Visual tracking in simulated salamander locomotion

Visual tracking in simulated salamander locomotion Auke Jan Ijspeert

Michael Arbib

Brain Simulation Laboratory, Hedco Neuroscience Building, 3614 Watt Way University of Southern California, Los Angeles 90089-2520, U.S.A, [email protected], [email protected]

Abstract

This article presents a rst step towards our aim of building comprehensive models of neural systems embedded into biomechanical simulations for investigating the neuroethology of lower vertebrates. It investigates visual tracking in a model of the salamander which incorporates 1) a biomechanical body actuated by springs-and-damper muscles, 2) a spinal locomotor circuit simulated as a leaky-integrator neural network, and 3) a visionbased control circuit. A simple visuomotor experiment is presented in which the vision-based control circuit uses the signals from the retinas and from \water" sensors to modulate the type of gait produced by the locomotor circuit as well as the direction of motion. The simulated salamander is thus given the capacity to track and approach a randomly moving target both in water and on ground. Although our aim is to integrate realistic models of the visual system into the salamander model, only a very abstract visual system is implemented in this rst experiment. The primary motivations of this article are 1) to integrate a locomotor circuit evolved in previous work into a new 3D biomechanical model of the salamander, 2) to investigate the stability of pattern generation of the locomotor circuit against constantly varying inputs, and 3) to illustrate how the locomotor circuit can serve as basis for adaptive behavior.

1. Introduction

Understanding behavior of vertebrates from studying their central nervous systems (CNSs) is a most challenging task because behavior is the result of the complex interaction of not only the multiple neural circuits forming the CNS, but also of the coupling of the CNS and the body, and of the interaction of the CNS-body pair with the environment. Investigating individual subcircuits of the CNS, although necessary, is not sucient to fully understand the neural mechanisms underlying behavior. There is therefore a need for integrative computational approaches, such as computational neuroethology (Beer, 1990, Cli, 1995), in which the interactions

between the dierent subcircuits of the CNS are investigated as components of a physical body in interaction with an environment. (Arbib, 1987) summarized Rana computatrix, a model of anuran visuomotor coordination and one of the earliest works in this computational approach. This work has continued (Cobas and Arbib, 1992, Arbib and Lee, 1994), and also led to robotic experiments in looming avoidance behavior (Arbib and Liaw, 1995). Several experiments in computational neuroethology inspired by simpler animals have recently been carried out. Simulated models of insect locomotion such as in stick insects (Cruse et al., 1995) and cockroaches (Beer, 1990) have, for instance, been developed, and later implemented in legged robots (Cruse et al., 1995, Quinn and Espenschied, 1993). The dynamics of sensory systems such as cricket phonotaxis (Webb, 1994) and visual systems of y (Franceschini et al., 1992) and hover y (Cli, 1992) have also been investigated using robotic means. In addition to Rana computatrix, vertebrates have inspired computational models such as the neuronal and mechanical model of lamprey swimming (Ekeberg, 1993), the Arti cial Fishes project (Terzopoulos et al., 1994), and models of classical conditioning (Vershure et al., 1995). The experiment presented in this article is part of a project to build a comprehensive model of a lower vertebrate |the salamander| which includes a CNS, a biomechanical body and a simple environment. A special emphasis is given to realistically represent the dynamical properties of the musculoskeletal structure of the body. Having a realistic model of the body is indeed an essential element of the computational neuroethology approach, since body movements strongly in uence perception of the world, and because the physical properties of the body introduce important constraints on the type of motor actions that can be performed|using Raibert's words, the CNS does not send commands to the body, only \suggestions" (Raibert and Hodgins, 1993). The choice of the salamander is motivated by the following considerations. Firstly, the salamander |an amphibian| is capable of both aquatic and terrestrial locomotion, and represents among vertebrates a key element in the evolution from aquatic to terrestrial habi-

