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In this study, we used a simulation of upcoming low-resolution visual neuroprostheses to evaluate the benefit of embedded computer vision techniques in a wayfinding task. We showed that augmenting the classical phosphene rendering with the basic structure of the environment -displaying the ground plane with a different level of brightness -increased both wayfinding performance and cognitive mapping. In spite of the low resolution of current and upcoming visual implants, the improvement of these cognitive functions may already be possible with embedded artificial vision algorithms.

I. INTRODUCTION

A. Visual neuroprosthesis

Visual neuroprosthesis and in particular retinal implants have been developed within the last decades to restore partial visual perception in blind people. In a retinal implant, an array of microelectrodes is attached to the retina. Ideally, each microelectrode can electrically elicit one visual percept in the form of a white or yellow dot called a phosphene. A maximum of 3 to 10 levels of brightness can be perceived when the intensity of the stimulation is modulated [1]. Since early in the development of visual prosthesis, several groups have been investigating the potential benefits from such implant via simulation. Even though Simulated Prosthetic Vision (SPV) systems cannot replace experiments with implantees, they are used to assess the functional capacities that could be restored with future implants (see e.g. [2]).

B. Navigation & Prosthetic vision

SPV studies have mostly focused on reading capabilities or object recognition while orientation or navigation have been less studied. The first study on this topic [3] used a narrow field of view (1.7°) and a very high resolution (625 phosphenes) that was relatively unrealistic but very stimulating for further studies. Following SPV studies have explored some aspects of mobility such as obstacle avoidance [START_REF] Dowling | human vision: The effects of spatial resolution and frame rate on Proceedings Active Media technology[END_REF] [START_REF] Barnes | and -viewpoint depth data in visually[END_REF] and to our knowledge, only one study has investigated the restoration of higher level functions such as wayfinding [8]. The main results of those studies on mobility were that the minimal number of phosphenes required to navigate with ease in an unknown environment is a few hundreds.

As a consequence, retinal implants recently introduced on the market, such as the Argus II (60 electrodes) from Second Sight Medical Products (Sylmar, California, USA), do not have a sufficient resolution to actively navigate in an unknown environment, and hence promote cognitive mapping. The more obvious solution would be to increase the array resolution but several technical problems are slowing down this evolution [START_REF] Picaud | prostheses: Clinical results and C[END_REF]. Waiting for higher resolution implants, another solution is to enhance the perception provided through low resolution implants with pertinent navigation cues selected in the environment. Most of the studies cited above aimed to enhance the contrast between phosphenes to highlight the structure of the environment or some obstacles located in front of the user. For instance, methods have been applied to automatically extract the ground plane in the camera image and highlight it in order to enhance contrast with the walls [START_REF]Annual International Conference of the IEEE[END_REF]. Similar methods were applied to all surface boundaries with more efficient algorithms [START_REF]vision using iso-Engineering in Medicine and Biology Society[END_REF]. Although the feasibility of realtime structure enhancement has been demonstrated, behavioral and cognitive benefits to the user have not been clearly addressed. In this study, we used SPV to realize a navigation task in an unknown virtual environment. We specifically assessed the improvement of wayfinding in relation to contrast enhancement of the visual scene. We also evaluated the quality of the maps that the subjects drew after navigation with standard vs. augmented environment renderings. The behavioral task was a game inspired by [START_REF] Merabet | [END_REF], which encourages subjects to navigate and memorize a mental map of the environment.

This study had two objectives: evaluate the wayfinding performance, and assess the quality of the cognitive mapping built during navigation in an unknown environment, both with a simulated low resolution visual implant.

II. METHODS

A. Subjects 12 subjects, (6 males and 6 females aged 23 to 39), participated in the experiment. Every participant had normal or corrected to normal vision. This experiment was conducted according to the ethical recommendations of the Declaration of Helsinki and was approved by a local ethical

Wayfinding with Simulated Prosthetic Vision: Performance comparison with regular and structure-enhanced renderings

Victor Vergnieux, Marc J.-M. Macé and Christophe Jouffrais committee (CLERIT) at the University of Toulouse. All subjects gave written informed consent to participate.

B. Protocol

The virtual environments were simple urban environments with medium size walls. We designed three environments containing seven segments defining three central blocks (see Fig. 1a). All the turns (3 to 5) and intersections (6) were 90° angles. In each environment, the corridors had a total length of 200 m, and the subject moved at the speed of 3 m/s. In order to equate the complexity among environments, the structure of the first one was scrambled to generate the second and third ones.

The subjects had to explore an unknown virtual maze to find and bring jewels back to the starting point (called . They had 5 minutes to collect 9 jewels in each environment. The subjects had the instruction to collect the jewels as fast as possible, and to memorize the environment in order to draw the corresponding map at the end of the game. To collect a jewel, the subject had to walk through it (the jewel was then picked up) and bring it back to the base (the jewel was then secured). In order to encourage subjects to memorize the spatial configuration of the environment, only 3 jewels could be carried at the same time. Hence they had to make at least 3 journeys in order to secure all 9 jewels. Three conditions were compared: two SPV conditions and one control condition (Fig. 1b). In the control condition, the subject saw the environment as originally displayed by the 3D engine. In the standard SPV rendering -called scoreboard (SB)-, the resolution of the camera image was reduced to 15*18 pixels and 4 levels of gray to match the resolution and color depth of the simulated implant. In the second SPV rendering -called augmented scoreboard rendering (ASB)-, the rendering was similar to SB but the ground was darkened to increase its contrast with the walls. Before playing the game, the subjects were trained to use each rendering by collecting 3 jewels in a very simple learning environment. They started the experiment when they declared being ready to do so. For each rendering condition (SB, ASB, Control), subjects played the game 3 times, in the same environment. The order of the three conditions and the condition/environment associations were counterbalanced across subjects. After completing each condition (block of three games), they had to draw the corresponding map, including the configuration of the corridors, and the location of the base and jewels. Subjects were previously informed that they will be asked to draw the map at the end of the game.

After completing the whole protocol, participants were invited to fill in a form with 5 main questions (on 7-points Likert scales). In this form, they had to evaluate the pleasure and difficulty to play the game with each rendering. They used the same scale to mention if the renderings were usable and provided enough information to complete the task. They finally quoted their own frequency of videogame playing.

C. Material

The virtual environment (VE) was displayed via a head mounted display (HMD) (NVisor SX-60 HMD, NVIS Inc., Reston, USA) with a resolution of 1280*1024 pixels and 44*34 degrees of visual angle. The orientation of the virtual camera was attached to the orientation of the head with a motion capture system (OptiTrack, Natural Point, USA). As a result, subjects could look around in the VE when moving the head. As subjects were seating, they could not rotate their body and rotation was provided in the VE using the left and right arrow keys of a keyboard. The virtual environments were generated and animated using the open source Irrlicht 3D Engine (v1.8). A basic audio feedback was provided with step sounds and a wall bump sound.

The different renderings were displayed in the HMD with a home-made SPV system. The simulated array had a resolution of 15*18 electrodes, which corresponds to the intended resolution of the next generation of implants (e.g. Second Sight Argus III). The phosphene array covered 9*9 degrees of visual angle. A typical dropout rate of 10% was used to simulate the electrodes that did not elicit any phosphene. The phosphene appearance was based on observation during clinical trials [1]. They were circular dots with a Gaussian luminance profile displayed on a greyscale with 4 levels. Further details about the system are available in [START_REF] Denis | Proceedings of the 2013 Conference on Human Factors in Computing Systems (CHI 2013)[END_REF].

D. Data and statistical analysis

As described before, the aim of the game was to secure 9 jewels within 5 minutes. If the 9 jewels were retrieved and secured before the end of the timer, elapsed time was recorded. If less than 9 jewels were secured at the end of the 5 minutes, the number of jewels was recorded. We then computed a performance index which was the average of 2 percentages:

Percentage of jewels secured.

Percentage of remaining time: percentage of 100% was granted for the minimum time needed to capture the 9 jewels (computed for each environment); and percentage of 0% was granted if the timer ended before bringing back the 9 jewels. Hence, a performance index of 50% meant that the subject had collected the 9 jewels in exactly 5 minutes. A lower performance index meant a failure in securing all the jewels in 5 minutes. A performance index higher than 50% meant that the subject succeeded in bringing back all the jewels, and in less than 5 minutes. We used the R software (v3.0.1) for statistics. Because the data did not follow a normal distribution, we used Wilcoxon tests for all comparisons (paired data). Statistical significance was set to p<0.05, and adjusted with a Bonferroni correction when needed.

III. RESULTS

A. Quantitative results

With the SB rendering, the number of secured jewels was only 5.2 (SD=2.3) in average, and hence significantly inferior (Z=4.4, p<0.001) to the average number of secured jewels with the ASB rendering (7.3 ±2.3) (see Fig. 2). Likewise, average game duration was significantly higher (Z=3.8, p<0.001) with the SB rendering (295 ±21s) than with the ASB rendering (265 ±47s). Accordingly, the performance index (PI) significantly differs (Z=4.6, p<0.001) between the SB rendering (30.5% ±16.7) and the ASB rendering (51.2% ±24.2). The averaged PI in the control condition (81.5% ±16.5) was significantly higher than the PI in both SPV conditions (SB: Z=5.2, p<0.001; and ASB: Z=5.0, p<0.001). Three judges were asked to evaluate the quality of the maps of the environment that the subjects drew after each condition. The judges were not involved in the experiment, and were not informed about the objectives. They were instructed to evaluate the similarity between each drawing and the real map of the environment without considering distance distortion. They could mark the drawings between 0 (drawing and map completely different) and 10 (drawing and map perfectly consistent). Examples of drawings are shown in Fig. 3.

