Differential adaptation: an operational approach to adaptation for solving numerical problems with CBR Case-based reasoning relies on four main steps: retrieval, adaptation, revision and retention. This article focuses on the adaptation step; we propose differential adaptation as an operational formalization of adaptation for numerical problems. The solution to a target problem is designed on the basis of relations existing between a source case (problem and solution) and a target case. Differential adaptation relies on the metaphor of differential calculus where small variations on variable values are related to variations of function values. Accordingly, variations between problems correspond to variations between variable values and variations between solutions to variations between function values. Operators inspired from differential calculus are able to manipulate the variations and to support the whole adaptation process. Differential adaptation is operational and provides generic operators that can be reused for different real-world numerical situations. Case-based reasoning (cbr) is widely used in many applications and tasks to solve problems in weak theory domains. cbr solves new problems by retrieving and adapting solutions of previously solved cases stored in a case base [35, 23, 25] . The basic knowledge unit is the case which represents a problem solving episode. A typical cbr cycle is composed of four main steps. Given a new problem, called a target problem, the retrieval step selects a source case from a case base. The adaptation step builds a solution to the target problem, relying on the differences between the source and target problems, and modifying accordingly the solution of the retrieved source case. The revision step improves the current target solution depending on actual and expected system results. Finally the retention step stores the newly solved case for further reuse.. In knowledge intensive cbr systems, cases are completed with domain knowledge which provides case vocabulary and semantics for interpreting situations, assessing similarity and supporting the adaptation process. Knowledge intensive cbr systems rely on several knowledge containers [34] : cases, domain knowledge, similarity measures, and adaptation knowledge. More generally, it is usually assumed in cbr that it is possible to rely on adaptation knowledge and variations between problems for finding and controlling variations between solutions: the less there are variations between problems the less there are variations between solutions. Nevertheless, modeling adaptation is a difficult task as it takes into account domain knowledge not always available or easy to acquire [15] . Most of the time, in practical applications, the adaptation step is either restricted to a simple copy of the source solution without any modification, or implemented in an ad hoc way in the framework of the application.. Adaptation in cbr has been studied in various situations, e.g. [21, 38, 32, 37, 15] , and there does not yet exist a general model of adaptation. By contrast, this article proposes differential adaptation as an operational approach to adaptation for solving numerical problems with cbr, i.e. problems where variables have numerical or totally ordered values. Adaptation is based on relations existing, on the one hand, between a source problem and a target problem, and on the other hand, between a source problem and the source solution. Differential adaptation materializes the research results of studies on adaptation within the cbr process, carried out by the authors for several years, e.g. [24, 18, 19, 12] , and more recently [13, 10, 17 ]. The main characteristics of differential adaptation can be summarized as follows:. • Retrieval and adaptation are intertwined: according to the adaptationguided retrieval principle [37] , a source case is considered as similar if it is possible to adapt its solution to the target case. The adaptation process can be performed gradually by building an adaptation path -in the solution space-aligned with a dual similarity path -in the problem space.. • Adaptation knowledge represents dependencies between problem descriptors and solution descriptors: there is a dependency if and only if a variation of the value of a problem descriptor entails a variation of (at least) a solution descriptor.. • Adaptation knowledge represents the influence of a variation of a problem descriptor on the variation of a solution descriptor.. Moreover, let us mention that interactions are not taken into account within differential adaptation. Interactions may occur when an adaptation operation interacts with another adaptation operation, preventing the achievement of the solution. Interactions can be avoided in some situations when they can be detected and then modifying and introducing appropriate descriptors and dependencies. Further studies have to be carried out to examine this problem more carefully.. Finally, based on the preceding section, two important issues on knowledge engineering for case-based reasoning can be noticed:. • Case elaboration -or what's in a case-needs a large amount of knowledge on the way of adapting a case; connections can be made with the objectives of knowledge intensive cbr [1, 30, 36] . Actually, the representation of a case for being manipulated by cbr is probably different from the user representation. In particular, the Prolabo experience shows that the representation of a case must be well-known by the user of the case-based reasoning system.. • Influences constitute the main knowledge units for adaptation and for similarity assessment. Influences do not generally rely on global functions, but rather on local functions depending on the value of the source solution descriptor, the value of the source problem descriptor, and on the magnitude of the differences to be adjusted between problem descriptors. Knowledge on influences is of first importance and should be elicited and/or mined (see for example [16] or [15] where they are obtained through a knowledge discovery process).. Differential adaptation has some limitations and the first one is to be well adapted to numerical problems, because of the metaphor of differential calculus, but much less actionable in other more symbolic domains. Actually, the availability of adaptation knowledge is a major concern for designing a good differential adaptation process. Moreover, we have seen in the Prolabo application that it is important to know the interactions between descriptors, in problems and solutions, and to be able to quantify these variations w.r.t. domains of values of the descriptors. Actually, the lack of a complete description of the problem descriptors and their variations prevents the application of differential adaptation. Thus, problems that can be represented or approximated by mathematical functions are good candidates for being solved by a differential adaptation approach. Indeed, this is confirmed by the experiments which are proposed in the next section. In this section, we discuss the place of differential adaptation w.r.t. close approaches. It can be noticed that references are not so recent as it seems that adaptation did not deserve so much attention in the cbr literature, at least for works close to differential adaptation. However, we will conclude the section with recent work on revision-based adaptation which is a complementary approach to differential adaptation.. In [6] , there is a proposition of using domain knowledge for explaining the solution of a specific problem. According to this approach, domain knowledge provides knowledge units for similarity measures and for adaptation operations as well. Actually, the paper highlights the key role played by dependencies between solution descriptors and problem descriptors. In the same way, a generic method is presented in [4, 3] , dealing with case abstraction and planning problem-solving.. In [31] , the formalization of adaptation in the context of design problems is based on a particular case representation allowing case processing with CSP (Constraint