tats. Secondly many data are available characterizing its locomotion, its visual system and its behavior, making it an interesting test-bed for the synthetic approach we advocate, in which current knowledge of the animal's CNS is complemented by techniques from arti cial neural networks (Ijspeert, 1999). Finally, the salamander is situated at the right level of complexity among vertebrates: it is simple enough for making possible a comprehensive model of the animal (it has, for instance, orders of magnitudes fewer neurons than mammals), while the similarities of its central nervous system with more complex vertebrates oer the possibility of general insights into the CNS-body relationships of vertebrates. The work presented here follows experiments in which a locomotor circuit was developed using evolutionary algorithms for controlling the gaits of a 2D lamprey (Ijspeert et al., 1999, Ijspeert and Kodjabachian, 1999) and a 2D salamander simulation (Ijspeert et al., 1998, Ijspeert, 1999, Ijspeert, 2000b). The locomotor circuit for the 2D salamander is here extended to control a new 3D biomechanical simulation of the body with more realistic limbs. The circuit is capable of generating trotting and swimming gaits, and the speed and direction of locomotion can be modulated by simple descending tonic (i.e. non oscillating) drive. In this article, the drive is provided by a control circuit which receives input from a simple visual system and from \water" sensors. The whole system is capable of generating a tracking behavior of a moving target, illustrating the stability of the locomotor circuit against constantly varying inputs. In the next sections, we rst present biological data on salamander locomotion and visuomotor coordination (Section 2), followed by the biomechanical simulation of the salamander (Section 3), its locomotor circuit (Section 4), and the simple visual system (Section 5). Results of the tracking experiment are presented in Section 6, followed by a discussion (Section 7).

2. Salamander locomotion and visuomotor coordination The salamander makes axial movements during locomotion. It swims using an anguiliform swimming gait, in which the whole body participates to movement creation, and in which a wave of neural activity is propagated from head to tail (Frolich and Biewener, 1992, Delvolve et al., 1997, Delvolve et al., 1999). On ground, the salamander switches to a trotting gait in which the body forms an S-shaped standing wave with the nodes at the girdles. The locomotor circuitry responsible for these two motor programs has not been decoded for the moment. It has been hypothesized that it is based on a lamprey-like swimming central pattern generator (Cohen, 1988, Delvolve et al., 1997).

In (Ijspeert et al., 1998, Ijspeert, 1999, Ijspeert, 2000b) we developed a model of the locomotor circuitry which is an implementation of such a hypothesis (see Section 4). Salamanders have been studied in detail by biologists and a large amount of literature exists describing their visual system (Grusser-Cornehls and Himstedt, 1976, Manteuel, 1984, Roth, 1987, Wiggers et al., 1995), and their visually-guided behavior (e.g., prey capture) (Roth, 1987). In this article, we will mainly focus on the mechanisms underlying feeding behavior. As described in (Roth, 1987), prey-capture behavior typically shows a sequence of the following reactions: 1) orienting movements of the head to xate the stimulus binocularly, 2) approaching toward the stimulus until it is within reach of the tongue (although some species use an \ambush strategy", waiting until the prey comes close), 3) binocular xation of the prey object, and 4) snapping. Note that this sequence corresponds to terrestrial feeding, salamanders feeding in water swallow (instead of snapping at) prey by creating a rapid in ow of water into the mouth through an expansion of the throat. In this article, we will only simulate the approach-towards-a-prey phase. We will furthermore use only a very simpli ed model of the salamander's visual system (more sophisticated models will be mentioned in Section 7).

3. Mechanical simulation The 3D mechanical simulation is composed of ten rigid links representing the trunk and the tail, and eight links representing the limbs (Figure 3.). The tail and trunk links are connected by one degree-of-freedom (DOF) joints, while the limb joints have 2 DOF at the shoulder and pelvis and 1 DOF at the knee/elbow. The torques on each joint are determined by pairs of muscles simulated as springs and dampers, whose spring constants are modi ed by the signals sent from the motoneurons. The simulation represents the salamander in a simple environment composed of at ground and water. It is implemented in a dynamical simulation package from MathEngine,1 which handles the internal forces necessary for keeping the links connected, as well as the contacts of the body with the ground. During terrestrial locomotion, friction forces are applied to all links in contact with the ground (e.g. the trunk and tail links slide on the ground while the salamander is trotting), while in water it is assumed that each link (limbs included) is subjected to inertial forces due to the water (with forces proportional to the square of the speed of the links relative to the water). A more detailed description of the simulation can be found in (Ijspeert, 2000a).

