to incoming requests with unequal probabilities. We need to find the probability p j that the SAS will return channel j in reply to an attacker's request. This is equivalent to the probability that channel j is the lowest available idle channel at the time of an attacker's request.

Let B j be the probability that an arriving request finds the first j channels busy. The conditional probability that an arriving request finding the first j -1 channels busy also finds channel j busy is B j /B j-1 . If γ j (z) is the Laplace-Stieltjes transform of the distribution function of elapsed time between successive times when an arriving request finds the first j -1 channels busy and is assigned channel j [3], then

γ j (µ) = B j B j-1 , (6)
where B 0 = 1 and γ j (z) is defined by the recurrence relation.

γ j+1 (z) = γ j (z + µ) 1 -γ j (z) + γ j (z + µ) , j = 1, 2, . . . (7)
γ 1 (z) = λ λ+z . Note that it follows from equation (6) and B 0 = 1 that

B j = γ 1 (µ) • • • γ j (µ), j = 1, 2, . . . (8)
Using the above, we calculate the probabilities j . Let I j be a random variable representing the state of channel j, where 1 means the channel is busy and 0 means that it is idle. Then,

p j = P r{I 1 = 1, ..., I j-1 = 1, I j = 0} = (1 -B j /B j-1 ) B j-1 = B j-1 -B j . (9)
Note that P B = B l and P B + l j=0 p j = 1. We can find E[X] by using the p j as calculated above in the solution to the coupon collector's problem for unequal probabilities in [START_REF] Ferrante | The coupon collector's problem[END_REF]

E[X] = l i=1 1 p i - i<j 1 p i + p j + i<j<k 1 p i + p j + p k -• • • (10) • • • + (-1) l+1 1 p 1 + • • • + p l .
2 ¡2 ¡ ¢2 ¢ £2 e v ¤ ¥ ¦ § ¤ ¨© ¤ ¥ © ¤ ¥ ¤ v ¤ ¥ !"#$% &'( ) 01)
"s%3&(#$)4 5 6 ¡2 (&3&(#$)4 5 6 ¡2 "s%3&(#$)4 5 6 ¡ (&3&(#$)4 5 6 ¡ "s%3&(#$)4 5 6 ¢2 (&3&(#$)4 5 6 ¢2 "s%3&(#$)4 5 6 ¢ (&3&(#$)4 5 6 ¢ "s%3&(#$)4 5 6 £2 (&3&(#$)4 5 6 £2 Fig. 2. Analytical results vs. simulation results for the ordered scheme IV. ANALYTICAL RESULTS

Our system includes one incumbent, one SAS and one attacker within the same area. The incumbent is operating on one channel. So, n -1 channels are available for use by SUs. We compute E[X] analytically and by simulation with a confidence interval of 95 % for different values of n and ρ. In Fig. 1, where channels are randomly assigned, we note that the simulation results are within the confidence interval of the analytical model results for all values of In Fig. 2, where channels are assigned order-wise, simulation results also match the analytical model results.

V. CONCLUSIONS

We have proposed an analytical model to calculate the average number of queries needed to infer the operational channel of the incumbent. This model provides insight into the limit that the SAS may set on the query rate in order to minimize the risk of inference to the incumbent.

Fig. 1 .

 1 Fig. 1. Analytical results vs. simulation results for the random scheme


Michel Valstar

Jonathan Gratch

Björn Schuller

Fabien Ringeval

Denis Lalanne

Mercedes Torres Torres

Stefan Scherer

Giota Stratou

Roddy Cowie

Maja Pantic

AVEC 2016 -Depression, Mood, and Emotion Recognition Workshop and Challenge

Keywords: A↵ective Computing, Emotion Recognition, Speech, Facial Expression, Physiological signals, Challenge

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The 2016 Audio-Visual Emotion Challenge and Workshop (AVEC 2016) will be the sixth competition event aimed at comparison of multimedia processing and machine learning methods for automatic audio, video, and physiological analysis of emotion and depression, with all participants competing under strictly the same conditions. The goal of the Challenge is to compare the relative merits of the approaches (audio, video, and/or physiologic) to emotion recognition and severity of depression estimation under welldefined and strictly comparable conditions, and establish to what extent fusion of the approaches is possible and beneficial. A second motivation is the need to advance emotion recognition for multimedia retrieval to a level where behaviomedical systems [START_REF] Valstar | Automatic behaviour understanding in medicine[END_REF] are able to deal with large volumes of non-prototypical naturalistic behaviour in reaction to known stimuli, as this is exactly the type of data that diagnostic and in particular monitoring tools, as well as other applications, would have to face in the real world.

