Fran De Aquino

Activation of Autophagy Process in Cancerous Cells at Quasi-Zero Gravity Environments

Keywords: Cancerous Cell, Autophagy, Microgravity, Quantum Controllers of Gravity

Autophagy is a well-known process of cell death. In this work we show that it can be actived in cancerous cells at Quasi-Zero Gravity environments. The result is the total destruction of the cancerous cells without use of medicaments.

The gravitational acceleration experienced by an object in a microgravity environment, by definition, is one-millionth (10 -6 ) of that experienced at Earth's surface . Consequently, a microgravity environment is one where the acceleration induced by gravity has very little effect

( ⊕ g ) ( ) ⊕ ≈ g g μ 1 .
Only three methods of creating a microgravity environment are currently known: to travel far enough into deep space so as to reduce the effect of gravity by attenuation, by falling, and by orbiting a planet.

The first method is the simplest in conception, but requires traveling an enormous distance, rendering it most impractical with the conventional spacecrafts. The second method, falling, is very common but approaches microgravity only when the fall is in a vacuum, as air resistance will provide some resistance to free fall acceleration. Also it is difficult to fall for long enough periods of time. There are also problems which involve avoiding too sudden of a stop at the end. The NASA Lewis Research Center has several drop facilities. One provides a 132 meter drop into a hole in the ground similar to a mine shaft. This drop creates a reduced gravity environment for 5.2 seconds. The longest drop time currently available (about 10 seconds) is at a 490 meter deep vertical mine shaft in Japan that has been converted to a drop facility.

Drop towers are used for experiments that only needs a short duration of microgravity, or for an initial validation for experiments that will be carried out in longer duration of microgravity. Aircraft can fly in parabolic arcs to achieve period of microgravity of 20 to 25 seconds with g-level of approximately 0.02 g. The airplane climbs rapidly until its nose is about 45-degree angle to the horizon then the engines are cut back. The airplane slows; the plane remains in free fall over the top of the parabola, then it nose-dives to complete the parabola, creating microgravity conditions.

Aircraft parabolic flights give the opportunity to perform medical experiments on human subjects in real microgravity environment. They also offer the possibility of direct intervention by investigators on board the aircraft during and between parabolas. In the mid-1980s, NASA KC-135, a modified Boeing 707, provided access to microgravity environment. A parabolic flight provided 15 to 20 seconds of 0.01 g or less, followed by a 2-g pull out. On a typical flight, up to 40 parabolic trajectories can be performed. The KC-135 can accommodate up to 21 passengers performing 12 different experiments. In 1993, the Falcon-20 performed its first parabolic flight with microgravity experiment on board. This jet can carry two experimenters and perform up to 3 experiments. Each flight can make up to

The third method of creating a microgravity environment is orbiting a planet. This is the environment commonly experienced in the space shuttle, International Space Station, Mir (no longer in orbit), etc. While this scenario is the most suitable for scientific experimentation and commercial exploitation, it is still quite expensive to operate in, mostly due to launch costs.

A space shuttle provides an ideal laboratory environment to conduct microgravity research. A large panoply of experiments can be carried out in microgravity conditions for up to 17 days, and scientists can make adjustment to avoid experiment failure and potential loss of data. Unmanned capsules, platforms or satellites, such as the European retrievable carrier Eureka, DLR's retrievable carrier SPAS, or the Russian Photon capsules, the US Space Shuttle (in connection with the European Spacelab laboratory or the US Spacelab module), provide weeks or months of microgravity.

A space station, maintaining a low earth orbit for several decades, greatly improves access to microgravity environment for up to several months.

Thus, microgravity environment can be obtained via different means, providing different duration of microgravity. While short-duration microgravity environments can be achieved on Earth with relative easiness, longer-duration microgravity environments are too expensive to be obtained.

In a previous paper we shown that the intensity of the local gravity can be controlled by means of a device called Quantum Controller of Gravity (QCG) [START_REF] De Aquino | Quantum Controller of Gravity[END_REF]. Fundamentally, a QCG can have any spherical form (ellipsoidal, spherical, spherical cylindrical, etc.). Figure 1 shows a system with 1 (one) spherical QCG (shell with thickness ).

x Δ

V f

Fig is the expression of the correlation between gravitational mass and the rest inertial mass of the QCG, which is given by [START_REF] De Aquino | Quantum Controller of Gravity[END_REF] [ ] { } ( )

1 1 10 64 . 2 1 2 1 3 0 - × + - = = -V m m i g χ
where V is the voltage applied (See Fig. 1). g Fig. 2 -A system with n QCG Here, we propose to use QCGs, in order to create, a Quasi-Zero Gravity 1 environments of longer-duration, at Earth's surface. Due to the cost of the QCGs to be relatively low, also the Quasi-Zero Gravity environments of longer-duration. will be produced with low costs.

This possibility is absolutely new and unprecedented in the literature.

The Quasi-Zero Gravity environments produced by QCGs will be a special tool for ultra-low gravity research. It will allow to improve and to optimize physical, chemical and biological processes on Earth that are important in science, engineering and also medicine.

In this work we show that the wellknown Autophagy process (cell death) can be actived in cancerous cells at Quasi-Zero Gravity environments of longer-duration.

Consider a non-relativistic system with mass and velocity in a gravitational field. Its kinetic energy is

m v 2 2 1 mv K =
and its potential energy in the gravitational field is r GMm U -= ; M is the mass of the body (spherical with radius r ) that creates the gravitational field. Under these circumstances, the total energy of the system, E , is given by ( )

2 2 2 1 r GMm mv U K E - = + =
Note that the potential energy reduces the total energy of the system. Consequently, if it is decreased then the total energy of the system will be increased.

The Eq. ( 2) can be rewritten in the following form:

( ) [ ] [ ] ( ) 3 2 2 2 2 1 2 2 2 1 r g v m r r GM v m E - = - = 1 ⊕ << g g μ 1
.

Here we use the term Quasi-Zero

Gravity because the term zero-gravity is, obviously inappropriate since the quantization of gravity [START_REF] Gravity | D of the Relativistic Theory of Quantum[END_REF] shows that the gravity can have only discrete values different of zero.

where is the gravity acceleration produced by the mass g M . Note that, if gravity is reduced the energy g E increases. This explains why the cellular metabolism increases in microgravity environments. That is, if a cell is placed in a microgravity environment, then, according to Eq. ( 3), its total energy increases and, consequently, its metabolism will be accelerated. Therefore, strongly reducing the gravity that acts on a cell it is possible strongly increase its cellular metabolism. The healthy cells are able to support this effect for a long-time. But the cancerous cells do not support by a long time the metabolic stress [START_REF] Danial | Cell death: critical control points[END_REF][START_REF] Lum | Autophagy in metazoans: cell survival in the land of plenty[END_REF][START_REF] Kelekar | Autophagy[END_REF] produced by the strong acceleration of their metabolisms and, at a given moment, they activate the Autophagy process which leads to death of the cancerous cells.

