Abderrahman Ben Khalifa
email: abderrahman.ben-khalifa@insa-lyon.fr

Razvan Stanica

Performance Evaluation of Channel Access Methods for Dedicated IoT Networks

Networking technologies dedicated for the Internet of Things are different from the classical mobile networks in terms of architecture and applications. This new type of network is facing several challenges to satisfy specific user requirements. Sharing the communication medium between (hundreds of) thousands of connected nodes and one base station is one of these main requirements, hence the necessity to imagine new solutions, or to adapt existing ones, for medium access control. In this paper, we start by comparing two classical medium access control protocols, CSMA/CA and Aloha, in the context of Internet of Things dedicated networks. We continue by evaluating a specific adaptation of Aloha, already used in low-power wide area networks, where no acknowledgement messages are transmitted in the network. Finally, we apply the same concept to CSMA/CA, showing that this can bring a number of benefits. The results we obtain after a thorough simulation study show that the choice of the best protocol depends on many parameters (number of connected objects, traffic arrival rate, allowed retransmission number), as well as on the metric of interest (e.g. packet reception probability or energy consumption).

I. INTRODUCTION

After almost two decades of research on multi-hop wireless sensor networks, we are witnessing today a paradigm shift, where small, energy constrained things are connected to the rest of the world through one-hop, cellular dedicated networks, also described as low-power wide area networks (LPWAN) [START_REF] Raza | Low Power Wide Area Networks: An Overview[END_REF]. Multiple technologies are competing in this dedicated Internet of Things (IoT) market, either proposed by new players (e.g. Sigfox [START_REF] Mo | Theoretical Analysis of UNB-based IoT Networks with Path Loss and Random Spectrum Access[END_REF], LoRa [START_REF] Iova | LoRa from the City to the Mountains: Exploration of Hardware and Environmental Factors[END_REF]), or backed up by well established standardization bodies, (e.g. NB-IoT from the 3GPP consortium [START_REF] Wang | A Primer on 3GPP Narrowband Internet of Things[END_REF], or IEEE 802.11ah from the WiFi Alliance [START_REF] Adame | IEEE 802.11ah: The WiFi Approach for M2M Communications[END_REF]). Practically, dedicated IoT networks are characterized by a cellular architecture, with a central base station or gateway, collecting data from a number of objects in its coverage.

Another common characteristic of all these technologies is that they follow one of two classical channel access schemes: Aloha or Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA). The only modification brought to these classical approaches is that, in some technologies, Aloha is modified in order to not transmit acknowledgment (ACK) messages, generally because a downlink is not always available in these networks.

Basically, three main MAC layer solutions are currently competing in the IoT world. First of all, the technologies coming from the 3GPP world, whether LTE-M or NB-IoT [START_REF] Lauridsen | Coverage and Capacity Analysis of LTE-M and NB-IoT in a Rural Area[END_REF], are using classical Aloha solutions. More precisely, these technologies use a slotted-Aloha approach [START_REF] Cherkaoui | LTE-A Random Access Channel Capacity Evaluation for M2M Communications[END_REF], where nodes can only access the medium on specific time-frequency blocks of the LTE random access channel.

A second class of IoT technologies, known as LPWAN, is also based on an Aloha MAC protocol. Indeed, Aloha is a very simple strategy, where the MAC layer directly transmits any message produced by the application layer. Easy to implement and without any strong synchronization requirements, Aloha was the obvious choice for new technologies, such as Sigfox [START_REF] Mo | Theoretical Analysis of UNB-based IoT Networks with Path Loss and Random Spectrum Access[END_REF] and LoRa [START_REF] Iova | LoRa from the City to the Mountains: Exploration of Hardware and Environmental Factors[END_REF]. However, these technologies also needed to cope with the well known poor scalability of Aloha; this was done by over-provisioning, the temporal Aloha space being expanded in the frequency domain (e.g. in Sigfox) or in the code domain (e.g. in LoRa). Moreover, these technologies are generally asymmetrical, meaning that the downlink is (very) limited. This has a direct consequence on the MAC layer, as the gateway does not acknowledge the reception of data messages from the nodes.

Finally, the most successful wireless technology nowadays, WiFi, is also making a place in the IoT world, through a new amendment known as WiFi HaLow, and standardized as IEEE 802.11ah [START_REF] Adame | IEEE 802.11ah: The WiFi Approach for M2M Communications[END_REF]. As all the technologies from the IEEE 802.11 family, WiFi HaLow is based on a CSMA/CA MAC layer. The main difference with respect to the classical Distributed Contention Function (DCF) used in IEEE 802.11 is that the existing stations are divided into groups, and the contention only happens between stations from the same group. The gateway defines the different time intervals for each contending group.

Our objective in this paper is not to study the specificities of each of these technologies. Instead, we want to focus on the basic properties of Aloha and CSMA/CA access strategies, in order to understand whether one of these solutions is more appropriate than the other in the IoT context.

As a matter of fact, Aloha and CSMA/CA have been well studied and compared in the literature, starting from the '70s [START_REF] Kleinrock | Packet switching in radio channels: Part I-Carrier sense multiple-access modes and their throughput-delay characteristics[END_REF] and until the modern days [START_REF] Blaszczyszyn | A Comparison of ALOHA and CSMA in Wireless Ad Hoc Networks under Different Channel Conditions[END_REF]. However, the performance of the two schemes is generally evaluated in terms of throughput, while considering stations with saturated traffic. This is normal in wireless local wireless networks, where the objective is to have a reliable and rapid communication, generally in terms of file transfer. However, IoT scenarios are very different, characterized by dense networks with sparse, unsaturated traffic. The classic use-case in these networks is data collection, where measures of some physical phenomenon (e.g. air pollution [START_REF] Boubrima | Optimal Deployment of Wireless Sensor Networks for Air Pollution Monitoring[END_REF] or vehicular traffic [START_REF] Komguem | WARIM: Wireless Sensor Network Architecture for a Reliable Intersection Monitoring[END_REF]) are uploaded to a central server. In this case, the throughput is no longer an essential metric, as the performance of the IoT applications is much better described by metrics such as the packet reception ratio.

In this paper, we focus on these IoT metrics, through an extensive simulation study, detailed in Sec. III. We compare classic Aloha and CSMA/CA in Sec. IV, showing that each of them is adapted to certain IoT scenarios and metrics. We evaluate the LPWAN flavor of Aloha, which does not use ACKs, in Sec. V. Interestingly, our results show that removing ACKs does not only conserve energy, but it can even improve the packet reception probability. Finally, for the first time in the literature, we apply the same concept of removing ACKs to CSMA/CA in Sec. VI, showing interesting performance gains.