Satisfaction Problems) methods. Following a similar approach as in [4, 3] , cases are decomposed into sub-cases, and global consistency is guaranteed by the constraint-solving method, which relies on an efficient heuristic: the source cases minimizing the number of constraints to be solved have to be preferred. Dependencies are expressed as constraints to be satisfied and the solver needs a detailed domain model for completing an efficient processing.. The two preceding approaches are mainly related to generative case adaptation, while some research papers have addressed transformational and substitution adaptation processes. In [5] , adaptation knowledge is presented under the form of local functions transforming a source case into a target case according to expected quality measures. Adaptation is then performed by applying a set of appropriate transformation functions allowing an improvement, i.e. a better quality measure of the target case. Hence, there is a need for a global function allowing the composition of local quality improvements into a global quality improvement.. In [8] , a simple local adaptation method uses interpolation functions for adapting a source solution descriptor depending on an observed difference between the source and target problem descriptors. Several interpolation techniques are enumerated according to the types of the descriptors.. In [2] , the general idea "the most similar case is the case that is the easiest to adapt" is considered as the basic principle. Accordingly, the authors introduce a "metric" based on the relations existing between the problem descriptors and the solution descriptors, i.e. an adaptation function for adapting a source solution into a target solution. Based on similar ideas, substitutional adaptation is provided with a working implementation for solving an industrial problem in [26] .. In [20] , the adaptation model is based on substitution as an adaptation operator. A case is connected to two individuals representing the problem and its solution in the considered case. Each solution individual is related through "dependency relations" to a set of individuals that are elementary descriptors of the solution. More recently, this research work has been extended in the context of knowledge intensive cbr [36] . The authors propose a domain independent algorithm for case adaptation based on planning techniques and heavily depending on a domain ontology. Here again, the role and the use of domain knowledge is considered as being of high importance.. Among more recent work on adaptation, [29] presents case-based adaptation of workflows. Adaptation is based on an anchor mapping algorithm which identifies the parts of the workflow where to apply the changes. In [22] , a method for increasing the context-awareness of case adaptation is proposed, with an application to a regression task. In this work, the context is used to improve the quality of adaptation rules that can be automatically extracted from the comparison of the cases. In [33] , adaptation in case-based design relies on k-nearest neighbors and is used for feature adaptation. These three papers show recent research directions on case-based reasoning and adaptation, and propose related adaptation strategies. However, they are not closely related to differential adaptation which relies on a different basis, namely differential calculus, which provides the rules for "computing adaptation" with the help of similarity paths and domain knowledge. Nevertheless, all approaches show that domain knowledge should be present for conducting a successful adaptation process.. For ending this discussion and providing a comparison with related work, we first summarize the characteristics of differential adaptation and then we compare these characteristics with respect to related work (see Table 3 ).. A1. Retrieval and adaptation are intertwined: a source case is selected in the case base if and only if it is possible to adapt its solution for solving the target problem. We have conducted some experiments to show the behavior, the usefulness and the efficiency of the differential adaptation approach. In this section, we present and discuss the results of these experiments. The global setting of the experiments relies on the use of numerical functions that are known but that should be approximated based on the differential adaptation framework. More precisely, we have the following setting:. m where m is a non null integer,. • a (target) function f : D −→ IR n which is continuous and differentiable, where n is a non null integer,. • the matrix of partial derivatives f : J f = ∂dy j ∂dx i ij is used as domain knowledge for differential adaptation.. A source case is a pair (x, y) where x ∈ IR m denotes a problem and y ∈ IR n denotes a solution. The target problem x can be randomly chosen on D and y = f (x) is computed accordingly. The case base can also be randomly defined. Case retrieval is based on the Euclidean distance on IR m . Then the closest case w.r.t. Euclidean distance is selected.. The experiment consists in comparing the approximation of the target function using on one side differential adaptation and on the other side "adaptation by copy" or "null adaptation". In both approaches, the selected case is closest case w.r.t. Euclidean distance. In adaptation by copy, the selected cased is reused as such. In differential adaptation, the selected case is transformed following 4 variations corresponding to the length of the similarity path: "basic differential adaptation" with q = 1, i.e. no intermediate problem, q = 2 with one intermediate problems, q = 3 with two intermediate problems, and finally q = 10 with nine intermediate problems. By contrast, adaptation by copy (also known as null adaptation) leads to a "retrieval-only CBR system".. For a given target problem x 0 and a case base B we compute:. • a series of intermediate problems:. • the error induced by basic differential adaptation (q = 1):. where ad(B, x 0 ) ∈ IR n denotes the results computed by the CBR system with differential adaptation,. • the error induced by differential adaptation for q ∈ {2, 3, 10}, • m = 2, n = 1,. The case base has 3 different sizes, namely 10, 100, 1000 cases. The process hereafter is then repeated 1000 times: (i) random generation of the case base, (ii) random generation of the target problem, (iii) computing the average error, (iv) computing the standard deviation. The results are given in Figure 5 . Moreover, Figure 6 and Figure 7 present four curves each time with a case base B respectively including 10 cases and 100 cases which are randomly generated. In each figure, the dotted line corresponds to the target function f (x) = sin x 1 + e x . In (a), the other curve corresponds to the result of adaptation by copy. In (b) (respectively in (c), (d)), the other curve corresponds to the result of differential with q = 1 (respectively q = 2, q = 3).. Then we can observe the following phenomena:. • Looking at (a) and (b) in Figure 6 or in Figure 7 , one can observe that the quality of differential adaptation with q = 1 is much better than that of adaptation by copy. This is the first main observation.. • The influence of parameter q: looking at curves (b), (c), and (d) in Figure 7 , we can observe that the more q is high the better differential adaptation is, even if it is more easy to check this fact in Figure 6 . This is the second main observation.. • The influence of the size of the case base: another time, looking at curves (b), (c), and (d) in both Figure 6 and Figure 7 , we can observe that the approximation is of higher quality in Figure 7 with 100 cases than in than in Figure 6 with 10 cases. This is the third main observation of these experiments.. This interpretation concludes this section on experiments and shows the very good behavior of differential adaptation in solving the problem of mathematical function approximation with a cbr approach. This shows also that being interested in dependencies between descriptors in adaptation is indeed a good idea and can lead to good implementations of the adaptation process.

