Abdellatif Chagdali

Salah Eddine Elayoubi

Antonia Maria Masucci

Impact of Slice Function Placement on the Performance of URLLC with Redundant Coverage

Keywords: 5G, network slicing, quality of service, ultrareliable low-latency communication (URLLC), resource allocation, redundancy, join the shortest queue

Network slicing has emerged as a promising technical solution to ensure the coexistence of the various 5G services. While the evolution of the 5G architecture for supporting slicing has been thoroughly studied, the impact of the architectural options on RAN resource allocation efficiency is still unclear. This article fills a gap in this area by assessing the impact of architecture choices on the quality of service of different services, with a focus on ultra-reliable low-latency communication applications. We propose architectural options based on the placement of the entities responsible for implementing these functions. We then assess their impact on the radio resource allocation flexibility when slices span two radio access technologies with redundant coverage. Our numerical experiments show that the placement of the slice management functions plays a crucial role in the choice of the radio resource allocation scheme that best fits URLLC slices.

I. INTRODUCTION

The fifth generation of mobile networks (5G) differs from its predecessors as it harbors a novel and unprecedented serviceoriented vision along with the evolutionary view. As a matter of fact, 5G systems will not provide just an increase in data rates but will also define new use cases in hand with legacy services. Delivering these new services requires a versatile, scalable, efficient, and cost-effective network, capable of accommodating its resource allocation to act upon the heterogeneous nature of demands. For instance, Enhanced Mobile Broadband (eMBB) services necessitate high data rates, widearea coverage, and high-user density. On the other hand, Ultrareliable and Low-Latency Communications (URLLC) define strict requirements in terms of latency and packet loss.

Network slicing has emerged as one of the fundamental concepts proposed to raise the efficiency and provide the required plasticity of 5G mobile networks. The idea is to provision resources for different vertical industries by building multiple End-to-End (E2E) logical networks over a shared infrastructure. Each network slice (i.e. logical network) is customized to deliver a specific service to a tenant.

Even though the concept of network slicing is relatively new, the corresponding literature that deals with it is already rich, especially on architecture and management aspects. For instance, [START_REF] Foukas | Network slicing in 5G: Survey and challenges[END_REF] offers a holistic approach by discussing the management and orchestration for E2E slices, including infrastructure layer, network function layer, and service layer. In paper [START_REF] Rost | Network slicing to enable scalability and flexibility in 5G mobile networks[END_REF], the authors discuss the architectural concepts for slicing, including the mapping of network functions (NFs) to satisfy the discordant performance targets of 5G use cases. While network slicing is an E2E concept, most of the research has focused on core slicing leading to mature architecture proposition powered by the emergence of cloud computing, Network Function Virtualization (NFV) and Software-Defined Networks (SDN) [START_REF] Foukas | Network slicing in 5G: Survey and challenges[END_REF], [START_REF] Zhou | Network slicing as a service: enabling enterprises' own software-defined cellular networks[END_REF], [START_REF] Ordonez-Lucena | Network slicing for 5G with SDN/NFV: Concepts, architectures, and challenges[END_REF].

However, Radio Access Network (RAN) slicing introduces a distinct set of issues compared to core slicing. Third Generation Partnership Project (3GPP) foresees novel Radio Access Technologies (RATs), new subcarrier spacing, and frame structure to provide RAN adaptability, given the dissonant nature of verticals' demands [START_REF] Gpp | Summary of rel-15 work items[END_REF]. Thus, a key challenge is to choose the propitious RATs for each service during the preparation phase of RAN slice creation. Besides, it's indispensable to design isolation mechanisms between RAN slices along with a charging framework that takes into consideration the role of third-party players.

The authors in [START_REF] Elayoubi | 5G RAN slicing for verticals: Enablers and challenges[END_REF] focus on slicing implementation in the RAN and identify its enablers, among which we can find: flexible numerology, mobile edge computing, and slice tiling. The latter arranges time-frequency resources with the same numerology in resource block groups that the scheduler allocates to the adequate slice type; for optimal resource allocation. In [START_REF] Sallent | On radio access network slicing from a radio resource management perspective[END_REF], the authors probe into RAN slicing management in a multi-cell network by studying four architecture proposals for radio resource sharing and discuss their different levels of granularity, isolation, and customization aspects. Moreover, the authors in [START_REF] Ferrus | On 5G radio access network slicing: Radio interface protocol features and configuration[END_REF] advocate for radio protocol layer descriptors that outline the features, policies, and resources needed to create and customize multiple RAN slices.

While these works paved the way for the definition of slicing concept in 5G, they did not tackle the impact of the 5G ecosystem openness to new actors on resource allocation implementation in the RAN. Indeed, even if the 5G New Radio (NR) has been designed as highly flexible to ensure efficient multiplexing between slices, the task of radio and computing resource allocation is still cumbersome. The multiplication of actors that have stakes in the RAN makes it arduous to allocate resources to the slices, as the resources supposedly belong to multiple Infrastructure Providers (InPs). The latter InPs contract Service Level Agreements (SLAs) with different Mobile Service Providers (MSP) and verticals. Our objective in this paper is to build on the concepts developed in the literature, to construct a Radio Resource Management (RRM) framework for URLLC and eMBB slices. We specifically: 1) identify the different actors that have stakes in RAN resource allocation and their ownership of the different slice and network functions, 2) propose a placement for the intelligent entities that take decisions on traffic steering and resource allocation, for all the involved actors, 3) quantify the impact of the defined architectural options on the Quality of Service (QoS) in the practical case of redundant coverage of two RATs. 4) compare the performances of different packet replication schemes, namely Join-the-Shortest-Queue and systematic redundancy, for different architectural options. The remainder of this paper is organized as follows. Section II describes slice management functions and stipulates their ownership and roles in the radio resource management. Section III presents the impact of the architectural options for the placement of these functions on the possible scheduling mechanisms for URLLC in an industrial scenario. Section IV compares the performances of these scheduling mechanisms and shows the best policies in each of the studied scenarios. Section V eventually concludes the paper.

II. RAN RESOURCE ALLOCATION AND TRAFFIC STEERING

Before describing the slice management function placement options, we aim in this section at identifying the role of each player in the slice management and the entities that are responsible for managing traffic and resources for the slices.

A. Slice management functions description and ownership

The MSP has to create and simultaneously maintain many Network Slice Instances (NSI). An NSI is composed of Core Network (CN) and RAN Network Slice Subnet Instances (NSSI), arranged to provide necessary resources and functionalities and thus deliver the tenants' services. Each NSSI encompasses Physical Network Functions (PNFs) and Virtual Network Functions (VNFs) that are either dedicated or common among different slices. According to the solution advocated by 3GPP and illustrated in Figure 1, the tenant's management function called the Communication Service Management Function (CSMF) forwards the service requirements to the Network Slice Management Function (NSMF). Then, the NSMF translates the E2E high-level performance requirements desired by the tenant to CN and RAN low-level requirements managed by the Network Slice Subnet Management Function (NSSMF). Thereafter, the RAN NSSMF converts the lowlevel requirements into RRM specific requirements and sets the resource allocation policy at the MAC scheduler of the Base Station (BS), whereas the CN NSSMF deploys and maps the service-oriented VNFs. Both the RAN and CN NSSMFs send periodic performance reports to the NSMF so that it can verify that the service requirements are respected. For example, if the RAN NSSMF violates the latency requirement of a network slice, the NSMF can adjust the scheduling policy by reserving more resource blocks. It can also alter the admission control procedure by rejecting any other network slice requests as long as the served slices SLAs are not respected. Table I summarizes these entities, their owners, and their roles in the slice resource allocation.

Note that the resource allocation task is particularly complicated in case several MSPs lease resources from multiple InPs. Indeed, the NSMF belongs to the MSP and has as objective to ensure that the tenant's SLA is respected. Nevertheless, there is a RAN NSSMF that belongs to each InP, which has control over the resources of this particular InP only, as illustrated in Figure 1. In the latter, we consider three slices belonging to three different tenants. For each slice, we deploy an NSSMF per InP RAN. The question here is how to design and implement resource management policies in such a distributed architecture while taking into consideration tenant, MSP, and InP perspectives.

B. Resource allocation from MSP perspective

From the MSP perspective, the NSMF translates the tenant requirements into a traffic steering policy that determines to which InP(s) the packets of a specific User's Equipment (UE) are to be forwarded. Such a policy may be generic, e.g. to privilege a particular InP when possible. Alternatively, it can be context-aware, which means examining the instantaneous load of the base station pertaining to an InP and its radio conditions with respect to the UE. For example, a potential policy is to connect a particular UE to a single InP, or to split its packets between several InPs, or even to duplicate them to increase reliability. Specifically, the NSMF can, for example, decide that 70% of generated packets go through the main InP while the remaining 30% go through secondary InP during the validity time of the high-level policy.

