Rashed Salem
email: rashed.salem@univ-lyon2.fr

Jérôme Darmont
email: jerome.darmont@univ-lyon2.fr

Omar Boussaïd
email: omar.boussaid@univ-lyon2.fr

Efficient Incremental Breadth-Depth XML Event Mining

Keywords: H.2.8 [Database Applications]: Data Mining Algorithms, Performance Mining logged events, XML mining, frequent itemsets, association rules

Many applications log a large amount of events continuously. Extracting interesting knowledge from logged events is an emerging active research area in data mining. In this context, we propose an approach for mining frequent events and association rules from logged events in XML format. This approach is composed of two-main phases: I) constructing a novel tree structure called Frequency XML-based Tree (FXT), which contains the frequency of events to be mined; II) querying the constructed FXT using XQuery to discover frequent itemsets and association rules. The FXT is constructed with a single-pass over logged data. We implement the proposed algorithm and study various performance issues. The performance study shows that the algorithm is efficient, for both constructing the FXT and discovering association rules.

INTRODUCTION

Recently, the eXtensible Markup Language (XML) has become widely used as the de facto standard for representing, exchanging, modeling, and maintaining semi-structured data. The widespread of XML-based applications and increasing amount of XML data pose several challenges for mining XML data. Modern XML-based applications log huge amounts of events at real-time, continuously. The logged event data describe the status of each application component and can be used to trace application activities. Applications that log events in XML format range from scientific to business and financial applications. Examples of such applications include XML-based data warehousing, web personalization and web-click logs, geographic information systems, and e-commerce. Mining and analyzing logged event from such applications help for achieving selfmanagement systems. Therefore, mining XML-formatted logged events is becoming increasingly important. It should have high attention from the database, data warehousing, data mining, and machine learning research communities.

Mining logged events is the process of extracting knowledge from continuous, rapid logged events. One of the most important data mining techniques is association rule mining. Association rule mining discovers interesting association and/or correlation relationships among large sets of logged events, and predicts upcoming events based on occurrence of previous ones. Mining association rules from incremental XML-formatted logged events is different than mining traditional static data, due to several specific issues and challenges either related to data arrival [START_REF] Gaber | Mining data streams: A review[END_REF][START_REF] Jiang | Research issues in data stream association rule mining[END_REF], or XMLformatting nature [START_REF] Feng | Mining interesting XML-enabled association rules with templates[END_REF][START_REF] Zhao | XML structural delta mining: Issues and challenges[END_REF].

When logging events, they arrive continuously at moderate or high speed, in unbounded amount, and changing data distributions. Unlike in traditional data mining, there is not enough time to rescan the whole database whenever an update occurs. Therefore, a single-pass over events is required. Logged events need to be processed incrementally as fast as possible. Processing speed should be faster than events arrival rate. Moreover, mined data should not need to be recalculated each time requested. Unbounded amount of logged events and limited system resources, such as disk storage, memory usage, and CPU power, lead to the need for event mining algorithms that adapt themselves to available resources, otherwise accuracy result decreases. Also, while traditional data mining techniques mine frequent itemsets and discard non-frequent itemsets, this property is not valid for logged events, where the frequency of itemsets is changing over time. On the other hand, extracting knowledge from XML data is more difficult than an operational data, because of the flexible, irregular, and semi-structured nature of XML data.

To the best of our knowledge, there is no algorithm proposed in the literature to discover interesting knowledge from incremental XML-formatted logged events. Therefore, we propose in this paper an incremental algorithm for this purpose. Our algorithm is composed of two main phases: firstly, we construct a new tree structure called Frequency XML-based Tree (FXT) that stores frequencies of events to be mined. Secondly, we query frequent event-sets and association rules efficiently from the constructed FXT using XQuery. Our algorithm handles most processing logged event issues. It satisfies a single-pass over data transactions to construct the compact FXT structure. Although the FXT is processed using XML technologies and constructed in XML format, its construction time is fast enough. Association rules with different minimum supports are queried at any time without re-constructing the FXT from scratch.

The rest of this paper is organized as follows. Related work is discussed in section 2. In section 3, we present our motivation and a description of logged events. Section 4 introduces the general structure of the novel Frequency XMLbased Tree (FXT) and our algorithm for constructing the FXT. Mining frequent itemsets and association rules from the FXT is presented in section 5. Performance study of our algorithm is discussed in section 6. Finally, we conclude and highlight future trends in section 7.

RELATED WORK

There are two main types of approaches for XML data mining in the literature. The first type of approaches applies relational data mining tools on XML data by mapping XML documents to relational data model and storing them in a relational database [START_REF] Zhang | A framework for efficent association rule mining in xml data[END_REF]. The second type of approaches applies data mining techniques directly onto native-XML data [START_REF] Braga | A tool for extracting XML association rules[END_REF][START_REF] Wan | Mining association rules from XML data using XQuery[END_REF][START_REF] Wang | Mining association rules from complex and irregular XML documents using XSLT and XQuery[END_REF]. We are interested with the second type of approaches, specifically mining frequent itemsets and association rules from XML data.

Mining association rules using XQuery.

Wan and Dobbie provide XQuery implementation of the well-known Apriori algorithm [START_REF] Agrawal | Fast algorithms for mining association rules[END_REF], to extract association rules from XML documents without any pre-processing or postprocessing [START_REF] Wan | Mining association rules from XML data using XQuery[END_REF]. Their algorithm is adapted to simple and well-defined XML format. This algorithm is extended with pre-processing step in order to mine more complex and irregular XML documents [START_REF] Wang | Mining association rules from complex and irregular XML documents using XSLT and XQuery[END_REF]. Authors actually transform complex documents into a format that can be mined by Wan algorithm using XSLT. Braga et al. propose XMINE [START_REF] Braga | A tool for extracting XML association rules[END_REF], a tool to extract XML association rules from XML documents. The XMINE operator is based on XPath and XQuery to express complex mining tasks on the content and the structure of XML data.

Tree-based mining algorithms.

Han et al. propose FP-Growth for mining frequent itemsets without generating candidate itemsets [START_REF] Han | Mining frequent patterns without candidate generation[END_REF]. FP-Growth requires two database scans for constructing its FP-Tree. Cheung and Zaiane extend FP-Tree by proposing a novel data structure called CATS Tree [START_REF] Cheung | Incremental mining of frequent patterns without candidate generation or support constraint[END_REF]. As FP-Tree, CATS tree allows frequent pattern mining without generation of candidate itemsets. It allows mining with a single pass over the database as well as efficient insertion or deletion of transactions at any time.

To the best of our knowledge, our algorithm is the first work proposed to mine frequent itemsets and association rules from incremental XML-formatted logged events, using XML technologies (e.g., XPath and XQuery). Table 1 shows differences between FXT versus tree-based techniques (i.e., FP-Growth and CATS) and XQuery-based im-plementation techniques (i.e., Apriori implementation). Although Apriori-implementation mines association rules from XML data using XQuery [START_REF] Wan | Mining association rules from XML data using XQuery[END_REF], it is designed to static transactions of XML data. Mining association rules with different minimum support by Apriori algorithm requires regenerating the largest itemsets from scratch. Compared to our algorithm, Apriori-implementation provides less performance particularly for large databases of transactions. Despite CATS [START_REF] Cheung | Incremental mining of frequent patterns without candidate generation or support constraint[END_REF] is not proposed for mining XML data, it is based on constructing an incremental frequency tree like our algorithm. Rather than CATS algorithm mines frequent patterns with a complicated algorithm named FELINE, it does not support mining association rules from CATS tree directly due to the absence of total size of transactions.

FXT FP- Growth CATS Apriori- imp. Data context static X X incremental X X Data format raw data X X XML data X X Items coverage all items X X only frequent X X Tree structure tree-based X X X Passing database single-pass X X two or more pass X X Transactions size included in tree X Ordering tree pre-ordering X ordering path items w.r.t support X X X sorting children X X sweeping items X Implementation- based programming language X X XML technologies X X
Table 1: FXT versus related works

LOGGING EVENTS

There are several software platforms that log a large amount of events incrementally every day, into simple text or XML format. Logged events are essential to understand and trace the activities of such platforms. For instance, we are motivated to mine logged events from XML-based data integration platforms [START_REF] Salem | Conceptual workflow for complex data integration using AXML[END_REF]. It worth to be noted that these platforms are developed, managed and maintained using XML technologies. Data integration is the process of extracting data from heterogeneous and distributed sources, transforming them into a unified format, and loading them into a repository (namely a warehouse), see Figure 1. Discovering interesting knowledge from logged events can be employed to self-maintain and configure the workflow behavior of these systems, how to achieve this issue is out scope of this paper.

Actually, logged events include much descriptive information about each activity (e.g., identification, occurring time, source, description, category, etc.). The more logging information, the more interesting knowledge can be discovered. In order to apply our algorithm for mining frequent events and association rules, we need to pre-process logged events and organize them into transactions as illustrated in the following sample. Each transaction has identification, its occurring time, and a set of items which represent platform events. The set of events is assumed to be logged in a window-size of time (time + window). The corresponding format of logged transactions can be obtained directly from their origin platforms, or can be transformed using the XSLT language to a format that can be processed by our algorithm in a preprocessing step. The most important thing to our algorithm is to define the listing of items of each transaction, which should be sorted alphabetically for performance purposes.

