Accurate template-based correction of brain MRI intensity distortion with application to dementia and aging Abstract-This paper examines an alternative approach to separating magnetic resonance imaging (MRI) intensity inhomogeneity from underlying tissue-intensity structure using a direct template-based paradigm. This permits the explicit spatial modeling of subtle intensity variations present in normal anatomy which may confound common retrospective correction techniques using criteria derived from a global intensity model. A fine-scale entropy driven spatial normalisation procedure is employed to map intensity distorted MR images to a tissue reference template. This allows a direct estimation of the relative bias field between template and subject MR images, from the ratio of their low-pass filtered intensity values. A tissue template for an aging individual is constructed and used to correct distortion in a set of data acquired as part of a study on dementia. A careful validation based on manual segmentation and correction of nine datasets with a range of anatomies and distortion levels is carried out. This reveals a consistent improvement in the removal of global intensity variation in terms of the agreement with a global manual bias estimate, and in the reduction in the coefficient of intensity variation in manually delineated regions of white matter.Index Terms-Bias field, B-Spline, template matching, image warping, normalized mutual information. Accurate and sensitive detection of tissue volume differences from high resolution MRI studies is dependent on the correct assignment of tissue classification based on the observed MRI intensity across a population being studied. In particular, applications requiring the localized detection and mapping of change in tissue volume will be the most sensitive to regional variations in tissue intensity. An example of such applications is serial deformation tensor morphometry [12] . Here, small-scale tissue volume changes are captured over time within each subject using a highly localized volume registration scheme. A group pattern of common volume change can be created [37] , by transforming each map to a common template. When analyzing these maps [36] acquired from different subjects, it is important to separate changes observed in different tissues types (for example contractions in white or gray matter from expansions in CSF), to ensure optimum separation of tissues. Accurate correction of intensity bias in the image data of each subject is then critical in assessing the anatomical location of volume change over time.. Large-scale population-based studies are increasingly important in the study of neurodegenerative conditions. In such studies it is common to maintain the same acquisition type and scanner throughout the entire study. It is in such studies where we feel this template-based approach can be most valuable in helping to extract accurate measures of tissue volume and volume change, by making use of a template optimized for the contrast properties of a particular study. Overall, the experimental results we have so far indicate a promising increase in the sensitivity of bias field detection using the template-based approach. We are currently further refining the technique using improved reference templates and extending the validation of the method to a larger set of data with different age ranges and disease conditions. Current retrospective methods of brain MRI bias field correction generally ignore the occurrence and spatial distribution of the range of intermediate tissue-intensity types that occur in normal T1-weighted brain MRI scans. Subtle normal differences for example, in the intensity of cortical and subcortical gray matter, pose a direct confound to the accurate estimation of nonuniformity, since global correction techniques may force these different tissue types to incorrectly exhibit the same intensity value. In this paper, we have, therefore, explored an alternative registration driven, template-based approach to correcting subtle sensitivity variations. Rather than imposing constraints purely on the global intensity distribution of an MRI scan in order to define a correction criterion, we have exploited the ability of an entropy driven spatial normalisation algorithm to map intensity distorted MRI data to a tissue reference template, in order to estimate the spatial variation in tissue intensity. Approaches to bias correction commonly make use of the assumption that the bias field is slowly varying, and that a given tissue naturally exhibits a uniform value throughout the brain, allowing the separation of anatomical structure and imaging effects. The most direct approach, exemplified by Dawant et al. [10] and Dale [9] , is to specifically identify voxels known to lie within a given tissue. The variation of the measured intensities is then used to estimate a correction field. Meyer [25] employed an initial segmentation, which was robust to intensity distortion, in order to extract tissue regions within which spatial intensity distortion could be estimated, relying on extrapolation of the slowly varying field to correct other regions of tissue. A natural development from this to handle all tissue types, is to build assumptions about global and local intensity variations into a spatial filtering scheme. Examples of such an approach are those of full homomorphic filtering [17] and its approximation in homomorphic unsharp masking described by [3] . Such an approach not only assumes a slowly varying field, but also that a local statistic (such as the mean intensity) should be constant across the image. This implicitly assumes that, at the chosen local filter scale, the proportion of gray and white matter (and 0278-0062/04$20.00 © 2004 IEEE other tissues) is uniform. A related approach, making use of differences in the local and global median intensities, is described by De-Carli [11] . Brinkmann et al. [4] examined the choice of filtering kernel width and the behaviour of homomorphic unsharp masking when using median or mean filters.. An extension of local mean or median filtering schemes is to introduce a more complex statistical model of the intensity distribution. A classic example of such an approach is that of Wells et al. [45] , [46] which assumes the presence of a known number of tissue classes and that these exhibit fixed intensities over the entire FOV. An E-M algorithm was used to refine the classification and provide a pixel-level estimate of the intensity distortion relative to the tissue labeling estimate, using a low pass spatial filter to stabilize the estimation. Van Leemput et al. [22] take a similar approach but employ a polynomial fitting to model the bias field. This was extended by Guillemaud and Brady [14] by the addition of an extra class to capture unknown tissues. A related method is that of Pham and Prince [27] and that of Lee and Vannier [20] , who drive the intensity tissue labeling using a fuzzy C-means algorithm. Bayesian and MAP estimation approaches have also been employed to carry out tissue labeling. Yan and Karp [49] combined such an approach with a B-Spline model for the inhomogeneity, to provide a combined labeling and inhomogeneity estimation. Similar approaches are described by Rajapakse [28] and Nocera [26] . Styner et al. [41] formulated a parametric correction technique with a fixed number of tissue classes to be solved with an evolution strategy, capable of separating large-scale distortions from image structure. Shattuck et al. [32] extended the MAP estimation approach with Gibbs priors and modeled the effect of partial volume between tissue classes. Ashburner [2] incorporated an inhomogeneity model into an atlas driven tissue labeling scheme, penalizing unrealistic higher spatial frequency components of the estimate using a cost function derived from the third derivatives of the bias field estimate.. A more generic approach is to compare and correct local intensity variation based on a comparison of intensity distributions directly, rather than a parametric description derived from them. This approach was used by Wang [43] to refine intensity estimates over the image. Such nonparametric approaches, that do not specifically model tissue classes present in the image, have proved both robust and accurate. Sled et al. [35] proposed such a technique, driving the correction process from a measure of sharpness of the intensity distribution, modeling the bias field using a coarsely parameterized B-Spline. This formed the basis for the now widely used N3 method of inhomogeneity correction, which we shall use in this paper for comparison with our methodology. A similar approach was later explored by Likar et al. [23] who used entropy as a correction criterion which was minimized by the removal of an estimate of the bias field described by a low order polynomial.