II. RELATED WORK

Aloha and CSMA/CA are among the first MAC protocols to be proposed in the history of wireless networks. As a consequence, they have been thoroughly studied and compared in the last four decades [START_REF] Kleinrock | Packet switching in radio channels: Part I-Carrier sense multiple-access modes and their throughput-delay characteristics[END_REF]. However, despite considering the impact of numerous parameters, such as the buffer size [START_REF] Saadawi | Analysis, Stability and Optimisation of Slotted Aloha with a Finite Number of Buffered Users[END_REF] or the number of retransmissions [START_REF] Raychaudhuri | Performance Evaluation of Slotted Aloha with Generalized Retransmission Backoff[END_REF], most of these studies focused on scenarios with saturated stations, i.e. users who always have packets to transmit to one another. This is quite different, both in terms of system functioning and metrics, from the dedicated IoT networks we are interested in.

While new theoretical tools, e.g. based on stochastic geometry [START_REF] Blaszczyszyn | A Comparison of ALOHA and CSMA in Wireless Ad Hoc Networks under Different Channel Conditions[END_REF], were developed recently, the studied scenarios remained generally the same. Even in the few studies where Aloha and CSMA/CA were compared in scenarios with unsaturated traffic [START_REF] Dai | Toward a Coherent Theory of CSMA and Aloha[END_REF], the system throughput was still used as the main metric. On the other side, in the cases where an evolution can be noticed in terms of the studied metrics (e.g. the distribution of the channel access delay [START_REF] Yang | Delay Distributions of Slotted ALOHA and CSMA[END_REF]), saturated traffic is considered.

In related fields, where new wireless network architectures are imagined, e.g. in mobile ad hoc networks [START_REF] Baccelli | Stochastic Analysis of Spatial and Opportunistic Aloha[END_REF] or in vehicular networks [START_REF] Sakata | Throughput Comparison of CSMA and CDMA slotted ALOHA in Inter-Vehicle Communication[END_REF], Aloha and CSMA/CA are always among the first MAC solutions to be tested. However, these studies remain focused on throughput in saturated traffic conditions.

Regarding dedicated IoT networks, two recent studies [START_REF] Li | 2D Time-Frequency Interference Modelling using Stochastic Geometry for Performance Evaluation in Low-Power Wide-Area Networks[END_REF], [START_REF] Song | An Analytical Model for S-ALOHA Performance Evaluation in M2M Networks[END_REF] evaluate the performance of Aloha-based techniques. Li et al. [START_REF] Li | 2D Time-Frequency Interference Modelling using Stochastic Geometry for Performance Evaluation in Low-Power Wide-Area Networks[END_REF] take a stochastic geometry approach, focusing on throughput and on the outage probability of a station, defined as the probability that a station observes a signal to noise and interference ratio (SINR) above a certain threshold. Song et al. [START_REF] Song | An Analytical Model for S-ALOHA Performance Evaluation in M2M Networks[END_REF] argue that packet delivery ratio is a more suitable metric in IoT use-cases, and they study the performance of slotted-Aloha with respect to this metric. However, the only parameter considered in [START_REF] Song | An Analytical Model for S-ALOHA Performance Evaluation in M2M Networks[END_REF] is the packet arrival rate.

Most of these studies focus on analytical models, which are essential tools in the understanding of a network protocol. However, this type of mathematical modeling usually requires some important simplifications: e.g. the use of slotted-Aloha instead of Aloha [START_REF] Song | An Analytical Model for S-ALOHA Performance Evaluation in M2M Networks[END_REF], independence of retransmissions [START_REF] Baccelli | Stochastic Analysis of Spatial and Opportunistic Aloha[END_REF], or simplified CSMA/CA back-off [START_REF] Blaszczyszyn | A Comparison of ALOHA and CSMA in Wireless Ad Hoc Networks under Different Channel Conditions[END_REF]. Instead, we propose a thorough simulation study, removing most of these artificial assumptions, in order to evaluate different MAC solutions in dedicated IoT networks.

III. SIMULATION METHODOLOGY

We use the Network Simulator 3 (ns3) to study a dedicated IoT network with N sender nodes and one sink node. The network topology is a circle with radius r and the base station sink node is its center, while the sender nodes are uniformly distributed inside this area and they all share the same channel.

Each sender node produces one packet of data each time period T , while the sink node only transmits ACK frames (in case the MAC protocol uses them). Different IoT technologies achieve very different data rates at the physical layer, from 100 b/s in Sigfox to several Mb/s in WiFi HaLow. In order to have a fair, but technology agnostic comparison, we are using as a parameter the transmission opportunity, T op = S/T , where S is the airtime of a MAC layer frame. As an example, a T op value of 165 • 10 -6 corresponds to a packet arrival every second in WiFi HaLow and every 20 minutes in SigFox.

Unlike previous studies, which mostly focus on the throughput as an evaluation metric, we use metrics more relevant for the IoT context: the packet success probability and the time each node spends in an ON state (receiving, transmitting or listening to the channel). We consider that this second metric is a good generic proxy for the energy consumption of a node. For the CSMA/CA protocol, we used the ns3 AdhocWifi-Mac as a MAC layer model, using the parameters indicated in Tab. I. Since ns3 does not directly provide an Aloha implementation 1 , we adapted the same AdhocWifiMac model used in the CSMA/CA case. This allowed us to have the same basis implementation for the two solutions, for a fair evaluation. The first adaptation required in order to model Aloha was to deactivate the clear channel assessment (CCA) mechanism, which implements the carrier sensing operation. Since Aloha does not use carrier sensing, we set the CCA threshold to an infinite value, so that the node always considers the channel as free and the transmissions are never blocked. Another adaption consists in deactivating the random backoff used in CSMA/CA before a new transmission; we do this by setting the maximum contention window to 0 in AdhocWifiMac.

We run simulations while varying the number of sender nodes. Every simulation lasts 30 seconds and it is repeated 10 times, with a different seed value each time. All the results presented in the remainder of the paper are shown with a confidence interval of 95%.

IV. ALOHA AND CSMA/CA COMPARISON We begin our study by comparing the classical Aloha and CSMA/CA solutions in a dedicated IoT context. We evaluate the packet success probability and the time spent by the nodes in an active ON state, while also looking at the impact of the number of authorized retransmissions.