FREQUENCY XML-BASED TREE (FXT)

FXT Structure

In order to mine frequent itemsets or association rules, the frequency of events (or items) needs to be calculated. Hence, we propose a novel tree structure that contains frequency of all logged items, named Frequency XML-based Tree (FXT). The FXT nodes, except root node, consist of two entries: item name and counter, where item name registers which item this node represents (e.g., Ii), and counter registers the number of transactions represented by the portion of the path reaching this node (e.g., Ni or N m|...|i ). As illustrated in figure 2, the FXT is composed of three main levels of nodes. Firstly, the Root node refers to the FXT root node. It represents the total number of logged transactions (Ntrans). Secondly, the Breadth nodes refers to all root's children nodes. It represents the count of each item appeared in any logged transaction. Thirdly, the Depth nodes refers to all root's grandchildren nodes. It represents a relative or conditional count of a specific item given other related items. The depth nodes are represented as set of paths, each path corresponds specific transactions itemsets. In figure 2, the dashed line annotated by double slashes "//" means that there is zero or more in-between nodes in a specific depth path. It worth to be noted that the FXT can handle both sorted and unsorted items of upcoming transactions, but we observed that handling sorted items results in more compact FXT structure and eases mining frequent itemsets and association rules from the FXT. Thus, letters (a, i, m, and z ) of items refer to their ordering. In addition, although FXT is designed to manage XML-formatted data, the same concept can be applied to raw data. Finally, there are some facts can be deduced from the FXT structure:

root N trans I a N a I i N i I z N z I i N i |…| a I z N z |…| a I z N z |..| i |..| a I m N m |…| i I z N z |…| i I z N z |..| m |
• Ntrans = T otal(trans) refers to the total number of transactions;

• Ntrans ≥ N k , where N k can be count of any item k;

• N k ≥ N v|...|k , where N v|...|k is a conditional count of Iv given I k and in-between items.

FXT Management

The first phase of our algorithm is to construct the FXT, by handling each logged transaction individually.

Insertion of transactions

Logged transactions are inserted into the FXT upon arrival. Our algorithm follows four steps for each logged transaction on constructing the FXT as presented by algorithm 1.

Step 1 (incrementing root counter, Ntrans).

This root counter represents the total number of logged transactions, which can be used to calculate item support.

Step 2 (incrementing breadth).

For each item of the transaction, our algorithm increments the item counter if it exists as one of root children (breadth nodes), otherwise the algorithm creates the item as new root child and initializes its counter at 1. Any item support can be easily calculated later via dividing item counter by Ntrans, see algorithm 2.

Step 3 (incrementing depth).

The algorithm increments the transaction path if it exists, otherwise creates it. While creating the path, item by item, respecting the transaction items ordering, the algorithm takes into account the previous occurrence of relative transaction items. This is reflected when initiating counter of the path items. The FXT path may not correspond only the same transaction that occurred once or several times, but also correspond many transactions that satisfy the same beginning portion of the path. This step is presented by algorithm 3.

Step 4 (updating other paths).

This step is required to ensure the correctness of counting of one given itemset across different FXT paths. For each transaction, some paths can be generated from transaction items that differ from the path built in step 3, called other paths. The algorithm checks only other paths existing in the FXT to be updated. In case if they do not already exist, the algorithm does not create them for compactness purpose, see algorithm 4.

Example

Figure 3(a-f) shows the four steps to construct the FXT by inserting transactions given in section 3. Because steps 1 and 2 are always applied directly for all transactions, we focus on how steps 3 and 4 are applied.

In figure 3(a) and figure 3(b), step 3 creates the paths "root/A/B/C/D" and "root/C/E", respectively. Step 4 is not evaluated, because there are no other paths available. In figure 3(c), in order to initialize counter of item "C" according to step 3, the algorithm detects item "C" as child of item "B" in the path "root/A/B/C/D". Thus, counter of item "C" in the existing path is incremented to become an initialization value of item "C" in the new path "root/B/C". In figure 3(d), step 3 initializes counter of item "D" at 2, be-

(: repeat starting with next item of T as parent of the path :)

update-other-paths(T, nexIdx) end end cause item "D" already exists as child of item "C" in the path "root/A/B/C/D". But, step 4 detects other path "root/C/E" in the FXT, thus the counter of item "E" is incremented. In figure 3(e), step 3 initializes the counter of item "D" at 2, because item "D" already exists as grandchild or child of items "B" and "C", respectively in the path "root/A/B/C/D". Moreover, step 4 detects portion of other path "root/C/D" in the FXT, thus counter of item "D" is incremented. In fig-ure 3(f), step 3 initializes the counter of item "C" at 2, because item "C" already exists as grandchild of item "A" in the path "root/A/B/C/D". Also, step 4 detects other path "root/C/E" in the FXT, thus counter of item "E" is incremented. Finally, the constructed FXT is as follows.

<? xml version="1.0" > <root counter = "6"> <A counter = "2"> <B counter = "1"> <C counter = "1"> <D counter = "1"/> </C> </B> <C counter = "2"> <E counter = "1"/> </C> </A> <B counter = "3"> <C counter = "3"> <D counter = "2"/> </C> </B> <C counter = "6"> <E counter = "3"/> <D counter = "3"> <E counter = "1"/> </D> </C> <D counter = "3"/> <E counter = "3"/> </root>

MINING FREQUENT ITEMSETS AND AS-SOCIATION RULES USING XQUERY

The main objective of constructing the FXT is to mine frequent itemsets and association rules easily using the XQuery language. Frequent itemsets are queried by traversing the FXT from breadth nodes to specific nodes (portion of paths), or to leaf nodes (complete paths). Frequent itemsets are filtered using a statistical called support. Support measures the proportion of transactions that contains a specific item (or itemset). A frequent itemset is an itemset whose support is greater than some user-specified minimum support. Frequent itemsets satisfy the Apriori property, which states that if a given portion of path does not satisfy minimum support, then neither will any of its descendants [START_REF] Agrawal | Fast algorithms for mining association rules[END_REF]. Examples for retrieving the support of items and itemset from the FXT follow.

Support(A) = root/A/@counter root/counter Support(B, C, D) = root/B/C/D/@counter root/counter Example:

The following example introduces the function for generating frequent itemsets from the FXT that constructed in main example (section 4.2.2).

declare variable $input := doc("tree.xml")/root; declare variable $rootCounter := $input/@counter; declare function local:getFrequentItemsets($parent as xs:string, $element as element(*, xs:untyped), $minSupport as xs:decimal) { let $path := concat($parent,'/',name($element)) where $element/@counter div $rootCounter>=$minSupport return (<frequent path="{$path}" count="{$element/@counter}" support="{$element/@counter div $rootCounter}"/>, for $child in $element/* (: call the function :) for $child in $input/* return local:getFrequentItemsets("", $child, 0.25)

The result of calling previous function to get frequent itemsets with min support=0.25 is as follows. <frequent path="/A" count="3" support="0.375"/> <frequent path="/A/B" count="2" support="0.25"/> <frequent path="/A/B/D" count="2" support="0.25"/> <frequent path="/A/C" count="2" support="0.25"/> <frequent path="/B" count="4" support="0.5"/> <frequent path="/B/C" count="3" support="0.375"/> <frequent path="/B/C/D" count="2" support="0.25"/> <frequent path="/C" count="6" support="0.75"/> <frequent path="/C/E" count="3" support="0.375"/> <frequent path="/C/D" count="3" support="0.375"/> <frequent path="/D" count="4" support="0.5"/> <frequent path="/E" count="4" support="0.5"/> Association rules have been first introduced in the context of retail transaction databases [START_REF] Agrawal | Fast algorithms for mining association rules[END_REF]. An association rule is an implication of the form X ⇒Y, where the rule body X and head Y are subsets of the set I of items (I =i1, i2, ..., in) within a set of transactions D and X ∩ Y = Φ. A rule X ⇒ Y states that the transactions T that contain the items in X are likely to also contain the items in Y. Association rules are characterized by two measures: the support, which measures the proportion of transactions in D that contain both items X and Y ; and the confidence, which measures the proportion of transactions in D containing items X that also contain items Y. Conf idence(X ⇒ Y ) can be expressed as the conditional probability p(Y |X). Thus, we define:

Support(X ⇒ Y ) = count(X∪Y ) N trans = root/X/Y /@counter root/counter (1) Conf idence(X ⇒ Y ) = support(X⇒Y ) support(X) = count(X∪Y ) count(X)
= root/X/Y /@counter root/X/@counter (2)

Example:

The following example introduces the XQuery function for generating a set of association rules from the FXT constructed in main example (section 4.2.2).

declare function local:generateRules($parent as xs:string, $x as element (*, xs:untyped), $min_sup as xs:decimal, $min_conf as xs:decimal) { let $path_x := concat($parent,'/',name($x)) return (for $y in $x/* let $y_given_x := name($y) let $support_xy := $y/@counter div $rootCounter let $support_x := $x/@counter div $rootCounter let $confidence := $support_xy div $support_x where $support_xy >= $min_sup and $confidence >= $min_conf return (<rule body="{$path_x}" head="{$y_given_x}" support="{$support_xy}" confidence="{$confidence}"/>, local:generateRules($path_x, $y,$min_sup, $min_conf))) };

(: call the function :) for $child in $input/* return local:generateRules("", $child, 0.25, 0.5)

The result of calling previous function to get association rules with min support=0.25 and min confidence=0.5 is as follows.

