EAD and PEBD: Two Energy-Aware Duplication Scheduling Algorithms for Parallel Tasks on Homogeneous Clusters Abstract-High-performance clusters have been widely deployed to solve challenging and rigorous scientific and engineering tasks. On one hand, high performance is certainly an important consideration in designing clusters to run parallel applications. On the other hand, the ever increasing energy cost requires us to effectively conserve energy in clusters. To achieve the goal of optimizing both performance and energy efficiency in clusters, in this paper, we propose two energy-efficient duplication-based scheduling algorithms-Energy-Aware Duplication (EAD) scheduling and Performance-Energy Balanced Duplication (PEBD) scheduling. Existing duplication-based scheduling algorithms replicate all possible tasks to shorten schedule length without reducing energy consumption caused by duplication. Our algorithms, in contrast, strive to balance schedule lengths and energy savings by judiciously replicating predecessors of a task if the duplication can aid in performance without degrading energy efficiency. To illustrate the effectiveness of EAD and PEBD, we compare them with a nonduplication algorithm, a traditional duplication-based algorithm, and the dynamic voltage scaling (DVS) algorithm. Extensive experimental results using both synthetic benchmarks and real-world applications demonstrate that our algorithms can effectively save energy with marginal performance degradation. W ITH the advent of powerful microprocessors and highspeed interconnects, and the increasing demand of computing capability, high-performance clusters have served as primary and cost-effective infrastructures for complicated scientific and commercial applications. Parallel applications running on clusters are generally computationintensive and data-intensive in nature. Accordingly, efficient parallel execution and prompt completion of massive parallel tasks are essential and desirable.. Due to the high-power consumption of microprocessors, networks, and storage disks, high-performance clusters consume significant amounts of energy. For example, the total power of a 360-Tflops high-performance cluster would exceed 10 megawatts, possibly approaching 20 megawatts. Ten megawatts is approximately equal to the amount of power used in 11,000 US households [1] . The Environment Protection Agency reported that, in 2006, the total energy consumption of servers and data centers of the United States was 61.4 billion KWh, which was almost equal to the total power cost of 5.8 million US households [2] .. It is obvious that high performance and high energy cost are two key features of modern clusters. Ignoring either of them is unreasonable and unpractical. Unfortunately, previous research on clusters has been primarily focused on performance improvement. Nowadays, high energy cost has become a salient constraint of clusters. Designing energyefficient and environmental friendly clusters is highly desirable. In this paper, we design novel scheduling algorithms to achieve the goal of maximizing performance and energy efficiency in clusters. More specifically, we propose two energy-aware duplication scheduling algorithms-the Energy-Aware Duplication (EAD) and Performance-Energy Balanced Duplication (PEBD) scheduling algorithms.. Task duplication strategies have been proved to be an efficient strategy to improve the performance of scheduling parallel tasks with precedence constraints [3] , [4] , [5] . This is mainly because unnecessary communication delay among multiple processors can be eliminated through task duplications, thereby reducing overall communication overheads in clusters. However, most existing duplication-based scheduling algorithms replicate all possible tasks to shorten schedule length without considering energy consumption caused by making replicas. In other words, the negative impact of task duplications was ignored in the previous studies. In contrast, our algorithms strive to make trade-off between schedule lengths and energy savings by judiciously replicating predecessors of a task if the replicas can improve performance without noticeably increasing energy.. To save energy, clusters can be built using lowfrequency, low-power processors with modest performance. In doing so, performance might be more efficiently enhanced through parallelism than through using higher power, higher frequency processors. Green Destiny at Los Alamos National Laboratory makes use of this approach to consume three times less energy per unit than the Accelerated Strategic Computing Initiative (ASCI) Q machine [6] . The other successful commercial cluster using this idea is the IBM Blue Gene/L supercomputer [7] . However, this approach may sacrifice too much per-node performance to achieve their low-power goals. For example, because Green Destiny uses more power-efficient microprocessors, it is approximately 15 times slower per node compared with high-performance nodes [6] . Using lowpower and low-frequency chips succeeds only if users can improve performance by scaling up to a large number of processors. Unfortunately, many commercial clusters are not large scale in terms of the number of computing nodes.. Alternatively, one can build clusters using power-hungry and high-performance processors coupled with smart power management mechanisms. Clusters designed using this approach are usually called power-scalable clusters. In power-scalable clusters, the power level will be scaled down when clusters are not fully utilized and scaled up when clusters are busy. Dynamic Voltage and Frequency Scaling or DVFS is one of the most effective strategies to reduce energy consumption in power-scalable clusters. For example, Intel developed the SpeedStep technology [8] and AMD developed the PowerNow! and Cool'n'Quiet technology [9] . While DVFS technologies have made important contributions in building energy-efficient clusters, most of them are only capable of saving energy in processors.. Increasing evidences have shown that in addition to processors, high-speed interconnections consume significant amounts of energy in clusters. For example, it is observed that interconnect consumes 33 percent of the total energy in an Avici switch [10] , whereas routers and links consume 37 percent of the total power budget in a Mellanox server blade [12] . This situation is getting worse with the emergence of next generation high-speed interconnections like Gigabit Ethernet, Infiniband, Myrinet, and QsNet II . For instance, measurements have shown that a 1 Gbps Ethernet consume about 4 W more energy than 100 Mbps Ethernet [13] . A 10 Gbps Ethernet may consume 10 to 20 W more energy in average [13] . Lack of energy conservation technology for cluster interconnects becomes a severe problem because, without such technology, reducing energy consumption caused by communication-intensive parallel applications is almost impossible.. In this paper, we investigate the possibility of saving energy through power-aware duplication-based scheduling for both processors and interconnects. Our algorithms leverage DVFS to save energy dissipation in processors. Rather than adjusting the voltage to the best fit to current workloads, our algorithms force processors to operate at the highest voltage and frequency levels as long as there is a task waiting in the processing queue and the input datum of this task is ready. Our idea of conserving energy is to immediately turn processors to the lowest voltage once no task is waiting or no task is ready for execution. This policy ensures that tasks can be executed as fast as possible. Meanwhile, tasks on the critical path will be duplicated under the condition that no significant energy overhead is introduced by the replicas. Duplications can avoid the performance degradation caused by waiting messages. The