This fact is not new, several papers [START_REF] Vassy | The effect of weightlessness on cytoskeleton architecture and proliferation of human breast cancer cell line MCF-7[END_REF][START_REF] Schatten | Spaceflight and clinorotation cause cytoskeleton and mitochondria changes and increases in apoptosis in cultured cells[END_REF][START_REF] Vercoutere | Integrin-Mediated Cellular Response to Hypergravity[END_REF][START_REF] Guignandon | Cell cycling determines integrin-mediated adhesion in osteoblastic ROS 17/2.8 cellsexposed to spacerelated conditions[END_REF] show that the cells are strongly affected by microgravity and under certain conditions can activate the Autophagy or Apoptosis process. The novelty is the possibility the use of QCGs in order to create, at the Earth surface, Quasi-Zero Gravity environments of longer-duration which can activate the Autophagy or Apoptosis process. Now consider that the body with the mentioned cancerous cells is on Earth's surface. Considering Eq. ( 3), in this case, we can take and m r r . The Quasi-Zero Gravity environment produced by the chamber ( ) will activate, after a time interval, the Autophagy process in all cancerous cells of the body inside the chamber. The result is the cure of the cancer. The time intervals, inside the Quasi-Zero Gravity Chamber, which each type of cancerous cell (or set of them) requires in order to be destroyed only can be determined by means of experimental studies.

. 1 -

 1 Fig.1 -The shell with thickness x Δ works as a Quantum Controller of Gravity.

  is possible to build a system with concentric QCGs (See schematic diagram in Fig.2.). In this case, the gravity inside the system becomes [

Fig. 3 -

 3 Fig. 3 -A Quasi-Zero Gravity Chamber on Earth's surface with 30 QCGs

parabolic trajectories, with each parabola lasting 75 seconds, with 15 to 20 seconds of microgravity at 0.01g or less.


Thomas Küchelmann
email: thomas.kuechelmann@uni-bielefeld.de

Paola Carolina

Manjunath Prasad
email: m.prasad@uni-bielefeld.de

Kai Essig
email: kai.essig@uni-bielefeld.de

Thomas Schack
email: thomas.schack@uni-bielefeld.de

Automatic Analysis of Players Behavior in Real Dyadic Chess Situations

Keywords: Human-machine-interaction, eye tracking, adaptive artificial assistive systems, virtual agents, attentive learning processes, human perception, multi-modal data, visual behavior, mental memory representations ACM CLASSIFICATION KEYWORDS Algorithms, documentation, experimentation, human factors, measurement

The present paper brings together solutions for fullautomatic analysis of chess moves and eye tracking data for real dyadic chess games. We combine an electronic chessboard with marker detection in order to automatically protocol relevant and situation-related chess moves and visual attention patterns on pieces and squares. Very first results from initial evaluation studies indicate that the presented solution allows for a reliable automatic offline analysis of the underlying strategic and attentional processes of chess behaviour in real game situations without any need for an error prone and time consuming manual data annotation. The proposed solution allows to run chess studies in shorter time and to analyse the differences between chess experts and novices with respect to visual attention and strategies in more detail. Finally, gained insights can be used to develop interactive and intuitive electronic chess assistant systems to analyse the weaknesses of both experts and novices and to recommend optimal moves in given chess situations, as well as to enhance players' expertise with individualized training methods and explanations.

INTRODUCTION

The techniques and experimental settings described in this paper have chess as a research object as it is a highly competitive expert domain enjoying worldwide popularity. Moreover, it is characterized by exactly differentiable skill levels and, although embedded into an easily controllable setting, limited in space, material and time, it is extremely complex in event space constellations. Therefore, chess involves great complexity in decision making, strategy and memory. This makes chess an outstanding research object in the fields of visual attention, artificial intelligence, acquisition of expertise, as well as the interplay between mental and emotional representation.

Performance and cognitive abilities of master chess players and the differences in the strategies and visual attention processes between chess experts and novices have been investigated in many studies of cognitive sciences. Pioneering work are the studies by de Groot [START_REF] De Groot | Het denken van den schaker[END_REF][START_REF] De Groot | Thought and choice in chess[END_REF] and Chase and Simon [START_REF]The mind's eye in chess[END_REF]. Both show that expert players could reproduce previously shown chess constellations much more accurately than less skilled ones. In the upshot, chess grand-masters use efficient perceptual encoding of chess configurations to generate the most promising candidate moves [START_REF] Reingold | Eye movements and visual expertise in chess and medicine[END_REF]. Therefore the encoding of chess configurations is a key determinant of chess skill. This leads to the theory of chunking [START_REF]The mind's eye in chess[END_REF] and templates. Chunks in chess are defined as structural units of up to five pieces which remain intact through encoding into a long-term memory if at least two thirds of its pieces remain together upon recall. Gobet and Simon [START_REF] Gobet | Templates in chess memory: A mechanism for recalling several boards[END_REF] have proposed "templates" as an alternative to chunks. Templates can be understood as bigger chunks of up to 15 pieces [START_REF] Chase | Skill and Working Memory[END_REF]. The divergent predictions of the chunking and template theory have been tested by Gobbet and Clarkson [START_REF] Gobet | Chunks in Expert Memory: Evidence for the Magical Number Four ... or is it Two? Memory[END_REF] who found that expert players recall more pieces than predicted by the chunking theory in its original form. Thus, chunking and template emergence seems to be the key to understanding why humans are superior in longrange planning and static evaluation despite their small capacity of working memory. Also reaction times in chess detection tasks give deeper insight into experts' perceptional superiority. E.g. in [START_REF] Reingold | Perceptual automaticity in expert chess players: Parallel encoding of chess relations[END_REF] players had to judge the presence or absence of a check in certain chess constellations with and without distracting pieces. Significantly higher reaction times for novices but not for experts when verifying non-checking constellations with additional distractors suggest automatic and parallel encoding procedures for chess relations in experts. Further Kiesel and Kunde [START_REF] Kiesel | Playing Chess Unconsciously[END_REF] have shown in a masked prime study with either a checking or non-checking chess configuration that expertise improves perceptual processing to an extent that allows complex visual stimuli to bias behaviour unconsciously.

With the advent of modern eye trackers gaze information has recently been used as a supplementing measure for investigating the perceptual aspects of chess skills [START_REF] Holding | The Evolution of Chess Positions[END_REF]. If chess experts encode chunks rather than individual pieces then this should result in fewer fixations and the visual span should increase as a matter of expertise, allowing players to make greater use of peripheral and parafoveal processing and therefore to extract information from a larger area of the chessboard during a fixation [START_REF] Reingold | Eye movements and visual expertise in chess and medicine[END_REF]. This was reflected by more recent research with modern eye trackers. Charness et al. [START_REF] Charness | The Perceptual Aspect of Skilled Performance in Chess: Evidence from eye movements Memory & Cognition[END_REF] found that experts produced more fixations on empty squares than intermediates. When fixating pieces, experts produced a greater proportion of fixations on relevant pieces than intermediates. Sheridan et al [START_REF] Sheridan | Chess players' eye movements reveal rapid recognition of complex visual patterns: Evidence from a chess-related visual search task[END_REF] found that experts show faster recognition of complex visual patterns than novices. A survey of the contribution of eye movement research to the study of human expertise in chess can be found in [START_REF] Reingold | Eye movements and visual expertise in chess and medicine[END_REF]. Contrary to the above mentioned studies, our techniques and experimental settings described in the following sections employ chess situations with a real chessboard and real chess pieces, and this scenario is much more complicated in terms of data recording and analysis [START_REF] Reingold | Eye movements and visual expertise in chess and medicine[END_REF]. This is in stark contrast to all previous studies mentioned as they were screen-based and have employed artificial chess stimuli only (i.e., images of artificial chessboards with different chess constellations). In studies where an eye tracker is used, participants look at artificial chessboards (protocolling chess movements in a temporal order) presented on the screen while their eye movements are analysed with regard to fixations on occupied and empty chess fields, as well as jumps between them. Because of this highly controlled experimental design, the recorded data can mainly be analysed automatically. One crucial disadvantage of such a controlled screen-based design is that it eliminates several factors of a real game situation, such as human opponents, the influences of gestures, deceptive movements and the audience. We are interested in the question in what way the results will be different as soon as they go into the real chess game setting and into task-oriented scenarios which call for solving chess tasks on real chessboards and with real chess pieces. How far will outcomes of previous studies resemble the results from real dyadic situations? What will be the influences of the other factors on players' behaviour, strategies, as well as visual attention processes? And how will this depend on players' expertise? In the real settings, manual data annotation is always possible since it can be done based on video material. But this is an ineffective alternative as it is tedious and error prone -especially in the context of rapid chess matches in which each player's time control is strictly limited to less than 10 minutes and in which pieces can be moved very fast (e.g. "blitz" matches with a total match time of 5 minutes only for each player). Additionally, participants can freely move their heads which makes the correlation of the gaze position to the respective chess field or chess piece much more difficult. Therefore, due to the best of our knowledge, there are so far no multi-modal studies on real dyadic chess games. The real chess situation requires the analysis of gaze videos and an automatic detection of the single chess pieces and fields, which goes along with a lot of environmental challenges (such as uncontrolled head movements and lighting conditions), not yet adequately solved. Therefore, in this paper an offline full-automatic annotation and analysis solution for real dyadic chess games and taskoriented scenarios with real chessboards and pieces is presented and described in the following section.