The mean drawing score for the SB condition was 2.7 (SD=2.3) and was significantly lower than the mean drawing score for the ASB condition (4.9 ±3.1; Z=3.1, p<0.01). The mean drawing score for the control condition (7.8 ±1.7) was significantly higher than the score of both SPV conditions (SB: Z=5.7, p<0.001, and ASB: Z=4.5, p<0.001). No statistical difference was found between the three environment configurations shown in Fig. 1a. B. Qualitative Results 1) Questionnaire 11 out of 12 subjects evaluated the task easier and more pleasant with the ASB rendering than with the SB rendering. The same proportion of subjects granted the ASB rendering to be more usable than the SB rendering. 10 subjects reported that the ASB rendering was providing enough information to complete the task. Only 3 subjects had the same opinion about the SB rendering.

The 2 subjects with the best ASB performance index were the only ones who not play video games at all were the 4 subjects with the worst performance indexes with the ASB and the SB rendering.

IV. DISCUSSION

In this experiment, we assessed the ability to navigate and build a mental representation of the travelled environment with two different simulated phosphene renderings. These renderings correspond to low resolution implants that will soon be evaluated within clinical trials.

We first observed that the control rendering provided the subjects with enough landmarks and spatial cues to complete the game and draw a consistent map of the environment. We then observed that the subjects were not able to complete the game with the standard (SB) rendering. Despite a strong contrast between the sky and the walls (see Fig. 1), they were unable to bring all the jewels back to the base, nor draw a map of the explored environment. In comparison, the ASB rendering brought very crude additional cues concerning the path (only the floor plane was rendered differently), but these cues were sufficient to complete both tasks more quickly and accurately. In average, subjects brought back 40% more jewels in ASB condition than in SB condition and their drawings of the environment received scores 80% higher. These large differences between the two conditions may be explained by a combination of factors. The first explanation is related to spatial updating which is necessary own displacements. When subjects were virtually walking in a corridor, or turning around, the enhanced floor cues were probably useful to better estimate self-motions. A second explanation could be related to the better detection and understanding of intersections and turns in the ASB condition, which could then be used as reliable landmarks to navigate towards the different parts of the maze but also to build a reliable mental representation of the environment [START_REF]elopment of spatial representations of large-Advances in Child Development and Behavior[END_REF].

The task used in this experiment is relatively different from the mobility task used in previous SPV studies. Most of them were performed in indoor environments and focused on detecting doors or obstacles in tasks that are closer to mobility than wayfinding (e.g. [START_REF] Dowling | human vision: The effects of spatial resolution and frame rate on Proceedings Active Media technology[END_REF]). Here, the cognitive functions that were improved during wayfinding in a virtual outdoor environment were related to path integration, selforientation and cognitive mapping. This would be a realistic solution to help people with visual implants navigate actively and independently.

A limitation of this study is that the designed environments and the interaction techniques (keyboard) are very similar to those encountered in videogames, which may favored the gamers. Although it does not change the observation that augmented rendering improves cognitive functions, it may be useful to address this issue. The solution may be to adopt a whole body interaction technique in order to move in the virtual environment, or to perform this experiment in a real outdoor environment with a mobile SPV.

V. CONCLUSION

In this SPV experiment, we obtained two main results. First, we confirmed the plausibility to actively explore an unknown environment with the upcoming generation of lowresolution retinal implants (15*18 electrodes). However, wayfinding and cognitive mapping will probably still be problematic with standard rendering. Embedded real-time artificial vision methods that are currently available can provide crude but useful cues about the environment. We showed that such a simple and realistic cue -augmented contrasts between the floor and the walls-would improve orientation, wayfinding and cognitive mapping.

More generally, we suggest that enhancing the low resolution rendering of visual implants with specific cues such as landmarks, obstacles ( [START_REF] Dowling | human vision: The effects of spatial resolution and frame rate on Proceedings Active Media technology[END_REF]) or waypoints will be useful for restoring the autonomy of implanted patients. To increase further the usability of the system, we could think of a computer vision-based system that would detect other types of objects in the environment such as faces, blocks of text [START_REF] Denis | Vision Engineering in Medicine and Biology Society (EMBC)[END_REF], etc., with a specific interaction technique to switch between these different detection modes.

Figure 1 .

 1 Figure 1. a. Environment maps: start base and jewels are indicated in yellow and blue respectively. The arrow represents the subject orientation at the beginning of the task. b. Samples of the three rendering conditions used in this study.

Figure 2 .

 2 Figure 2. Performance index per condition: Scoreboard (SB), Augmented Scoreboard (ASB), and Control condition. Mean number of secured jewels in each condition is written in white within the columns. Error bars are IC95.

Figure 3 .

 3 Figure 3. Left: Map and drawing examples (from different subjects) a. Map of environment #1; b. Drawing after SB condition; c. after ASB condition; d. after Control condition. Right: Mean drawing scores per condition (n=12 subjects). Error bars are IC95.


Carlos Canal

Gwen Salaün

Model-Based Adaptation of Software Communicating via FIFO Buffers

Software Adaptation is a non-intrusive solution for composing black-box components or services (peers) whose individual functionality is as required for the new system, but that present interface mismatch, which leads to deadlock or other undesirable behaviour when combined. Adaptation techniques aim at automatically generating new components called adapters. All the interactions among peers pass through the adapter, which acts as an orchestrator and makes the involved peers work correctly together by compensating for mismatch. Most of the existing solutions in this field assume that peers interact synchronously using rendezvous communication. However, many application areas rely on asynchronous communication models where peers interact exchanging messages via buffers. Generating adapters in this context becomes a difficult problem because peers may exhibit cyclic behaviour, and their composition often results in infinite systems. In this paper, we present a method for automatically generating adapters in asynchronous environments where peers interact using FIFO buffers.

Introduction

The construction of new software in modern environments is mostly achieved by reusing and composing existing software elements. These elements (peers in this paper) can correspond to a large variety of software, such as Web servers, databases, Graphical User Interfaces, Software-as-a-Service in the cloud, Web services, etc. In order to make possible the composition of such heterogeneous software pieces, all peers are equipped with public interfaces, which exhibit their provided/required services as well as any other composition constraints that must be respected to ensure the correct execution of the composition-to-be. However, although a set of peers may appear as adequate for a new software system under construction, it is likely that their interfaces present mismatch, especially if they have been independently developed by third parties. Mismatch takes different forms such as disparate operation names or unspecified message receptions, and it prevents the direct assembly of the peers.

Software Adaptation [START_REF] Yellin | Protocol Specifications and Components Adaptors[END_REF][START_REF] Canal | Software Adaptation[END_REF] is a non-intrusive solution for composing blackbox software peers that present interface mismatch, leading to deadlock or other undesirable behaviour when peers are combined. Adaptation techniques aim at automatically generating new components called adapters, and usually rely on an adaptation contract, which is an abstract description of how mismatch can be worked out. All interactions pass through the adapter, which acts as an orchestrator and makes the involved peers work correctly together by compensating for mismatch. Many solutions have been proposed since the seminal work by Yellin and Strom [START_REF] Yellin | Protocol Specifications and Components Adaptors[END_REF], see, e.g., [START_REF] Bracciali | A Formal Approach to Component Adaptation[END_REF][START_REF] Brogi | Automated Generation of BPEL Adapters[END_REF][START_REF] Seguel | Generating Minimal Protocol Adaptors for Loosely Coupled Services[END_REF][START_REF] Mateescu | Adaptation of Service Protocols Using Process Algebra and On-the-Fly Reduction Techniques[END_REF][START_REF] Gierds | Reducing Adapter Synthesis to Controller Synthesis[END_REF][START_REF] Inverardi | Automatic Synthesis of Modular Connectors via Composition of Protocol Mediation Patterns[END_REF].

These approaches vary in different aspects, such as expressiveness of interface descriptions (signatures, behaviour, Quality-of-Service, semantics), abstraction level (from abstract models to programming languages), algorithmic techniques (discrete controller synthesis, planning, enumerative approaches, etc.), or application areas (software components, Web services, agent-oriented systems etc.). Most existing approaches assume that the peers interact using synchronous communication, that is rendez-vous synchronizations. Nonetheless, asynchronous communication, i.e., communication via buffers, is now omnipresent in areas such as cloud computing and Web development.

Asynchronous communication highly complicates the adapter generation process, because the corresponding systems are not necessarily bounded and may result into infinite systems. It is known that in this context, the verification problem and more particularly the boundedness property are undecidable for communicating finite state machines [START_REF] Brand | On Communicating Finite-State Machines[END_REF]. Therefore, if we want to generate an adapter in an asynchronous environment, how could we proceed? What bound should we choose for buffers during the generation process? Arbitrarily bounding buffers is an option, but we want to avoid imposing any kind of bounds on buffers, cyclic behaviour, or the number of participants, since it may unnecessarily restrict the behaviour of the whole system.

Recent results introduced the notion of synchronizability [START_REF] Basu | Deciding Choreography Realizability[END_REF] and showed how to use it for checking certain properties on asynchronously communicating systems [START_REF] Ouederni | Compatibility Checking for Asynchronously Communicating Software[END_REF]. These results show that a set of peers is synchronizable if and only if the system generates the same sequences of messages under synchronous and unbounded asynchronous communication, considering only the ordering of the output messages and ignoring the ordering of input messages. Focusing only on output messages makes sense for verification purposes because: (i) output messages are the actions that transfer messages to the network and are therefore observable, (ii) input messages correspond to local consumptions by peers from their buffers and can therefore be considered to be local and private information. Synchronizability can be verified by checking the equivalence of the synchronous version of a given system with its 1-bounded asynchronous version (in which each peer is equipped with one input FIFO buffer bounded to size 1). Thus, this property can be verified using equivalence checking techniques on finite systems, although the set of peers interacting asynchronously can result in infinite systems.