rationale behind our approach is twofold. First, energy overhead incurred by task replicas could be offset by energy savings in interconnects and by shortening schedule length. Second, the overall performance will be improved by the virtue of replicas.. The rest of the paper is organized as follows: In Section 2, we present related work. Next, Section 3 introduces mathematical models including a system model, a task model, and an energy consumption model. In Section 4, we present the energy-aware scheduling strategies. Experimental environment and simulation results are demonstrated in Section 5. Finally, Section 6 provides the concluding remarks and future research directions. Since many parallel applications running in clusters require intensive data processing and data communication, scheduling strategies deployed in clusters have a large impact on overall system performance. Basically, parallel scheduling strategies can be classified to three primary categories, called priority-based scheduling, cluster-based scheduling, and duplication-based scheduling, respectively. Priority-based scheduling involves the assignment of priorities to tasks and then maps those tasks to processors based upon assigned priorities [14] . Cluster-based scheduling algorithms cluster as many intercommunicating tasks as possible in a group and allocate it to the same processor, thereby eliminating communication overheads [15] . The basic idea of duplication-based scheduling is to replicate as many as predecessor tasks in the critical paths provided that the schedule length can be shortened. Duplication scheduling outperforms other scheduling algorithms in most cases, especially when communication time dominates the execution time of parallel applications. However, the performance improvement increases energy consumption because many tasks are duplicated and thus executed more than once by multiple processors. To address this problem, we propose two energyaware duplication algorithms (EAD and PEBD) in this paper. Instead of duplicating all performance-oriented tasks, our algorithms replicate tasks with the consideration of both performance improvement and energy cost.. There has been a large body of previous studies investigating power-aware techniques to reduce energy consumption in processor and memory resources [16] , [17] , [18] , [19] in the late 90's. Dynamic power management is a design methodology aiming to achieve specified performance with minimum number of active components or a minimum load on such components [20] . Dynamic power management consists of a collection of energy-efficient techniques that adaptively turn off cluster components or bring performance down when the components are idle or partially unexploited. For example, based on the observation of past idle and busy periods, predictive shutdown policies can make power management decisions before a new idle period starts [21] .. Researchers have focused on energy-aware algorithms for power-scalable clusters. Among these algorithms, Dynamic Voltage Scaling (DVS) technology [22] , [23] , [24] , [25] , [26] , [27] has been widely exploited to make processors energyefficient in both portable and nonportable computing systems. Dynamic Frequency Scaling (also known as CPU throttling) is another similar technique in which a processor runs at a less-than-maximum frequency when it is not fully utilized in order to conserve power [23] . Very recently, many studies have been reported in utilizing the Dynamic Voltage and Frequency Scaling (DVFS) technology to reduce power dissipations in clusters and high-performance computing platforms [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] . Results have shown that these proposed schemes can achieve high energy efficiency for processors, indicating that DVFS is capable of saving significant amount of energy for computation-intensive applications. The benefits of DVFS may diminish when it comes to communication-intensive applications, because the energy consumed by interconnects dominates the total power consumption.. To address the above problem, researchers in Princeton University investigated the possibility of introducing DVS technology to interconnections [35] . Shang [39] .. One of the feasible approaches to conserving power consumption caused by interconnects is to make task duplication. Compared with existing energy-efficient techniques, duplication-based strategies have their unique advantages. First, task replicas can avoid communication overheads among tasks, thereby improving performance (see, for example, [3] , [4] , [5] ). Second, as for communicationintensive applications, huge energy consumption in interconnects can be reduced. We will address this point in the following sections in detail. Third, the duplication strategies can be seamlessly integrated with the DVS technology to reduce energy dissipations in processors. Last but not the least, the duplication-based schemes can be used in combination with the Adaptive Link Rate technology if the required network devices are available on the market in the future.

O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


On the discrete version of Picone's identity For a real number p with 1 < p we consider the first eigenvalues of the p-Laplacian on graphs, and estimates for the solutions of p-Laplace equations on graphs. We provide a discrete version of Picone's identity and its application. More precisely, we prove a Barta-type inequality for graphs with boundary. Finally, we provide a discrete version of the anti-maximum principle. Crown In the last decade there has been an increasing interest in the p-Laplacian, which plays an important role in geometry and partial differential equations. The p-Laplacian is a natural generalization of the Laplacian, which corresponds to p = 2. Although the Laplacian has been much studied, little is known about the nonlinear case p = 2. On the other hand, the discrete analogue of the Laplacian on Riemannian manifolds has recently been investigated. For the Laplacian on an infinite graph, Dodziuk and Kendall [8] proved a discrete analogue of a Cheeger-type inequality, which gave a lower bound for the bottom of the spectrum in terms of an isoperimetric constant.. The eigenvalues of the Laplacian have many physical interpretations, for example, as the frequencies of vibration of a membrane, as the rates of decay for the heat equation (or mass diffusion). In [14] are presented recently discovered connections between photoelectron spectra of saturated hydrocarbons (alkanes) and the Laplacian eigenvalues of the underlying molecular graphs; other applications are given in [4] [5] [6] . So it is significant and necessary to investigate the relations between the graph-theoretic properties of a graph G and its eigenvalues.. However, the eigenvalues of the p-Laplacian can be calculated explicitly only for a few special graphs, most notably for regular graphs.. In this paper we study the discrete p-Laplacian, which is the analogue of the operator div(|∇ · | p−2 ∇·). We will give some characterization and estimates of the first eigenvalue of the p-Laplacian and also generalize Picone's identity to the p-Laplacian for graphs. Some results concerning − p had long been known for the ordinary Laplacian, i.e. for p = 2: it is the purpose of this paper to continue in this direction but for the discrete p-Laplacian.. This paper is organized as follows. In Section 2, we define the discrete p-Laplacian. First eigenvalue for graphs with boundary is defined in Section 3. In Section 4 the minimum principle is given. Picone's identity for discrete graphs is advocated in Section 6. Section 4 deals with the minimum principle and Section 7 with discrete version of Barta's theorem. Finally, Section 9 concludes the paper and provides the anti-maximum principle for the discrete p-Laplacian.