O B 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 B O O O O B 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 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 B I 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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 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 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 B 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 B 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 B 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 B O O O O O O O O B O O O O O O O O B I 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 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 B 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B 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 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 O O O O O O O O O O O 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CBRISK: Colored Binary Robust Invariant Scalable Keypoints BRISK (Binary Robust Invariant Scalable Keypoints) works dramatically faster than well-established algorithms (SIFT and SURF) while maintaining matching performance. However BRISK relies on intensity, color information in the image is ignored. In view of the importance of color information in vision applications, we propose CBRISK, a novel method for taking into account color information during keypoint detection and description. Instead of grayscale intensity image, the proposed approach detects keypoints in the photometric invariant color space. On the basis of binary intensity BRISK (original BRISK) descriptor, the proposed approach embeds binary invariant color presentation in the CBRISK descriptors. Experimental results show that CBRISK is more discriminative and robust than BRISK with respect to photometric variation. key words: color space, photometric invariant, binary descriptor Feature matching is at the base of many Computer Vision applications, e.g. image retrieval, object recognition and matching, visual mapping. Due to ever growing consumption of visual content and real-time requirement for such visual applications, there exists an urgent need for fast and efficient methods to compute local descriptors and match them afterwards. It is difficult to satisfy this demand using existing methods (SIFT [1] , SURF [2] ) relying on costly descriptors for detection and matching.. To address the above mentioned problem, binary descriptors, the bit strings directly computed from image patches, are proposed. The similarity between the binary descriptors can be evaluated using the Hamming distance, which can be computed much faster than the Euclidean one between floating-point descriptors [1] , [2] on modern CPUs.. Calonder et al. [3] proposed efficient BRIEF (Binary Robust Independent Elementary Features) descriptors that are computed using simple intensity comparisons at random pre-determined pixel locations. The performance of BRIEF is similar to SIFT in many respects, including robustness to lighting, blur, and perspective distortion. However, it is very sensitive to image rotation and scale changes restricting its application to general tasks. Rublee et al. [4] presented the oriented BRIEF descriptor ORB (Oriented FAST and Rotated BRIEF). Inspired by the rapid computation of FAST (Features from Accelerated Segment Test) cor- ner detector [5] , they applied FAST to detect keypoints and added a fast and accurate orientation operator to FAST for computing the orientation of keypoints. Then they steered BRIEF descriptor according to the orientation of keypoints for obtaining the oriented BRIEF descriptors. Although ORB is rotation invariant, it still cannot efficiently handle the scenes with scale changes. Leutenegger et al. [6] introduced a rotation and scale invariant binary descriptor BRISK (Binary Robust Invariant Scalable Keypoints). They proposed a novel scale-space FAST-based detector and generated the descriptor by comparing the intensities retrieved by dedicated sampling of each keypoint neighborhood. BRISK achieves comparable quality performance with well-established algorithms (SIFT and SURF) at much less computation time. However, BRIEF, ORB, and BRISK are all designed mainly for grayscale images.. In this letter, we aim to generate high-performance and low-computation binary descriptor for color images. We present a novel Colored BRISK (CBRISK), which not only contains the color information but also possesses good robustness with respect to color, rotation and scale changes.. The rest of the letter is organized as follows. The analysis of BRISK method is described in Sect. 2. Section 3 introduces the details of the proposed method CBRISK. Section 4 is devoted to the results and comparative analysis. Finally, the conclusion is drawn in Sect. 5. In this paper, we introduced a novel method named CBRISK, which tackles the problem of the intensity-based BRISK lacking photometric invariance and discriminative power. In keypoint detection, the photometric invariant is used as the input to construct a scale-space pyramid, where the corners are identified as keypoints by CBRISK. For a colored invariant descriptor, the magnitude relationship of RGB values of each pixel sampled arround the keypoint is applied as the invariant color information. Then the CBRISK feature descriptor is gained by combining both the binary presentation of invariant color information and the original binary intensity BRISK descriptor. The experiments show CBRISK outperforms BRISK and I2CBRISK generated according to the C-SIFT method.

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


Integrating an internet-mediated walking program into family medicine clinical practice: a pilot feasibility study Background: Regular participation in physical activity can prevent many chronic health conditions. Computerized self-management programs are effective clinical tools to support patient participation in physical activity. This pilot study sought to develop and evaluate an online interface for primary care providers to refer patients to an Internet-mediated walking program called Stepping Up to Health (SUH) and to monitor participant progress in the program. Methods: In Phase I of the study, we recruited six pairs of physicians and medical assistants from two family practice clinics to assist with the design of a clinical interface. During Phase II, providers used the developed interface to refer patients to a six-week pilot intervention. Provider perspectives were assessed regarding the feasibility of integrating the program into routine care. Assessment tools included quantitative and qualitative data gathered from semi-structured interviews, surveys, and online usage logs. Results: In Phase I, 13 providers used SUH and participated in two interviews. Providers emphasized the need for alerts flagging patients who were not doing well and the ability to review participant progress. Additionally, providers asked for summary views of data across all enrolled clinic patients as well as advertising materials for intervention recruitment. In response to this input, an interface was developed containing three pages: 1) a recruitment page, 2) a summary page, and 3) a detailed patient page. In Phase II, providers used the interface to refer 139 patients to SUH and 37 (27%) enrolled in the intervention. Providers rarely used the interface to monitor enrolled patients. Barriers to regular use of the intervention included lack of integration with the medical record system, competing priorities, patient disinterest, and physician unease with exercise referrals. Intention-to-treat analyses showed that patients increased walking by an average of 1493 steps/day from pre-to post-intervention (t = (36) = 4.13, p < 0.01). Primary care providers can successfully refer patients to an Internet-mediated walking program using a webbased interface. Patients who chose to enroll in the program significantly increased their walking. However, providers rarely used the interface to monitor patient progress in the program. A number of barriers to provider use of the interface were identified during the program. The results of this study will enable the research team to conduct a large randomised-clinical trial to compare program results with other intervention strategies (e.g., phone, face-to-face counseling) and to evaluate the prospects for large-scale implementation of the SUH program in clinical practice. Results demonstrate the feasibility of using an online clinical tool to enable PCPs to promote physical activity in high-risk patients. The developed clinical interface is a promising approach to help reorient primary care providers on lifestyle factors such as physical activity promotion [33] [34] [35] . The PCMH concept of care combines information technology tools with a collaborative team approach to provide more time for services like physical activity counseling. Programs like SUH help support the PCMH concept of care by emphasizing the efficient application of information technology to facilitate coordination between patients and their providers [24] . SUH supports patients with personalized walking goals and feedback, facilitates ongoing patient-provider communication, and gives PCPs the ability to prospectively monitor patient progress and safety.. The SUH intervention and clinical interface have several advantages over