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Figure 1: Mechanical simulation. The body is composed of 18 rigid links. Body (trunk and tail) links are connected by one-DOF hinge-joints, with vector B as axis of rotation. Limbs are attached to the body by two-DOF joints with one vertical axis of rotation PV and one horizontal PH . Finally, knee/elbow joints have one DOF and they rotate around axis K.

4. Locomotor circuit The locomotor circuit presented in this paper is an extension of a circuit developed in (Ijspeert, 2000b) (see also (Ijspeert et al., 1998, Ijspeert, 1999) for previous experiments). Only a general description of the circuit will be given here. The locomotion controller is simulated as a leaky integrator recurrent neural network. It is composed of a body CPG and a limb CPG (Figure 2). The body CPG is lamprey-like with an interconnection of 40 segmental networks for the generation of traveling waves of neural activity. The limb CPG is made of two interconnected oscillators projecting to the limb motoneurons and to the body CPG segments, creating a unilateral coupling between the two CPGs. The network is made of a total of 360 neurons. While the general organization of the controller is set by hand, the time parameters, biases and synaptic weights of the neurons are instantiated using a genetic algorithm. This is done in three stages, with rst the evolution of segmental oscillators, second, the evolution of intersegmental coupling for the body CPG, and nally the evolution of the limb CPG connectivity (see (Ijspeert, 2000b)). A similar approach had previously been used to develop swimming controllers for a simulated lamprey (Ijspeert et al., 1999) (see also (Ijspeert and Kodjabachian, 1999) for another approach which uses a developmental encoding to develop controllers in a single stage). Motoneurons in the body CPG determine the muscular activity along the body (left-right motoneurons in nine equally spaced neural segments from segment 4 to segment 36 determine the torques of the nine body joints). Each limb is activated by 3 pairs of exor-extensor neurons. Note that the limb 1

MathEngine Inc., San Fransisco, USA, www.mathengine.com

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Figure 2: Organization of the salamander's locomotor circuitry. The circuit is composed of a body CPG and a limb CPG which can be activated by four pathways from the brain stem (BS). Each limb is activated by 3 pairs of exor-extensor neurons (only one shown here).

CPG was initially developed for a 2D simulation of the salamander. Two motoneurons for the vertical exor and extensor muscles at the shoulder and pelvis (FV and EV ), were added by hand to the network. These motoneurons oscillate with a phase of approximately 90 degrees compared to the horizontal motoneurons, so that the limbs perform approximate circles at the shoulders and pelvis. Motoneurons for the knee/elbow muscles were also added by simply copying the motoneurons for the horizontal shoulder/pelvis muscles (knee/elbow muscles are therefore in synchrony with horizontal shoulder/pelvis muscles, FH and EH ). The synaptic weights of the circuitry are given in appendix (Tables 1 and 2).

4.1 Neuron model Leaky-integrator neurons, i.e. neurons of intermediate complexity between abstract binary neurons used traditionally in arti cial neural networks and detailed compartmental models used widely in computational neuroscience, are used for implementing the neural controllers. Instead of simulating each activity spike of a real neuron, a neuron unit computes its average ring frequency. According to this model, the mean membrane potential mi of a neuron Ni is governed by the equation:

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X wi;j xj

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4.2 Gait modulation

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Gait modulation is obtained by varying how tonic (i.e. non oscillating) drive is applied to the network. Each neuron in the network receives a connection from the brain stem. As illustrated in Figure 2, there are four independent pathways by which the tonic drive can be applied: drives to each side of the body CPG (BS B), and drives to each side of the limb CPG (BS L). The swimming gait, i.e. a traveling wave of neural activity, is obtained when tonic drive is given to the body CPG only. In that case, segmental oscillators in the body CPG start to oscillate, with a small phase lag between consecutive segments. The typical anguiliform swimming observed in salamanders and lampreys is thus produced (Figure 3). Increasing the level of tonic drive leads to an increase of the oscillation frequency, which amounts to an increase of the speed of swimming in the mechanical simulation. Note that during swimming, tonic signals are also sent to the horizontal exors of the limbs in order to keep the limbs against the body. Turning can be induced by giving asymmetrical inputs between left and right sides of the body CPG. The extra excitation to one side of the body leads to increased bendings towards that side. If the asymmetry is permanent, the salamander swims in a circle, and if it is temporary it can be used to change the heading of swimming. The trotting gait is obtained when tonic drive is applied to both the body CPG and the limb CPG. Limb oscillators are then activated, and the unilateral coupling from the limb oscillators forces the chain of segmental oscillators of the body CPG to produce a standing wave. The coupling indeed forces the body CPG (which would normally propagate a traveling wave) to be in perfect synchrony in the upper part of the body and in the tail, with an abrupt change of phase at the level of the posterior girdle (i.e. where the in uence of the anterior limb oscillator stops and that of the posterior limb oscillator begins). Figure 4 illustrates the resulting trotting gait. The body makes an S-shaped movement which is coordinated with the movements of the limbs to increase their reach when they are in the swing phase. Turning during trotting can be induced by applying asymmetrical input to both the limb and the body CPGs. Turning is then mainly due to the extra bending of the body which enables the simulated salamander to make relatively sharp turns. Interestingly, the simulated trotting salamander did not present rolling problems in this 3D simulation. This is partly due to the fact that, in this rst approximation of a salamander, joints connecting body links have been simulated as hinges (i.e. with only 1 DOF) therefore preventing torsion, but also to the intrinsic property of the salamander's trotting gait in which the whole body slides on the ground with a stabilizing S-shape, therefore signi cantly reducing postural instability compared to

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5. Vision-based control circuit A hand-coded vision-based control circuit composed of a very simple visual system and a "water" sensor is developed. The visual system is represented as a mathematical function which computes two signals which are proportional to the horizontal bearing of a speci c target compared to the axis of each eye (Figure 5). The outputs of the visual system and the sensor determine the tonic drive applied to the locomotor network by the circuit illustrated in Figure 6. The tracking behavior is implemented by having excitatory projections from the visual system to the locomotor circuit. Projections to the body CPG are only ipsilateral, leading therefore to increased bendings of the body towards the

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6. Simulated tracking A set of preliminary experiments investigating the tracking of a randomly moving was carried both on ground and in water. The target was made to move randomly in a horizontal plane, starting from a position somewhere in front of the salamander. Figure 7 illustrates the trajectory of the salamander while tracking the target on ground. Through modulation of the neural activity in the body CPG, the salamander is capable of changing the heading of its motion such as to approach the target. The signals produced by the visual system during the tracking are illustrated in Figure 7 (second from top). These signals have both a random component which corresponds to the movements of the target and a periodic component due to the rhythmic head movements linked with the salamander motion. These varying signals modulate the neural activity of the locomotor circuit but without disturbing the pattern generation. A similar behavior is observed during swimming (data not shown). An example of gait transition due to the signals from the "water" sensor is given in Figure 8. Here a groundwater-ground sequence is illustrated. The limb CPG is therefore turned on-o-on, which means that it switches between forcing the body CPG to produce a standing wave and releasing it to produce the traveling wave. After the swimming gait, the trotting gait resumes after a little delay. The delay is due to the time needed for the limb CPG to pass from the almost symmetrical state forced by the temporary inhibition to the asymmetrical trotting gait. This capacity to return to the desired phase relation between limbs despite unfavorable initial

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7. Discussion This article presented an experiment in which a simple vision-based control circuit is implemented on top of a locomotor circuit for enabling a simulated salamander to track and approach a moving target. The visual system in this article is only a very abstract representation of the salamander's system. In future work we intend to simulate the retinas, op-

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conditions illustrates the stability of pattern generation of the locomotor controller. The transition from swimming to trotting could be accelerated with the application of a short asymmetry of tonic drive between anterior and posterior limb oscillators. Note that the locomotor circuit does not rely on sensory feedback for pattern generation, and that sensory feedback (for instance, from muscle spindles) was not integrated in the current study. Feedback is important for \shaping" the neural activity and coordinating it with the body movements, especially when the environment is not uniform (e.g. the ground is not at). In the lamprey model, for instance, feedback was shown to be important for swimming in non-stationary water (Ekeberg et al., 1995, Ijspeert et al., 1999). Animations of the results presented in this article can be viewed at http://rana.usc.edu:8376/ijspeert/ .