In case the MSP applies the decided policy without coordination with the InPs, an entity hosted in the UE, capable of implementing the NSMF scheduling strategy, is required. Otherwise, the traffic steering policy can be implemented as a shared NF among multiple slices on the InPs infrastructure, or as dedicated NF with some cooperation between slices to meet the heterogeneous optimization targets and for effective use of the radio resources [START_REF] Ferrus | On 5G radio access network slicing: Radio interface protocol features and configuration[END_REF].

C. Resource allocation from tenant perspective

From the tenant perspective, the CSMF determines dynamically the amount of resources that need to be allocated to the slice for continuously respecting the SLA, knowing the current traffic demand. In order for these requests to be accurate, the CSMF has to rely on the information originating from the application server and/or from the end-users. The time scale for these traffic reports has to be larger than the actual scheduler time scale, i.e. in the order of tens of seconds. In the specific case where the tenant is a "big" vertical that can deploy its own infrastructure (e.g., railway and highway management companies), it has the ability to bypass the MSP and acquire the resources directly from InPs, having thus the same behavior of MSPs, described previously.

D. Resource allocation from InP perspective

From the InP perspective, the NSSMF receives the resource allocation requests from the UEs belonging to different slices and applies some scheduling/admission control policies to them. The devised policies of the InP have to dynamically share the resources among the slices to raise the overall resource efficiency, especially that leasing fixed shares of resources will limit the multiplexing gains.

Note that, from an InP perspective, [START_REF] Samdanis | From network sharing to multi-tenancy: The 5G network slice broker[END_REF] introduces the socalled 5G network slice broker, hosted in the NSSMF of the InP, that gathers global network load measurements and configures the RAN scheduler policies based on the negotiated SLA and the size of the network slice. Moreover, the openness of the mobile network may lead to an adversarial behavior of MSPs consisting of maximizing the acquired share of resources. In order to deal with this issue, a share-constrained proportional allocation mechanism is exploited in [START_REF] Caballero | Network slicing games: Enabling customization in multi-tenant mobile networks[END_REF], and the share obtained by each tenant is determined by the equilibrium point of a network slicing game. In the same context, the authors in [START_REF] Caballero | Network slicing for guaranteed rate services: Admission control and resource allocation games[END_REF] investigate resource allocation mechanisms between tenants using game theory tools to model the noncooperative behavior of slices. However, these works are limited to multiple tenants sharing a single InP infrastructure.

III. IMPACT OF PLACEMENT OF INTELLIGENT ENTITIES ON RADIO RESOURCE ALLOCATION FOR SLICES

We now study the placement of entities in charge of resource allocation in light of the above description of the slice management functions. We consider, for illustration, the case of a smart factory where several base stations (5G NR and/or legacy) are deployed to establish a redundant coverage, essential for ensuring URLLC QoS 1 , as illustrated in Figure 2. The tenant may own and manage some small cells deployed within the factory, while the InP manages base stations, operating in the sub 2 GHz spectrum for ensuring full coverage. While some UEs will be covered by the macro cells only, it is envisioned that most locations will be covered by at least two overlapping cells, providing flexibility in resource allocation and redundancy for ensuring reliability. We hereafter display three potential resource allocation schemes exploiting these advantages.

EMBB Traffic URLLC Traffic EMBB Traffic #3 #4 #1 #2 #3 #4 #2 #1 #2 #1

A. Intelligence placed at the level of a shared RAN NSSMF

In this case, the traffics of all RAN slices and the radio resources of all base stations are managed via a shared RAN NSSMF with a single compound MAC scheduler. The latter has access to real-time information concerning the timefrequency matrix of each base station, thus allowing grantbased resource allocation. This case is enabled when the resources of all base stations are centrally managed within a common Cloud-RAN linked to the base stations by a high capacity fronthaul, as illustrated in Figure 3a.

A dynamic strategy can thus be applied by the NSSMF to URLLC traffic, which consists of sending packets to the BS with the lowest instantaneous load in order to minimize latency. As of eMBB traffic, it is served by one of the two base stations independent of the instantaneous load, i.e. each base station has its own eMBB traffic to serve and manages the URLLC traffic jointly with the other base station, as illustrated in Figure 2. This strategy can be applied in both uplink and downlink; it is straightforward in the downlink where the application server sends the URLLC packets to the NSSMF that directs them to the adequate base station for transmission. As of the uplink, the UE sends a scheduling request to NSSMF that issues a scheduling grant on one of the base stations. Consequently, the uplink case is more challenging as this control process may introduce latency between the moment the loads are observed by the NSSMF and the moment the scheduling grant is issued for the URLLC user.

1 5G NR and 4G base stations can natively cooperate via a common core network, whereas [START_REF] Gpp | Access to the 3GPP 5G core network (5GCN) via non-3GPP access networks (N3AN)[END_REF] prescribes the Non-3GPP Interworking Function (N3IWF) for combining accesses using proprietary or WiFi technology.

B. Intelligence placed at the NSMF level

When there is restricted coordination between the InPs, and between the MSP and the InPs, as in the case where each base station has its own Baseband Units (BBU), loosely linked to other BBUs, performing intelligent steering of each packet based on the instantaneous load of each cell is difficult to achieve. This is illustrated in Figure 3b. In this case, a long-term policy (e.g. based on a time granularity of tens of seconds) is to be applied, managed by the NSMF located somewhere at the level of the core network. For this policy to be effective, the UEs (in the uplink) and the application server (in the downlink) have to apply the policy provided by the NSMF on a packet basis, but without further information on the instantaneous load of each cell. When the decision about the destination of the packet is taken, the remainder of the scheduling process is performed in a classical way, and the RAN NSSMF does not need to know about the slice policy. We consider hereafter two feasible policies for URLLC:

1) Long-term traffic steering with no redundancy: It entails the division of the URLLC traffic proportionally, based on the base stations' average capacities as estimated by the NSMF, or as provided to the MSP by the RAN NSSMF of each InP. 2) Long-term traffic steering with redundancy: In the absence of any information about the capacities of the different base stations, and in order to ensure reliability, redundancy is a costly yet simple strategy. This implicates sending systematically the arriving URLLC packets to both base stations. While packet redundancy can achieve high reliability as it enables the experience of minimum queuing latency between the BSs, it leads to the under-utilization of radio resources. The NSMF broadcasts the policy to the URLLC user equipment during the slice instantiation.

IV. PERFORMANCE EVALUATION First, we simulate the system presented in Figure 2, with only URLLC packets, via a resource reservation scenario for URLLC slice. Then, we consider a use case where eMBB and URLLC slices share the same resources. The goal is to obtain quantitative insights on the impact of architectural consideration on delivering the hard latency requirement of the URLLC service for different architecture options.

We consider three Poisson processes of arriving packets. URLLC packets are steered with regard to the network architecture and the placement of resource management entities (see Figure 3). The mean number of packets generated by URLLC users is 100 packets/s. When URLLC and eMBB slices share the same resources, we assume that eMBB users are sending packets with two independent processes for the two base stations, as illustrated in Figure 2. The eMBB packets' size is set to 1500 bytes, whereas the size of the URLLC packets is 32 bytes. Motivated by the flexibility of the 5G NR air interface, we consider that URLLC packets are served on a mini-slot basis, of 2 OFDM symbols, while eMBB packets are served on a legacy 1 ms TTI [START_REF] Ji | Ultra-reliable and low-latency communications in 5G downlink: Physical layer aspects[END_REF]. Service times of URLLC and eMBB packets depend on the used modulation and coding scheme. The latter varies from one user to another, depending on its average radio conditions. Hence, we set the uplink and downlink average spectral efficiency for eMBB packets equal to 6.75 and 9 bits/Hz/s, respectively [START_REF] Itu-R | Minimum requirements related to technical performance for IMT-2020 radio interface (s)[END_REF]. Additionally, we model the uplink and downlink spectral efficiency for URLLC packets as a discrete uniform distribution over the set {1, 1.5, 2, 2.5} bits/Hz/s.

We evaluate through Monte Carlo simulations the outage probability of URLLC traffic originating from the placement of the intelligent entities, for both cases discussed above. We send packets for a time window of 50 seconds, and we carry the same experiment 100 times. The outage probability is defined as the probability that the packets' latency exceeds a predefined threshold, which depends on the target latency. We set the target latency threshold for URLLC to 0.5 ms. First, we study the impact of slicing architecture on URLLC traffic. In order to isolate them from eMBB traffic, we reserve for this type of traffic a sub-band on each base station. In this setting, we assume a reserved bandwidth of 1 MHz and 2 MHz on BS1 and BS2, respectively. In Figure 4, we plot the URLLC traffic outage probability stemming from the different policies while varying the number of URLLC users. We consider two procedures and their variants:

• Decision in a shared RAN NSSMF: When the scheduling decision is taken at the RAN NSSMF level, the packet steering policy depends on the load of the base station. We consider two practical variants. The first variant supposes the knowledge of the instantaneous load with no delay. The second case takes into account the control plane signaling delay, especially for the uplink, where the user terminal relies on information sent by the NSSMF some time ago (100 µs in the numerical example) to make its decision. • Decision in a far NSMF: When the instantaneous load is not available as the decision is taken at the NSMF level, we consider two variants. First, an NSMF proportional traffic steering based on the average capacities (1/3 of the traffic over BS1 and 2/3 over BS2 in our case) is implemented; this corresponds to probabilistic routing of the packet based on long-term policies sent by the NSMF. Second, we consider the instance where each packet is duplicated to the two interfaces for profiting all the time from the interface with the lowest load. When having a global look at the performance, we observe two regimes, each giving an advantage for one of the architectural options. First, in medium to high load regimes, placing the intelligence at a shared RAN NSSMF has a clear advantage over the management in a far NSMF entity. While these regimes are classically targeted for eMBB, they are not suitable for URLLC where a very low outage probability is sought, in the order of 10 -6 to 10 -5 , corresponding to a low load regime. In this latter, the traffic steering at a common RAN NSSMF is not sufficient for the URLLC traffic, and a large control delay worsens the performance. Only a systematic redundant replication is able to achieve the target performance in this low load regime, and this approach can be implemented at the NSMF level, without the need for tight cooperation. Note that an NSMF proportional traffic steering based on the average capacities has the worst performance in the low load regime, but outperforms the redundancy case in high load regime as it avoids overloading.