<rule body="/A" head="B" support="0.25" confidence="0.666"/> <rule body="/A/B" head="D" support="0.25" confidence="1"/> <rule body="/A" head="C" support="0.25" confidence="0.666"/> <rule body="/B" head="C" support="0.375" confidence="0.75"/> <rule body="/B/C" head="D" support="0.25" confidence="0.666"/> <rule body="/C" head="E" support="0.375" confidence="0.5"/> <rule body="/C" head="D" support="0.375" confidence="0.5"/> Note that, it is possible to apply other XQuery functions to discover some statistics or mine more association rules. For instance, to query the reverse rule(Y ⇒ X), a function is firstly required to sort the rule body and the rule head alphabetically in order to calculate the support(Y ⇒ X), whereas count(Y ∪ X) = count(X ∪ Y ) = root/x/y/@counter. But, when calculating the conf idence(Y ⇒ X), the rule body does not change in the denominator, i.e., support(Y ), see equation (2).

PERFORMANCE STUDY

We have implemented the FXT construction algorithm using some Java libraries for manipulating XML data structure (i.e., JDom, SAXPath, and Jaxen). Mining frequent itemsets and association rules are performed using the XQuery language. We experimented with different synthetic datasets, starting from 10 transactions to 100K of transactions. The average lengths of transactions are 15 items per transaction. All experiments are performed on a 2.80 GHz PC with 3 GB RAM, running on Windows 7, with minimum Java heap size 128 MB and maximum Java heap size 512 MB.

We study the impact of constructing the FXT on the machine resources. Figure 4(a) plots CPU time for new transaction insertion given different FXT sizes. It can be easily observed that the CPU runs fast for inserting new transaction even though FXT has large size (e.g., it takes 5ms to insert new transaction into a 100K FXT size). Likewise, figure 4(b) plots memory usage, it can be observed that our algorithm consumes a small size of memory for new transaction insertion with different FXT sizes. Figure 4(c) plots disk storage of the FXT document against different sizes of transactions. As shown in the figure, although the increasing relationship, the required storage remains small. Due to the FXT compact structure, the repeated or similar insertions of transaction need to only update item counters without consuming further storage space.

Since we are interested in mining XML data using XML technologies, to the best of our knowledge there is only one most related work (i.e., implementation of Apriori algorithm using XQuery [START_REF] Wan | Mining association rules from XML data using XQuery[END_REF]). The Apriori algorithm always deals with static database of transactions. Figure 5 shows the performance comparison between our algorithm and the XQuery-based implementation of Apriori, for mining association rules from XML using XQuery. It shows that our algorithm is always providing better performance than Apriori, specifically for larger amount of transactions (see figure 5(a)), and also for different values of minimum support (see figure 5(b)). Apriori generates frequent itemsets and association rules each time from scratch, while our algorithm construct the FXT incrementally. Then frequent itemsets and association rules can be queried directly at any time from the FXT.Moreover, FXT is very compressed if compared with transactions document of Apriori algorithm.

Finally, we conclude that our algorithm is very efficient to

CONCLUSIONS

In this paper, we propose an incremental approach for mining association rules from XML logged events. Our approach applies an incrementing breath-then-depth algorithm, for constructing a novel frequency XML-based tree structure. The algorithm composes of four steps for inserting transaction into the tree. The constructed tree can be directly queried using XQuery language for retrieving frequent itemsets and association rules, without applying complex data mining techniques. Our algorithm handles incremental logged events. Thus, it is featured with a single-pass of dataset, incremental processing of transaction, compressed structure of the tree, fast for inserting new transactions, fast for querying frequent itemsets or association rules, and efficient to limited resources. These features are validated by implementing the algorithm and experimenting its performance.

In future, we aim at mining association rules from logged events taking account their real-time of logging, and discovering the relationships among events against their logged real-time. Moreover, we intend to apply our algorithm for mining XML events that logged from our data integration platform [START_REF] Salem | Conceptual workflow for complex data integration using AXML[END_REF]. This algorithm can be used to discover in-teresting knowledge, in order to maintain, automate, and re-activate the workflow behavior of the ETL tasks.

( a )Figure 3 :

 a3 Figure 3: Constructing the FXT document.

  return local:getFrequentItemsets ($path, $child, $minSupport)) };

Figure 4 :Figure 5 :

 45 Figure 4: Machine resources for inserting new transaction to FXT

  ..| i

				Root node
		/	/	/
				Breadth
				nodes
	//	//	//	//
				Depth
	//		//	nodes
		Figure 2: FXT structure


Michael Zollhöfer

Michael Martinek

Günther Greiner

Marc Stamminger

Jochen Süßmuth

Automatic Reconstruction of Personalized Avatars from 3D Face Scans

Keywords: personalized avatars, face scanning, face reconstruction, face model fitting, Microsoft Kinect sensor

We present a simple algorithm for computing a high quality personalized avatar from a single color image and the corresponding depth map which have been captured by Microsoft's Kinect sensor. Due to the low market price of our hardware setup, 3D face scanning becomes feasible for home use. The proposed algorithm combines the advantages of robust non-rigid registration and fitting of a morphable face model. We 1 Page 14 of 41 http://mc.manuscriptcentral.com/cavw -For Peer Review Computer Animation and Virtual Worlds obtain a high quality reconstruction of the facial geometry and texture along with oneto-one correspondences with our generic face model. This representation allows for a wide range of further applications such as facial animation or manipulation. Our algorithm has proven to be very robust. Since it does not require any user interaction, even non-expert users can easily create their own personalized avatars.

Introduction

During the past few years, massive multiplayer online games (MMOGs) such as World of Warcraft, Aion or Second Life have gained tremendous attention. In these games, millions of users, each represented by a virtual character -known as avatar -meet in a threedimensional virtual world. Since the users should be distinguishable from each other, each user must have a unique avatar. Most MMOGs offer a character editor in which the user can select his avatar from a set of existing models. These avatars can be further customized using simple user interfaces which allow the user to morph between different shapes or to include customized textures or models.

As the graphics in computer games become ever more realistic and the focus of the games changes from fantasy scenarios towards real life settings, the demand for photorealistic avatars, which resemble the users themselves, is constantly increasing. Unfortunately, current in-game avatar editors offer only a limited expressibility, making it almost impossible for a user to create a virtual clone for the online world.

Besides their usage in online games and chats, personalized 3D avatars are also important in gadget applications such as aging simulations or digital 3D beauty salons.

In this paper, we present a fully automatic method for the generation of realistic threedimensional face models with textures. As input for our algorithm we use a depth scan and a color image that were recorded using the Microsoft Kinect sensor. This device was initially released as a video game controller for the Microsoft Xbox. drivers have been released which enable the general purpose usage of the device on a regular personal computer. Due to the low market price and its widespread use, the Microsoft Kinect sensor is ideally suited for recording personalized 3D avatars. Using our system, everyone can automatically digitalize his face and create a personalized avatar within seconds.

Related Work

The reconstruction of personalized 3D face models has become very popular during the last years. Two different approaches exist for this purpose: algorithms which try to reconstruct the 3D model solely from color images and algorithms which reconstruct the 3D model by fitting a template mesh to a depth scan of the face.

The first class of algorithms reconstructs the facial geometry directly from one or more 2D images. Tang and Huang [START_REF] Tang | Automatic Construction of 3D Human Face Models Based on 2D Images[END_REF] automatically extract salient facial features from a front and profile face image. The detected features are then used to adapt a coarse template mesh.

Since this method requires a one-to-one relationship between facial features and the vertices of the template mesh, it can only produce very coarse reconstructions. Blanz and Vetter [START_REF] Blanz | A Morphable Model for the Synthesis of 3D Faces[END_REF] employ an iterative optimization to adapt the parameters of a three-dimensional morphable model by projecting the current morphable model onto the image plane and then minimizing the difference between the pixel colors. To improve the stability of their method, the optimization is performed in a coarse to fine manner. Breuer et al. [START_REF] Breuer | Automatic 3D Face Reconstruction from Single Images or Video[END_REF] or FaceShop also compute a 3D avatar from features in 2D images. These features can either be automatically detected or hand-picked by the user. Common to all methods which reconstruct the 3D face model solely from photographs is that while they can accurately reconstruct the face in feature-rich regions, the fitting in feature-less regions like the cheek or the forehead is rather poor. Methods of the second category reconstruct the 3D face by fitting a template mesh to depth scans. Weissenfeld et al. [START_REF] Weissenfeld | Adaptation of a Generic Face Model to a 3D Scan[END_REF] construct a multi-resolution detail pyramid of the input face scan by successive Laplace smoothing. Using a set of manually selected features, they fit a generic face model to the multi-resolution detail pyramid in a coarse-to-fine manner. Blanz et al. [START_REF] Blanz | Fitting a Morphable Model to 3D Scans of Faces[END_REF] describe an iterative algorithm for fitting a morphable model to a textured depth scan. In each iteration, the current morphable model is projected onto a twodimensional cylindrical image. An energy term which considers both, the color and the depth value after the projection, is then minimized to get a better-fitting morphable model. Basso and Verri [START_REF] Basso | Fitting 3D Morphable Models using Implicit Representations[END_REF] approximate the input depth scan by an implicit function and then solve for the parameters of a morphable face model such that the distance between the face and 5

Page 18 of 41 http://mc.manuscriptcentral.com/cavw -For Peer Review Computer Animation and Virtual Worlds the depth scan is minimized. To improve the convergence of their method, they split the template mesh into four sub-meshes which are fitted independently. The sub-meshes are then smoothly blended to obtain the final reconstruction. Li et al. [START_REF] Li | Global Correspondence Optimization for Non-Rigid Registration of Depth Scans[END_REF] employ a sophisticated non-linear optimization process to fit a source mesh to a target depth scan. By enforcing local rigidity and global smoothness of the deformation, they obtain high quality registrations given a good initial alignment. Most similar to the proposed algorithm is the work recently published by Kim et al. [START_REF] Kim | Realistic 3D Face Modeling Using Feature-Preserving Surface Registration[END_REF] since they also use non-rigid registration to fit a common template mesh to a depth scan. However, our algorithm is more robust in practice since we do not rely on robust 2D facial features during the non-rigid registration and since our regularization term tries to maintain surface features while their regularization term only minimizes surface stretch.