In this paper, we rely on synchronizability for generating adapters for peers interacting asynchronously via (possibly unbounded) FIFO buffers. Given a set of peers modelled using Labelled Transition Systems and an adaptation contract, we first reuse existing adapter generation techniques for synchronous communication, e.g., [START_REF] Canal | Model-Based Adaptation of Behavioural Mismatching Components[END_REF][START_REF] Mateescu | Adaptation of Service Protocols Using Process Algebra and On-the-Fly Reduction Techniques[END_REF]. Then, we consider the system composed of the set of peers interacting through the generated adapter, and we check whether it satisfies the synchronizability property. If this is the case, this means that the system will behave exactly the same whatever bound we choose for buffers, therefore this adapter is a solution to our composition problem. If synchronizability is not preserved, a counterexample is returned, which is used for refining the adaptation contract. Our approach works iteratively by refining the contract until preserving synchronizability. It is worth observing that the main reason for non-synchronizability is due to output messages, which are uncontrollable in an asynchronous environment, hence have to be considered properly in the adaptation contract. Our approach is supported by tools for generating the adapter (Itaca [START_REF] Cámara | ITACA: An Integrated Toolbox for the Automatic Composition and Adaptation of Web Services[END_REF]) and checking synchronizability (CADP [START_REF] Garavel | CADP 2010: A Toolbox for the Construction and Analysis of Distributed Processes[END_REF]), and was applied to several case studies for evaluation purposes. A very early version of this work was sketched in [START_REF] Canal | Adaptation of Asynchronously Communicating Software[END_REF] and is fully developed here.

The organization of this paper is as follows. Section 2 defines our models for peers and introduces the basics on (synchronous) software adaptation. Section 3 defines the synchronizability property for adapted systems. Section 4 presents our approach for generating adapters assuming asynchronous communication semantics. Finally, Section 5 reviews related work, and Section 6 concludes.

Models

In this section, we first present the interface model through which peers are accessed and used. Then, we define adaptation contracts and explain briefly how adapters are generated from peer interfaces and contracts.

Interfaces

We assume that peers are described using a behavioural interface in the form of a Labelled Transition System (LTS).

Definition 1 (LTS).

A Labelled Transition System is a tuple (S, s 0 , Σ, T ) where: S is a set of states, s 0 ∈ S is the initial state, Σ = Σ ! ∪ Σ ? ∪ {τ } is a finite alphabet partitioned into a set Σ ! (Σ ? , resp.) of send (receive, resp.) messages and the internal action τ , and T ⊆ S ×Σ ×S is the transition function.

The alphabet of the LTS is built on the set of operations used by the peer in its interaction with the world. This means that for each operation p provided by the peer, there is an event p? ∈ Σ ? in the alphabet, and for each operation r required from its environment, there is an event r! ∈ Σ ! . Events with the same name and opposite directions (a!, a?) are complementary, and their match stands for inter-peer communication through message-passing. Additionally to peer communication events, we assume that the alphabet also contains a special τ event to denote internal (not communicating) behaviour.

Note that as usually done in the literature [START_REF] Magee | Behaviour Analysis of Software Architectures[END_REF][START_REF] De Alfaro | Interface Automata[END_REF][START_REF] Plasil | Behavior Protocols for Software Components[END_REF], our interfaces abstract from operation arguments, types of return values, and exceptions. Nevertheless, they can be easily extended to explicitly represent operation arguments and their associated data types, by using Symbolic Transition Systems (STSs) [START_REF] Mateescu | Adaptation of Service Protocols Using Process Algebra and On-the-Fly Reduction Techniques[END_REF] instead of LTSs. However, this would render the definitions and results presented in this work much longer and cumbersome, without adding anything substantial to the technical aspects of our proposal.

Adaptation Contracts

Typical mismatch situations between peers appear when event names do not correspond, the order of events is not respected, or an event in one peer has no counterpart or matches several events in another one. All these cases of behavioural mismatch can be worked out by specifying adaptation rules. Adaptation rules express correspondences between operations of the peers, like bindings between ports or connectors in architectural descriptions. Adaptation rules are given as vectors, as defined below: Definition 2 (Vector). An adaptation vector (or vector for short) for a set of peers {P 1 , . . ., P n } with P i = (S i , s 0 i , Σ i , T i ), is a tuple e 1 , . . . , e n with e i ∈ Σ i ∪ { }, meaning that a peer does not participate in the vector.

In order to unambiguously identify them, event names may be prefixed by the name of the peer, e.g., P i : p?, or P j : r!, and in that case can be omitted. For instance, the vector p 1 : a!, p 3 : b?, p 4 : c? represents an adaptation rule indicating that the output event a! from peer p 1 should match both input events b? and c? in p 3 and p 4 , respectively, while peer p2 does not participate in this interaction.

In some complex adaptation scenarios, adaptation rules should be taken contextually (i.e., vectors cannot be applied at any time, but only in certain situations). For this purpose, we use regular expressions (regex) on vectors, indicating a pattern for applying them that will constrain the adaptation process, enforcing additional properties on the adapter. In this work we use standard regex notation, where "|", and " " stand for alternation and Kleene star, respectively. For instance, V 1 (V 2 | V 3 ) V 4 states that the vector V 1 should be applied first, followed by several uses of V 2 and V 3 , and always ending with V 4 . In the absence of regex, we assume that adaptation rules are not contextually dependent and can be applied at any time during the adaptation process.

Definition 3 (Adaptation Contract

). An adaptation contract V for a set of peers {P 1 , . . ., P n } is a set of adaptation vectors for those peers, together with a (possibly empty) regex describing a pattern for applying the vectors.

Writing the adaptation contract is the only step of our approach which is not handled automatically. This step is crucial because an inadequate contract would induce the generation of an adapter that will not make the composition of peers to behave correctly (for instance, some expected interactions may be discarded by the adapter, in order to avoid deadlock). However, the adaptation methodology that we propose is iterative (see Figure 3 in Section 4), which helps in writing the adaptation contract. For more details on the adaptation contracts and the kinds of adaptations that can be resolved with them, we refer to [START_REF] Canal | Model-Based Adaptation of Behavioural Mismatching Components[END_REF].

Adapter Generation

Given a set of interfaces and an adaptation contract, an adapter can be automatically derived using, e.g., [START_REF] Canal | Model-Based Adaptation of Behavioural Mismatching Components[END_REF][START_REF] Mateescu | Adaptation of Service Protocols Using Process Algebra and On-the-Fly Reduction Techniques[END_REF]. This approach relies on an encoding into process algebra together with on-the-fly exploration and reduction techniques. The adapter is given by an LTS which, put into a non-deadlock-free system yields it deadlock-free. All the exchanged events will pass through the adapter, which can be seen as a coordinator for the peers to be adapted. Code generation is also supported by our approach, thus BPEL adapters can be automatically synthesised from adapter LTSs. All these steps are automated by the Itaca toolset [START_REF] Cámara | ITACA: An Integrated Toolbox for the Automatic Composition and Adaptation of Web Services[END_REF].

In order to generate an adapter, not only event correspondences stated in the adaptation rules must be taken into account, but also the LTSs describing the behaviour of the peers. Blindly applying adaptation rules without taking into account peers' behaviour may lead the system to a deadlock state if any of the events represented in a rule cannot be accepted by the corresponding peer in its current state. Hence, the adapter has not only the responsibility of following the adaptation rules and regex in the contract, but also to accommodate their use to the LTSs describing the behaviour of the peers, reordering and remembering events when required.

Notice that the adaptation algorithms in [START_REF] Canal | Model-Based Adaptation of Behavioural Mismatching Components[END_REF][START_REF] Mateescu | Adaptation of Service Protocols Using Process Algebra and On-the-Fly Reduction Techniques[END_REF] generate synchronous adapters, that is, they assume a synchronous communication model for peers. In our present work we show how these results can be applied to asynchronous adaptation, where peers communicate asynchronously and are equipped with an input message buffer.

Case Study

This section describes the case study that will be used as running example throughout this work. Let us consider a multi-cloud scenario for creating virtual machines (VM) in IaaS clouds such as Google Compute Engine or Windows Azure. These clouds offer different APIs for VM creation and management, which allows us to show how adaptation can solve mismatch. The names of the events used here are inspired by the actual names of the corresponding operations in Google and Azure, although the scenario is conveniently simplified in order to abstract from many details that would make it unnecessarily long and complex.

The core element of the system is a Deployment Manager (DM). The LTS describing its behaviour is shown in Figure 1 (d). After receiving a request (request?), the DM creates a new VM instance (instantiate!), checks its status (status?) and returns it (instance!). Notice that the DM is not bound to any particular cloud (Google or Azure), nor it is described in the LTS how one of them is actually chosen. We will show later on how a specific cloud selection policy can be enforced by the adaptation contract.

The behaviour of Google Compute Engine, is shown in Figure 1 (b). In Google's IaaS cloud, the operation for creating a VM is named addInstance, and the status of a machine can be checked with getInstance. Additionally, we assume that the cloud sends statistical information about CPU and memory Fig. 1. LTSs describing the interfaces of the different peers usage (statistics!). Figure 1 (c) shows the LTS corresponding to Windows Azure. We assume that some credentials must be received first (credentials?). Then, machine creation is performed with the operation newAzureVM?, while VM status is reported with getAzureVM!. The LTS describing the behaviour of a possible client, requesting several VMs, is shown in Figure 1 (a).