B. Coexistence of eMBB and URLLC Slices

We now move to a setting where URLLC and eMBB slices share the same resources, i.e. we use the overall bandwidth without reserving a fixed band for URLLC traffic. The overall bandwidth of BS1 and BS2 is 10 MHz and 20 MHz, respectively. Our objective is twofold. First, we aim at studying the impact of eMBB and URLLC slice resource multiplexing on the URLLC performance, and second, we aim at reinspecting the URLLC slice function placement impact. We gradually increase the URLLC traffic while maintaining the eMBB load set to 70% of the cell's capacity. In Figure 5, we plot the outage probability for URLLC packets. We remark that the outage probability has higher values compared to the previous case (separated URLLC/eMBB) since the URLLC packets compete with large eMBB packets. Ultra-reliability is thus very difficult to achieve when there is no strict resource reservation for URLLC traffic. We now have a deeper look at the performance of the different URLLC slice management policies. The performance trend is similar to that of the case of resource reservation. In particular, blind redundancy degrades the performance for high loads but is essential for achieving high reliability. Indeed, even if it increases the load, redundancy increases the chance to have a link with no eMBB packet ahead in line. However, tight coordination at the RAN NSSMF level offers altogether good results but still outperformed in low load regimes by packet duplication. In this configuration, the proportional policy offers the worst performance because it is a long term strategy that does not consider the evolution of traffic over time.

V. CONCLUDING REMARKS

In this article, we explored the concept of network slicing with the objective of achieving seamless resource allocation at the RAN level while enabling multi-tenancy. We identified the different actors in RAN resource allocation while shedding light on their ownership of the different slice management functions. We studied various options for the placement of intelligent entities involved in resource allocation and traffic steering decisions while focusing on the challenging use case of URLLC traffic in the uplink. Our results show that, regardless of the architectural solutions, redundant scheduling is essential for achieving ultra-reliability.

As of future work, we aim at extending our study to other forms of redundancy, e.g. time and frequency packet replication, in addition to the spatial replication considered in this paper, and explore the feasibility and effectiveness of these schemes for different slicing architectural options.

Fig. 1 :

 1 Fig. 1: Overview of the infrastructure and management Layer in a network slicing scenario.

Fig. 2 :

 2 Fig. 2: Traffic steering in industry 4.0 use case. Two base stations in the neighborhood of URLLC user equipment.

Fig. 3 :

 3 Fig. 3: Distribution of Management Functions in a factory scenario. (a) Intelligence placed at the level of a shared RAN NSSMF; (b) Intelligence placed at the NSMF level.

Fig. 4 :

 4 Fig. 4: Outage probability in the case of bandwidth reservation for URLLC packets.

Fig. 5 :

 5 Fig. 5: Outage probability in the case of coexistence of eMBB and URLLC packets without bandwidth reservation.

TABLE I :

 I Entities involved in RAN resource allocation and their roles.

TABLE II :

 II Parameters for performance evaluationA. Bandwidth Reservation Case for URLLC Slice

ACKNOWLEDGEMENTS

This work is supported by MAESTRO-5G project funded by the French Agence Nationale de la Recherche (ref. ANR-18-CE25-0012).


Ph.D Maria Giavazzi
email: maria.giavazzi@ens.fr

Robert Daland

Stefano Palminteri

Sharon Peperkamp

Pierre Brugieres

Charlotte Jacquemot

Catherine Schramm

Laurent Cleret De Langavant

Anne-Catherine Bachoud-Lévi

Pierre Brugières

Anne-Catherine Bachoud -Lévi

The role of the striatum in linguistic selection: Evidence from

Keywords: CORTEX Language, Huntington's disease, basal ganglia, brain mapping

come   L'archive ouverte pluridisciplinaire

M A N U S C R I P T A C C E P T E D

INTRODUCTION

Though research on the neural basis of language processing has mainly focused on cortical structures and their connections [START_REF] Fedorenko | Functional specificity for high-level linguistic processing in the human brain[END_REF][START_REF] Friederici | The cortical language circuit: from auditory perception to sentence comprehension[END_REF][START_REF] Friederici | The language network[END_REF][START_REF] Hickok | The cortical organization of speech processing[END_REF], subcortical structures and connections between cortical and subcortical systems are also part of the language network. The striatum is one of the most important subcortical structures involved in language processing. Evidence of striatal involvement in language was initially observed in neuropsychological studies of patients with focal striatal lesions [START_REF] Cambier | Hemorrhage of the head of the left caudate nucleus: disorganization of speech and graphic expression, and disturbances in gestures (author's transl)[END_REF][START_REF] Cappa | Subcortical aphasia: two clinical-CT scan correlation studies[END_REF][START_REF] Damasio | Aphasia with nonhemorrhagic lesions in the basal ganglia and internal capsule[END_REF][START_REF] Demonet | Subcortical aphasia(s): a controversial and promising topic[END_REF][START_REF] Gronholm | Predominance of caudate nucleus lesions in acute ischaemic stroke patients with impairment in language and speech[END_REF][START_REF] Nadeau | Subcortical aphasia[END_REF], and patients with neurodegenerative diseases causing striatal dysfunction, i.e.

Huntington's and Parkinson's disease [START_REF] Douaud | Distribution of grey matter atrophy in Huntington's disease patients: a combined ROI-based and voxel-based morphometric study[END_REF][START_REF] Stoessl | Imaging insights into basal ganglia function, Parkinson's disease, and dystonia[END_REF]. In a series of verb conjugation tasks Ullman and colleagues [START_REF] Ullman | A neurocognitive perspective on language: the declarative/procedural model[END_REF][START_REF] Ullman | Is Broca's area part of a basal ganglia thalamocortical circuit?[END_REF][START_REF] Ullman | A Neural Dissociation within Language: Evidence that the Mental Dictionary Is Part of Declarative Memory, and that Grammatical Rules Are Processed by the Procedural System[END_REF] found that English speaking Huntington's Disease (HD) patients overregularize irregular verbs (e.g. *he runned instead of he ran) and produced doublesuffixations on regular verbs (e.g. walk-ed-ed). The authors interpret this deficit within a dichotomic model of language processing [START_REF] Pinker | How the mind works[END_REF], which consists of a 'mental lexicon' storing information, and a computational 'mental grammar' computing rules over stored abstract representations [START_REF] Nemeth | Language deficits in pre-symptomatic Huntington's disease: evidence from Hungarian[END_REF][START_REF] Ullman | Contributions of memory circuits to language: the declarative/procedural model[END_REF][START_REF] Ullman | Is Broca's area part of a basal ganglia thalamocortical circuit?[END_REF][START_REF] Ullman | A Neural Dissociation within Language: Evidence that the Mental Dictionary Is Part of Declarative Memory, and that Grammatical Rules Are Processed by the Procedural System[END_REF].

Based on patients' deficits, the authors localize the neural correlates of the model's components, attributing lexical processing to the medial temporal lobe network, and grammatical processing to the fronto-striatal circuits. HD patients would thus be specifically impaired with the processing of linguistic rules. Teichmann and colleagues conducted similar experiments with French patients testing them on the production of future tense forms of non-

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

6 existing (nonce) verbs [START_REF] Teichmann | The role of the striatum in rule application: the model of Huntington's disease at early stage[END_REF][START_REF] Teichmann | Language processing within the striatum: evidence from a PET correlation study in Huntington's disease[END_REF]. French has two regular patterns for the formation of the future tense: a frequent default pattern (first conjugation, e.g. manger-mangera) and a less frequent, non-default pattern (second and third conjugation, e.g. dormir-dormira), also called 'subregular'. In addition, like English, French also has a variety of highly restricted irregular alternatives (e.g. venir-viendra). The authors found that HD patients over-applied the most frequent rule to items belonging to the less frequent conjugation (e.g. saurentir -*saurentera, instead of saurentira). The authors interpreted the results along Ullman's proposal. However, since the application of the default rule was spared in first conjugation verbs, they characterized the deficit in HD as being restricted to 'subregular' rules. In addition to this rule application learning deficit, De Diego-Balaguer and colleagues observed a rule-learning deficit in a comparable sample of early French Huntington's disease patients tested on the learning of a simplified artificial language where words and rules could be extracted [START_REF] Diego-Balaguer | Striatal degeneration impairs language learning: evidence from Huntington's disease[END_REF]. The authors also report results from pre-manifest carriers of the HD mutation, whose performance was not quantitatively different from the one of matched controls in the learning task, but who showed a qualitative difference in the level of abstractedness of the acquired rule.

