Ahmed Khalifa
email: ahmed.khalifa@ec-nantes.fr

Olivier Kermorgant
email: olivier.kermorgant@ec-nantes.fr

Salvador Dominguez
email: salvador.dominguez-quijada@ec-nantes.fr

Philippe Martinet
email: philippe.martinet@ec-nantes.fr.

Philippe Martinet Vehicles

Vehicles Platooning in Urban Environment: Consensus-based Longitudinal Control with Limited Communications Capabilities

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

I. INTRODUCTION

Shared transportation systems in urban environments are the current trend to overcome the transportation problems toward an eco-friendly city. One of the recent trends is to use a car-sharing system. However, one of the main problems of the car-sharing system is related to the relocation/redistribution strategies such that the cars are always available and well distributed in all stations. These relocation strategies require more sophisticated techniques to be implemented on cities. An alternative is to guide the cars to move in platoon to relocate them in the available stations.

One of the first and most popular platooning application is developed within the California Partners for Advanced Transit and Highways (PATH) program [START_REF] Steven | PATH at 20History and major milestones[END_REF]. Other projects are also proposed in [START_REF] Tsugawa | An automated truck platoon for energy saving[END_REF][START_REF] Coelingh | All aboard the robotic road train[END_REF] that address the problem of platooning in Highways. Unlike the Highways environment, In urban environments each vehicle nevertheless whole the vehicles in the platoon intend to follow a path. Thus, for vehicle control, localization has to be with respect to a path to be followed. So, the path coordinates can be used instead to represent the vehicle model and control law.

The VALET project proposes a novel approach for solving car-sharing vehicles redistribution problem using vehicle platoons guided by professional drivers who comes to pick up and drop off vehicles over the stations.

In general, the global architecture of platooning has main three layers, including Management, Communication, and Guidance layers. The Guidance layer consists of two sublayers: Intelligent Sensing sub-layer that is a set of sensors and algorithms to determine the vehicle's actual state and Vehicle Control sub-layer that brings the vehicle at the desired states, which consists of two modules, including Longitudinal control and lateral control modules. Each of them has two sub-modules, including Upper-Level Controller (ULC) and Lower-Level Controller (LLC). In this study, we are interested in designing the Longitudinal ULC that provides the desired vehicle linear acceleration that the car has to follow by the Longitudinal LLC to achieve the desired longitudinal states.

The vehicle longitudinal dynamics are inherently nonlinear. For platoon modeling, different models are used in the literature, including linear and nonlinear models. The linear models are frequently used. Several linear models are commonly used. First, single integrator model, which is the simplest one and it is widely different from the real vehicle dynamics [START_REF] Fu Lin | Optimal control of vehicular formations with nearest neighbor interactions[END_REF]. The second model is the double integrator model [START_REF] Yan | Consensus Based Platoon Algorithm for Velocity-Measurement-Absent Vehicles with Actuator Saturation[END_REF]. The third approach is to use a third order model by adding another state to model approximately the input/output behavior of the power-train which adds complexity to the control design and analysis [START_REF] Jeroen | Consensus control for vehicular platooning with velocity constraints[END_REF]. To the best of our knowledge, despite huge amount of relevant literature to date, few studies in the literature have handled the problem of platooning in the urban environment/path coordinates, for instance in [START_REF] Shengbo | Minimum fuel control strategy in automated car-following scenarios[END_REF]. In these studies, the authors uses the first order model of the platoon which has some limitations as it is mentioned before. Therefore, in this research, a second order longitudinal dynamic model is used and its corresponding one in the path coordinates is derived such that one can design a controller to achieve control objectives in the path (operational) coordinates.

The simplest platoon controller is proposed in [START_REF] Winner | Adaptive cruise control system aspects and development trends[END_REF] that is called Adaptive Cruise Control (ACC), which controls only the vehicles gas and brake throttle, to maintain a safe distance with the front vehicle. Recently, platoon control is based on a distributed controller known as Cooperative Adaptive Cruise Control (CACC) [START_REF] Vanderwerf | Modeling effects of driver control assistance systems on traffic[END_REF]. In the literature there are four main approaches in designing a platoon controller, including Linear, Optimal, H ∞ -based, Sliding Mode, Model predictive, and Consensus-based controller. Different types of Linear Controllers (LC) are widely used in the literature [START_REF] Chehardoli | Thirdorder leader-following consensus protocol of traffic flow formed by cooperative vehicular platoons by considering time delay: constant spacing strategy[END_REF]. Some studies propose a sliding mode controller to achieve the string stability of platoon as in [START_REF] Wu | Distributed sliding mode control for multi-vehicle systems with positive definite topologies[END_REF]. In [START_REF] Zheng | Platooning of connected vehicles with undirected topologies: Robustness analysis and distributed h-infinity controller synthesis[END_REF], H ∞ controller is proposed to achieve system robustness.

The last type is what is called consensus-based controller. Consensus problems of multi-agent systems have attracted an ever-increasing interest in the control community due to their great potential in various applications such as cooperative unmanned air vehicles, automated highway systems scheduling, air traffic control, sensor networks [START_REF] Namerikawa | Consensus-based cooperative formation control for multiquadcopter system with unidirectional network connections[END_REF]. Recently, CACC control problems using consensus-based algorithms have a tremendous surge of interest among researchers and various algorithms have been developed. Several studies in the literature propose a consensus-based control for platooning in Highways applications as in [START_REF] Santini | A consensus-based approach for platooning with intervehicular communications and its validation in realistic scenarios[END_REF] for example. However, non of theses works consider the control in the path coordinates. In addition, they assume that the leader travel with constant velocity that is not applicable to platooning in urban environment in which, the leader is driven by human, so it may travel with variable velocities. Thus, in this study, the authors propose a controller that can achieve asymptotic stability of the tracking errors and the platoon string stability as well even if the leader travels with variable velocity.

The Information Flow Topology (IFT) represents the Intervehicles communication topology that the vehicles can utilize to acquire the information from its surrounding vehicles. It has a significant impact on the platoon performance. Thanks to the rapid advancement of vehicle-to-vehicle (V2V) communication technology, various IFTs are developed, including Predecessor Following (PF), Predecessor -Leader Following (PLF), Bidirectional (BD), etc. Several approaches have been proposed to improve string stability of a platoon. One of them is to broadcast the leader information to every following vehicle, resulting in the PLF topology [START_REF] Swaroop | Constant spacing strategies for platooning in automated highway systems[END_REF]. This approach is commonly used in the literature in which the leader communicates with all the vehicles in broadcast, and every other vehicle also considers information from its predecessor to compute the control action. However, for low coast communication solution, due to limited bandwidth capabilities of the on-board communication module two channel communication is not feasible. Thus, in this study, the proposed control law depends on a hybrid PLF topology. That is, the leader broadcasts its information (position, velocity, and acceleration) to all the vehicles via a communicationbased link. For the inter-followers communication, the intervehicle distance is measured by a distance sensor, e.g., laser, i.e., by a sensor-based link. In addition, the proposed control law does not depend on the predecessor velocity.

To sum up, the main contributions of this research are,

• developing a second-order longitudinal platoon control framework in the path coordinates; • designing a consensus-based controller that is applicable to both motion in urban environment and limited communication capabilities of the vehicles; • driving conditions for the platoon stability (internal and string).

II. PROBLEM STATEMENT

A. Car-like Vehicle Kinematic Model

Simplifying the car-vehicle system model to a kinematic bicycle model is a common approximation [START_REF] Forrest | Steering control of an autonomous ground vehicle with application to the DARPA urban challenge[END_REF]. Consider a car-like vehicle shown in Fig. 1. The kinematic bicycle model combines the left and right wheels into a pair of single wheels at the center of the front and rear axles. The wheels are assumed to have no lateral slip and only the front wheel is steerable.

ݔ ݕ ܱ ௩ ߜ ݎ ܮ ܱ ܯ ݒ ߠ Path ߰ ݕ ௩ ݔ ௩ ܸ ܩ Fig. 1: Kinematic model in Cartesian & Curvilinear coordi- nates. 1) Cartesian Coordinates Model: Let {V }, O v -x v y v ,
denotes the vehicle body-fixed reference frame with its xaxis in the vehicles forward direction and its origin at the center of the rear axle, O v , see Fig. 1. The configuration of the vehicle, with respect to the world-fixed inertial reference frame, {G}, O-x y, is represented by the generalized coordinates z = [x y θ], where its position is given by p 2), while its orientation in the global frame is represented by θ. δ is the steering angle in the body frame. The vehicles velocity is by definition v in the vehicles x-direction, x v , and zero in the y-direction, y v , since the wheels cannot slip sideways. If the front wheel is located at distance L from the rear wheel along the orientation of the vehicle, then the kinematic model is given by

= [x y] T ∈ C where C ⊂ SE(
ẋ = v cos(θ), (1a) ẏ = v sin(θ), (1b) θ = v L tan(δ). (1c)
2) Path Coordinates Model: Let us define the curvilinear coordinates (s r ψ) T , as shown in Fig. 1. The tracking path, C, defined in the Global Frame, can be represented as a function of its length s (Curvilinear abscissa) at the closest point M to O v , the relative angle (angular deviation), ψ = θ -θ c , of the vehicle with respect to the path, where θ c is the angle between the path tangent at M and the x-axis, and finally, the lateral distance (lateral deviation), r, which is the signed orthogonal distance from the center of the rear axle, O v , to the closest point on the path, M . From the geometry in Fig. 1, the kinematic model in the path coordinates is given by

ṡ = v cos(ψ) 1 -rκ(s) , ( 2a
) ṙ = v sin(ψ), (2b)
ψ = v ( tan(δ) L - κ(s) cos(ψ) 1 -rκ(s) ) , ( 2c
)
where κ(s) is the curvature of path at point M .

3) Lateral Controller: Motion control of autonomous vehicles moving either alone or in platoon requires design of lateral and longitudinal control to achieve performance objectives in the lateral and longitudinal directions. The lateral controller will provide the desired steering angle as the control signal. The vehicle lateral control will be designed to achieve the lateral control objectives which are: independently from the longitudinal states/controller, r → 0 and ψ → 0 as t → ∞. An interesting and useful method for controlling kinematic models of car-like vehicle systems given by (2) can be found in [START_REF] Thuilot | Accurate automatic guidance of an urban electric vehicle relying on a kinematic GPS sensor[END_REF] which is based on the chained forms. In this work, the lateral control law is given by

δ = atan ( L ( cos 3 (ψ) (1 -rκ) 2 ( dκ ds r tan(ψ) -k d (1 -rκ) tan(ψ) -k p r + κ(1 -rκ) tan 2 (ψ) ) + κ cos(ψ) 1 -rκ ) ) , (3)
where k p and k d are the controller parameters to be tuned for a desired system response.