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


Binary join trees for computing marginals in the Shenoy-Shafer architecture Abstract We describe a data structure called binary join trees that is useful in computing multiple marginals efficiently in the Shenoy-Shafer architecture. We define binary join trees, describe their utility, and describe a procedure for constructing them. The main goal of this paper is to describe a data structure called binary join trees that are useful in computing multiple marginals efficiently in the Shenoy-Shafer architecture . We define binary join trees, describe their utility, and describe a procedure for constructing them.. In the last decade, much work has been done in the uncertain reasoning community on exact computation of marginals using local computation [see, e.g., Pearl 1986 , Kong 1986 , Lauritzen and Spiegelhalter 1988 , Dempster and Kong 1988 , Jensen et al. 1990 , Almond 1995 , Lauritzen and Jensen 1996 , Shafer 1996 . The main idea behind local computation is to compute marginals of the joint distribution without actually computing the joint distribution. Local computation can be described as message passing in data structures called join trees. Join trees are also called junction trees [Jensen et al. 1990 ], clique trees [Lauritzen and Spiegelhalter 1988] , qualitative Markov trees , and hypertrees .. The efficiency of the message-passing algorithms depend on the sizes of the subsets in a join tree. The problem of finding a join tree that minimizes the size of the largest subset has been shown to be NP-complete [Arnborg et al. 1987] . Consequently, much attention has been devoted to finding heuristics for constructing good join trees [see, e.g., Olmsted 1983 , Kong 1986 , Zhang 1988 , Kjaerulff 1990 .. In this paper, we focus on another aspect of join trees, the number of neighbors of nodes in a join trees. If a node in a join tree has many neighbors, then it leads to much inefficiencies, especially in the Shenoy-Shafer architecture. This motivates the definition of binary join trees which is a join tree such that no node has more than three neighbors. The main idea behind a binary join tree is that all combinations are done on a binary basis, i.e., we combine functions two at a time.. Local computation has also been studied in many other domains besides uncertain reasoning such as solving systems of equations [Rose 1970 ], optimization [Bertele and Brioschi 1972] , and relational databases [Beeri et al. 1983] . In order to keep the applicability of the results as wide as possible, we describe our work using the abstract framework of valuation networks [Shenoy 1989 [Shenoy , 1992a [Shenoy , 1994a [Shenoy , 1994b [Shenoy , 1994c ].. An outline of this paper is as follows. Section 2 introduces the framework of valuation networks. Section 3 describes three axioms that enable local computation. Section 4 describes a fusion algorithm for computing a marginal of the joint valuation. Section 5 describes the fusion algorithm in terms of message passing in join trees. Section 6 describes a message passing algorithm for computing multiple marginals-the Shenoy-Shafer architecture. Section 7 introduces the concept of binary join trees, its utility in reducing the number of combinations done in computing marginals, and a procedure for constructing them. Finally Section 8 contains concluding remarks. The main goal of this paper is to describe a data structure called binary join trees that are useful in computing multiple marginals efficiently using the Shenoy-Shafer architecture. We define binary join trees, describe their utility, and describe a procedure for constructing them. The join tree construction process described here is superficially different from the method described in Lauritzen and Spiegelhalter [1988] which consists of moralizing a directed acyclic graph, triangulating the moral graph using the maximum cardinality search method, and then arranging the cliques of the triangulated moral graph in a join tree. Instead of starting from a directed acyclic graph, we start with a more general setting-a hypergraph consisting of all subsets for which we have valuations and all subsets for which we desire marginals, and we use the fusion algorithm as a guide to constructing a join tree. Thus the join tree can be regarded as a data structure to organize the computations of the fusion algorithm.. Binary join trees further refine the data structure so that unnecessary computations are minimized. In particular, we identify three sources of inefficiencies associated with non-binary join trees that are eliminated in binary join trees, and we describe an automatic procedure for constructing them based on the idea of binary fusion. Although we have restricted our discussion in this paper to the Shenoy-Shafer architecture, binary join trees are also useful in the Lauritzen-Spiegelhalter [1988] and Hugin [Jensen et al. 1990, Lauritzen and Jensen 1996] architectures, albeit to a lesser extent. This is because in the Lauritzen-Spiegelhalter and Hugin architectures, some of the combination operations are replaced by the division operations. Since the main role of the binary join trees is to reduce the computation in combinations, their utility is less in these other architectures. An interesting question is the relative computational efficiencies of the three architectures. It is commonly believed that the Hugin architecture is the most efficient (at least for the case of probabilistic reasoning). Ongoing work [Lepar and Shenoy 1996 ] leads us to believe that if binary join trees are used, then the Shenoy-Shafer architecture is at least as computationally efficient asif not more than-the Hugin architecture.

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


A Characterization of C.E. Random Reals A real is computably enumerable if it is the limit of a computable, increasing, converging sequence of rationals; is random if its binary expansion is a random sequence. Our aim is to o er a self-contained proof, based on the papers 7, 14, 4 , 1 3 , of the following theorem: a r eal is c.e. and random if and only if it a Chaitin real, i.e., the halting probability of some universal self-delimiting Turing machine.