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A Coding Algorithm for Constant Weight Vectors: A Geometric Approach Based on Dissections Abstract-We present a novel technique for encoding and decoding constant weight binary vectors that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight of the code. The encoder and decoder mappings are then interpreted as a bijection between a certain hyper-rectangle and a polytope in this Euclidean space. An inductive dissection algorithm is developed for constructing such a bijection. We prove that the algorithm is correct and then analyze its complexity. The complexity depends on the weight of the vector, rather than on the block length as in other algorithms. This approach is advantageous when the weight is smaller than the square root of the block length. W E consider the problem of encoding and decoding binary vectors of constant Hamming weight and block length . Such sets of vectors (hereafter referred to as codes) are useful in a variety of applications: a few examples are faulttolerant circuit design and computing [15] , pattern generation for circuit testing [25] , identification coding [28] , and optical overlay networks [26] .. The problem of interest is that of designing the encoder and decoder, i.e., the problem of mapping all binary (information) vectors of a given length onto a subset of length-vectors of constant Hamming weight in a one-to-one manner. In this work, we propose a novel geometric method in which information and code vectors are represented by vectors in -dimensional Euclidean space, covering polytopes for the two sets are identified, and a one-to-one mapping is established by dissecting the covering polytopes in a specific manner. This approach results in an invertible integer-to-integer mapping, thereby ensuring unique decodability. The proposed algorithm has a natural recursive structure, and an inductive proof is given for unique decodability. The issue of efficient encoding and decoding is also addressed. We show that the proposed algorithm has complexity , where is the weight of the codeword, independent of the codeword length .. Compared to a linear-time encoding algorithm [16] , the algorithm presented here is faster only when , in which case the rate of the resulting code, , approaches zero as . However, we view this paper as the starting point of a new approach to the classic problem of encoding and decoding constant-weight codes, and we believe there is considerable room for improvement. Some steps in this direction can be found in [22] , [27] . Further, the geometric view advanced here is also of potential significance to areas such as source coding and simulation.. Dissections are of considerable interest in geometry, partly as a source of puzzles, but more importantly because they are intrinsic to the notion of volume. Of the 23 problems posed by David Hilbert at the International Congress of Mathematicians in 1900, the third problem dealt with dissections. Hilbert asked for a proof that there are two tetrahedra of the same volume with the property that it is impossible to dissect one into a finite number of pieces that can be rearranged to give the other, i.e., that the two tetrahedra are not equidecomposable. The problem was immediately solved by Dehn [6] . In 1965, after 20 years of effort, Sydler [24] completed Dehn's work. The Dehn-Sydler theorem states that a necessary and sufficient condition for two polyhedra to be equidecomposable is that they have the same volume and the same Dehn invariant. This invariant is a certain function of the edge lengths and dihedral angles of the polyhedron. An analogous theorem holds in four dimensions (Jessen [11] ), but in higher dimensions it is known only that equality of the Dehn invariants is a necessary condition. In two dimensions, any two polygons of equal area are equidecomposable, a result due to Bolyai and Gerwein (see Boltianskii [1] ). Among other books dealing with the classical dissection problem in two and three dimensions we mention in particular Frederickson [7] , Lindgren [13] , and Sah [19] .. The remainder of the paper is organized as follows. We provide background and review relevant previous work in Section II. Section III describes our geometric approach and gives some low-dimensional examples. Encoding and decoding algorithms are then given in Section IV, and the correctness of the algorithms is established. Section V summarizes the paper. We propose a novel algorithm for encoding and decoding constant-weight binary codes, based on dissecting the polytope defined by the set of all binary words of length and weight , and reassembling the pieces to form a hyper-rectangle corresponding to the input data. The algorithm has a natural recursive structure, which enables us to give an inductive proof of its correctness. The proposed algorithm has complexity , independent of the length of the codewords . It is especially suitable for constant weight codes of low weight.

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Using an E-Health Intervention to Promote the Health of Cancer Survivors With Preexisting Disabling Conditions The potential for e-health-the delivery of healthcare services and information via the Internet and related technologies 1 -to improve the services patients receive and their health is vast. Indeed, 80% of US Internet users (53% of US adults) have looked online for information about health topics. 2 Internet-based resources are typically available around the clock, generally without cost, and can provide both a private resource in patients' healthcare management or a forum for community support. 2 Given the potential of e-health in general, it is hardly surprising that healthcare researchers interested in improving the care and outcomes of cancer patients have explored the potential of e-health interventions. Such research has considered the Internet as a source for cancer information, 3,4 as well as a potential resource for online support groups to help those coping with cancer diagnoses and recovery. 5,6 More recent studies have examined the cancer patient characteristics that predict preferences for various Web-based supports. 7 Even as this kind of research progresses, however, there remains a need for empirical testing and validation of the Internet as a vehicle to improve the health of cancer survivors.Similarly, e-health has been seen as a tool to potentially improve healthcare for people living with disabilities and chronic health conditions. For example, Lorig et al 8, 9 reported that those participating in online self-care management interventions for diabetes or arthritis had improved self-efficacy, hemoglobin A 1c levels, and self-reported symptoms, compared with usual-care control groups. Although the preliminary response was promising, future efforts should determine the efficacy of LiveAble with larger and more diverse samples of survivors with preexisting disabling conditions. The participants' reactions also point out that the challenge of such e-health interventions may not be in providing useful information, but in galvanizing the target population to use this information for making meaningful behavior change. Nurses are increasingly challenged to identify alternative ways to help both their patients cope with chronic disabling conditions and patients' families promote their health. E-health interventions hold great promise because of their convenience, adaptability, and the interest they can engender. However, these programs must be carefully constructed and evaluated to meet patient needs. 23 Preliminary results from this initial pilot of LiveAble suggest that the participants found it provided useful information that was relevant to cancer survivors with preexisting disabling conditions. None indicated that they would have preferred a face-to-face group intervention, although one person pointed out that there are definitely some people who prefer the group contact. We also note that the majority of those contacted chose not to participate in the online study, and this is a reminder that not everyone is attracted to Internet interventions.. Although the feedback was generally positive, participants clearly wanted a system that was easier to navigate. Both the Blackboard interface and the participants' computer familiarity may have contributed to the relatively lower rating of the navigation item. One person who had difficulty initiating the intervention said the phone assistance provided the hands-on guidance needed to open the online modules and start the intervention. Because the majority of the participants in this study reported multiple sclerosis as their primary disabling condition, some may have had cognitive limitations, so such assistance may have been particularly important with this group.. Cancer is most likely to be diagnosed in older adults, and older computer users may have a wider range of computer literacy skills compared with younger computer users. 24 Therefore, many cancer survivors who are older adults may need help in accessing and navigating e-health interventions. Also, when designing a program that may be used by older adults or those with disabilities, the principles of universal design will be particularly important to incorporate. 