B. Car-like Vehicle Longitudinal Dynamic Model

For each vehicle, several factors determine its longitudinal dynamic behavior, which is inherently nonlinear, including the engine, drive line, brake system, aerodynamics drag, tire friction, rolling distance, and gravitational force, . . ., etc [START_REF] Desantis | Path-tracking for car-like robots with single and double steering[END_REF]. To make a balance between accuracy and conciseness, it is assumed that: Assumption 1. The vehicle body is considered to be rigid and symmetric.

Assumption 2. The driving and braking inputs are integrated into one control input. Assumption 3. The influence of pitch and yaw motions is considered to be neglected.

Therefore, the longitudinal dynamic equation can be represented by

M v a + C v v + G v = F v , ( 4
)
where a = v denotes the vehicle's acceleration in the vehicle frame, and M v , C v , G v , and F v are the vehicle's Inertia effect, Coriolis effect, Gravity effect, and input force, respectively. The inverse model compensation technique is frequently used to eliminate the non-linearities in longitudinal dynamics for the purpose of controller design [START_REF] Zheng | Stability and scalability of homogeneous vehicular platoon: Study on the influence of information flow topologies[END_REF].

The control law of the inverse dynamics technique is given by

F v = M v µ + C v v + G v , ( 5
)
where µ is the new input signal after system linearization which has to be designed such that the control objectives can be achieved. By applying this lower-level controller, one can obtain a linear model for vehicle longitudinal dynamics as a = µ, (

Most of the research consider the Cartesian coordinates for control design. However, as we intended to platoon in the urban environment, then the relation between the dynamics in the path and Cartesian coordinates will be derived such that the controller can be designed in the path coordinates.

Let us recast (2a) as

ṡ = T v, ( 7
)
where T is given by

T = cos(ψ) ( 1 -rκ ) . ( 8
)
Vehicle's acceleration in the path coordinates can be found from the differentiation of ( 7) with respect to (w.r.t) time as follows

η = T a + Ṫ v, ( 9
)
where η = q = s and q = ṡ are the vehicle's acceleration and velocity in the path coordinates respectively. Consequently, if the mapping from the control signal (i.e., desired acceleration) in the path coordinates, u, to that in the Cartesian coordinates, µ, is given by

µ = 1 T (u -Ṫ v), (10)
then, the vehicle longitudinal dynamic model in the path coordinates can be represented by ṡ = q, (11a) q = η = u.

(11b)

C. Platoon Longitudinal Model

From a control viewpoint, the main goal is to create the platoon and then maintain a spacing policy in the presence of perturbations. Consider N + 1 vehicles are required to move in a platoon, as illustrated in Fig. 2, including a leading vehicle (noted as the leader with index 0) and N following vehicles (noted as followers with index i; i = 1, 2, . . . , N ). The platoon runs on urban and flat road, and the vehicles can share information either sensor-based or communicationbased way. All the vehicles are assumed to have equal dynamics. The position, velocity, acceleration, and control input (i.e., desired acceleration.) of vehicle i are denoted with s i , q i , η i , and u i in the path coordinates. Consequently, the dynamics can be written in the path coordinates as:

ṡi = q i , (12a) qi = u i , ( 12b
)
where the transformation between the two coordinates can be implemented via (2a) and [START_REF] Chehardoli | Thirdorder leader-following consensus protocol of traffic flow formed by cooperative vehicular platoons by considering time delay: constant spacing strategy[END_REF].

For the string of vehicles, the inter-vehicle distance, d i = s j -s i , is the actual curvilinear distance between vehicle i and its predecessor j = i -1, and d r,i is the desired inter-vehicle distance between vehicles i and j. Several spacing policies are proposed in the literature [START_REF] Dvahg Swaroop | A comparision of spacing and headway control laws for automatically controlled vehicles1[END_REF][START_REF] Santhanakrishnan | On spacing policies for highway vehicle automation[END_REF]. For high capacity, small vehicle to vehicle spacing, the constant spacing policy method is utilized.

D. Control Objectives

The platoon has to travel in urban environment (curvilinear path) and track a leader that is either autonomous or manually driven, and each follower vehicle, i, has the following information:

• position, velocity, and acceleration of the leader, s 0 , q 0 , η 0 via communication-based link; • position of the front vehicle, i.e., its predecessor s i-1 via sensor-based link due to the limited communication capability of the on-board communication module. Under these conditions, ∀ i = 1, . . . , N , the following goals have to be achieved:

• Asymptotic stability of the tracking errors.

• String stability.

III. CONTROL DESIGN

The information flow structure among platoon can be modeled by a graph in which each vehicle is a node whose dynamics are described by [START_REF] Zheng | Platooning of connected vehicles with undirected topologies: Robustness analysis and distributed h-infinity controller synthesis[END_REF]. The information flow among followers can be modeled by a directed graph (digraph) G = (V, E, M) characterized by the set of nodes V = 1, . . . , N and set of edge E ⊆ V × V. Each edge represents a directional information exchange between two vehicles. The topology of the graph is described by an adjacency matrix M = [m ij ] N ×N , in which the element m ij = 1 if vehicle i can obtain information from vehicle j; otherwise, m ij = 0. Also, the self-edges are not allowed, i.e., m ii = 0. To include the leader (with index 0) in the network, an augmented digraph Ḡ is used.

Authors propose the following control law

u i = η 0 + b(q 0 -q i ) + N ∑ j=0 k ij m ij (s j -s i -d r,ij ), (13)
where, b and k ij are tuning parameters, d r,ii-1 is given by

d r,ii-1 = l f,i + d bb,ii-1 + l r,i-1 , ( 14
)
where l f,i and l r,i is the distance from the front and rear bumpers to the rear axle center, O vi , of vehicle i, respectively, and d bb,ii-1 is the desired constant space between vehicle i and its predecessor (bumper-to-bumper distance).

For the Predecessor -Leader Following (PLF) information flow topology, where the leader communicates with all the vehicles in broadcast, and every other vehicle also considers information from its predecessor, ( 13) can be recast as

u i = η 0 + be q,i0 + k 0 e s,i0 , ∀ i = 1, (15)
and

u i = η 0 + be q,i0 + k 0 e s,i0 + k 1 e s,i , ∀ i > 1, ( 16
)
where e s,i0 = s 0 -s i -d r,i0 , e q,i0 = q 0 -q i , e s,i = s j -

s i -d r,i , for k i0 ; assume k 10 = k 20 = • • • = k N 0 = k 0 , and for k ij ; assume k 21 = k 32 = • • • = k N N -1 = k 1 .
Theorem 1. Consider a N car-like vehicle platoon following a leader, the longitudinal model expressed as (1), ( 2), (4 -10), and [START_REF] Zheng | Platooning of connected vehicles with undirected topologies: Robustness analysis and distributed h-infinity controller synthesis[END_REF], with assumptions 1 -3, and the control algorithm described in [START_REF] Swaroop | Constant spacing strategies for platooning in automated highway systems[END_REF] and ( 16) is applied to it. Then, the system is asymptotically stable and the platoon is strong string stable as long as the following conditions are satisfied:

∀ γ < 1, b > 0, c = 0.25b 2 , k 1 = γc, and k 0 = (1 -γ)c.
Proof. Firstly, the internal stability analysis is done as follows.

Applying the control law (16) to the system ( 12), and if one define the inter-vehicle distance error, e s,i , in terms of the errors with leader, e s,i0 , as e s,i = s j -s i -d r,i = e s,i0e s,j0 , d r,i = d r,i0 -d r,j0 , j = i -1, then the error dynamics in terms of the error with leader is given by ės,i0 = e q,i0 , ėq,10 = -be q,10 -k 0 e s,10 , ėq,i0 = -be q,i0 -(k 0 + k 1 ) e s,i0 + k 1 e s,j0 , ∀ i > 1.

(17)

Let us define e s = [e s,10 , . . . , e s,i0 , . . . , e s,N 0 ] T and e q = [e q,10 , . . . , e q,i0 , . . . , e q,N 0 ] T as the position and speed error vectors, respectively, then the error state vector, X (t) = [e s e q ] T , is given by

Ẋ (t) = AX (t), (18)
where A is described as follows

A = [ O N I N -P -D ] , ( 19
)
where I n and O n denote (n × n) identity and (n × n) null matrices, respectively, D = diag{b, . . . , b} ∈ R N ×N , and

P = [p ii ] ∈ R N ×N is represented by p ii =            k 0 , j = i, i = 1, k 0 + k 1 , j = i, i > 1, -k 1 , j = i -1, i > 1, 0, otherwise. (20)
The eigenvalues of P , λ p,i , can be calculated as

λ p,i = { k 0 , i = 1, k 0 + k 1 , i > 1. (21)
Thus, ∀ k 0 > 0 and k 1 > 0, the matrix P is positive stable. In addition, ∀ b > 0, the matrix D is positive stable.

Lemma 1. Schur's formula [START_REF] Cao | Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication[END_REF]. Let matrices According to Lemma 1, the characteristics polynomial of A can be calculated as follows:

F
det (SI 2N -A) = det ( [ SI N -I N P SI N + D ] ) = det ( S 2 I N + bI N S + P ) = N ∏ i=1 ( S 2 + bS + λ p,i
) .

