Joint segmentation of multivariate time series with hidden process regression for human activity recognition The problem of human activity recognition is central for understanding and predicting the human behavior, in particular in a prospective of assistive services to humans, such as health monitoring, well being, security, etc. There is therefore a growing need to build accurate models which can take into account the variability of the human activities over time (dynamic models) rather than static ones which can have some limitations in such a dynamic context. In this paper, the problem of activity recognition is analyzed through the segmentation of the multidimensional time series of the acceleration data measured in the 3-d space using body-worn accelerometers. The proposed model for automatic temporal segmentation is a specific statistical latent process model which assumes that the observed acceleration sequence is governed by sequence of hidden (unobserved) activities. More specifically, the proposed approach is based on a specific multiple regression model incorporating a hidden discrete logistic process which governs the switching from one activity to another over time. in an unsupervised context by maximizing the observed-data log-likelihood via a dedicated expectation-maximization (EM) algorithm. We applied it on a real-world automatic human activity recognition problem and its performance was assessed by performing comparisons with alternative approaches, including well-known supervised static classifiers and the standard hidden Markov model (HMM). The obtained results are very encouraging and show that the proposed approach is quite competitive even it works in an entirely unsupervised way and does not requires a feature extraction preprocessing step. The problem of human activity recognition is central for understanding and predicting the human behavior, in particular for a prospective of assistive services to elderly people. In fact, assistive services related to the aging population has gained an increasing attention in the last decades due the fact that this population is increasing and having more socio-economic impact. The aim is therefore to facilitate the daily lives of elderly or dependent people at home, increase their autonomy and improve their safety. The emergence of novel adapted technologies such as wearable and ubiquitous technologies is becoming a privileged solution to provide assistive services to humans, such as health monitoring, well being, security, etc. For example, the recognition of the activity from data measured by sensors can play important role in minimizing the risk of human fall (Hirata et al., 2008; Kangas et al., 2008; Noury et al., 2009; Lindemann et al., 2005) . In addition, remote monitoring based systems can reduce considerably the amount of admission to hospitals by early detection of gradual deterioration in elderly health status (Scanaill et al., 2006) .. In the context of activity recognition from measurements, the main measurement techniques used to quantify human activities are based on the use of inertial sensors (Altun et al., 2010; Trabelsi et al., 2011; Preece et al., 2009; Kavanagh and Menz, 2008; Parkka et al., 2006) . Other sensors are also used to recognize human activities such as video-based systems (Cappozzo et al., 1996 (Cappozzo et al., , 2005 Aminian et al., 1999) , goniometers (Kostov et al., 1995) , elec-tromyography (EMG) (Hussein and Granat, 2002) , etc. However, the videobased approach is less adapted regarding particularly the personal privacy aspects. In addition, technological advances and miniaturization of wearable inertial sensors made easier the collection of data for a wide range of human activities. As a consequence, the technique based on wearable-sensors has gained more attention for activity recognition as well as in many application domains including medical applications such as rehabilitation program and medical diagnosis (Jovanov et al., 2005) . In the context of werable-sensors based activity recognition, the accelerometers are the most commonly used inertial sensors due to the advances in micro-electromechanical systems technology which have greatly promoted the use of accelerometers thanks to the considerable reduction in size (miniaturazation), in cost and in energy consumption. These sensors have shown satisfactory results to measure the human activities in both laboratory, clinical and free-living environment settings (Mathie et al., 2004) . More specifically, the tri-axial accelerometers are more privileged (Yang and Hsu, 2010) with respect to uniaxial accelerometers.. The studied activities can be either static ones (postures) such as standing, sitting, lying or dynamic ones (movements) such as standing up, sitting down, walking, running, climbing stairs, etc. In general, the activity recognition from acceleration data is preceded by a preprocessing step of feature extraction. For example features, such as the mean, the standard deviation, the skewness, the kurtosis, etc. can be extracted from original data and used afterwards as classifier inputs (Altun et al., 2010; Ravi et al., 2005; Yang and Hsu, 2010) . However, these methods are static ones as the models do not exploit the temporal dependence of the data. An alternative approach may use features such as zero-velocity crossings (ZVC) (Fod et al., 2002) . A method for dynamic signal segmentation for activity recognition has been proposed in (Kozina et al., 2011) ; However, it has lower accuracy with transition instances in learning and testing set. Additional details on classification approaches for human activity recognition can be found in the recent reviews (Yang and Hsu, 2010; Altun et al., 2010; Preece et al., 2009; Kavanagh and Menz, 2008) . Among the techniques used in the literature for the human activity classification, one can distinguish those using supervised machine learning-based approaches. These techniques provide a statistical association of a given activity feature to a possible class. For example, one can cite K-nearest neighbor (K-NN) classification algorithm (Foerster, 1999) , the naive Bayes classifier (Long et al., 2009 ) and the support vector machines (SVM) (Lau et al., 2009) . For the unsupervised context, one can cite the approach based on Gaussian mixture models (GMM) (Allen et al., 2006) and the one based on hidden Markov model (HMM) or HMM with GMM emission probabilities (Mannini and Sabatini, 2010) .. In this study, the human activities are detected over time through the segmentation of the accelerations time series. The data are measured over time during the activity of a given person, and at each time step, the three acceleration components, which we denote by (y 1 , y 2 , y 3 ), are recorded. These data consist therefore in multidimensional time series with several regime changes over time, each regime is associated with an activity (e.g., see Figure 1 ). The problem of activity recognition can therefore be reformulated as the one of a joint segmentation of multidimensional time series, each segment is associated with an activity. The proposed statistical approach is dedicated to temporal segmentation by including a hidden process where the process probabilities change over time according to the most likely activity. The approach performs in an unsupervised context from raw acceleration data. More specifically, the proposed model consists in a multiple regression model governed by a discrete hidden process. The configuration of the hidden process, at each time step, corresponds to an activity described by a regression model. The hidden process configuration depends on time and the regression model parameters are time-varying according to the most likely posture. Furthermore, although only the acceleration measurements are available, the classes of activities being unknown, the unknown class labels are stated in the model as latent variables. In this way, we formulate an efficient and computationally tractable statistical latent data model. The resulting model is therefore a kind of latent data model which is particularly well adapted for performing unsupervised activity recognition. Let us recall that, from a statistical prospective, latent data models (Spearman, 1904) aim at representing the distribution p(y) of the observed data in terms of a number of latent variables z. In this context of activity recognition, the observed data are the acceleration data and the latent data represent the activities (the class labels). Mixture models McLachlan and Peel. (2000) and hidden Markov models (Rabiner, 1989) are two well-known widely used examples of such models. The unsupervised learning task for the proposed approach is achieved by maximizing the observed-data log-likelihood via a dedicated iterative algorithm known as the expectation-maximization (EM) algorithm. In this paper, the problem of temporal activity recognition from acceleration data is reformulated as the one of unsupervised learning of a specific statistical latent process model for the joint segmentation of multivariate time series. The main advantages of this statistical approach is that it directly uses the raw acceleration data and performs in an unsupervised context which can be beneficial in practice. For example, this may be helpful for avoiding the investments in labelling flows of acceleration data or in finding adapted preprocessing feature extraction approaches. Moreover, the model formulation explicits the switching from one activity to another during time through a flexible logistic process which is also particularly well adapted for abrupt or smooth transitions. Furthermore, the expectation-maximization algorithm offers a stable efficient optimization tool to learn the model. The proposed MRHLP approach is applied on a real-world activity recognition problem based on multidimensional acceleration time series measured using body-worn accelerometers. The approach has shown very encouraging results compared to alternative models for activity recognition. In its current formulation, the proposed algorithm runs in a batch-mode and requires the entire data sequence to be presented. A perspective of this work is to train the proposed model with an online Expectation-Maximization (EM) algorithm (as in Cappé and Moulines (2009) ) for a real-time use perspective. Future work will also concern the use of other non-linear models to describe each activity signal rather than polynomial bases. This may improve in particular the representation of each