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Predictive publish/subscribe matching A new publish/subscribe capability is presented: the ability to predict the likelihood that a subscription will be matched at some point in the future. Knowing that some phenomenon of interest is about to take place, applications can take proactive steps to prevent the situation from occurring altogether, or speculatively begin reacting to the event even before it has transpired. A publish/subscribe matching algorithm is developed in which composite subscriptions consisting of temporal and logical operators are efficiently represented by a set of finite state machines and rules. The algorithm trains a Markov model to an application's event workload, and predicts the probability that a given subscription will match within a window in the future event stream. Evaluations demonstrate that the memory and processing costs of the algorithm scale well with the number of subscriptions, and the prediction precision is high, especially when the workload characteristics do not change rapidly. Furthermore, a comparison with a hand-crafted Markov model using real data traces shows that the algorithm consumes much less memory and processing power, yet still delivers prediction precision that approaches that of the hand-crafted model. This is especially impressive since the algorithms lack any of the domain expertise embedded in the hand-crafted model. A wide variety of scenarios require the detection, correlation, and aggregation of events. For example, a credit card fraud detection system may correlate users' purchases to determine suspicious usage patterns. Current event processing engines and publish/subscribe systems support the real-time detection of such complex patterns [1, 3, 5, 7, 14, 15, 19] . In many applications, however, it is too late to raise an alert of a malicious activity after it has occurred. What is needed is a way to predict the likelihood of a given pattern matching at some point in the future. This paper proposes a novel publish/subscribe matching algorithm that computes the probability that a subscription, or pattern, will match based on events observed in the past, application workload, and partial subscription matches.. Many applications benefit from predictive subscription matching capabilities. For example, in a network monitoring system [8] , a particular pattern of login attempts and port scan operations may not constitute a successful attack per se, but experience may indicate that it is a precursor to an intrusion. The system may then proactively block the intruder or take other defensive measures. Other scenarios that may exploit predictive matching include algorithmic trading [13] , business analytics and business activity monitoring [8] , and epidemic warning [22] .. One approach to realize predictive capabilities is to define additional subscriptions whose match indicates some likelihood that an activity is about to occur. For example, the increased sales of a cough medication followed by long hospital wait times may signify an 80% probability of a flu outbreak. The problem with this approach, however, is that defining these additional subscriptions and rules requires domain expertise, can be complex and time consuming, and may need to be revised as the workloads change.. The predictive publish/subscribe matching engine in this paper, on the other hand, is easy to use, and can predict when a subscription is about to be matched without requiring any domain expertise or additional rules to be defined. The prediction is dynamically tuned to the current application workload based on the history of events. Furthermore, the user is able to control the quality of the prediction, in terms of the number of false positives, by specifying the minimum prediction threshold and how far into the future to look ahead. The predictive publish/subscribe capabilities are implemented in our P-ToPSS prototype (the Predictive Toronto Publish/Subscribe System.). This work complements probabilistic databases and event processing approaches [4, 6, 17, 22] that work with uncertain data. Whereas these systems are designed for scenarios where there is imprecision in the event stream and event values, this paper assumes that the events themselves are precise; the only uncertainty is in the future event stream. This work also complements existing pub-lish/subscribe research [1, 5, 7, 14, 17] that determines matching subscriptions based on published events, but can not predict future matches based on events observed in the past. This paper makes three main contributions:. 1. A set of algorithms are developed to represent arbitrarily complex subscriptions consisting of temporal and Boolean operators. Temporal sub-expressions of a subscription are matched by a finite state machine and Boolean sub-expressions by a rule-based engine. This partitioning avoids the state explosion of FSMs with Boolean expressions. As well, some common sub-expressions among a set of subscriptions are merged so as to reduce computation and memory costs.. 2. An efficient algorithm is proposed to predict matches of subscriptions. A Markov model is used to perform the prediction, and the model is continually tuned to the application workload. The algorithm can be configured to report only those predictions above a given threshold and within a given time in the future.. 3. A thorough quantitative evaluation of the costs of the algorithms are conducted. The computation and memory consumption scalability of the algorithms are presented, the quality of the predictions under a variety of situations is analyzed, and a comparison of the prediction engine to a hand-crafted Markov model for a real-world scenario is made.. The paper continues with a comparison of P-ToPSS to the literature in Sec. 2. P-ToPSS's subscription language and data model are outlined in Sec. 3 followed by a description of the subscription data structures in Sec. 4 , and matching and prediction algorithms in Sec. 5. Sec. 6 presents a detailed quantitative analysis of the algorithms. This paper presents the new P-ToPSS publish/subscribe model that, in addition to reporting when a subscription has matched, predicts the likelihood a subscription will match in the future. The system requires no additional subscriptions to be defined, and dynamically adapts its prediction to the application workload.. Content-based publish/subscribe semantics are supported including both temporal and Boolean operators. The temporal sub-expressions of a subscription are stored as finite state machines, and the Boolean parts as Boolean trees, thereby avoiding state explosion that would result from representing Boolean operators in the state machine. Furthermore, some common sub-expressions are merged to reduce memory consumption and matching efficiency.. The finite state machines, which are also Markov chains, are trained using an application's event history, and model the transition probabilities among the partial match states of the subscription. The Markov model is then used to predict the probability of a subscription matching within some number of transitions in the future given its current partial match state.. Experiments show the memory and computation performance of the prediction algorithms scale with the number of subscriptions, and that the merging optimizations can significantly reduce the state machine sizes especially when subscriptions exhibit locality. Moreover, as expected, the prediction quality, in terms of precision, improves when only higher probability predictions are considered, and as the lookahead into the future is decreased. Also, interestingly, when the system is trained and tested using the same distribution of events, the prediction precision for different lookahead distances improves and converges. When the system is trained using a different set of data, however, while the precision may still be high, increasing the lookahead does impair the precision. Therefore, if an application event distribution does not fluctuate rapidly and a user is only interested in highly precise predictions, there is no harm in asking for predictions further into the future.. The prediction algorithms are also compared to a hand-crafted Markov model for a real application workload. The predictions in the hand-crafted model are expected to be better, but require expertise to construct and are much more expensive computationally and memory-wise. Results show that despite being much cheaper to evaluate, the prediction precision of the model in this paper is not much worse than the hand-crafted one. In fact, when the lookahead is increased, the learned model performs much better.. As this is the first paper to propose predictive publish/subscribe matching, there are many opportunities to extend the work. One such avenue is to support predictions with imprecisely defined subscriptions. For example, in an intrusion detection system, there may be many ways to perform an intrusion that are similar to, but not exactly like, the intrusion signatures defined by an administrator. This paper complements ideas developed in probabilistic databases, event processing systems, and publish/subscribe systems that operate on uncertain data.. Probabilistic Database: Probabilistic databases are currently an active area of research. A probabilistic database is an uncertain database in which the possible worlds have associated probabilities. Fuhr introduced a probabilistic relational algebra to represent imprecise attribute values and integrate vague queries in database systems [10] . While there are currently no commercial probabilistic database systems, several research prototypes exist including Trio [4] , Orion [20] , MystiQ [6] and MayBMS [2] .. Trio [4] is a database management system which integrates data, uncertainty of the data, and data lineage. Trio is based on an extended relational model. The ORION database system [20] , is an uncertain database management system with built-in support for probabilistic data as first class data types. In contrast to other uncertain databases, Orion supports both attribute and tuple uncertainty with arbitrary correlations. MystiQ [6] is a system that uses a probabilistic data model to find answers among large numbers of data sources exhibiting various kinds of imprecisions. Moreover, users sometimes want to ask complex, structurally rich queries, using query constructs typically found in SQL queries such as joins, subqueries, existential/universal quantifiers, aggregate and groupby queries. MayBMS [2] uses probabilistic versions of conditional tables as the representation system, but in a form engineered for admitting the efficient evaluation and automatic optimization of most operations of a language using robust and mature relational database technology. In this section we experimentally evaluate our approach. All the algorithms are implemented in Java and the experiments are run on a 3GHz Linux machine with 4GB of RAM. We are using two workloads for experimentation: a synthetic load that lets us independently examine various aspects of our approach by running controlled experiments and a second real-world data set to demonstrate the behaviour of our approach under realistic conditions. Our workloads comprise composite subscriptions and events.. The synthetic subscription workload is generated as follows. Ncs composite subscriptions are generated, each containing Lengthcs primitive subscriptions. Primitive subscriptions in turn are generated to match exactly one of the events in a predefined event pool of size Nep. Of the Lengthcs − 1 operators in a composite subscription, Nnon_contiguous_op are uniformly selected to be the non-contiguous sequence operator and the remainder the contiguous sequence operator. By default, Ncs = 1000, Lengthcs = 10, Nep = 50, and Nnon_contiguous_op = 2.. Two sets of subscription workloads are used, characterized by the distribution of the primitive subscriptions. In the uniform_cs subscription workload, each primitive subscription matches a random event uniformly drawn from the event pool, whereas in the gaussian_cs subscription workload, events are selected following a Gaussian distribution.. Since the number of partial and full matches of subscriptions will affect the prediction algorithm, we control the number of partial and full matches of a composite subscription, Npm and N f m , respectively, when generating the event stream workload. As shown in the example in Figure 8 , the event stream contains sequences of events that partially or fully match a given subscription. In addition, a number of irrelevant events that do not match any primitive subscriptions are interspersed among the partial and full match sequences. The event stream is generated as follows. First, we determine with 50% probability whether to generate a set of irrelevant events. If so, a sequence of Lengthirr irrelevant events are appended to the event stream. Otherwise, one of the composite subscriptions whose quota of partial or full matches (Npm or N f m ) has not been met is randomly selected, and a sequence of events that correspond to either a partial or full match is generated. If a full match is required, the necessary set of events is added to the event stream, otherwise a partial match of length Lengthpm is appended to the stream. By default Npm = 20, N f m = 20 and Lengthirr is a uniform distribution in the range [1, 100] . Two sets of event stream workloads are used, characterized by the distribution of the partial match lengths, Lengthpm. In the uniform_pub workload, Lengthpm follows a uniform random distribution in the range [1, Lengthcs −1], whereas in the gaussian_pub workload it varies with a Gaussian distribution over the same range.. It should be noted that the event stream workload only loosely controls the length and number of partial and full matches of the composite subscriptions. In reality, the events generated to achieve a partial or full match of a particular composite subscription may contribute to matching other composite subscriptions.. In the following experiments, all measurements are performed after the subscriptions have been inserted into the matching engine. To evaluate the matching algorithm, the parameters of interest include the effect of the number of composite subscriptions, their lengths, the number of non-contiguous operators and the size of the event pool (i.e., more or less diverse primitive subscriptions,) For the prediction algorithm, the evaluated factors include the ratio of full matches to partial matches, the number of prediction steps, and the prediction threshold.