(

) 22
The polynomial S 2 + bS + λ p,i is Hurwitz stable, according to Lemma 2 and the conditions b > 0, k 0 > 0, k 1 > 0. This implies that all eigenvalues of A have negative real parts. Consequently, the error dynamics is asymptotically stable i.e., lim t→∞ X (t) = 0. Secondly, the string stability analysis is done as follows. For simplicity, let us define the following errors e i = s j -

s i -d r,i , ėi = q j -q i , ëi = u j -u i , e i0 = s 0 -s i -d r,i0 , and ėi0 = q 0 -q i .
Form [START_REF] Forrest | Steering control of an autonomous ground vehicle with application to the DARPA urban challenge[END_REF] one can write ëi as

ëi = u j -u i = b ėj0 + k 0 e j0 + k 1 e j -b ėi0 -k 0 e i0 -k 1 e i , (23)
Writing [START_REF] Parks | Stability theory[END_REF] in the S-domain results in

S 2 E i (S) = bSE j0 (S) + k 0 E j0 (S) + k 1 E j (S) -bSE i0 (S) -k 0 E i0 (S) -k 1 E i (S).
Substituting with e i0 = e i +e j0 or E i0 (S) = E i (S)+E j0 (S) into [START_REF] Darbha | String stability of interconnected systems: An application to platooning in automated highway systems[END_REF], then the transfer function H(S) = Ei(S) Ej (S) can be defined as

H(S) = k 1 S 2 + bS + c , ( 24
)
where c = k 0 + k 1 .

Conditions for string stability:

• In time domain, for strong string stability: h(t) 1 < 1 • In frequency domain for strong string stability: H(S) ∞ < 1 and h(t) > 0 The poles of H(S), second order system, are p 1,2 = -0.5b ± √ (0.5b) 2 -c, To achieve h(t) > 0, the response of H(S) has to be overdamped, i.e., (0.5b) 2 > c, or critical-damped, i.e., (0.5b) 2 = c. However, for faster response the parameters of H(S) are chosen for a critical-damped response, i.e., (0.5b) 2 = c. In this case, the impulse response is represented by

h(t) = k 1 te -0.5bt . ( 25
)
Thus, ∀ k 1 > 0, one can obtain h(t) > 0.

Lemma 3. [START_REF] Darbha | String stability of interconnected systems: An application to platooning in automated highway systems[END_REF]. If F (s) is a stable, proper transfer function, with F (0) = β, and if f (t) = L -1 {F (s)} is its impulse response, then h(t) 1 = β if and only if h(t) does not change sign.

According to Lemma 3,

h(t) 1 = H(0) = k 1 c = γ, (26)
Thus, by choosing k 1 = γc with γ < 1, then h(t) 1 < 1 and as a result the platoon is strong string stable.

IV. RESULTS

A. Environment

The previously proposed control strategy is simulated in MATLAB/SIMULINK program for the considered Urban cars platooning. We consider a platoon composed of a homogeneous 4 vehicles plus a manually driven leader. For emulation of motion in urban environment, the trajectory shown in Fig. 3, is used as a reference trajectory to be followed by all the cars. The vehicles are initially parked near the reference path with different initial poses. The lateral controller (3) is in charge of producing steering angle of the vehicle. Gains of the lateral control law are tuned in order to get a satisfactory response of the lateral and angular deviations, see Fig. 3 for the results. The path tracking capability of the vehicle is enlightened in Fig. 3 The longitudinal controller is implemented at rate of 100 Hz assuming that the vehicle states are available at this rate. Control parameters are selected to guarantee the internal stability and string stability. The selected control parameters are reported in Table I.

B. Normal Platooning

Fig. 4 shows the results for the normal consensus scenario. The leader travels with constant velocity. The results confirm the capability of the proposed approach of creating and maintaining the platoon in case of leader travel with constant velocity. The vehicles are starting from distances different from the one required by the spacing policy and reach the consensus and the curvilinear position and speed errors converge asymptotically. Moreover, the followers track the leader zero acceleration (i.e., the control effort reaches zero after consensus).

C. Variable Speed Scenario

Fig. 5 shows the results for the leader tracking consensus scenario. The results confirm the capability of the proposed approach of creating and maintaining the platoon in case of a manually driven leader (i.e., the velocity is not constant). The vehicles are starting from distances different from the one required by the spacing policy and reach the consensus and the curvilinear position and speed errors converge asymptotically. Furthermore, the followers track the leader acceleration that has a trapezoidal shape.

D. Braking Scenario

To investigate the controller robustness against different driving scenarios, we test the ability of the proposed strategy in case of the leader sudden braking. Results in Fig. 6 show how the platoon reacts in the case of a braking maneuver performed by the leader from 1.5 m /s to a full stop. The results show that the inter-vehicle distance between vehicle 0 and vehicle 1, d 1 , suffers an approximately 0.6 m decrease, while d 2 suffers an approximately 0.09 m decrease, and d 3 and d 4 is further smaller. These results illustrate that the sudden disturbance on the platoon is attenuated along the rest of the platoon (i.e., string stable platoon). A consensus-based control technique for platooning in urban environment is proposed. A second-order longitudinal model of the platoon in the path coordinates is driven. General architecture is proposed to design the controller in the path coordinates in order to achieve some objectives defined the path coordinates with a relation that maps the control signals in the Cartesian and path coordinates. The proposed algorithm does't need for the predecessor's velocity, so one can depend only on the distance sensor without the need to communicate with the predecessor's such that lower bandwidth communication module can be utilized. A constant-spacing policy is used to get a high capacity flow of vehicles. The controller is design to achieve zero tracking errors in case the leader is manually driven (i.e., leader travels with variable velocity) to be suited to work in VALET project. Internal stability is analyzed and the asymptomatic stability of the tracking errors is proven. Conditions for platoon string stability are driven. Efficiency of the proposed control framework and control algorithm are enlightened via numerical analysis.

Fig. 2 :

 2 Fig. 2: Platoon representation in the path coordinates.

Fig. 3 :

 3 Fig. 3: Lateral Control Results: R: Reference Trajectory, L: Leader Actual Trajectory, and F i : Follower i Actual Trajectory.

Fig. 4 :

 4 Fig. 4: Normal Platooning Longitudinal Control Results

Fig. 5 :Fig. 6 :

 56 Fig. 5: Variable Speed Platooning Longitudinal Control Results

  11 , F 12 , F 21 , F 22 ∈ R N ×N and M = 11 , F 12 , F 21 , F 22 commute pairwise, i.e., F rs F nm = F nm F rs for all possible pairs of indices r, s and n, m, then the determinate of M, det(M ) = det(F 11 F 22 -F 12 F 21 ) Lemma 2. [23]. Let a complex coefficient polynomial, f (z) = z 2 +(a+ib)z+(c+id), where a, b, c, and d ∈ R. f (z) is Hurwtiz stable if and only if a > 0 and abd+a 2 c-d 2 > 0.

	[	F 11 F 12 F 21 F 22	]	.
	If F

TABLE I :

 I Simulation Parameters

	Parameter	Value	Parameter	Value
	L	1 m	amax	1 m /s 2
	a min	-3 m /s 2	vmax	8 m /s
	v min	0 m /s	b	1.6
	d r,i	3 m	γ	0.1

ACKNOWLEDGMENTS

This paper describes a work carried out in the framework of the Valet project, reference ANR-15-CE22-0013-02.


Abbie Hantgan
email: ahantgan@gmail.com

Johann-Mattis List

DOCULECT NOBLE SLAVE TONGS FIGHT FOAM NEW LOUSE WORK Jenaama *, *, *, , , , Bambara *, *, *, , , Bunoge *, , *, , , , , Mombo *, , , , , Penange *, *, , , , Tiranige Diga

Bangime: Secret Language, Language Isolate, or Language Island?

Keywords: comparative method, historical linguistics, African language isolates, sound correspondences, computational linguistics

We report the results of a qualitative and quantitative lexical comparison between Bangime and neighboring languages. Our results indicate that the status of the language as an isolate remains viable, and that Bangime speakers have had different levels of language contact with other Malian populations at different time periods. Bangime speakers, the Bangande, claim Dogon ancestry, and the language has both recent borrowings from neighboring Dogon varieties and more rooted vocabulary from Dogon languages spoken to the east from whence the Bangande claim to have come. Evidence of multi-layered long-term contact is clear: lexical items have even permeated even core vocabulary. However, strikingly, the Bangande are seemingly unaware that their language is not intelligible with any Dogon variety. We hope that our findings will influence future studies on the reconstruction of the Dogon languages and other neighboring language varieties to shed light on the mysterious history of Bangime and its speakers.

Introduction

Spoken by an estimated 1,500 people among seven villages situated in a cove at the western edge of the Bandiagara escarpment in central-eastern Mali, Bangime translates as 'secret language' in many of the Dogon languages spoken along the eastern-edges of the cliff range. Bangime speakers, correspondingly depicted as Bangande, identify themselves and their language as Dogon, and yet they are unaware that the terms used for their group and language are actually exonyms with the meaning of 'secret'. While the reason Bangande essentially do not have an endonym remains part of their mystery, their unfamiliarity with the lexical root [banɡ-], meaning 'secret, hidden, furtive' is due to the fact that the Dogon speakers in their immediate vicinity do not use the same lexical root, which alone suggests that Bangime-speakers once co-existed with Dogon-speaking populations who differ from those near them now.

This paper employs qualitative and quantitative methods for historical lexical comparison to propose scenarios to explain Bangime and its speakers' relationship to surrounding Dogon languages and their speakers along Mali's well-known Bandiagara escarpment. Scholars also contest foregone conclusions about Dogon ethnographic and linguistic affiliations. Thus, we compare portions of both the Dogon and Bangime lexica with those from neighboring Mande, Atlantic, and Songhay languages in order to rule out any genetic affiliation between Bangime and languages beyond the Dogon escarpment. Placing Bangime in the context of other languages in Mali further supports its status as a linguistic isolate. Not only is it disparate from the Dogon varieties, it also shares little, if anything, with the surrounding languages -Fulfulde, Songhay, or those of the Mande group -although our findings support contact with all of them, and yet at different stages in history.

Our quantitative studies are based on state-of-the-art methods for automatic word comparison across various languages (List et al. 2017b). We propose a combination of conservative approaches that closely model the traditional comparative method [START_REF] Ross | Introduction[END_REF] while taking regular sound correspondences across all languages in the dataset into account, as in the LexStat method (List 2012a), and using simpler approaches that mainly pick up surface similarities between words, as in the Sound-Class-Based Alignment method (List 2012b). By combining these approaches and comparing their results directly, we can automatically identify potential layers of contact between Bangime and its neighboring varieties that reflect different contact periods. These layers can then be further analyzed qualitatively by comparing the automatic findings in detail.

In this study, we limit our analyses to lexical similarities but note that many grammatical features in Bangime, discussed in detail by [START_REF] Heath | A Grammar of Bangime[END_REF], are also distinct from those found at least among Niger-Congo and Nilo-Saharan families. By investigating socio-linguistic, cultural, and historic implications, we hope to suggest avenues for future research.