AVEC 2016 will address emotion and depression recognition. The emotion recognition sub-challenge is a refined re-run of the AVEC 2015 challenge [START_REF] Ringeval | AVEC 2015-The first a↵ect recognition challenge bridging across audio, video, and physiological Data[END_REF], largely based on the same dataset. The depression severity estimation subchallenge is based on a novel dataset of human-agent interactions, and sees the return of depression analysis, which was a huge success in the AVEC 2013 [START_REF] Valstar | AVEC 2013 -The Continuous Audio / Visual Emotion and Depression Recognition Challenge[END_REF] and 2014 [START_REF] Valstar | AVEC 2014 -The Three Dimensional A↵ect and Depression Challenge[END_REF] challenges.

• Depression Classification Sub-Challenge (DCC):

participants are required to classify whether they are to be classified as depressed or not, where the binary ground-truth is based on the severity of self-reported depression as indicated by the PHQ-8 score for every human-agent interaction. For the DCC, performance in the competition will be measured using the average F1 score for both classes depressed and not depressed.

Participants are encouraged to provide an estimate of the severity of depression, by calculating the root mean square error over all HCI experiment sessions between the predicted and ground-truth PHQ-8 score. In addition, participants are also encouraged to report on overall accuracy, average precision, and average recall to further analyse their results in the paper accompanying their submission.

• Multimodal A↵ect Recognition Sub-Challenge (MASC) participants are required to perform fully continuous a↵ect recognition of two a↵ective dimensions: Arousal, and Valence, where the level of a↵ect has to be predicted for every moment of the recording.

For the MASC, two regression problems need to be solved: prediction of the continuous dimensions Valence and Arousal. The MASC competition measure is the Concordance Correlation Coe cient (CCC), which combines the Pearson's correlation coe cient (CC) with the square di↵erence between the mean of the two compared time series, as shown in 1.

⇢c = 2⇢

x y 2

x + 2 y + (µx µy) 2 (1)
where ⇢ is the Pearson correlation coe cient between two time series (here prediction and gold-standard),

2
x and 2 y are the variance of each time series, and µx and µy are the mean value of each. Therefore, predictions that are well correlated with the gold standard but shifted in value are penalised in proportion to the deviation.

To be eligible to participate in the challenge, every entry has to be accompanied by a paper presenting the results and the methods that created them, which will undergo peerreview. Only contributions with a relevant accepted paper will be eligible for challenge participation. The organisers reserve the right to re-evaluate the findings, but will not participate in the Challenge themselves.

DEPRESSION ANALYSIS CORPUS

The Distress Analysis Interview Corpus -Wizard of Oz (DAIC-WOZ) database is part of a larger corpus, the Distress Analysis Interview Corpus (DAIC) [START_REF] Gratch | The distress analysis interview corpus of human and computer interviews[END_REF], that contains clinical interviews designed to support the diagnosis of psychological distress conditions such as anxiety, depression, and post-traumatic stress disorder. These interviews were collected as part of a larger e↵ort to create a computer agent that interviews people and identifies verbal and nonverbal indicators of mental illness [START_REF] Devault | SimSensei kiosk: A virtual human interviewer for healthcare decision support[END_REF]. Data collected include audio and video recordings and extensive questionnaire responses; this part of the corpus includes the Wizard-of-Oz interviews, conducted by an animated virtual interviewer called Ellie, controlled by a human interviewer in another room. Data has been transcribed and annotated for a variety of verbal and non-verbal features.

Information on how to obtain shared data can be found in this location: http://dcapswoz.ict.usc.edu. Data is freely available for research purposes.

Depression Analysis Labels

The level of depression is labelled with a single value per recording using a standardised self-assessed subjective depression questionnaire, the PHQ-8 [START_REF] Kroenke | The PHQ-8 as a measure of current depression in the general population[END_REF]. This is similar to the PHQ-9 questionnaire, but with the suicidal ideation question removed for ethical reasons. The average depression severity on the training and development set of the challenge is M = 6.67 (SD = 5.75). The distribution of the depression severity scores based on the challenge training and development set is provided in Fig. 1. A baseline classifier that constantly predicts the mean score of depression provides an RM SE = 5.73 and an MAE = 4.74.

Depression Analysis Baseline Features

In the following sections we describe how the publicly available baseline feature sets are computed for either the audio or the video data. Participants can use these feature sets exclusively or in addition to their own features. For ethical reasons, no raw video is made available.

Video Features

Based on the OpenFace [2] framework 1 , we provide di↵erent types of video features:

• facial landmarks: 2D and 3D coordinates of 68 points on the face, estimated from video

• HOG (histogram of oriented gradients) features on the aligned 112x112 area of the face

• gaze direction estimate for both eyes

• head pose: 3D position and orientation of the head 1 https://github.com/TadasBaltrusaitis/CLM-framework

In addition to that, we provide emotion and facial action unit continuous measures based on FACET software [START_REF] Littlewort | The computer expression recognition toolbox (CERT)[END_REF]. Specifically, we provide the following measures:

• emotion: {Anger, Contempt, Disgust, Joy, Fear, Neutral, Sadness, Surprise, Confusion, Frustration}