Hardware

For the mapping of each piece's identity onto its actual position and a transcript of all moves, a DGT (Digital Game Technology) electronic chessboard (e-board; see Fig. 1 and https://www.webwiki.com/digitalgametechnology.com) is used that transmits game data via Bluetooth or USB to a computer [13]. It does so in the common algebraic chess notation (short or long notation can be chosen) in accordance with the FIDE [14] (Fédération Internationale des Échecs, the World Chess Federation) rules, e.g. 1.Nf3 when the first move in a match is knight from square g1 to f3. The e-board can identify both type and colour of every chess piece and its location with a sample rate of 6 times per second which is sufficiently high for blitz chess matches. The internal memory of the echess games can store up to 500 moves. programs can be employed for recording and analysis. The board design is classic (standardized tournament regulations: 55 x 55 mm tournament-size squares thickness, chessboard classical wooden piece design and size).

For the recording of eye movements we have used the non invasive mobile and binocular Eye Tracking Glasses (ETG 2) from Sensomotoric Instruments (SMI) [15] is a binocular system with a sampling rate of up to 120 Hertz and a gaze tracking accuracy of 0.5° over all distances. For our recordings we have used the scene camera resolution of 960x720 pixels, 30 fps.

.

ELECTRONIC CHESSBOARD PROGRAMMING AND HANDLING

Automatically tracking of players' movements, positions of all chess pieces, and particularly the position of the chunks at all time is necessary in order to analyse correlations between visual attention and individual chess order to do this, we use the DGT e-board and Fig. 1) connected to the computer, and a software to handle the communication between the board and the computer. The original software from DGT the movements of the game but lacks the tracking and needs an external clock to annotate times. include these two important features, we developed our own software, based on an API (Application Programming Interface) provided by DGT. By using the API we can send commands via the serial port directly to the e the corresponding data, such as chess movements and state of each cell (i.e., which pieces are on each cell at a given time). The two main additions to our software to the official one are the time annotation without using an external clock -we use the compu internal clock instead-, as well as the tracking of chunks. Our software allows to mark chess pieces can identify both type and colour of every sample rate of 6 times per second which is sufficiently high for blitz chess -board for recording chess games can store up to 500 moves. Different chess programs can be employed for recording and analysis. The board design is classic (standardized tournament size squares, 8 mm classical wooden piece design and f eye movements we have used the noninvasive mobile and binocular Eye Tracking Glasses (ETG-Sensomotoric Instruments (SMI) [15] (Fig. 2). This is a binocular system with a sampling rate of up to 120 Hertz and a gaze tracking accuracy of 0.5° over all distances. For our recordings we have used the scene camera resolution of 960x720 pixels, 30 fps. mobile Eye tracking game play.

BOARD -PROGRAMMING AND HANDLING

movements, positions of pieces, and particularly the position of the chunks at all time is necessary in order to analyse correlations individual chess behaviour. In board (See Section 2, computer, and a software to between the board and the iginal software from DGT allows to track the movements of the game but lacks the feature for chunk and needs an external clock to annotate times. To nclude these two important features, we developed our Application Programming T. By using the API we can send commands via the serial port directly to the e-board to get movements and state which pieces are on each cell at a given our software with respect to the official one are the time annotation functionality we use the computer the tracking of chunks. pieces of chunks at the beginning of the game and to track match (see Fig. 3). In this way, we are able to annotate the position of all pieces from the chunk at any time, which is useful to finally compare it with the visual attention patterns recorded by the eye-

The messages from the electronic board to the computer can be of two kinds. We call them 'state' message, and 'update' message. A state message is a 64 message, where each byte refers The value of the byte indicates zero-, or if it is occupied by a piece piece code. There are 12 pieces codes, one for each type of figure and colour: white pawn 1, white rook 2, white knight 3, white bishop 4, white queen 5, white king 6, 7, black rook 8, etc. The sensors do not distinguish between pieces of a same colour and figure, i.e. the same code 1, both black knights are code 9, etc. update message is sent by the board every time a sensor notices a change, i.e. when The update message contains two important bytes; one is the sensor cell code, and the other (empty, or occupied by piece). For a complete simple movement (with no capture involved) t are sent: one when the piece is removed, and one when the piece is placed on the new cell. For movements where capture is involved, the number of up vary from two to five, depending on the capturing style of the player. When two pieces are on the same cell, it may also happen that no message is sent removed. Finally, the actual movement can be calculated by analysis of all the related update mes One challenge when analysing do not have clear information of when the movement is finished in order to start analysing the messages, and count the next messages as part of the next movement. For the case of a simple non-capture movement, it is very easy to know when the movement is finished. However, when a capture is involved, each new message has to be checked in order to know if the movement is complete or not. This may be problematic since each movement depends on how the update messages belonging to the former movement a classified. For instance, if an error happened in the analysis of the messages from a given movement, some of the messages may be wrongly considered as part of the next movement, creating more and more errors to movements. To avoid possible 'chain check using also state messages. After each movement is considered finished (by checking each update message), we ask and receive a state message. By comparing the stat message with the one before the movement happened, we can calculate the movement. We then compare this movement with the one resulting from analysing the movement's messages. If both movements (from the state messages and from the updates messages) coinc consider that everything is running the game and to track them during the chess ). In this way, we are able to annotate the position of all pieces from the chunk at any time, which is e it with the visual attention -tracker.

The messages from the electronic board to the computer can be of two kinds. We call them 'state' message, and 'update' message. A state message is a 64-byte long each byte refers to one cell from the board. he value of the byte indicates if the cell is empty -value , or if it is occupied by a piece -value equal to the piece code. There are 12 pieces codes, one for each type of r: white pawn 1, white rook 2, white knight 3, white bishop 4, white queen 5, white king 6, black pawn

The sensors do not distinguish between r and figure, i.e. all white pawns have the same code 1, both black knights are code 9, etc. An update message is sent by the board every time a sensor when a piece is removed or added. The update message contains two important bytes; one is the sensor cell code, and the other the new state of the cell (empty, or occupied by piece). For a complete simple movement (with no capture involved) two update messages are sent: one when the piece is removed, and one when the piece is placed on the new cell. For movements where capture is involved, the number of update messages may to five, depending on the capturing style of the player. When two pieces are on the same cell, it may also happen that no message is sent when one of them is . Finally, the actual movement can be calculated by analysis of all the related update messages.