A. Packet Success Probability

The essential performance metric in IoT networks is the success probability of a message. The small size of the messages transmitted by the nodes allows their encapsulation into single packets, which are possibly transmitted multiple times as MAC layer frames. Since we are interested in the overall performance of the MAC layer, in Fig. 1 we present the average packet success probability of the two MAC protocols studied in this section, calculated for different number of contending nodes and packet arrival periods (given as a varying number of transmission opportunities). In Fig. 1a, showing the packet success probability obtained for a transmission opportunity T op = 165 • 10 -5 and for different number of nodes, we can distinguish two different regions. In the first region, for small networks up to 100 nodes, the CSMA/CA and Aloha success probabilities are both equal or near to 1. In the second region, for medium size and dense networks, the performance of the two protocols starts decreasing, with CSMA/CA getting the best results. This is expected, as CSMA/CA is using a CCA mechanisms to reduce the number of collisions and a back-off technique to avoid their repetition.

To complement these results, we also show the packet success probability for a transmission opportunity value ten times smaller in Fig. 1b. This corresponds to scenarios with a more reduced packet arrival rate. A similar trend can be observed, but the capacity of the network, in terms of number of nodes, increases.

B. Node ON Time

The energy consumption is an important metric for most IoT devices, constrained in terms of size, hence battery. In this work, we do not directly compute the node energy consumption, as this would limit us to the numeric values of a particular technology. Instead, we calculate a correlated metric: the duration each node spends in an ON state, i.e. the time the node is using its radio module, either for transmission, reception or listening the channel. In the case of Aloha, we consider that the node is continuously listening the channel while waiting for an ACK message. In the case of CSMA/CA, we consider that the node is ON to sense the channel during the back-off slots and after the transmission, listening to the channel waiting for an ACK message. Fig. 2 shows the average ON time for the two protocols, for two values of the transmission opportunity parameter and for different number of nodes. We observe that, for a low density network, both protocols have almost the same energy consumption, because we are not facing any collision or CSMA/CA back-off yet. Interestingly, as the number of nodes increases, CSMA/CA becomes more energy-friendly than Aloha for a while, since the latter solution results in more collisions and therefore requires more retransmissions. However, after a certain threshold, Aloha demonstrates a much better performance, consuming 10 times less energy than CSMA/CA. This trend is observed for both values of T op , in Fig. 2a and in Fig. 2b.

C. Retransmission Number Impact

Both CSMA/CA and Aloha use backoff-based retransmissions in case of a missing ACK. In CSMA/CA, the retransmissions follow a binary exponential back-off, which increases for each missing ACK. When the maximum number of retransmissions R is reached, the message is dropped and the packet is considered as lost. We simulated Aloha and CSMA/CA with a maximum number of retransmission of 3, 5 and 7, while keeping the other default MAC layer parameters from Tab. I. Fig. 3a shows the packet success probability with a variable maximum number of retransmission, showing the significant impact of this parameter. For Aloha, we notice that the lower the number of retransmissions, the better the performance of the protocol. This is because a higher number of authorized retransmissions increases the collision probability. Aloha is also obtaining the best energy consumption results with the lowest number of retransmissions, as shown in Fig. 3b.

For CSMA/CA, the results are more mitigated: the packet success probability first decreases with R, just as in Aloha, but it then increases again (CSMA/CA with R = 7 gives the best performance in Fig. 3a). This is the consequence of two opposite behaviors: the increased overall collision probability with more retransmissions and the binary exponential back-off which reduces the collision probability for higher retransmission indices.

We can see as well that CSMA/CA is obtaining better results than Aloha almost all the time in terms of reliability, except with R = 5 for a network of 250 nodes. This comes with an energy price, as CSMA/CA consumes more energy in networks of more than 250 nodes and this energy consumption increases with R (please note the log-scale on the y-axis in Fig. 3b). However, we still observe that CSMA/CA energetically outperforms Aloha for networks of 10 to 250 nodes.

From all these results, we can conclude that the best choice between Aloha and CSMA/CA in an IoT context depends on the metric we want to satisfy: Aloha gives better results energy-wise, while CSMA increases the packet success probability. The environment, e.g. the number of nodes and the packet arrival rate, also plays a major impact on the protocol choice, and so are the different parameters of the two protocols (maximum number of retransmissions, back-off mechanism).

V. ALOHA FOR DEDICATED IOT NETWORKS

As explained above, Aloha has been adapted to LPWAN technologies by removing the ACK messages. This mainly comes from a limitation of LPWAN solutions, where a downlink is not always available [START_REF] Raza | Low Power Wide Area Networks: An Overview[END_REF]. Instead, for reliability reasons, K copies of each message are transmitted by the nodes.

In this context, we study the impact of the absence of ACK messages, as well as that of the number of transmitted copies K, on the network performance. For this, we simulate a modified version of Aloha, under the same conditions as the previous simulations. This modified Aloha version, which we denote as Aloha No Ack, sends each packet K times at the MAC layer, without waiting for any ACK message. For example, Sigfox currently uses a static value of K = 3 in their system. For the case of K = 1, the node sends the packet only once and goes back to sleep. For the case of K > 1, the node wakes up and sends the packet once, and then sleeps a random number of slots before waking up again to send the next copy of the packet.

Fig. 4 shows the results of transmission reliability and energy consumption obtained when comparing Aloha No Ack and classical Aloha. We remark that removing the ACK messages is not only a necessity to cope with a missing downlink, but it actually improves the packet success probability. Indeed, Aloha No Ack with K = 3 is outperforming all the other Aloha and Aloha No Ack flavors in terms of reliability.

On the energy consumption side, Aloha No Ack has a constant ON time, which only depends on the number of transmitted copies K and it can be computed as K • S. Aloha No Ack with K = 3 consumes more energy than classical Aloha for a network with less than 250 nodes, but it outperforms the ACK-based approach for denser networks.

We note that ACK messages are considered as a prominent mechanism for reliability purposes at the MAC layer. In any throughput-focused solution, ACKs represent an essential feed-back to the transmitter. However, the results we obtained in this section demonstrate that removing ACKs actually brings benefits in IoT networks, when focusing on metrics such as packet success probability and energy consumption.