previous strategies used to promote lifestyle change in primary care. One advantage is that the automated referral process requires minimal provider time and can reach large numbers of patients with a a Some participants self-identified as more than one race. b 100% of sample was overweight (BMI > 25) with n = 1 reporting BMI < 30.. consistent approach [36] in contrast to more traditional strategies such as face-to-face provider counseling [37] [38] [39] or referral by clinical staff to community programs [33, 40, 41] . A second advantage is that the clinical interface gives clinical providers ongoing feedback and monitoring regarding the progress of patients' walking programs. This second strength is further enhanced by the capability of patients and providers to email each other as needed so that the intervention is not disconnected from clinical practice after referral [41, 42] . This is consistent with the PCMH model of care in that the primary health care team remains informed about all aspects of care. The clinical interface provided PCPs with the option of either directly referring patients to SUH during a clinical encounter or using a clinical database to identify eligible patients to send a referral letter by mail. Over 25% of the patients referred to SUH were enrolled despite some providers expressing lack of confidence in their physical activity counseling skill. This lack of confidence is a known barrier to successful implementation of practice-based physical activity interventions [43, 44] . It is possible that training programs for providers that directly address physical activity counseling skills may increase program adoption by patients. Nonetheless, use of a physical activity program by 25% of a practice network's high-risk patients could yield a significant population effect on morbidity and mortality, service utilization, and patient quality of life and optimal function.. Although providers were successful in referring patients to the program, they rarely used the clinical interface to monitor patients enrolled in SUH. This may have been due to the short duration of the follow-up period, lack of time for providers, and lack of integration of the clinical interface into the clinics' EMR infrastructure. Prior studies of automated clinical tools to support behavior change have noted that full integration of these tools with the practice EMR is desirable but challenging. Integration allows efficient access information for patient monitoring and consultation [45] .. Implementation of SUH could be improved by emphasizing a team-based approach to patient referral and by ongoing program monitoring. Involving MAs more regularly in participant monitoring might have strengthened the effect on patient adoption and use of SUH. Time constraints faced by physician providers necessitate greater reliance on nurses and MAs [24] . Furthermore, evidence suggests health behavioral change interventions are more effective when allied health personnel are trained to augment physician brief counseling and education efforts [46] [47] [48] [49] .. While the focus of this study was on testing the feasibility of the SUH as a clinical practice tool [50] , Phase II testing revealed encouraging preliminary patient outcome results. Referred patients who chose to participate in the walking program significantly increased their physical activity over six weeks from an average of 45 min/ wk to 72 min/wk. Despite the automated nature of the SUH walking program, participants reported high levels of satisfaction with the program. As demonstrated in previous walking studies, high-risk patients were able to successfully participate without experiencing serious adverse events [51] .. This study used a combination of evaluation methods suited to assessing the feasibility of implementing an intervention in real world settings [52] . First, this study employed an iterative, user-centered design process to ensure that the clinical interface met the needs of the providers [28] . Multiple qualitative interviews with providers identified user needs and barriers to implementation that could not be easily understood using quantitative data alone [29, 53] . Second, we recognized the competing priorities and time limitations faced by providers during clinical encounters and automated the SUH referral processes to minimize PCP burden. Finally, to focus on implementation rather than efficacy, there was minimal contact between researchers and provider Physical activity is recommended as first-line medical therapy for preventing and managing many chronic diseases [1] [2] [3] [4] . Moderate-intensity physical activity such as walking can reduce the risk of developing chronic diseases, particularly among individuals at high risk for type 2 diabetes and cardiovascular disease [5] [6] [7] [8] [9] [10] . However, there are few effective interventions for promoting physical activity in the primary care setting [11, 12] .. Medical guidelines emphasize the active role primary care physicians (PCPs) should play in helping patients initiate and sustain physical activity programs. Provider recommendations can help motivate patients to initiate an exercise program. PCPs can also be instrumental helping patients safely re-engage in activity after an illness or medical issue [9, 13, 14] . In practice, a provider's ability to promote physical activity has been limited by time constraints, lack of training in exercise prescription, concerns over monitoring patient safety, and lack of access to cost-effective resources that help patients remain active [11, 12, [15] [16] [17] . Internet-based, computertailored intervention programs may make it easier for providers to support patients with personalized selfmanagement information and encouragement and thus facilitate sustained adherence to physical activity [18] [19] [20] .. We previously developed and tested Stepping Up to Health (SUH), an Internet-mediated walking program for people with chronic illness. SUH is a multi-component, theory-based physical activity intervention that uses uploading pedometers to objectively monitor and track daily walking and to set personalized goals [21, 22] . SUH was specifically designed to help sedentary patients diagnosed with type 2 diabetes, coronary artery disease, or obesity become physically active and reduce their cardiovascular disease risk. The program focuses on homebased unsupervised walking, a low-risk mode of physical activity that can be performed without direct clinical supervision even in high-risk patients [8] . SUH increased walking among sedentary individuals with diabetes by an average of approximately 1 mile or 20 minutes of walking per day over a six-week period [21] . These high-risk individuals are precisely the patient population that is most likely to derive the greatest benefit from moderate increases in activity through reduced cardiovascular mortality and morbidity [23] . However, like many promising Internet-based physical activity programs, SUH has not been translated into a clinical tool that could enable providers to effectively promote physical activity as part of routine care.. Clinical tools for primary care practice that improve efficient resourcing and patient outcomes are fundamental to the patient-centered medical home (PCMH) model of care. The PCMH model aims to improve patient outcomes through the use of technological innovations, shared responsibilities among collaborative provider teams (e.g., physicians, nurses, physician assistants, and medical assistants), and personally-tailored preventive health programs delivered at a population level [24, 25] . While Internet-based patient self-management programs offer the benefits of reaching many patients at low cost, they must first be integrated into clinical practice through iterative testing and refinement with provider input [26, 27] . The potential of SUH to help PCPs achieve PCMH goals is limited if PCPs do not find SUH easy to use in combination with other key clinical tools such as the electronic medical record (EMR).. This pilot study was designed to accomplish two objectives: 1) to develop a clinical interface with provider input that allows PCPs to efficiently refer patients to SUH and to serially monitor their progress and safety; and 2) to evaluate the feasibility of incorporating the SUH intervention into clinical practice using qualitative interviews, process and satisfaction measures and objective measures of patient physical activity via daily pedometer step counts. The design and implementation of the clinical interface for SUH was driven by the principles of the PCMH model to improve patient-centered care and outcomes through the use of an e-health technology accessible by practice care teams. This pilot study was funded through the University of Michigan's Institute for Clinical & Health Research (UL1RR024986), which is funded by a National Institutes of Health Clinical and Translational Sciences Award program. We used a two-phased, mixed-method design to: 1) develop an online clinical interface allowing providers to refer patients to the SUH intervention and to monitor their program compliance; and 2) evaluate the feasibility of implementing SUH in clinical practice. This study was approved by the University of Michigan Institutional Review Board (HUM00016019), and both provider and patient participants completed an informed consent process.