• AUs: {AU1, AU2, AU4, AU5, AU6, AU7, AU9, AU10, AU12, AU14, AU15, AU17, AU18, AU20, AU23, AU24, AU25, AU26, AU28, AU43}

Audio Features

For the audio features we utilized COVAREP(v1.3.2), a freely available open source Matlab and Octave toolbox for speech analyses [START_REF] Degottex | COVAREP -A collaborative voice analysis repository for speech technologies[END_REF] 2 . The toolbox comprises well validated and tested feature extraction methods that aim to capture both voice quality as well as prosodic characteristics of the speaker. These methods have been successfully shown to be correlated with psychological distress and depression in particular [START_REF] Scherer | Automatic audiovisual behavior descriptors for psychological disorder analysis[END_REF][START_REF] Scherer | Self-reported symptoms of depression and PTSD are associated with reduced vowel space in screening interviews[END_REF]. In particular, we extracted the following features:

• Prosodic: Fundamental frequency (F0) and voicing (VUV)

• Voice Quality: Normalized amplitude quotient (NAQ), Quasi open quotient (QOQ), the di↵erence in amplitude of the first two harmonics of the differentiated glottal source spectrum (H1H2), parabolic spectral parameter (PSP), maxima dispersion quotient (MDQ), spectral tilt/slope of wavelet responses (peak-Slope), and shape parameter of the Liljencrants-Fant model of the glottal pulse dynamics (Rd)

• Spectral: Mel cepstral coe cients (MCEP0-24), Harmonic Model and Phase Distortion mean (HMPDM0-24) and deviations (HMPDD0-12).

In addition to the feature set above, raw audio and transcripts of the interview are provided, allowing participants to compute additional features on their own. For more details on the shared features and the format of the files participants should also review the DAIC-WOZ documentation3 .

EMOTION ANALYSIS CORPUS

The Remote Collaborative and A↵ective Interactions (RECOLA) database [START_REF] Ringeval | Introducing the RECOLA multimodal corpus of remote collaborative and a↵ective interactions[END_REF] was recorded to study socio-a↵ective behaviours from multimodal data in the context of computer supported collaborative work [START_REF] Ringeval | On the influence of emotional feedback on emotion awareness and gaze behavior[END_REF]. Spontaneous and naturalistic interactions were collected during the resolution of a collaborative task that was performed in dyads and remotely through video conference. Multimodal signals, i. e., audio, video, electro-cardiogram (ECG) and electro-dermal activity (EDA), were synchronously recorded from 27 French-speaking subjects. Even though all subjects speak French fluently, they have di↵erent nationalities (i. e., French, Italian or German), which thus provides some diversity in the expression of emotion. Data is freely available for research purposes, information on how to obtain the RECOLA database can be found on this location: http://diuf.unifr.ch/diva/recola.

Emotion Analysis Labels

Regarding the annotation of the dataset, time-continuous ratings (40 ms binned frames) of emotional arousal and valence were created by six gender balanced French-speaking assistants for the first five minutes of all recordings, because participants discussed more about their strategy -hence showing emotions -at the beginning of their interaction.

To assess inter-rater reliability, we computed the intraclass correlation coe cient (ICC(3,1)) [START_REF] Shrout | Intraclass correlations: Uses in assessing rater reliability[END_REF], and Cronbach's ↵ [START_REF] Cronbach | Coe cient alpha and the internal structure of tests[END_REF]; ratings are concatenated over all subjects. Additionally, we computed the root-mean-square error (RMSE), Pearson's CC and the CCC [START_REF] Li | A concordance correlation coe cient to evaluate reproducibility[END_REF]; values are averaged over the C 6 2 pairs of raters. Results indicate a very strong interrater reliability for both arousal and valence, cf. Table 1. A normalisation technique based on the Evaluator Weighted Estimator [START_REF] Grimm | Evaluation of natural emotions using self assessment manikins[END_REF], is used prior to the computation of the goldstandard, i. e., the average of all ratings for each subject [START_REF] Ringeval | Prediction of Asynchronous Dimensional Emotion Ratings from Audiovisual and Physiological Data[END_REF]. This technique has significantly (p < 0.001 for CC) improved the inter-rater reliability for both arousal and valence; the Fisher Z-transform is used to perform statistical comparisons between CC in this study.

The dataset was divided into speaker disjoint subsets for training, development (validation) and testing, by stratifying (balancing) on gender and mother tongue, cf. Table 2.

Emotion Analysis Baseline Features

In the followings we describe how the baseline feature sets are computed for video, audio, and physiological data.

Video Features

Facial expressions play an important role in the communication of emotion [START_REF] Ekman | Facial action coding system[END_REF]. Features are usually grouped in two types of facial descriptors: appearance and geometric based [START_REF] Valstar | FERA 2015 -Second Facial Expression Recognition and Analysis Challenge[END_REF]. For the video baseline features set, we computed both, using Local Gabor Binary Patterns from Three Orthogonal Planes (LGBP-TOP) [START_REF] Almaev | Local Gabor Binary Patterns from Three Orthogonal Planes for Automatic Facial Expression Recognition[END_REF] for appearance and facial landmarks [START_REF] Xiong | Supervised descent method and its applications to face alignment[END_REF] for geometric features.