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


Generalizing WDN simulation models to variable tank levels In water distribution network (WDN) steady-state modelling, tanks and reservoirs are modelled as nodes with known heads. As a result, the tank levels are upgraded after every steady-state simulation (snapshot) using external mass balance equations in extended period simulation (EPS).This approach can give rise to numerical instabilities, especially when tanks are in close proximity. In order to obtain a stable EPS model, an unsteady formulation of the WDN model has recently introduced. This work presents an extension of the steady-state WDN model, both for demand-driven and pressure-driven analyses, allowing the direct prediction of head variation of tank nodes with respect to an initial state. Head variations at those nodes are introduced as internal unknowns in the model, the variation of tank levels can be analyzed in the single steady-state simulation and EPS can be performed as a sequence of simulations without the need for external mass balances. The extension of mass balance at tank nodes allows the analysis of some technically relevant demand components. Furthermore, inlet and outlet head losses at tank nodes are introduced and large crosssectional tank areas are allowed by the model and reservoirs become a special case of tanks. The solution algorithm is the generalized-global gradient algorithm (G-GGA), although the proposed WDN model generalization is universal. An expanded generalized framework for WDN modelling has been presented which is applicable to both demanddriven and pressure-driven analyses and allows consideration of varying tank levels and mass balances at tank nodes. This is in contrast to the classical network hydraulic models which assume a constant head level at tank nodes and thus neglect the relevant mass balance components.. The stability of the resulting G-GGA was tested using the simple case study from Todini (). Subsequently, the G-GGA was applied to a larger network by modelling the filling/emptying processes of tanks situated at all the nodes. G-GGA is a promising enhancement to the hydraulic network model in WDN analysis because it can account for the volume balance in tanks (by recovering the related mass balance equation) during EPS and also for single steadystate simulation.

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 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


Transforming text into hypertext for a compact disc encyclopedia A hypertext version of a multi-volume engineering encyclopedia on a compact disc is described. The methods for characterizing the explicit and implicit structure of the document, the novel user interface to the compact disc version, and the design and development lessons that apply to any hypertext project involving realistic amounts of text and graphics are discussed. The Engineering Data Compendium [3] is a highly specialized encyclopedia containing comprehensive reference data about human perception and performance. Its four volumes include nearly 3000 pages of text and more than 2000 figures, tables, and illustrations. The. Compendium's primary users are designers of aircraft cockpits, control rooms, or other systems with complex user interfaces.. Recently, I led a team that designed and built a compact disc version of the Compendium. A user-oriented and document-oriented methodology was implied by our objectives:

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


Systematic prediction of linear dependencies in the concentration profiles and implications on the kinetic hard-modelling of spectroscopic data A novel method is presented for the systematic identification of the minimum requirements regarding mathematical pre-treatment, a priori information, or experimental design, in order to allow optimising rate constants and pure component spectra associated with a kinetic model via multivariate kinetic hardmodelling of spectroscopic data. Rank deficiencies in the kinetic concentration matrix represent a major problem for the calibration free method developed by Maeder and Zuberbühler, as its pseudo-inverse, required for the optimisation process, is not defined. In this contribution, the underlying linear dependencies in the concentration profiles are systematically elucidated and appropriate strategies are discussed in order to break them. Also, conditions are predicted for which full spectral resolution can be expected. The method is based on the kernel of a time invariant augmented matrix covering potential rank deficiency due to stoichiometry and rate laws, also relevant for the concentration matrix. Compared to employing the full concentration matrix, this augmented matrix does not require a numerical integration of the differential equations describing the kinetic model and thus can easily be set up. The kernel can be calculated numerically by Singular Value Decomposition (SVD) or determined in a symbolical way, the latter allowing the detection of particular stoichiometric conditions leading to spectral resolution of species. The capabilities of the method are demonstrated analysing three kinetic mechanisms of increasing complexity covering consecutive and parallel reactions. In recent years, chemometric methods dedicated to the analysis of evolutionary multivariate data (e.g. as in kinetic and equilibrium investigations) measured by spectroscopy (e.g. mid-IR, UV-Vis, Raman or fluorescence) have considerably progressed in chemistry and chemical engineering [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] . Kinetic hard-modelling is one of these chemometric methods. It is used to determine the kinetic parameters (e.g. rate constants) of a chemical reaction [2, 8, [10] [11] [12] [13] [14] . As it is based on a hard model, kinetic hard-modelling has excellent predictive capabilities, as long as all chemical and physical effects are covered by the model [15] . For a good overview of the different hard-modelling techniques, we refer to [16, 17] .. Under the assumption of bi-linearity, time and wavelength resolved spectroscopic data can be decomposed according to Beer's law into the concentration profiles and the molar spectra of the pure components. In kinetic hard-modelling, these concentration profiles are usually obtained by numerical integration of the rate laws describing the underlying kinetic hard model. [2] suggested that the associated kinetic parameters are adjusted by non-linear optimisation, so that the residuals between the measured absorbances and those modelled by Beer's law become minimal in the least-squares sense. In this calibration free method, sometimes referred to as kinetic fitting by implicit direct calibration [16, 17] , the pure component spectra, which are linear parameters, are eliminated from the nonlinear optimisation and determined at each iteration by linear regression using the pseudo-inverse of the matrix comprising the concentration profiles. If the number of reactive species equals the rank of the concentration matrix, all concentration profiles are linearly independent and pure component spectra can be resolved. However, if the rank of the concentration matrix is lower than the number of species, i.e. if some concentration profiles are linearly dependent, the pseudo-inverse and thus the pure component spectra cannot be directly computed. In such cases, there are at least five different strategies, as described in Table 1 , to treat rank deficiency problems in the concentration matrix and to allow the fitting of pure component spectra [18] . The determination of a reaction mechanism based on spectroscopic kinetic investigations is an evolutionary process requiring a constant adaptation of the postulated kinetic model in order to comply with the main experimental observations made by chemists. When the underlying kinetic model is known (as it was assumed here in the presented examples), more attention has to be given to the determination of accurate related kinetic parameters, as this information is then used by chemical engineers in order to optimise the reaction conditions. For this two-fold task, kinetic hard-modelling is a particularly suitable technique. It allows the validation of the postulated model and of its related optimised kinetic parameters, on one hand by statistical means (e.g. goodness of the fit, analysis of the residuals or uncertainty estimation on the optimised parameters), but more importantly by comparing the optimised rate constants and the fitted component spectra with the experimenter's chemical knowledge or expectations.. For this purpose, we developed a novel method applicable to any type of bilinear spectroscopic data to be analysed by the kinetic hardmodelling technique proposed by Maeder and Zuberbühler. This method identifies in a systematic way, under ideal conditions, the minimum requirements in terms of mathematical pre-treatment (strategy 1), a priori information (strategy 2), or experimental design (strategies 3 and 4) in order to allow optimising the rate constants of a kinetic model. The method also predicts the conditions for which full spectral resolution can be expected. In case of partial spectral resolution (strategy 1), the method determines the complex linear combinations of the true pure component spectra leading to the fitted (unresolved) component spectra.. This systematic method is based on the kernel of a time invariant augmented matrix Ω that is pseudo-equivalent to the time variant concentration matrix C and covers rank deficienies due to the stoichiometry (matrix N) and to the rate laws (matrix E). Compared to matrix C, setting up matrix Ω is a simple task that can be quickly performed at the Matlab prompt, as it does not require any numerical integration of the differential equations. The kernel of matrix Ω can be easily computed with Matlab's null command, based on Singular Value Decomposition (SVD). Symbolic calculation of the kernel allows detecting particular stoichiometric conditions leading to spectral resolution of some species. For the common mechanism of Example 2 (A +B→C, A +C→D), we have shown, for example, that the fitted pure component spectra of species C and D are only fully resolved under stoichiometric (c 0,B /c 0,A = 1) and halfstoichiometric (c 0,B /c 0,A = 1/2) conditions respectively.. The method relies on the strict assumption that the rank deficiency in the measured spectroscopic data is due to a rank deficiency in the concentration matrix and not in the true pure component spectra of the absorbing species. The validity of this hypothesis depends on the spectroscopic nature of the signal. This assumption generally holds for mid-IR spectroscopy with a fairly high resolution and a low probability of linear dependent component spectra. For UV-Vis spectroscopy, however, the absorption peaks are generally much broader and linear dependencies cannot be totally excluded. The method also assumes that all absorbing species contribute to the measured spectroscopic data, i.e. in time as well as in wavelength direction. In time direction, this assumption only depends on the technical capabilities of the instrument in terms of acquisition time, certain fast reactions requiring for example stopped-flow equipment or model reduction by applying a steady state approximation. In wavelength direction, the fulfilment of this assumption depends on the absorbing nature (absorptivities) of the reactive species with respect to the signal to noise ratio.. Although some of the underlying assumptions mentioned in Section 2.2 are rather idealised, knowing the optimal design to perform a kinetic analysis under ideal conditions is the first step to successfully complete this analysis under real conditions.