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


A Characterisation of First-Order Constraint Satisfaction Problems Abstract. We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction problem is first-order definable: we show the general problem to be NP-complete, and give a polynomial-time algorithm in the case of cores. A slight modification of this algorithm provides, for firstorder definable CSP's, a simple poly-time algorithm to produce a solution when one exists. As an application of our algebraic characterisation of first order CSP's, we describe a large family of L-complete CSP's. The Constraint Satisfaction Problem (CSP) consists of determining, given a finite set of variables with constraints on these, whether there exists an assignment of values to these variables that satisfies all the given constraints. The great flexibility of this framework has made the CSP the focus of a great deal of attention from researchers in various fields (see for instance the recent survey [CJ06] ). In general the problem is NP-complete, but restricting the type of constraint relations involved may yield tractable problems. In fact, Schaefer [Sch78] and more recently [ABISV05] have completely classified the complexity of Boolean CSP's and from their work it follows that Boolean CSP's are either trivial, first-order definable, or complete (under AC 0 reductions) for one of the following standard classes of problems: L, NL, P, ⊕L and NP. One of the outstanding problems in the field is the so-called dichotomy conjecture [FV93] that states that every CSP should be either in P or NP-complete.. In this paper we adopt the convenient point of view offered in [FV98] where CSP's are viewed as homomorphism problems with a fixed target. In other words, if A is a finite relational structure, then A-CSP consists of all structures that admit a homomorphism to A. Viewed this way, it becomes natural to ask which CSP's can be described in various logics. For instance in [LT07] , the result of Allender et al. mentioned earlier is given a descriptive complexity analog, whereby it is shown that Boolean CSP's that lie in the classes L and NL are precisely those whose complement is describable in symmetric and linear Datalog respectively. Arguably the simplest CSP's (other than trivial ones) are those whose members are describable by a first-order sentence. A very natural question in the vein of the dichotomy conjecture is then the following: can we determine (easily) from the constraint relations whether a given CSP is first-order definable ? Related questions for Datalog and its restrictions remain open [Dal05] , [FV98] . An important first step in this direction is Atserias' result [Ats05] proving that FO-definable CSP's are precisely those with finite duality, i.e. those target structures A for which there exists a finite set F of structures such that B admits no homomorphism to A precisely if some structure in F admits a homomorphism to B. This result was followed closely by the more general result for homomorphism-closed classes by Rossman [Ros05] .. In this paper, we give several equivalent characterisations of FO-definable CSP's. We first give a characterisation with an algebraic flavour: core structures with an FO-definable CSP are characterised by the existence of special near-unanimity operations preserving their basic relations (Theorem 4.5). For general structures, we prove that the problem of determining if A-CSP is first-order definable is NP-complete (Theorem 6.1); if the structure A is a core, then in fact there exists a simple polynomial-time algorithm to determine this (Theorem 6.2). We shall also describe in this case a simple algorithm that produces a solution in polynomial-time (Theorem 7.2). Let A be a core structure such that A-CSP is first-order definable, and let B be a structure with the same universe, such that the basic relations of B are constraint relations "inferred" from those of A, i.e. each is describable by a primitive positive formula with atomic formulas of the form x ∈ θ with θ a basic relation of A; these inferred relations play a crucial role in the study of the complexity of CSP's (see e.g. [CJ06] ). It is known that B-CSP is logspace reducible to A-CSP [Jea98] , but in general it will not be first-order definable. As a simple application of our algebraic characterisation of first-order definable CSP's (Corollary 4.3 and Proposition 4.4) we describe precisely which B-CSP are first-order definable; the others turn out to be L-complete, with their complement definable in symmetric Datalog [ELT07] , a fragment of linear Datalog.. To illustrate briefly the above results, we outline the algorithms in the special case of digraphs. For two vertices u, v of a digraph H, we say that v dominates u if every outneighbour of u is also an outneighbour of v and every inneighbour of u is also an inneighbour of v. If there exists a sequence H = H 0 , H 1 , . . . , H n = R of digraphs such that H i is obtained from H i−1 by removing a dominated vertex for i = 1, . . . , n, we say that H dismantles to R. More generally, R is a retract of H if there exists a homomorphism from H to R whose restriction to R is the identity. The square R 2 of a digraph R has vertex set R 2 where the arcs are the couples ((u 0 , u 1 ), (v 0 , v 1 )) such that (u 0 , v 0 ) and (u 1 , v 1 ) are arcs of R, and its diagonal ∆ R 2 is the set of vertices of R 2 with both coordinates equal.. The main algorithm to determine whether H-CSP is first-order definable proceeds as follows: in H 2 , remove any dominated element outside the diagonal, if any. Repeat this procedure until no element can be removed. If the resulting set is the diagonal, then the problem is first-order definable. Assuming that H is a core, i.e. that it has no proper retract, then the converse also holds. In the figure above, T 3 is the transitive tournament on three vertices. In T 2 3 , the two isolated vertices (0, 2), (2, 0) are dominated by all other vertices, the sources (0, 1), (1, 0) are dominated by (0, 0) and the sinks (1, 2), (2, 1) are dominated by (2, 2). Hence T 2 3 dismantles to ∆ T 2 3 , which shows that T 3 -CSP is first-order definable. In fact it is well known that a directed graph G admits a homomorphism to T 3 if and only if there is no homomorphism from the directed 3-path P 3 to G, and this condition is described by the first-order sentence. , where A(x, y) denotes the existence of an arc from x to y. P 3 -CSP is not first-order definable; indeed the path P 3 is a core and P 2 3 can only be dismantled down to P 2 3 \ {(a, d), (d, a)}. The square of C cannot be dismantled to its diagonal, but C admits T 3 as a retract, whence C-CSP is first-order definable. Also, it is easy to check that C × T 3 dismantles to the "graph" {(x, φ(x)) : x ∈ C} of a homomorphism φ : C → T 3 . In Section 7, we will see that such dismantlings of products can always be used to produce solutions of first-order definable constraint satisfaction problems. We have described a simple polynomial-time