activity. Then, another extension may consist int integrating the model into a Bayesian non-parametric model which will be useful for any kind of complex activities and in which the number of activities will not have to be fixed. The sensors used for data acquisition consisted of three MTx 3-DOF inertial trackers developed by Xsens Technologies (Enschede, 2009) . Each MTx unit includes a tri-axial accelerometer measuring the acceleration in the 3-d space (with a dynamic range of ±5g where g represents the gravitational constant). The sensor's placements is chosen to represent the human body motion while guaranteeing less constraint and better comfort for the wearer as well as its security. The sensors were placed at the chest, the right thigh and the left ankle respectively as shown in Figure 2 . As shown in Bouten et al. (1997) , points near the hip and torso exhibit a 6g range in acceleration. Our experiences show also that the measured ankle-sensor accelerations during the different activities do not excceed the limit of ± 5g . The sampling frequency is set to 25 Hz, which is sufficient and larger than 20 Hz the required frequency to assess daily physical activity (Bouten et al., 1997) . The sensors were fixed on the subjects with the help of an assistant before the begining of the measurement operation. Sensors placement is chosen to represent predominantly upper-body activities such as standing up, sitting down, etc. and predominantly lower body activities such as walking, stair ascent, stair descent, etc. To secure each MTx unit in place, specific straps are used. This combination allows for efficient inter-subject transfer. The MTx units are connected to a central unit called Xbus Master which is attached to the subject's belt. Raw acceleration data are collected over time when performing the activities and the data transmission between units and the receiver is carried out through a Bluetooth wireless link. The experiments were conducted at the LISSI Lab/University of Paris-Est Créteil (UPEC) by six different healthy subjects of different ages (who are not the researchers) in the office environment. In order to gather representative dataset, the recruited volunteers subjects have been chosen in a given marge of age (25-30) and weight (55-70)kg. Activity labels were estimated by an independent operator. Data are stored on a file and acceleration signals are analyzed using MATLAB software. Twelve activities and transitions were studied and are shown in Table 1 and some of these activities are illustrated on Figure 3 . The activities were chosen to have an appropriate representation of everyday activities involving different parts of the body. The recognized activities and transition differ in duration and intensity level. The subjects were asked to perform the activities in their own style and were not restricted on how the activities should be performed but only with the sequential activities order. Note that the activities A 3 , A 5 , A 7 , A 9 and A 11 represent dynamic transitions between static activities.. For the three sensor units, each unit being a tri-axial accelerometer, a 9-dimensional acceleration time series are recorded overtime for each activity. The time series present regime changes over time, in which each regime is associated to an activity. Figure 1 illustrates an example of three acceleration data measured on the chest inertial sensor for the three activities' scenario: standing -transition (standing to sitting) -sitting -(transition) sitting to standing -standing.

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


A comprehensive method for comparing mental models of dynamic systems Mental models are the basis on which managers make decisions even though external decision support systems may provide help. Research has demonstrated that more comprehensive and dynamic mental models seem to be at the foundation for improved policies and decisions. Eliciting and comparing such models can systematically explicate key variables and their main underlying structures. In addition, superior dynamic mental models can be identified. This paper reviews existing studies which measure and compare mental models. It shows that the methods used to compare such models lack to account for relevant aspects of dynamic systems, such as, time delays in causal links, feedback structures, and the polarities of feedback loops. Mental models without those properties are mostly static models. To overcome these limitations of the methods to compare mental models, we enhance the widely used distance ratio approach (Markóczy and Goldberg, 1995) so as to comprehend these dynamic characteristics and detect differences among mental models at three levels: the level of elements, the level of individual feedback loops, and the level of the complete model. Our contribution lies in a new method to compare explicated mental models, not to elicit such models. An application of the method shows that this previously non-existent information is essential for understanding differences between managers' mental models of dynamic systems. Thereby, a further path is created to critically analyze and elaborate the models managers use in real world decision making. We discuss the benefits and limitations of our approach for research about mental models and decision making and conclude by identifying directions for further research for operational researchers. This paper provides means for comparing mental models of dynamic systems. Generally speaking, a mental model is an abstract representation of a situation or a system in the mind of an individual (Forrester, 1961 (Forrester, , 1992 . ''Mental models reflect the beliefs, values, and assumptions that we personally hold, and they underlie our reasons for doing things the way we do" (Maani and Cavana, 2007: 15) . They are used for inductive and deductive reasoning (Johnson-Laird, 1999 , 2001 ). Ford (1998, 1999) have defined a mental model of a dynamic system (MMDS) as ''a relatively enduring and accessible, but limited, internal conceptual representation of an external system (historical, existing, or projected) whose structure is analogous to the perceived structure of that system" (Doyle and Ford, 1999: 141) . 1 Mental model research is relevant in operational research (Eden, 1988; Howick et al., 2008) , management (Lim and Klein, 2006; Markóczy and Goldberg, 1995; Tyler and Gnyawali, 2009) , and organizational research (Calori et al., 1994; Fokkinga et al., 2009; Rouwette et al., 2002; Smith-Jentsch et al., 2001) . This is especially the case where enhancing the accuracy of decision makers' mental models of either a situation or a system is one of the goals of modelling. There is evidence that the accuracy of mental models indeed moderates performance when acting in such systems (Capelo and Dias, 2009; Gary and Wood, forthcoming; Jonson and O'Connor, 2008) . However, when feedback-driven dynamic systems come into play, research lacks a comprehensive method to compare mental models which include the essential conceptual elements of such systems. Conceptual elements are categorical building blocks used to formalise the content of a mental model.. Up to now, comparative mental model research has used several approaches to account for the models' conceptual structure: the distance ratio approach (Markóczy and Goldberg, 1995) , the closeness ratio approach (Schvaneveldt, 1990) , or related approaches (Doyle et al., Research about mental models of dynamic systems has gained attention in the operational research community. In particular, insights into the conceptual elements of mental models are important for understanding human decision making in dynamic environments. Extensive research has demonstrated that although humans are most often not capable of forming adequate mental models of dynamic systems, none the less the capability of dynamic thinking can be enhanced (Sterman, 2010) .. Until now, the exploration of the content and structure of mental models has used a diversity of representational and comparison approaches, mainly either the distance ratio (Markóczy and Goldberg, 1995) or the closeness ratio (Schvaneveldt, 1990) . As a consequence, the results from these different studies are difficult to compare, and both the accumulation of knowledge and the subsequent progress of research are limited. Furthermore, the existing approaches neglect relevant conceptual elements and levels of description of dynamic systems. They therefore oversimplify the complexities of such dynamic systems and lead to insufficient representations of them. To overcome these shortfalls, we enhance the distance ratio approach to account for relevant characteristics of dynamic systems. By considering delays in causal links, feedback loops, and the polarities of feedback loops, we make it possible to analyze and compare mental models more comprehensively, enabling the detection of differences between mental models at three levels: the element level (element distance ratio, EDR), the level of the individual feedback loop (loop distance ratio, LDR), and the level of the complete model (model distance ratio, MDR). An application of the method shows that this previously non-existent information concerning the feedback loops is essential for understanding differences between mental models of dynamic systems.. The comprehensive method proposed here can be used to compare several versions of mental models both within and between subjects. In the former case, the effects of exposing subjects to simulators, interactive learning environments, and other educational devices-but also modelling interventions-on MMDS can now be studied in a way that allows cross-study comparison and accumulation. Also, systems thinking repertory (Sweeney and Sterman, 2007) and other studies belonging to that group can generate more comparable results. In other words, we believe this method can help most operational researchers interested in mental models of dynamic systems as a means for shaping decisions and decision policies. Future research will allow one to incorporate the distinction between different types of variables into the comparison; also, behavioural inferences deduced from the causal structure may become accessible to elicitation and thus comparable. In this section we discuss the contribution of the comparison method, reflect on the methodological characteristics and the method's relation to the issue of elicitation and measurement of mental models. As a final point, we elaborate on the method's limitations.