One challenge when analysing update messages is that we do not have clear information of when the movement is finished in order to start analysing the messages, and count the next messages as part of the next movement. For the capture movement, it is very easy to know when the movement is finished. However, when a capture is involved, each new message has to be checked in order to know if the movement is complete or not. This may be problematic since each movement depends on how well onging to the former movement are classified. For instance, if an error happened in the analysis of the messages from a given movement, some of the messages may be wrongly considered as part of the next and more errors to the following movements. To avoid possible 'chain-errors', we double check using also state messages. After each movement is considered finished (by checking each update message), we ask and receive a state message. By comparing the state message with the one before the movement happened, we can calculate the movement. We then compare this movement with the one resulting from analysing the movement's messages. If both movements (from the state messages and from the updates messages) coincide, then we consider that everything is running smoothly. In case of a mismatch, we execute a refreshing, which consists on deleting all possible update messages in the queue so that the next movement is not compromised, update the position of the pieces using the last state message, and restore the maximum number of pieces from the chunks as possible. Restoring the pieces from chunks is necessary to not lose track of them. Because of the ambivalence of piece codes, we cannot know for certain where all chunk pieces are placed after a wrongly interpreted movement. At the moment we implemented the simplest mechanism which is to restore all pieces belonging to chunks that have not changed position after the misinterpreted movement. However, this is far from ideal, and as future improvements, another method should be implemented. One possible simple improvement is to check if the piece code is unique, for instance, when only one non-pawn figure is remaining on the board. In any case, each update message is checked carefully, so that all the common possibilities are taken into account, and the movement annotation is practically free from error. Errors of the type explained in this paragraph may only occur when the player moves pieces incorrectly, such as removing pieces without capturing.

The output of the automatic game annotation can be seen in Fig. 3a. The game data is saved in text format, indicating the chunk positions, and the complete configuration of the board in FEN-like (Forsyth-Edwards Notation) [START_REF]Forsyth-Edwards Notation[END_REF] format at each time a movement happens. The FEN notation consists of two parts. The first part encodes the empty squares and the position of all pieces on the board from white's perspective line by line just like a matrix, starting with square a8 and ending with h1, two lines always separated via forward slash. The second part follows after a space character and gives information about who is to move next, who is still allowed to castle, the number of played moves since the last piece has been captured or the last move of a pawn, respectively. We only use the first part of the FEN code because we are interested in the complete configuration of the board at each step of the game play. E.g. Fig. 3a documents 7 steps within a task handling, each step represented by a block of 4 rows. In the last block the following information is given: At the time 650s and after the last move Rb7-d7, player 1 chunks the pieces on the squares b2, f1 and d7, player 2 chunks those on c4, d2, h8 and b5. The complete board configuration is denoted by 7R/3r1P1P/6P1/1P6/2Q5/5pp1/1q1R3p/1k1k1b2 which is the position displayed in Fig. 3b (line by line, "7R" means "8 th row: a to g empty and black rook on h"; "3r1P1P" means "7 th row: a to c empty, white rook on d, e empty, black pawn on f, g empty, black pawn on h"). The single chess pieces of the chunks can be selected manually before starting the game, or automatically using a database.

CHESSBOARD DETECTION AND STABILIZATION WITH MARKERS

For analyzing the eye fixations on the chessboard, we use computer vision algorithms to automatically detect the chess fields from the video stream (960x720 pixel, 30 fps) provided by the scene camera located in the center of the eye tracking glasses (see Fig. 2, 5 and 6). Here the stabilization of the chessboard is important because of chess players' head, upper body and hand movements during gameplay. These movements cause changes in view angle and perspective towards the chessboard or they eclipse parts of the board. Furthermore, existing chessboard detection algorithms are not feasible with real chess pieces. The pieces can partly overlap due to perspective. In order to handle these challenges, we employ ArUco markers (see Fig. 5 and6) to extract the chessboard region and to divide this region equally into 64 sub-regions to get the coordinates for the single chess fields in scene video frames provided by the eye tracker. These sub-regions are assigned with the corresponding chess labels. The calculated information allows then for a precisely timed assignment of the recorded eye fixations to the corresponding chess fields.

ArUco markers [START_REF]Detection of ArUco markers[END_REF][START_REF] Garrido-Jurado | Automatic generation and detection of highly reliable fiducial markers under occlusion[END_REF] are synthetic square markers composed by a wide black border and an inner binary matrix which determines its identifier (id). The size of the internal matrix depends on the marker size, e.g. 16 bits for a 4x4 ArUco marker. The black border facilitates its fast detection in the image and the binary codification allows its identification and the application of error detection and correction techniques.

We use the OpenCV [START_REF] Bradski | Learning OpenCV: Computer vision with the OpenCV library[END_REF] library (version 3.2.0) for processing the scene video frames and ArUco marker(s) detection library for locating the markers in the 2D scene video recorded by the eye tracker (see Fig. 5 and6). Both libraries were developed using the C++ programming language. Initially, we randomly created four different default ArUco markers [START_REF] Garrido-Jurado | Generation of fiducial marker dictionaries using mixed integer linear programming[END_REF] with a marker size of ~35 mm and a padding of ~10 mm and placed them at the corners of the chessboard (Fig. 5 and6). Employing a large padding is an advantage to avoid the overlapping of chess pieces with the markers. After all markers are detected, the markers' corners are sorted and their identifiers are allocated as lefttop (LT), right-top (RT), left-bottom (LB) and right-bottom (RB). The LT and/or RT markers had fluctuations in detection because of noise to decode the marker dictionary pixels. To overcome these instabilities in the marker detection, we estimated the correlation of markers' shift to determine the positions of the missing markers between the previous and the current frame. I.e., whenever the LT and/or the RT marker is/are missing in the current frame then the coordinate shift between the LB and/or RB marker positions in the previous and current frame are determined. This shift is then adapted to the LT and/or RT marker positions in the previous frame.

In the test cases where the eye tracker and four markers (see Fig. 5 (i)) are used, the bottom markers are often not seen in the frame due to the distance between the scene camera and the chessboard. Thereupon, two more markers have been added at the mid of left-side and right-side of the chessboard (see Fig. 5 (ii)) which alternatively act as LB and RB when the bottom markers could not be detected. This approach keeps the continuity of chessboard detection but only detects one half of the chessboard if bottom markers are missing. Therefore, two more markers have additionally been added (in total 8 markers, see Fig. 5 lowest picture) between the mid-markers and the bottom markers that overlay most part of the chessboard.

From bottom to top, the LB and RB switch automatically according to the bottom markers' visibility. Therefore, at least four markers should be visible or estimated to extract the chessboard region (fully or partially). When any four markers are detected a 2D trapezium surface of the chessboard, spanned by the extracted marker position in the respective scene video frame, is created (see overlaid red drawing in Fig. 5 and6). The nonlinear trapezoidal is then divided into 8 parts with 9 coordinate points on each side, using the 2D perspective transformation the correlation ratio with respect to the camera projection is achieved. These coordinates are connected to opposite sides by drawing vertical and horizontal lines which construct 8x8 sub-regions inside the trapezium representing the 64 chess fields. By finding the intersection of each vertical and horizontal line, the sorted boundaries of sub-regions (i.e. 81 coordinate points) are assigned to the chess field labels.