Finally, the vectors for composing the whole system, adapting the Client, the Deployment Manager, and Google's and Azure's clouds are as follows:

V request = c:vmRequest!, dm:request? V instantiateG = dm:instantiate!, g:addInstance? V statusG = dm:status?, g:getInstance! V credentialsA = a:credentials? V instantiateA = dm:instantiate!, a:newAzureVM? V statusA = dm:status?, a:getAzureVM! V instance = c:vmInstance?, dm:instance! These vectors mostly show correspondence of events with different names. Note also that event a:credentials? has no correspondence in the DM, so it has no counterpart in the V credentialsA rule: this event will be issued by the adapter when required by the cloud. Additionally, a vector for event g:statistics! is omitted, since this event has no counterpart in the rest of the system. We can now automatically generate an adapter using Itaca's tools. The resulting adapter is shown in Figure 2.

Synchronizability of Adapted Systems

In this section, we present a few definitions characterizing the synchronizability property for adapted systems. The adapted synchronous composition of a set of Fig. 2. Adapter LTS peers corresponds to the system where a communication occurs when one peer can send (receive, resp.) an event and the adapter can receive (send, resp.) it.

Definition 4 (Adapted Synchronous Composition). Given a set of peers {P 1 , . . ., P n } with P i = (S i , s 0 i , Σ i , T i ) and an adapter A = (S, s 0 , Σ, T ), their synchronous composition is the labelled transition system LT S as = (S as , s 0 as , Σ as , T as ) where:

-S as = S 1 × . . . × S n × S s 0 as ∈ S as such that s 0 s = (s 0 1 , . . . , s 0 n , s 0 ) -Σ as = ∪ i Σ i ∪ Σ -T as ⊆ S as × Σ as × S as , and for s = (s 1 , . . . , s n , s a ) ∈ S as and s = (s 1 , . . . , s n , s a ) ∈ S as we have that (p2a)

s m -→ s ∈ T as if ∃i ∈ {1, . . . , n} : m ∈ Σ ! i ∩ Σ ? where ∃ s i m! --→ s i ∈ T i ,
and

s a m? --→ s a ∈ T such that ∀k ∈ {1, . . . , n}, k = i ⇒ s k = s k (a2p) s m -→ s ∈ T as if ∃j ∈ {1, . . . , n} : m ∈ Σ ! ∩ Σ ? j where ∃ s a m! --→ s a ∈ T ,
and

s j m? --→ s j ∈ T j such that ∀k ∈ {1, . . . , n}, k = j ⇒ s k = s k (int) s τ -→ s ∈ T as if ∃i ∈ {1, . . . , n}, ∃ s i τ -→ s i ∈ T i such that ∀k ∈ {1, . . . , n}, k = i ⇒ s k = s k and s a = s a
However, in an asynchronous scenario, peers communicate with the adapter asynchronously via FIFO buffers. Hence, each peer P i is equipped with an unbounded input message buffer Q i , and the adapter A with an input buffer Q. A peer can either send a message m ∈ Σ ! to the tail of the adapter buffer Q at any state where this send message is available, read a message m ∈ Σ ? from its buffer Q i if the message is available at the buffer head, or evolve independently through an internal τ transition. The adapter works in the same way. We recall that we focus on output events, since reading from the buffer is private non-observable information, which is encoded as an internal transition in the asynchronous system.

Definition 5 (Adapted Asynchronous Composition). Given a set of peers {P 1 , . . ., P n } with P i = (S i , s 0 i , Σ i , T i ), Q i being its associated input buffer, and an adapter A = (S, s 0 , Σ, T ) with input buffer Q, their asynchronous composition is the labelled transition system LT S aa = (S aa , s 0 aa , Σ aa , T aa ) where:

-S aa ⊆ S 1 × Q 1 × . . . × S n × Q n × S × Q where ∀i ∈ {1, . . . , n}, Q i ⊆ (Σ ? i ) * and Q ⊆ (Σ ? ) * -s 0
aa ∈ S aa such that s 0 aa = (s 0 1 , , . . . , s 0 n , , s 0 , ) (where denotes an empty buffer)

-Σ aa = ∪ i Σ i ∪ Σ -T aa ⊆ S aa × Σ aa × S aa , and for s = (s 1 , Q 1 , . . . , s n , Q n , s a , Q) ∈ S aa and s = (s 1 , Q 1 , . . . , s n , Q n , s a , Q ) ∈ S aa we have that (p2a!) s m! --→ s ∈ T aa if ∃i ∈ {1, . . . , n} : m ∈ Σ ! i ∩ Σ ? , (i) s i m! --→ s i ∈ T i , (ii) Q = Qm, (iii) s a = s a , (iv) ∀k ∈ {1, . . . , n} : Q k = Q k , and (v) ∀k ∈ {1, . . . , n} : k = i ⇒ s k = s k (p2a?) s τ -→ s ∈ T aa if m ∈ Σ ? , (i) s a m? --→ s a ∈ T , (ii) mQ = Q, (iii) ∀k ∈ {1, . . . , n} : Q k = Q k ,
and (iv) ∀k ∈ {1, . . . , n} :

s k = s k (a2p!) s m! --→ s ∈ T aa if ∃j ∈ {1, . . . , n} : m ∈ Σ ! ∩ Σ ? j , (i) s a m! --→ s a ∈ T , (ii) Q j = Q j m, (iii) Q = Q, (iv) ∀k ∈ {1, . . . , n} : k = j ⇒ Q k = Q k , and (v) ∀k ∈ {1, . . . , n} : s k = s k (a2p?) s τ -→ s ∈ T aa if ∃i ∈ {1, . . . , n} : m ∈ Σ ? i , (i) s i m? --→ s i ∈ T i , (ii) mQ i = Q i , (iii) ∀k ∈ {1, . . . , n} : k = i ⇒ Q k = Q k , (iv) ∀k ∈ {1, . . . , n} : k = i ⇒ s k = s k , (v) Q = Q, and (vi) s a = s a (int) s τ -→ s ∈ T aa if ∃i ∈ {1, . . . , n}, (i) s i τ -→ s i ∈ T i , (ii) ∀k ∈ {1, . . . , n} : Q k = Q k , (iii) ∀k ∈ {1, . . . , n} : k = i ⇒ s k = s k (iv) Q = Q, and (v) s a = s a
We use LT S k aa to define the bounded adapted asynchronous composition, where each message buffer is bounded to size k. The definition of LT S k aa can be obtained from Definition 5 by allowing send transitions only if the message buffer of the receiving peer has less than k messages in it. Otherwise, the sender is blocked, i.e., we assume reliable communication without message losses.

The synchronizability property applies here by considering the adapter as a peer whose peculiarity is to interact with all the other participants. Definition 6 (Branching Synchronizability). A set of peers {P 1 , . . . , P n } and an adapter A are branching synchronizable if ∀k ≥ 1, LT S as ≡ br LT S k aa .

It was proved that checking the equivalence between the synchronous composition and the 1-bounded asynchronous composition, i.e., LT S as ≡ br LT S 1 aa , is a sufficient and necessary condition for branching synchronizability [START_REF] Ouederni | Compatibility Checking for Asynchronously Communicating Software[END_REF].

Theorem 1 (Deadlock-freeness). A synchronizable system consisting of a set of peers {P 1 , . . . , P n } and an adapter A is deadlock-free when all participants communicate asynchronously via k-bounded or unbounded FIFO buffers.

Proof. An adapter generated using synchronous synthesis techniques is deadlockfree (DF ) according to [START_REF] Canal | Model-Based Adaptation of Behavioural Mismatching Components[END_REF][START_REF] Mateescu | Adaptation of Service Protocols Using Process Algebra and On-the-Fly Reduction Techniques[END_REF], that is, LT S as |= DF . The system (peers interacting via an adapter) being synchronizable, we have LT S as ≡ br LT S aa . Since branching equivalence [START_REF] Van Glabbeek | Branching Time and Abstraction in Bisimulation Semantics[END_REF] preserves deadlock-freeness, if LT S as is deadlock-free then LT S aa is deadlock-free, thus LT S as |= DF ⇔ LT S aa |= DF .

Asynchronous Adaptation

In this section, we present our approach for adapter synthesis when peers interact via FIFO buffers, its application to our running example, and a short overview of tool support.

Methodology

Figure 3 shows how our approach works for generating adapter LTSs in asynchronous environments. First of all, we apply compatibility checking techniques, e.g., [START_REF] Ouederni | Compatibility Checking for Asynchronously Communicating Software[END_REF], for understanding whether the set of selected peers can be reused and composed directly, that is, without using adaptation techniques for compensating mismatch. If an adapter is required, the user needs to provide an adaptation contract. Note that this is the only step of our approach that requires human intervention. Given a set of peer LTSs and an adaptation contract, an adapter LTS is automatically synthesised by means of synchronous adapter generation techniques, e.g., [START_REF] Canal | Model-Based Adaptation of Behavioural Mismatching Components[END_REF][START_REF] Mateescu | Adaptation of Service Protocols Using Process Algebra and On-the-Fly Reduction Techniques[END_REF]. Then, we check whether the adapted synchronous composition and the 1-bounded adapted asynchronous composition are equivalent. If this is the case, it means that the system is synchronizable and its observable behaviour will remain the same whatever bound is chosen for buffers. Thus, the adapter generated using generation techniques relying on synchronous communication can be used as is in an asynchronous context.