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


MethylPCA: a toolkit to control for confounders in methylome-wide association studies Background: In methylome-wide association studies (MWAS) there are many possible differences between cases and controls (e.g. related to life style, diet, and medication use) that may affect the methylome and produce false positive findings. An effective approach to control for these confounders is to first capture the major sources of variation in the methylation data and then regress out these components in the association analyses. This approach is, however, computationally very challenging due to the extremely large number of methylation sites in the human genome. Result: We introduce MethylPCA that is specifically designed to control for potential confounders in studies where the number of methylation sites is extremely large. MethylPCA offers a complete and flexible data analysis including 1) an adaptive method that performs data reduction prior to PCA by empirically combining methylation data of neighboring sites, 2) an efficient algorithm that performs a principal component analysis (PCA) on the ultra highdimensional data matrix, and 3) association tests. To accomplish this MethylPCA allows for parallel execution of tasks, uses C++ for CPU and I/O intensive calculations, and stores intermediate results to avoid computing the same statistics multiple times or keeping results in memory. Through simulations and an analysis of a real whole methylome MBD-seq study of 1,500 subjects we show that MethylPCA effectively controls for potential confounders. Conclusions: MethylPCA provides users a convenient tool to perform MWAS. The software effectively handles the challenge in memory and speed to perform tasks that would be impossible to accomplish using existing software when millions of sites are interrogated with the sample sizes required for MWAS. Controlling for confounders in MWAS presents a major computational challenge because of the very large number of possible methylation sites. In this article we introduced MethylPCA that is specifically designed to handle this problem. We tested and demonstrated MethylPCA using simulations and empirical MWAS data from 1,500 subjects. Results showed that MethylPCA effectively controlled for possible confounders. A wide variety of other existing methods can in principle be used to analyze MWAS data. For example, surrogate variable analysis (SVR) developed in the context of microarray experiments [33] can be used to identify and remove unknown latent noise, such as batch effects. However, direct application of these packages [33] , may not be practical because of the ultra high dimension of methylation data. Instead, efficient analysis of MWAS data is likely to require tailored computational tools that employs parallel computing, uses a low level programming language for CPU intensive calculations, stores intermediate results to avoid computing the same statistics multiple times or storing results in memory, and uses algorithms specifically designed for high dimensional data.. Our empirical data showed that the risk of false positives in MWAS is very high, likely because of the many differences between cases and controls (e.g. life style, diet, medication use) that affect the methylome. This stressed the need of controlling confounders for which the package MethylPCA was designed. It seems reasonable to assume that if confounders have such pervasive effects on the methylome, the pathogenic processes that cause the disease may also involve many methylation sites. A careful inspection of the PCs (e.g. using the loadings generated by MethylPCA) is important to prevent that disease processes are being regressed out in the MWAS.. As the input methylation data are quantitative values for a set of genomic locations, MethylPCA can be applied to methylation data generated by any assay. Furthermore, because the PCA components can be run independently, in principle it can also be applied to other ultra high dimensional data, such as genome-wide sequence data as long as the specific input format is followed. Methylation studies are a promising complement to genetic studies of DNA sequence variation. First, as methylation is typically associated with transcriptional repression [1, 2] , it may account for additional variation in disease susceptibility. Second, methylation studies can shed a unique light on clinical phenomena [3] such as sex differences [4, 5] , genotype environment interactions [6] , and disease course over time [7] . Finally, methylation sites are potential new drug targets [8] and have good properties from a translational perspective such as being stable and enabling cost-effective assays in biosamples that are relatively easy to collect [9] .. Because detailed prior biological knowledge is lacking, it will be critical to perform methylome-wide association studies (MWAS) to detect disease relevant sites [10, 11] . The most comprehensive approach uses next-generation sequencing (NGS) to interrogate DNA methylation on a genome-wide basis after bisulfite conversion of unmethylated cytosines. The single base resolution afforded by bisulfite sequencing is attractive but currently this approach is not economically feasible for the large sample sizes required for MWAS [12] . In a cost-effective alternative the genome is fragmented and the methylated fragments are bound to antibodies [13] (e.g. MeDIP) or other proteins [14] (e.g. MBD-seq) with high affinity for methylated DNA. The unmethylated genomic fraction is washed away, and then only the methylation-enriched portion is sequenced. A final option involves arrays. Examples are the commercially available Infinium system from Illumina [15] that interrogates >450,000 loci or genomewide tiling arrays and the 45 million probe array set from Affymetrix [16] that offers more comprehensive coverage of the methylome.. In addition to technical factors associated with processing samples, in MWAS there are many possible differences between cases and controls that may affect the methylome. Examples include differences in life style, diet, and medication use. As these confounding variables correlate with both the dependent (case-control status) and independent variable (methylation status) they will cause spurious associations that are not of direct substantive interest because they are unrelated to disease processes. Controlling for confounders in MWAS is critical to avoid a flood of false positive findings. If measured, such variables can be regressed out. However, the list of potential confounders is long, only a subset of these variables will have been measured, and many confounders may simply be unknown. Statistical methods that first capture the major sources of variation in the methylation data, and then regress out these components when performing the association analyses may provide an effective solution. However, because of the ultra high dimension of methylation data (e.g. the methylation of DNA cytosine residues at the carbon 5 position (5 me C) occurs in the vast majority of cases at CpG sites of which already 27 million exist in the human reference genome), standard statistical packages or existing software for the analysis of large scale methylation data cannot be used [17] [18] [19] [20] . To address the computational challenges we developed a toolkit called MethylPCA that is specifically designed to control for confounders in MWAS.. MethylPCA uses principal component analysis (PCA) to capture the major sources of variation in the methylation data. Although other options exist, PCA has the advantage of being well developed (e.g. algorithms exist that enable PCA on ultra-high dimensional data), is computationally efficient, and has already been successfully applied to high-dimensional biological data [21] . EIGENSOFT [21, 22] also performs PCA. However, 1) MethylPCA provides an adaptive procedure designed to combine methylation data of neighboring sites into larger blocks prior to PCA; 2) Even after this data reduction step, calculation of the input matrix for the PCA would be prohibitive in terms of memory and CPU time for large sample sizes. MethylPCA allows partitioning the data into a userspecified number of sets to compute sub-matrices in parallel on a cluster and then assemble those to obtain the complete input matrix; 3) To enable a complete and flexible data analysis pipeline, MethylPCA provides options to perform PCA based on the covariance matrix and/or correlation matrix and includes an association testing procedure where covariates such as the calculated principal component scores (PCs) can be regressed out; 4) EIGENSOFT is designed to process categorical SNP data while our software can work on the quantitative methylation data. The design philosophy of MethylPCA is to build small independent executable components first and then combine them to perform complex tasks. A user-friendly interface is provided in the form of a parameter file that controls which and how procedures are performed (see Additional file 1 for detailed description of software). For example, the above three procedures can be performed sequentially or individually by putting the parameters corresponding to the procedures in the parameter file. Each procedure has multiple parameters to be set in the parameter file in order to run it properly. The computational and I/O intensive parts of MethylPCA are implemented in C++ and the remainder in the R language.