Background

Previous Research on Bangime

Bangime is considered to be one of only four undisputed African isolates (Blench 2017, p. 167). 1 However, as [START_REF] Campbell | Language Isolates and Their History, or, What's Weird, Anyway[END_REF]Campbell ( , 2017) ) advises, a language's confirmed classification as an isolate should not preclude a thorough investigation into its origins. Although Bangime was once classified as Dogon, those who have discussed the Dogon languages and peoples have long recognized the Bangime speech community as an outlier (Calame- [START_REF] Calame-Griaule | Les dialectes Dogon[END_REF][START_REF] Hochstetler | Sociolinguistic Survey of the Dogon Language Area[END_REF][START_REF] Plungian | Vers une description sociolinguistique du pays Dogon: attitudes linguistiques et problèmes de standardisation[END_REF]. While Bertho (1953, pp. 413-414) went so far as to state that Bangime was distinct, not only from Dogon, but also from Fulfulde and Bozo, [START_REF] Blench | Bangime, a language of unknown affiliation in northern Mali[END_REF] was the first researcher to suggest it was an isolate. According to the Dogon and Bangime Linguistics Project (Moran et al. 2016, http://dogonlanguages.org), within the variation attested among the now estimated 22 distinct Dogon languages, the lowest limit for mutual intelligibility based on lexical estimates is 32 percent [START_REF] Prokhorov | Dogon classification[END_REF]. In contrast, we now estimate that Bangime shares less than 20 percent of its core vocabulary with Dogon, and even these few lexical items, such as numerals, were likely borrowed long-ago from Dogon languages for the sake of identity-inclusion.

Bangime has been called by many other names in the literature. Among those discussed by Hantgan (2013, p. 5), one remained a mystery. Blench (2005, p. 1) describes the "intrusive -ri-" as it appears in /báŋeri mé/ (Calame- Griaule 1956, p. viii). Table 1 shows, in Dogon words for 'hide, conceal', the [-ri-] suffix and its allomorphs represent the Dogon causative, or transitive, morpheme. The suffix [-mɛ] or [-jɛ] in Bangime denotes a language from the name of the speakers (Hantgan 2013, p. 112), and yet [-jɛ] also corresponds with the medio-passive suffix among the Dogon languages. Thus, the word bangime could be seen as a mix between the Dogon root [banɡ] and the Bangime suffix [mɛ], or simply an alternate (and often attested) pronunciation of the medio-passive form of the verb [banɡ-i-jɛ], meaning 'it is hidden' among the Dogon languages with this root.

In either case, what is surprising is that, shown in Figure 1, the languages with words that most resemble the term listed by Calame-Griaule (first column, from where Bangime is spoken. Among the languages spoken closest to where Bangime is spoken (third column), none uses anything like the term that most closely resembles the name of their language and people. Therefore, it is likely that the name of the language and speakers was given at a time when, and place where, the ancestors of the Bangande and the now eastern Dogon were in contact. The map in Figure 1 also shows the area in Mali where the other languages that impact Bangime are spoken.2 Geographically, Mali encompasses three regions -Sahara, Sahel, and sub-Sahel -each with its own heterogenous and independent ethnological-linguistic societies. Tuareg and Songhay live in the north; Dogon, Fulani, and Bozo Soninke in the center; and Bambara live primarily in the south and west, but some have migrated to other regions. The only genetic overlap among these groups is between Bozo Soninke and Bambara. Even with all this diversity, Bangime stands out as a linguistic isolate. Moreover, genetic studies demonstrate that its speakers represent a genetic deme [START_REF] Babiker | The genetic identity behind the masks: Bangande and Dogon of Western Africa[END_REF]. Bangime is spoken among seven villages at the end of a valley that runs east, perpendicular to the Niger river, directly into the central-western edge of the Bandiagara escarpment. Two villages sit atop the mountain range, and the rest reside just below on the sandy soil. The Gueou valley stretches into the Sahelian plains and, approximately 250 kilometers north, emerges at Timbuktu in the Sahara. The Gueou valley's other inhabitants speak a Bozo variety called Jenaama. Most other Bozo languages are spoken along the Niger river.

Bangime

The location of Bangime speakers necessitates constant contact with Fulfulde, Bozo-Jenaama, and Dogon-Tiranige speakers. In terms of wider contact areas, Bangande travel to the weekly markets in the Fulani city Konna (35 kilometers northwest) and the Soninke town Sambere (25 kilometers west), mainly to sell wild-grown and gathered fruits but also tobacco and other cultivated crops. Younger people travel to the regional capital Sevare-Mopti and the country's capital Bamako, where they learn to speak Bambara. Few Bangande travel north and thus rarely speak Songhay, though Songhay has made a historical impact on the Dogon languages, discussed in Section 2.2.

Fulani herders and their livestock roam throughout northern Africa, building temporary camps, many in the mountains to prevent their animals from destroying crops planted in the fields on top of the cliff and in the plains. Songhay groups live adjacent to the Dogon, directly south of the fabled city Timbuktu and further east along the single paved road that stretches south from the Malian capital, Bamako, to Gao. Most Bangande are fluent in Fulfulde and use it as a language of wider communication with groups other than Fulani since Bangime is unintelligible to the speakers of any neighboring languages, despite the Bangande people's insistence that it is Dogon.

Although the single term, 'Dogon' implies a linguistic and cultural homogeneity, substantiated by descriptions of a unified Dogon language [START_REF] Bendor-Samuel | Dogon[END_REF]) and genetically cohesive people [START_REF] Tishkoff | The Genetic Structure and History of Africans and African Americans[END_REF], even early depictions of the Mali Bandiagara Escarpment's inhabitants illustrate their diversity and heterogeneity [START_REF] Desplagnes | Le Plateau Central Nigerien[END_REF]. According to the Dogon and Bangime Linguistics Project (Moran et al. 2016, http://dogonlanguages.org), Dogon as a group constitutes at least 22 separate languages and upwards of 60 dialects. Dogon languages are primarily spoken among villages located at varying levels of a rocky cliff range known as the Bandiagara Escarpment, which is bordered on both sides by Sahelian plains. Some Dogon villages have descended to the plains within the past decade and a few Dogon languages are spoken across the border with Burkina Faso. Each secluded cliff village speaks its own variety, plus a reduced and often mixed Dogon variety for the purposes of wider communication such as Tommo So or Jamsay.

Historical Context

Those known as Dogon are thought to have moved to the Bandiagara escarpment from its eastern edges some 700-500 years ago. The 500-year estimate was proposed by Griaule (1938, p. 28), who claims to have uncovered nine Sigui masks at a site in the village Ibi in 1933. The Sigui is an eastern-Dogon ritual that is performed every 60 years, with one mask made for each festival. Thus, Griaule estimated a date of the first Sigui mask at 1430 A.D. Methodological concerns aside, note that not all Dogon villages have a tradition of mask dancing. Bedaux (1972, p. 41) asserts that the Dogon did not originally constitute a single culturally homogeneous group; they may have migrated to the cliffs from various directions.

Paleo-climatological investigations and archeological evidence amassed by [START_REF] Mayor | Dogon": une réevaluation de l'histoire du peuplement en Pays dogon (Mali)[END_REF] and [START_REF] Mayor | Population dynamics and Paleoclimate over the past 3000 years in the Dogon Country, Mali[END_REF], [START_REF] Macdonald | More forgotten tells of Mali: an archaeologist's journey from here to Timbuktu[END_REF] and [START_REF] Bedaux | Tellem, reconnaissance archéologique d'une culture de l'Ouest africain au Moyen-Age: recherches architectoniques[END_REF] place the date of Dogon occupation of the Bandiagara Escarpment from the 16 th to 20 th centuries. One scenario presented by [START_REF] Mayor | Population dynamics and Paleoclimate over the past 3000 years in the Dogon Country, Mali[END_REF] depicts the Dogon fleeing the area's invaders sometime between 1230 and 1430 AD. We especially see linguistic evidence of the effect of the Songhay Empire on currently occupied Dogon areas. Most of the Najamba-speaking villages on the north-western portions of the Escarpment are still known by outsiders only by their Songhay names. Some include, Koira Beiri [kòjrà bé:rì] 'big town', Ibissa [í-bìs-â] 'I have passed', Borko [bòrkìn] 'noble', and Tondifere [tóndì fèrè] 'stone brick'. However, the contact has not been unidirectional as the Songhay village Kikara [kì-kárá], adjacent to where Dogon language Bankan Tey is spoken, translates to 'armpit' in Jamsay and many other Dogon varieties.

Dogon oral traditions describe a migration from Mande [START_REF] Dieterlen | Mythes et organisation sociale au Soudan français[END_REF][START_REF] Izard | Introduction à l'histoire des royaumes mossi[END_REF][START_REF] Marchal | Vestiges d'occupation ancienne au Yatenga (Haute-Volta): une reconnaissance du pays Kibga[END_REF]), thought to be located in present-day southwest Mali or northeast Guinea to a village called Kani-Gogouna, located adjacent to Ibi, the village where Griaule found the Sigui masks. Bangande also recount that they moved from Mande with the Dogon, settled in the village of Kani-Gogouna, and then relocated northwest, over and down the escarpment, to their current villages. However, a more likely scenario based on recent fieldwork (Hantgan 2013, pp. 407-410), proposes that instead of traveling south-east and then over the arduous cliff range, the move went in a straight line east, through a series of villages located along the Gueou valley. Since the Bangande also recount many stories of war with the Jenaama-Bozo, they were probably driven back down the valley to finally settle in the current location at the edge of the Escarpment.

According to a widely-known Malian legend, the Jenaama-Bozo, along with the other groups subsumed under the larger Mande branch, are said to have traveled with the Dogon from Mande but split away due to a disagreement between brothers. Indeed, the name Dogon, pronounced by its speakers as [dɔɡɔ-nɔ] or [dɔɡɔ-n] derives from the term [dɔɡɔ-nín] which means 'little brother' in many Mande languages. One of the consequences of the split between the brothers was a law forbidding Bozo and Dogon to intermarry. As the Bozo ethnicity is defined by its trade as fishermen, the Jenaama who live in the Gueou valley are technically outsiders: they do not fish but live off subsistence millet farming like the Bangande and Dogon, yet neither Bangande nor Dogon intermarry with them.