The LGBP-TOP are computed by splitting the video into spatio-temporal video volumes. Each slice of the video volume extracted along 3 orthogonal planes (x-y, x-t and y-t) is first convolved with a bank of 2D Gabor filters. The resulting Gabor pictures in the direction of x-y plane are divided into 4x4 blocks. In the x-t and y-t directions they are divided into 4x1 blocks. The LBP operator is then applied to each of these resulting blocks followed by the concatenation of the resulting LBP histograms from all the blocks. A feature reduction is then performed by applying a Principal Component Analysis (PCA) from a low-rank (up to rank 500) approximation [START_REF] Halko | An algorithm for the principal component analysis of large data sets[END_REF]. We obtained 84 features representing 98 % of the variance.

In order to extract geometric features, we tracked 49 facial landmarks with the Supervised Descent Method (SDM) [START_REF] Xiong | Supervised descent method and its applications to face alignment[END_REF] and aligned them with a mean shape from stable points (located on the eye corners and on the nose region). As features, we computed the di↵erence between the coordinates of the aligned landmarks and those from the mean shape, and also between the aligned landmark locations in the previous and the current frame; this procedure provided 196 features in total. We then split the facial landmarks into groups according to three di↵erent regions: i) the left eye and left eyebrow, ii) the right eye and right eyebrow and iii) the mouth. For each of these groups, the Euclidean distances (L2-norm) and the angles (in radians) between the points are computed, providing 71 features. We also computed the Euclidean distance between the median of the stable landmarks and each aligned landmark in a video frame. In total the geometric set includes 316 features.

Both appearance and geometric feature sets are interpolated by a piecewise cubic Hermite polynomial to cope with dropped frames. Finally, the arithmetic mean and the standard-deviation are computed on all features using a sliding window, which is shifted forward at a rate of 40 ms.

Audio Features

In contrast to large scale feature sets, which have been successfully applied to many speech classification tasks [START_REF] Schuller | The INTERSPEECH 2013 Computational Paralinguistics Challenge: Social Signals, Conflict, Emotion, Autism[END_REF][START_REF] Schuller | The INTERSPEECH 2014 Computational Paralinguistics Challenge: Cognitive & Physical Load[END_REF], smaller, expert-knowledge based feature sets have also shown high robustness for the modelling of emotion from speech [START_REF] Ringeval | Emotion recognition in the wild: Incorporating voice and lip activity in multimodal decision-level fusion[END_REF][START_REF] Bone | Robust unsupervised arousal rating: A rule-based framework with knowledge-inspired vocal features[END_REF]. Some recommendations for the definition of a minimalistic acoustic standard parameter set have been recently investigated, and have led to the Geneva Minimalistic Acoustic Parameter Set (GeMAPS), and to an extended version (eGeMAPS) [START_REF] Eyben | The Geneva Minimalistic Acoustic Parameter Set (GeMAPS) for Voice Research and A↵ective Computing[END_REF], which is used here as baseline.

The acoustic low-level descriptors (LLD) cover spectral, cepstral, prosodic and voice quality information and are extracted with the openSMILE toolkit [START_REF] Eyben | Recent developments in openSMILE, the Munich open-source multimedia feature extractor[END_REF].

As the data in the RECOLA database contains long continuous recordings, we used overlapping fixed length segments, which are shifted forward at a rate of 40 ms, to extract functionals; the arithmetic mean and the coe cient of variation are computed on all 42 LLD. To pitch and loudness the following functionals are additionally applied: percentiles 20, 50 and 80, the range of percentiles 20 -80 and the mean and standard deviation of the slope of rising/falling signal parts. Functionals applied to the pitch, jitter, shimmer, and all formant related LLDs, are applied to voiced regions only. Additionally, the average RMS en-ergy is computed and 6 temporal features are included: the rate of loudness peaks per second, mean length and standard deviation of continuous voiced and unvoiced segments and the rate of voiced segments per second, approximating the pseudo syllable rate. Overall, the acoustic baseline features set contains 88 features.

Physiological Features

Physiological signals are known to be well correlated with emotion [START_REF] Koelstra | DEAP: A database for emotion analysis using physiological signals[END_REF][START_REF] Knapp | Physiological signals and their use in augmenting emotion recognition for human-machine interaction[END_REF], despite not being directly perceptible the way audio-visual are. Although there are some controversies about peripheral physiology and emotion [START_REF] Schachter | Cognition and peripheralist-centralist controversies in motivation and emotion[END_REF][START_REF] Keltner | Emotion[END_REF], we believe that autonomic measures should be considered along with audio-visual data in the realm of a↵ective computing, as they do not only provide complementary descriptions of a↵ect, but can also be easily and continuously monitored with wearable sensors [START_REF] Sanoa | Quantitative analysis of wrist electrodermal activity during sleep[END_REF][START_REF] Picard | A↵ective media and wearables: surprising findings[END_REF][START_REF] Chen | AIWAC: A↵ective interaction through wearable computing and cloud technology[END_REF].