If the system is not synchronizable, the user should refine the adaptation contract using the diagnostic returned by equivalence checking. This counterexample indicates the additional behaviour present in the asynchronous composition and absent in the synchronous one, which invalidates synchronizability. The violation of this property has two main causes: either the adapter does not capture/handle all reachable output messages, or the adapter is too restrictive wrt. message orderings, e.g., the adapter requires a sequence of two messages, which cannot be ensured in the asynchronous composition because both messages can be executed simultaneously. This latter case particularly arises when the adaptation contract enforces additional constraints by the use for instance of regex on vectors. This iterative process always terminates because these issues can be solved by modifying the adaptation contract, and the number of problems is finite since the input models are finite. It is worth emphasizing that the reasons for non-synchronizability can be used as guidelines when writing the adaptation contract. Keeping that in mind should help the user to converge more rapidly to a synchronizable system.

Application to the Case Study

Let us go back to our multi-cloud running example. Given the participant LTSs and the set of vectors presented in Section 2, we can generate automatically the corresponding adapter. We first check synchronizability for this adapter composed with the peer LTSs. As a result, the verdict is false and we obtain the following counterexample: c:vmRequest!, dm:request!, dm:instantiate!, g:addInstance!, and g:statistics!, where the very last event appears in the asynchronous system but not in the synchronous one. Note that synchronizability checking focuses on output messages, hence the counterexample above contains only events sent by a peer to the adapter (c:vmRequest!, dm:instantiate!, g:statistics!) or by the adapter to a peer (dm:request!, g:addInstance!). This violation is due to the fact that the emission of statistics is not captured by a vector (yet), and this emission is inhibited in the synchronous system, while it is possible in the asynchronous system because reachable output messages cannot be inhibited under asynchronous communication.

In order to correct this problem, we extend the adaptation contract by adding the following vector: V statisticsG = g:statistics! . The corresponding adapter (not shown here) is generated and it consists of 25 states and 41 transitions. We check again synchronizability and the system composed of the four peers interacting through the adapter is synchronizable, which means that the adapter can be used under asynchronous communication and the system will behave exactly the same whatever bound is chosen for buffers.

However, in this system the Deployment Manager may always decide to instantiate the same kind of VM (Google or Azure). If we want to enforce the DM to instantiate a VM in one of the two clouds alternatively, we have to impose a specific sequence in the application of vectors during the adapter generation process. This can be specified by means of the following regex:

( V request V instantiateG V statisticsG V statusG V instance V request V credentialsA V instantiateA V statusA V instance )
The adapter generated using the aforementioned vectors and this regex contains 21 states and 24 transitions. However, when we check synchronizability with this new adapter, the check returns false with a counterexample containing 18 events. The problem in that case is that Windows Azure works in connected mode, in the sense that it receives credentials once, and then several new VM instances can be created. Nonetheless, the regular expression requires credentials to be submitted before any new instantiation. Therefore, when we arrive at the second instantiation of an Azure VM, the adapter submits again the credentials! event whereas the Azure peer does not expect it: this emission appears in the asynchronous system but not in the synchronous version.

To solve this problem, we need to relax the regular expression by avoiding the strict sequence of vectors. A simple idea is to say that after each request, we can execute in any order the vectors where one of the two VM providers (Google or Azure) is involved. This discards the problem encountered with the credentials, whose rule is executed the first time only. Here is the new regex:

( V request ( V instantiateG | V statisticsG | V statusG | V instance ) V request ( V credentialsA | V instantiateA | V statusA | V instance ) )
The corresponding adapter consists of 32 states and 38 transitions. When we check synchronizability with this new adapter, the system is synchronizable and accordingly this adapter can be used under asynchronous communication.

Tool Support

Tool support consists of two parts: a set of tools for generating adapters and some automated techniques for checking synchronizability. As for adapter synthesis, we reuse the Itaca toolbox [START_REF] Cámara | ITACA: An Integrated Toolbox for the Automatic Composition and Adaptation of Web Services[END_REF]. Itaca takes as input a set of Symbolic Transition Systems (LTSs are STSs without message parameters) and an adaptation contract, and generates an adapter LTS, from which BPEL code can be generated, see [START_REF] Mateescu | Adaptation of Service Protocols Using Process Algebra and On-the-Fly Reduction Techniques[END_REF] for details. As for synchronizability, we rely on process algebra encodings and equivalence checking. More precisely, we developed a Python script, which generates for all input LTSs (peers and adapter) some code in the LNT process algebra. Then, we use the CADP toolbox [START_REF] Garavel | CADP 2010: A Toolbox for the Construction and Analysis of Distributed Processes[END_REF], which accepts LNT specifications as input. Particularly, we rely on CADP exploration tools for computing the required (synchronous/asynchronous) compositions and CADP equivalence checker for checking synchronizability.

Table 1 presents experimental results for some real-world examples. The table gives for each example the number of peers (P), the total number of states (S) and transitions (T) involved in these examples, the size of the 1-bounded asynchronous system (minimised modulo branching reduction), and the overall time for checking synchronizability (including composition generations, minimisations, and equivalence checking). It is worth noting that out of these 14 examples, 7 of the adapters generated for synchronous communication can be directly reused as they are in asynchronous environments, while 7 require to use our approach in order to replay adapter synthesis techniques until obtaining an adapter which satisfies synchronizability.

Related Work

In this section, we present the most relevant and recent results in the software adaptation area. First of all, notice that adaptation differs from automatic software composition approaches, particularly studied in the Web services area, where services involved into a new composition are assumed to perfectly match altogether with respect to certain compatibility property.

Van der Aalst et al. [START_REF] Van Der Aalst | Service Interaction: Patterns, Formalization, and Analysis[END_REF] propose a solution to behavioural adaptation based on open nets, a variant of Petri nets. Their generation algorithm produces an adapter which is obtained through several steps. First, a message transformation net, called engine, is generated from a set of message transformation rules. Then, a behavioural controller (a transition system) is synthesised for the product net of the services and the engine. Adapters are finally implemented in the BPEL orchestration language. In [START_REF] Nezhad | Protocol-Aware Matching of Web Service Interfaces for Adapter Development[END_REF], the authors identify several kinds of mismatch between Web service interfaces. They provide a method for identification of the split/merge class of interface mismatch and a semi-automated, behaviour-aware approach for interface-level mismatch that results in identifying parameters of mapping functions that resolve that mismatch. They use and extend approaches in ontology matching for static matching of service interfaces to identify split/merge mismatch. In addition, they propose depth-based and iterative reference-based approaches that incorporate behavioural information during interface matching.

In [START_REF] Canal | Model-Based Adaptation of Behavioural Mismatching Components[END_REF][START_REF] Mateescu | Adaptation of Service Protocols Using Process Algebra and On-the-Fly Reduction Techniques[END_REF], the authors proposed automated techniques for generating an adapter model from a set of service interfaces and a contract. The approach relies on an encoding into process algebra together with on-the-fly exploration and reduction techniques. Verification of contracts is also possible by using model checking techniques. Last, code is automatically generated from the adapter model to BPEL, which may finally be deployed. Inverardi and Tivoli [START_REF] Inverardi | Automatic Synthesis of Modular Connectors via Composition of Protocol Mediation Patterns[END_REF] formalise a method for the automated synthesis of modular connectors. A modular connector is structured as a composition of independent mediators, each of them corresponding to the solution of a recurring behavioural mismatch. The paper proves that the connector decomposition is correct and shows how it promotes connector evolution on a case study. Bennaceur et al. [START_REF] Bennaceur | Automated Mediator Synthesis: Combining Behavioural and Ontological Reasoning[END_REF] propose a technique for automated synthesis of mediators using a quotient operator, that is based on behavioural models of the components and an ontological model of the data domain. The method supports both off-line and run-time synthesis. The obtained mediator is the most general component that ensures deadlock-freedom and the absence of communication mismatch.

It is worth observing that, although all these papers present interesting approaches tackling software adaptation from different points of view, they assume that peers interact synchronously. There were a few attempts to generate adapters considering asynchronous communication. Padovani [START_REF] Padovani | Contract-Based Discovery and Adaptation of Web Services[END_REF] presents a theory based on behavioural contracts to generate orchestrators between two services related by a subtyping (namely, sub-contract) relation. This is used to generate an adapter between a client of some service S and a service replacing S. An interesting feature of this approach is its expressiveness as far as behavioural descriptions are concerned, with support for asynchronous orchestrators and infinite behaviour. The author resorts to the theory of regular trees and imposes two requirements on the orchestrator, namely regularity and contractivity. However, this work does not support name mismatch nor data-related adaptation. Seguel et al. [START_REF] Seguel | Generating Minimal Protocol Adaptors for Loosely Coupled Services[END_REF] present automatic techniques for constructing a minimal adapter for two business protocols possibly involving parallelism and loops. The approach works by assigning to loops a fixed number of iterations, whereas we do not impose any restriction, and peers may loop infinitely. Gierds and colleagues [START_REF] Gierds | Reducing Adapter Synthesis to Controller Synthesis[END_REF] present an approach for specifying behavioural adapters based on domain-specific transformation rules that reflect the elementary operations that adapters can perform. The authors also present a novel way to synthesise complex adapters that adhere to these rules by consistently separating data and control, and by using existing controller synthesis algorithms. Asynchronous adaptation is supported in this work, but buffers/places must be arbitrarily bounded for ensuring computability of the adapter.

Conclusion

Software adaptation is the only solution for building new systems by combining black-box services that are relevant from a functional point of view, but do not exactly match one with another and therefore require adjustments during the composition process. Most existing approaches focus on systems relying on synchronous communication. In this paper, we tackle the adapter generation question from a different angle by assuming that peers interact asynchronously via FIFO buffers. This highly complicates the synthesis process because we may have to face infinite systems when generating the adapter behaviour. Our approach provides a solution to this problem by using the synchronizability property and adapter generation techniques for synchronous communication. This enables us to propose an iterative approach for synthesising adapters, which work properly in asynchronous environments. Our approach is tool-supported and has been applied to a large variety of real-world examples found in the literature.