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


An open-source compiler and PCB synthesis tool for digital microfluidic biochips This paper describes a publicly available, open source software framework designed to support research efforts on algorithms and control for digital microfluidic biochips (DMFBs), an emerging laboratory-ona-chip (LoC) technology. The framework consists of two parts: a compiler, which converts an assay, specified using the BioCoder language, into a sequence of electrode activations that execute out the assay on the DMFB; and a printed circuit board (PCB) layout tool, which includes algorithms to reduce the number of control pins and PCB layers required to drive the chip from an external source. The framework also includes a suite of visualization tools for debugging, and a collection of front-end algorithms that generate mixing/dilution trees for sample preparation. A digital microfluidic biochip (DMFB) is an emerging microfluidic technology that manipulates discrete droplets of liquid on a 2-dimensional electrode grid [62] . DMFBs are poised to enable fully integrated laboratories-on-a-chip (LoCs), which have the potential to miniaturize and automate many chemical and biochemical reactions, with applications to fields such as drug discovery, heathcare and public health, environmental monitoring, and many others. Over the past decade, there has been a significant effort to develop DMFB technology and fabrication processes [14, 27, 38, 55, 58] ; meanwhile, a small cadre of computer scientists and engineers have worked to develop techniques to program, control, and automatically optimize DMFB architectures.. Despite these fundamental research efforts, very little software has been publicly released. Researchers who work on DMFB compilation introduce new algorithms every year, but these algorithms are developed in isolation, and there appears to be no interoperability between the implementations. Ideally, the algorithms would be compatible with one another and widely disseminated, which would eliminate the need for research groups to implement each other's algorithms to facilitate experimental comparisons. Moreover, it is difficult to identify synergies between algorithms published by different research groups that have not been tested together. Further, both paper writing and software development is prone to human error; and pseudocode in one paper may not precisely match the implementation, or may omit key details. Lastly, researchers who implement algorithms based on pseudocode written by others may inadvertently implement certain steps incorrectly, potentially skewing their experimental results.. To address these concerns, this paper describes in detail an open source DMFB compiler and printed circuit board (PCB) synthesis tool suite developed at UC Riverside. The framework employs well-defined internal data structures and interfaces between each step of the compilation and synthesis process. Several algorithms have been implemented and tested for each stage. The software described in this paper has been released publicly and is available for non-commercial use at [26, 73] .. The compiler converts biochemical reactions specified using a domain-specific programming language into an executable format appropriate for DMFBs, while the PCB synthesis tool optimizes the control interface and PCB layout. In addition to the core algorithmic features listed above, the framework also includes:. A software tool that generates mixing and dilution trees for sample preparation.. Extensive visualization tools that create high-quality graphical output after each step; in our experience, these tools have Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/vlsi proven invaluable for debugging and comparison, and we believe that they will provide similar value to other researchers as well.. An execution interface to control a direct addressing [62] or active matrix [27, 58] DMFB through a microcontroller that communicates with a host PC via USB. This enables direct execution of biochemical reactions on the chosen target device.. We envision three classes of users for the proposed framework: (1) DMFB designers will leverage the back-end synthesis tools to produce optimized PCB layouts, thereby reducing the design, fabrication, and testing costs for their devices; (2) computer scientists and engineers will disseminate and compare optimization algorithms; and (3) biochemists and bioengineers will compile and execute biochemical reactions in their laboratories, thereby increasing scientific productivity through automation. We expect these contributions to be invaluable as DMFB technology evolves over the next decade. Fig. 1 illustrates DMFB technology and the process of droplet transport via electrode actuation. The underlying micromechanical phenomenon that enables droplet transport is called elecrowetting-on-dielectric (EWoD), in which a hydrophobic dielectric layer insulates the liquid droplet from the electrodes. Fig. 2 shows the basic instruction set of a DMFB, which consists of five operations: droplet transport, splitting, merging, mixing, and storage. Additional operations can be realized by adding external devices to the device such as heaters [45] , optical detectors [47, 87] , integrated sensors [13, 57, 68] , etc. Fig. 3 illustrates the algorithmic stages of the DMFB compiler and PCB synthesis toolflow. The input to the framework is a biochemical reaction to perform, which is specified as a directed acyclic graph (DAG). One fundamental limitation of this input, as well as the framework in its current form, is that control flow operations are not supported. Future work will integrate support for real-time decision-making based on sensory feedback, fault tolerance and error recovery, etc. We encourage researchers who want to study or otherwise use DMFB compilation and PCB synthesis to download and use our framework. We hope that researchers with a background in computer science and engineering will develop and contribute new algorithms and features to the framework, as it provides a common, standardized platform for dissemination and comparison. We also hope that practitioners who use DMFBs in their laboratories will adopt the framework, eventually switching to BioCoder as a specification language. In the long term, we intend to leverage the framework at UC Riverside to create undergraduate and graduate courses on programmable microfluidics (focusing on DMFB technology specifically) and to support undergraduate senior design projects and graduate-level projects and theses. Absent pin sharing, the operations most likely to necessitate the insertion of GVs are those that activate an electrode for many consecutive time-steps, i.e., storage