High above Bara, one of the Bangime-speaking villages, is a group of buildings carved directly into the rock face. Found throughout the escarpment, these constructions within the caves are currently used by Bangande and Dogon as both burial grounds and granaries for storing millet, but the local populations believe they were housing built by a group known in most Dogon languages spoken in the eastern portions of the Escarpment as Tellem [tɛĺɛ-m], and translated to mean 'those before' by [START_REF] Mayor | Early social complexity in the Dogon Country (Mali) as evidenced by a new chronology of funerary practices[END_REF]). 3First identified by archaeological excavations by [START_REF] Bedaux | Tellem, reconnaissance archéologique d'une culture de l'Ouest africain au Moyen-Age: recherches architectoniques[END_REF], the Tellem are said to have occupied the cliffs from the 11 th to 16 th centuries AD. More recent work by [START_REF] Mayor | Dogon": une réevaluation de l'histoire du peuplement en Pays dogon (Mali)[END_REF] depicts pre-Dogon populations as a cultural "mosaic" but with a distinct change in material cultural practices occurring around 400-600 years ago. They speculate that the populations who inhabited the escarpment prior to the Dogon either died or were subsumed into a new culture, that of the present-day Dogon, around 400-600 years ago.

Our results, given in Section 4, support evidence for the supposition that the Bangande were among the pre-Dogon groups; that they occupied the cliffs before the Dogon arrived. Further, we propose that there were separate waves of Dogon settlement, with indications of recent contact between Bangime-speakers and their immediate neighbors, and yet longer-term contact with Dogon groups that live to east of their current location. While we do not provide proof of certain dates, we suggest that the different Dogon waves occurred at different times in history, and perhaps from different directions. We explore these findings in the sections below.

Materials and Methods

All of the data were gathered independent of this study. The primary data were obtained through lexical elicitation for a Dogon-comparative word-list [START_REF] Heath | Dogon Comparative Wordlist[END_REF], with the addition of data collected for Bangime [START_REF] Heath | A Grammar of Bangime[END_REF], and Jenaama [START_REF] Hantgan | Bangime lexicon[END_REF], and Mande language data from the RefLex database [START_REF] Segerer | RefLex: Reference Lexicon of Africa[END_REF]. Fulfulde lexical data are drawn from [START_REF] Osborn | A Fulfulde (Maasina)-English-French lexicon: a root-based compilation drawn from extant sources followed by English-Fulfulde and French-Fulfulde listings = Lexique Fulfulde (Maasina)-Anglais-Francais[END_REF] and Songhay Kiini and Sinni data from [START_REF] Heath | Tondi Songway Kiini (Songhay, Mali) : reference grammar and TSK-English-French dictionary[END_REF][START_REF] Heath | Dogon Comparative Wordlist[END_REF], respectively.

The Dogon language data were gathered by a team of eight researchers as part of the ongoing US National Science Foundation (NSF)-funded Dogon and Bangime Linguistics Project. Lexical, grammatical, and geographic information about the Dogon languages may be found at The Dogon and Bangime Linguistics website (dogonlanguages.org, Moran et al. 2016). Language identifiers, classification hierarchies, and geographic data for the remainder of the languages used in the sample are drawn from Glottolog (http://glottolog.org/, [START_REF] Hammarström | Glottolog 3.2[END_REF].

Lexical Data Preparation

Given the diversity of the original sources, we had to normalize the data in various ways to render it comparable. Our first step was to convert each lexical spreadsheet to a file that could be read and interpreted by LingPy (List et al. 2017a), a Python library for automatic tasks in historical linguistics (http://lingpy.org), EDICTOR (List et al. 2017b), a web-based tool for creating, editing, and inspecting etymological datasets (http://edictor.digling.org), and similar packages that are part of recently proposed tool chains for computer-assisted language comparison [START_REF] List | Concepticon. A resource for the linking of concept lists[END_REF], developed in close collaboration with the Cross-Linguistic Data Formats (CLDF) initiative (https://cldf.clld.org, Forkel et al. forthcoming).

Thus, we converted the various lexical spreadsheets organized by rows into separate, five-columned, tab-separated files. In the first column of each file, we specified a unique ID to each row, followed by the language name, and then the individual lexical form in IPA adjacent to its English and French gloss. In cases where more than one form was listed for a particular lexical item, we treated them as individual entries in that language. These entries are not duplicates; rather, they represent important synonyms that may lead to deeper connections among the related languages.

Next, due to the multitude of glosses used to elicit the same meanings in different contexts, we used the semi-automatic tools provided by the Concepticon project (http://concepticon.clld.org, [START_REF] List | Concepticon. A resource for the linking of concept lists[END_REF]List et al. , 2018b) ) to systematically identify equivalent concepts across all datasets by linking all elicitation glosses to Concepticon concept sets. The linking procedure is strictly semi-automatic: in the first pass, we used the Concepticon API to link all elicitation glosses automatically to one or more Concepticon concept sets (e.g., linking 'arm (of hand)' and 'arm (body)' to #1673 ARM). In a further step, we manually checked and corrected all automatic linkings.

The automatic cognate detection methods included with the LingPy software package require that the orthographies in the data be error-free and comparable; that is, every sound must be represented in a consistent manner. Confusion can arise when one dataset does not follow traditional IPA conventions. For example, the Africanist tradition of writing IPA [j] as y, and [dʒ] as [j] can be particularly confusing. If one dataset follows traditional IPA conventions and another does not, the discrepancies can lead to a depiction of the lack of a sound change between IPA [j] to [dʒ] among cognates as in [dija] to [didʒa] in Bangime, 'eat'. The algorithms for automatic cognate detection rely heavily on consistent transcriptions. If transcriptions are inconsistent, the methods may either cease to work at all, or the results may be largely problematic.

Therefore, in an additional step to render the data comparable, we used orthography profiles (Moran and Cysouw 2017), as implemented in the Segments package [START_REF] Moran | cldf/segments: segments 1[END_REF] in order to segment the transcriptions in the data into units representing single sounds in the languages under investigation and to convert the data to a plain IPA representation accepted by the automatic cognate detection methods provided by LingPy. Data in Table 2 show an example of how orthography profiles work: much of the Mande words listed in the RefLex database use an underscore tilde [ ~] to represent nasalization while that of the Dogon comparative spreadsheet uses a superscript [ⁿ] following the segment, and then Bangime data were transcribed with a tilde above the segment [ ~]. Diacritics and tonal markings on vowels and sonorants were converted to a number corresponding to the 5-tonal step pattern used for Chinese, followed by a tilde in the cases of nasalized segments. Once properly defined, orthography profiles were used to automatically tokenize unsegmented transcriptions in the varying orthographies and convert them to our desired target transcription system. The tokenized representation is usually indicated by inserting spaces between graphemes (consisting of one or more characters) to indicate the start of a new unit that could phonetically or phonologically be perceived as a sound on its own. Without these implementations, potential cognates would likely be missed due to mismatched orthographic conventions. After we created compatible transcriptions and translations, we combined our various wordlists into one multilingual comparative file that essentially contains a (new) unique ID, a language name without spaces or special characters, both the original IPA transcription and the tokenized form produced by our orthography profile, original glosses, and concept identifiers from the Concepticon concept sets. This method resulted in a wordlist consisting of 315 concepts translated into 38 of the estimated 68 Malian languages (Simons and Fennig 2018). To make sure that languages were equally represented, showing high mutual coverage (see List et al. 2018a and[START_REF] Rama | Are automatic methods for cognate detection good enough for phylogenetic reconstruction in historical linguistics?[END_REF] for details on the concept of average mutual coverage in wordlist data) and as few missing translations per concept set as possible, we further extracted a selection of 22 languages and 300 concepts (see the Appendix for the entire list of 300 concepts). Table 3 illustrates the overlap of our 300-item concept list with other well-known concept lists. The overlap with the larger lists is above 50 percent and even higher with the smaller lists.

List

Source Coverage Blust-2008-210 Greenhill et al. 2008 126 (60%) Swadesh-1952-200 Swadesh 1952 117 (59%) Matisoff-1978-200 Matisoff 1978 117 (59%) Gregersen-1976-217-1 Gregersen 1976 115 (53%) Swadesh-1955-100 Swadesh 1955 73 (73%) Tadmor-2009-100 Tadmor 2009, (Leipzig-Jakarta) 70 (70%)

Table 3: Overlap with popular basic vocabulary lists.

Our initial selection procedure aimed to achieve a good mix of cultural and cross-linguistically interesting concepts, while selecting language data that would elucidate the ancestry of Bangime with the overall goal of providing a balanced sample of high coverage and interesting concepts.

Lexical Data Comparison Identifying Layers of Contact

Using automatic methods for cognate detection on languages that we know are unrelated such as Bangime and its neighbors, can produce many false positives that reflect neither recent contact nor ancient relations.

To address this problem, we propose a new workflow for automatic word comparison inspired by general approaches to exploratory data analysis [START_REF] Morrison | Phylogenetic networks: a new form of multivariate data summary for data mining and exploratory data analysis[END_REF]. Our main idea is not to restrict our analysis to one method only but to take advantage of the methods LingPy offers for automatic cognate detection, which are quite different in their underlying basic models and strategies.

The LexStat-Infomap approach (List et al. 2017b) has been shown to outperform earlier approaches, coming quite close to expert judgments on cognates in multilingual wordlists. 4 Its strategy closely resembles the classical comparative method, searching the data for regular sound correspondences before assigning words to common cognate sets. Regular sound correspondences usually reflect deep genetic signals but can also result from intensive language contact. The family of LexStat approaches tends to single out sporadic borrowings to some degree (List 2012a), but borrowings can be easily confused with cognates where language contact is intensive [START_REF] List | Networks of lexical borrowing and lateral gene transfer in language and genome evolution[END_REF]. We expect that applying the LexStat-Infomap approach will propose cognate sets that reflect (a) a true genetic signal among closely related languages, and (b) ancient layers of contact intense enough to surface (potentially weakly) as regular sound correspondences.

In contrast to the conservative and highly sophisticated LexStat-Infomap approach, LingPy offers simpler methods that are especially useful for quick data exploration, especially when the number of languages and concepts is large. The Sound-Class-Based Alignment (SCA) approach (List 2012b) derives pairwise word similarity scores from pairwise phonetic alignments between all word pairs in a given concept slot without taking regular sound correspondences into account. As a result, it may select true genetic cognates, or it may assign to the same cognate sets words that are similar only due to spurious borrowings or coincidental similarities. We can use this seeming disadvantage to our advantage when dealing with complex linguistic situations like the one we encounter with Bangime.