VI. CSMA/CA FOR DEDICATED IOT NETWORKS

Similarly to how Aloha has been adapted for LPWANs, we propose removing ACKs from CSMA/CA as well. This solution, similar to what is used to transmit broadcast traffic in WiFi networks [START_REF] Ma | Performance Analysis of IEEE 802.11 Broadcast Scheme in Ad Hoc Wireless LANs[END_REF], has not been priorly tested in IoT scenarios. In this solution, denoted as CSMA No Ack, we use a similar parameter for the number of transmitted copies, K. Practically, a node wakes up to transmit a copy of the message and follows the CCA procedure. If the medium is detected as busy, the node transmits at the end of the back-off procedure. In order to transmit the next copy of the message, the procedure is repeated. However, in order to avoid collisions, a back-off procedure is needed between the transmission of two copies. Since no ACK messages are used, the contention window used by the back-off mechanism, denoted as CW , can not be dynamically adapted. In Fig. 5, we compare the performance of the classical CSMA/CA and the modified CSMA/CA version, where no ACK messages are used. For the packet success probability, shown in Fig. 5a, classical CSMA/CA obtains better performance for a network with less than 250 nodes. When the network density increases, we observe a phenomenon similar to the Aloha case: removing the ACK messages actually reduces congestion on the channel and allows CSMA No Ack to obtain up to 20% better performance than classical CSMA/CA. On the energy side (Fig. 5b), CSMA No Ack has an almost constant behavior: the slight increase one can notice for CSMA No Ack with K = 1 is a consequence of the longer time required by the back-off procedure under high network density. On the other side, the classical approach shows a significant energy consumption increase in dense networks, where more retransmissions are needed.

An important parameter for CSMA No Ack is the size of the contention window, CW , used between the transmission of two message copies. Fig. 5b shows the impact of this parameter on the active ON time of a node, for K = 2. Basically, the higher CW , the higher the node ON time and the higher its energy consumption. In Fig. 6, we compare the two modified versions, Aloha No Ack and CSMA No Ack. Fig. 6a shows the packet success probability for the two protocols, with a K varying from 1 to 3. The simple fact of using a CCA mechanism before a transmission improves the packet success probability by close to 10% in high dense networks. However, this comes with a price on the energy side, as shown in Fig. 6b. For K = 1, CSMA No Ack only spends the extra-energy of a CCA mechanism. However, when K increases, the cost of the backoff mechanism is added and the consumption of CSMA/CA can reach up to 100x the consumption of Aloha.

VII. CONCLUSIONS

In this paper, we discuss MAC layer solutions for dedicated IoT networks and evaluate them through ns3 simulation. We show that the best MAC layer approach depends on parameters such as the number of competing nodes and the packet arrival rate. In addition, we remark that using ACK frames can have a negative impact, always reducing the network performance in terms of reliability and energy consumption.

Following this study, we believe that the MAC strategy for dedicated IoT network needs to adapt to the network state and to the target metric. Moreover, depending on the local traffic density, different MAC solutions can be used in different parts of the cell, orchestrated by a smart gateway. We will explore such approaches in our future work.

  (a) Top = 165 • 10 -5 (b) Top = 165 • 10 -6

Fig. 1 .

 1 Fig. 1. Packet success probability for Aloha and CSMA/CA in an IoT context.

  (a) Top = 165 • 10 -5 (b) Top = 165 • 10 -6

Fig. 2 .

 2 Fig. 2. Average ON time for Aloha and CSMA/CA in an IoT context (please note the log-scale of the y-axis).

Fig. 3 .

 3 Fig. 3. Impact of the maximum number of retransmissions in Aloha and CSMA/CA.

Fig. 4 .

 4 Fig. 4. Comparison of classical Aloha and Aloha No Ack.

Fig. 5 .

 5 Fig. 5. Comparison of classical CSMA and CSMA No Ack.

Fig. 6 .

 6 Fig. 6. Comparison of Aloha No Ack and CSMA No Ack.

ns3 provides an implementation of the Aloha protocol in the Uan package, used to simulate underwater acoustic communications. This implementation is not compatible with radio communication models in the simulator.

ACKNOWLEDGMENT This work has been partly supported by the INSA Lyon -SPIE ICS chair on the Internet of Things.


Jean-Pierre Borel
email: jean-pierre.borel@unilim.fr

Lama Tarsissi
email: lama.tarsissi@unice.fr

Laurent Vuillon
email: laurent.vuillon@univ-smb.fr

Inflation of digitally convex polyominoes

Keywords: Digital convexity, Discrete Geometry, Christoffel words, step by step inflation nj

), or equivalently have a common unit square with the convex hull of the polyomino. Remove any square s i , then the new polyomino is still digitally convex, and this process can be iterated.

This property has two consequences.

Introduction

In the literature, many papers introduced and studied different convexity notions. For example, Kim and Rosenfeld in [START_REF] Kim | Digital straight lines and convexity of digital regions[END_REF] investigated different notions of discrete convex sets, where a set in Euclidean geometry is convex if and only if for any pair of points p 1 , p 2 in a region R, the line segment joining them is completely included in R. In discrete geometry on square grids, this notion refers to the digitally convex convexity. We recall that a polyomino is a finite 4-connected set of unit squares in the lattice Z 2 . If P is a polyomino and if for all p 1 , p 2 inside P and such that the discret segment joining them is completely included in P then P is a digitally convex polyomino. Digitally convex polyominoes are also the discretization of convexes of R 2 , except when this discretization is not 4-connected. It implies that the intersection of two such polyominoes is also digitally convex, as soon as it is 4-connected.

In this talk, we would like to study discrete geometrical constructions to deflate or inflate digitally convex polyominoes.

How to deflate a digitally convex polyomino?

We first study how to deflate a digitally convex polyomino P. This polyomino P can be decomposed into four paths. Indeed, a polyomino P is a finite set thus we define the minimal bounded box which is a rectangle such that P touches the four sides of the rectangle. Those paths start at the first unit square of intersection with each side of the rectangle. We denote the unit squares of intersection by W (the lowest unit square on the leftmost side), N (the leftmost unit square in the top side), E (the highest unit square on the rightmost side) and S (the rightmost unit square on the bottom side). The contour of a convex polyomino is then the union of the four (clockwise) paths W N , N E, ES and SW .

We use the result given by Brlek et al. [START_REF] Brlek | Lyndon + Christoffel=digitally convex[END_REF] where they introduced a link between convexity and combinatorics on words by encoding the contour of the convex polyomino. Their result was based on Christoffel and Lyndon words. They considered each path of the convex polyomino and used the alphabet A = {0, 1, 0, 1} to code the boundary of each polyomino where 0, 1, 0, 1 encode →, ↑, ←, ↓ respectively.

The main result in [START_REF] Brlek | Lyndon + Christoffel=digitally convex[END_REF] states that a convex polyomino is characterized by the fact that the W N path admits a unique Lyndon factorization n1 1 . . . n k k where the i 's have decreasing slopes and they are primitive Christoffel words, and similar results for the three other paths.

It is not difficult to deflate the digitally convex polyomino. Indeed, we look at the set {s 1 , s 2 , • • • , s k+1 } of unit squares (called corners) in the boundary of the polyomino such that each s i are exactly the unit square corresponding to the extremities of each factor 1. Given two digitally convex polyomino C 1 ⊂ C 2 , C 2 can be deflated to C 1 in such a way that at each step one unit square only is canceled and such that at each step we have a digitally convex polyomino: as the polyomino C 2 is bigger than C 1 it contains a corner which is not in C 1 , then cancel this corner.