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Figure 6: Vision-based control circuit. Signals from the visual system determine the tonic input applied to the locomotor circuit via the four brain stem pathways (left/right projections to the body CPG, BS B, and the limb CPG, BS L). Inhibition from the water sensor implements the gait transition between trotting and swimming (see text).

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tic tectum and pretectum of the salamander more realistically using leaky-integrator neural networks like those of the locomotor circuit. We will therefore build upon the neural network implementation of rana computatrix (Arbib, 1987, Cobas and Arbib, 1992, Arbib and Lee, 1994) and of comparative simulations of frog and salamander vision (Lamb, 1997). The two Simulander simulations which model stimulus tracking with head movements, and depth perception in salamander will also be of particular interest here (Eurich et al., 1995, Eurich et al., 1997). The aims of making a simulation study which combines a visual system, a locomotor circuit and a body are two-fold. First, we aim to analyze the in uence of body motion on visual perception. The experiment presented in this paper illustrated for instance, that, as expected, body motion introduces a signi cant rhythmic component to the visual signals. The extent of how much this biomechanical aspect complicates (e.g. for the estimation of the velocity of a stimulus) or facilitates (e.g. by disambiguating the depth perception of a stimulus through multiple sampling) visual perception remains to be analyzed, and is a question which applies to vertebrates

in general. In frogs, for instance, it has been hypothesized (Schipperheyn, 1963) and con rmed by simulation (Lee, 1994) that small movements due to the respiratory cycle can improve the detection of stationary objects. The second aim of the study is to be able to use and explain behavioral data. A signi cant amount of what we know of the salamander visual system comes from behavioral and lesion studies (Roth, 1987). For instance, (Luthardt-Laimer and Roth, 1983) investigated salamander binocular and monocular depth perception by analyzing how salamanders approach a stimulus, and comparing animals with intact eyes, animals with one eye covered by one cap, and animals in which one eye had been removed one year before the experiment. Having complete models of the CNS and the body of vertebrates will allow one to reproduce such experiments in silico, and to test whether potential models of subcircuits of the CNS can explain behavioral data when connected together and embedded into a model of the body in interaction with an environment. The primary aim of this article was to extend our model of the salamander's locomotor circuit to a new 3D biomechanical model, and to investigate how it could be driven by higher control centers for simple sensori-motor coordination. When modeling a locomotor circuit, it is indeed important to not only demonstrate that a circuit can produce a locomotor pattern, but also that the locomotor pattern can be modulated by command signals for changing the speed and direction of locomotion, i.e. pattern modulation is at least as important as pattern generation. In the case of the salamander, pattern modulation means, in addition to changing speed and direction, the capacity to switch between swimming and trotting. In our model, the coupling from the limb CPG to the body CPG explains the capacity of the salamander to produce two dierent types of waves along its body: the traveling wave for swimming when the limb CPG is not activated, and a standing wave for trotting when the body CPG is forced by the unilateral coupling from the activated limb CPG. In agreement with this hypothesis, it has been recently found that salamander spinal circuits tend to propagate a traveling wave when completely isolated (Delvolve et al., 1999). The idea underlying the model is that during evolution from a lamprey-ancestor, the coevolution of bodies and locomotor circuits has seen the generation of ns and then limbs accompanied by a specialization of some segmental oscillators to control these new limbs (Cohen, 1988). As the salamander has kept a partially aquatic habitat, it has kept the control circuitry for aquatic locomotion and developed a new motor program for terrestrial locomotion. In our model, we assume that the gait transition is obtained by the modulation of simple non-oscillating signals from the brain stem. Similar approaches have been taken to model gait transition (e.g from walk to trot