By increasing the number of markers, the error rates in chessboard detection significantly decreased which results in reliable automatic annotations of gaze positions on chess fields. In case of a partially detected chessboard due to the invisibility of bottom markers in the frame and/or gaze coordinates outside of the chessboard boundary, frames have to be manually post-annotated. In order to find these frames, we implemented a binary traffic light feature (see Fig. 4). On a timeline, all frames are represented by small and short vertical lines. If the automatic detection provides good results, the corresponding vertical line is drawn in green color. Frames, where a later manual annotation is necessary because the chess fields could not be detected or the player did not fixate the chessboard, are represented by red vertical lines in the traffic light. (iii) upper half chessboard extracted.

PRELIMINARY RESULTS

In this section we present some examples of how we use automatic chunk tracking combined with eye tracking to generate plots of visual attention on chunks (Fig. 6d and Fig. 9e,f), as well as attentional landscapes over the whole board (Fig. 8b,c and Fig. 9c,d). These two types of data visualisations are useful to analyse the behaviour of different players for the same task (Fig. 8), or one single player during different tasks (Fig. 9).

The plots of visual attention on chunks (Fig. 8d and Fig. 9c,d) show the amount of time a player spent on 'fixating' pieces from the chunk over a given time interval. A 'fixation' is here defined as looking at a same position for a period of time equal or longer than a chosen threshold T min (in seconds or frames). The plots can be adapted to show only the data for a selected time interval from the total duration of the game, by specifying a starting and end time value 't0' and 't1' (in seconds or frames), respectively (see Fig. 8a). For a set of different thresholds for T min (e.g. from 2-5s on the x-axis in Fig. 8d), the percentage of attention on the chunk (shown on the y-axis) is calculated by adding all the fixations on pieces from the chunk during the selected time interval [t0, t1]. The result is the cumulative fixation time (in seconds or frames) which is then divided by the total time duration of the chosen interval. Note, that in this case, and just for the examples presented here, we do not differentiate between fixations on the single chess pieces of a selected chunk. Rather, we increase the cumulative fixation duration for a selected chunk as a whole whenever the player fixates on one of the chess pieces belonging to the respective chunk. In future work we will extend this feature to be able to calculate the cumulative fixation duration for each piece of a chunk separately.

A further type of analysis we present are the attentional landscapes [START_REF] Pomplun | Disambiguating complex visual information: Towards communication of personal views of a scene[END_REF] using a Gaussian distribution of standard deviation σ equal to the length of 1 cell of the chessboard, i.e. σ=5.5cm [13] (Fig. 8b,c and Fig. 9e,f). For the settings for the colour mapping in the attentional landscapes we follow the recommendations in [22, p. 238] and choose in a first estimate a value of around 4° for the visual angle (diameter), which gives an indication of what is looked at with the fovea, i.e. the area of the retina with the highest visual acuity, and also includes the closest area of the peripheral field. As described in [22, p.238] this chosen value is a first estimation, because items can still be perceived in the further periphery (therefore in the work of [START_REF] Blignaut | Visual span and other parameters for the generation of heatmaps[END_REF] the perceptual span is incorporated into the attention map settings). In our settings, the distance between the player's head and the chessboard plane is about 50cm, and the separation between the player and the position fixated on the board ranges from 20 to 64cm, depending on the fixated cell. From these three values and simple trigonometry, we can calculate the corresponding region on the board falling on the fovea and nearest periphery to 4.7cm for the closest cells on the board and 7.2cm for the furthest ones (see Fig. 7). For simplicity, and since the value is close to the length of one cell of the board (5.5cm), we approximate σ to the cell length 5.5cm for the examples herein. By using σ equal to one cell length, we can plot the attentional landscape on the 2D virtual board by simply discretizing the 2D representation of the chess board (see Fig. 8a) in 64 cells. Fig. 7 illustrates the calculation of the field of view in cm on the board, with α equal to the visual angle of 4° and H equal to the distance of the player's head to the board plane (in cm). The attentional landscape can be twitched to show only the result during a defined range of time, and for fixations equal or longer than T min .

After choosing values for t0, t1, and T min , the attentional landscape is then calculated by adding all fixations in the selected time interval [t0, t1] of at least T min length as a Gaussian of standard deviation equal to 1 cell, centred at the fixation location (provided by the eye tracker in x-y coordinates of the scene video). Finally, the total landscape for each cell is normalized so that the sum of all 64 cells equals to 1, or 100 for percentages. After choosing values for t0, t1, and T min , the attentional landscape is then calculated by adding all fixations in the selected time interval [t0, t1] of at least T min length as a Gaussian of standard deviation equal to 1 cell, centred at the fixation location (provided by the eye tracker in x-y coordinates of the scene video). Finally, the total landscape for each cell is normalized so that the sum of all 64 cells equals to 1, or 100 for percentages.

As a pre-test to evaluate whether the results on both type of plots described above reproduce the expected values, we created a well-defined dataset of eye tracking data to emulate two kinds of different chess behaviour for the same task (Fig. 8). The details about the task are not relevant, only how the emulated dataset for the scenario is created, which is as follows:

• For 154 seconds the configuration of the board is the one in Fig. 8a, the pieces in red are the chunk. • The eye gaze dataset for player 1 is created using a uniform distribution between 1 and 64, so that each chess field is chosen with equal probability. • On the other hand, the eye gaze dataset for player 2 is created as follows: at each frame the player chooses with a probability of ½ a cell occupied by the chunk, and with probability ½ to all 64 cells with equal probability.

Fig. 8b and8c show the attentional landscapes for each player using a Gaussian distribution of standard deviation equal to 1 cell, during 154 frames and for T min =1 frame (Fig. 8b), as well as for T min =3 frames (Fig. 8c). From the figures we can see that the attentional landscapes reflect the expectations and illustrate effectively the outcomes.

Because the fixation data of player 1 was equally distributed over all chess fields, the corresponding landscape show no focused attention on any specific chess piece (Fig. 8b). Player 2, in contrast, for whom fixations on the chunk have a higher probability in the well-defined dataset than for the rest of the chess field, focuses on the chunk, illustrated by higher values in the upper left corner of the corresponding attentional landscape (see Fig. 8b right). Fig. 8d shows the percentage of the player's visual attention focussed on the chunk plotted versus T min (from 2-5 frames). As expected, the proportion on attention on chunks for player 1 is close to 0, i.e. (1/64) n for T min =n frames. On the contrary, for player 2, the proportion for T min =n frames is (1/2 + 2/64) n , as shown in Fig. 8d for T min =2, 3, 4, and 5 frames.

As a second pre-test (with more realistic eye tracking data), we use the data from one participant (randomly chosen) from a series of real-time chess experiments we conducted.

In this experiment (conducted with 8 participants) the chess player had to solve a set of fixed classical chess tasks such as "White has to move, mate in 3 moves." within a set of chess constellations. All players had to deal with the same set of tasks under time pressure (2 minutes time for each task). Their gaze behaviour was recorded, starting from the first look at each task and ending either as soon as they presented a correct solution or when the handling time expired.