Within the neuropsychological literature, other experimental results suggest that, rather than being recruited for rule learning and rule application, the striatum is needed at late processing stages requiring selection and inhibition between competing alternatives [START_REF] Copland | Brain activity during automatic semantic priming revealed by eventrelated functional magnetic resonance imaging[END_REF][START_REF] Garcia | Action-semantic and syntactic deficits in subjects at risk for Huntington's disease[END_REF][START_REF] Longworth | The basal ganglia and rule-governed language use: evidence from vascular and degenerative conditions[END_REF][START_REF] Sambin | The role of the striatum in sentence processing: disentangling syntax from working memory in Huntington's disease[END_REF] and syntactic reanalysis [START_REF] Kotz | Syntactic language processing: ERP lesion data on the role of the basal ganglia[END_REF].

Neuroimaging studies of healthy subjects also provide data compatible with this alternative proposal. The left dorsal striatum in particular is activated in tasks requiring reanalysis of ambiguous or incorrect sentences (Friederici & Kotz, 2003;[START_REF] Mestres-Misse | An anterior-posterior gradient of cognitive control within the dorsomedial striatum[END_REF][START_REF] Moro | Syntax and the brain: disentangling grammar by selective anomalies[END_REF][START_REF] Tettamanti | Basal ganglia and language: phonology modulates dopaminergic release[END_REF]. A role of the striatum in M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT linguistic tasks requiring cognitive control also emerges from studies of bilingual speakers (Abutalebi et al., 2013;[START_REF] Crinion | Language control in the bilingual brain[END_REF][START_REF] Friederici | What's in control of language?[END_REF].

In sum, despite the wide variety of data showing an involvement of the striatum in language processing, its specific role remains unclear. Ullman's proposal that the striatum is recruited for the computation of grammatical rules is challenged by French HD data, showing rather that only certain rules are affected by striatal atrophy, and by the large body of data showing that the striatum is implicated in syntactic reanalysis and in the inhibition of competing alternatives. Moreover, the dichotomist distinction between regular and irregular morphological processes underlying Ullman's and Teichmann's proposals has been questioned in the morphological literature by proposals of unified systems subsuming both processes [START_REF] Albright | Rules vs. analogy in English past tenses: a computational/experimental study[END_REF][START_REF] Meunier | Regularity and irregularity in French verbal inflection[END_REF][START_REF] Plunkett | From rote learning to system building: acquiring verb morphology in children and connectionist nets[END_REF][START_REF] Rumelhart | Parallel distributed processing : explorations in the microstructure of cognition[END_REF].

In this paper we propose that in order to identify the specific role of the striatum in language processing it is necessary to consider an alternative to the proposals sketched above. More precisely, it is necessary to consider that the striatum plays a more general role in linguistic processing, akin to the role it plays in other cognitive domains, such as motor control, attention, planning and decision-making [START_REF] Alexander | Parallel organization of functionally segregated circuits linking basal ganglia and cortex[END_REF][START_REF] O'doherty | Dissociable roles of ventral and dorsal striatum in instrumental conditioning[END_REF]. Results obtained from neurophysiology and neuroimaging suggest that this structure filters cortical information to drive decision-making. Specifically, the striatum, and particularly its dorsal parts (caudate nucleus and putamen), plays a key role in the 'action selection' process [START_REF] Kable | The neurobiology of decision: consensus and controversy[END_REF][START_REF] Montague | Neural economics and the biological substrates of valuation[END_REF][START_REF] Rangel | A framework for studying the neurobiology of value-based decision making[END_REF], by weighting the values assigned to the different options made available by the prefrontal cortex [START_REF] Hare | Dissociating the role of the orbitofrontal cortex and the striatum in the computation of goal values and prediction errors[END_REF][START_REF] Padoa-Schioppa | The representation of economic value in the orbitofrontal cortex is invariant for changes of menu[END_REF].

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In the domain of linguistic theory, this decomposition of the decision process into value assignment and selection exhibits strong analogies with the processes assumed within the framework of Optimality Theory (OT) (Prince & Smolensky, 1993/2004). OT divides speech production into two components. The evaluation component assigns wellformedness values to possible spoken outputs given an underlying lexical input. The selection component selects the optimal output on the basis of these values, like action selection. According to OT, optimization is a general organizing principle underlying neural computation that can be adapted to the theory of language. Whereas evaluation is dependent on language-specific grammatical constraints, the operations of the selection component can be viewed as domaingeneral, analogous to those involved in non-linguistic selection.

Here, we use OT as it provides us with the framework allowing us to assess whether the role of the striatum in linguistic processing is analogous to its role outside of language.

Specifically, we hypothesize that the striatum is recruited for the selection of linguistic alternatives, as for the selection of motor and other programs. To test this hypothesis we studied patients with HD, as this inherited neurodegenerative disease is a good model of striatal lesion in its early stages [START_REF] Douaud | Distribution of grey matter atrophy in Huntington's disease patients: a combined ROI-based and voxel-based morphometric study[END_REF][START_REF] Tabrizi | Biological and clinical manifestations of Huntington's disease in the longitudinal TRACK-HD study: cross-sectional analysis of baseline data[END_REF][START_REF] Vonsattel | Neuropathological classification of Huntington's disease[END_REF]. We independently validated our HD population as an appropriate model of patients with striatal lesions, by comparing structural brain atrophy in these patients and a population of healthy matched controls, by voxel-based morphometry (VBM).

The linguistic tasks previously used to reveal a role of the striatum in language processing do not allow us to test our hypothesis. Tasks involving verbal conjugation in English and French (e.g. Today he walks, yesterday he … walked) [START_REF] Teichmann | The role of the striatum in rule application: the model of Huntington's disease at early stage[END_REF][START_REF] Teichmann | Language processing within the striatum: evidence from a PET correlation study in Huntington's disease[END_REF][START_REF] Ullman | A Neural Dissociation within Language: Evidence that the Mental Dictionary Is Part of Declarative Memory, and that Grammatical Rules Are Processed by the Procedural System[END_REF] are not suited to test the selection process, as a limited number of alternatives is available (i.e. English past tense: regular vs. irregular; French future tense: regular, 'subregular', irregular). In addition to being very few in number, the alternatives

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within the set are not comparable with each other as some are regular alternations undergone by a large set of lexical items and others are irregular, i.e. lexically very restricted. Tasks involving syntactic reanalysis or lexical inhibition are in principle better suited to test linguistic selection processes. However, these tasks are not standardly modeled within OT and thus the relative contribution of the selection and the evaluation component is hard to assess.

We therefore set out to design a new task which could be modeled within OT, and in which several comparable linguistic alternatives must be evaluated before selection. To assess whether the striatum holds a role in evaluation or in selection processes, we compared the performance of HD patients in this task with that of matched controls.

The grammar of French adjectives is the ideal paradigm to test linguistic selection. Unlike in English, where gender differences are not pronounced (compare small-FEMININE (FEM) and small-MASCULINE (MASC)), in French adjectives take on different forms depending on their gender (compare sportive-FEM and sportif-MASC 'athletic'). There are four common patterns of alternation, Fig. 1A. These patterns are regular and instantiated by a large number of items in the French lexicon. This allows investigating the role of the striatum in evaluation and selection without the confounding distinction between regular, subregular and irregular morphological processes. We designed an elicitation task, in which participants were given the feminine form of a nonce adjective, and had to produce the corresponding masculine. The feminine form was provided, as it is the underlying form of the adjective, i.e. the form from which the masculine is derived.

The task requires grammatical knowledge about the four patterns and about their respective wellformedness values in different linguistic contexts (evaluation). It also requires selecting among these patterns, to produce the one with the highest value (selection).

If the evaluation process is impaired, patient should produce responses incompatible with the underlying grammar of control participants. More specifically, patients' responses should be

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10 the outputs of a grammar in which constraints are ranked differently than those in the grammar of controls, and thus evaluated differently. By contrast, if the selection process is impaired, they should produce a response patterns should be very similar to those of the controls -i.e. evaluated by the same language-specific constraint ranking, but with increased randomness, with a more frequent selection of non-optimal alternatives.