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


Dynamics

of

the

quorum

sensing

switch:

stochastic

and

non-stationary

effects

Background:

A

wide

range

of

bacteria

species

are

known

to

communicate

through

the

so

called

quorum

sensing

(QS)

mechanism

by

means

of

which

they

produce

a

small

molecule

that

can

freely

diffuse

in

the

environment

and

in

the

cells.

Upon

reaching

a

threshold

concentration,

the

signalling

molecule

activates

the

QS-controlled

genes

that

promote

phenotypic

changes.

This

mechanism,

for

its

simplicity,

has

become

the

model

system

for

studying

the

emergence

of

a

global

response

in

prokaryotic

cells.

Yet,

how

cells

precisely

measure

the

signal

concentration

and

act

coordinately,

despite

the

presence

of

fluctuations

that

unavoidably

affects

cell

regulation

and

signalling,

remains

unclear.

Results:

We

propose

a

model

for

the

QS

signalling

mechanism

in

Vibrio

fischeri

based

on

the

synthetic

strains

and

Our

approach

takes

into

account

the

key

regulatory

interactions

between

LuxR

and

LuxI,

the

autoinducer

transport,

the

cellular

growth

and

the

division

dynamics.

By

using

both

deterministic

and

stochastic

models,

we

analyze

the

response

and

dynamics

at

the

single-cell

level

and

compare

them

to

the

global

response

at

the

population

level.

Our

results

show

how

fluctuations

interfere

with

the

synchronization

of

the

cell

activation

and

lead

to

a

bimodal

phenotypic

distribution.

In

this

context,

we

introduce

the

concept

of

precision

in

order

to

characterize

the

reliability

of

the

QS

communication

process

in

the

colony.

We

show

that

increasing

the

noise

in

the

expression

of

LuxR

helps

cells

to

get

activated

at

lower

autoinducer

concentrations

but,

at

the

same

time,

slows

down

the

global

response.

The

precision

of

the

QS

switch

under

non-stationary

conditions

decreases

with

noise,

while

at

steady-state

it

is

independent

of

the

noise

value.Our

in

silico

experiments

show

that

the

response

of

the

LuxR/LuxI

system

depends

on

the

interplay

between

non-stationary

and

stochastic

effects

and

that

the

burst

size

of

the

transcription/translation

noise

at

the

level

of

LuxR

controls

the

phenotypic

variability

of

the

population.

These

results,

together

with

recent

experimental

evidences

on

LuxR

regulation

in

wild-type

species,

suggest

that

bacteria

have

evolved

mechanisms

to

regulate

the

intensity

of

those

fluctuations.

Herein

we

have

introduced

deterministic

and

stochastic

modelling

approaches

for

describing

the

core

functionality

of

the

LuxI/LuxR

regulatory

network

in

quorum

sensing

systems.

We

have

focused

on

synthetic

constructs,

and

that

reproduce

the

behaviour

of

the

wild-type

system

and

allow

for

controlled

experiments

that

have

provided

quantification

of

the

activation

process

The

deterministic

approach

has

allowed

us

to

estimate

different

parameters

of

the

model

and

reproduce

the

Figure

The

growth

rate

conditions

the

phenotypic

variability.

In

the

context

of

a

growing

colony,

the

autoinducer

concentration

increases

as

the

colony

does:

purple

lines

show

schematically

two

exponential

growth

conditions

for

the

autoinducer

concentration

as

a

function

of

time.

Our

results

on

the

MFPT,

valid

at

fixed

autoinducer

concentrations,

can

be

extrapolated,

qualitatively,

to

the

case

of

increasing

autoinducer

levels.

Fast

growth

results

in

a

large

cell

variability

and

large

critical

colony

size

for

achieving

a

global

response,

while

slow

growth

produces

reduced

cell

variability

and

a

smaller

critical

population

size.

Increasing

fluctuations

in

LuxR

have

two

opposite

effects:

in

the

slow

growth

case,

increasing

the

noise

(blue

curves:

b

R

green

curves:

b

R

decreases

the

critical

population

size

while

hardly

changing

the

variability,

in

the

fast

growth

case,

increasing

noise

increases

the

critical

population

size

and

increases

greatly

the

variability..

switch-like

behaviour

of

the

QS

network.

Thus,

our

simulations

reveal

that

the

interplay

between

non-stationary

and

stochastic

effects

are

key

and

that,

for

an

extended

range

of

autoinducer

concentrations,

a

bimodal

phenotypic

variability

develops

such

that

cells

fail

to

produce

a

global

response.

In

this

context

we

have

introduced

the

concept

of

precision

of

the

QS

switch,

as

the

inverse

of

the

width

of

the

bimodal

phenotypic

region..

By

computing

the

statistics

of

the

activation

dynamics

of

cells,

we

have

shown

that

the

QS

precision

depends

on

the

gene

expression

noise

at

the

level

of

LuxR

and

is

independent

from

that

of

LuxI.

Our

results,

together

with

the

experimental

evidences

on

LuxR

regulation

in

wild-type

species,

suggest

that

the

noise

at

the

level

of

LuxR

controls

the

phenotypic

variability

of

the

LuxR/LuxI

QS

systems

and

that

bacteria

have

evolved

to

control

its

intensity.

In

addition,

the

robust

stabilization

of

the

phenotype

once

is

fully

induced

indicates

that,

albeit

synthetic

strains

as

and

summarize

many

features

of

the

wildtype

operon

during

the

activation

process,

they

fail

to

capture

crucial

aspects

of

the

deactivation

phenomenon..

Most

insight

in

regards

of

the

effect

of

LuxR

noise

on

the

dynamics

of

cell

activation

is

given

by

the

study

of

the

mean

first

passage

time

(MFPT).

In

terms

of

the

timing

of

activation,

we

have

observed

two

opposite

effects

depending

on

the

control

parameter

c

A

for

c

A

nM,

the

larger

the

noise

in

LuxR,

the

quicker

the

cells

become

activated,

while

for

c

A

nM,

we

observe

the

opposite

effect

and

noise

slows

down

cell

activation.

We

suggest

that

this

effect

can

be

explained

by

the

stochastic

stabilization

of

the

low

state.

Moreover,

the

calculation

of

additional

properties

of

the

statistics

of

the

first

passage

time

have

allowed

us

to

relate

the

concept

of

precision

of

the

switch

with

the

variability

of

the

FPT

by

estimating

the

and

quantiles..