Fig. 3 .

 3 Fig. 3. Approach overview

Table 1 .

 1 Computation times are quite short since all the examples found in the literature are quite small. Experimental results

	Example	|P|+1 |S|/|T | LT S 1 a (|S|/|T |) Synchro. Time
	FTP Transfer [5] Client/Server [11]	3 3	20/17 14/13	13/15 8/7	× √	52s 54s
	Mars Explorer [7] Online Computer Sale [14]	3 3	34/34 26/26	19/22 11/12	× √	49s 53s
	E-museum [12] Client/Supplier [9] Restaurant Service [1] Travel Agency [28] Vending Machine [16]	3 3 3 3 3	33/40 31/33 15/16 32/38 15/14	47/111 17/19 10/12 18/21 8/8	× √ √ √ √	53s 49s 55s 52s 49s
	Travel Agency [4]	3	42/57	23/34	×	45s
	Client/Server [29]	4	19/24	18/32	×	64s
	SQL Server [27] SSH Protocol [20]	4 4	32/38 26/28	20/27 16/18	× √	62s 56s
	Booking System [21]	5	45/53	27/35	×	85s


PhD Pia Horvat
email: pia.horvat.10@ucl.ac.uk

PhD Marcus Richards

MD Ruzena Kubinova

MD, PhD Andrzej Pajak

MD, PhD Sofia Malyutina

MD Sergey Shishkin

PhD Hynek Pikhart

PhD Anne Peasey

FRCP M G Marmot

PhD Archana Singh-Manoux

MD Martin Bobak

Objective: To investigate associations of frequency, quantity, binge, and problem drinking with cognitive function in older Eastern European adults. Methods: The investigation included 14,575 participants, aged 47 to 78 years at cognitive assessment in 2006-2008 from Novosibirsk (Russia), Krakow (Poland), and 6 Czech towns participating in the HAPIEE (Health, Alcohol, and Psychosocial Factors in Eastern Europe) prospective cohort study. Average response rates were 59% at baseline (2002-2005) and 63% in 2006-2008. Alcohol consumption was assessed at baseline and in 2006-2008. Cognitive tests included immediate and delayed word recall, semantic fluency (animal naming), and letter cancellation. Associations between alcohol indices and cognitive scores were analyzed crosssectionally (all measures from 2006 to 2008) and prospectively (alcohol and covariates from 2002 to 2005 and cognition from 2006 to 2008).

Results:

In cross-sectional analyses, nondrinkers had lower cognitive scores and female moderate drinkers had better cognitive performance than light drinkers. Heavy, binge, and problem drinking were not consistently associated with cognitive function. Few associations were replicated in prospective analyses. Participants who stopped drinking during follow-up had worse cognition than stable drinkers; in men, regression coefficients (95% confidence interval) ranged from 20.26 (20.36, 20.16) for immediate recall to 20.14 (20.24, 20.04) for fluency.

Conclusion:

Regular and episodic heavy drinking were not consistently associated with cognitive function. Worse cognition in participants who stopped drinking during follow-up suggests that inclusion of less healthy ex-drinkers may partly explain poorer cognition in nondrinkers.

drinkers. [START_REF] Sabia | Alcohol consumption and cognitive decline in early old age[END_REF] These inconsistencies may partly reflect the relatively small numbers of heavy drinkers in most studies. [START_REF] Anstey | Alcohol consumption as a risk factor for dementia and cognitive decline: metaanalysis of prospective studies[END_REF] Potential effects of regular or episodic heavy drinking (binge drinking) on cognition have received less empirical attention. We identified 2 reports from one cohort, in which binge drinking was found to increase the risk of cognitive impairment [START_REF] Virtaa | Midlife alcohol consumption and later risk of cognitive impairment: a twin follow-up study[END_REF] and dementia. [START_REF] Jarvenpaa | Binge drinking in midlife and dementia risk[END_REF] There is emerging evidence that binge drinking independently increases cardiovascular disease (CVD) risk, [START_REF] Rehm | Alcohol and cardiovascular disease: more than one paradox to consider. Average volume of alcohol consumption, patterns of drinking and risk of coronary heart disease-a review[END_REF] and because CVD is associated with cognitive aging, [START_REF] Spiro | Integrating health into cognitive aging: toward a preventive cognitive neuroscience of aging[END_REF] a link between binge drinking and cognitive function seems plausible.

Our aim was to investigate the associations of quantity, frequency, binge, and problem drinking with cognitive function in older adults, using data from 3 Eastern European populations, where alcohol is an important cause of morbidity and premature mortality. [START_REF] Rehm | Alcohol accounts for a high proportion of premature mortality in Central and Eastern Europe[END_REF] METHODS Study populations and participants. The HAPIEE (Health, Alcohol, and Psychosocial Factors in Eastern Europe) Study is a multicenter prospective cohort study conducted in Novosibirsk (Russia), Krakow (Poland), and 6 Czech towns. Details of the study protocol have been reported elsewhere. [START_REF] Peasey | Determinants of cardiovascular disease and other non-communicable diseases in Central and Eastern Europe: rationale and design of the HAPIEE Study[END_REF] Briefly, 28,947 men and women aged 45 to 69 years at baseline (2002-2005) were randomly selected from population registers and electoral lists (Novosibirsk). Response rates were 61% in Krakow and Novosibirsk and 55% in Czech towns. At baseline, participants completed an extensive health questionnaire and a brief physical examination. Russian and Czech participants were invited for examination in a clinic, while Polish participants were visited and examined in their homes. Reexamination of participants was completed in 2006-2008 (response rate 63%). At baseline, cognitive tests were performed on all participants older than 60 years, and in a random sample of approximately 20% of adults aged 45 to 59 years (n 5 12,594). At reexamination, cognition was assessed in all returning participants (n 5 17,543). The eligible sample for this study consisted of all participants with cognitive data at reexamination; for 54% (n 5 9,436) of them, it was their first assessment of cognitive function.

Standard protocol approvals, registrations, and patient consents. The study was approved by ethics committees at Uni- versity College London and University College Hospital and local ethics committees in each participating center. All participants gave written informed consent.

Measurements. Cognitive function (assessed 2006-2008).

Cognitive function was assessed by trained nurses using 4 neuropsychological tests. First, 10-word list recall was used to assess verbal memory and learning. Word lists, consisting of 10 common nouns, were the same in each center. Immediate recall was assessed by correctly recalled words summed over 3 consecutive 1-minute trials (range 0-30). Delayed recall was assessed after an interval during which other cognitive tests were administered (range 0-10). Second, verbal fluency was assessed by asking participants to name as many animals as possible within 1 minute. Third, letter cancellation test was used to assess attention, mental speed, and concentration. Participants were instructed to cross out 2 target letters, P and W (P and Ш in Novosibirsk), embedded in a random letter grid as quickly and as accurately as possible within 1 minute (range 0-65).

Alcohol consumption (assessed 2002-2005 and 2006-2008). Self-reported alcohol intake in the past year was measured using the graduated frequency questionnaire (GFQ). [START_REF] Rehm | Measuring quantity, frequency, and volume of drinking[END_REF] The baseline questionnaire contained 9 mutually exclusive categories of frequency (ranging from "never" to "almost every day") and 6 mutually exclusive categories of amounts, expressed in local units of beer, wine, and spirits ($10, 7-9, 5-6, 3-4, 1-2, and 0.5 drink; 1 drink equals 0.5 L of beer, 0.2 L of wine, and 0.05 L of spirits or 20 g of ethanol). Because only 3 categories of amounts ($5, 3-4, 2-0.5 drinks) were used at reexamination, the data were harmonized across the waves. Several alcohol indices were derived from harmonized GFQ data for both data waves. First, drinking frequency in the past year was categorized as follows: never, ,1 monthly, 1-3 times monthly, 1-4 times weekly, and 51 times weekly. Second, the frequency of consuming a given number of alcoholic drinks in the past year was converted into total amount of alcohol consumed in grams and divided by 365 to obtain an estimate of average daily alcohol consumption. Participants were then grouped into 4 categories of average daily alcohol intake, using lower cutoffs in women: nondrinkers (0 g/d), light (#5/10 g/d), moderate (5-20/10-40 g/d), and heavy drinkers ($20/40 g/d). Third, binge drinking was defined as consuming $60 and 100 g of ethanol in women and men in one episode at least monthly. Baseline information on long-term abstention was not available. Therefore, for all measures, participants reporting no alcohol consumption in the past year were categorized as nondrinkers. Weekly alcohol consumption and alcohol intake in the last 3 months were also available, but were not used for these analyses, because they correlated strongly with the GFQ.

Finally, using average daily alcohol intake at baseline and reexamination, participants were categorized into the following: stable nondrinkers (consistently abstained), ex-drinkers (abstained at follow-up but not baseline), stable drinkers (stable consumption), reduced drinking (higher consumption at baseline), increased drinking (higher consumption at follow-up), and those who started drinking (abstained at baseline but not follow-up).

Problem drinking (assessed 2002-2005 and 2006-2008). Problem drinking was assessed by the CAGE (cutting down, annoyance by criticism, guilty feeling, and eye-openers) questionnaire [START_REF] Ewing | Detecting alcoholism: the CAGE questionnaire[END_REF] on both survey occasions. Positive responses to 2 or more items indicate potential problem drinking.