and any operation that activates an external device for an extended period of time. Without loss of generality, electrodes involved in mixing operations cannot share the same pin as electrodes involved in storage operations that are scheduled at the same time. The electrodes that perform mixing repeatedly switch on and off, while the electrodes that perform storage remain activated (before GV insertion): a pair of electrodes that require simultaneous activation and deactivation cannot share the same pin.. KAMER and VT minimally consider the operations that they place and neither tries to optimize for pin sharing or power/ reliability when making decisions. KAMER places operations that use external devices on regions of the chip that are accessible to those devices; beyond that, its objective is simply to obtain a legal placement at each time-step. VT also accounts for external devices and considers whether each work module is performing mixing or storage at a given time-step. VT may transport a droplet from one module to another during storage to free up the former module for another operation. VT makes these decisions this without considering the implications for pin sharing and power/reliability insertion. Thus, it is difficult to ascertain whether the differences between VT and KAMER reported in Figs. 24-26 are inherent to the placement algorithms, or essentially just random effects. To better answer this question, future work should focus on synergistically optimizing scheduling and placement with pin sharing while considering power reduction and/or reliability. Fig. 27 depicts the device interface and control software. An application written in Java runs on a host PC; it communicates Fig. 21 . Runtimes of the Maze-Greedy [64] , Maze-DP [32, 64] , HP-Greedy [12, 64] , and HP-HP [12] routing algorithms across the 10 benchmarks from Table 3 using the KAMER and Virtual Topology (VT) placement heuristics. To the best of our knowledge, no comparable software platform for DMFB control has been released to the wider research community. The closest related project is an open source hardware/ software system developed at the University of Toronto called DropBot [17] . DropBot provides real-time monitoring of droplet position and velocity and application of constant droplet driving forces in the presence of variations in amplifier load and device capacitance due to physical variations in the insulator. DropBot does not provide automatic compilation. The user must manually select electrodes to activate and deactivate over time; rather than clicking on an image of the chip, as in our system, the user is presented with a webcam video overlay of the chip.. Bhattacharjee et al. [5] described a formal verification checking system for DMFBs, which share some principle similarities with the verification steps in our system, as described in Section 4.4; they do not provide verification rules for pin mapping and PCB escape routing. The paper mentions a DMFB simulator called SimBioSys, and provides a screenshot; however, no such software could be located online. We considered 10 assays commonly used in peer-reviewed publications on programmable microfluidics: one PCR mixing tree, five multiplexed in vitro diagnostics assays with a varying number of samples and reagents ("in Vitro xs_yr" means x samples and y reagents), and four exponential protein dilution assays with a varying number of splits. We compiled the assays using two synthesis flows with two different placers: KAMER (Fig. 11(a) ) [2, 44] , and a virtual topology (VT) (Fig. 11(b) ) [21, 22] ; we used the same scheduling and routing algorithms in both experiments. We expected that the VT placer would yield smaller state machines, because all mixing operations would have identical geometries and occur in the exact same set of restricted locations on the chip, while KAMER can place any operation at any location.. First, we compiled each assay into a linear state machine using both synthesis flows, similar in principle to Fig. 4 ; the memory requirement of every single assay exceeded the capacity of the ATmega2560. Next, we compressed the state machines using dictionary compression only (D) and dictionary compression in conjunction with state machine optimization (DþSM). Fig. 30(a) and (b) reports the program and data sizes for the two respective synthesis flows. The C programs generated by our synthesis flow are converted to .elf files, and the results shown in Fig. 30 report the.elf file size in KB. Fig. 30 shows that compression fails for two benchmarks (Protein and Protein Split 3) with KAMER, but succeeds for all benchmarks for VT. The general trend is that program and data segment sizes are smaller for VT than for KAMER.. Compression using the dictionary and state machine optimization (D þSM) yielded lower overall memory requirements than dictionary compression alone (D). Luo et al. [48] , it should be noted, achieved even greater reductions in dictionary size using run length encoding; however, the decoding process is complex, 00 01 10 11 00 01. Dictionary 00 0000010000000000 01 0000000001000000 10 0000000000100000 11 0000001000000000 Fig. 29 . Illustration of dictionary compression: redundant bit vectors are identified and put into a dictionary. Each state's output is now an index into the dictionary. The original Moore Machine had 6 Â 16 ¼ 98 output bits; the compressed Moore Machine has a dictionary consisting of 4 Â 16 ¼ 64 bits, while the state machine requires 6 Â 2 ¼12 output bits, for a total of 76 bits. Fig. 30 . Effectiveness of compression algorithms on program/data sizes using the (a) KAMER [2, 44] and (b) virtual topology (VT) [21, 22] placers.. and Luo et al. offloaded the task onto a small FPGA; to minimize the cost and complexity of our microcontroller interface, we avoid runlength encoding. It remains possible to specify assays whose state machine implementations are too large to fit into microcontroller memory, even with compression. In this case, there is no tangible benefit to compression, as the PC is still required to run the system. In principle, a PC could store the state machine and dictionary as data and decompose them into chunks that can fit into the microcontroller's memory; when the state machine executing on the microcontroller enters a state or accesses a dictionary entry that is not in the microcontroller's memory, the access could be forwarded back to the PC, which then delivers a new chunk of code and data. For large chunks, the transmission latency could be significant, potentially causing the assay to pause. Rather than trying to mitigate this overhead, it is easier to execute the assay in an uncompressed form with predictable communication, as described in Section 6.2.