As baseline features, we extracted features from both ECG and EDA signals with overlapping (step of 40 ms) windows. The ECG signal was firstly band-pass filtered ([3 27] Hz) with a zero-delay 6th order Butterworth filter [START_REF] Ringeval | Prediction of Asynchronous Dimensional Emotion Ratings from Audiovisual and Physiological Data[END_REF], and 19 features were then computed: the zero-crossing rate, the four first statistical moments, the normalised length density, the non-stationary index, the spectral entropy, slope, mean frequency plus 6 spectral coe cients, the power in low frequency (LF, 0.04-0.15 Hz), high frequency (HF, 0.15-0.4 Hz) and the LF/HF power ratio. Additionally, we extracted the heart rate (HR) and its measure of variability (HRV) from the filtered ECG signal [START_REF] Ringeval | Prediction of Asynchronous Dimensional Emotion Ratings from Audiovisual and Physiological Data[END_REF]. For each of those two descriptors, we computed the two first statistical moments, the arithmetic mean of rising and falling slope, and the percentage of rising values, which provided 10 features in total.

EDA reflects a rapid, transient response called skin conductance response (SCR), as well as a slower, basal drift called skin conductance level (SCL) [START_REF] Dawson | The electrodermal system[END_REF]. Both, SCL (0-0.5 Hz) and SCR (0.5-1 Hz) are estimated using a 3rd order Butterworth filter, 8 features are then computed for each of those three low-level descriptors: the four first statistical moments from the original time-series and its first order derivate w.r.t. time.

CHALLENGE BASELINES

For transparency and reproducibility, we use standard and open-source algorithms for both sub-challenges. We describe below how the baseline system was defined and the results we obtained for each modality separately, as well as on the fusion of all modalities.

Depression

The challenge baseline for the depression classification subchallenge is computed using the scikit-learn toolbox 4 . In particular, we fit a linear support vector machine with stochastic gradient descent, i.e. the loss is computed one sample at a time and the model is sequentially updated. We validated the model on the development set and conducted a grid search for optimal hyper-parameters on the development set of both the audio data and video data separately. Features of both modalities are taken from the provided challenge baseline features. Classification and training was performed on a frame-wise basis (i.e., at 100Hz for audio and 30Hz for video); temporal fusion was conducted through simple majority voting of all the frames within an entire screening interview. For both modalities we conducted a grid search for the following parameters: loss function 2 {logarithmic, hinge loss}, regularization 2 {L1, L2}, and ↵ 2 {1e1, 1e0, . . . , 1e 5}. For the audio data the optimal identified hyper-parameters are loss function = hinge loss, regularization = L1, and ↵ = 1e 3. For the video data the optimal identified hyper-parameters are loss function = logarithmic, regularization = L1, and ↵ = 1e0. The ensemble of audio and video was computed through a simple binary fusion of a logical AND. The test performance was computed on a classifier trained using the found optimal parameters from the grid search. Since the positive outputs of the video modality are a subset of those of the audio the ensemble classifier's performance is exactly the same as the video modality for both the development and test sets. Results are summarized in Table 3.

In addition to classification baseline, we also computed a regression baseline using random forest regressor. The only hyper-parameter in this experiment was the number of trees 2 10, 20, 50, 100, 200 in the random forest. For both audio and video the best performing random forest has trees = 10. Regression was performed on a frame-wise basis as the classification and temporal fusion over the interview was conduced by averaging of outputs over the entire screening interview. Fusion of audio and video modalities was performed by averaging the regression outputs of the unimodal random forest regressors. The performance for both root mean square error (RMSE) and mean absolute error (MAE) for development and test sets is provided in Table 4.

Table 5: Size of the window W in seconds used to extract features on the di↵erent modalities, and delay D in seconds applied to the gold-standard, according to the emotional dimension, i. e., arousal (A), and valence (V ); parameters were obtained as the result of an optimisation of the performance measured as CCC on the development partition.

Arousal

Affect

Mono-modal emotion recognition was first investigated separately for each modality. Baseline features were extracted as previously described, with a window size W ranging from four to 14 seconds, and a step of two seconds. The window was centred, i. e., the first feature vector was assigned to the center of the window (W/2), and duplicated for the previous frames; the same procedure was applied for the last frames. For video data, frames for which the face was not detected were ignored. For EDA, SCL, and SCR, test data from the subject #7 was not used, due to issue during the recording of this subject (sensor was partially detached from the skin). Two di↵erent techniques were investigated to standardise the features: (i) online (standardisation parameters µ and are computed on the training partition and used on all partitions), and (ii) speaker dependent (µ and are computed and applied on features of each subject). In order to compensate time reaction of the raters, a time delay D is applied to the gold-standard, by shifting back in time the values of the time-series (last value was duplicated), with a delay ranging from zero to eight seconds, and a step of 400ms.