In

summary,

our

results

indicate

that

in

bacterial

colonies

driven

by

the

QS

mechanism

there

is

a

trade-off

between

the

activation

onset

and

a

global

response

due

to

non-stationary

and

stochastic

effects.

On

one

hand,

large

levels

of

noise

at

the

level

of

LuxR

imply

that

cells

require

smaller

autoinducer

levels

for

achieving

an

activation

onset

but,

at

the

same

time,

a

global

response

requires

a

substantial

autoinducer

concentration.

On

the

other

hand,

if

the

LuxR

noise

levels

are

small,

the

activation

onset

is

shifted

toward

larger

values

of

the

autoinducer

concentration

but

the

global

response

is

achieved

for

smaller

concentration

values.

Our

study

could

be

useful

for

Synthetic

Biology

approaches

that

exploit

the

QS

mechanism.

The

fact

that

some

important

features

of

the

QS

mechanism,

e.g.

precision,

rely

on

the

burst

size

of

one

component,

opens

the

door

to

modifications

of

the

LuxI/LuxR

operon

for

regulating

the

response

depending

on

the

problem

under

consideration.

Finally,

further

research

is

needed

about

the

general

validity

and

applicability

on

the

noise-induced

stabilization

phenomenon

of

particular

phenotypic

states

in

other

gene

regulatory

systems

beyond

the

QS

mechanism.

Work

in

that

direction

is

in

progress.

The

response

of

bacterial

colonies

driven

by

the

QS

signalling

mechanism

under

noisy

conditions

has

been

addressed,

in

a

broad

sense,

by

different

authors.

In

particular,

the

characterization

of

the

collective

response

as

a

synchronization

phenomenon

where

the

phenotypic

variations

can

be

generically

predicted

has

been

proposed

However,

this

approach

requires

gene

regulatory

interactions

controlling

the

QS

switch

that

do

not

induce

bistability

and

lead

to

a

monostable

behaviour,

e.g.

negative

feedback

loops

Our

study

focus

on

strains

that

display,

as

the

wild-type

LuxI/LuxR

system

do,

bistability

and,

consequently,

an

alternative

method

to

quantify

the

phenotypic

variability

induced

by

noise

was

needed,

i.e.

the

precision

concept.

Moreover,

previous

works

assume

stationary

conditions

and

disregard

the

role

of

the

cell

cycle

duration.

Herein,

in

agreement

with

experimental

results,

we

have

shown

that

the

time

for

reaching

a

steady

expression

rate

is

much

larger

than

the

cell

cycle

duration

(see

As

a

result,

we

have

revealed

that

the

interplay

between

non-stationary

and

stochastic

effects

is

key

for

understanding

the

global

response

of

the

colony

and

the

phenotypic

variability.

Finally,

we

have

shown

that

the

intrinsic

noise

is

able

to

stabilize

a

particular

phenotypic

state.

This

effect,

namely

the

fluctuations

inducing

a

slowing

down

in

the

activation

of

the

cells,

emerges

because

noise

extends

the

bistable

region

compared

to

the

deterministic

system.

While

such

a

noise-induced

phenomenon

has

been

characterized

in

population

models

and,

more

recently,

in

theoretical

studies

on

bistable

switches

to

the

best

of

our

knowledge,

this

is

the

first

time

that

is

reported

in

the

context

of

QS

systems.

All

in

all,

from

the

viewpoint

of

the

comprehension

of

how

noisy

inputs

may

condition

phenotypic

variability

in

bacterial

colonies,

our

study

introduces

a

number

of

advances..

Herein,

we

have

characterized

how

the

precision

of

the

QS

switch

depends

on

the

stochasticity

levels

and,

importantly,

elucidated

which

noisy

component

of

the

LuxI/LuxR

regulatory

network

drives

the

observed

phenomenology.

Thus,

we

have

found

that

under

nonstationary

conditions,

LuxR

controls

the

phenotypic

variability

and

that

changing

the

noise

intensity

at

the

level

of

LuxI

has

no

effect

on

the

precision

of

the

switch.

A

plausible

explanation

for

this

reads

as

follows.

The

fluctuations

at

the

level

of

LuxI

are

transmitted

to

the

autoinducer.

However,

the

diffusion

mechanism

rapidly

averages

out

the

stochasticity

levels

of

the

latter.

This

is

not

possible

for

LuxR

which

is

kept

within

the

cell.

As

a

consequence

the

amount

of

activation

complex,

that

is

ultimately

the

responsible

for

the

activation,

is

driven

by

the

fluctuations

of

LuxR

but

not

by

those

of

LuxI..

Recent

experimental

work

has

measured

the

bioluminescence

levels

of

individual

V.

fischeri

cells

at

fixed

autoinducer

concentration

In

agreement

with

our

results,

the

authors

observed

that

cells

differed

widely

in

terms

of

their

activation

time

and

luminescence

distribution.

Interestingly,

other

experiments

have

revealed

the

presence

of

additional

regulatory

interactions

for

controlling

the

LuxR

noise

levels.

For

example,

molecules,

a

second

QS

signal

in

V.

fischeri,

has

been

suggested

to

reduce

the

noise

in

bioluminescence

output

of

the

cells

at

low

autoinducer

concentrations

In

the

same

direction,

in

V.

harveyi,

the

number

of

LuxR

dimers

is

tightly

regulated

indicating

a

control

over

LuxR

intrinsic

noise

In

fact,

wild-type

V.

harveyi

strains

have

two

negative

feedback

loops

that

repress

the

production

of

LuxR

and

this

kind

of

regulatory

circuit

is

known

to

reduce

noise

levels

In

this

context,

our

results

provide

a

feasible

explanation

for

the

network

structure

in

wild-type

strains:

since

noise

in

LuxR

controls

the

phenotypic

variability

of

the

LuxR/LuxI

QS

systems,

bacteria

have

evolved

mechanisms

to

control

its

noise

levels.

An

additional

argument

in

this

regard

arises

from

our

results

about

the

deactivation

of

cells:

once

they

are

fully

induced

we

do

not

observe

reversibility

of

the

phenotype

(FPT

larger

than

h).

First,

these

results

are

in

agreement

with

other

switching

systems

as

the

gallactose

signalling

network

in

yeast

and

with

theoretical

results

that

explain

the

asymmetric

switching

dynamics

due

to

stochastic

effects

Second,

they

reveal

the

importance

of

additional

interactions

that

regulate

negatively

luxR

in

wild-type

strains

and

indicates

that

synthetic

strains

as

and

summarize

many

features

of

the

wild-type

operon

during

the

activation

process

but

fail

to

capture

some

of

dynamical

aspects

of

the

deactivation

phenomenon..

Finally,

our

simulations

indicate

that

non-stationary

effects

are

essential

during

the

activation

of

the

QS

response.

While

speculative,

these

results

can

be

extrapolated

to

growing

colonies

where

the

cell

density

is

not

kept

constant.

A

good

supply

of

nutrients

implies

short

induction

times

since

the

concentration

of

autoinducer

will

quickly

grow

(exponentially)

as

the

population

size

does.

According

to

our

results,

this

fast

growing

condition

decreases

the

precision

of

the

switch

and,

consequently,

promotes

variability

at

the

population

level

(see

Figure

In

addition,

the

full

collective

activation

of

the

system

would

require

a

large

population

size.

On

the

other

hand,

if

the

colony

grows

in

a

poor

nutrient

environment,

the

system

will

have

time

to

reach

a

steady-state

more

easily

and

the

precision

would

increase.