2. It is possible to inflate step by step from C 1 to C 2 , by the reverse process. However, it does not give a practical way to choose the unit square that we must add at each step.

How to inflate a digitally convex polyomino?

It is more difficult to get effective methods to inflate a convex polyomino C 1 to a convex polyomino C 2 where C 1 ⊂ C 2 with the constraint that we must add a single unit square at each step and maintain the digitally convex property at each step until reaching C 2 .

The spiral and strate constructions

First of all we take C 1 as a unit square anywhere inside C 2 . We first investigate the spiral construction by adding a corner around the polyomino from a unit square polyomino by adding at each step a corner in a clockwise order (see Figure 2). This construction leads to an octogonal shape digitally convex polyomino. However, by keeping only those unit squares which are contained in C 2 (see Figure 3 left and center), we get a global construction of C 2 such that we maintain the convexity property at each step. In fact, we have many variants of this construction, by considering 4-connected spiral or 8-connected spiral or strate construction (see Figure 3). The strate construction consists in taking at first the lowest unit squares from the left to the right, and to continue to the second row in a correct order, and so on (see Figure 3, right). It has many variants.

If we try to inflate some digitally convex polyomino by the spiral method, it works only when we take special octogones (see Figure 4, left). In the general case, the convexity property disappears at some steps (see Figure 4, right, unit square number 8). Thus now we must add unit squares using one construction of the paper of Dulio et al. [START_REF] Dulio | First Steps in the Algorithmic Reconstruction of Digital Convex Sets[END_REF], the authors introduces the split operator (based on the Borel Laubie standard factorization of Christoffel words [START_REF] Borel | Quelques mots sur la droite projective réelle[END_REF]) in order to add unit square to the border of a digitally convex polyomino. By this operation the Christoffel property of words along the four paths is maintained and thus the difficult part of the inflation remains to maintain the monotony of the slopes of each Christoffel word along the four paths.

The split operator

From now on, we are working on the W N path. The split operator, as mentioned in [START_REF] Dulio | First Steps in the Algorithmic Reconstruction of Digital Convex Sets[END_REF], considers the furthest point of the Christoffel word i with respect to its line segment and switches the factor 01 to 10. Using this operator and replacing the factors is equivalent to adding a unit square to the polyomino. We obtain in this case two new Christoffel words + i and - i , where i = - i + i is the standard factorization of the Christoffel word, and - i < i < + i both for slopes and lexical order. The split operator consists in replacing i by + i i in the coding word of the path. Then the convexity property remains true in the simple case :

i+1 ≤ - i < + i ≤ i-1 .
but these inequalities can fail. So we might have different cases and situations, that we will present in the next section depending on the property of each unit square to add.

Adding one unit square:

We start by considering the case, where we will add one unit square to the convex C 1 (j) for a given j (C 1 (j) represents the jth step of the construction that is C 1 with j added unit squares). Which means that with this case we reach the step C 1 (j + 1). In fact, three different cases can occur:

1. The first case, where we add a unit square on the Christoffel word i with n i = 1 of a given path using the split operator and no problems are faced. Which means the monotone order of slopes is maintained, i.e., as the split operator consists in replacing i by + i i in the coding word of the path:

i+1 ≤ - i < + i ≤ i-1 .
and the convexity is conserved.

2. The second case also needs n i = 1. It is if we add a unit square to i of a given path we keep the Lyndon factorization property, but this factorization is not as in the first case

n1 1 . . . ( ni-1 i-1 + i ) - i ni+1 i+1 . . . n k k .
The convexity is conserved in this second case.

3. The third case that we can face, is if we add a unit square to i of a given path we loose the Lyndon factorization property; which means the monotone order of slopes is no longer correct, and the new polyomino is not digitally convex.

However, we can get a characterization of the first case. We give this characterization in the simplest case, which corresponds to n i = 1. Going back to the factorization n1 1 . . . n k k of the W N path, cases 1 or 2 occur when the following conditions are satisfied.

i+1 ≤ -

i or i+1 = -k i for some positive integer k and some Christoffel word ;

2. i-1 ≥ + i or i-1 = +k i
for some positive integer k and some Christoffel word .

An inflation method

We consider as before two distinct digitally convex polyominoes C 1 ⊂ C 2 . Then there always exists in each of the four paths describing C 1 at least one Christoffel word corresponding to the cases 1 or 2 before. More precisely, we can choose the longest Christoffel word of the path, among those which does not correspond to some side of C 2 . It gives an effective method to inflate C 1 to C 2 and conserving the convex property at each step.

Some other methods based on completely different considerations could be investigated. For example we can use a continuous and increasing deformation of the border of the convex hull of C 1 to the border of the convex hull of C 2 , such that this deformation contains at any time at most one integer point. An effective construction of such a deformation can be made, using simple arguments but encountering some technical difficulties.

Figure 1 :

 1 Figure 1: A digitally convex polyomino, its convex hull and its corners (grey unit squares) and a smaller digitally convex polyomino.

Figure 2 :

 2 Figure 2: The spiral construction

Figure 3 :

 3 Figure 3: Two spiral and a strate construction of a digitally convex polyomino

Figure 4 :

 4 Figure 4: The spiral inflation


Chad Stephens
email: chad.l.stephens@nasa.gov

Frédéric Dehais
email: frederic.dehais@isae-supaero.fr

Raphaëlle N Roy
email: raphaelle.roy@isae-supaero.fr

Angela Harrivel
email: angela.r.harrivel@nasa.gov

Mary Carolyn Last
email: mary.c.last@nasa.gov

Kellie Kennedy

Alan Pope
email: alan.t.pope@nasa.gov

Biocybernetic Adaptation Strategies: Machine awareness of human engagement for improved operational performance

Keywords: Biocybernetic adaptation, Adaptive training, Engagement

Human operators interacting with machines or computers continually adapt to the needs of the system ideally resulting in optimal performance. In some cases, however, deteriorated performance is an outcome. Adaptation to the situation is a strength expected of the human operator which is often accomplished by the human through self-regulation of mental state. Adaptation is at the core of the human operator's activity, and research has demonstrated that the implementation of a feedback loop can enhance this natural skill to improve training and human/machine interaction. Biocybernetic adaptation involves a "loop upon a loop," which may be visualized as a superimposed loop which senses a physiological signal and influences the operator's task at some point. Biocybernetic adaptation in, for example, physiologically adaptive automation employs the "steering" sense of "cybernetic," and serves a transitory adaptive purpose -to better serve the human operator by more fully representing their responses to the system. The adaptation process usually makes use of an assessment of transient cognitive state to steer a functional aspect of a system that is external to the operator's physiology from which the state assessment is derived. Therefore, the objective of this paper is to detail the structure of biocybernetic systems regarding the level of engagement of interest for adaptive systems, their processing pipeline, and the adaptation strategies employed for training purposes, in an effort to pave the way towards machine awareness of human state for self-regulation and improved operational performance.