As machine learning, we used a linear Support Vector Machine (SVM) to perform the regression task with the liblinear library [START_REF] Fan | LIBLINEAR: A library for large linear classification[END_REF]; the L2-regularised L2-loss dual solver was chosen (option -s 12) and a unit bias was added to the feature vector (option -B 1), all others parameters were kept to default. The complexity of the SVM was optimised in the range [10 5 10 0 ]. In order to compensate for scaling and bias issues in the predictions, but also noise in the data, we used the same post-processing chain as employed in [START_REF] Trigeorgis | Adieu features? End-to-end speech emotion recognition using a deep convolutional recurrent network[END_REF]. The window size W and the time delay D were optimised by a grid search with an early stopping strategy, i. e., evaluations were stopped if no improvement was observed over the best score after two iterations. Experiments were always performed for both standardisation strategies, i. e., online and per speaker. The best value of complexity, window size, time delay, and standardisation method were obtained by maximising the performance -measured as CCC -on the development partition with the model, learned on the training partition. Table 5 lists the best parameters for W and D, for each modality and emotional dimension, and shows that, the valence generally requires longer window size (to extract features) and time delay (to compensate for reaction time) than for arousal; WA = 5.3, WV = 9.3, DA = 1.2, DV = 1.8. Moreover, the results show that, a separate processing of features related to ECG, i. e., HRHV, and those related to EDA, i. e., SCL, and SCR, is justified as the best parameters obtained those signals di↵er from the ones obtained on their original signal. Regarding the standardisation technique, the online approach worked best for audio on both dimensions, and video data on valence, whereas standardisation of the features per subject worked best for all physiological features.

Mono-modal performance is reported in Table 6. Results show that, a significant improvement has been made for all modalities compared to the AVEC 2015 baseline [START_REF] Ringeval | AVEC 2015-The first a↵ect recognition challenge bridging across audio, video, and physiological Data[END_REF], excepted for the EDA features. In agreement with the stateof-the-art, audio features perform significantly better than any other modality on arousal, and video features on valence. Interestingly, emotion prediction from the HRHRV signal performs significantly better than with the original ECG signal, and it is ranked as the most relevant physiological descriptor for arousal, when taken alone.

Multimodal emotion recognition is performed with three di↵erent late-fusion models, because frames might be missing on the video, and EDA related features; (i) audio-ECG, used for missing video and EDA; (ii) audio-ECG-EDA, used for missing video; (iii) audio-ECG-EDA-video, used otherwise. In order to keep the complexity low, and estimate the contribution of each modality in the fusion process, we build the fusion model by a simple linear regression of the predictions obtained on the development partition, using Weka 3.7 with default parameters [START_REF] Hall | The WEKA data mining software: an update[END_REF]. Obtained predictions were then post-processed with the same approach used for the mono-modal predictions.

P redm = ✏m + N X i=1 i ⇤ P redu(i), (2)
where P redu(i) is the mono-modal prediction of the modality i from the N available ones (ranging from two to eight), i and ✏m are regression coe cients estimated on the development partition, and P redm is the fused prediction.

Performance is reported in Table 6. Results show that, the baseline for the AVEC 2016 MASC is highly competitive, with the performance obtained on valence for the test partition being slightly better than the top-performer of AVEC 2015 [START_REF] He | Multimodal A↵ective Dimension Prediction Using Deep Bidirectional Long Short-Term Memory Recurrent Neural Networks[END_REF]. In order to depict the contribution of each modality in the prediction of emotion, we normalised the linear regression coe cients that were learned for the multimodal fusion model (iv) into a percentage:

Ci = 100 ⇤ | i| P N k=1 | k | , ( 3
)
where Ci is the contribution of the modality i in percentage, and k are the regression coe cients of the multimodal fusion model; N = 8.

Results show that, even if the mono-modal performance can be low for a given modality and emotion, e. g., EDA for arousal or SCR for valence, cf. Table 6, all modalities contribute, to a certain extent, to the prediction of arousal and valence in the fusion scenario, cf. Figure 2. This is especially the case for SCR features on arousal and for SCL features on valence, which did not perform well when used in isolation, but contribute even outperformed appearance features in the fusion model.

CONCLUSION

We introduced AVEC 2016 -the third combined open Audio/Visual Emotion and Depression recognition Challenge. It comprises two sub-challenges: the detection of the a↵ective dimensions of arousal and valence, and the estimation of a self-reported level of depression. This manuscript describes AVEC 2016's challenge conditions, data, baseline features and results. By intention, we opted to use open-source software and the highest possible transparency and realism for the baselines by refraining from feature space optimisation and optimising on test data. This should improve the reproducibility of the baseline results.

Figure 1 :

 1 Figure 1: Histogram of depression severity scores for DESC challenge. Data of training and development set are provided here.