By comparing the findings for the conservative, yet rather accurate LexStat-Infomap approach with the SCA method, we can systematically search for discrepancies between our genotypic and phenotypic [START_REF] Lass | Historical linguistics and language change[END_REF]) cognate detection approaches. As a rule of thumb, we can say that when both algorithms identify certain words as cognates, they generally are, notwithstanding certain erroneous judgments that arise for several reasons. We expect to find most of these cases in languages already known to be related. However, if the SCA method identifies certain words as cognate, and LexStat-Infomap does not, we may assume we are dealing with either chance similarities or rather recent instances of borrowing. 5 The more cases of borrowing we find in specific language pairs, the stronger the argument for recent borrowing.

Although our approach is relatively simple, we think it offers several improvements over previously proposed approaches to the automatic identification of borrowings. In contrast to [START_REF] Mennecier | A Central Asian language survey[END_REF] and [START_REF] Ark | Preliminary identification of language groups and loan words in Central Asia[END_REF], for example, who use a version of the edit distance [START_REF] Levenshtein | Dvoičnye kody s ispravleniem vypadenij, vstavok i zameščenij simvolov[END_REF] to search for borrowings between unrelated language varieties only, or phylogeny-based approaches (List 2015;[START_REF] List | Networks of lexical borrowing and lateral gene transfer in language and genome evolution[END_REF]) that can only be applied to related languages, our approach can be applied to both related and unrelated languages. Since we generally assume that LexStat-Infomap is sufficient to detect very clear cases of cognates, we are also confident that cognates it does not accept but SCA does are probably true instances of borrowings.

Note that we do not expect the cognate sets proposed by LexStat-Infomap for the unrelated languages given in 4 to reflect true, deep cognates. Given the spuriousness of these findings, LexStat-Infomap is probably capturing ancient layers of contact, which is all the more interesting given the unknown history of Bangime. Hence, our approach offers an automatic stratification analysis [START_REF] Lee | No limits to borrowing: The case of Bai and Chinese[END_REF]: by applying methods with different degrees of conservatism, we can extract different layers of shared words. The ones LexStat-Infomap recognizes represent the oldest layer, and the ones identified only by SCA represent more recent layers.

Shared Vocabulary Statistics

We wanted to know the degree to which the languages of different genetic origins in our sample shared words, especially with respect to Bangime. We viewed the problem as similar to admixture analyses in population genetics [START_REF] Pritchard | Inference of population structure using multilocus genotype data[END_REF], although analyses in biology automatically determine which genes are most likely to represent a certain ancestral population. We are in a much more comfortable position; thanks to classical approaches to linguistic reconstruction, we often have an independent account on the words that were used in a given proto-language, so we do not need sophisticated algorithms to determine which words in our Bangime sample are shared with other language families. Instead, we can simply consider all inferred cognate sets in our data for a given language or group of languages and count how many are shared exclusively between the given language or group and the other languages and groups in the sample. Again, by contrasting LexStat-Infomap and SCA results when calculating the inferred cognate set statistics, we can better assess the degree to which the 'admixture' of a given language or group of languages differs.

Implementation

Our approach is implemented in the form of Python scripts, which are available in the supplementary material. They use the parameters indicated in List et al. (2017b) for the LexStat-Infomap and the SCA approach to cognate detection. The data output are given in the supplemental materials in tabular form for manual inspection (e.g., by using the EDICTOR tool) or as matrices that can be fed to phylogenetic software like SplitsTree [START_REF] Huson | SplitsTree: analyzing and visualizing evolutionary data[END_REF] to compute splits networks (e.g., with the NeighborNet algorithm, [START_REF] Bryant | Neighbor-Net. An agglomerative method for the construction of phylogenetic networks[END_REF]) and as plots that visualize specific aspects of the data.

Results

Word-list Statistics

Table 4 summarizes the coverage statistics for each of the 22 languages selected for our study. Subgroupings for the Mande and Songhay languages are based on Glottolog [START_REF] Hammarström | Glottolog 3.2[END_REF]. The Dogon grouping sub-classification follows [START_REF] Moran | Investigating the Relatedness of the Endangered Dogon Languages[END_REF] and [START_REF] Prokhorov | Dogon classification[END_REF], except that our findings, indicated by the asterisk in the table and discussed below, align Najamba with the western rather than the eastern group. We note that, based on the genetic relationship to Jenaama, Soninke might have been a more appropriate choice for an additional Mande language spoken in the area of Bangime, but the available Soninke wordlist did not cover our selected concepts well enough to be included in the subsample. Further, Bambara has a somewhat surprising influence on the Bangime lexicon as found in our sample and explored below.

Language ID Language name Items Coverage

Using the selected languages and concepts with the coverages shown in Table 4, we performed both methods, SCA and LexStat-Infomap, on the condensed 300-item wordlist. Both models require thresholds that determine at which level of similarity or distance words are considered to be cognate. For our analysis, we employed the thresholds reported by List et al. (2017b), who determined on empirical data of six language families, manually coded for cognates by experts, which thresholds yield the best results on average. This yielded a threshold of 0.55 for the LexStat-Infomap approach and 0.45 for the SCA approach.

Shared Similarities

Bangime is undoubtedly a language isolate, but it is not an insular language; we expect to see clear effects of contact with its neighbors. The most likely impact is from the Dogon languages, yet questions remain about when and which varieties left their mark. The LexStat-Info method shows us the deeper levels of contact. We can then compare these findings to the surface levels SCA brings out.

LexStat

The dark blue patterning along the rows adjacent to Bangime in the heat map (Fig. 2) indicates that the LexStat method finds practically no notable cognates between Bangime and the other languages in the sample. We still see more similarities between Bangime and Dogon than between Dogon and Fulfulde or Songhay. That is, while Bangime is certainly not genetically related to any of the surrounding languages, it has deep lexical affiliations, particularly with the Dogon languages. We explore the implications of this finding in detail below. The cognates chosen by the LexStat-Infomap approach which appear here as lighter colors on the spectrum towards red in the middle, where each language is compared with itself, can be interpreted either as true cognates or deep levels of contact.

We observe that the phylogenetic tree produced by the model accurately captures the accepted rela-tionships among the languages in the sample. Furthermore, we see below that this unrooted tree shows contributions to both Bangime and the Dogon languages from unrelated Songhay and Fulfulde donor words that are borrowings from Arabic as well as, although more recently, the Mande languages Bambara and Jenaama. Therefore, we see a connection between Bangime and the Dogon languages through, not phylogeny, but contact. Most interesting, as noted in Section 2.1, we see a connection with Dogon languages spoken at quite a distance from where Bangime is spoken, making the internal reconstruction of the Dogon languages important to the relationship with Bangime. While we see the same east-west split first depicted by [START_REF] Prokhorov | Dogon classification[END_REF], here, we propose a departure from the grouping described by [START_REF] Moran | Investigating the Relatedness of the Endangered Dogon Languages[END_REF]. Even though we use the same methods, SCA and LexStat, they place Najamba within the eastern Dogon subgroup, while we place it in the western branch, where it is geographically located.

In fact, the phylo-genetic tree pictured in Figure 3 essentially reproduces the location of the languages shown in the map in Figure 1, verifying the clarity of the signal among the lexical data used in this study. The only difference between the grouping in the figure below from that above is the additional subgrouping of Nanga with its subbranches Bankan Tey and Ben Tey. While Fulfulde may appear as somewhat of an outlier, we attribute its diversion to the lack of related languages in the sample; Maasina Fulfulde is the only Atlantic, and also non-tonal, language spoken in Mali. In many instances, both computational methods rejected similar words between Fulfulde and the other languages in the sample due to the lack of tones in Fulfulde, even though many borrowings are known to be found among the languages with Fulfulde as the source. Jenaama is not thought to be closely related to Bambara within the Mande language group, thus it is not entirely surprising that deep levels of shared cognates are not picked up by the LexStat-Info method. Data from languages more closely related to Jenaama, among the Bozo subgroup, can be viewed in the larger dataset from which the subset was drawn but due to coverage gaps these languages were omitted for the purposes of the current study.

Figure 4 shows percentages of shared vocabulary as judged by both our methods. Examining the specific relationships between Bangime and the other languages in the sample shows that, despite the fact that Bangime is the smallest single language represented, it is the least homogenous. The graphs confirm our expectations that Bangime has been heavily influenced by both Dogon and Mande languages. The first row of pie charts was produced based on the cognates found by the LexStat-Info method. As discussed in Section 3, the lexical similarities found by LexStat are not necessarily true cognates, though they are likely to reflect long-term contact between languages. We see that even the conservative estimate shows that only 75 percent of Bangime lexical items are unique and the generous estimate posits a mere 41 percent. Not surprisingly, the largest contribution of affinities in the lexicon are from the Dogon languages. Again, although, we find no evidence to support a genetic relationship between Bangime and the other languages used in the sample, shown in the following subsection, the differences between LexStat and SCA results are striking, splitting recent borrowings and ancestral contact into different categories of language contact.

SCA

The overall SCA-generated results represented by the heat map in Figure 5 are similar to those shown in the LexStat-generated heat map. Here, they have a lighter shade overall, portraying more recent stages of contact, that is, mostly through borrowing.

Compared with the LexStat-Infomap heat map above, the SCA generated heat map here is far lighter in color, illustrating the tendency of SCA to reflect much more recent stages of language contact. While the Dogon languages' affiliations remain largely the same in both figures, Bangime is more clearly aligned with its neighboring languages such as those in the western group and Jenaama, than was shown in the darker borders of the LexStat-Infomap diagram.

Another representation of the results generated by the SCA-method through a distance matrix tree further illustrates the place of Bangime somewhat in between the Western Dogon languages and the Mande languages. Indeed, the speakers' position geographically is precisely between these two populations. We do note once again the split between the Dogon languages along east-west lines is maintained in both diagrams; the results of both methods indicate a separation of the Dogon languages into two distinct subgroupings, furthering our postulation that the Dogon dispersal of the Bandiagara Escarpment could have happened from different directions, and/or distinct time periods. The "cognates" selected by the SCA approach which appear here as lighter colors on the spectrum towards red in the middle, where each language is compared with itself, can be interpreted either as borrowings rather than leading us towards genetic affinities.