Overview

The proposed algorithm automatically reconstructs a high quality 3D face model with texture from an RGB image and a depth map by fitting a morphable face model to the input data. We use the Microsoft Kinect sensor to capture an RGB image and the corresponding depth map from which a metric point cloud is computed. Using four automatically detected feature points, we estimate an initial rigid alignment of a common template mesh with the recorded point cloud. Since this alignment is in general not good enough to be used as input for the morphable model fitting, we non-rigidly register the average face of the morphable

Data Acquisition

In this section, we briefly describe the way to obtain a raw depth image of the face of a person sitting in front of the Kinect and the augmentation of this image with valuable feature points as well as color information.

Input Device

The Kinect is a device which combines a regular RGB camera and a 3D scanner, consisting of an infrared (IR) projector and an IR camera as shown in Figure 2. The projector sends several thousands of structured IR rays into the scene which are reflected by objects and recaptured by the IR camera. The distortion between the emitted and the received pattern is used to reconstruct the depth values for each reflected ray. The driver interpolates the depth values between the rays and outputs a 640x480 depth grid with a precision of 11 bits @ 30 Hz. Microsoft officially specifies a depth range of 1.2m -3.5m but in our experiments we 7 found that a minimum distance of 0.5m is sufficient to receive good 3D images.

The RBG image is provided in the same resolution and framerate as the depth data, however, the two signals do not naturally match due to different extrinsic and intrinsic camera parameters. The exact parameters may even vary among different Kinect devices which makes an individual calibration unavoidable.

Data Preparation

To assist the calibration of the IR and the RGB camera, we use OpenCV's [START_REF] Bradski | The OpenCV Library[END_REF] calibration routines to specify the required DOFs. After the calibration, the data is available as 3D point cloud with natural metric units and a corresponding RGB value is assigned to each point.

Yet, we still maintain the topology information in form of the 640x480 grid from the raw data to simplify the feature detection and face segmentation, which requires neighborhood information for each point.

The depth data we recieve from the Kinect in a single frame is quite noisy and can contain holes at arbitrary positions. To reduce these effects, we average the depth values of eight successive frames, which leads to a much smoother result. Also, missing points in one frame may be compensated by other frames in which the device was able to capture these points. In addition, we apply a Gauss filter and simple hole-filling to the temporally smoothed data, which further improves the input data. Figure 3 shows a face scan at different stages of the preparation pipeline.

8

To avoid motion blurring artifacts, it is required that the user remains motionless for at least eight frames (0.27s) while capturing the image.

Face and Feature Detection

Assuming that exactly one person is sitting in front of the Kinect, we first detect the face along with a number of significant feature points to assist the alignment of the scanned data at a later stage. We particularly aim to detect the middle point of each eye, the nose tip and the chin. Our idea is to locate regions of significant face parts in the RGB image, then map these regions onto the geometry data and to proceed the detection of feature points in the geometry domain.

For the first part, we use OpenCV to find the bounding rectangles of the face, the eyes and the nose in the RGB image (see Figure 4). After we have detected the face on the entire range of the input RGB image, we reduce the further searching domain in the image to the face's bounding box and detect the eyes and the nose. This reduction does not only provide better performance, but also increases robustness since the algorithm might falsely identify background parts as an eye or a nose.

Due to the fact that the RGB data is aligned with the point cloud and that the topology is the same in both spaces, we can apply the rectangular regions directly in the geometry domain.

In order to find the nose tip, we loop through all 3D points inside the detected nose 9 rectangle and pick the one with the smallest depth value as nose feature.

For the chin, no feature detectors are available in OpenCV which allow for a preselection of the chin's region in the RGB image. As a solution, we use the following heuristic: We first perform a line search from the detected nose tip down the y-axis until we find a significant ascend of the depth values. The resulting point is a temporary feature point which we call the chin edge. From this point, we sample the same line back to the nose until we detect a local maximum of the depth values. This second temporary feature point is named the chin groove. We now define the final chin feature to be the point between the chin groove and the chin edge which is closest to the camera. In order to compensate

for a small roll of the subject's head (if the main face axis is not perfectly aligned with the y-axis), we extend the search region by a small offset of ±5 pixels in x-direction.

An eye feature would ideally be the point on the eyeball closest to the camera. However, the resolution and the quality of the input data is not sufficient to robustly find these points on the geometry. As an approximation, we take the center point of the detected bounding box which turned out to be a robust estimate for the initial alignment at a later stage. Figure 4 (right) shows the final feature points on a scanned face.

Since the feature detection runs in real-time, a person sitting in front of the camera gets real-time feedback of the resulting face scan together with the detected feature points (see Figure 1). This allows the user to optimize his position before he eventually captures the current data. To further stabilize the features, we perform a smoothing operation over various frames as we did on the raw depth data.

Face Segmentation

The recorded depth data still contains unnecessary background data at this point. In order to reduce the costs in the next steps, we separate the face from the rest of the input data as seen in the scanned images from Figure 4. From the feature detection, we already know some points which definitly belong to the face. The rest of the points is found with a floodfill-like algorithm using the detected face feature points as seed. In each recursion, we check the four-neighborhood of a current face point whether the depth values change by more than 5mm. If this is not the case, we add the corresponding point to the list of face points and recursively call the routine with this point. This method has turned out to robustly separate the face from the background and the body of the user.

Fitting a Generic Face Model

The point cloud that was generated in the previous step represents the geometry of the scanned face. However, except for the few detected feature points, the geometry does not contain any semantic information which would be necessary to animate or further process the face. To attribute the scanned face with a semantic meaning, we fit a morphable face model [START_REF] Blanz | A Morphable Model for the Synthesis of 3D Faces[END_REF] to the scan. Therefore, we compute a rough initial alignment of the scanned point cloud P and the average face T of our morphable model. Given the previously computed features points and the corresponding points on the generic face model, we can compute the shape-preserving transformation which best aligns the two data sets by performing a 11 generalized Procrustes analysis [START_REF] Gower | Generalized Procrustes Analysis[END_REF].

Theoretically, one could now solve for the parameters of the morphable model in such a way that it approximates the input scan as good as possible. Unfortunately, morphable models are not invariant under shape-preserving transformations which means that the input shape must be perfectly scaled and aligned with the morphable model to generate satisfactory results. We found that it is very difficult to produce such a rigid alignment without any user assistance or very accurate marker positions since a registration using the ICP algorithm [12] tends to converge into a local minimum if the deformation between the source and the target shape is too large. To obtain a more robust alignment for the final fitting of the morphable model, we compute a non-rigid registration of the template model T and the input scan.

Given a template mesh T and a coarsly aligned input scan P, the goal of the non-rigid registration is to find a plausible space deformation Φ such that the distance between the deformed template mesh Φ(T ) and the input scan P is minimized.

Following Suessmuth et al. [13], we formulate the non-rigid registration as a variational problem. Therefore, we define a registration energy E reg , which is composed of a fitting term E fit , that attracts the template mesh towards the input scan geometry, and an internal energy term E def , that serves as regularizer and prevents unnatural deformations of the template mesh. The deformation Φ which best aligns the template mesh with the input scan is then found by minimizing the registration energy.

Fitting Energy Term

As can be seen in the left image of Figure 5, the pre-processed scanner data is still noisy, contains striping artifacts and may contain holes. To alleviate these artifacts, we do not register the template mesh directly with the scanner data but with an implicit function f which has been fitted to it. Since the implicit function f is computed in such a way that its zero-set approximates the input data in a least squares sense, it reduces the noise and closes the remaining holes. Given the implicit function f : R 3 → R, the distance d of a point x to the zero-set of f can be approximated by

d(x, f ) = |f (x)| ∥∇f (x)∥ 2 .
The distance between the deformed template mesh Φ(T ) and the zero-set of f , which provides us with the fitting energy term, can then be defined as the sum over the squared distances at the vertices vi of Φ(T ):

E fit = ∑ vi ∈Φ(T ) ( |f (v i )| ∥∇f (v i )∥ 2 ) 2 (1)

Regularization Energy Term

We use a variant of the embedded graph based mesh deformation algorithm by Sumner et al. [START_REF] Sumner | Embedded Deformation for Shape Manipulation[END_REF] to model the deformation of the template mesh. Thereby, a global space deformation is obtained by blending neighboring affine transformations

A i (x) = M i (x -p i ) + p i + t i
with local support, which are organized in a sparse graph. Here, M i is a 3x3 matrix, p i 13 is the node's position and t i is a translation vector. The local transformations define how the surrounding space is deformed. To obtain a deformation, which maintains local surface features, the local transformations should be close to rigid. An energy term E rot , which punishes the deviation of a local transformation M i from being rigid, can be defined as:

E rot (M i ) = ∥M T i M i -I∥ 2 F ( 2
)
Since neighboring transformations have overlapping influence, they affect a common region in space. It is therefore important that they are consistent w.r.t. one another. This is enforced by a consistency energy term E con , which measures the distance between the position to where a graph node is transformed by its own transformation and the position where it is mapped to by the transformation of a neighboring graph node:

E con (e ij ) = ∥A i (p j ) -A j (p j )∥ 2 2 (3)
+ ∥A j (p i ) -A i (p i )∥ 2 2 ,
where e ij is the edge connecting the two nodes i and j and p i and p j are the respective node positions.