Figure 2 :

 2 Figure 2: Percentage of contribution of each modality in the prediction of emotion; values are derived from the multimodal fusion model; V-APP: video appearance; V-GEO: video geometric; ECG: electrocardiogram; HRHV: heart rate and heart rate variability; EDA: electrodermal activity; SCL: skin conductance level; SCR: skin conductance resistance.

Table 1 :

 1 Inter-rater reliability on arousal and valence for the 6 raters and the 27 subjects of the RECOLA database; raw or normalised ratings[START_REF] Ringeval | Prediction of Asynchronous Dimensional Emotion Ratings from Audiovisual and Physiological Data[END_REF].

		RMSE CC CCC ICC	↵
			Raw
	Arousal	.344	.400 .277 .775 .800
	Valence	.218	.446 .370 .811 .802
			Normalised
	Arousal	.263	.496 .431 .827 .856
	Valence	.174	.492 .478 .844 .829

Table 2 :

 2 Partitioning of the RECOLA database into train, development, and test sets.

	#	train	dev	test
	female	6	5	5
	male	3	4	4
	French	6	7	7
	Italian	2	1	2
	German	1	1	0

age µ ( ) 21.2 (1.9) 21.8 (2.5) 21.2 (1.9)

Table 3 :

 3 Baseline results for depression classification. Performance is measured in F1 score for depressed and not depressed classes as reported through the PHQ-8. In addition, precision and recall are provided. Values for class not depressed are reported in brackets.

	Partition	Modality	F1 score	Precision	Recall
	Development Audio	.462 (.682) .316 (.938) .857 (0.54)
	Development Video	.500 (.896) .600 (.867) .428 (.928)
	Development Ensemble .500 (.896) .600 (.867) .428 (.928)
	Test	Audio	.410 (.582) .267 (.941) .889 (.421)
	Test	Video	.583 (.851) .467 (.938) .778 (.790)
	Test	Ensemble .583 (.851) .467 (.938) .778 (.790)

Table 4 :

 4 Baseline results for depression severity estimation. Performance is measured in mean absolute error (MAE) and root mean square error (RMSE) between the predicted and reported PHQ-8 scores, averaged over all sequences.

	Partition	Modality	RMSE MAE
	Development Audio	6.74	5.36
	Development Video	7.13	5.88
	Development Audio-Video	6.62	5.52
	Test	Audio	7.78	5.72
	Test	Video	6.97	6.12
	Test	Audio-Video	7.05	5.66

Table 6 :

 6 Baseline results for a↵ect recognition on the development (D) and test (T) partitions from audio, video (appearance and geometric), and physiologic (ECG, HRHRV, EDA, SCL, and SCR) feature sets, and their late fusion (multimodal). Performance is measured in Concordance correlation coe cient.

	Modality	Arousal Valence
	D-Audio	.796	.455
	D-Video-appearance	.483	.474
	D-Video-geometric	.379	.612
	D-ECG	.271	.153
	D-HRHRV	.379	.293
	D-EDA	.073	.194
	D-SCL	.068	.166
	D-SCR	.073	.085
	D-Multimodal	.821	.683
	T-Audio	.648	.375
	T-Video-appearance	.343	.486
	T-Video-geometric	.272	.507
	T-ECG	.158	.121
	T-HRHRV	.334	.198
	T-EDA	.075	.228
	T-SCL	.066	.216
	T-SCR	.065	.145
	T-Multimodal	.683	.639

http://covarep.github.io/covarep/

http://dcapswoz.ict.usc.edu/wwwutil files/ DAICWOZDepression Documentation.pdf

http://scikit-learn.org/

Acknowledgements

The research leading to these results has received funding from the EC's 7th Framework Programme through the ERC Starting Grant No. 338164 (iHEARu), and the European Union's Horizon 2020 Programme through the Innovative Action No. 645094 (SEWA), and the Research Innovative Action No. 645378 (ARIA-VALUSPA), and No. 688835 (DE-ENIGMA).


Luca Roatta
email: lucaroa@gmail.com

Discretization of space and time: consequences of modified gravitational law

Assuming that space and time can only have discrete values, it is shown that the modified law of gravitational attraction implies that the third principle of dynamics is not fully respected and that only bodies with sufficient mass can exert gravitational attraction.

Introduction

Let's assume, as work hypothesis, the existence of both discrete space and discrete time, namely spatial and temporal intervals not further divisible; this assumption leads to some interesting consequences. Here we find that in this discrete context the modified gravitational law obtained in a previous document [START_REF] Roatta | Discretization of space and time: a slight modification to the Newtonian gravitation which implies the existence of black holes[END_REF] causes a (little) violation of the third principle of dynamics. We also find that not all bodies can exert gravitational attraction: the condition that allows a body to deform the discrete space, and consequently exert a gravitational force, is that its mass must not be lower than a minimum mass.