Introduction

Human operators generally face a complex, dynamics and uncertain environment under time pressure. The occurrence of unexpected events (e.g., critical failure) requires flexibility and cognitive regulation policies to meet task demand [START_REF] Sperandio | The regulation of working methods as a function of work-load among air traffic controllers[END_REF]. Various strategies may be employed by humans to achieve adaptation. In a study of the physiological effects of a kinetically adaptive environment, [START_REF] Jager | Reciprocal Control in Adaptive Environments[END_REF] describe the reciprocal relationship between adaptive humans and such environments. [START_REF] Schwarz | Multidimensional Real-Time Assessment of User State and Performance to Trigger Dynamic System Adaptation[END_REF] point out that "humans are adaptive systems themselves", that is, they are able to mitigate critical user states by applying self-regulation strategies. They cite as examples "investing more effort if task demands increase or drinking coffee to combat fatigue". Additionally, the system itself can be made to adapt to the human. Schmorrow proposes a system that adapts to a trainee's level in the context of flight training: "Imagine an aviation recruit experiencing a simulator that is tailored to the trainee at the most fundamental neurophysiological level. Imagine that this simulator's integrated helmet and sensor suite are hooked up to a 'black box' that modifies the simulated flight exercise based on a real-time assessment of the student pilot's cognitive state, using information collected by the sensor suite." [START_REF] Schmorrow | Aviation Training: A Future Avenue[END_REF]. Similarly, the task modulation concept embodied in the self-regulation training technology based on biocybernetic adaptation may be adapted for use in task simulators. The simulator embodiment of the closed-loop modulation concept, Stress Counter-response Training [START_REF] Palsson | Stress Counterresponse Training of Pilots via Instrument Functionality Feedback[END_REF], integrates physiological self-regulation training into the practice of mission-relevant tasks. Stress Counter-response Training is based upon the concept of instrument functionality feedback which ties the functionality of a simulator to the requirement to maintain the physiological equanimity suited for optimal cognitive and motor performance under emergency events in an airplane cockpit.

Further examples of the integration of simultaneous human and system adaptation are aimed at psychophysiological goal achievement, not necessarily at the achievement of optimal performance. Biocybernetic adaptation has been employed as a self-regulation training method for application in clinical and sports settings. In these technologies, the adaptation approach involves physiological signals modulating some aspects of the training tasks in such a way as to reward trainees for approaching a target signal [START_REF] Pope | Biocybernetic Adaptation as Biofeedback Training Method[END_REF]). These physiological self-regulation training technologies are designed to improve adherence to a training regimen by delivering the training through engaging, motivating, and entertaining experiences. The processing employed in these technologies is minimal to enable real-time feedback. Likewise, the decision rules are usually simple, e.g., modulating a single task element based upon signal level. For instance, some consequences in a digital game or simulation reward the user for achieving a psychophysiological goal by diminishing an undesirable effect in a game (analogous to negative reinforcement). Other consequences reward the user for achieving a psychophysiological goal by producing a desirable effect (analogous to positive reinforcement) such as additional scoring opportunities. That is, some modulation effects enable superimposed disadvantages in a digital game or simulation to be reduced by progression toward a psychophysiological goal, whereas others enable advantages to be effected by progression toward a psychophysiological goal. In these technologies, the physiological modulation method is tailored to the overall game or simulation task, but without regard for changes in the task context or other situational factors. [START_REF] Fuchs | Towards a Dynamic Selection and Configuration of Adaptation Strategies in Augmented Cognition[END_REF] identify this as a "hard-coded" adaptation strategy, where the system triggers a predetermined adaptation strategy.

Self-regulation training can be deliberate as just described or could occur inadvertently as a result of an operator's exposure to an adaptive system. Technology in the field of self-regulation training has commonly taken into account the fact that the physiological self-regulation behavior and skill of the trainee changes as training progresses. These systems have incorporated algorithms that respond to momentary, transient changes in physiological signals in real time, as well as longer time course changes that reflect a trainee's emerging ability to voluntarily control physiological parameters. The momentary changes are displayed as information and reward feedback for learning of self-regulation skill, while the longer time course measurements are assessed to guide the setting of higher and higher self-regulation performance goals. An outcome of selfregulation training accomplished with an adaptive system is improved cognitive state management skill which is effectively meta-awareness on the part of the trainee. This effect demonstrates an observing system as defined in second order cybernetics (von Foerester, 1995).

Biocybernetic loop implementation for adaptive systems

A first and important step for biocybernetic adaptation is to determine what temporal and magnitude changes in physiological signals reflect operator or trainee state changes that warrant mitigation. Indeed, one important concern with the implementation of such assisting systems is to succeed in providing assistance in a timely and appropriate manner (Parasuraman et al., 1999). Spurious triggering of the assistance system may have negative consequences on human operators (Parasuraman et al., 1997). Therefore, an approach is to target mental states that are 1) relevant predictors of human performance and 2) that can be robustly identified via behavioral and neurophysiological measures. Mental states of interest are discussed, followed by a description of the biocybernetic adaptation pipeline.

Traditionally, most of the research has focused on mental workload-based biocybernetical adaptation. However, the usability of the mental workload construct remains limited. Although theoretically and practically interesting, it remains ill-defined (Mandrick et al., 2017), providing a non-specific and generic index rather like a thermometer. Moreover, mental workload should not be viewed as the result of an external demand applied on an individual passively adapting to it, but rather as an active process that depends on the human operator's level of engagement. For instance, a highly demanding situation will not necessarily induce high workload if an individual does not engage to achieve. Several reasons may account for this lack of engagement such as excessive task difficulty (Durantin, Gagnon, Tremblay, & Dehais, 2014), repetitive and boring tasks [START_REF] Durantin | Characterization of Mind Wandering using fNIRS[END_REF] and cognitive fatigue [START_REF] Hopstaken | A multifaceted investigation of the link between mental fatigue and task disengagement[END_REF]. Conversely, an over-engagement in a non-priority and non-demanding task could induce high workload (e.g., interacting with the entertainment system or texting while driving) and jeopardize safety [START_REF] Lee | Dynamics of driver distraction: The process of engaging and disengaging[END_REF][START_REF] Dehais | Cognitive conflict in human automation interactions: a psychophysiological study[END_REF]. Thus, human cognitive performance has to be considered the byproduct of the level of task demand by the level of task engagement. Interestingly, the concept of engagement is related to a triad of attentional states: attentional disengagement, attentional over-engagement, and attentional in-engagement. Also, the study of engagement is richer than the concept of workload: this concept accounts for neurophysiological and behavioral phenomena and it can be characterized with portable measurement tools (Verdiere, [START_REF] Verdière | Detecting pilot's engagement using fNIRS connectivity features in an automated vs manual landing scenario[END_REF]. For example, a biocybernetic system was designed to mitigate task disengagement due to automation by triggering changes in task mode based on the fluctuations of an engagement index constructed as a ratio of EEG band powers [START_REF] Scerbo | A Biocybernetic System for Adaptive Automation[END_REF]. Derivation of the engagement index was based on the proposition that the closed-loop paradigm that represents the adaptive configuration in which physiological indices are to have a steering role can also serve as a prior validation test bed for the indices themselves [START_REF] Pope | Biocybernetic System Validates Index of Operator Engagement in Automated Task[END_REF].