To determine the specific function of the striatum in language, we instantiated computational models of both evaluation and selection deficits using OT. We modeled the French adjective system within Maximum Entropy Harmonic Grammar (MaxEntHG [START_REF] Goldwater | Learning OT constraint rankings using a maximum entropy model[END_REF][START_REF] Hayes | A Maximum Entropy Model of Phonotactics and Phonotactic Learning[END_REF]), a probabilistic variant of OT, and trained our model on the data from our population of healthy controls. The computational model was then 'impaired' in two ways to test our hypothesis. One impairment model simulated a grammatical deficit, introducing noise in the constraint-based evaluation process [START_REF] Goldrick | Linking speech errors and phonological grammars: Insights from Harmonic Grammar networks[END_REF]. The other model simulated a selection deficit by increasing randomness in the selection process [START_REF] Palminteri | Critical roles for anterior insula and dorsal striatum in punishment-based avoidance learning[END_REF], i.e. by selectively attenuating the signaling of the possible outcomes.

Computational modeling allows to refine our hypotheses and to directly test their predictions.

If patients' impairment is in the evaluation process, we expect the model simulating a grammatical deficit to provide a better fit to the data produced by the patients. On the contrary, if their impairment is in the selection process, we expect the model simulating a selection deficit to provide a better fit to their data.

Additionally, we used VBM to assess whether the linguistic deficit in HD patients was correlated with striatal atrophy. All patients were evaluated with the UHDRS, which includes the Verbal Letter Fluency test [START_REF] Cardebat | Formal and semantic lexical evocation in normal subjects. Performance and dynamics of production as a function of sex, age and educational level[END_REF], the Trial-Making Test A and B (TMT A and B) [START_REF] Tombaugh | Trail Making test A and B: Normative Data Stratified by Age and Education[END_REF], the Symbol Digit Modalities Test (SDMT [START_REF] Wechsler | Wechsler adult intelligence scale -revised manual[END_REF]) and the Stroop interference test [START_REF] Golden | Stroop color and word test[END_REF]. Patients also completed the Mattis Dementia

MATERIAL AND METHODS

Participants

Rating Scale (MDRS [START_REF] Mattis | Mental status examination for organic mental syndrome in the elderly patient[END_REF]. 2004) Table 1 Demographic and genetic information for HD patients, demographic data for controls, and results from the neurological and neuropsychological assessments of HD patients

Behavioral task

Stimuli and procedure. Stimuli belonged to the four common alternation patterns present in the French lexicon (type frequency >100 per million [START_REF] Bybee | Regular morphology and the lexicon[END_REF][START_REF] New | Une base de données lexicales du français contemporain sur internet: LEXIQUE[END_REF])) (alternatives 1-4 in Fig. 1A). The token frequency of the different patterns is Responses that matched the expected form were coded as correct; all other responses were coded as incorrect. For one of the eleven feminine ending types, "-te", two masculine responses were coded as correct, i. Aberrant (e.g. derer), (Fig. 1C).

Data analysis. R package lme4 [START_REF] Bates | Fitting Linear Mixed-Effects Models Using lme4[END_REF] [START_REF] Ashburner | Unified segmentation[END_REF]. GM segments for each subject were modulated using non-linear components of the normalization only, thereby preserving actual tissue values locally, to take individual brain size into account globally. Modulated, normalized GM segments were smoothed with a 6-mm FWHM Gaussian kernel.

A full factorial design model assessed group differences in GM volume between control and HD patients with group as main factor and age as covariate. An average GM mask was created from the normalized GM segments of the twenty-five healthy controls, thresholded at a value of 0.20 (voxels with > 20% GM fraction values). This mask was used to restrict statistical comparisons to the GM. Results were corrected for multiple comparisons using (http://cnl.web.arizona.edu/mricro.htm). A binary mask was created by pooling the significant clusters in this group analysis, representing the areas of GM atrophy in HD patients (Fig. 3A andB). This mask was used for subsequent correlation analyses with behavioral data.

Correlations between behavioral data and GM atrophy

Correlation analyses within the GM mask. A multiple regression analysis explored the correlation between linguistic performance and whole brain GM volumes in HD patients, with education level as covariate. Statistical outcomes were observed with corrected p-values inferior to 0.05 using Family-Wise Error (FWE) and a minimum of 25 voxels per cluster.

Correlation analyses within the mask of GM atrophy in HD patients. A multiple regression

analysis explored the correlation between linguistic performance and GM volumes in HD patients, restricted to regions showing atrophy in HD patients in comparison with controls, with education level as covariate. Statistical outcomes were observed with corrected p-values inferior to 0.05 using Family-Wise Error (FWE) and a minimum of 25 voxels per cluster.

The same analyses were conducted to investigate the correlation between GM volume and clinical scores (Stroop interference, SDMT, UHDRS motor score and disease burden score [START_REF] Penney | CAG repeat number governs the development rate of pathology in Huntington's disease[END_REF]).

Correlation analyses with mean probability of GM in five striatal ROIs. The striatum was manually segmented into five bilateral a priori anatomical masks (caudate body, caudate head, anterior putamen, posterior putamen and ventral striatum, including the nucleus

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accumbens). ROIs were defined for each hemisphere with MRIcro applied to the singlesubject T1 template of SPM8 software as follows: The ventral striatum comprises all striatal voxels in which the demarcation between caudate and putamen is not visible; the anterior and posterior putamen comprise the putaminal voxels with 'y' coordinates higher and lower than zero, respectively; the caudate head and body comprise the caudate voxels with 'y' coordinates higher and lower than zero, respectively [START_REF] Douaud | Distribution of grey matter atrophy in Huntington's disease patients: a combined ROI-based and voxel-based morphometric study[END_REF]. The mean probabilities of GM found in these ROIs were extracted. Multiple linear regression analyses assessed the association of performance in the linguistic task with mean probability of GM in each bilateral striatal ROI, for all HD patients. Education level was used as covariate. Results were Bonferroni-corrected.

Computational modeling

Baseline model. The modeling process began with a phonological analysis of the French adjective system in MaxEntHG. In MaxEntHG, speech production consists of an evaluation stage and a selection stage. The evaluation stage begins with an input lexical representation (here, the feminine form of the adjective) and a small number of possible output pronunciations (potential masculine forms). Each input-output mapping is assessed by constraints. There are two types of constraints: faithfulness constraints, according to which the input should be similar to output, and markedness constraints, according to which the output should be simple to produce and to perceive. Constraints are associated with weights and the harmony of a mapping is the weighted sum of its constraint violations. Thus, the evaluation stage involves the assignment of harmony values to every possible mapping: In the selection stage, a particular output is selected with a probability proportional to its harmony:

Harmony(i, o j ) = å k w k •C k (i, o j ), where [1]
Pr(o j | i) = exp(Harmony(i, o j ))/Z i , where [2]
Z i = å j' exp(Harmony(i, o j' )) (a normalizing constant)

Thus, for a given constraint set and a given set of weights, Equation [2] predicts a probability distribution over all outputs for each input.

The analysis involved choosing constraints that could yield the French adjectival system. We used eight standard phonological constraints. The optimal weights for a given set of data were determined by maximizing the likelihood of the data, according to Equation [2] (assuming independence). The optimum was identified by gradient ascent, using the BFGS_B method in NumPy [START_REF] Byrd | A limited memory algorithm for bound constrained optimization[END_REF] We derived two classes of deficit models from these equations. In the evaluation deficit model, a speaker s is assumed to differ from the baseline model by the addition of a constant noise vector η s drawn from a zero-centered Gaussian distribution with standard deviation η.

Evaluation deficit

Harmony s (i,

o j ) = (w base + η s )• C(i, o j ) [3]
In the selection deficit model, a speaker s is assumed to differ from the baseline model in that the harmony is multiplied by a constant weakening factor λ s , drawn from a uniform

distribution over the interval [a, b], 0 ≤ a ≤ b ≤ 1. Selection deficit Pr s (o j | i) = exp(λ s • Harmony(i, o j ))/Z i [4]
Thus, the evaluation deficit model has the 'noise level' η as a free parameter, and the selection deficit model has the 'weakening level' λ as a free parameter.

Simulation. Monte-Carlo method was used to derive predictions from a stochastic theory by explicitly simulating the stochastic process repeatedly. A run R proceeded as follows. First, thirty copies of the control grammar were produced (matched to the number of HD patients).

Each copy was then perturbed according to the selection deficit or evaluation deficit above. The deficit models were assessed by determining which one assigned higher probability to the data. On individual runs, either the evaluation or the selection deficit model might assign higher data likelihood, indicating that the ability to account for the data was not baked into either. Nonetheless, the selection deficit model provided a better fit to the data on an average run, indicating it is a closer match to HD patients' speech production process.

RESULTS

Behavioral results

HD patients performed worse than controls (76.4% and 89.9% accuracy, respectively [F 1, 58 =4.77, P<0.05]).

merive [məʀiv] meri [məʀi] merin [məʀɛ ] merif [məʀif] merta [məʀta]
Table 2 Distribution of participants' responses for each alternation. Lines correspond to the different feminine ending types. Columns correspond to the alternation pattern used by participants to produce the masculine form. Shaded cells correspond to responses coded as 'correct', non-shaded cells correspond to cells coded as errors (for the ending type "-te" see the stimuli description in the Material and Methods section). Numbers in each line correspond to percentages out of the total number of responses, across participants (Controls, left and HD patients, right). Feminine and masculine forms are provided according to the French orthography (in italics) and according to the International Phonetic Alphabet (IPA) (in square brackets), which correspond to the actual pronunciation of the form.