to gallop) in mammals (Collins and Richmond, 1994, Canavier et al., 1997), based on observations of gait transition stimulated by simple electric signals in cats, for instance (Shik et al., 1966). As the speed, direction, and type of gait of locomotion are modulated by simple tonic signals, the spinal circuit was easily integrated into a sensing-to-acting chain. The important outcome of this experiment is that the continuously changing command signals due to the visionbased circuit do not disturb the pattern generation of our locomotor circuit. From a control point of view, these command signals can be seen as a (both random and rhythmic) perturbation to the system. The perturbation is sucient for modulating the direction of locomotion such as to implement the tracking behavior, but does not interrupt the rhythmogenesis. The 3D biomechanical simulation is a central aspect of our approach as it allowed us 1) to investigate what phases and shapes motoneuron signals should have for ecient locomotion, 2) to analyze the modulation of the speed and direction of locomotion, and 3) to implement a simple sensorimotor experiment. These investigations can not be realized by studying a CPG model in isolation. The approach could potentially be extended to robotics, for controlling robots using animal-like type of gaits (see, for instance, (Jalbert et al., 1995) for a lamprey-like robot and (Lewis, 1996) for a quadruped robot with exible spine). The main diculty with animal-like locomotion is that it requires control mechanisms which can transform simple commands concerning the speed and direction of motion into complex coordinated rhythmic signals sent to the multiple actuators necessary for ecient locomotion. The CPG presented in this paper has the capacity to do this transformation, and the experiment reported here shows that it can do it robustly.

8. Conclusion This article presented a simulated sensorimotor coordination experiment in a model of lower vertebrate. A model of a salamander was developed which incorporates 1) a biomechanical model of the body, 2) a locomotor circuit simulated as a leaky-integrator neural network, and 3) a vision-based control circuit. The experiment illustrated the stability of pattern generation of our model of the salamander's locomotor circuit, and demonstrated how it could be modulated by higher control centers for implementing a stable tracking and approach behavior towards a moving stimulus. The salamander model will be incrementally extended by integrating new models of subcircuits of the central nervous system (CNS). Our aim is to develop a comprehensive simulation of a lower vertebrate in order to investigate how behavior emerges from neural mechanisms, and to analyze in detail the dynamics which result from

1) the interaction of the multiple neural circuits forming the CNS, 2) the coupling of the CNS and the body, and 3) the interaction of the CNS-body pair with the environment. Acknowledgments: Facilities were provided by the University of Southern California. Auke Ijspeert is supported by a grant for young researcher from the Swiss National Science Foundation.

Table 1: Neuron parameters and connectivity of the body CPG. The synaptic weights of the segmental oscillators are given. Numbers in brackets indicate extents of coupling in the rostral and caudal directions, respectively. See (Ijspeert, 2000b) for details. A 20ms 0.2 M { A { B -0.3 [3,4] C -0.3 [5,2] cM { cA -1.5 [1,1] cB { cC {  b

B 297ms 2.9 -1.2 [5,1] { -1.2 [1,3] -1.6 [5,0] { -1.1 [1,1] -1.3 [2,4] {

C Input 57ms 20ms -6.4 5.6 -5.0 [1,0] 5.0 { { { 8.2 -0.7 [3,2] 2.9 -1.3 [1,1] { -0.7 [3,0] { -1.4 [5,1] { -5.0 [0,1] {

Table 2: Connectivity of the limb CPG. See (Ijspeert, 2000b) for details. F E A B C cF cE cA cB cC pA pB pC pcA pcB pcC bA bB bC bcA bcB bcC

A { -1.4 { -2.1 -2.2 { -0.4 -4.4 { { -2.0 -0.8 { -1.0 -1.6 -1.2 -0.3 -0.9 -0.4 -0.9 -0.6 -0.2

B C Input -8.2 -10.0 3.3 { -2.3 5.4 { { { -5.8 { 8.2 -9.7 -4.0 2.9 -0.7 -2.7 { -7.4 -10.0 { -3.4 -2.8 { -8.8 -9.6 { { -9.9 { -1.5 -0.5 { -0.3 -0.9 { -1.2 -1.9 { -1.3 -0.6 { -1.1 -0.1 { -1.1 -0.7 { -0.7 -1.9 { -0.9 -1.2 { -0.3 -0.2 { { -1.1 { -1.7 -0.2 { -0.1 -1.0 {

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