So, if we suppose that neither space nor time are continuous, but that instead both are discrete, and following the terminology used in a previous document [START_REF] Roatta | Discretization of space and time in wave mechanics: the validity limit[END_REF] , we call l 0 the fundamental length and t 0 the fundamental time.

Difference between discrete gravitational force and Newtonian

In a previous document [START_REF] Roatta | Discretization of space and time: a slight modification to the Newtonian gravitation which implies the existence of black holes[END_REF] we obtained that in a discrete context the modified expression of the gravitational force exerted by a body A having mass M on a body B having mass m at the distance r>d from A is:

f (r )=-mc 2 r (r -l 0 ) d (r-d) 2 (1)
where

d= GM c 2 (2)
is the radius of the black hole of mass M.

If r»l 0 Eq. (1) becomes:

f (r )=- GMm (r-d ) 2 (3)
The Newtonian force acting on B is:

f N (r)=- GMm r 2 (4)
The difference between Eq. (3) and Eq. ( 4) f(r)-f N (r), when r»d, is:

f (r )-f N ( r)=- 2 GMmd r 3 (5)
that is the exact expression of a tidal force. It seems that in this discrete context the new expression of the gravitational force contains a term which takes account of tidal effects. It is an aspect that should be further investigated.

A (little) violation of the third principle of dynamics

The term d in Eq. ( 2) is also present in the expression [START_REF] Roatta | Discretization of space and time: how matter deforms space and time[END_REF] of the discrete space deformed by matter:

l 0 (r )=l 0 r -d r (6)
Depending d on the mass of only one body (in this case the body A), it's evident that the value of l 0 (r) is different if we consider how the body B modifies the discrete space, because in this case we have:

d= Gm c 2 (7)
The difference in Eq. ( 6) when d is expressed by Eq. ( 2) or by Eq. ( 7) becomes irrelevant when r»d, but it evidences a quite surprising fact: also Eq. ( 1), that expresses the force that the body A exerts on the body B, depends on d so, if we consider the force exerted by B on A, we obtain a different result, due to the presence of a different value of d at the denominator of Eq. ( 1).

This means that the gravitational force exerted by A on B is different from the gravitational force exerted by B on A. This difference (that when calculated for r»d has the exact form of two tidal forces, one acting on A and one acting on B) tends to disappear when r»d, but it implies the violation of the third principle of mechanics, at least in this gravitational context.

Many other documents [START_REF] Harvey | Einstein, the reality of space and the action-reaction principle[END_REF][5][6] [START_REF] Buenzli | Violation of action-reaction and self-forces induced by nonequilibrium fluctuations[END_REF] speak about the violation of the action-reaction principle in particular circumstances, so it doesn't seem to be a completely new concept.

In this discrete context, however, the expected violation can be useful to design an experiment that could confirm or disprove this theory: with a sufficiently sensitive torsion balance, it would be possible to test this difference.

The minimum mass for gravitational attraction

In a previous document [START_REF] Roatta | Discretization of space and time in wave mechanics: the validity limit[END_REF] we have already determined the existence of a maximum frequency and its value. For black holes there is a similar limit: as for any length, also for d=GM/c 2 , the radius of the black hole of mass M, must be d≥l 0 . This means M≥l 0 c 2 /G; so there is a minimum mass a body must have to be a black hole:

m min = l 0 c 2 G (8)
A mass lower than m min can not generate a black hole, because its radius should be less than l 0 . Also in this case, as can be noted, in the continuous context (l 0 → 0) there is no lower limit for the mass of a black hole.

The fact that must be d≥l 0 implies that in Eq. ( 1) it is impossible to have arbitrarily small masses, because the limit M≥m min must always be satisfied.

Of course it does not mean that masses lower than m min can not exist: it means however that lower masses can not originate gravitational attraction and, or rather because, they can not warp space, as shown in a previous document [START_REF] Roatta | Discretization of space and time: how matter deforms space and time[END_REF] .

This has the consequence that General Relativity is not valid for masses lower than m min , which so constitutes the lower limit of applicability of General Relativity, similarly to the mass indicated in [2], which constitutes the upper limit of applicability of wave mechanics and therefore also of quantum physics.

It is known or supposed that General Relativity breaks down at the Planck scale [START_REF] Durrer | Dark energy and modified gravity[END_REF] , or inside of a black hole [START_REF] Smolin | The fate of black hole singularities and the parameters of the standard models of particle physics and cosmology[END_REF] , or at high energies [START_REF] Tao | Free-fall Frame Black Hole in Gravity's Rainbow[END_REF] , or at singularities [START_REF] Cristinel | Spacetimes with Singularities[END_REF] ; so also the limit of applicability of General Relativity found in this discrete context does not seem to be a completely new concept.

Conclusion

Assuming that space and time can only have discrete values, it has been shown that the modified law of gravitational attraction implies that the third principle of dynamics is not fully respected and that only bodies with sufficient mass can exert gravitational attraction. Both arguments do not represent completely new concepts.