Optimization

A combination of the fitting energy term and the two regularization energy terms leads to an energy function E reg , which is a measure for the quality of a registration introduced by a 14 given deformation graph:

E reg = αE fit + β ∑ i E rot (M i ) + γ ∑ e ij E con (e ij ). (4)
Here, the first sum runs over all nodes in the deformation graph and the second sum runs over all edges. An optimal deformation Φ, which registers the template mesh T with the input scan can now be computed by minimizing Equation ( 4) for the unknown node transformations using a modified Gauss-Newton algorithm. As proposed by Li et al. [START_REF] Li | Global Correspondence Optimization for Non-Rigid Registration of Depth Scans[END_REF], we increase the influence of the fitting energy in each iteration by doubling α. Initially, we set

α = 4, β = γ = 1.

Fitting the morphable face model

The result of the non-rigid registration step is a deformed template mesh Φ(T ) which tightly fits the input scan. However, as can be seen in Figure 5 (middle), this mesh still contains the bumps and dents that were originally present in the scanner data. To obtain the final 3D reconstruction of the face, we fit a morphable face model [START_REF] Blanz | A Morphable Model for the Synthesis of 3D Faces[END_REF] to the deformed template obtained by the non-rigid registration. This projects the solution into the space of reasonable faces and thereby removes the mentioned artifacts.

Since the deformed template mesh provides one-to-one correspondences with the average shape of our morphable model, we can now robustly align Φ(T ) with the morphable model using a Procrustes analysis again. Let T be the deformed template mesh that was aligned with the average face T of the morphable model and E the (reduced) eigenbasis of 15 the morphable model. We can thus construct a new face F from a given coefficient vector c by transforming the coefficient vector back into face space and adding the average face:

F = T + E • c.
We find the coefficients c of the morphable model which approximate T best by minimizing the least squares distance to the computed morph F:

min c ∥(T + E • c) -T ∥ 2 2 .
To obtain c, we solve the resulting normal equations:

E T E • c = E T • ( T -T ). (5)
Since the pseudo-inverse of the system matrix E T E can be precomputed for the given morphable model, the unknown coefficients can be computed by a simple matrix-vector multiplication.

Results

We have tested the proposed method on 20 individuals. In all cases, the proposed method was able to automatically produce accurate results. The results for four test persons are Newton iterations to warp the template mesh towards the input scan. The reconstruction of the fully textured facial avatars took on average 18 seconds on an Intel Core i7 processor at 2.93GHz.

To assess the quality of the reconstructed 3D face geometries, we compare a face model that was reconstructed using our algorithm to ground truth data in Figure 7. The ground truth face model was generated by scanning the test person with a high quality structured light scanner. The maximum deviation of our reconstruction from the ground truth model is 4.7mm, while the average deviation is roughly 2mm.

Since the morphable face model generated by our algorithm has one-to-one correspondences with the average face, we can directly transfer semantic informations that are annotated to the average face onto our reconstruction. For example, facial animations (cf.

Figure 6) can be easily cloned onto the new geometry.

Conclusion

We have presented a novel system for the automatic generation of high-quality personalized avatars using the Microsoft Kinect sensor. The proposed system allows a huge audience to generate high-quality facial models within seconds. Using non-rigid registration to compute correspondences for the subsequent morphable model fitting makes our approach very robust and allows to generate convincing results even for bad input data.

The rather small morphable model we are using is currently one of the limiting factors. 17 We plan to extend our data base and to handle models of the whole head. We further plan to extract geometry and texture information from multiple views and to capture whole head scans in super-resolution by registering the obtained input data. By using a segmented head model, we could further improve the expressability of the morphable model. In addition, we plan to animate the computed results and provide the user the possibility to customize his avatar.

Meanwhile, official open source 3 Page

 3

  use Support Vector Machines to detect the face in a 2D image and then extract facial features using a 4 Page 17 of 41 http://mc.manuscriptcentral.com/cavw -For Peer Review Computer Animation and Virtual Worlds regression-and classification-based approach. After that, they apply a flip-flop optimization to determine the best-fitting morphable model for the detected features, which is, in turn, used to improve the feature detection and classification. Instead of reconstructing the three-dimensional facial model from features in 2D images, Lee et al. [4] fit a morphable face model in such a way that the shading of the model is as close to the shading of the input image as possible. Commercially available software tools such as AvMaker, FaceGen

6

  Page 19 of 41 http://mc.manuscriptcentral.com/cavw -For Peer Review Computer Animation and Virtual Worlds model with the input scan. Finally, we use the morphable model to compute the face which approximates the deformed template face best. The result of the proposed algorithm is a high-quality 3D model of the scanned face which has one-to-one correspondences to the faces in the morphable model. Thus, it can be easily analyzed, animated or modified. To add more realism, we compute a corresponding texture for the faces using the captured RGB data.

10 Page

 10

shown in Figure 8 .

 8 As texture, we project the RGB image back onto the reconstructed face. The morphable model that we used for face fitting has been constructed from 53 faces, which were registered using the proposed algorithm for non-rigid registration. For all examples shown in this paper, we used the 25 most significant principal components of the face space to span the eigenbasis E. In the non-rigid registration, we performed six Gauss-

Figure 1 :

 1 Figure 1: Overview of the proposed avatar reconstruction. The upper image shows our

Figure 2

 2 Figure 2: Microsoft Xbox Kinect sensor

Figure 3 :

 3 Figure 3: Left: raw data from a single frame. Middle: temporally smoothed data. Right:

Figure 4 :Figure 5 :Figure 6 :Figure 7 :

 4567 Figure 4: Left: face-, nose-and eye-detection on the RGB image. Middle: temporary chin

Figure 8 :

 8 Figure 8: Face reconstruction results for four individuals. (from left to right) input RBG and

For Peer Review Computer Animation and Virtual Worlds

	Page 27 of 41

http://mc.manuscriptcentral.com/cavw -

Acknowledgements

Our morphable model includes 30 scans of the GavabDB database [15] and 10 scans provided courtesy of Utrecht University by the AIM@SHAPE Shape Repository. This work was partly funded by the German Research Foundation (DFG) under grant STA-662/3-1.


Jonathan Flint

Iain Mathieson

Marcus R Munafò

Meta-analysis indicates that common variants at the DISC1 locus are not associated with schizophrenia

Keywords: DISC1, schizophrenia, meta-analysis, association, case-control, GWAS

published or not. The documents may come

Introduction

Schizophrenia is a debilitating psychiatric illness with a lifetime prevalence of around 0.4% 1 and a heritability estimated to be between 80 and 85% [START_REF] Sullivan | Schizophrenia as a complex trait -Evidence from a meta-analysis of twin studies[END_REF][START_REF] Cardno | Twin studies of schizophrenia: from bow-andarrow concordances to star wars Mx and functional genomics[END_REF] . One schizophrenia susceptibility gene that has attracted much attention is Disrupted-in-Schizophrenia -1 (DISC1). DISC1 is one of three genes (with DISC2 and TSNAX) lying at the site of a balanced t(1;11)(q42.1;q14.3) translocation which has a strong association (LOD=7.1) with schizophrenia and other mental illness in a large Scottish pedigree 4 5 .

Further evidence that DISC1 genetic variants predispose to schizophrenia in particular comes from four sources. First, the expression of the protein product DISC1 is reduced in the Scottish pedigree in which the translocation segregates.

Second, DISC1 interacts physically with PDE4B. Another Scottish family with schizophrenia has a translocation that reduces the expression of PDE4B [START_REF] Millar | DISC1 and PDE4B are interacting genetic factors in schizophrenia that regulate cAMP signaling[END_REF] . Third, association between schizophrenia and variants at the DISC1 locus has been reported [START_REF] Callicott | Variation in DISC1 affects hippocampal structure and function and increases risk for schizophrenia[END_REF][START_REF] Cannon | Association of DISC1/TRAX haplotypes with schizophrenia, reduced prefrontal gray matter, and impaired short-and long-term memory[END_REF][START_REF] Chen | Casecontrol association study of Disrupted-in-Schizophrenia-1 (DISC1) gene and schizophrenia in the Chinese population[END_REF][START_REF] Ekelund | Replication of 1q42 linkage in Finnish schizophrenia pedigrees[END_REF][START_REF] Hashimoto | Impact of the DISC1 Ser704Cys polymorphism on risk for major depression, brain morphology and ERK signaling[END_REF][START_REF] Hennah | DISC1 association, heterogeneity and interplay in schizophrenia and bipolar disorder[END_REF][START_REF] Hennah | Haplotype transmission analysis provides evidence of association for DISC1 to schizophrenia and suggests sex-dependent effects[END_REF][START_REF] Hodgkinson | Disrupted in schizophrenia 1 (DISC1): association with schizophrenia, schizoaffective disorder, and bipolar disorder[END_REF][START_REF] Qu | Positive association of the Disrupted-in-Schizophrenia-1 gene (DISC1) with schizophrenia in the Chinese Han population[END_REF][START_REF] Rastogi | Genetic association and post-mortem brain mRNA analysis of DISC1 and related genes in schizophrenia[END_REF][START_REF] Saetre | Association between a disrupted-in-schizophrenia 1 (DISC1) single nucleotide polymorphism and schizophrenia in a combined Scandinavian case-control sample[END_REF][START_REF] Schumacher | The DISC locus and schizophrenia: evidence from an association study in a central European sample and from a meta-analysis across different European populations[END_REF][START_REF] Thomson | Association between the TRAX/DISC locus and both bipolar disorder and schizophrenia in the Scottish population[END_REF][START_REF] Zhang | Genetic association between schizophrenia and the DISC1 gene in the Scottish population[END_REF] . Fourth, sequencing part of the DISC1 gene in 288 cases identified six rare coding variants not found in 10,000 controls [START_REF] Song | Identification of high risk DISC1 structural variants with a 2% attributable risk for schizophrenia[END_REF] .