For this example, we show the result for one task the player could solve ('task 1') Fig. 9a, c, e), or one he could not solve ('task 2') (Fig. 9b,d,f), within the time limit of two minutes. The configuration of the pieces for 'task 1' and 'task 2' are shown in Fig. 9a and 9b, respectively. The pieces in yellow are the chunks for each of the tasks. In this experiment we used our software to automatically track the chunks' positions (see Section 3), and manually annotated the gaze video provided by the eye tracker. For the manual annotation of the gaze video we used common media player software (VLC player; www.vlc.de) and protocolled every ~100 ms at which cell the player was looking at. In this first approach we chose a threshold of ~100ms because the minimum processing duration during a fixation is 100-150ms [START_REF] Goldberg | Computer interface evaluation using eye movements: Methods and constructs[END_REF]. In this way we can ensure that we get all fixations and could do a relatively fast manual annotation for a coarse data analysis. In future work we will look closer into the fixation duration distribution in the recorded data files and select the threshold accordingly, because the mean fixation durations in chess are usually longer and depend on expertise, task conditions and chess constellations. For example, in [START_REF] Reingold | Perceptual automaticity in expert chess players: Parallel encoding of chess relations[END_REF] mean fixation durations in a chess detection task are reported from 230-330ms depending on chess skill and condition. The conditions consisted of 'no-cued' trials with two attackers and two conditions in which a cued non-checking attacker appeared together with an attacker that was either congruent (i.e. non-checking) or incongruent (i.e. checking). From the results in Fig. 9c and9d, it can be seen that the plots of attention on chunks show higher percentages for 'task 1' (Fig. 9c), the one the player could solve, than for 'task 2' (Fig. 9d), in agreement with previous studies of correlation of expertise and visual attention on chunks [START_REF] Reingold | Eye movements and visual expertise in chess and medicine[END_REF]. On the other hand, the attentional landscapes for T min =1 frame (Fig. 9e, f) look quite similar and show some degree of focused attention on chunks for both cases.

CONCLUSIONS AND FUTURE WORK

In this paper we have introduced a novel and efficient approach for the automatic analysis of chess players' visual behavior in real-time chess scenarios (solving tasks or playing live blitz chess matches on a real chessboard). We additionally implemented the functionality to select chunks and to analyse players' attention on these chunks over the game play. Although, the system and its evaluation are still in a quite preliminary state, first results show that it works reliable and resembles expected outcomes. Our approach works with a real chessboard and real chess pieces and is able to handle influences by environmental challenges, such as uncontrolled head movements, overlays between chess pieces and chess fields, as well as changing lighting conditions. By preserving the detected chessboard grid size in each frame in a future step we can further enhance the accuracy of our solution and reduce its' error rate. This is in stark contrast compared to existing pure Computer Vision based approaches (such as described in [START_REF] Losing | Guiding Visual Search Tasks Using Gaze-CContingent Auditory Feedback[END_REF]) that do not provide reliable automatic tracking and analysis results because they are not able to handle adequately the above mentioned environmental challenges occurring in real chess game play. Furthermore, due to the use of complicated Computer Vision algorithms they need much more processing time and computer power than our approach. With the proposed solution it will be possible to analyze the behavior of different players for the same chess task or of one single player for different tasks in real chess games without the need for a cumbersome and error-prone manual data annotation. By introducing the traffic light feature, the user is directly pointed to those frames, where the automatic annotation did not work sufficiently (e.g. when several markers cannot been detected in the scene video or when gaze coordinates are outside of the chessboard coordinates). Only for those frames the data still has to be manually postannotated.

As mentioned in section 2, the gaze coordinates and the eboard data are post-processed and analysed after the game play. We intend to go from offline to online processing and therefore to refine our techniques described in sections 2 to 4 in order to perform the data analysis and the data acquisition part both in parallel. For this online automatic analysis of game play the algorithms for e-board handling (section 3), chessboard detection and eye gaze analysis (section 4) have to be combined into a single program in the future. From both eye and chunk tracking the correlations between visual attention and chunk positions can then be identified and extracted on the fly. In future work, we will evaluate and optimize our solution with more data from real chess studies and compare our results to the ones using Computer Vision algorithms for automatic chessboard detection (see [START_REF] Losing | Guiding Visual Search Tasks Using Gaze-CContingent Auditory Feedback[END_REF] as an example). By deploying the 3D mapping and localization of markers with respect to the scene camera we might tackle the head and body movements (right and left) issues (see [START_REF] Muñoz-Salinas | Mapping and localization from planar markers[END_REF]). In fact, the synchronization of all-in-one software will provide an online feedback with less post-processing effort. On the one hand, our refined techniques will have practical applications in the setting of natural and intuitive electronic chess assistant systems for an individualized training. These assistant systems will be able to identify the expertise and the weaknesses of chess players and guide them through individual training sessions. These sessions could also include virtual chess agents giving feedback about optimal moves in given chess situations. Both experts and novices will profit from these individual feedbacks. On the other hand, the techniques described can offer deeper insight into the chunking processes of chess players. In future work, this may contribute interesting data and findings to the controversy about chunking and templates in the theory of chess [START_REF] Gobet | Chunks in Expert Memory: Evidence for the Magical Number Four ... or is it Two? Memory[END_REF].

Figure 1 .

 1 Figure 1. DGT electronic chessboard connected via USB to a computer.

Figure 2 .

 2 Figure 2. Chess player wearing the SMI mobileGlasses during game play.

Figure 3 .

 3 Figure 3. Acquisition of the game data (movements, chunks position and configuration of the board at each time) using the DGT e-board connected to the computer by USB and the software developed by us. In this example, we track two chunks, one for each player (yellow and blue pieces in (b)).(a)The game data is saved in a text file. Every time a player makes a movement, the time in ms with respect to the beginning of the game is written to the file, followed by the movement in algebraic long notation according to the FIDE

Figure 4 .

 4 Figure 4. The traffic light shows the single frames of the scene video along the time axis. Each frame is represented as a small and vertical line. If the automatic annotation for a frame was successful, the line is drawn in green, otherwise in red (i.e. when the chessboard could not be automatically detected or if the fixation is not on the board). In this example, only frames 4, 11, 12, 30 and 40 could not be processed automatically and still have to be manually post-annotated.

Figure 5 .Figure 6 .

 56 Figure 5. Usage of: (i) four markers; (ii) six markers -upper half of the chessboard extracted.

Figure 7 .

 7 Figure 7. Sketch for the calculation of the field of view in cm on the board (l 1 and l 2 ) from the field of view in angle (α), the distance of the player's head to the board plane (H) and the distance between the player and the fixated cell on the board (variable from 10cm to 54.4cm).

Figure 8 .

 8 Figure 8. Screenshot of two types of plots for quantifying the visual attention from eye tracking measurements over the chessboard during the game.

Figure 9 .

 9 Figure 9. Screenshot of the attentional landscapes and plots of attention on chunks as a function of T min , for a single participant and two different tasks in a real chess game. (a), (c) and (e) correspond to a mate in 3 moves task that the participant could solve after two minutes. On the other hand, (b), (d) and (f) correspond to another mate in 3 moves task that the participant could not solve in the two minutes given to solve it. The attentional landscapes are calculated for T min =1 frame.

ACKNOWLEDGEMENTS

This research/work is funded by the German Research Foundation (DFG) in the CEEGE (Chess Expertise by Eye Gaze and Emotions) project [27]. Additionally, we thank the DGT (Digital Game Technology) for their advices concerning the handling of the DGT e-board and their technical support.