Interestingly, we see that Jenaama and Bambara are still not considered to be as closely related as, for example, Songhay Kiini and Songhay Senni. This finding is reasonable in that the two Mande groups have neither shared proximate ancestry nor frequent language contact, whereas the two Songhay groups have both. Thus, both of the computational methodologies we used found very similar end-results in terms of language relatedness, with the locus of the largest difference between methods being found in the Bangime results. The congruence of the comparison between the two methodologies, shown in Figure 7 clearly leads us to identify Bambara and Tommo So as likely sources of both borrowings and cognates.

What is fascinating about the graph in Figure 7 is the strong indication towards an affiliation between Bangime and Bambara, on the one hand, and Tommo So on the other. Many young Bangande now speak Bambara as a result of traveling to the southern part of the country, and thus the language is having an inevitable effect on their speech, especially if they depart the village at a young age without having the opportunity to learn Bangime.

We ascribe the influence of Tommo So to three factors: [START_REF] Moran | Investigating the Relatedness of the Endangered Dogon Languages[END_REF] all Dogon and Bangande perform songs in Tommo So, regardless of whether the people speak the language; (2) legend describes the Dogon migration arriving first at the currently Tommo So-inhabited village Kani-Gogouna, so the language may express a type of ancestral lineage; and (3) Tommo So is centrally spoken, and many use it as a linguafranca, especially in the region surrounding Bandiagara.

Considering the Bangande-projected Dogon identity, we are not entirely surprised to find that Dogon languages have lexically influenced even core Bangime vocabulary, specifically we will see in the next section, low numerals, body parts, and culturally significant items. However, what is somewhat surprising is the geographical distance at which we find evidence of this deep language contact. We explore specifics in the next section. [START_REF] Huson | Application of Phylogenetic Networks in Evolutionary Studies[END_REF]) from an alignment site matrix produced by the SCA method.

Discussion

Areal Comparisons

As explained in Section 3, both the SCA and LexStat methods may indicate borrowings, but the latter certainly reveals both true cognates and deeper levels of contact. Here, we focus on those instances when both methods select a word as 'cognate' with Bangime. In this way, we can concentrate on long-term contact between Bangande and surrounding speakers. As Campbell (2017) points out, one way to find the lost ancestors of a language isolate is through areal comparisons within the Sprachbund. Almost all instances of LexStat cognates are shared with the SCA method, though obviously the reverse does not hold true. Since Bangime is an isolate, it does not have cognates per se with surrounding languages, but it certainly shares vocabulary worth exploring in further detail. First, we illustrate the distribution of numerals Bangime shares with the languages in our sample (Table 5) because we note that this area of the language's core vocabulary greatly resembles languages from different groups spoken in Mali. Check marks indicate where both the SCA and LexStat-Info method selected the concept and language has having a 'cognate' with Bangime. The grey shading highlights the most prevalent languages and concepts. Both of our methods highlight the numerals THREE, FOUR, and SIX as areal; that is, they are found spanning several language families in the region. Bangime's most common source languages are found in the eastern Dogon subgroup; only one western neighboring language, Bunoge, shares four of the ten lower numerals with Bangime, as compared to five eastern Dogon languages. However, the numeral SEVEN is shared only with the distantly spoken Songhay languages, not any of the nearby Dogon varieties, as might be expected. The numeral EIGHT appears to come from the Mande group, though it could also be from Najamba or Yanda Dom. The only numerals exclusive to Bangime are TWO, NINE, and TEN. The numerals ONE through FIVE are the most essential to both the Bangande and Dogon; the week is five days with a different village's market rotating on one day of the five-day week. This traditional method of keeping track of the days is being lost in favor of the seven day week, but the date of many performances and events crucially rely on the five-day week.

Among other core vocabulary items, we do witness, although less often, similarities for certain body parts as shown in Table 6. Blench (2005, p. 15) states that the Bangime words for 'ear' and 'mouth' are commonly viewed roots among Niger-Congo languages, yet neither of our analyses find a significant connection to any languages of Mali used in our sample. Among numerals and body parts, we see many core Bangime words are shared with Jamsay, including the word for 'chest', also found in Songhay. Even some of the more integral body parts, such as HEAD and HAND, were selected by the SCA method as being potential cognates/borrowings from both the Dogon languages and also Bambara. Another caste concept, BLACKSMITH, among the Dogon languages likely derives from [zèmò] 'to forge' in Songhay Senni. Despite that many Tiranige Diga speaking blacksmiths live among the Bangande villages, the word for blacksmith in Bangime bears no resemblance to any form in Dogon. In fact, the term most closely resembles that of Bambara in our sample, but since neither of our automatic detection methods determines the source, it is likely a recent acquisition into the language. The concept CHIEFTAIN also comes from Bambara. The form for God, misattributed to Jenaama [ālà], more likely comes from the widely-used Mande [ŋàlà], the pre-Islamic form for God. Other recently acquired concepts in our sample include PIG, from Jenaama, DONKEY, likely from Bunoge or Tiranige Diga, and SHEEP from Bunoge or Penange.

We can propose that many recently introduced domesticated animal and crops names are equally recent borrowings; this coupled with the fact that only the SCA method and sometimes neither method discovers the target concepts. Further, recent borrowings into Bangime are overwhelmingly from the languages that surround the location of the Bangime speakers. However, both our methodologies concur that the concepts given in Table 9 belong to Bangime and the Dogon languages from the eastern, rather than the more geographically proximate, western, sub-grouping.

In addition to the accepted knowledge that verbs are less commonly borrowed than nouns (Myers-Scotton 2002), the nouns in the sample that are selected as being shared between Bangime and the Eastern Dogon languages have significance, and are thus more susceptible to being borrowed into Bangime vocabulary to further portray their projected Dogon identity. The Dogon were made famous by the assertion of [START_REF] Griaule | Le Renard Pâle[END_REF] that the Dogon Sigui ritual celebrates the presence of a star that is unable to be viewed without a telescope. Although it is unlikely that Dogon possess the ability to view the particular star in question, stars are an integral part of daily Dogon life, providing navigational guidance in the barren plains and details by which they plan events such as rituals and plantings. As mentioned above in Section 4, throughout the Dogon and Bangande communities, songs are almost always performed in Tommo So, independent of whether or not the person singing speaks or understands the language. Even the word in our dataset for the concept ROOF, listed as [taŋa] and attributed to Jenaama by Blench (2005, p. 12), is more likely from the languages listed in Table 10, and yet Bangande building style with two-story houses is not shared with Dogon, nor any other village construction in Mali.

Conclusion

Our study confirms that Bangime is a language isolate, yet the effects of both recent and distant contact, crucial to solving the mysteries surrounding and positing a reasonable history of these 'secret' people, are difficult to observe using automatic cognate detection methods alone. The more conservative method rejects borrowings, while even the lenient method sometimes misses them, requiring careful manual inspection of the wordlists informed by additional knowledge of Bagande culture and their own understanding of their ethnological and linguistic identity. [START_REF] Alinei | Conservation and Change in Language[END_REF] speaks of "alloglottic linguistic colonies", and notes that language enclaves survive because their speakers want to retain an identity associated with their homeland. In the case of Bangime, the opposite holds true -Bangande claim that their homeland lies with the Dogon in Mande, and yet one of their most important sources of perceived identity, their language, speaks a different story.

While Bangande consider themselves Dogon, and Dogon consider themselves to be the young brothers of the Mande, there is no lexical evidence to suggest that any of these groups are related to each other. More likely, the Bangande escaped whatever caused the annihilation of their ancestors and came to settle in the secluded Geou valley prior to Dogon settlement. As the influence of the western Dogon languages seems relatively more recent than that of the eastern groups, the Dogon peoples seem to have come to the Bandiagara escarpment from different directions and settled at different times. No dating or archeological research has been conducted in the area where the Bangande reside, but if they did live in the cliffs before the Dogon, then perhaps they are 'those who came before' --the Tellem.

But, if the Bangande have been, not only in contact, but practically immersed in the surrounding Dogon cultures for at least half a millennium then it is that much more surprising that they have managed to keep their language intact. Samar and Bhatia (2017, p. 62), "...we are not sure if there is such a case where two compatible languages have been in contact for more than, say, 500 years, without any of them dying". If so, then Bangime represents an interesting and vanishingly rare counterexample. Not only is it not dead, it is thriving; around 1,500 speakers use it on a daily basis in their homes and with their children.

Given the neighboring Dogon groups' disdain for the Bangande, we can propose that a reason why Bangande have not mixed genetically with their Dogon neighbors (cf [START_REF] Babiker | The genetic identity behind the masks: Bangande and Dogon of Western Africa[END_REF]) is because Dogon village men do not accept to marry Bangande wives; though the opposite holds true. In traditional West African society, arranged marriages forbid the joining of certain groups to one another, such as between the Bozo and the Dogon. However, given the geographic proximity, language contact is inevitable. Bangime is a 'secret language' to its neighbors; linguists classify it as an isolate; and since it is likely currently spoken in a remote location, at a great remove from its original, ancestral speakers, it is a language island. In identifying the words that have washed up on its shores over time, we may someday be able to track its passage, explain its practices, and gain from its knowledge and experiences. Future interdisciplinary research should be pursued, aided by computational resources that can decipher the linguistic, genetic, and anthropological clues.

Figure 1 :

 1 Figure 1: Bangime and its surrounding languages.

Figure 2 :

 2 Figure 2: Heat Map generated from the cognate percentages inferred by the LexStat-Infomap approach.The cognates chosen by the LexStat-Infomap approach which appear here as lighter colors on the spectrum towards red in the middle, where each language is compared with itself, can be interpreted either as true cognates or deep levels of contact.

Figure 3 :

 3 Figure3: An equal-angle Neighbor-Net tree created in Splits Tree[START_REF] Huson | Application of Phylogenetic Networks in Evolutionary Studies[END_REF]) from an alignment site matrix produced by the LexStat-Info method.

Figure 5 :

 5 Figure5: Heat Map generated from the cognate percentages inferred by the SCA approach. The "cognates" selected by the SCA approach which appear here as lighter colors on the spectrum towards red in the middle, where each language is compared with itself, can be interpreted either as borrowings rather than leading us towards genetic affinities.