These findings, along with evidence of DISC1's involvement in other mental illnesses including bipolar disorder [START_REF] Thomson | Association between the TRAX/DISC locus and both bipolar disorder and schizophrenia in the Scottish population[END_REF] , depression [START_REF] Hashimoto | Impact of the DISC1 Ser704Cys polymorphism on risk for major depression, brain morphology and ERK signaling[END_REF] and autism [START_REF] Kilpinen | Association of DISC1 with autism and Asperger syndrome[END_REF] have spurred research into understanding what DISC1 does in the brain. Studies of DISC1's interactome have revealed that it is involved in synaptic development pathways [START_REF] Camargo | Disrupted in Schizophrenia 1 Interactome: evidence for the close connectivity of risk genes and a potential synaptic basis for schizophrenia[END_REF] and interacts with proteins important for neural development such as NDEL1 [START_REF] Brandon | Disrupted in Schizophrenia 1 and Nudel form a neurodevelopmentally regulated protein complex: implications for schizophrenia and other major neurological disorders[END_REF][START_REF] Morris | DISC1 (Disrupted-In-Schizophrenia 1) is a centrosome-associated protein that interacts with MAP1A, MIPT3, ATF4/5 and NUDEL: regulation and loss of interaction with mutation[END_REF][START_REF] Ozeki | Disruptedin-Schizophrenia-1 (DISC-1): mutant truncation prevents binding to NudE-like (NUDEL) and inhibits neurite outgrowth[END_REF] .

These results seem promising for DISC1's role in schizophrenia in light of the common hypothesis that the origin of the condition is neurodevelopmental.

However, there has been no comprehensive meta-analysis of schizophrenia association study findings for DISC1, despite the fact that the association evidence is not totally consistent. Association has been reported over almost the entire gene (Figure 1 [START_REF] Callicott | Variation in DISC1 affects hippocampal structure and function and increases risk for schizophrenia[END_REF][START_REF] Cannon | Association of DISC1/TRAX haplotypes with schizophrenia, reduced prefrontal gray matter, and impaired short-and long-term memory[END_REF][START_REF] Chen | Casecontrol association study of Disrupted-in-Schizophrenia-1 (DISC1) gene and schizophrenia in the Chinese population[END_REF][START_REF] Ekelund | Replication of 1q42 linkage in Finnish schizophrenia pedigrees[END_REF][START_REF] Hashimoto | Impact of the DISC1 Ser704Cys polymorphism on risk for major depression, brain morphology and ERK signaling[END_REF][START_REF] Hennah | DISC1 association, heterogeneity and interplay in schizophrenia and bipolar disorder[END_REF][START_REF] Hennah | Haplotype transmission analysis provides evidence of association for DISC1 to schizophrenia and suggests sex-dependent effects[END_REF][START_REF] Hodgkinson | Disrupted in schizophrenia 1 (DISC1): association with schizophrenia, schizoaffective disorder, and bipolar disorder[END_REF][START_REF] Qu | Positive association of the Disrupted-in-Schizophrenia-1 gene (DISC1) with schizophrenia in the Chinese Han population[END_REF][START_REF] Rastogi | Genetic association and post-mortem brain mRNA analysis of DISC1 and related genes in schizophrenia[END_REF][START_REF] Saetre | Association between a disrupted-in-schizophrenia 1 (DISC1) single nucleotide polymorphism and schizophrenia in a combined Scandinavian case-control sample[END_REF][START_REF] Schumacher | The DISC locus and schizophrenia: evidence from an association study in a central European sample and from a meta-analysis across different European populations[END_REF][START_REF] Thomson | Association between the TRAX/DISC locus and both bipolar disorder and schizophrenia in the Scottish population[END_REF][START_REF] Zhang | Genetic association between schizophrenia and the DISC1 gene in the Scottish population[END_REF] ), but the largest study to date failed to detect any association [START_REF] Sanders | No significant association of 14 candidate genes with schizophrenia in a large European ancestry sample: implications for psychiatric genetics[END_REF] , and genome-wide association studies (GWAS) have not found a clear signal at DISC1. Meta-analysis of DISC1 findings is difficult to carry out because the gene is large (414 Kb) and includes many variants (2,603 SNPs in dbSNP 131). There is no consensus about which markers have the strongest association, no markers are tested in all studies, and most are tested in only a small number of studies.

Therefore we decided to try to combine data from studies that use different markers by imputation. This method estimates results from a marker that has not been genotyped by exploiting linkage disequilibrium (LD) with markers that have been genotyped.

Until recently there was insufficient sequence information at the DISC1 locus to make imputation feasible; however release of data from phase 3 of the International HapMap project [START_REF] Altshuler | Integrating common and rare genetic variation in diverse human populations[END_REF] and from the first 1000 Genomes pilot [START_REF] Durbin | A map of human genome variation from population-scale sequencing[END_REF] provide the most comprehensive catalogue of common human genetic variation available today, including rare variants. We set out to use these publicly available data to impute genotypes in DISC1 association studies and to combine results from all available sources, including both GWAS and candidate gene studies, thus overcoming the problems described above.

Methods

Selection of studies for inclusion

We identified candidate gene studies and GWAS for schizophrenia or schizoaffective disorder in unrelated case-control samples drawn from populations of predominantly European ancestry with at least 100 cases and controls. Studies reporting data on both male and female cases and controls were included. We did not include studies where data from multiple individuals was pooled and analyzed together. We excluded studies where the samples overlapped significantly with another identified study.

Systematic literature search

We considered all studies listed for DISC1 on the SZGene database [START_REF] Allen | Systematic meta-analyses and field synopsis of genetic association studies in schizophrenia: the SzGene database[END_REF] . We also searched PubMed with the search terms "DISC1" AND "Schizophrenia" AND "Association" and also for the terms "Schizophrenia" AND "GWAS". Once these had been collected, their bibliographies were then searched for additional references.

The abstracts of studies thus identified were examined with respect to the inclusion criteria above. Studies failing to meet the criteria were discarded, and the full text of remaining studies was examined to determine whether or not they should be included.

Data extraction

For each study, the following data were extracted: 1) Author(s) and year of publication, 2) Sample size, 3) Data (individual genotypes, genotype counts or minor allele frequencies in order of preference). Where the required data were not available in the published study or from web-based supplementary information, we contacted the authors of the paper by e-mail to request access to the data. For GWAS we requested data for the region extending 100Kb upstream of DISC1 and downstream of TSNAX (Chr1:231,572,000-232,277,000 in the hg19 genome assembly), which covers all reported associations.

Quality control

In addition to any quality control performed by the authors of the studies, we excluded any SNPs which failed the following tests: 1) Minor allele frequency (MAF) in cases or controls < 0.01. 2) Where alleles were given in the study data, we checked them against dbSNP alleles [START_REF]Database of Single Nucleotide Polymorphisms (dbSNP)[END_REF] and excluded the SNP if the reported alleles differed from the dbSNP alleles and could not be explained by a strand flip. We also excluded the SNP if no alleles were specified in the study data and the MAF was > 0.45; otherwise we coded the SNP by the minor allele. 3) For studies where we had genotype counts available, we excluded SNPs that had a Hardy-Weinberg equilibrium test P-value of < 0.001.

Imputation

One of the problems encountered in previous attempts at meta-analysis is the lack of overlap between studies in terms of tested SNPs. We addressed this problem by imputing genotypes for studies where we had full genotype data. Imputation was carried out using IMPUTE v2 [START_REF] Marchini | A new multipoint method for genome-wide association studies by imputation of genotypes[END_REF][START_REF] Howie | A flexible and accurate genotype imputation method for the next generation of genome-wide association studies[END_REF] with reference panels of CEU haplotypes from (http://mathgen.stats.ox.ac.uk/impute/impute.html). For studies where we did not have full genotype data (we had genotype counts or minor allele frequencies), we imputed minor allele frequencies using the linear predictor implemented in the BLIMP package [START_REF] Wen | Using linear predictors to impute allele frequencies from summary or pooled genotype data[END_REF] and the CEU haplotypes from 1000 Genomes pilot 1. We attempted to impute for all studies which genotyped at more than ten SNPs.

Size and power calculations

To calculate the size and power of the meta-analysis, we simulated case-control data from haplotypes drawn from the 1000 Genomes pilot 1. To calculate the Pvalue required to obtain a given significance level, we sampled data from the 1000 Genomes haplotypes, with the same characteristics as the studies in the sample (numbers of cases, controls and testing the same SNPs), calculated effect sizes and P-values as described below and obtained the empirical significance levels for each SNP. We repeated the simulation and determined the required nominal point-wise significance level required to achieve a gene-wide significance level of 0.05.

To calculate the power of the meta-analysis, we again sampled from the 1000

Genomes data with the same characteristics as the meta-analysis samples, but in each simulation, we chose a SNP at random and weighted the sampling probabilities in cases to ensure that the chosen SNP had a specified OR in cases relative to controls. We performed the analysis as described below and recorded whether the significance level determined above was reached by any SNP. The proportion of tests with any SNP reaching significance gave us an estimate of the power of the meta-analysis for a given effect size. For size calculations we performed 10,000 simulations, and for power calculations we performed 1000 per datapoint.