As Figure 2 shows, HD patients followed the same response pattern as Controls, but more noisily. We found an interaction between subject group and error type [F 4, 232 [START_REF] New | Une base de données lexicales du français contemporain sur internet: LEXIQUE[END_REF], than a Use-if error (e.g. nurfale -nurfif), where the Useif alternation is less frequent in the French lexicon (token frequency=0.83 per million words).

Second, HD patients perseverated more than controls. A perseverative error was defined as an error due to the erroneous application of the same alternation pattern as the one given in the previous two trials (HD patients: mean=5.3, controls: mean=3.8, P<0.05). These perseverations were not due to the fact that randomization yielded a greater number of consecutive trials in HD patients than in controls. In fact the difference between then two groups was restricted to perseveration errors but there was no difference between groups for correct consecutive responses of the same type (HD patients: mean=4.13, controls: mean=4.03, P=0.7).

---Figure 2 values for 2 min for the 3 letters P, R and V; f [START_REF] Golden | Stroop color and word test[END_REF], color/words; g Wechsler (1981);

h [START_REF] Tombaugh | Trail Making test A and B: Normative Data Stratified by Age and Education[END_REF]

Brain damage delineation

The between-group VBM analysis revealed reduced GM volume in HD patients as compared to healthy controls, in the basal ganglia (caudate nucleus and putamen, bilaterally, and right globus pallidus) and the frontal cortex (precentral and orbital) (Fig. 3A, Table 4). No

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ACCEPTED MANUSCRIPT 24 significant increase in regional GM volume was found in HD patients relative to controls. A binary GM mask including significant clusters for this group effect (Controls vs. HD patients, CON>HD) was built (Fig. 3B) for subsequent analyses of correlations with behavioral data.

---Figure 3 4 Results of voxel-based analysis for assessing regional GM differences between controls and Huntington's Disease patients, with age as a covariate (FWE-corrected, p < 0.05). * indicates contiguous clusters. Only clusters larger than 50 contiguous voxels are reported.

Correlations between linguistic performance and GM atrophy

Multiple regression analyses explored the correlation between accuracy in the linguistic task and GM volume in the twenty-five HD patients who underwent structural MRI. Like the whole cohort, these patients responded less accurately than their matched controls (79.8% and 89.9% correct responses, respectively [F 1, 53 =4.11, P<0.05]). See Table 3 for correlation analyses with demographic and neuropsychological data.

Correlation analyses within the GM mask. In the correlation analysis on the whole brain, did no reveal any correlation between GM regions, cortically and subcortically, and accuracy in the linguistic task.

Correlation analyses within the mask of GM atrophy in HD patients. The analysis was restricted to the GM mask obtained from the between-group comparison (CON>HD, 3A and 3B). A positive correlation was found between accuracy in the linguistic task and GM volume Correlation analyses with mean probability of GM in five striatal ROIs. Among the five striatal regions of interest (ROIs) (Fig. 3D), accuracy in the linguistic task only correlated with the mean probability of GM in the caudate heads and the caudate bodies (β=0.54, P<0.05 and β=0.52, P<0.04, respectively, Bonferroni-corrected, Fig. 3E). No neuropsychological or clinical score correlated with GM in the five ROIs, apart from the UHDRS motor score, which negatively correlated with caudate head (β=-0.51, P<0.05), anterior putamen (β=-0.59, P<0.01) and ventral striatum (β=-0.66, P<0.01).

Computational results

There was a linear relationship between the log frequency of HD patients' responses and the responses of controls for the same feminine-masculine adjective pair (R 2 =0.87). This suggests that a log-linear model is suited to model the alternation, since in log-linear models the probability of generating an item is proportional to the exponential of some score function. As the correlation is quite strong in the log domain, it suggests that the score function for HD patients is 'close' to the score function for controls, i.e. HD can be understood as applying some simple transform to the score function. Since in the field of morpho-phonology, a log- We first determined the constraint weights of the baseline model by maximizing the likelihood of the aggregated production data for the control population. We then derived two classes of deficit models from the baseline model. In the evaluation deficit model, a speaker s is assumed to differ from the baseline model by the addition of a constant noise vector η s . In the selection deficit model, a speaker s is assumed to differ from the baseline model in that the harmony is multiplied by a constant weakening factor λ s . The 'best' values for η and λ were determined empirically by trying a variety of values. The values which assigned the greatest likelihood on average to the HD patient data were η = 0.9 and λ = 0.6.

Monte-Carlo method was used to derive predictions from a stochastic theory by explicitly simulating the stochastic process repeatedly. One thousand runs were conducted with each deficit model. Outputs from each speaker s within the run were aggregated and the log probability of each run was determined. Results show that the selection deficit model accounts significantly better for the data (mean log likelihood -3867.81, median -3864.53; heteroscedastic t-test t 1005 = -22.27, P < 0.001) than the evaluation deficit model (mean log likelihood -3909.08, median -3902.66).

DISCUSSION

We investigated the mechanisms underlying language impairment in patients with striatal lesions, using HD as a model. Moving beyond phenomenological descriptions of the impairment, we used behavioral, imaging and modeling methods to investigate the

M A N U S C R I P T A C C E P T E D
computational mechanisms of language processing. This approach allowed us to test a new hypothesis of the role of the striatum in language and, thus, to propose a new theory of the source of language impairment in striatal lesions.

Patients with early HD performed worse than their matched controls in the linguistic task.

Their accuracy (76.4%) was comparable to the one reported by previous studies testing morphological abilities in these patients (e.g. ca. 75% in [START_REF] Teichmann | The role of the striatum in processing language rules: evidence from word perception in Huntington's disease[END_REF]). This poor performance was associated with reduced striatal volume, as revealed by the VBM analysis. Patients produced errors falling in the four standard patterns for French adjectives. This response pattern was qualitatively similar to the one of control participants. Quantitatively, however, it was different, in that the number of selected nonoptimal alternatives was higher. Our behavioral result thus indicates that the core grammatical component responsible for generating the possible masculine outputs is spared in HD patients.

The observed similarity between the two response patterns is problematic for theories assigning the striatum a role in the computation of linguistic rules [START_REF] Nemeth | Language deficits in pre-symptomatic Huntington's disease: evidence from Hungarian[END_REF][START_REF] Teichmann | The role of the striatum in processing language rules: evidence from word perception in Huntington's disease[END_REF][START_REF] Teichmann | The role of the striatum in rule application: the model of Huntington's disease at early stage[END_REF][START_REF] Teichmann | Language processing within the striatum: evidence from a PET correlation study in Huntington's disease[END_REF][START_REF] Ullman | Is Broca's area part of a basal ganglia thalamocortical circuit?[END_REF][START_REF] Ullman | A Neural Dissociation within Language: Evidence that the Mental Dictionary Is Part of Declarative Memory, and that Grammatical Rules Are Processed by the Procedural System[END_REF]. If HD patients had a core grammatical deficit, we would expect them to produce responses that are incompatible with the grammar of French (i.e. responses of the type Aberrant), contrary to fact.

Our computational analysis using MaxEntHG sheds light on the specific nature of the deficit in HD. Provided that the chosen computational model and its parameters are accurate abstractions of language production mechanisms in humans, these modeling results support the hypothesis that the language deficits observed in patients are caused by a selection deficit rather than by an impairment of underlying grammatical knowledge. We showed that the noisier distribution of responses following striatal damage can be captured specifically, by introducing randomness in the selection process (simulated by the selection deficit model). By Our modeling results are consistent with the notion that, even in language processing, the striatum is responsible for processing the outcomes of the evaluation component, to favor the more frequent selection of the best option, as suggested in studies of reinforcement and punishment learning [START_REF] O'doherty | Dissociable roles of ventral and dorsal striatum in instrumental conditioning[END_REF][START_REF] Palminteri | Critical roles for anterior insula and dorsal striatum in punishment-based avoidance learning[END_REF].