24, 25 Several key takeaways for converting the paper-based manual to an online format emerged over the course of this process. The most noteworthy were the following:. Much of the paper-based manual contained large chunks of text that could be translated into images and videos for the online format. In this process, organization is key. Having an outline, or a folder, to keep track of which images and videos go in which section of the online guide facilitates the process of uploading and arranging files on the Internet platform. It is important to preview the intervention as a user. For online platforms, the editor's view is often different from the user's view. Previewing both formats allows for consistent, accurate display of intervention material. It is useful to test the intervention using different Internet browsers. What may appear accurately in Internet Explorer may appear altered when viewed in Firefox. Although Blackboard was a useful tool for quickly executing a feasibility pilot with limited resources, a more flexible platform would have been better at converting content to an online format-particularly when trying to design a user-friendly intervention for users with a variety of disabilities. was presented in eight 90-minute sessions, so the online participants were spending considerably less time with the materials. Participants were instructed in advance that this study was a pilot study and that the purpose was to determine their feedback, so it is possible that they focused on evaluating the program rather than trying to learn from the content or interact with others in the discussion board. A major benefit of this kind of e-health intervention is the ability of participants to (1) move through materials at their own pace and (2) select and focus on content that is most relevant or novel. Additional investigation of ''actual'' LiveAble users-rather than pilot users asked to provide feedback as reviewers and testers-is necessary to determine how long users would spend with the content, whether they go through the educational content quickly or slowly over time, which modules they use, and how they utilize the discussion board.. Given the small sample of 11 participants, it is not surprising that the changes in self-efficacy observed here did not reach conventional levels of statistical significance. However, the associated effect sizes (Cohen d values) suggest that the changes following exposure to the online program were moderately large for the total selfefficacy score and the stress management subscale. With this small, self-selected sample, these preliminary results may not generalize. Also, baseline self-efficacy scores were collected about 22 months before participants reviewed LiveAble, on average. A randomized controlled trial with a much larger sample and a shorter time between pretesting and posttesting would be needed to determine if changes in self-efficacy could be attributed to the LiveAble program. Such studies should also determine who prefers e-health interventions, as opposed to other intervention modalities.. Only 51% of these participants agreed that LiveAble motivated them to take action to improve their health. To turn information into action, participants may need additional support and encouragement. One person suggested that telephone follow-up would enhance their ability to work toward health-promotion goals; other participants needed assistance in navigating the program. Future studies should explore the most effective ''mix'' of online and personal components for the LiveAble intervention. One possible model is the successful online interventions of Lorig et al 8, 9 that include peer facilitators who encourage participation, monitor discussion board use, and provide individual problem-solving feedback.. Another way to promote health-promotion changes may be to encourage more interactive discussions among users. A recent study by Richardson and colleagues 26 found that adding an online communities component to an Internet-mediated exercise program reduced attrition, although it did not increase the number of steps taken. Also of interest is their finding that participants who reported lower social support at baseline were more likely to post more messages and viewed more of others' posts, compared with those who reported higher social support. Particularly in the early stages of the community when the discussion is not yet active, the program facilitators may need to post questions or other information to promote online discussions.. Pilot participants' comments also suggested that the power of a Web-based program should be harnessed to personalize the intervention. The average time since cancer diagnosis was 8 years for this group. Some participants indicated that although the information appeared useful, they were already aware of much of it and that it might be more helpful to those with more newly diagnosed condition. Therefore, a short online assessment component that could utilize background information to direct users to the most appropriate sections might significantly increase the utility of LiveAble.

O O B O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Archetype relational mapping - a practical openEHR persistence solution Background: One of the primary obstacles to the widespread adoption of openEHR methodology is the lack of practical persistence solutions for future-proof electronic health record (EHR) systems as described by the openEHR specifications. This paper presents an archetype relational mapping (ARM) persistence solution for the archetype-based EHR systems to support healthcare delivery in the clinical environment. Methods: First, the data requirements of the EHR systems are analysed and organized into archetype-friendly concepts. The Clinical Knowledge Manager (CKM) is queried for matching archetypes; when necessary, new archetypes are developed to reflect concepts that are not encompassed by existing archetypes. Next, a template is designed for each archetype to apply constraints related to the local EHR context. Finally, a set of rules is designed to map the archetypes to data tables and provide data persistence based on the relational database. Results: A comparison study was conducted to investigate the differences among the conventional database of an EHR system from a tertiary Class A hospital in China, the generated ARM database, and the Node + Path database. Five data-retrieving tests were designed based on clinical workflow to retrieve exams and laboratory tests. Additionally, two patient-searching tests were designed to identify patients who satisfy certain criteria. The ARM database achieved better performance than the conventional database in three of the five data-retrieving tests, but was less efficient in the remaining two tests. The time difference of query executions conducted by the ARM database and the conventional database is less than 130 %. The ARM database was approximately 6-50 times more efficient than the conventional database in the patient-searching tests, while the Node + Path database requires far more time than the other two databases to execute both the data-retrieving and the patient-searching tests. Conclusions: The ARM approach is capable of generating relational databases using archetypes and templates for archetype-based EHR systems, thus successfully adapting to changes in data requirements. ARM performance is similar to that of conventionally-designed EHR systems, and can be applied in a practical clinical environment. System components such as ARM can greatly facilitate the adoption of openEHR architecture within EHR systems. This paper presents an ARM persistence solution for archetype-based EHR systems. ARM uses archetypes to generate relational databases and achieve similar performance as compared to conventional databases in data-retrieving queries. ARM takes great advantage of the CKM public archetype repository to facilitate data manipulation with well-defined archetypes for clinicians and to achieve better performance in patient-searching queries. System components like ARM can facilitate the adoption of open-EHR architecture in EHR systems. The authors will continue to complete the mapping rules according to the semantics of archetypes, improve ARM constraints and the performance of the generated databases, design and implement data access services, and perform thorough tests of the ARM approach in real clinical environments. This paper presents an ARM persistence solution for archetype-based EHR systems. While the ARM approach is designed to generate a relational database from archetypes and templates and can achieve performance similar to a conventionally-designed database, there were several encountered challenges and issues. Currently, an electronic health record (EHR) system is essential to support clinical practice with information technology in healthcare environments. EHR is a repository of information regarding the health status of a subject of care in computer processable form [1] . However, healthcare data is generally too complicated, flexible, and changeable to capture a universal, comprehensive and stable schema of information, which is the foundation of the entire EHR architecture. Highly-specialized and complex EHR systems cannot acclimate to the evolution of healthcare data requirements, which require EHR systems to embrace a dynamic, state-of-the-art, rapidly evolving information infrastructure [2] . In order to protect EHR systems from changes in the healthcare domain, openEHR [3] has published a series of specifications to guide the development of future-proof EHR systems. Solutions span from information modelling to system architecture, to meet the continually evolving needs of EHR systems.. The concept of openEHR focuses on systems and tools necessary to the computation of complex and constantly evolving health information at a semantic level, according to the following three paradigms: separation of information models, domain content models, and terminologies; separation of responsibilities; and separation of viewpoints [4] . Among these three paradigms, the separation of information models, domain content models and terminologies promotes a significant shift from the single-level modelling approach of information system development to a twolevel modelling approach. In the single-level modelling approach, domain concepts that are processed by the EHR system are hard-coded directly into the application and database models. In two-level modelling, the semantics of information and knowledge are separated into a small, comprehensible, non-volatile reference model (RM), which is used to build information systems and knowledge models; archetypes are used as formalisms and structures to express numerous and volatile domain concepts [5] .. The RM represents the general features of health record components, their method of organization, and necessary contextual information to satisfy both the ethical and legal requirements of the health record. The RM encompasses the stable features of the health record by defining the set of classes that composes