Covariates (assessed 2002-2005 and 2006-2008). Covariates included study center, age, education (primary or less, vocational, secondary, and university), household asset index (microwave, dishwasher, washing machine, color TV, car, freezer, satellite TV, VCR, camcorder, mobile phone and telephone; range 0-11 for the number of items owned), smoking status (never, current, former), leisure-time physical activity (none vs some), high depressive symptoms (yes vs no) measured by the CESD-10 (Center for Epidemiologic Studies Depression Scale), and self-reported chronic conditions (CVD, diabetes, and hypertension; all yes vs no). Because some of the health conditions could either mediate or confound the association between alcohol and cognition, we show analyses unadjusted and adjusted for chronic conditions.

Statistical analysis.

Cognitive test results obtained at reexamination, the main outcome of these analyses, were converted to z scores (mean 5 0; SD 5 1) using whole sample means and SDs to allow comparison between tests. Cross-sectional and prospective associations between alcohol and cognitive ) 0.00 0.00, 0.00 0.00 0.00, 0.00 0.00 0.00, 0.00 0.00 0.00, 0.00 functions were estimated using multiple linear regression.

In cross-sectional analyses, only variables measured at reexamination were used; in prospective analyses, we used from reexamination and alcohol and covariates from baseline. All regression analyses were adjusted for cognitive measurement occasion (first vs repeated).

Analyses were conducted separately by sex because of large differences in alcohol consumption between men and women. To formally test for heterogeneity, alcohol-sex interactions were included in regression models. Heterogeneity of associations between study centers was examined by including interactions between alcohol measures and center, and by conducting analyses stratified by center. For alcohol indices, the lowest level of drinking was used as the reference group. In additional analyses, models for binge drinking were further adjusted for, or stratified by, alcohol volume. Sensitivity analyses were conducted to account for missing covariate data and attrition. Analyses were conducted in Stata 13. [START_REF]Stata Statistical Software: Release 13[END_REF] RESULTS Complete data on all cognitive tests were available for 17,022 participants in 2006-2008, 14,575 of whom also had data on alcohol and all covariates and were included in the analytic sample. Table 1 shows baseline and follow-up characteristics of included participants (descriptive statistics by alcohol use categories are shown in table e-1 on the Neurology ® Web site at Neurology.org). Proportions of binge drinkers and problem drinkers as well as average alcohol use were higher in men than in women; baseline median daily alcohol intake was 5. 3 and 0.6 g, respectively.

Baseline and follow-up alcohol measures were strongly associated with each other. Spearman coefficients were 0.62 and 0.58 for quantity and frequency of drinking. Tetrachoric coefficient for binge drinking was 0.60. For categories of alcohol intake, 58% of participants were in the same group on both occasions, and 44% of participants were in the same or adjacent category for drinking frequency.

In regression analyses, heterogeneity between centers was observed in only a few instances and was mostly weak. In fully adjusted models, several alcohol-sex interactions, especially for recall tests, were evident at p , 0.05. Results of regression analyses adjusted for potential confounders are shown in table 2 (men) and table 3 (women). Age-adjusted regression results are available in the online supplement (table e-2 [men] and table e-3 [women]). In men, the quantity and frequency of drinking were generally not significantly associated with cognitive test scores, either prospectively or cross-sectionally, after adjusting for socioeconomic and lifestyle confounders. The only consistent exception was lower cognitive scores in nondrinkers compared with the reference group in cross-sectional models.

In women, nondrinkers had consistently lower cognitive scores than light drinkers in both prospective and cross-sectional analyses. Better cognitive performance in moderate drinkers observed in ageadjusted models (table e-3) was largely attenuated by subsequent adjustment for socioeconomic and lifestyle factors. In cross-sectional analyses, moderate drinking frequency and intake were associated with better scores, compared with lower levels of drinking. In prospective analyses, only women drinking a few times a month showed better performance on the verbal cognitive tests than those who drank less frequently than that, whereas average intake was not associated with better cognition.

Binge drinking was not significantly associated with cognitive performance in either sex in prospective analyses; cross-sectional associations were also few and inconsistent. CAGE was also not related to cognitive performance, although in women, the number of problem drinkers was relatively small.

Results for drinking pattern, measured by combining data on frequency and quantity per occasion, did not yield any additional insights and are reported in the online supplement separately for men (table e-4) and women (table e-5).

Results for change in alcohol intake during follow-up showed that, especially in men, participants who stopped drinking had significantly lower cognitive scores than drinkers. There were almost no statistically significant differences between stable drinkers and other drinkers. In women, stable nondrinkers and those who started drinking during follow-up also had lower cognitive scores. In men, lower verbal performance in stable nondrinkers was marginally significant. Results for change in drinking frequency or combining information on frequency and intake during follow-up were similar (table e-6).

Finally, additional adjustment for health conditions resulted in little change in associations with cognition for all alcohol measures (tables e-7 and e-8).

Results of sensitivity analyses using inverse probability weighting to account for longitudinal attrition (table e-9) and multiple imputation to account for missing covariate data (tables e-10 and e-11) are available in the online supplement.

DISCUSSION In this large Eastern European study with relatively high levels of male regular and episodic heavy drinking, we found only modest associations between different measures of alcohol consumption and cognitive performance in older persons. Quantity and frequency of drinking were not associated with cognitive performance in men, whereas in women, moderate drinkers had slightly better cognition than those drinking less, particularly in cross-sectional analyses. The most consistent findings were worse cognitive performance in female nondrinkers and those who stopped drinking during follow-up. Binge and problem drinking were not consistently associated with cognitive function.

Our study has limitations. First, the analytic sample was restricted to participants with cognitive measures at follow-up. Attrition was higher in participants with lower cognitive scores, nondrinkers, and frequent drinkers at baseline, and could possibly bias the results of our study. However, sensitivity analysis accounting for missing cognition data by inverse probability weighting yielded similar results (table e-6).

Second, self-reported alcohol measures typically underestimate actual consumption. [START_REF] Stockwell | Under-reporting of alcohol consumption in household surveys: a comparison of quantity-frequency, graduated-frequency and recent recall[END_REF] In this study, systematic underreporting among men seems unlikely but, because of sex differences in social acceptability of drinking, underreporting may be greater in women. [START_REF] Bobrova | Gender differences in drinking practices in middle aged and older Russians[END_REF] Among available alcohol measures, the GFQ appeared to be least prone to underreporting. In addition, correlations between different alcohol measures were generally high, and serum GGT (g-glutamyltransferase) values showed expected associations with alcohol, although the correlations were weaker in women.

Third, alcohol measures used may not fully reflect lifelong consumption. Particularly, participants may have stopped or reduced drinking before the baseline, and those who stopped drinking during follow-up had worse cognition than stable drinkers. However, unstable drinkers generally did not differ from stable drinkers, and the few significant differences may be attributable to chance. While this would suggest that results for drinkers were not affected by inclusion of those who had reduced their consumption, it is also possible that regression to the mean affected our estimates in relation to change in alcohol consumption, leading to regression dilution bias. However, this does not affect our prospective and cross-sectional results.

Fourth, response rates were relatively low and responders were healthier than nonresponders. [START_REF] Peasey | Determinants of cardiovascular disease and other non-communicable diseases in Central and Eastern Europe: rationale and design of the HAPIEE Study[END_REF] While this is also true of most contemporary studies, it suggests that heavier drinkers and individuals with cognitive impairment may have been less likely to participate. Low response and differences in characteristics between responders and nonresponders do not inevitably bias estimates of associations. [START_REF] Stang | Nonresponse research: an underdeveloped field in epidemiology[END_REF] However, if in our study heavy drinkers had lower participation rates and higher likelihood of cognitive Finally, the study did not examine representative samples and extrapolation beyond urban settings requires caution.

A particular strength of this study is the use of Eastern European population samples with relatively high alcohol consumption and rates of male binge drinking in the former Soviet Union, [START_REF] Popova | Comparing alcohol consumption in Central and Eastern Europe to other European countries[END_REF] and a higher proportion of CVD and premature mortality estimated to be attributable to alcohol than elsewhere in Europe. [START_REF] Rehm | Alcohol accounts for a high proportion of premature mortality in Central and Eastern Europe[END_REF] Indeed, our study had a high prevalence of male binge and problem drinking. Second, the GFQ is well suited for identifying heavy and binge drinkers. [START_REF] Rehm | Measuring quantity, frequency, and volume of drinking[END_REF] Third, the large numbers in the pooled sample provide adequate statistical power in men, although the numbers of heavy drinkers were small in women. Finally, unlike most previous studies, our emphasis was on the cognitive effects of regular and episodic heavy drinking, not just light to moderate drinking.

We did not find convincing evidence of worse cognitive performance in heavy drinkers. More specific tests of executive function could show greater sensitivity to the effects of alcohol, as previously reported for phonemic fluency. [START_REF] Gross | Alcohol consumption and domain-specific cognitive function in older adults: longitudinal data from the Johns Hopkins Precursors Study[END_REF] A study in British civil servants reported faster cognitive decline in middle-aged men drinking $36 g/d, compared with ,20 g/d, but no effect in women. [START_REF] Sabia | Alcohol consumption and cognitive decline in early old age[END_REF] It is possible that regular and/or episodic heavy alcohol use is associated with faster cognitive decline in Eastern European populations, but we do not yet have a long enough follow-up to examine trajectories of cognitive decline.