I Kaltenmark

L Brun

G Auzias

J Lefèvre

C Deruelle

O Coulon

SPARSE DESCRIPTION OF THE CORTICAL SURFACE PEDIATRIC DEVELOPMENT: A SULCAL PITS STUDY

Keywords: brain development, cortical folding, sulcal pits, sulcal basins, varifolds

Despite the large variability of sulcal folds, their deepest points, namely the sulcal pits, provide a sparse and reproducible description of the cortical surface. Their role during the antenatal and pediatric development of the brain remains unclear. This work is the first study of the evolution of all sulcal pits during healthy pediatric development. We propose a new method to identify sulcal pits across subjects that benefits from the input of sulcal basins using a varifold metric. We then present a procedure to extract the amplitude and principal direction of sulcal pits trajectories.

INTRODUCTION

A major interest of sulcal pits is to define a finite set of robust landmarks on the cortical surface allowing local comparison across individuals. They have been often used to describe adult cortical morphometry [START_REF] Takerkart | Structural graph-based morphometry: A multiscale searchlight framework based on sulcal pits[END_REF] or atypical sulcal pattern in pathologies [START_REF] Im | Atypical sulcal pattern in children with devel-opmental dyslexia and at-risk kindergarteners[END_REF] but they have been largely neglected to study the typical post-birth cortical folding. The longitudinal study of [START_REF] Meng | Spatial distribution and longitudinal development of deep cortical sulcal landmarks in infants[END_REF] on the first two years of life highlighted a stable spatial distribution of pits in the few major deepest folds already present at term birth. Authors also reported a regionally heterogeneous increase of sulcal pits depth, especially in the high-order association cortex. Another study on children between 18 months and 10 years and covering both deep and shallow folds showed that the number of pits increases with age suggesting an increase of the number of folds even after term birth [START_REF] Brun | Localized misfolding within brocas area as a distinctive feature of autistic disorder[END_REF], which regarding previous results would likely concerns shallow folds. However, the exact location and time table of these changes remain unexplored, probably because of the lack of comprehensive model to track the position of sulcal pits across subjects and time. Moreover, the high spatial inter-individual variability can hinder the detection of subtle temporal changes.

While a high spatial consistency has been often reported for the deepest sulcal pits, the most shallow pits yet show greater spatial variability across subjects [START_REF] Auzias | Deep sulcal landmarks: Algorithmic and conceptual improvements in the definition and extraction of sulcal pits[END_REF]. These shallow pits are also less represented across the population, with a possible phenomenon of spatial pattern modes in the popula-tion. This observation is inherent to the fact that these pits, compared to the deepest ones, are probably under lesser genetic control and rather subject to mechanical influence during the surface folding process.

The identification of homologous pits across subjects, either by clustering after registration [START_REF] Auzias | Deep sulcal landmarks: Algorithmic and conceptual improvements in the definition and extraction of sulcal pits[END_REF][START_REF] Im | Spatial distribution of deep sulcal landmarks and hemispherical asymmetry on the cortical surface[END_REF] or graph matching [START_REF] Im | Quantitative comparison and analysis of sulcal patterns using sulcal graph matching: A twin study[END_REF][START_REF] Takerkart | Structural graph-based morphometry: A multiscale searchlight framework based on sulcal pits[END_REF], is made difficult by the large inter-subject variability. Several studies avoid this issue by considering only the deepest folds (e.g. [START_REF] Meng | Spatial distribution and longitudinal development of deep cortical sulcal landmarks in infants[END_REF]).

This paper presents a new method to describe the postnatal developmental trajectory of sulcal pits relying on two main contributions. First, we suggest several improvements in the definition of the group-wise labeling by combining information from sulcal pits position and the basins around those pits using a varifold metric. Second, we propose to use an exponential smoothing to extract the spatial trajectory of each labeled pit across time, out of the inter-individual spatial variability. In the following, we detail the methodological improvements of our contributions and we apply this framework to investigate the spatio-temporal trajectory of sulcal pits on linearly aligned brains of 155 children between 9 months and 18 years.

PITS IDENTIFICATION

Data Acquisition

The Cincinnati MR Imaging of Neurodevelopment (C-MIND) project provides MRI data of 209 healthy children between 0 and 18-years-old (04/30/2015 release), among them 59 subjects were scanned longitudinally with two or three timesteps. For each timestep, one or two T1w images were acquired on a Philips 3T MRI scanner with the following protocol: matrix size = 256 x 224, spatial resolution = 1 mm x 1 mm x 1 mm, TR/TE = 8.1/3.7 ms, flip angle = 8, TI = 939 ms. These images were denoised using SPM8 (SANLM algorithm) and a grey/white matter segmentation was performed using FreeSurfer 5.3. We selected 155 subjects from the Cincinnati Childrens Hospital Medical Center study site, ages between 9 months and 18 years, whose images were properly segmented and grey-white interface correctly extracted. Among them, 10 subjects were manually corrected using the control points of FreeSurfer.

Image Processing, Cortical Surface and Sulcal Pits Extraction

The extraction of sulcal pits was performed using the procedure of [START_REF] Auzias | Deep sulcal landmarks: Algorithmic and conceptual improvements in the definition and extraction of sulcal pits[END_REF], designed to yield reproducible sulcal pits especially in children populations. For each subject, we first estimated the sulcal depth map using the depth potential function, a measure that integrates both curvature and convexity information [START_REF] Boucher | Depth potential function for folding pattern representation , registration and analysis[END_REF]. Then, we applied a watershed by flooding algorithm that computes the sulcal basin associated to each depth maximum of the cortical surface and provides a complete parcellation of this surface. A merging of sulcal basins was performed during the flooding in order to filter spurious extrema caused by noise in the depth map. Filtering parameters were optimized as described in [START_REF] Auzias | Deep sulcal landmarks: Algorithmic and conceptual improvements in the definition and extraction of sulcal pits[END_REF]. We obtained a set of 97 ± 6.9 pits by subject, increasing with age.

Pits Clustering

The next step consists in defining a group-level clusters of pits that is usually computed by a watershed algorithm on the density map of the pits positions after spherical alignment of the meshes on a smooth atlas surface [START_REF] Meng | Spatial distribution and longitudinal development of deep cortical sulcal landmarks in infants[END_REF][START_REF] Auzias | Deep sulcal landmarks: Algorithmic and conceptual improvements in the definition and extraction of sulcal pits[END_REF]. We chose to use a preexisting cluster map [START_REF] Auzias | Deep sulcal landmarks: Algorithmic and conceptual improvements in the definition and extraction of sulcal pits[END_REF] with 108 regions of an adult population to ensure its stability.

According to our best knowledge, the reproducibility of the sulcal basins has not been studied and yet seems significant. The regions defined by the cluster map could thus be seen as an atlas of sulcal basins. In the literature, the label of a pit (affectation to its cluster) is estimated by a simple projection on the atlas surface (Method 1) [START_REF] Meng | Spatial distribution and longitudinal development of deep cortical sulcal landmarks in infants[END_REF][START_REF] Auzias | Deep sulcal landmarks: Algorithmic and conceptual improvements in the definition and extraction of sulcal pits[END_REF]. However, if one considers now the cluster map as an atlas of basins, then the global registration of the surface does not always perform a good registration of the basins and the pit of a subject can fall close to the boundary of an atlas basin, questioning its affectation. With our population, we count 8.2% of pits that are projected on the boundary of an atlas basin and 15.3% are very close to the boundary (in a two-ring neighborhood).