the blocks which in turn constitute the record. Archetypes define entire, coherent informational concepts from the clinical domain [6] . An archetype is a hierarchical combination of components from the RM with available restrictions placed on names, possible data types, default values, cardinality, etc. These structures, although sufficiently stable, may be modified or replaced by others as clinical practice progresses and evolves [7] . Archetypes are deployed at runtime via templates that specify particular groups of archetypes to be used for a particular purpose, often corresponding to a screen form. A template is a specification that creates a tree structure of one or more archetypes, and each constraining instance of various RM types such as composition, section, entry subtypes, etc. Templates typically closely correspond to screen forms, printed reports, and generally complete information to be captured or sent at the application level; they may therefore be used to define message content [4] . By utilizing a two-level modelling approach, EHR systems can be built on a stable RM as a general framework, and thus use archetypes as the domain information model to achieve greater flexibility and stability, particularly in situations in which the domain concepts are vast in number, have complex relationships, and evolve continuously. The responsibilities of specialists from the information technology domain and the healthcare domain are disengaged: developers focus only on the technical components of EHR systems, while specialists develop the structural model based on domain concepts and archetypes. This enables domain specialists to participate directly in the production of the artefacts that are interpreted by EHR systems, to organize and present healthcare information, and to control the EHR system without intervention from the system supplier or re-programming.. Syntactic and semantic interoperability between different EHR systems is facilitated by the use of archetypes. However, agreement between data content and the information models is necessary for real integration and semantic interoperability [8] . In the single-level modelling approach, the domain concepts are implicitly contained within the EHR systems. No consensus healthcare domain models exist in healthcare domain models to which EHR systems may conform; each system may model different aspects and granularity levels of domain concepts, resulting in heterogeneity. In the two-level modelling approach, the RM ensures that EHR systems can always send information to other systems and receive readable information in return, thus ensuring data interoperability. Archetypes can be used as the common knowledge repository to share evolving clinical information that can be processed by the receiving systems, thus enabling semantic interoperability [9] . The openEHR system maintains Clinical Knowledge Manager (CKM) as an official archetype repository to support the governance of international domain knowledge.. Specifications of openEHR can be used to create and sustain a flexible EHR ecosystem that consists of may integrated services, which is too complex to be accurately processed by single applications [10] . The general architectural approach can be considered as five layers: persistence (data storage and retrieval), back-end services (including EHR, demographics, terminology, archetypes, security, record location, etc.), virtual EHR (a coherent set of APIs to the various back-end services and an archetype-andtemplate-enabled kernel responsible for creating and processing archetype-enabled data), application logic (user applications or another service, such as a query engine), and presentation (the graphical interface of the application) [4] . The archetypes share the openEHR innovation of adaptability because they are external to the software, while key components of the software are derived from the archetypes [11] . Much current research has been devoted to the use of archetypes to drive the persistence, accessibility, and presentation of healthcare information systems [12] [13] [14] [15] [16] .. Most EHR systems in the healthcare field are built according to the single-level modelling approach, despite the many advantages of two-level modelling. One of the primary reasons is that the persistence layer is inadequate to meet the requirements of clinical practice. As the foundation of EHR systems, the persistence layer determines the EHR system architecture, and thus also function as a performance bottleneck. The openEHR system promotes a Node + Path persistence solution that serializes sub-trees of fine-grained data into blobs or strings based on the object or relational systems [17] . The data can be serialized according to different granularity levels, from top-level information objects to the lowest leaf nodes. In essence, the Node + Path solution is an entity-attribute-value (EAV) approach, which takes advantage of the semantic paths in openEHR data to improve the serialized-blob design. The greatest advantages of the Node + Path approach are flexibility and simplicity; all data nodes are serialized, and their paths are recorded adjacently in a two-column table of < node path, serialized node value>. However, the simplicity of the data storage structure induces complex data retrieval logic, which strains the performance of data insertion and query, which requires flexibility [18] . Some researchers have reported similar performances in the processing of entity-centered queries by conventional and EAV models, but that EAV models were approximately 3-5 times less efficient in the processing of attribute-centered queries [19] . Evaluations of persistence solutions using an XML database also indicates that XML databases were considerably slower and required much more space than the relational database [20] . There has also been similar research into the data persistence of alternative approaches based on two-level modelling, such as EN13606 [21] or HL7 Version 3 [22] . In a proof-of-concept work of EN13606 [7] , the data storage was developed by applying Object Relational Mapping (ORM) [23] to the RM of EN13606; this approach was investigated by the authors in earlier work [24] . The deep inheritance and complicated relationships of the EN13606 RM induces excessive JOIN operation during data query. Additionally, classes near the top hierarchy become heavily overloaded with data. For example, DATA_VALUE is the basic class of all data types, and contains the common attributes of all instances of all data classes, but it is unable to operate in real time [7] . IBM Clinical Genomics medical research developed a hybrid data model based on the HL7 Version 3 Reference Information Model (RIM) [25] . The hybrid data model combines elements of both the ORM and EAV approaches, which is well-suited to the sparse and flexible data of a medical research data warehouse. However, it demonstrates similar problems to other ORM and EAV approaches in that it does not improve the performance enough to support effective clinical transactions.. The relational database is still of primary importance to the data persistence of EHR systems, and its excellent performance has already been well proved in many successful EHR projects and widely-accepted EHR productions. The primary challenge to the application of a two-level modelling approach to a relational database is that the domain information model is hard-wired into the database model; when the domain information model changes, the relational database must be redesigned in order to facilitate the new domain information model. There are two approaches to support the adaptation of the persistence layer to changes in archetypes. One approach is to use a general data storage structure that is independent of archetypes, such as Node + Path, which has been well-investigated. The other approach is to generate a database model to design a persistence layer driven by archetypes.. This work presents an archetype relational mapping (ARM) persistence solution based on a relational database that can achieve similar performance to the conventional database in practical clinical environments. This work extends the basic ARM method introduced in a previous proof-of-concept work [24] by providing a more sophisticated mapping approach based on templates and archetypes in order to map archetypes to relational tables. Performance optimization rules and details are then provided. First, the ARM approach is introduced in detail, including archetype modelling, template definition, and mapping rules. Then, the ARM is applied to the EHR data requirements of a tertiary hospital in China. A comparison of the generated ARM database, the conventional database deployed in the hospital, and the openEHR official Node + Path database is conducted. After analysis, the challenges encountered during ARM development are discussed, and conclusions are provided. An underpinning principle of openEHR is the use of archetypes and templates, which represent formal models of domain content that are used to control data structure and content during creation, modification, and querying [26] . The ARM approach employs archetypes and templates to generate a persistence model and provide data access based on a relational database. The ARM is intended to fulfill several functionalities: 1) Effective adaptation to changes in archetypes.. Archetypes reflect the changing realities of EHR, and existing archetypes are updated over time. Archetype changes result in several challenges to ARM, such as the application of new archetypes to the relational database, and the possibility of incompatible versions among archetypes, among other potential challenges. 2) Generation of customized persistence models for various EHR requirements. Archetypes define widely reusable components of information, and templates encapsulate the local usage of archetypes and relevant preferences. In order to apply to the local EHR context, ARM employs templates in order to customize the data persistence model. There are three steps to employ ARM in the implementation of the persistence layer: archetype modelling, template definition, and database mapping.