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


Analytical spherical-mode-based compensation of mutual coupling in uniform circular arrays for direction-of-arrival estimation An analytical circuit model with a limited number of parameters is presented to describe mutual coupling in uniform circular arrays. The model, which is based on a spherical-mode expansion, provides physical insight into the frequency dependence and the dependence on azimuth and elevation angle of the coupling between antenna elements. It is shown that the number of circuit elements, required to describe the open-circuit voltages and the mutual impedances at the different antenna ports, depends on the overall size of the array and not on the spacing between the antenna elements. Based on this observation, an analytical technique is described to derive a coupling matrix representing the mutual coupling effects. Relying on the phase-mode-based circuit elements, dedicated eigenstructure techniques are developed for direction-of-arrival (DOA) estimation with uniform circular arrays. By considering several synthetic reference scenarios, it is shown that even in the presence of severe mutual coupling, root-MUSIC combined with a limited number of phase-mode components gives very robust DOA estimations for the azimuth angle, when all signals are incident on the array from a fixed elevation angle. Antenna arrays play a key role in the development of highperformance mobile communications systems. Although a lot of theoretical work has been done on how the use of antenna arrays improves the system performance, relatively few contributions take into account the actual electromagnetic (EM) characteristics of the antenna system. Several authors, however, have shown that mutual coupling between antenna elements can drastically change the system behavior and its communication characteristics. This is due to a different EM behavior of the antenna elements in an array configuration, compared to their stand-alone characteristics, because of two important effects. First, terminal currents induced in the loads of neighboring elements introduce an extra voltage contribution in the antenna element under consideration. This effect is described by the impedance matrix Z. In [1] , this impedance matrix is used to study the effect of mutual coupling on the performance of an adaptive linear array. A second important effect is the deformation of the radiation pattern of the stand-alone antenna elements due the detailed current distributions induced in the opencircuited neighboring antenna elements (shadowing effects) or neighboring scatterers (platform effects). As this effect occurs for a zero terminal current in the neighboring antenna elements, it only influences the diagonal elements of the impedance matrix Z, but not the off-diagonal elements. Instead, for a receiving antenna array, the open-circuit voltage at a particular terminal, which results not only from the current distributions induced in the antenna element itself, but also from the induced current distributions of the open-circuited neighboring antenna elements and neighboring scatterers, then depends on the direction of the incoming signal, even if the array consists of omnidirectional standalone antenna elements. To accommodate for this second phenomenon as well, in [2] the concept of impedance matrix Z is generalized to a coupling matrix C to account for mutual coupling. Based on this approach, the multiple signal classification (MUSIC) algorithm is modified in [3] to take into account mutual coupling. As described in [4, 5] , in many cases the coupling matrix is able to compensate for mutual coupling. It is also demonstrated, however, that in some cases mutual coupling cannot be accounted for by means of a coupling matrix. This is especially so when platform effects play an important role. In [6] [7] [8] , compensation of the mutual coupling effects in wire antenna arrays is performed by means of simulation data obtained by the Method-ofMoments (MoM), and in [9, 10] numerical simulation data from full-wave [EM] solvers is applied to eliminate mutual coupling in planar and conformal arrays. In [11] , an estimated current distribution is used to compensate for mutual coupling in arrays consisting of dipole elements and in [12] , the mutual coupling is estimated together with the directions of arrival. The effect of mutual coupling on capacity of multi-element antenna systems is studied in [13] [14] [15] [16] .. In this paper, we construct an analytical circuit model describing mutual coupling effects in a uniform circular array (UCA). The classical circuit models for antenna arrays in transmit and receive mode, as reviewed in Section 2, do not allow to fully exploit the symmetries present in an UCA. By expanding the open-circuit voltages and the impedance matrix of the UCA into phase modes, introduced in [17] , and spherical modes, we reduce the number of circuit elements in the model without reducing its accuracy, as shown in Section 2. The use of phase-modes allows to fully exploit the rotational symmetry in the UCA, both for the open-circuit voltage and the array impedance matrix contributions. It is shown that the number of circuit elements, required to describe the open-circuit voltages and the mutual impedances at the different antenna ports, depends on the overall size of the array but neither on the element spacing nor on the degree of mutual coupling between the antenna elements. In [18] , dedicated eigenstructure techniques for direction-ofarrival (DOA) estimation with uniform circular arrays are considered, without taking into account mutual coupling effects. In Sections 3 and 4, these techniques are extended to include both mutual coupling phenomena described in Section 1. Existing techniques that compensate for mutual coupling using the impedance matrix Z, as in [1] , or using the coupling matrix C, as in [2, 3] , have been proven to be inaccurate in certain cases. In [4, 5] , this problem is identified without further investigating the physical reasons. In this paper, however, it is shown that the problem is due to the second phenomenon described in Section 1: the deformation of the radiation pattern. Expanding the open-circuit voltage of the receiving antenna elements into spherical modes provides physical insight into this problem and allows to distinguish between cases for which compensation guarantees accurate results and the cases where radiation pattern deformation cannot be compensated. Therefore, in Section 5 we show how to construct a coupling matrix based on phase modes and we derive a criterion that shows that an accurate description is possible as long as the number of elements in the UCA is large compared to the largest electrical dimension of the array. The only assumption about the configuration is that the mutual coupling and the environment factors are rotationally invariant. In Section 6, the dedicated MUSIC algorithms and the use of a coupling matrix are applied for UCAs composed of dipole and dual-band dipole antenna elements. For the UCAs composed of dipole elements, we introduce a simple platform effect by placing a short-circuited dipole element in the center of the array. The effect of the electrical size of the array, the number of antenna elements, the impedance mismatch, and the frequency on DOA estimation techniques are investigated. An expansion of the open-circuit voltages and the mutual impedances into phase modes and spherical modes was used to derive a rigorous circuit model with a limited number of parameters that describes mutual coupling in uniform circular arrays. The model provides physical insight on how mutual coupling between antenna elements depends on frequency, azimuth angle, and on the overall size of the array. It was shown that the number of circuit elements, required to describe the open-circuit voltages and the mutual impedances at the different antenna ports, depends on the overall size of the array. For a fixed overall size of the array, the number of circuit elements did not depend on the element spacing nor on the degree of mutual coupling between the antenna elements. Based on this observation, an analytical technique was described to derive a coupling matrix representing the mutual coupling effects. This technique can compensate for all mutual coupling and environment effects, provided they are rotationally invariant. Relying on the phase-mode-based circuit elements, dedicated eigenstructure techniques are developed for DOA estimation in such arrays. In the presence of antenna mismatch and of errors in modelling the mutual coupling effects, the root realbeamspace implementation in general provides more robust DOA estimates than the real-beamspace and the use of the coupling matrix together with the element-space MUSIC implementation. It is expected that the model for describing mutual coupling can also be combined with recently derived DOA estimation techniques, such as the rank-reduction (RARE) estimator [22] and the unitary root-MUSIC technique [23] for UCAs.