OT allows us to disentangle two distinct processes occurring during language processing: grammatical evaluation and selection. We now are now able to unveil the mechanisms giving rise to apparently incongruent results collected with HD patients tested on morphological tasks [START_REF] Nemeth | Language deficits in pre-symptomatic Huntington's disease: evidence from Hungarian[END_REF][START_REF] Teichmann | The role of the striatum in processing language rules: evidence from word perception in Huntington's disease[END_REF][START_REF] Teichmann | The role of the striatum in rule application: the model of Huntington's disease at early stage[END_REF][START_REF] Teichmann | Language processing within the striatum: evidence from a PET correlation study in Huntington's disease[END_REF][START_REF] Ullman | Is Broca's area part of a basal ganglia thalamocortical circuit?[END_REF][START_REF] Ullman | A Neural Dissociation within Language: Evidence that the Mental Dictionary Is Part of Declarative Memory, and that Grammatical Rules Are Processed by the Procedural System[END_REF]. In fact, the error pattern induced by a selection deficit will depend on the specific properties of the morphological paradigm used to test patients. In English, for instance, there is only one default regular alternation for the past tense. Since the irregular patterns in English are not comparable in their frequency and in their scope to this one regular alternative [START_REF] Albright | Rules vs. analogy in English past tenses: a computational/experimental study[END_REF], a selection deficit will result in an abnormal rate of selection of the -ed pattern. This is in line with what was observed by Ullman and colleagues [START_REF] Ullman | A Neural Dissociation within Language: Evidence that the Mental Dictionary Is Part of Declarative Memory, and that Grammatical Rules Are Processed by the Procedural System[END_REF]. More recently, Nemeth and colleagues observed a similar over-regularization pattern in pre-manifest HD subjects tested on the inflection of irregular nouns in Hungarian [START_REF] Nemeth | Language deficits in pre-symptomatic Huntington's disease: evidence from Hungarian[END_REF]. the most frequent one. In addition French also has a variety of highly restricted irregular alternatives [START_REF] Meunier | Regularity and irregularity in French verbal inflection[END_REF]) that have a low probability of being considered as part of the set of possible alternatives being considered for each given nonce verb. A patient with a selection deficit would most likely select the default alternative (i.e.

first conjugation) for items belonging to the less frequent conjugation class. HD patients will also produce the reverse error pattern -though to a lesser extent -i.e. they will select the less frequent alternative instead of the most frequent one. In fact, this is in line with the response pattern found by Teichmann and colleagues [START_REF] Teichmann | The role of the striatum in processing language rules: evidence from word perception in Huntington's disease[END_REF][START_REF] Teichmann | The role of the striatum in rule application: the model of Huntington's disease at early stage[END_REF][START_REF] Teichmann | Language processing within the striatum: evidence from a PET correlation study in Huntington's disease[END_REF].

Our paradigm, with four possible and equally regular alternatives, allows us to show that previously observed error patterns looked as if they were due to a grammatical deficit, because of the specific properties of the morphological paradigms. We could recover the mechanisms through which controls perform the task and compare them to the patients', because we have access to the error pattern of the control population. This was possible because our task was significantly harder than previously used tasks and did not yield ceiling performance in control subjects.

Recently it has been proposed that linguistic operations involving movement such as sequential and hierarchical processing in syntax or lexico-semantic mapping of movement in action verbs, are subserved by the frontostriatal network that coordinates motoric information [START_REF] Birba | Losing ground: Frontostriatal atrophy disrupts language embodiment in Parkinson's and Huntington's disease[END_REF]. Within this neuronal recycling framework [START_REF] Dehaene | Cultural recycling of cortical maps[END_REF], the different substructures of the striatum may play distinct roles in linguistic operations requiring movement, e.g. with the substantia nigra being involved in functional role assignment [START_REF] Garcia | Action-semantic and syntactic deficits in subjects at risk for Huntington's disease[END_REF]. In our study, we focused on a linguistic process -a morphological alternationwhich is not based on movement but on the evaluation and selection of linguistic alternatives and showed that it relies on the caudate.

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Our proposal that the striatum holds a role in the selection of linguistic alternatives provides a new framework to reconsider further previous findings of a striatal implication in a coherent way.

For instance, research on syntactic processing proposes that the striatum is recruited for syntactic reanalysis, for the resolution of ambiguities and for selecting references in the discourse [START_REF] Hinzen | A systematic linguistic profile of spontaneous narrative speech in pre-symptomatic and early stage Huntington's disease[END_REF][START_REF] Kotz | Syntactic language processing: ERP lesion data on the role of the basal ganglia[END_REF][START_REF] Mestres-Misse | An anterior-posterior gradient of cognitive control within the dorsomedial striatum[END_REF][START_REF] Sambin | The role of the striatum in sentence processing: disentangling syntax from working memory in Huntington's disease[END_REF]. In all of these studies, the role of the striatum can be reinterpreted as one pertaining to the selection of one among several syntactic parses. Similarly, in lexical processing the proposed role of the striatum in the inhibition among competing alternatives [START_REF] Copland | Brain activity during automatic semantic priming revealed by eventrelated functional magnetic resonance imaging[END_REF][START_REF] Garcia | Action-semantic and syntactic deficits in subjects at risk for Huntington's disease[END_REF][START_REF] Longworth | The basal ganglia and rule-governed language use: evidence from vascular and degenerative conditions[END_REF] can be restated as a role in the selection among alternatives. A selection deficit could also be at the origin of the rule-learning deficit observed in early HD patients [START_REF] Diego-Balaguer | Striatal degeneration impairs language learning: evidence from Huntington's disease[END_REF], since learning an artificial language requires not only the extraction of regularities from the speech stream, but also the selection of the abstract rule which best characterizes the language to be learned. Finally, our proposal can also account for neuroimaging studies of healthy subjects showing striatal activation in tasks requiring monitoring and controlling the language in use in bilingual speakers [START_REF] Crinion | Language control in the bilingual brain[END_REF][START_REF] Friederici | What's in control of language?[END_REF], as these tasks also involve selecting among several available linguistic constructions.

The correlation analysis within the five striatal subregions allowed us show that linguistic performance was not correlated indiscriminately with atrophy in any striatal region. Within the dorsal striatum, the correlation between GM atrophy and linguistic performance was statistically predominant in the caudate nucleus. This result is consistent with the fact that this striatal sub-territory receives projections from the lateral frontal cortex and Broca's area [START_REF] Alexander | Parallel organization of functionally segregated circuits linking basal ganglia and cortex[END_REF]. Atrophy in the caudate nuclei thus undermines the selection process The model used here is necessarily different from those adopted in, e.g., reinforcement learning studies (e.g. Q-learning models [START_REF] Sutton | Reinforcement Learning: An Introduction[END_REF])), because it was developed in the field of computational linguistics, which deals with very different objectives and modeling constraints. Despite these differences, comparisons across cognitive domains can be fruitfully established, provided equivalent parameters can be identified across the different models.

Specifically, the 'deficit' that can be captured by modifying the selection parameter λ of our linguistic MaxEntHG is computationally equivalent to the 'deficit' that can be introduced by modifying the choice randomness parameter in a punishment-learning model [START_REF] Palminteri | Critical roles for anterior insula and dorsal striatum in punishment-based avoidance learning[END_REF].

Within the broader perspective of the language network, the relationship between cortical language areas and the striatum is analogous to that identified in other domains, between cortical areas and structures of the basal ganglia. The striatum operates as a centralized selection mechanism choosing between alternative options which are assigned weight values in designated connected cortical areas [START_REF] Alexander | Parallel organization of functionally segregated circuits linking basal ganglia and cortex[END_REF][START_REF] Redgrave | The basal ganglia: a vertebrate solution to the selection problem?[END_REF], Fig. 4. For instance, in the motor domain, the putamen selects between weighted motor programs evaluated by connected cortical premotor areas [START_REF] Alexander | Parallel organization of functionally segregated circuits linking basal ganglia and cortex[END_REF][START_REF] O'doherty | Dissociable roles of ventral and dorsal striatum in instrumental conditioning[END_REF]. A different corticostriatal circuit is responsible for behavioral goals, that are weighted and assigned reward values in the orbito-frontal cortex and selected by the ventral striatum [START_REF] Hare | Dissociating the role of the orbitofrontal cortex and the striatum in the computation of goal values and prediction errors[END_REF][START_REF] Kable | The neurobiology of decision: consensus and controversy[END_REF][START_REF] Montague | Neural economics and the biological substrates of valuation[END_REF][START_REF] Padoa-Schioppa | The representation of economic value in the orbitofrontal cortex is invariant for changes of menu[END_REF][START_REF] Rangel | A framework for studying the neurobiology of value-based decision making[END_REF]. We propose that, through a parallel mechanism, linguistic alternatives evaluated in the left frontal and temporal cortices are selected within the caudate nucleus via the fiber tracts connecting these cortical areas with this subcortical structure. Broca's area (BA 44, 45) [START_REF] Draganski | Evidence for segregated and integrative connectivity patterns in the human Basal Ganglia[END_REF][START_REF] Ford | Broca's area and its striatal and thalamic connections: a diffusion-MRI tractography study[END_REF][START_REF] Lehericy | 3-D diffusion tensor axonal tracking shows distinct SMA and pre-SMA projections to the human striatum[END_REF][START_REF] Teichmann | A cortical-subcortical syntax pathway linking Broca's area and the striatum[END_REF]. Moreover, recent results on the modification of corticostriatal connections in HD have shown a decrease in bilateral connections from frontal areas to the dorsal striatum [START_REF] Marrakchi-Kacem | Mapping cortico-striatal connectivity onto the cortical surface: a new tractography-based approach to study Huntington disease[END_REF]. Among the degenerated connections are the ones linking the caudate nucleus with BA 44, 45 and 47. This degeneration may provide the basis for the language impairment observed in patients with early HD in the present study.