Hence,

the

variability

would

be

diminished,

and

full

activation

would

require

smaller

colony

sizes.

Most

phenotypic

changes

induced

by

the

QS

mechanism

refer

to

bacterial

strategies

for

survival

and/or

colonization.

In

this

context,

our

results

suggest

that

both

the

QS

activation

threshold

and

the

phenotypic

variability

might

depend

on

the

growth

rate

of

the

colony

and,

as

a

consequence,

on

the

environmental

conditions.

This

is

in

agreement

with

recent

studies

that

show

that

the

collective

response

of

a

population

of

cells

depends

not

only

on

the

underlying

genetic

circuit

and

the

environmental

signals,

but

also

on

the

speed

of

variation

of

these

signals

Bacteria,

long

thought

having

a

solitary

existence,

were

found

to

communicate

with

one

another

by

sending

and

receiving

chemical

messages

Their

communication

mechanism

results

in

the

ability

to

synchronize

the

activity

of

the

colony

as

a

whole.

The

latter

leads

to

a

coordinated

behaviour

that

in

some

cases

resembles

that

of

multicellular

organisms,

e.g.

the

so-called

community

effect

during

development

Thus,

by

means

of

the

quorum

sensing

(QS)

mechanism,

cells

produce,

export,

and

import

signalling

molecules

(autoinducer).

As

the

colony

grows,

more

cells

produce

and

export

autoinducer,

leading

to

an

increasing

concentration

of

the

signalling

molecule

in

the

environment

and

in

the

cells.

Upon

reaching

a

concentration

threshold,

the

autoinducer

activates

the

expression

of

QS-controlled

genes

therefore

coordinating

the

cells

in

a

density-dependent

manner.

Importantly,

QS

controls

a

number

of

relevant

phenotypic

changes

in

bacteria

as

for

example

the

virulence

in

S.

aureus

In

addition,

it

has

become

a

model

system

for

studying

the

emergence

of

coordinated

behaviour

in

communicating

cells.

All

in

all,

QS

has

opened

a

research

field

with

promising

technological

applications

as

for

example,

the

environmentally

controlled

invasion

of

cancer

cells

The

QS

systems

in

gram-negative

bacteria

share

a

core

network

architecture.

In

this

regard,

a

characteristic

model

system

is

the

LuxR/LuxI

regulatory

network

in

Vibrio

fischeri

LuxR

protein

is

an

autoinducer-dependent

activator

of

the

lux

operon

that

drives

the

autocatalytic

expression

of

luxR

and

of

the

autoinducer

synthase,

luxI,

together

with

that

of

the

genes

responsible

for

the

production

of

bioluminescence.

The

up-regulation

of

luxI

increases

the

production

of

autoinducer

molecules

that

in

turn

activates

further

gene

expression.

The

resulting

positive

feedback

loop

leads

to

a

bistable

switch-like

behaviour

depending

on

the

concentration

of

the

autoinducer

as

shown

by

in

silico

and

in

vivo

experiments

Such

switch-like

behaviour

has

been

observed

at

the

population

level

by

measuring

the

average

gene

expression

level.

However,

how

individual

cells

behave

remains

puzzling.

In

fact,

as

observed

in

Vibrio

harveyi

Vibrio

fischeri

Pseudomonas

aeruginosa

and

luxI/luxR-GFP

strains

of

E.

coli

the

cellular

response

to

QS

signals

seems

to

be

highly

heterogeneous

at

the

level

of

the

distribution

of

both

the

population

phenotype

and

the

response

times

of

individual

cells..

A

number

of

studies

have

shown

that

noise

plays

an

important

role

in

bistable

systems

Therefore,

the

aforementioned

heterogeneity

may

be

caused

by

the

random

fluctuations

that

unavoidably

affect

cell

regulation

and

signalling.

This

poses

the

intriguing

question

of

how

cells

achieve

a

coordinated

response

in

the

presence

of

noise.

Indeed,

the

QS

mechanism

may

produce

a

robust

and

synchronized

behaviour

at

the

level

of

the

population

both

experimentally

and

theoretically

However,

how

this

behaviour

at

the

collective

level

arises

from

the

stochastic

dynamics

of

individual

cells

is

still

an

open

question.

At

the

end,

in

the

framework

of

QS,

a

collective

response

means

a

precise

information

exchange

in

the

colony.

Consequently,

how

can

a

bacterial

population

estimate

its

number

of

constituents

precisely

if

such

information

is

fuzzy

at

the

single

cell

level?

Herein,

we

shed

light

on

this

problem

and

investigate

how

noise

affects

the

QS

transition

both

at

the

level

of

individual

cells

and

at

the

level

of

the

cell

population..

In

the

context

of

QS

modelling,

most

research

has

focused

on

the

understanding

of

the

intracellular

circuit

i.e.

single

cell

studies,

while

few

of

them

have

considered

an

ensemble

of

communicating

cells

Yet,

so

far

no

study

has

taken

into

account

the

coupling

of

the

signalling

mechanism

at

the

single

cell

and

collective

levels

by

stochastic

means

together

with

realistic

dynamics

of

the

proliferation

process.

In

this

work,

we

model

the

QS

mechanism

by

using

both

deterministic

and

stochastic

approaches

and

taking

into

account

the

key

regulatory

interactions

between

LuxR

and

LuxI,

the

autoinducer

transport,

the

cellular

growth

and

the

division

dynamics.

Our

results

indicate

that

the

cell

response

is

highly

heterogeneous

and

that

noise

in

the

gene

expression

of

luxR

is

the

main

factor

that

determines

this

variability.

Moreover,

we

show

that

the

transition

of

the

QS

switch

near

the

critical

concentration

of

autoinducer

is

very

slow

compared

to

other

characteristic

temporal

scales

of

the

process

and

that,

as

a

consequence,

the

non-stationary

effects

are

crucial

for

setting

a

precise

switch.

As

we

show

further

below,

the

dilution

due

to

cell

growth

and

division

is

a

key

element

required

for

an

in-depth

understanding

of

the

QS

response

dynamics.

In

addition,

we

demonstrate

that

noise,

depending

on

the

cell

density,

can

either

prevent

or

promote

phenotypic

changes

indicating

a

beneficial

role

played

by

stochasticity.

Altogether,

we

find

that

the

precision

of

the

QS

switch

for

determining

the

number

of

cells

in

the

colony

is

highly

dynamic

and

context

dependent,

which

in

turn

favors

adaptability.

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


GENLIB:

an

R

package

for

the

analysis

of

genealogical

data

Background:

Founder

populations

have

an

important

role

in

the

study

of

genetic

diseases.

Access

to

detailed

genealogical

records

is

often

one

of

their

advantages.

These

genealogical

data

provide

unique

information

for

researchers

in

evolutionary

and

population

genetics,

demography

and

genetic

epidemiology.

However,

analyzing

large

genealogical

datasets

requires

specialized

methods

and

software.

The

GENLIB

software

was

developed

to

study

the

large

genealogies

of

the

French

Canadian

population

of

Quebec,

Canada.

These

genealogies

are

accessible

through

the

BALSAC

database,

which

contains

over

million

records

covering

the

whole

province

of

Quebec

over

four

centuries.

Using

this

resource,

extended

pedigrees

of

up

to

generations

can

be

constructed

from

a

sample

of

present-day

individuals.

The

GENLIB

R

package

was

developed

to

facilitate

a

broader

and

more

extensive

use

of

available

genealogical

data

from

founder

populations

across

the

world.