B I I O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B O O O O O O


Grammar resources for modelling dialogue dynamically Abstract This paper argues that by analysing language as a mechanism for growth of information (Cann et al. in The Dynamics of Language, Elsevier, Oxford, 2005; Kempson et al. in Dynamic Syntax, Blackwell, Oxford, 2001), not only does a unitary basis for ellipsis become possible, otherwise thought to be irredeemably heterogeneous, but also a whole range of sub-types of ellipsis, otherwise thought to be unique to dialogue, emerge as natural consequences of use of language in context. Dialogue fragment types modelled include reformulations, clarification requests, extensions, and acknowledgements. Buttressing this analysis, we show how incremental use of fragments serves to progressively narrow down the otherwise mushrooming interpretational alternatives in language use, and hence is central to fluent conversational interaction. We conclude that, by its ability to reflect dialogue dynamics as a core phenomenon of language use, a grammar with inbuilt parsing dynamics opens up the potential for analysing language as a mechanism for communicative interaction. In confronting the challenge of providing formal models of dialogue, with its plethora of fragments and rich variation in modes of context-dependent construal, it might seem that linguists face two types of methodological choice. Either (a) conversation demonstrates genre-specific characteristics, for which a grammar specific to such activity must be provided (Atterer and Schlangen 2009; Fernández 2006; Ginzburg 2009; Ono and Thompson 1995; Polanyi and Scha 1984; Schegloff 1979; cf. Schlangen 2003) ; or (b) the crossspeaker flexibility and variation characteristic of dialogue has to be seen as due to the specifics of the parsing/production systems which are based upon, but nevertheless distinct from, the mode-neutral grammar characterising the individual's competence in that language (see e.g. Chomsky 1965 ). Both alternatives raise issues for an empirical account of what language users' knowledge of a given language amounts to. One core phenomenon where such issues are vividly displayed is ellipsis, a phenomenon observed both in monologue and dialogue genres. Ellipsis simultaneously constitutes one of the most fundamental characteristics of dialogue while, nevertheless, being subject to restrictions diagnostic of grammar-internal mechanisms. Thus ellipsis would seem to straddle the remits of dialogue-modelling and grammar-design in a way that does not allow for a unified explanation given conventional grammar formalisms. Preserving the separation between discourse phenomena and core grammar constraints, this has been taken to indicate a division between discourse ellipsis and grammar-internal ellipsis (Stainton 2006) , confirming what is widely taken to constitute the heterogeneity of ellipsis phenomena (Merchant 2007 ). But such a move notably fails to reflect the fact that the single most defining feature of all types of ellipsis is systemic contextdependence. Even when this feature of ellipsis is recognised, the presumed split between discourse-based and grammar-constrained ellipsis has been taken to vindicate the claim that a dialogue-specific grammar is necessary to deal with dialogue elliptical phenomena.. In this paper, to the contrary, we will show that ellipsis phenomena in general are characterisable by grammarinternal mechanisms without any stipulation specific to their use in dialogue. This result is achieved by developing a grammar formalism that directly reflects the dynamics of language processing as the basis for explaining structural properties of language. More specifically, the grammar tracks the incremental and progressive growth of interpretation in real time. Procedures, equivalently actions, determining growth of represented information are central to the formal specification of the grammar itself, not a characteristic of just the parser or the generator. Accordingly, the methodology of preserving a gulf between the design of the grammar-formalism and performance considerations is no longer sustained.. The approach within which we set out our account of fragment construal, is that of Dynamic Syntax (DS) (Cann et al. 2005; Kempson et al. 2001) . In this framework, the usually static notion of ''syntax'' as a set of principles assigning structures over strings of words is replaced by ''syntax'' as the progressive construction of semantic representations set in context, reflecting the dynamics of human parsing. Language production is presumed to be parasitic on the very same information-growth processes, following the dictates of the grammar formalism.. Such a framework is well suited to modelling ellipsis in all its forms: the diverse grammar-internal constraints on ellipsis postulated by standard frameworks emerge in DS from the definition of the dynamics of the time-linear accumulation of information. This consists of three dimensions:. (a) as the parser operates incrementally left-to-right, the set of words processed progressively increases; (b) the semantic representations, which in DS take the form of gradually updated tree structures, progressively grow in that they become more specified both in terms of structure and content annotations; (c) the set of actions used in constructing tree representations accumulates.. In Purver et al. (2006) and Cann et al. (2007) it is argued that context should then be accordingly defined as incorporating a record of (a) words processed, 1 (b) structures established, and (c) actions that led to this structure. This model of context is what allows DS to deal with ellipsis in a unified way as context-dependency (see Cann et al. 2007; Purver et al. 2006 for details). Storage of actions allows a straightforward account of cases of ellipsis that have been argued to provide crucial evidence for idiosyncratic syntactic/semantic restrictions. In particular, both semantic and syntactic restrictions on fragments are dealt with in the same way, as constraints on tree growth. Sets of actions/procedures, what lexical items are presumed to consist in, are sequentially executed and subsequently stored in the context record. They can then be available for recovery and re-use, and some types of ellipsis crucially rely on this feature of context for their resolution. So, on this account, the concept of procedure emerges as central to what context amounts to as well.. In this paper we adopt this analysis as background for demonstrating how a range of elliptical phenomena which might, at first sight, seem specific to conversational dialogue-acknowledgements, clarifications, reformulations, utterance-exchanges involving interruption and intra-sentential switch of speaker-hearer roles-can be modelled without any stipulation specific to such functions. The immediate advantage of such an account is that it preserves, indeed directly reflects, the intuition that ellipsis occurs when the context fully determines construal as far as the message conveyed is concerned except for the elliptical fragment presented. In addition, we shall conclude that grammars that are defined as dynamical systems directly reflecting mechanisms for growth of interpretation in real time also allow for dynamic adjustment of the information conveyed according to the feedback received by the other interlocutor. Accordingly, grammars can be seen as a mechanism for communicative interaction: the human capacity for language is thus grounded directly in the interactional activity which it serves.. 