Recent reservoir computing models reflecting the contribution of frontal-striatal circuits in language processing [START_REF] Hinaut | Real-time parallel processing of grammatical structure in the fronto-striatal system: a recurrent network simulation study using reservoir computing[END_REF][START_REF] Szalisznyo | Corticostriatal language pathways dynamically adjust for syntactic complexity: A computational study[END_REF] have built on the brain connectivity literature to model the processing of complex syntactic structures and of thematic role assignment within a recurrent network of structurally segregated frontal-striatal circuits. Although both the computational models and the level of linguistic processing are very distinct from the focus of the present study, future research will have to explore to what extent the two lines of research make similar or different predictions -and test them both from a behavioral and from a computational perspective.

In addition, other brain regions, e.g. the anterior insula and the ventro-lateral prefrontal cortex have been reported to be involved in selection processes occurring post semantic retrieval, which resolve competition between simultaneously active representations. Activity in these areas was observed during the selection of words (e.g. in verb generation, confrontation naming, word recognition) or visual patterns [START_REF] Badre | Frontal lobe mechanisms that resolve proactive interference[END_REF], 2007;[START_REF] Bourguignon | The neural dynamics of competition resolution for language production in the prefrontal cortex[END_REF][START_REF] Kan | Selection from perceptual and conceptual representations[END_REF][START_REF] Thompson-Schill | Verb generation in patients with focal frontal lesions: a neuropsychological test of neuroimaging findings[END_REF]. The relative specificities of the different selection mechanisms and their possible connections remain to be elucidated.

Finally, we investigated here the mechanism by which a specific type of linguistic alternatives is selected. Given the generality of the selection mechanism, it seems likely that the dorsal striatum, particularly the caudate nucleus, plays a similar role for other language components.

F

  = female, M = male, R = right-handed, L = left-handed; a Number of CAG repeats in the Htt gene; b Diseaseburden score=age×(CAG length-35.5), Penney et al. (1997). c UHDRS= United Huntington Disease Rating Scale, TFC = total functional capacity score, Huntington Study Group (1996); *Normal values were obtained from: d Mattis (1976); e Cardebat et al. (1990) -values for 2 min for the 3 letters P, R and V; f Golden (1978), color/words; g Wechsler (1981); h Tombaugh (

Figure 1

 1 Figure 1 Description and model of the linguistic task. Model of the linguistic task with two

  e. Deletion and No change, since both alternation patterns are attested in the French lexicon for these feminine forms (compare e.g. petite-FEM [pətit]petit-MASC [pəti] 'small', and tacite-FEM [tasit] -tacite-MASC [tasit]), although the first one is much more frequent than the second one. As an example of how responses were coded, if the speaker heard deronne, the correct response, deron, would be considered to correspond to Nasalization, whereas the incorrect responses deronne, dero and derif would be coded as No change, Deletion, and Use -if errors, respectively; all other incorrect responses were coded as

  error (FWE-corrected, P<0.05). Anatomical labeling of significant clusters

i

  is the feminine form (the input) and o j is a possible pronunciation of the masculine form (the output) C k is the k th constraint, and C k (i, o j ) is the number of violations w k is the weight associated with C k

  . Constraint weights of the baseline model were determined from the aggregate production data of the control population. The baseline model thus represents the behavior of a typical speaker, as estimated from the outputs produced by control participants. Deficit models. It is convenient to write the evaluation and the selection steps in vector form, i.e. letting w base = [w 1 , w 2 , ...] and C(i, o j ) = [C 1 (i, o j ), C 2 (i, o j ), ...], where w base represents the weights of the baseline model, as estimated above: o j ) = w base • C(i, o j ) Selection Pr(o j | i) = exp(Harmony(i, o j ))/Z i

  Thus, every s models a typical speaker of French afflicted by either a selection deficit or an evaluation deficit. Within a run, every s has the same deficit. All thirty s's perform the same task as HD patients, generating masculine adjective forms from the feminine forms, according to the distributions generated by Eq.'s[1][2][3][4]. Outputs from each speaker s within the run are aggregated, yielding a sample from the predicted distribution (for the selection or evaluation on the run), with Fr R (o j | i) representing the total number of times the masculine form o j was produced for for feminine form i. The log probability of a run R is determined by Eq. [5]:L(R) = Σ (i,j) Fr R (o j | i) ln Pr HD (o j | i) [5]Conditional probabilities Pr HD (o j | i) in Eq. [5] are estimated from the HD patient data using add-one smoothing, e.g. Pr HD (o j | i) = (1+Fr HD (i, o j ))/(Σ k 1+Fr HD (i, o k )). The log probability of a run is a relative measure of how much the sample output distribution (selection or evaluation deficit) resembles the actual output distribution from HD patients. One thousand runs were conducted with each deficit model.

M

  =3.64, P<0.01], due to a combination of two factors, as shown by two post-hoc analyses. First, HD patients made errors concerning the most frequent alternation patterns in the French lexicon more frequently than controls [F 1, 177 =9.27, P<0.01]. For instance, HD patients were more likely to produce a Nasalization error (e.g. nurfale -nurfan), where the lexical token frequency is 4.4

Figure 2

 2 Figure 2 Behavioral responses. Response types provided by the subjects for the 5 feminine

  demographic data, clinical and cognitive assessment and genetic measurements, and the results of a Welch two-sample t-test for sex (degrees of freedom in parentheses). n.s. = nonsignificant (P>0.05); *P<0.05; **P<0.01; ***P<0.001. a UHDRS = United Huntington Disease Rating Scale, TFC = total functional capacity score, Huntington Study Group (1996); b Number of CAG repeats in the Htt gene; c Disease-burden score=age×(CAG length-35.5), Penney et al. (1997); d Mattis Dementia Rating Scale, Mattis (1976); e Cardebat et al. (1990) -

Figure 3

 3 Figure 3 Neural correlates of linguistic performance in Huntington's Disease using

  caudate nucleus of HD patients (FWE-corrected, P<0.05) (Fig.3C), but not in the frontal areas. Scores of executive function tests (SDMT and Stroop) did not correlate with GM volume within the striatum. The SDMT correlated with GM volume in the inferior orbitofrontal gyrus, bilaterally (FWE-corrected, P<0.05). Conversely, the UHDRS motor score correlated bilaterally with GM volume in both the putamen and the caudate nuclei, and the disease burden score was negatively correlated with GM volume in the right caudate nucleus (FWE-corrected, P<0.05).

  -based model called MaxEntHG already exists and many properties of the scoring function are understood, it was used to model the alternation. MaxEntHG allows one to separate the process of attributing values to masculine output options from the process of selecting amongst masculine outputs, by capturing them with different parameters.

  noise in the harmony calculation (simulated by the evaluation deficit model) yielded a poor fit to the patients' data.

  Irregular nouns in Hungarian belong to a very restricted class. Alternations within this class are therefore not comparable in terms of frequency and scope to the regular ones. Like in the English past tense paradigms, an incipient selection deficit in this population would thus more likely result in the erroneous selection of the regular alternative instead of the irregular one (i.e. over-regularization error), than the opposite error pattern. French, by contrast, has two regular alternations for the formation of the future tense (first conjugation and second/third conjugation). The default pattern is also

  domain. This impairment results in the more frequent selection of suboptimal outcomes (i.e. outcomes with low harmony scores) than in healthy controls.

Figure 4

 4 Figure 4 Schematic representation of evaluation and selection processes through

  observed parallelism between results from within and outside the domain of language raises questions about computational equivalence across domains. We are now in a position to address these questions.

Table 1

 1

	summarizes demographic and clinical data of

Table 2

 2

	illustrates the distribution of responses for each alternation
	included in the experiment.

Table 3

 3 ).

		Linguistic performance
	Whole cohort of HD patients	Subgroup of HD patients with	Controls

Table 3

 3 Results of the partial correlation analyses between linguistic performance and

ACKNOWLEDGMENTS

We thank A. Sliwinski, K. Youssov, L. Lemoine and G. Morgado (CIC) for help with patient assessment, L. Debernard for help with the preprocessing of MRI data, and A. Braatz for help with the drawing of Fig. 4.

FUNDING

This research was supported by: ANR (French Research Agency) grant ANR-11-JSH2-0006 (M.G. and Ch.J.); biomarker program NCT01412125 (Assistance Publique -Hôpitaux de Paris) (A.C.B.L.); Gis-maladies rares A04159JS (Centre de référence maladies rares -maladie de Huntington; Hôpital Henri Mondor, Créteil) (A.C.B.L); NeuroStemcell Consortium FP7 222943 (C.S.); ANR-11-INBS-0011 -NeurATRIS (C.S.); ATIP-Avenir starting grant (St.P.); ANR-10-LABX-0087 IEC and ANR-10-IDEX-0001-02 PSL grants (Département d'Etudes Cognitives of the Ecole Normale Supérieure).

Abutalebi, J., Della Rosa, P. A., Gonzaga, A. K., Keim, R., Costa, A., & Perani, D. (2013).

The role of the left putamen in multilingual language production. Brain Lang, 125(3), 307-315. doi:10.1016Lang, 125(3), 307-315. doi:10. /j.bandl.2012.03.009 .03.009

DECLARATION OF INTEREST

The authors declare no conflict of interest.