Firstly, attentional disengagement occurs when task demand is too low leading to episodes of mind wandering [START_REF] Durantin | Characterization of Mind Wandering using fNIRS[END_REF] or when task demand exceeds mental capacity. In these two extreme situations, human operators generally drop the primary task to focus on automatic secondary tasks. These two states are characterized by the disengagement of the executive network, underpinned by the deactivation of the dorsolateral prefrontal cortex (Durantin et al., 2014;[START_REF] Harrivel | Monitoring attentional state with fNIRS[END_REF]. Secondly, attentional over-engagement, also referred to attentional tunneling [START_REF] Wickens | Attentional Tunneling and Task Management[END_REF] and "channelized attention" [START_REF] Harrivel | Psychophysiological Sensing and State Classification for Attention Management in Commercial Aviation[END_REF], is defined as "the allocation of attention to a particular channel of information, diagnostic hypothesis or task goal, for a duration that is longer than optimal, given the expected cost of neglecting events on other channels, failing to consider other hypotheses, or failing to perform other tasks". Some authors postulate that this impaired attentional state results from a disengagement deficit of the orientation network underpinned by the thalamus (LaBerge et al., 1992). Whereas the assessment of such brain structure remains difficult to be perform in operational context -it requires the use of fMRI -some studies have disclosed that attentional over-engagement is associated with an attentional shrinking and long fixation time (Dehais et al., 2011). Recently, the EEG engagement index proposed by [START_REF] Pope | Biocybernetic System Validates Index of Operator Engagement in Automated Task[END_REF] was shown to be sensitive to episodes of over-engagement leading to inattentional deafness to auditory alarm under real-flight settings [START_REF] Dehais | Failure to detect critical auditory alerts in the cockpit: evidence for inattentional deafness[END_REF].

Lastly, recent work has shown the existence of an attentional in-engagement state whereby human operators are unable to engage their attention to process relevant information when facing critical situations. One could describe this state as "panic mode" in a vernacular fashion. This state, that is the exact opposite of attentional tunneling, is explained in terms of impaired thalamus tonic mode to maintain focused attention. This state of "attentional confusion" or "attentional entropy" is associated with high saccadic activity and absence of long fixations [START_REF] Durantin | Characterization of Mind Wandering using fNIRS[END_REF].

Another interesting approach could be to identify the dynamic model of such features. Tools derived from the linear algebra and control communities to perform an approximation of the neurophysiological features model that could be explored to monitor the engagement of an operator. The method provides a smooth interpolation of all the data points enabling the extraction of frequency features that reveal fluctuations in engagement with growing time-on-task [START_REF] Poussot-Vassal | A Loewner-based Approach for the Approximation of Engagement-related Neurophysiological Features[END_REF]. Alternatively, the use of large-scale EEG connectivity is a relevant approach not only to detect but also to predict future performance and fluctuation of engagement [START_REF] Senoussi | Pre-stimulus antero-posterior EEG connectivity predicts performance in a UAV monitoring task[END_REF].

The implementation of the biocybernetic adaptation pipeline mostly consists of the classical steps of a Brain-Computer Interface, that is to say a signal acquisition step (e.g., EEG), a preprocessing step that generally deals with artifacts (e.g., eye blinks) and better conditions the signal, a feature extraction step (e.g., extraction of the average power in specific frequency bands), a machine learning step (e.g., a classification step), and lastly an adaptation step [START_REF] Roy | Neurophysiological Markers for Passive Brain-Computer Interfaces[END_REF]. This last step can consist of providing the estimated mental state to the system's decisional unit. The decisional unit system allows the loop to be closed. This is done by implementing a decisional unit driven by a policy resulting from the resolution of a (Partially Observable) Markov Decision Process ((PO)MDP) that takes into consideration uncertainties on actions, partial observable states (i.e., mental states) or potentially non-deterministic behavior of the human operator [START_REF] Gateau | Considering human's non-deterministic behavior and his availability state when designing a collaborative human-robots system[END_REF][START_REF] Drougard | Mixed-initiative mission planning considering human operator state estimation based on physiological sensors[END_REF]. Eventually, a last step is to design a catalogue of adaptive solutions to mitigate decline in performance and improve human performance. These solutions are presented in the next section.

Successful implementation of adaptive solutions

An early example is an electromyographic biofeedback training system that implemented a shaping procedure by adjusting the gain of the feedback loop after each interval of training based on a trainee's success at lowering EMG levels [START_REF] Pope | Computer Automation of Biofeedback Training[END_REF]. This system employed a fixed strategy by which task characteristics are adapted to the individual. A training strategy implies a set of assertions relating strategy characteristics and their effects on training progress. In a more advanced implementation, a data base of these assertions could be updated on-line and the training system would be self-improving. In effect, the system would evaluate the results of mini-experiments with various strategy versions within a session and modify the strategy accordingly. O' Shea and Sleeman (1973) developed this hierarchical framework in the context of adaptive teaching systems. Similarly, physiologically adaptive systems will need to be designed to respond appropriately not only to transient changes and spontaneous drifts in operator state due to developing conditions such as fatigue, but also to conditioning of physiological changes as a result of an operator's extended exposure to information feedback about their physiological state. Accordingly, an adaptive implementation that took into consideration the operator "training" effect of its information feedback employed a continually updated model of the operator analogous to the "template of average performance" in the "symbionic cockpit" [START_REF] Reising | The Symbionic Cockpit[END_REF]. Techniques developed for adapting a brain-computer interface classifier to adjust for possible features drift could be applied to address this type of consequence [START_REF] Vidaurre | Machine-Learning-Based Coadaptive Calibration for Brain-Computer Interfaces[END_REF]. Configuration of an adaptive system that takes into consideration these long-term and short-term processes is depicted in Figure 1. The Adjustable System has adjustable parameters, such as automation level. The Adjustable System is adjusted by the currently invoked Short-Term Adaptation Strategy and is driven by input from the human user. The Selectable Short-Term Adaptation Strategy has a catalog of selectable strategies, each one of which is in effect for a selectable duration. The currently invoked Strategy is selected by the Long-Term Adaptation Scheme and is driven by the discrepancy between the desired criteria and actual engagement status. The Long-Term Adaptation Scheme is driven by the discrepancy between the desired and actual engagement trend. The Achieved Engagement Output is the level of an engagement index derived from physiological and behavioral measures and is driven by the Adjustable System.