algorithm that determines if a finite relational structure is a core with first-order definable CSP (Theorem 6.2), and have proved that deciding FO-definability is NP-complete (Theorem 6.1). We have also given various characterisations of FO-definable structures in terms of sets of obstructions (Theorem 2.5), and proved that core structures with finite duality admit a 1-tolerant near-unanimity operation (Corollary 4.3 and Lemma 4.4).. Feder and Vardi's Theorem 2.6 shows that the problem of determining whether an input structure A has tree duality is decidable. In fact the proof of Theorem 6.1 also implies that this problem is NP-hard, but for the moment it is not known to belong to NP or even to P-space. It would be interesting to have these issues resolved.. In the case of first-order definable CSP's, we now have an algorithm which outputs a yes-no answer to the question as to whether an input structure A has a first-order definable CSP. Using Lemma 2.3, it is possible to modify it so that in the case where A-CSP is firstorder definable, it outputs a first-order sentence Φ A such that B admits a homomorphism to A if and only if Φ A is true on B. However the upper bound on the length of Φ A involves a tower of exponents. It is not clear whether this is realistic; [NT05] reports cases where the length of Φ A can be logarithmic in terms of the size of A, but there are no examples in the direction of the other extreme.

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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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


Identifying Genes of Gene Regulatory Networks Using Formal Concept Analysis AbstractIn order to understand the behavior of a gene regulatory network, it is essential to know the genes that belong to it. Identifying the correct members (e.g. in order to build a model) is a difficult task even for small subnetworks. Usually only few members of a network are known and one needs to guess the missing members based on experience or informed speculation. It is beneficial if one can additionally rely on experimental data to support this guess. In this work we present a new method based on formal concept analysis to detect unknown members of a gene regulatory network from gene expression time series data.We show that formal concept analysis is able to find a list of candidate genes for inclusion into a partially known basic network. This list can then be reduced by a statistical analysis so that the resulting genes interact strongly with the basic network and therefore should be included when modeling the network. The method has been applied to the DNA repair system of Mycobacterium tuberculosis. In this application our method produces comparable results to an already existing method of component selection while it is applicable to a broader range of problems. Gene expression data is one of the most often analyzed kind of data in the field of bioinformatics as it serves as a basis to answer several different questions. One of the goals is the understanding of processes in the cell on a molecular level. Time series measurements of gene expression levels can reveal the different regulatory interactions between genes. A gene regulatory network is defined as a graph with genes as nodes and their interactions as edges. Often functions are assigned to the edges to determine the dynamic behavior of the concentrations of the corresponding mRNAs (see for example [Gebert et al., 2006 ). In most studies only subgraphs representing a small subnetwork and the corresponding interactions are examined. In order to build a reasonable model for such a subnetwork, it is essential that all components of the network are identified. Usually, some genes are known to be responsible for most of the behavior of the subnetwork. Their mutual influences might be known to some extent as well. We will call such genes seed genes hereafter. Now the question is: How to determine possible other members of the network when gene expression time series data are available? In this paper we will present a method which finds genes that might have an important influence on the gene regulatory network defined by the seed genes and that should be added to this network. A mathematical method, called formal concept analysis, is used to detect a list of candidate genes that can be analyzed afterwards in the same way as proposed in [Radde et al., 2006] . In that paper a graph theoretical approach was used to detect such a list of genes, which is further described in [Cabusora et al., 2005] . The graph theoretical approach needs interaction data as well as expression data to find k-shortest paths in the graph built from the interaction data. In our new approach the availability of interaction data is not a prerequisite. Nevertheless, if such data are available they are included in the preprocessing step of our approach based on formal concepts and statistical analysis. Another method concerning the choice of components in gene regulatory networks has been proposed by [Hashimoto et al., 2004] . They use gene expression data to grow a gene regulatory network out of a seed consisting of one or more genes and apply their method to a glioma gene expression data set. Iteratively new genes are adjoined to the seed so that the autonomy of the network is enhanced. Autonomy is defined with the help of two properties of subnetworks: The genes should interact significantly and they should not be strongly influenced by genes outside the network. Later, another approach for growing a subnetwork around a gene of interest was proposed by [Bansal et al., 2006] . They perturbed the gene of interest and measured the following gene expression profiles at several time points to infer gene regulatory networks. Instead of growing a regulatory network from few genes the opposite approach is also possible. Standard clustering algorithms find genes that are co-regulated. However, there are two problems. Genes are usually only assigned to one cluster although they might play a role in more than one regulatory module, and they might be active in only few experiments so that the noise level is very high (see [Kloster et al., 2005] ). Signature algorithms as the one proposed by [Ihmels et al., 2002] can overcome these problems. This algorithm determines a set of co-regulated genes together with conditions under which they are coregulated. An extension of the algorithm which uses the knowledge of already identified modules in each iteration step can be found in [Kloster et al., 2005] . Our method is based on formal concept analysis and is applied to the DNA repair system of Mycobacterium tuberculosis. The method proposed in [Radde et al., 2006] uses the same data set so that the methods can be compared with each other. The bacterium M. tuberculosis has been discovered by Robert Koch in 1882. Its genome was sequenced in 2000, thus enabling the understanding of processes in its cell on molecular level. Detailed knowledge about regulatory mechanisms