1 There are two main reasons for the storage of words: firstly, there is the fact that people can remember them, at least in the short term; secondly, word/action pairs need to be available for the modelling of lexical/syntactic alignment (see Pickering and Garrod 2004; Purver et al. 2006) . A reviewer points out that recall of words (qua phonological units) decays faster than content (but cf. Keenan et al. 1977; Kintsch and Bates 1977) . To integrate this assumption, to the extent that it holds, in the DS model we have to introduce mechanisms that model decay of information in context (see e.g. Lewis and Vasishth 2005) , an extension which is in any case required for modelling decay of accessibility of competing antecedents for anaphora/ellipsis.. Dynamic Syntax (DS) has three main characteristics underlying the modelling of how contextual information can be incorporated AS IT ARISES with linguistic information during interaction in dialogue. First, DS provides a fully incremental parsing model, based on a strictly monotonic process of interpretation update.. Second, this process of update is goal-directed as it is dynamically driven by requirements for update at each initial or intermediate stage. As will be shown shortly, these two characteristics are closely related, and together allow for the third DS distinguishing feature, the fact that the same mechanisms are exploited to model both parsing (=understanding) and generation (=production). In natural language use, people often talk to each other with apparently fragmentary utterances, a phenomenon broadly known as ellipsis: Despite a robust folk intuition that ellipsis can occur whenever the context makes obvious how the apparently fragmentary expression of thought is to be ''completed'', ellipsis has very generally been seen as a heterogeneous set of phenomena not subject to a uniform explanation. The reason for this concerns the various complications that arise in defining the way interpretation of such fragments is achieved in each case.. Amongst the rich array of ellipsis effects, there are cases of elliptical fragments where the linguistic surface form of the antecedent 2 provides the resolution. These cases have been subject to a great deal of study over recent years-VP-ellipsis as in (1b), sluicing, stripping (as in (1d)), gapping, pseudo-gapping (as in (1c)), etc. Each sub-type is said to display different structural constraints on their construal, justifying their distinct analyses. What brings these together is that they, in some sense, constitute a complete sentence, given their interpretation as suitably completed by the provided antecedent, so that ellipsis can be seen as requiring syntactic/semantic rules defined over adjoined sentences (though see Stainton 2006) . But, even for these cases, the effects ellipsis resolution induces remain very puzzling as they appear, from that point of view, unresolvably heterogeneous. For example, there are cases where relative to a single antecedent source ambiguity may arise, with a single string admitting either a strict or a sloppy reading:. (2) John checked over his mistakes, and so did Bill/Bill too.. 'Bill checked Bill's mistakes' (sloppy) 'Bill checked John's mistakes' (strict). This phenomenon would seem to be broadly a phenomenon of construal, requiring a semantic basis for explanation under which the CONTENT of the antecedent has somehow to be manipulated by making available alternative forms of abstracts to match what is required at the ellipsis site (hence the classic account in terms of various abstraction operations applicable to the content of the first conjunct to yield a novel predicate applicable to the subject of the second, higher order unification, see Dalrymple et al. 1991) . However, the semantic account is not adequate on its own: elliptical phenomena also appear to be sensitive to the very same constraints that affect surface syntactic operations. For example, as a general observation across languages and phenomena, relative clause constructions interfere with ''movement'' operations (they are islands). In the syntactic literature, this constraint is called the Complex NP constraint. Now exactly the same type of interference seems to be responsible for the ungrammaticality of the VP-ellipsis construction in (4) below:. (3) John interviewed every student who Bill already had. (4) *John interviewed every student who Bill ignored the teacher who already had.. What is displayed in (3) is the phenomenon of antecedent contained deletion (or antecedent-contained ellipsis), so called because the ellipsis site appears to be contained within the antecedent (interviewed every student who...) from which the interpretation of the ellipsis site itself is to be constructed. Such circularity apart (for which different solutions are promulgated depending on the framework), the observation is that such structures preclude any dependency of the relative pronoun, who, on a verb appearing across a relative-clause boundary. Accordingly, (4) is ungrammatical because there is no possibility of resolving the ellipsis site indicated by had by means of the containing matrix verb in the way that (3) appears to allow. This pattern is reminiscent of restrictions on so-called long-distance dependencies which are taken to be diagnostic of a syntactic phenomenon, non-reducible to semantic terms:. (5) The man who Sue is worried that her sister is planning to marry lives in Austria. (6) *The man who Sue is concerned about her sister who is planning to marry lives in Austria.. Though (5) is wellformed with who construed as the object of marry, no such dependency for the first relative pronoun in (6) is possible, because there is a further relative clause boundary (an island) between the relative pronoun who and the same verb marry that who has to be associated with (the observation goes back to Ross 1967) . Because such restrictions are not expressible in semantic terms-for example, the lambda calculus (the logic taken to underpin semantic combinatorics) would impose no such restriction-they have been taken as evidence for a concept of syntax independent of both semantics and phonology, and a diagnostic of what constitutes a syntactic process. Some types of ellipsis at least are thus argued to be within the remit of natural-language syntax, involving low-level deletion of phonological material (PF Deletion: see Fiengo and May 1994; Merchant 2001 Merchant , 2007 It might seem, and it has traditionally been assumed, that the grammar/syntax, which under orthodox assumptions has to do with sentence strings and propositions, should have nothing to say about such fragmented dialogue turns, as they constitute ''performance'' data. But firstly, as was pointed out early on Morgan (1973) , there are grammatical sequences of words other than sentences, as can be seen in all the examples above; and the grammar should be able to characterise those and distinguish them from plain ''word-salad''. Secondly, the grammar is responsible for characterising certain dependencies among lexical items in grammatical sentences. Consider then the licensing of the negative polarity item (NPI) in (10): such NPIs are only licensed by appearing in sentences that contain some explicit ''affective'' element, namely negation, question etc. (see e.g. Ladusaw 1979 ). Now, in (10), the only element that can license the NPI is the interrogative morphology registered at A's turn. It would seem then that A and B's turns should somehow be joined together to form a single utterance, otherwise we would not be able to match the intuition that the discourse is perfectly well-formed. Now one might be tempted to conclude that, indeed, this vindicates a grammar which characterises sentence strings as it would seem that this licensing occurs only when we assume that a single string of words is spread over two turns. But this would be too hasty: notice what happens with the second A and B exchange in (11). The licensing of the reflexive anaphor myself is only possible because its antecedent, namely B, is part of the CONTENT of the turn started by A. But if we now try to join the two strings together (#but did you burn myself) 4 the result is not what the exchange was meant to convey. The same problem would arise with (14) . From that point of view, it seems then that this phenomenon of turn-sharing, loosely characterised as split utterances, has to do with the sharing of contents rather than strings.. Given this conclusion, one might presume that what is needed is a grammar for dialogue, with the specific remit of determining how content is jointly constructed over turns by interlocutors (see e.g. Ono and Thompson 1995; Schegloff 1979) . Since content computation is known to rely crucially on context, such a grammar would have to regiment the pragmatic inferencing that results in the derivation of what interlocutors actually do with their utterances, including specification of the utterance's speech-act function in the dialogue (see e.g. Ginzburg et al. 2003 ). Let's see whether this would be a desirable move according to the data presented here. While the NP fragments in (11)- (14) might be characterised as distinct utterance types, serving severally rather different functions of clarification, acknowledgement, correction, they also illustrate how both interlocutors may progressively contribute to the joint enterprise of establishing some shared communicative content. In such examples, each