Figure 6 :

 6 Figure6: An equal-angle Neighbor-Net tree created in Splits Tree[START_REF] Huson | Application of Phylogenetic Networks in Evolutionary Studies[END_REF]) from an alignment site matrix produced by the SCA method.

Figure 7 :

 7 Figure 7: Comparing the discrepancies between cognate percentages inferred by LexStat-Infomap andSCA. If no difference is encountered, we set the value in the heatmap to 0.5. If the proportions differ, we first subtract the LexStat-Infomap value from the SCA value and then add this value to our baseline of 0.5. As a result, comparing one language with itself will always yield the baseline, and values larger than 0.5 indicate to which degree SCA infers more cognates for the respective language pair, while values less than 0.5 indicate that SCA infers less cognates. We suspect that those cases in which SCA infers a larger number of more cognates point to recent borrowings between the varieties.

Table

Table 1 :

 1 ) are those that are currently spoken furthest away Dogon terms for concept 'HIDE, CONCEAL SOMETHING'

	Language	IPA	Language	IPA
	Ben Tey ourou Jamsay Tebul Ure ogo Kan ommo So bàŋú-ndá Nanga bàŋɡì-rí Bunoge bàŋà-rá Tiranige Diga dʒíná-ŋɡó jɔɡɛG bàŋà-rá Mombo dábú-rè bàŋɡì-rí Penange kúj-rɛT bàŋú-rù Donno So dʒɔɔ-rɔT dǎw-rí Yanda Dom báá-ndɛ́Najamba síbí-r Yorno So bàŋá-rá Toro Tegu sútù Toro So bàŋì-rí Perge Tegu súɡú-ró

Language Source Transcription Tokenized Representation Source Gloss Concepticon Concept

	Bangime Mombo Tiranige Diga kǔ:ⁿ kĩ ́ĩ ̄k ĩː ⁵³ ∼ kí:ⁿ k ĩː ⁵ ∼ k ũː ¹⁵ ∼ Jenaama kūⁿ k ũ ³ ∼ Bambara kúrṵ́k u ⁵ r u ⁵ ∼	boat boat boat boat boat (skiff)	BOAT BOAT BOAT BOAT BOAT

Table 2 :

 2 Illustration of data conversion in our workflow.

Table 4 :

 4 Coverage and sources of our data

	Subgroup	Source

  Figure 4: Comparing exclusively shared cognates across language families in our sample for LexStat-Infomap (top row) and SCA (bottom row). The "non-exclusive" group refers to cases where inferred cognate sets are attested in more than two families.

	6.0%	16.0%	3.9%	2.8%			5.5% 5.9%		4.1% 9.6%	Bangime Atlantic
		75.7%	94.0%			91.7%			86.3%		84.8%	Dogon Mande
		Bangime										Songhai
		20.7%	7.1%	6.1% 5.9%	6.4%	6.9%	0.2% 5.5%	15.3%	4.1%	0.9% 1.1%	13.1%	non-exclusive
										19.8%
	41.0%	29.3%					23.6%		51.3%		65.1%
			86.5%			73.8%
	Bangime Atlantic	Dogon	Mande	Songhai

Table 7

 7

	shows examples of

Table 9 :

 9 Recent Shared Cultural Vocabulary into two classes: slave and royal, with depictions of slave raids happening in the villages and surroundings told through oral histories. At least at the western side of the Bandiagara Escarpment where Bangime is spoken, the results of language contact appear to be recent. Specific concepts within the domain of castes, central to Malian cultural hierarchies, such as NOBLE and SLAVE are likely from Soninke, passed into Bangime and western Dogon languages, yet not the Dogon languages of the east.

[START_REF] Campbell | Language Isolates and Their History, or, What's Weird, Anyway[END_REF] and Simons and Fennig (2018) list ten isolate or unclassified languages, only four of which are considered to be undisputed.

Coordinates were given for the ethnolinguistic areas closest to the seven Bangande villages; the data used can be found in the supplemental materials.

While the suffix[-m] can be assumed to be the animate noun class morpheme, used in Ben Tey and Bankan Tey, only the root [tɛĺɛ] is listed in the Dogon comparative wordlist, with the meaning of 'almost'. Thus, we cannot confirm the translation of 'those before' however, we do note the similarity to the Mande root [télí] meaning 'quickly'.

The method by[START_REF] Jäger | Using support vector machines and state-of-the-art algorithms for phonetic alignment to identify cognates in multi-lingual wordlists[END_REF] seems to outperform LexStat-Infomap on certain datasets, but according to[START_REF] Rama | Are automatic methods for cognate detection good enough for phylogenetic reconstruction in historical linguistics?[END_REF], the difference is minimal and may be in favor of LexStat.

As our dataset shows, in recent borrowings, donor and recipient word tend to resemble each other more than older borrowings do since borrowings are usually nativized over time and adjusted to the phonotactic system of the target language.

Acknowledgements

We gratefully acknowledge the support and generosity of Professor Russel Gray, Hiba Babiker, and the Department of Linguistic and Cultural Evolution at the Max Planck Institute for the Science of Human History, without which the present study could not have been completed. Abbie Hantgan's work was additionally supported by Jeffrey Heath and the Dogon and Bangime Linguistics Project under NSF Grant award #BCS-1263150. Johann-Mattis List was funded as part of the European Research Council Starting Grant 'Computer-Assisted Language Comparison: Reconciling Computational and Classical Approaches in Historical Linguistics'. We immensely appreciate the assistance and support provided by MPI colleagues Heidi Colleran, Anne-Maria Fehn, Tom Güldemann, Simon Greenhill, Martin Haspelmath, Ezequiel Koile, Ana Kondic, Adam Powell, Martine Robbeets, Christoph Rzymski, Robert Spengler, Natalie Uomini, Annemarie Verkerk, as well as the organizers and participants of the Workshop on Linguistic Islands in Africa. Responsibility for any errors in the resulting work remains our own.

Shared Numerals words for body parts that appear unique to Bangime, and yet are found in some Dogon languages, albeit with a different meaning; these items were hand-selected as neither of our automatic methods detected them.

There is a precedent for switched meanings in Bangime. [START_REF] Hantgan | Aspects of Bangime Phonology, Morphology, and Morpho-syntax[END_REF] describes portions of the Bangime lexicon with purposely reversed meanings such as the naming of plants used in traditional medicines by reversed colors than they appear to be. Even though practically no one outside the Bangande community speaks Bangime, they claim that the use of reverse meanings further protects them from potential eavesdropping.

Other terms shared areally between Bangime across language families are shown in Table 8. Concepts COW and MEAT, along with HUNDRED, GOLD, FORGIVE, and MOSQUE are likely attributed to the wide distribution Fulfulde lexical items, some of which are originally from Arabic, while CASSAVA probably has a source among the southern-spoken Mande languages from where the crop originated. The fact that both our methods selected MAIZE as being shared between Bangime and Jamsay is somewhat unexpected given the word in Jamsay [pòròː ɲúː] bears little resemble to Bangime [bìrɔ̀ndɔń]. However, the Jamsay word differs from that of the other Dogon languages, thus this warrants further inspection in the future.

Our methods somewhat incorrectly attribute the source of some Arabic borrowings to Songhay rather than Fulfulde. We attribute this error to the fact that Songhay shares the tonal properties with the other Malian languages whereas Fulfulde does not. The only clear cases of a borrowing from Songhay into nearly all the surrounding languages are COUNTRY and CLOUD. The original source of these Songhay shared words is likely not from Arabic. Curiously, neither the Bangande nor many of the more geographically isolated Dogon speakers, has not adopted the term ANIMAL from Arabic [√dbb] via Fulfulde [dabba], as most of the plains-speaking Dogon villages and even Jenaama spoken in the valley have. This fact, coupled with the assertion of Blench (2005, p. 2) who states that Bangime crop names are distinctive, supports the hypothesis that the Bangande lived in their current location before the Dogon. Our results concur that the most essential crop to the area, MILLET, is indeed unique to Bangime, while many of the Dogon languages may share the term with southern Mande varieties. In the table above, only Jamsay was selected by both of our methods as sharing the term MAIZE with Bangime. CASSAVA, with a likely source from Bambara and other Mande varieties, is a DOCULECT CASSAVA COW GRASS HORN MAIZE MARROW MEAT Fulfulde , ,

, , , ,

Table 8: Shared Agriculture Vocabulary recently introduced crop, selected by our methods as being a shared term.

Group-specific Comparisons

While words from Bambara are shown in Figure 7 to be particularly prevalent in Bangime, we actually attribute many of the words in our dataset, particularly those to do with the caste system, to Soninke. The Mande influence of the Mali Empire on Bangime and the Western-Dogon languages is evidenced through culturally significant vocabulary shown in Table 9.

Recently acquired vocabulary was often not picked up by either of our methods, and yet manual inspection reveals that there is clear evidence of a connection between the above listed words and the languages spoken to the west of the Bangande speakers. We attribute these relatively recent borrowings to the Mali Empire. The Mali Empire, with Mande rule of the western portions of Mali from the 1200's to 1600's A.D., is evidenced by relatively recent borrowings with specific cultural meanings found in Bangime and the languages spoken to the west of the Bangande-speaking region.

While most researchers assume that the Dogon villages came to be occupied as a result of escaping from prior empires, [START_REF] Nunn | Ruggedness: The Blessing of Bad Geography in Africa[END_REF] provide statistical support for the unique benefits of living in rocky terrain in Africa in order to avoid the repercussions of the slave trades from 1400 and 1900 A.D. As explained in [START_REF] Hantgan | Aspects of Bangime Phonology, Morphology, and Morpho-syntax[END_REF]

, , , , 2018) makes correlations that languages spoken in Africa's secluded and mountainous regions are more likely to be preserved than those spoken in more easily accessible areas. Bangime, and the Dogon languages, are excellent examples of this trend. The mountains have undoubtedly contributed to the cohesiveness of the Dogon languages as a whole, and yet Bangime has not succumbed to its speakers pressures to preserve a Dogon identity.

Supplemental Material

The supplementary material contains the Python code along with the data that are needed to replicate the analyses discussed in this study along with usage instructions. The supplementary material has been submitted to the Zenodo, where it can be accessed at https://zenodo.org/ record/1407141. The data is curated at GitHub, where it can be accessed at https://github. com/lingpy/language-islands-paper.