can build the basis for drug intervention. One of these regulatory mechanisms is the DNA repair system. The system consists of the proteins LexA and RecA as well as up to 40 genes that are regulated by these two proteins together. If a damage in the DNA occurs which results in single-stranded DNA, then the DNA repair system is activated. The protein RecA binds to this single-stranded DNA and produces a change of the structure of the protein LexA. In this form LexA cannot bind to the regulatory regions called SOS boxes on the DNA any longer. The associated SOS genes will be no longer repressed by LexA and transcription starts. Both genes recA and lexA have an SOS box as well. Additionally to the SOS regulation there exists another mechanism in M. tuberculosis to activate some of the SOS genes in the case of DNA damage (see [Dullaghan et al., 2002] ). In [Radde et al., 2006 ] the gene Rv2719c is predicted to play an important role in the DNA repair system. We will compare our results with this prediction. In section 'Methods' we will present the analysis of gene expression data and interaction data with formal concept analysis followed by the statistical analysis proposed by [Radde et al., 2006] . In section 'Application' we apply this method to data of M. tuberculosis and in section 'Discussion' we will compare the results with the results given in [Radde et al., 2006] and discuss the prospectives of our approach. The section 'Conclusion' will give a short summary of this paper. We propose a new method to find genes that should be included into regulatory network models that uses formal concept analysis. The method uses gene expression time series and a set of seed genes which are known to be important components of the network. A correlation based characterization of the expression profiles is used to produce a concept lattice from which the candidate genes for inclusion into the network can be extracted. Further refinement of the list is achieved by a subsequent statistical analysis which only keeps those candidate genes that show a statistically significant correlation to the expression profiles of the seed genes. We apply the method to the DNA repair system of M. tuberculosis with 4 seed genes and identify a list of 5 genes that should be included into the network model. The majority of these genes are known or suspected to play a role in the DNA repair system. Five genes are added to the subnetwork consisting of the seed genes recA, lexA, ruvC and linB. The function of most of these genes is already known or conjectured. • Rv2719c: This gene has been shown to be a DNA-damage inducible gene and is thought to be regulated by LexA (see [Dullaghan et al., 2002] ).. • dnaE2: It probably encodes a DNA polymerase, which is a complex enzyme responsible for most of the replicative synthesis in bacteria.. • dnaB: It probably encodes a replicative DNA helicase.. • fadD21: It probably encodes a fatty-acid-CoA ligase.. • fadD23: It also probably encodes a fatty-acid-CoA ligase.. The information about the gene functions are listed in the genomic database TubercuList 1 of the Pasteur Institute in Paris. One of these genes, Rv2719c, has been discovered to play an important role in the DNA repair system before (see [Dullaghan et al., 2002 ). Rv2719c is the gene that was included in the model of the DNA repair system by [Radde et al., 2006] , which resulted in an improvement of the simulations compared to the first model without that gene. The genes dnaE2 and dnaB are also involved in DNA repair or replication and therefore seem to be a biologically reasonable result. The last two genes fadD21 and fadD23 have both relatively different functions in contrast to the other three genes. Also, their expression profiles show a downregulation, while the other three candidate genes are up-regulated along with the seed genes. The proposed method based on formal concept analysis has two advantages compared to the method suggested in [Radde et al., 2006] . Interaction data may be used but they are not a prerequisite. Only in few cases interaction data are available for the whole genome so that applications are limited if interaction data are necessary for the method. Moreover, the concept lattice gives a good overview of the correlation dependent structure between gene expression profiles if the templates are constructed thoroughly. The combination of template matching and formal concept analysis is better than working with the correlations between seed genes and other genes directly for a decisive reason: It captures the qualitative behavior of the expression profiles while ignoring much of the variation introduced by noise and outliers. We thus can take a step back and observe the big picture instead of getting lost in disorienting details.. In this paper, we use formal concept analysis to structure a set of genes according to the characteristics of gene expression profiles. As concept lattices can be built on any kind of object-attribute data, numerous other applications of this method to biological data sets are imaginable. To extend the use of formal concept analysis on biological problems, further research is underway. The key issue here will be to make formal concept analysis applicable to large data sets as they are produced in the molecular biological sciences and to provide a flexible and informative visualization of the produced concept lattices. We assume that G = {g 1 , ..., g n } is the set of all genes of an organism and a subset S ⊆ G is our set of seed genes. We want to find another subsetS ⊆ G \ S of genes that interact strongly with the network defined by S. Moreover, we want to determine the structure of the new network consisting of genes S and S. This means, we want to find pairs of genes that influence each other. Let R ⊆ G × G be a relation that contains interaction data and M an n × l matrix consisting of gene expression time series data of length l. If (g i , g j ) ∈ R we know that g i and g j interact with each other, for example g i inhibits g j or g j activates g i . The kind and direction of interaction is not given here. The matrix M consists of the entries m ij which is the expression of gene i at time point j in the experiment. The rows of M are vectors of the form m i = (m i1 , . . . , m il ) and describe the expression of gene i at time points 1, . . . , l. We will use the term expression profile to refer to such a vector m i throughout the paper. We will proceed in three steps: 1. In a preprocessing step we use the relation R to get a first list of interesting genes. If no interaction data are available, this step is skipped and we start directly with the second step using the whole gene set G as the first list. 2. Now we construct a concept lattice from the gene expression data to reduce the number of genes on the first list. 3. In the last step we calculate probabilities for the correlation coefficients between the genes that result from the second step and genes of S in order to obtain significant interactions.