In our study, binge drinking was not consistently associated with cognitive performance. We were therefore unable to replicate findings from one study of Finish twins, in which binge drinking was independently associated with cognitive impairment [START_REF] Virtaa | Midlife alcohol consumption and later risk of cognitive impairment: a twin follow-up study[END_REF] and dementia. [START_REF] Jarvenpaa | Binge drinking in midlife and dementia risk[END_REF] The main hypothesized mechanism for the association between alcohol and cognition involves effects on the cardio-and cerebrovascular systems. [START_REF] Spiro | Integrating health into cognitive aging: toward a preventive cognitive neuroscience of aging[END_REF] Heavy drinking and abstention have been linked to higher cardiovascular risk than light to moderate drinking, and binge drinking may independently increase cardiovascular risk. [START_REF] Rehm | Alcohol and cardiovascular disease: more than one paradox to consider. Average volume of alcohol consumption, patterns of drinking and risk of coronary heart disease-a review[END_REF] In a prospective study in Novosibirsk, regular but not episodic heavy drinking increased risk of cardiovascular death. [START_REF] Malyutina | Relation between heavy and binge drinking and all-cause and cardiovascular mortality in Novosibirsk, Russia: a prospective cohort study[END_REF] Binge drinking was also not consistently associated with high blood pressure [START_REF] Pajak | Binge drinking and blood pressure: cross-sectional results of the HAPIEE Study[END_REF] or all-cause and cardiovascular mortality in this cohort (unpublished findings). Thus, the absence of association between binge drinking and cognitive performance could plausibly reflect the apparent lack of adverse effects of binge drinking on CVD in this cohort.

Most observational studies report moderate drinking to be beneficial for cognitive function in mid-to later life 2 with anti-inflammatory effects postulated among the underlying mechanisms. [START_REF] Collins | Alcohol in moderation, cardioprotection, and neuroprotection: epidemiological considerations and mechanistic studies[END_REF] Consistent with this, we observed significantly better cognitive scores in moderate drinkers than low-level drinkers in women. However, compared with cross-sectional results, the prospective associations were modest and inconsistent. This discrepancy suggests that reverse causality, selection, or confounding by social or lifestyle factors may partly account for the positive correlation between moderate drinking and cognitive performance, as previously suggested. [START_REF] Corley | Alcohol intake and cognitive abilities in old age: the Lothian Birth Cohort 1936 Study[END_REF][START_REF] Cooper | Alcohol in moderation, premorbid intelligence and cognition in older adults: results from the Psychiatric Morbidity Survey[END_REF] A causal association was also not supported by negative findings of mendelian randomization studies in Chinese men [START_REF] Yeung | Evaluation of moderate alcohol use and cognitive function among men using a mendelian randomization design in the Guangzhou Biobank Cohort Study[END_REF] and Europeans. [START_REF] Kumari | Alcohol consumption and cognitive performance: a mendelian randomization study[END_REF] However, a recent study in a Scottish birth cohort suggested that the effects of alcohol on late-life cognition may be modified by genetic ability to metabolize alcohol. [START_REF] Ritchie | Alcohol consumption and lifetime change in cognitive ability: a gene 3 environment interaction study[END_REF] Similarly, lower cognitive scores in participants who stopped drinking during follow-up may partly reflect confounding by poor health. In fact, at reexamination, more than half of these participants reported stopping drinking because of poor health. However, adjustment for self-reported chronic conditions had little effect on the associations.

Our study has implications. Better cognitive performance was only inconsistently associated with moderate drinking, with some of the associations possibly explained by selection bias or confounding. This cautions against specific recommendations about beneficial drinking levels for cognitive function. Poorer cognition in current nondrinkers and recent quitters suggests greater attention should be given to the health status of this group. Although adverse effects of binge drinking on cognition were not detected over a short follow-up period or cross-sectionally, our findings do not preclude the possibility of faster cognitive decline in the long term among binge drinkers.

Table 1

 1 Descriptive characteristics of the study sample

		Baseline (2002-2005)	Reexamination (2006-2008)
		Men (n 5 6,608)	Women (n 5 7,967)	Men (n 5 6,608)	Women (n 5 7,967)
	Age, y, mean (SD)	57.8 (7.0)	57.3 (7.0)	61.3 (7.0)	60.8 (6.9)
	Alcohol use, n (%)
	Nondrinker	857 (13.0)	1,919 (24.1)	749 (11.3)	1,651 (20.7)
	Light	3,299 (49.9)	4,736 (59.4)	3,518 (53.2)	4,964 (62.3)
	Moderate	2,088 (31.6)	1,027 (12.9)	1,815 (27.5)	1,099 (13.8)
	Heavy	364 (5.5)	285 (3.6)	526 (8.0)	253 (3.2)
	Drinking frequency, n (%)
	Never	857 (13.0)	1,919 (24.1)	749 (11.3)	1,651 (20.7)
	<1 mo	919 (13.9)	2,690 (33.8)	939 (14.2)	3,129 (39.3)
	1-3 mo	1,524 (23.1)	2,095 (26.3)	1,670 (25.3)	1,920 (24.1)
	1-4 wk	2,166 (32.8)	1,022 (12.8)	2,225 (33.7)	1,053 (13.2)
	51 wk	1,142 (17.3)	241 (3.0)	1,025 (15.5)	214 (2.7)
	Binge drinking, n (%)
	Nondrinker	857 (13.0)	1,919 (24.1)	749 (11.3)	1,651 (20.7)
	Nonbinger	4,540 (68.7)	5,590 (70.2)	4,471 (67.7)	5,799 (72.8)
	Binge drinker	1,211 (18.3)	458 (5.7)	1,388 (21.0)	517 (6.5)
	CAGE, n (%)
	Nondrinker	857 (13.0)	1,919 (24.1)	749 (11.3)	1,651 (20.7)
	CAGE <2	4,963 (75.1)	5,936 (74.5)	5,022 (76.0)	6,213 (78.0)
	CAGE 21	788 (11.9)	112 (1.4)	837 (12.7)	103 (1.3)
	Household asset score, mean (SD)	6.3 (2.1)	5.7 (2.1)	6.7 (2.0)	6.2 (2.0)
	Educational level, n (%)
	Primary or less	482 (7.3)	858 (10.8)
	Vocational	1,871 (28.3)	1,995 (25.0)
	Secondary	2,220 (33.6)	3,202 (40.2)
	University	2,035 (30.8)	1,912 (24.0)
	Smoking status, n (%)
	Never smoked	2,045 (30.9)	5,363 (67.3)	2,048 (31.0)	5,497 (69.0)
	Former smoker	2,164 (32.7)	1,167 (14.6)	2,354 (35.6)	1,220 (15.3)
	Current smoker	2,399 (36.3)	1,437 (18.0)	2,206 (33.4)	1,250 (15.7)
	CVD, n (%)	1,317 (19.9)	1,295 (16.3)	1,488 (22.5)	1,481 (18.6)
	Hypertension, n (%)	3,273 (49.5)	4,432 (55.6)	3,694 (55.9)	4,888 (61.4)
	Diabetes, n (%)	608 (9.2)	608 (7.6)	671 (10.2)	699 (8.8)
	Leisure-time physical activity, n (%)
	None	2,808 (42.5)	3,609 (45.3)	2,236 (33.8)	3,099 (38.9)
	Some	3,800 (57.5)	4,358 (54.7)	4,372 (66.2)	4,868 (61.1)
	High depressive symptoms, n (%)	692 (10.5)	1,681 (21.1)	843 (12.8)	1,976 (24.8)
	Immediate recall, mean (SD)			21.5 (4.2)	23.0 (3.8)
	Delayed recall, mean (SD)			7.3 (1.9)	8.0 (1.8)
	Verbal fluency, mean (SD)			22.3 (7.2)	22.2 (7.0)
	Letter cancellation, mean (SD)			17.2 (4.8)	18.5 (5.0)

Abbreviations: CAGE 5 cutting down, annoyance by criticism, guilty feeling, and eye-openers; CVD 5 cardiovascular disease. Figures are means (SDs) for continuous variables and counts (%) for categorical variables. For categories of average daily alcohol intake (lower cutoffs are for women): nondrinker 0 g, light #5/10 g, moderate 5-20/10-40 g, and heavy $20/40 g.

Table 2

 2 Regression results for alcohol consumption and standardized cognitive scores in men (n5 6,608)

		Immediate recall	Delayed recall	Verbal fluency	Letter cancellation
		Coef.	95% CI	Coef.	95% CI	Coef.	95% CI	Coef.	95% CI
	Prospective
	Average alcohol use
	0 g/d	20.06	20.13, 0.01	20.08 a	20.15, 20.01	20.05	20.12, 0.02	20.01	20.08, 0.06
	<10 g/d (ref.

Table 2

 2

	Continued
		Immediate recall	Delayed recall	Verbal fluency	Letter cancellation
		Coef.	95% CI	Coef.	95% CI	Coef.	95% CI	Coef.	95% CI
	Stable drinker (ref.)	0.00	0.00, 0.00	0.00	0.00, 0.00	0.00	0.00, 0.00	0.00	0.00, 0.00

Table 3

 3

	Continued
		Immediate recall	Delayed recall	Verbal fluency	Letter cancellation
		Coef.	95% CI	Coef.	95% CI	Coef.	95% CI	Coef.	95% CI
	Stable drinker (ref.)	0.00	0.00, 0.00	0.00	0.00, 0.00	0.00	0.00, 0.00	0.00	0.00, 0.00

Neurology 84January 20, 2015

20.27, 20.14 20.18 a 20.25, 20.12 20.15 a 20.22, 20.08 20.20 a 20.27, 20.13 Quit drinking 20.20 a 20.26, 20.13 20.19 a 20.26, 20.11 20.06 20.13, 0.01 20.07 20.15, 0.00 Continued

Neurology 84 January 20, 2015

STUDY FUNDING

This work was supported by the Wellcome Trust (grants 064947 and 081081); the US National Institute on Aging (grant R01 AG23522); and MacArthur Foundation Research Network (grant 712058).

AUTHOR CONTRIBUTIONS

M.B. and P.H. conceptualized the study. P.H. performed statistical analysis and wrote first and successive drafts of manuscript. M.B., M.R., R.K., A. Pajak, S.M., S.S., H.P., A. Peasey