Pits Labeling

For this study, we propose a new method, Method 2, to assign a subject pit to an atlas basin. With the procedure of [START_REF] Auzias | Deep sulcal landmarks: Algorithmic and conceptual improvements in the definition and extraction of sulcal pits[END_REF], subject basins and template basins define respectively a complete parcellation of the subject cortical surface and the atlas surface. The central idea is to compare registered subject basins to atlas basins with a similarity measure M on surfaces. For this purpose, we used an oriented varifold metric which compare positions, areas, and orientations of the surfaces [START_REF] Charon | The varifold representation of nonoriented shapes for diffeomorphic registration[END_REF][START_REF] Kaltenmark | A general framework for curve and surface comparison and registration with oriented varifolds[END_REF]. This new method relies thus on the reproducibility of the sulcal basins. Observations of the data showed that this hypothesis is yet patently not satisfied in one situation: a subject misses pits in a region and one of its basin covers thus one or more atlas basins. For this reason, we define an algorithm that relies either on the pit or the basin of the subject. Atlas basins are ordered by the group-watershed algorithm: most reproducible basins are in the top of this list denoted Q. As the number of pits varies across individuals, our method might compensate impossible pairing with the second best option. To prevent this situation, we add a reject criteria grounded on the overlap between two paired basins. We denote B ∩ B > P %B if the intersection of two basins B and B fills at least P % of B. The overlap criteria ensures that if a pit is not assigned to its parent cluster, its cluster does overlap subsequently with the pit's basin. Given a registered subject:

1. Order subject basins by decreasing area in a queue Q.

For each basin B ∈ Q, consider the atlas basin B that contains the subject pit. With the natural cluster assignation, Method 1, if several pits fall in the same cluster, the deepest one is kept, the others are unassigned. Our algorithm prevents any multiple assignments.

Optimization of the atlas basins

To quantify the reproducibility of pits for each atlas basin, we computed the percentage of subjects who have one and only one pit assigned to this basin, called the N 1 measure [START_REF] Auzias | Deep sulcal landmarks: Algorithmic and conceptual improvements in the definition and extraction of sulcal pits[END_REF]. At the individual level, the sulcal basins generated by the watershed algorithm from the depth potential map fit the geometry of the cortical surface. At the group level however, the density map induces a bias on the atlas basins, overextending the clusters of the most represented pits at the expense of shallow pits. We therefore optimized the atlas basins after a first run of our method with a weighted voting strategy. For each vertex of the atlas surface, we computed among the projection of subject basins the occurrence of each label weighted by the N 1 value of the label. This provides a new atlas parcellation for which we apply again our labeling method.

PITS TRAJECTORIES

Labeling the pits allows us to return to the baseline surfaces and follow the evolution of the pits across the population for each label independently. All subject surfaces are aligned with a rigid registration on a reference surface chosen as the subject surface that minimizes the distance to its closest neighbors and whose age is close to the mean of the population. We then regroup the pits among the whole population according to their label. Each pit is given as a point in the 3D-space with a temporal marker that corresponds to the age of the subject from which it is extracted. Hence, for each label, we have a cloud {t i → y i ∈ R 3 } i=1..N of N 3D-points (y i ) indexed by age (t i ). To analyze this type of data, we performed an exponential smoothing as follows:

ŷi =   N j=1 y j exp -|t i -t j | 2 σ 2     N j=1 exp -|t i -t j | 2 σ 2   .
This filtering aims at reducing the spatial variability of the pits across the population while preserving the temporal variability, as long as the scalar parameter σ remains small. In our experiments, σ = 1.5 year. Fig. 1 illustrates this process for one label. The next step is to perform a linear regression on the smooth pits with respect to age. In most cases, the p-value is highly significant (median at 10 -26 ). However, although the pits may be aligned, the speed of the trajectory with respect to age is not necessarily linear. We projected the trajectory on the image of the linear regression to better fit the data as illustrated in Fig. 1. At last, we extracted the single vector that represents the projection of the pits on this line and hence indicates the main direction and amplitude of temporal development. For the few basins with poor p-value (> 10 -5 ), we visualized the results to ensure that this vector gives a good first order approximation of the trajectory.

The exponential smoothing turns each cloud of pits into a smooth trajectory. In order to ensure that the linear structure is a meaningful description of the pits evolution with respect to time, we perform the following test. For each label, we applied the exponential smoothing for n = 30000 random permutations of the age index of the pits and we computed the ratio of the standard deviation before and after exponential smoothing. The ratio for the original index can then be compared to those obtained by random permutation. If the reduction of the standard deviation is lower than 95% of the ratios randomly generated, we consider that age is a significant factor to explain the position of the pits. With this threshold, 32 basins are retained.

RESULTS AND DISCUSSION

Fig. 3. On the top: N 1 map for Method 2. On the bottom: N 1 increase with respect to Method 1. Fig. 2 compares the atlas basins before and after the voting strategy. One can observe that the new boundaries better fit the geometry of the surface and some artifacts of the initial map are corrected (see in the temporal lobe). The proposed Method 2 labels 85.1% of the pits against 77.8% for the Method 1. This increase mostly benefits to shallow pits as displayed in Fig. 3 alongside the N 1 score for Method 2. Moreover, the two methods attribute different labels to 21.7±4.9% of a subject's pits. A visual validation of the results showed that in most conflicting cases our method was Fig. 4. First order approximation of the pits trajectories in the basins for which temporal variability prevails over inter-subject variability. From left to right, amplitude and projections on the 3 orthogonal axes. Each axis is highlighted by an arrow. an improvement. Finally, Fig. 4 illustrates for the 32 retained basins the amplitude of the pits trajectories (after first order approximation) and the projections on the x, y, z axes. Pits trajectories from the central sulcus to the occipital lobe evolve in the posterior direction, contrary to the temporal lobe where sulcal basins move anteriorly towards the temporal pole. Pits in the prefrontal lobe evolves in an anterior and dorsal direction.

In this paper, we presented a methodological framework to study pediatric cortical shape development. Our results are preliminary and use only a first order approximation of trajectories, but the full use of the discrete smooth trajectories (Fig. 1), in conjunction with a study of sulcal basins depth, made possible by our pits labelling method, could provide an efficient sparse description of cortical shape development. Another extension could be the study of the temporal development of sulcal basin shape.

  (a) If B ∩ B > 80%B, the pit is assigned to B and B is removed of Q. (b) If the area of B is twice larger than the area of B, and if B ∩ B > 50%B, the pit is assigned to B and B is removed of Q. 2. For each atlas basin B ∈ Q, ordered unassigned subject basins in a new list Q by decreasing distance to B with respect to the similarity measure M. Select the first subject basin B ∈ Q that satisfies the overlap criteria: either B ∩ B > 50%B or B ∩ B > 50%B.

Fig. 1 .

 1 Fig. 1. Illustration of the procedure for one label. Front: Exponential smoothing of the pits. Back: Linear regression and projection of the smoothed pits.

Fig. 2 .

 2 Fig. 2. Optimization of the atlas basins.

ACKNOWLEDGEMENTS

This work was funded by the Fondation de France (Grant #2015-00059546). Data presented in this work was obtained from the Cincinnati MR Imaging of NeuroDevelopment (C-MIND) database, provided by the Pediatric Functional Neuroimaging Research Network and supported by contract from the Eunice Kennedy Shriver National Institute of Child Health and Human Development (HHSN275200900018C).