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


Tree-Code modeling and addressing for non-ID physical objects in the Internet of Things The Internet of Things (IoT) is an emerging network paradigm, and realizes the interconnection among ubiquitous things, along with its corresponding applications and services in both Physical-world and Cyber-world. Some researches have been worked on IoT modeling and addressing, which are mainly based on objects with a unique identifier (ID). However, in practical scenarios, there are several objects without any available ID, namely non-ID (i.e., nID) physical objects, including the objects unattached any ID itself, and the objects attached unreadable or un-trusted ID. It turns out that the nID physical objects related issues become noteworthy. In this paper, we focus on the nID physical objects to present a modeling and addressing solution. Concretely, (1) nID physical objects are described along with the discussion of applying nID solution; (2) a tree-like code structure (i.e., Tree-Code) is introduced to establish a unified modeling scheme for the nID physical objects according to abstracted data elements, and also achieves the compatibility with the ID physical objects considering the ID based data elements; (3) Tree-Code based addressing scheme is The Internet of Things (IoT) is developing fast with increasingly worldwide attentions. The original IoT is thought to be a network paradigm in which all physical objects are tagged with radio frequency identification (RFID) transponder with a globally unique identifier (ID), i.e., electronic product code (EPC) [1] . Now IoT concept has been expanded and it's not limited to RFID technology. The vision for future IoT is ubiquitous, "everything connected, intelligent controlling, and anywhere covering". Towards IoT, studies have been worked on its models and frameworks [2] [3] [4] [5] [6] [7] . The realization of future IoT will probably require dramatic changes in systems, architectures, communications and networking, especially identification for "everything".. As an important feature of future IoT, ubiquitous sensing and controlling lay the foundation for the mapping between Physical-world and Cyber-world, which is the prerequisite of IoT applications (e.g., intelligent living environment, and intelligent logistics) [8] [9] [10] . However, ubiquitous sensing alone is not enough for this mapping process, things' modeling and addressing are also important. Things' modeling is responsible for describing things with the data from ubiquitous sensors (e.g., RFID, radar, and video sensor), and it can be used for identification. Things' addressing has a wide range of meanings, such as determining the detailed informa-tion about the thing based on the modeling results, locating the things within a certain range, and even deducing or predicting future trend through combining the modeling results with the context information. There are two typical directions in things addressing process. For the first direction, things are queried from Physical-world and the addressing result exists in Cyber-world. While, for the second direction, things in Physical-world are queried from Cyber-world for some purpose (e.g., locating). For example, in the semantic web, computers can automatically query things (both physical objects and cyber entities) which are modeled by Ontology based languages [11] , such as resource description framework (RDF). In some cases, both directions will combine with each other to accomplish a task.. With the development of computer science and Internet, Cyber-world has been proven to be helpful in modeling and addressing some limited physical objects (e.g., computers, routers, and servers) and cyber entities due to its nearly real time communication capability and strong computing power. Some examples (but not limited to) include IP address, domain name system (DNS), Web services, and search engine applications. The IoT was originally designated to model the physical objects with predefined code stored in a tag, and with the help of appropriate mechanisms such as ONS, the objects can be addressed for some purposes such as getting the objects' information and identifying the objects. In this paper, the above code based physical object modeling schemes are defined as ID based modeling schemes since ID is introduced for object modeling. Towards the ID based physical object modeling schemes, EPC [12] and Ubiquitous ID (UID) [13] are two representatives which utilize RFID technology for object identification. Current IoT applications (e.g., retail industry, and logistics) are mainly based on the ID-based systems [14] [15] [16] [17] [18] .. After more than ten years development, the meaning of IoT has been greatly enriched, which refers to everything connected at anytime and in anyplace. Compared with the original RFID based objects modeling and addressing mechanisms, the adoption of multiple sensing technologies (e.g., RFID, and wireless sensor networks (WSN), smart mobile devices [19] , and global positioning system (GPS)) have made the physical object modeling and addressing to be unprecedented complicated. Moreover, in many practical applications, there are objects without any available ID, called Non-ID (nID) physical objects. The nID physical objects include the objects unattached any ID itself, and objects attached unreadable or untrusted ID. In such cases, ID-based solutions become inapplicable. However, in IoT vision, identification of everything is significant for the realization of everything connected. Thus, it is urgent to explore new modeling and addressing schemes for physical objects without ID. Additionally, the uniform modeling and addressing for the ID and nID physical objects become the future trend in the IoT. In this paper, we are trying to solve the problem to model the physical objects by abstracting data elements, and to design the corresponding addressing mechanisms.. The main contributions of this paper are as follows: (1) introducing the concept of nID physical objects, and discussing the main significance of adopting nID modeling and addressing solutions; (2) proposing a unified modeling scheme (i.e., Tree-Code) for the nID physical objects in IoT applications which is also compatible with the ID based object modeling; (3) establishing a Tree-Code based addressing scheme, by which both ID and nID physical objects can be addressed in a unified form.. The rest of this paper is organized as following. Some related works are introduced in Sect. 2. Section 3 gives some preliminaries of nID physical objects. In Sect. 4, a Tree-Code structure is built for modeling the nID physical objects which also take ID data element into considerations. In Sect. 5, we give the addressing process for Tree-Code with dynamic updating mechanism specification. Section 6 concludes the paper and presents some open challenges.

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


Automatic Generation of CHR Constraint Solvers In this paper, we present a framework for automatic generation of CHR solvers given the logical specification of the constraints. This approach takes advantage of the power of tabled resolution for constraint logic programming, in order to check the validity of the rules. Compared to previous work (Apt and Monfroy 1999; Ringeissen and Monfroy 2000; Abdennadher and Rigotti 2000; Abdennadher and Rigotti 2001a), where different methods for automatic generation of constraint solvers have been proposed, our approach enables the generation of more expressive rules (even recursive and splitting rules) that can be used directly as CHR solvers. Constraint Handling Rules (CHR) (Frühwirth 1998) is a high-level language especially designed for writing constraint solvers. CHR is essentially a committed-choice language consisting of multi-headed rules that transform constraints into simpler ones until they are solved. CHR defines both simplification of and propagation over user-defined constraints. Simplification replaces constraints by simpler constraints while preserving logical equivalence. Propagation adds new constraints, which are logically redundant but may cause further simplifications. Consider the constraint min, where min(X, Y, Z) means that Z is the minimum of X and Y . Then typical CHR rules for this constraint are: method of propagation rules into simplification rules. For clarity reasons, we will use an abstract representation for the generated rules. In Section 5, we present how these rules can be encoded in CHR. We discuss related work in Section 6, and finally we conclude with a summary and possibilities of further improvements. In this paper, we have presented three algorithms that can be integrated to build an environment to help solver developers when writing CHR programs.

O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O