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 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 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 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 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


A RULE INDUCTION ALGORITHM FOR KNOWLEDGE DISCOVERY AND CLASSIFICATION Abstract: Classification and rule induction are key topics in the fields of decision making and knowledge discovery.The objective of this study is to present a new algorithm developed for automatic knowledge acquisition in data mining.The proposed algorithm has been named RES-2 (Rule Extraction System). It aims at eliminating the pitfalls and disadvantages of the techniques and algorithms currently in use. The proposed algorithm makes use of the direct rule extraction approach, rather than the decision tree. For this purpose, it uses a set of examples to induce general rules. In this study, 15 datasets consisting of multiclass values with different properties and sizes and obtained from the University of California, Irvine, have been used. Classification accuracy and rule count have been used to test the proposed method. This method presents an alternative 3-step method to classify categorical, binary, and continuous data by taking advantage of algorithms for data mining classification and decision rule generation. The method aims at improving the classification accuracy of the algorithms that extract the decision rules. Experimental studies were conducted on the benchmark datasets and the results of the comparisons with some known algorithms for decision rule generation have shown that the proposed method performs classification with a higher accuracy and generates fewer rules. Data mining is described as the process of accessing information in large databases and extracting generalized information, or, in other words, searching, revealing, and providing correlations in large databases that will enable us to make estimations about the future with the help of computer programs. Data mining covers basics like statistics, databases, programming techniques, and high performance processing, as well as all works for formulizing and applying induction procedures that would extract significant and useful information from available data [1] . Structural patterns and hidden knowledge in the large databases can be represented in various ways, such as decision tables, decision trees, association rules, and classification rules. Algorithms are needed for generating rules that determine the description of the concepts to be learned. However, the description is only one of many possible interpretations of the training data and may impose a completely different meaning that is far from the meaning of the concept [2] .. A major problem encountered in the design of learning algorithms is the generation of a complex description from noisy examples. Learning from noise-corrupted data may result in a large number of complicated decision rules describing trivial instances. Hence, the resulting concept description may not reflect general situations. Such a case is referred to as 'overfitting', which refers to a tendency to force the rule induced from the training data to agree with the data too closely, at the cost of generalization for other examples. Poor concept description is another cause of overfitting. Researchers have studied the methods to overcome the overfitting caused by noise for a long time [2, 3] .. In recent years, many algorithms in the literature have been developed in order to discover the relationships between the input data and the output data for generating rules. In these algorithms, approaches such as divide and conquer, association rules, covering rule induction, decision trees, and naïve Bayes are used [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] . Apart from these, there are also other algorithms that generate rules using techniques such as neural networks, ant colony optimization, genetic algorithms, particle swarm optimization, fuzzy logic, and support vector machines [14] [15] [16] [17] [18] [19] . In this study, the covering rule induction method has been used in order to obtain generalized rules.. Tan et al. [20] presented a hybrid evolutionary algorithm using genetic algorithms and a support vector machine for the attribute selection. Elalfi et al. [21] proposed an algorithm for extracting accurate and intelligible rules from databases via a trained artificial neural network using genetic algorithms. Kahramanli and Allahverdi [22] presented a method that extracts rules from trained adaptive neural networks using artificial immune systems. The authors iterated the purpose of the study as to develop a new adaptive function and a new method for rule generation. In their study, the results of the proposed algorithm on 2 benchmark datasets were compared with the results obtained from the previous works in the literature. Rodríguez et al. [14] presented an efficient distributed genetic algorithm for classification rule extraction based on the island model and enhanced it for scalability with data training partitioning in data mining. In this study, they calculated the acquisition rate, rule count, and standard deviation for many datasets. Cohen et al. [7] introduced an automatic, general, decision-tree-based framework for instance-space decomposition with a contrasted population miner rule using grouped gain-ratio. Thabtah and Cowling [11] proposed an algorithm that resolves the overlapping between rules in the classifier by generating rules that do not share training objects during the training phase, resulting in a more accurate classifier. Their results, obtained from experimenting on 20 binary, multiclass, and multilabel datasets, show that the proposed technique is able to produce classifiers that contain rules associated with multiple classes. Cios and Kurgan [12] described a hybrid inductive machine learning algorithm called CLIP4. In this algorithm, data are first partitioned into subsets using a tree structure and then production rules are generated only from the subsets stored at the leaf nodes. The unique feature of the algorithm is the generation of rules that involve inequalities. Moreover, this algorithm-generated model of the data consists of well-generalized rules, and it ranks the attributes and selectors that can be used for feature selection. Thabtah et al. [9] proposed a new associative classification method called multiclass classification based on association rules (MCAR). This method takes advantage of vertical format representation and uses an efficient technique for discovering frequent items based on recursively intersecting the frequent items of size n to find potential frequent items of size n+ 1. Coenen and Leng [10] showed that the choice of appropriate values for the support and confidence thresholds could have a significant effect on the accuracy of classifiers obtained by classification association rule mining (CARM) algorithms. They examined the effect of the choices on the predictive accuracy of the CARM methods, showed that the accuracy can almost always be improved by a suitable choice of parameters, and described a hill-climbing method for finding the best parameter settings. Su et al. [8] proposed the differential evolution (DE)/quantum-inspired differential evolution (QDE) algorithm for the discovery of classification rules. This algorithm combines the characteristics of the conventional DE algorithm and the QDE algorithm. Based on some strategies of the DE and QDE algorithms, the DE/QDE algorithm can directly cope with the continuous, nominal attributes without discretizing the continuous attributes in the preprocessing step. The comparisons of the DE/QDE algorithm with Ant-Miner and CN2 on 6 datasets from the University of California, Irvine (UCI) datasets showed competitive results.. These algorithms generate general concept definitions from special examples with the help of special procedures. These algorithms are classified into 2 main groups. The first is decision-tree-based algorithms and the other is rule-based algorithms.. Decision tree is one of the data mining and machine learning techniques with applications in various fields. A decision tree is a tree structure representation of the given decision problem, such that each nonleaf node is associated with one of the decision variables, each branch from a nonleaf node is associated with a subset of the values of the corresponding decision variable, and each leaf node is associated with a value of the target variable [23] . Decision-tree-based algorithms usually use the information entropy measure to grow a decision tree by searching for a feature that gives the maximum information gain [3] . The procedure of growing a decision tree continues by dividing examples into smaller subsets until the training examples are correctly classified based on a user-specified termination criterion. An example of the first-type algorithm is the incremental decision (ID) family of algorithms, such as ID3 [24] and C4.5 [6] .. In real-world applications, training examples are usually insufficient to define a concept description uniquely. Therefore, learning algorithms need the flexibility to produce different generalizations from given examples. In decision-tree-based algorithms, the description of a subset of examples in a leaf node of a tree is uniquely described as a series of feature tests from the root to the bottom of a tree. This approach does not have the flexibility of describing a target concept in different ways.. Rule-based algorithms have the ability to generate multiple descriptions of a concept. An example is the algorithm quasi-optimal (AQ)15, where the empirical learning was treated by Michalski [25] as the general covering problem. The basic term of a cover, as used in the AQ family of algorithms, implies that there may be multiple covers to include positive training examples. This resulted in the development of procedures that produce a quasi-optimal solution in polynomial time. Generally, AQ algorithms follow a greedy heuristic that tries to include/exclude as many as possible of the positive/negative examples when searching for a complex.. There are many information display forms of data mining classification algorithms that are used as output formats. Among them are decision rules, decisions lists, decision trees, inductive logic programs, and neural networks. Decisions rules are the simplest display form of these output formats: If Condition Then Class. Here, the 'If' part is composed of attribute-value pairs with the help of AND/OR logical operators and the 'Then' part shows the corresponding class value of the given condition. Generally, these decision rules are extracted during the training process through data mining classification algorithms in such a manner that all of the training set is covered. The purpose of extracting decision rules from training data is to obtain generalized rules that define the classes from the special data. The generalization process ends when new rules cannot be generated or the specified termination criteria are met. The extracted decision rules are used to classify the samples in the test set. The output formats of the data mining algorithms, such as decision trees and neural networks, can be easily converted to decision rules.. The proposed algorithm will be described and exemplified on a simple dataset in the next section. The comparisons of the proposed algorithm with the other algorithms in the literature over 15 datasets are given in Section 3. Finally, the results are discussed in Section 4. In this article, a new algorithm directly producing rules with a simple and at the same time effective rule search mechanism has been presented. This algorithm explores all of the cases that could generate rules using the search technique, without performing any calculations in the rule generation stage, and turns them into rules. The search technique is based on testing whether the attributive-value combinations that could be rules correspond to only one class or not. Thus, it generates all of the rules and ensures that the most general rules are chosen. Fewer rules are generated by eliminating unnecessary and repeated rules at the end of the procedure. Furthermore, it classifies the training set with 100% accuracy, as it does not use a pruning method. According to the results obtained using the benchmark datasets taken from real life, the proposed method produces better results than many other algorithms in terms of both the accuracy and rule number. In the future, it may be possible for the algorithm to eliminate unqualified rules and generate fewer rules by applying a pruning procedure and calculating the quality of the obtained rules. Additional issues to be further studied include examining how the proposed algorithm can be implemented using other classification methods such as support vectors machines, ant colony optimization, or Bayesian networks.