speaker contributes parts to a single collaborative utterance (as seen by the preservation of such grammatical constraints as those discussed above) and thus these also fall under the phenomenon loosely characterised as split utterances. Here the dialogue participants jointly construct an utterance even though they may well NOT have identical messages in mind guiding what they are going to say. Speakers can divert or preempt the other interlocutor's planned utterance and this is a facet of dialogue that is easily handled by the participants. Moreover, each speaker's contribution is not necessarily intended to have the same function as the previous speaker's incomplete utterance which it continues. Even (7), an acknowledgement, can be seen as part of a split utterance, for it is similar in form to an afterthought extension added to A's sentential utterance. As (12) shows, joint construction of content can proceed incrementally: B provides a reformulation as a clarification request, resolved by A within the construction of a single proposition. In (13), the fragment A provides functions as a correction of some aspect of B's understanding, with A and B having to negotiate as to whose information is more reliable in order to secure coordination. Nevertheless the correction in (13) also constitutes an extension, so that a single conjoined propositional content is derived DURING which coordination is achieved. (14) represents an intermediate case, in which the respondent, realising what the question is, answers THROUGH his completion of the question; the fragment thus serves simultaneously both as question and answer (see e.g. Bunt 2009 ).. Such diversity of fragment uses might, then, seem evidence of conversation-specific rules disambiguating the function of such fragments as part of a grammar. Taking such a line, Fernández (2006) presents a thorough taxonomy, as well as detailed formal and computational modelling of non-sentential utterances, referring to contributions like (7) as repeated acknowledgements involving reformulation. Fernández (2006) models such constructions via type-specific ''accommodation rules'' which make a constituent of the antecedent utterance ''topical''. The semantic effect of the acknowledgement is then derived by applying an appropriately defined utterance type for such fragments to the newly constructed context. A distinct form of contextual accommodation is employed to model so-called helpful rejection as in (13) and so on. Under this view, the distinct dialogue acts that can be accomplished by a fragment consisting of a single NP, e.g. the accounts guy, have to be characterised by postulating distinct appropriate grammatical and contextual rules that constitute part of the dialogue management process. However, if, as seems to be the case, 5 what actions speakers and hearers can perform and recognise in dialogue is limitless and nondeterministic, shaped through feedback, 6 an a priori taxonomy like this is not a desirable move, for it requires that a single linguistic form such as an NP-fragment will have to be characterised as syntactically multiply ambiguous, relative to a set of predetermined dialogue acts. And moreover, such a taxonomy still faces the problem of specifying the exact function(s) each form performs, as this depends on a full specification of its context of occurrence, which is also necessary for resolving the postulated ambiguity. Additionally, what such an account fails to bring out is how these phenomena are structurally replicated in monologue in apposition structures, possibly extraposed (for a similar observation see also Poesio and Rieser 2009):. (15) Bob, the accountant, is coming to stay. (16) Bob left, the accountant.. Furthermore, even these construction-specific analyses of fragments in dialogue are taken to require a sentential form of analysis: the fragment is assigned a type which in combination with a suitable abstract with respect to what is provided in context will yield a propositional form of meaning. But, as (13) indicates, such fragments can be used at early points in a dialogue exchange when there may be no complete propositional content available in the context relative to which the fragment can be provided a suitable abstract. Nonetheless the participants in the dialogue can exchange a clarificatory request and reply unproblematically so that the communicative exchange can proceed. The challenge posed by split exchanges for orthodox grammar, parsing and production mechanisms is considerable, and they have not been much addressed (though see Poesio and Rieser 2009 ). The problem is as follows: speakers shift into hearing as though they had been hearing all along: parsers shift into production as though they had been speaking all along. But, until recently, parsing and generation systems have been defined relative to a grammar whose remit is syntactic and semantic analysis of complete sentence-strings. And, even now, though parsing and generation systems are increasingly reflecting incrementality (Atterer and Schlangen 2009; Skantze and Schlangen 2009; Stoness et al. 2004) , such incrementality must generally come from the processing model, with the grammar defined statically and independently. Yet, to deal with split utterances, parsing/generation systems have to be defined with a flexibility allowing either one to take up from where there has been a switch, despite the fact that both the string preceding or following the switch may fall outside the set of strings licensed as well-formed by the grammar. Many incremental systems adopt ad hoc grammar relaxation rules to deal with the incremental nature of dialogue. A grammar defined in terms of incremental growth of interpretation and, as a corollary, context is not faced with this problem though. To the contrary, if, by assumption, the same mechanisms for incremental monotonic growth are shared by both systems, parsing and production, it is this type of framework that, uniquely, can model this unproblematic shift of role as a wholly natural, indeed a predictable consequence. This suggests that incrementality in both generation and parsing, and the potential to provide update from whatever intermediate point speaker-hearer switch takes place, is at the core of the explanation for the frequency of split utterances in conversation.. Accordingly, we now turn to exploring the use of grammar-internal resources to capture such phenomena. In this type of grammar, as we shall see, it will be actions/ procedures for interpretation which replace the static notions of (representations of) denotational content as the central notion. The relevant conceptual point here is that conversational dialogues emerge incrementally over the course of the interaction through the distinct contributions of the participants, each employing no more than resources internal to the grammar.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A symbolic data-driven technique based on evolutionary polynomial regression This paper describes a new hybrid regression method that combines the best features of conventional numerical regression techniques with the genetic programming symbolic regression technique. The key idea is to employ an evolutionary computing methodology to search for a model of the system/process being modelled and to employ parameter estimation to obtain constants using least squares. The new technique, termed Evolutionary Polynomial Regression (EPR) overcomes shortcomings in the GP process, such as computational performance; number of evolutionary parameters to tune and complexity of the symbolic models. Similarly, it alleviates issues arising from numerical regression, including difficulties in using physical insight and overfitting problems. This paper demonstrates that EPR is good, both in interpolating data and in scientific knowledge discovery. As an illustration, EPR is used to identify polynomial formulae with progressively increasing levels of noise, to interpolate the Colebrook-White formula for a pipe resistance coefficient and to discover a formula for a resistance coefficient from experimental data. The process of building mathematical models of complex systems based on observed data is usually called system identification. Colour coding of mathematical modelling is often used to classify models according to the level of prior information required, i.e. white-box models, black-box models and grey-box models (Ljung 1999; Giustolisi 2004

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