An additional strategy is the exercise of self-regulation skill acquired as a result of self-regulation training. [START_REF] Prinzel | Physiological Self-regulation and Adaptive Automation[END_REF] demonstrated that participants given feedback of the accuracy of their estimates of engagement levels, across a partitioning of the range of an EEG-based engagement index into six subranges, were able to achieve "a 70% level of correct identifications." Further, while interacting with an adaptive automation system, "Participants in the self-regulation condition were better able to maintain their task engagement level within a narrower range of task modes, thereby reducing the need for task mode changes. The effect of this was an increase in task performance as well as a decrease in reported workload. [START_REF] Prinzel | Physiological Self-regulation and Adaptive Automation[END_REF] further comment, "The neurofeedback provided during training may have allowed these participants to better manage their cognitive resources and thereby regulate their engagement state, allowing them to better respond to a change in automation mode. The results of this study support other research that has shown that physiological self-regulation could enhance the cognitive resource management skills of pilots and complement the benefits of adaptive automation."

Human

In addition to clinical and sports applications, biocybernetic adaptation as self-regulation training is applied in a third area, the aircrew training context [START_REF] Stephens | Crew State Monitoring and Line-Oriented Flight Training for Attention Management[END_REF]. The instructor-trainee interaction is influenced, closing the loop on a broader time scale. Here the adaptation involves an attention management training approach to complement the usual observations of airline training instructor pilots by informing them, in the training context, of the occurrence of attention-related human performance limiting states (AHPLS) experienced by their trainees. Classifier models are trained to recognize trainee state during simulated flight scenarios based on patterns of the physiological signals measured during benchmark tasks [START_REF] Harrivel | Psychophysiological Sensing and State Classification for Attention Management in Commercial Aviation[END_REF]. Machine learning models' real time determinations of the cognitive states induced by the scenario tasks are displayed as gauges embedded in a mosaic of windows that also displays real time images of the scenario tasks that the trainee is performing (e.g., scene camera, simulator displays, animation of simulator controls), and this mosaic1 is video recorded [START_REF] Harrivel | Prediction of Cognitive States during Flight Simulation using Multimodal Psychophysiological Sensing[END_REF]. The loop is closed when their state information is conveyed to the trainee as part of each session debrief. This approach involving trainee-trainer interaction leverages the effective bio-social influences on learning specified by Kamiya [START_REF] Strehl | What learning theories can teach us in designing neurofeedback treatments[END_REF]. Like the adaptive automation application, the adaptation strategy here takes into consideration contextual parameters such as the instructor's discretion regarding the appropriateness of conveying particular state information to the trainee.

This psychophysiologically-based AHPLS detection and mitigation system is modeled after the Hypoxia Familiarization Training (HFT) employed in aviation. The focus of HFT is on recognizing symptoms of hypoxia and taking steps to recover from the hypoxia being experienced. Similarly, recognition and recovery from AHPLS is intended to improve self-monitoring of and response to one's own attentional performance, maintaining more effective states and managing attention. Such meta-awareness results from this form of self-regulation training intended to develop attention management skill. If deployed in ground-based commercial aviation training contexts, the intent is to mitigate potential in-flight loss of airplane state awareness (ASA) and thus reduce aviation accidents and incidents.

In general, biocybernetic adaptation can be applied within autonomous systems to imbue further intelligence into the systems about humans involved in operations. In a potential adaptive automation application, the cognitive state of the operator of a semiautonomous vehicle would be tracked by the vehicle system. The system uses the cognitive state information to judge the operator's ability to take back control of the system in critical or noncritical hand-off instances2 .

Conclusion

The implementations of specific adaptations described in this paper represent actual systems designed for improving human/machine interaction and furthermore enabling human operators to improve self-regulation skills. The adaptation strategies described herein include combinations of technological advances in the areas of neuroscience and psychophysiology designed for specific contexts including clinical, aviation, and sports. The example implementation systems instantiate concepts and enable practical and empirical testing to evaluate adaptation strategies. Adaptation management issues were discussed including dynamic selection and configuration of adaptations. Development of adaptation strategies can create further questions for consideration such as how to handle possible side effects on the human operator caused by setting up a biocybernetic loop. This and other questions require empirical results to be sufficiently addressed. Ongoing research efforts at NASA and the Institut Supérieur de l'Aéronautique et de l'Espace (ISAE) seek to apply adaptation strategies to answer these questions and reveal further questions with the ultimate goals or improved safety and efficiency in aerospace operations.

Fig. 1 .

 1 Fig.1. Configuration of an adaptive system for managing human user engagement. The Desired Short-Term Engagement Criteria and Long Term Engagement Trends vary according to context (e.g., phase of flight). The Adjustable System has adjustable parameters, such as automation level. The Adjustable System is adjusted by the currently invoked Short-Term Adaptation Strategy and is driven by input from the human user. The Selectable Short-Term Adaptation Strategy has a catalog of selectable strategies, each one of which is in effect for a selectable duration. The currently invoked Strategy is selected by the Long-Term Adaptation Scheme and is driven by the discrepancy between the desired criteria and actual engagement status. The Long-Term Adaptation Scheme is driven by the discrepancy between the desired and actual engagement trend. The Achieved Engagement Output is the level of an engagement index derived from physiological and behavioral measures and is driven by the Adjustable System.

This concept is captured in a non-provisional patent application: Stephens, C., Harrivel, A., Pope, A., & Prinzel, L. (2017, patent pending) "System and Method for Training of State-Classifiers." [NASA Case No.: LAR-18996-1]

2 This concept is captured in a non-provisional patent application: Harrivel, A., Stephens, C., Kennedy, K., & Pope, A. (2017, patent pending) "Multivariate Monitoring for Human Operator and Machine Teaming" [NASA Case No.: LAR-19051-1].