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


Stochastic geometry modeling and analysis of cognitive heterogeneous cellular networks In this paper, we present a cognitive radio (CR)-based statistical framework for a two-tier heterogeneous cellular network (femto-macro network) to model the outage probability at any arbitrary secondary (femto) and primary (macro) user. A system model based on stochastic geometry (utilizing the spatial Poisson point process (PPP) theory) is applied to model the random locations and network topology of both secondary and primary users. A considerable performance improvement can be generally achieved by mitigating interference in result of applying the CR idea over the above model. Novel closed-form expressions are derived for the downlink outage probability of any typical femto and macro user considering the Rayleigh fading for the desired and interfering links. We also study some important design factors which their role and importance in the determination of outage and interference cannot be ignored. We conduct simulations to validate our analytical results and evaluate the proposed schemes in terms of outage probability for different values of signal-to-interference-plus-noise ratio (SINR) target. The best solution to the spectrum saturation and bandwidth availability problems in multi-tier cellular networks is to adopt technologies that make the most efficient use of existing spectrum through frequency reuse schemes [1, 2] . In universal frequency reuse scheme, the existing spectrum can be aggressively and effectively reused by all of the coexisting network tiers. This will lead to higher spatial spectrum utilization and network usage capacity at the expense of an increased possibility of interference among network tiers and of a reduced quality of service (QoS). In multi-tier cellular networks, interference is increasingly becoming a major performancelimiting factor, and hence, interference modeling, coordination, and avoidance are the primary focus of interest for both the industry and academic communities. Applying the cognitive radio (CR) technology in multi-tier cellular networks to be aware of and adapt to communication environments, some of the above challenges can be tackled. In fact, CR is the key enabling technology for interference management and avoidance in multi-tier cellular networks [2, 3] . On the other hand, the aggregate interference environment is more complicated to model, and evaluating the performance of communication techniques in the presence of heterogeneous interference is challenging. For interference characterization, if the base stations (BSs) of the cellular network follow a regular grid (e.g., the traditional hexagonal grid model), then the SINR characterization will be either intractable [3, 4] or inaccurate due to unrealistic assumptions [5] . Moreover, as urban areas are built out, the BS infrastructure is becoming less like points on a hexagonal lattice and more random. Hence, the use of a hexagonal grid to model the BS locations is violated and is considered too idealized [6] . Furthermore, according to [3, 4, 6] for snapshots of a cellular network at different locations, the positions of the BSs with respect to each other follow random patterns due to the size and unpredictability of the BSs in these kind of networks. Therefore, the need for a powerful mathematical and statistical tool for modeling, analysis, and design of wireless networks with random topologies is quite obvious.. A new modeling approach called 'stochastic geometry' has been recently applied to the analysis of multi-tier cellular networks due to its ability to capture the topological randomness in the network and its aim at deriving accurate and tractable expressions for outage probability [3, 6] . Stochastic geometry stems from applied probability and has a wide range of applications in the analysis and design of wireless networks in particular for modeling and analyzing systems with random channel access (e.g., ALOHA [7, 8] and carrier sensing multiple access (CSMA) [9] ), single-and multi-tier cellular networks [6] , and networks with cognitive abilities [7, 10] . Multi-tier cellular networks have been investigated from different perspectives such as power control [11, 12] , spectrum allocation [13, 14] , and exploiting CR techniques [15, 16] , and recently, many works have been done based on the similar concepts to adopt and extend the stochastic geometric approach to different network models and scenarios (see [17] [18] [19] [20] ). This paper discusses this new theoretical model to provide a better understanding of the heterogeneous cellular networks of tomorrow and their challenges (interference modeling, coordination, and avoidance) that must be tackled in order for these networks to reach their potential. We focus on a two-tier femto-macro network where low-power and small-coverage local nodes (femto nodes) are distributed in the coverage of macro nodes. We provide an insight into the role of CR in interference mitigation in two-tier heterogeneous networks. We derive closed-form expressions for the outage probability of any typical femto and macro user in the network. We also study the effect of several important design factors which play vital roles in the determination of outage and interference.. Our main contributions in this work which is an extension of [21] are therefore the following: (1) We analyze the Laplace transforms of all four types of aggregate interference between macro and CR femto networks (including the interference between macro nodes among themselves and femto nodes among themselves, the cross-interference from femto to macro network and vice versa) in perfect and imperfect spectrum sensing CR-based femto networks, considering simultaneously the Poisson point process (PPP) model, and some important design factors (such as spectrum access probability) which can play a major role in determining interference and outage. (2) This article provides an insight into the role of CR in interference mitigation in orthogonal frequency-division multiple-access (OFDMA) two-tier heterogeneous networks. (3) Closedform expressions are derived for the outage probability of any typical femto and macro user considering the Rayleigh fading assumption for the desired and interfering links with the possibility of using the CR ability for the femto network. It should be noted that in most of the available studies in this area, none of the network tiers is equipped with the CR capability; they are mostly based on the existence of only one macro-BS (along with the macro users and the femto network); and the effect of considering multiple macro-BSs is ignored in the analysis of outage probability. Authors in [22] [23] [24] [25] have considered the twotier heterogeneous networks imposing the CR ability to the femto tier. Different from [22] , in our work, we consider both the perfect and imperfect sensing scenarios for the CR femto-BSs, however authors in [22] ignore the effect of sensing errors on the opportunistic channel access probability and consequently the outage probability of each tier. On the other hand, in our work, the mathematical demonstration of the obtained expressions (channel access probability and outage probability expressions) is quite different from the mentioned works. In this paper, utilizing the spatial Poisson point process (PPP) theory, we presented a tractable model to derive the outage probability of a typical femto and macro user in a two-tier heterogeneous network which provides insight into system design guidelines. In other words, for the case of the node locations modeled by a PPP and the desired and interfering channels are subject to Rayleigh fading, we demonstrated the use of the cognitive radio (CR)-based framework to evaluate the outage probability at any arbitrary user. Exact closed-form expressions were obtained as a result. In addition, we observed that in the downlink analysis, the outage probability is a function of the network topology and several important system design parameters such as SINR target, exclusion regions, MAC mechanisms such as ALOHA (p tx ), and the resource block (RB) selection constraint (p RB ) which is controlled by the spectrum sensing measurements.

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