Statistical analysis

Log-odds ratios (equivalent to logistic regression coefficients) and their standard deviations were calculated for each SNP in each study and then combined across studies using fixed and random effects models [START_REF] Dersimonian | Meta-analysis in clinical trials[END_REF] . We tested whether any of the pooled P-values were more significant than the thresholds calculated above. We also tested whether the distribution of P-values differed significantly from that expected under the null hypothesis. For each SNP, we investigated whether there was any evidence for heterogeneity using the I 2 statistic [START_REF] Higgins | Quantifying heterogeneity in a meta-analysis[END_REF] .

For the imputed genotypes, we calculated the test statistics using SNPTEST

32

, which takes into account the genotype uncertainty generated by the imputation.

For imputed allele frequencies, we calculated the proportion of the genotypic variance explained by the imputation, and filtered out any SNP where this was below 80%. We then calculated test statistics as for the original data. These were then combined with the test statistics from genotyped SNPs as above. We considered separately: 1) the genotyped data, 2) the genotyped data plus the imputed data, but considered only loci that were genotyped in at least one study, and 3) the genotyped data plus all the imputed data. We removed each study from the meta-analysis in turn to determine whether any single study had a disproportionate effect on the analysis. We also calculated Wakefield approximate Bayes factors [START_REF] Wakefield | Bayes factors for genome-wide association studies: comparison with P-values[END_REF] from estimates of the standardized effect sizes and their variances, assuming a prior for the effect size that was normally distributed with mean 0 and variance 0.015. This prior is equivalent to the belief that for each SNP, there is a 95% probability that its odds ratio lies between 0.79 and 1.28.

Results

We obtained data for eleven candidate gene studies and four GWAS containing a total of 11,626 cases and 15,237 controls (Table 1). We could not obtain data from one case-control study and one GWAS matching our criteria because there was no response from the authors. Three studies were excluded because they overlapped substantially with other studies ( For testing the 401 genotyped loci we used a point-wise significance level of 1.92×10 -4 corresponding to a gene-wide significance level of 0.05. We generated this threshold by simulation, using the exact SNPs and sample sizes available in the included studies. It is equivalent to a multiple testing correction for 260 (95% CI 250-269) independent tests. For the 1,241 SNPs in the imputed data, the correction is equivalent to 444 independent tests (95% CI 424-467). With these cutoffs, we estimated that for common variants (MAF>5%) the power to detect a true association at OR=1.5 with the imputed data restricted to genotyped loci was 99%.

For OR=1.1 the power was 51%.

For rare variants, power is much lower. For variants with MAF between 1% and 5%, the corresponding figures are 92%, and 6%. For variants with MAF below 1%, which we did not try to test, the power is very low, even for high odds ratios.

These figures are the power to detect an association at any locus given the odds ratio at the causal locus, which is not necessarily the one detected. Figure 2 shows power as a function of minor allele frequency for different odds ratios at the causal allele.

Using these significance thresholds, we detected no significant association with any tested SNP (figures 3 and 4). The most associated SNP was rs1765805, 160 Kb upstream of DISC1 (p=6×10 -4 , genotyped in 1860 cases and 2389 controls), but this was heavily dependent on a single study [START_REF] International | Common polygenic variation contributes to risk of schizophrenia and bipolar disorder[END_REF] and not supported by nearby SNPs. The next highest associations were found in the regions of rs1331046 (p=1.4×10 -3 , imputed in 3610 cases and 3938 controls), downstream of the gene, and rs17817356 (p=7×10 -3 , genotyped in 4405 cases and 7427 controls, imputed in 2291 cases and 2293 controls), between exons 6 and 7, and about 30Kb upstream from DISC2. Like rs1765805, the association at rs1331046 was driven by the ISC data, but the association at rs17817356 was supported by the ISC and other datasets as well. In the random effects analysis, the associations at rs1765805 and rs17817356 remained at the same significance level but the association at rs1331046 was substantially reduced (p>0.03).

Excluding the ISC study significantly altered our results, and was the only study whose omission did so. As noted above, the associations at rs1765085 and rs1331046 were supported only by the ISC. However, this may be because few other studies tested these SNPs. Both SNPs are outside the gene, in a region where we had lower coverage, since most candidate gene studies have concentrated on SNPs inside the gene.

To assess heterogeneity, we calculated the I 2 statistic for all SNPs. This was zero for the majority (70%) of loci and distributed between 0 and 80% for the rest.

Tests of heterogeneity are generally underpowered when, as here, there are few studies [START_REF] Huedo-Medina | Assessing heterogeneity in meta-analysis: Q statistic or I2 index?[END_REF][START_REF] Kavvoura | Methods for meta-analysis in genetic association studies: a review of their potential and pitfalls[END_REF] , so we cannot make conclusive statements about the presence or absence of heterogeneity. However given that most genetic associations display between-study heterogeneity [START_REF] Ioannidis | Replication validity of genetic association studies[END_REF] and that fixed and random effects models give the same results when there is no heterogeneity, it seems prudent to use the more conservative random effects model to estimate effect size or to prioritize markers for further analysis.

Using the effects estimated by the random effects model, the approximate Bayes factors reveal a similar pattern to the p-values (figure 5), and indicate that the region around rs17817356 has the most evidence in favor of association and that there is no consistent evidence for association elsewhere in the gene.

There are three commonly tested non-synonymous SNPs in the gene, rs3738401, rs821616 and rs6675281. The variants rs821616 and rs6675281 have been reported to have functional effects, affecting centrosomal PCM1 localization [START_REF] Eastwood | DISC-1 Leu607Phe alleles differentially affect centrosomal PCM1 localization and neurotransmitter release[END_REF][START_REF] Eastwood | The DISC1 Ser704Cys substitution affects centrosomal localization of its binding partner PCM1 in glia in human brain[END_REF] , expression of splice variants [START_REF] Nakata | DISC1 splice variants are upregulated in schizophrenia and associated with risk polymorphisms[END_REF] , hippocampal function [START_REF] Callicott | Variation in DISC1 affects hippocampal structure and function and increases risk for schizophrenia[END_REF] and interaction with NDEL1 which is important for neurite outgrowth [START_REF] Kamiya | DISC1-NDEL1/NUDEL protein interaction, an essential component for neurite outgrowth, is modulated by genetic variations of DISC1[END_REF] . However we detected no significant associations at any of these SNPs (p= 0.11, 0.51 and 0.93 in the raw data and 0.49, 0.60 and 0.28 in the imputed).

Given the potential contribution of rare variants in DISC1 to schizophrenia risk, we searched additional sources of data to identify further functional variants not represented in dbSNP. In the 1000 Genomes pilot data, we found one additional non-synonymous coding SNP. We also looked in the results from a recent exome sequencing study of 200 Danish individuals [START_REF] Li | Resequencing of 200 human exomes identifies an excess of low-frequency non-synonymous coding variants[END_REF] and identified five novel nonsynonymous SNPs. Of these six variants, two had been discovered in cases and controls in Song et al. [START_REF] Song | Identification of high risk DISC1 structural variants with a 2% attributable risk for schizophrenia[END_REF] and 4 were novel (Table 3 ).

Discussion

We have carried out a comprehensive analysis of candidate schizophrenia susceptibility variants in the DISC1 gene. We found no significant association with any variant. We calculated approximate Bayes factors for each SNP to identify the regions where there was most evidence of association and found that the best evidence of association was in a region between exons 6 and 7 Second, to what extent have we excluded the involvement of common variants throughout the gene? Third, can we draw any conclusions about the role of rare variants at the DISC1 locus? Finally, why have we been unable to replicate the many previously reported associations?

Power calculations help to answer the first question (figure 2). Power depends critically on the sample size, which is not straightforward to estimate. While the total number of cases and controls in our sample was 11,626 and 15,237, not every SNP was tested in every individual. In the raw data, the mean numbers of cases and controls testing any single SNP were 2,781 and 3,782. We cannot directly calculate the sample sizes for the imputed data since we used imputed genotype probabilities in our tests, but comparison of the variance of test statistics suggest that the mean improvement was equivalent to increasing the sample size by 49% to a mean of 4,144 cases and 5,653 controls. These figures are heavily skewed in the sense that some variants have much larger sample sizes. Imputation also allowed us to test variants that had not been genotyped in any study.

Our power calculations are only approximate since we sampled from a fairly limited set of haplotypes. However, they can give us an indication of what effects we have tested. For variants with MAF > 5%, we had 99% power to detect an effect with OR=1.5 and 51% power to detect an effect with OR=1.1. However, it is possible that effects will be too small to detect, even for high frequency variants. Robust association for common variants with OR of < 1.1 have been reported in a study of height [START_REF] Lettre | Identification of ten loci associated with height highlights new biological pathways in human growth[END_REF] and it is not inconceivable that similarly small effects operate in schizophrenia [START_REF] Wray | Narrowing the Boundaries of the Genetic Architecture of Schizophrenia[END_REF] . It has been argued that such variants can explain a significant proportion of the heritability for common diseases and traits [START_REF] International | Common polygenic variation contributes to risk of schizophrenia and bipolar disorder[END_REF][START_REF] Wray | Narrowing the Boundaries of the Genetic Architecture of Schizophrenia[END_REF][START_REF] Yang | Common SNPs explain a large proportion of the heritability for human height[END_REF] .

Results from the HapMap and 1000 Genomes projects provide an answer to the second question. Genotyped SNPs included 32% of all SNPs with MAF > 5% in the 1000 Genomes, and imputed SNPs included 89%. For SNPs with MAF between 1% and 5%, the corresponding figures are 10% and 41%. For genotyped loci, 95% of the gene is within 5.0Kb of a tested SNP, 50% is within 1.4Kb and the maximum distance without a tested SNP is 13.7Kb. For the imputed data, the figures are 2.6Kb, 0.6Kb and 7.2Kb. These small regions make it unlikely that any common SNP could exist that we have not, at least indirectly, tested.

Third, the effects may arise from alleles too rare to be tested here. It is not surprising that common variants do not have a large effect on susceptibility to such a debilitating disease, but we might expect rare variants to have larger effects. While we tested variants down to a MAF of 1%, we had very low power at this level, and we could not even test all the known variants of this frequency. Further stages of the 1000 Genomes project will allow most variants at this frequency to be tested. On the other hand, association between DISC1 and the disease might derive from extremely rare, essentially private, mutations of large effect [START_REF] Mcclellan | Schizophrenia: a common disease caused by multiple rare alleles[END_REF][START_REF] Mitchell | Rethinking the Genetic Architecture of Schizophrenia[END_REF] . One study reported the identification of coding mutations in schizophrenia cases that were not detected in 10,000 control subjects [START_REF] Song | Identification of high risk DISC1 structural variants with a 2% attributable risk for schizophrenia[END_REF] . However this study did not search in healthy controls for rare variants that were not found in cases. In two studies sampling 260 individuals in total, we found four novel nonsynonymous mutations, and rediscovered two that had been identified in the previous study. This suggests that coding mutations in DISC1 may be more common in healthy individuals than previously assumed. However it should also be noted that control subjects were not actively screened for the absence of SZ, a family history of SZ, or related mental illnesses.

Finally, many previous studies have reported association. There are a number of reasons why we might have failed to replicate these results; publication bias, winner's curse, allelic heterogeneity and population, sex, or subgroup specific heterogeneity. We have not attempted to investigate these here, but it is worth noting that the presence of heterogeneity of effects would particularly tend to confound large GWAS and meta-analyses such as this one.

Our meta-analysis does not address the question of DISC1's involvement in other mental illness, such as bipolar disorder, major depressive disorder or autism spectrum disorder, nor does it answer all the questions about the association of DISC1 with schizophrenia. Although we found no significant association with common variants, many studies have reported sex specific, and interaction effects [START_REF] Chen | Casecontrol association study of Disrupted-in-Schizophrenia-1 (DISC1) gene and schizophrenia in the Chinese population[END_REF][START_REF] Hashimoto | Impact of the DISC1 Ser704Cys polymorphism on risk for major depression, brain morphology and ERK signaling[END_REF][START_REF] Hennah | DISC1 association, heterogeneity and interplay in schizophrenia and bipolar disorder[END_REF][START_REF] Schumacher | The DISC locus and schizophrenia: evidence from an association study in a central European sample and from a meta-analysis across different European populations[END_REF][START_REF] Thomson | Association between the TRAX/DISC locus and both bipolar disorder and schizophrenia in the Scottish population[END_REF] , which we did not test. Consideration of the power required to detect such effects suggests that if they do exist, significantly larger studies will be required to detect them convincingly. For example, if we were to test all pairwise SNP-SNP interactions for all imputed SNPs in this study, we would be increasing the multiple testing factor by around 100,000. We would also be reducing the sample size for each test, particularly for combinations of rare variants making it difficult, if not impossible, to reach statistical significance. Hypothesis driven tests derived from functional studies and model systems may prove more productive than data mining in this case.

Whatever the true effect of the factors described above, it seems likely that we will need to consider new study designs, and new statistical techniques in order to further investigate the effect of DISC1 variation on schizophrenia and other psychiatric illnesses.

Tables

Captions; Specifically, i we received an initial response but no response to two further emails, ii no response after three initial emails.

HapMap 3

 3 and the 1000 Genomes pilot 1. The CEU haplotypes are taken from samples from the Centre d'Etude du Polymorphisme Humain collected from individuals living in Utah, USA, with ancestry from northern and western Europe.

  Figure1: Reported DISC1 associations including both family and association studies from population of all ethnicities and indicating regions reported as being significantly associated with schizophrenia[START_REF] Callicott | Variation in DISC1 affects hippocampal structure and function and increases risk for schizophrenia[END_REF][START_REF] Cannon | Association of DISC1/TRAX haplotypes with schizophrenia, reduced prefrontal gray matter, and impaired short-and long-term memory[END_REF][START_REF] Chen | Casecontrol association study of Disrupted-in-Schizophrenia-1 (DISC1) gene and schizophrenia in the Chinese population[END_REF][START_REF] Ekelund | Replication of 1q42 linkage in Finnish schizophrenia pedigrees[END_REF][START_REF] Hashimoto | Impact of the DISC1 Ser704Cys polymorphism on risk for major depression, brain morphology and ERK signaling[END_REF][START_REF] Hennah | DISC1 association, heterogeneity and interplay in schizophrenia and bipolar disorder[END_REF][START_REF] Hennah | Haplotype transmission analysis provides evidence of association for DISC1 to schizophrenia and suggests sex-dependent effects[END_REF][START_REF] Hodgkinson | Disrupted in schizophrenia 1 (DISC1): association with schizophrenia, schizoaffective disorder, and bipolar disorder[END_REF][START_REF] Qu | Positive association of the Disrupted-in-Schizophrenia-1 gene (DISC1) with schizophrenia in the Chinese Han population[END_REF][START_REF] Rastogi | Genetic association and post-mortem brain mRNA analysis of DISC1 and related genes in schizophrenia[END_REF][START_REF] Saetre | Association between a disrupted-in-schizophrenia 1 (DISC1) single nucleotide polymorphism and schizophrenia in a combined Scandinavian case-control sample[END_REF][START_REF] Schumacher | The DISC locus and schizophrenia: evidence from an association study in a central European sample and from a meta-analysis across different European populations[END_REF][START_REF] Thomson | Association between the TRAX/DISC locus and both bipolar disorder and schizophrenia in the Scottish population[END_REF][START_REF] Zhang | Genetic association between schizophrenia and the DISC1 gene in the Scottish population[END_REF] . These includes family based linkage studies and studies in non-European populations which were not included in the present study.

Figure 2 :

 2 Figure 2: Estimated power as a function of minor allele frequency at the causal allele, showing results for different odds ratios. The power was simulated using variants and haplotypes from the 1000 genomes data and the curves have been fitted as smooth splines of degree 6.

Figure 3 :

 3 Figure 3: Pooled P-values for association. Each point represents a single SNP. The horizontal axis indicates chromosomal position, and the vertical axis indicates negative log 10 of the fixed effect pooled P-value for that SNP. The black points show the imputed SNPs, and the grey points show the subset of the imputed SNPs which were genotyped in at least one study. The horizontal dashed lines show the corrected significance level which is equivalent to a 5% gene-wide significance level for each dataset.

Figure 4 :

 4 Figure 4: Quantile-quantile plot of P-values. QQ plot of the p-values shown in figure 2. The solid line shows the expected values under the null hypothesis of no association and the dashed lines show the upper and lower 95% quantiles.

Figure 5 :

 5 Figure 5: Wakefield approximate Bayes factors for each SNP. Calculated from the random effects pooled P-values and Z-scores assuming a Normal prior on the logodds ration with mean 0 and variance of 0.015. A Bayes factor > 0 is evidence for association while a Bayes factor <0 is evidence against.

Table 2 )

 2 . The total number of separate SNPs genotyped in any study was 401. Imputation dramatically increased the number of studies testing each SNP. Before imputation, 100 SNPs were tested in a single study only. After imputation, there were only 13 such SNPs. The mean number of studies testing each SNP increased from 2.6 to 4.3, if only sites genotyped in a single study were considered, and to 3.4 if all imputed sites were used. Ultimately, we obtained data on a total of 1,241 separate SNPs. Many of the SNPs in the full imputed dataset were tested in only two studies and were heavily dependent on the International Schizophrenia Consortium data 38 .

Table 1 :

 1 Details of studies analysed.

C Candidate gene(s). G GWAS. M Minor allele frequencies. S Summary genotypes F Full genotypes. Gen genotyped. Imp Imputed.

Table 2 :

 2 Studies which met our inclusion criteria but which were not included. "No response from author" refers to email response to the corresponding author.

Table 3 :

 3 Nonsynonymous SNPs not found in dbSNP identified in 260 individuals. Two have been found in a previous study and four are novel.

	Table 1
			SNPs Tested
	Study	Year	Gen	Imp	Cases	Controls
	Devon et al. CM 53	2001	3	0	656	344
	Hodgkinson et al. CF 14	2004	38	62	242	213

Yes

Acknowledgments

Iain Mathieson and Jonathan Flint are supported by the Wellcome Trust. The authors would like to thank all the researchers who provided data for this study.

The authors declare no conflict of interest.

Conflict of Interest

Wood et al. CF

Study Year Reason for Exclusion

Thomson et al. [START_REF] Thomson | Association between the TRAX/DISC locus and both bipolar disorder and schizophrenia in the Scottish population[END_REF] 2005 Samples reported in Hennah et al. [START_REF] Hennah | DISC1 association, heterogeneity and interplay in schizophrenia and bipolar disorder[END_REF] Zhang et al. [START_REF] Zhang | Genetic association between schizophrenia and the DISC1 gene in the Scottish population[END_REF] 2006 Samples partially reported in Hennah et al. [START_REF] Hennah | DISC1 association, heterogeneity and interplay in schizophrenia and bipolar disorder[END_REF] Lencz et al. [START_REF] Lencz | Converging evidence for a pseudoautosomal cytokine receptor gene locus in schizophrenia[END_REF] 2007 Samples reported in Hodgkinson et al. [START_REF] Hodgkinson | Disrupted in schizophrenia 1 (DISC1): association with schizophrenia, schizoaffective disorder, and bipolar disorder[END_REF] Nicodemus et al.