The

package

provides

a

user

friendly

and

flexible

environment

to

analyze

genealogical

data,

allowing

a

more

efficient

and

easier

integration

of

different

types

of

data

and

analytical

methods

and

making

it

ideal

for

further

developments.

Using

GENLIB

simply

requires

a

minimal

knowledge

of

R

and

provides

many

functions

to

manage,

describe

and

analyze

genealogical

data.

Our

description

of

a

Quebec

genealogical

sample

and

our

simulation

study

illustrated

the

use

of

GENLIB

and

further

highlighted

regional

differences

present

in

the

population.

We

also

provided

insight

on

factors

influencing

the

resulting

IBD

sharing

in

founder

populations.

GENLIB

is

an

improvement

over

existing

software

in

that

it

provides

gene-and

segmentdropping

simulations

and

other

new

functionalities

and

in

that

it

can

be

used

within

R,

which

is

a

computing

environment

familiar

to

many

statistical

geneticists.

Hence,

it

is

a

highly

valuable

tool

to

researchers

studying

extended

genealogies.

In

this

paper,

we

presented

GENLIB,

an

R

package

for

the

analysis

of

complex

genealogical

data.

GENLIB

can

handle

large

extended

human

pedigrees,

extended

genealogical

data

from

human

founder

populations

or

extended

animal

pedigrees.

We

were

able

to

read

and

describe

a

fictive

pedigree

with

a

size

over

and

a

depth

of

generations.

Some

memory

limits

may

be

encountered,

depending

on

the

computer

used,

when

trying

to

perform

calculations

(e.g.,

kinship)

for

a

large

number

of

individuals

at

the

same

time

in

complex

genealogies,

but

these

issues

can

easily

be

fixed

by

performing

calculations

in

batches

instead..

GENLIB

is

designed

to

be

easily

accessible

and

used

by

researchers

familiar

or

not

with

genealogical

information.

The

only

requirement

is

a

basic

knowledge

of

the

R

environment.

GENLIB

includes

functions

to

describe

genealogies,

to

compute

different

genealogical

indices

and

to

perform

simulations

based

on

genealogical

relationships.

Given

the

flexibility

of

the

R

environment,

users

can

also

create

their

own

functions

to

further

describe,

summarize

and

present

(e.g.,

graphs)

GENLIB

results..

We

used

genealogies

from

the

Quebec

founder

population

to

illustrate

the

utility

of

GENLIB

to

describe

and

analyze

genealogical

data.

In

addition,

we

performed

simulations

to

track

the

transmission

of

alleles

or

chromosomal

segments

through

the

genealogy.

Allele-

or

segment-dropping

simulations

that

consider

the

complete

genealogical

structure

can

help

to

predict

the

risk

of

sharing

disease

mutations

introduced

by

founders,

or

to

identify

ancestral

sources

of

variation

in

a

trait

of

interest

In

our

simulations,

we

highlighted

the

fact

that

specific

population

characteristics,

such

as

the

number

of

shared

ancestors

and

the

distance

to

these

shared

ancestors,

can

help

discriminate

among

founders

more

or

less

likely

to

have

transmitted

segments

IBD.

The

fact

that

individuals

from

Saguenay

share

more

common

ancestors

that

are

more

distant

on

average

compared

to

Acadians

explains,

in

part,

why,

for

similar

kinship

values,

we

can

observe

quite

different

IBD

segment

distributions.

Genedropping

simulations

can

also

be

used

to

predict

the

risk

of

future

loss

of

genes

contributed

by

the

various

founders..

In

addition,

distributions

of

IBD

probabilities

for

any

individuals

can

be

generated

through

simulations.

We

plan

to

continue

to

improve

existing

functions,

for

example

by

adding

more

flexible

options

for

individual

fitness

in

the

simulations.

We

also

plan

to

extend

the

range

of

functions

available.

Examples

of

planned

additions

include

implementing

more

data

importation

and

graphical

functionalities,

incorporating

information

about

probands

and

ancestors,

such

as

birth

places

and

dates,

implementing

a

function

to

flag

unrelated

components

(subpedigrees)

within

a

kindred,

and

implementing

statistical

tests

to

compare

kinship

and

inbreeding

distributions

between

different

groups.

Another

planned

addition

is

to

include

an

option

in

the

segment-dropping

simulations

to

recover

the

length

of

transmitted

segments

instead

of

only

its

status

(fully

transmitted

or

not).

With

its

flexibility,

GENLIB

provides

an

important

contribution

towards

an

improved

and

optimal

way

to

combine

information

coming

from

genealogies

and

genetic

material.

These

two

sources

of

data

are

complementary

and

using

them

together

could

improve

genetic

data

analysis

in

founder

populations,

for

example

in

the

context

of

estimating

relatedness,

imputing

genomic

data

or

haplotyping

Studying

founder

or

isolated

populations

is

a

major

asset

in

reducing

or

taking

into

account

the

heterogeneity

of

genetic

and

environmental

factors

involved

in

complex

diseases.

Indeed,

potential

advantages

of

founder

populations

include

greater

genetic

and

environmental

homogeneity

and

in

some

instances,

the

availability

of

extensive

genealogical

records

Many

founder

populations

across

the

world

are

currently

studied,

among

others

Iceland

the

Amish

the

Hutterites

the

Mormons

Finland

Newfoundland

the

Sardinians

and

the

French

Canadian

founder

population

of

Quebec

As

the

value

of

genealogical

resources

is

increasingly

recognized

efforts

have

been

made

to

obtain

extended

genealogical

information

and

build

genealogical

databases

for

use

in

genetic

studies.

To

our

knowledge,

there

are

two

available,

freestanding

packages

for

genealogical

analysis,

named

PEDSYS

and

PedHunter

However,

each

lacks

some

functionality

that

we

have

found

useful

in

our

studies

of

the

Quebec

population

and

neither

PEDSYS

nor

PedHunter

can

be

used

within

a

statistical

computing

environment

such

as

R..

The

BALSAC

database

is

an

example

of

a

large

genealogical

database

that

has

proven

very

valuable

for

genetic

and

demographic

research

in

the

Quebec

founder

population

Briefly,

the

arrival

of

French

settlers

in

the

province

of

Quebec,

Canada,

at

the

beginning

of

the

century

followed

by

the

British

Conquest

about

a

century

and

a

half

later

shaped

the

colonization

history

of

Quebec

and

led

to

successive

regional

founder

effects

settlers,

the

French

speaking

population

now

represents

about

of

the

almost

million

inhabitants

of

Quebec

This

fast

population

expansion

and

the

regional

founder

effects

have

shaped

genetic

variation

and

population

structure

in

Quebec.

The

related

demographic

information

can

be

accessed

using

the

BALSAC

database,

created

years

ago,

which

now

includes

over

million

vital

event

records

providing

information

on

million

individuals

These

records

have

been

linked

allowing

for

the

reconstruction

of

ascending

genealogies

from

present-day

individuals

going

back

over

four

centuries.

The

BALSAC

data

access

policy

and

the

procedures

to

request

access

to

the

BALSAC

genealogical

data

can

be

found

on

the

BALSAC

website

Specialized

software

is

required

in

order

to

optimally

exploit

the

full

potential

of

these

well

preserved,

exhaustive

and

detailed

genealogical

data.

The

S-Plus

library

of

functions

GENLIB

was

originally

developed

to

work

with

the

BALSAC

database

to

manage,

describe

and

visualize

genealogies

as

well

as

perform

alleledropping

simulations.

The

GENLIB

S-Plus

library

has

been

used

to

study

the

selective

advantage

to

be

on

an

expanding

wave

front

during

a

range

expansion

the

genetic

contribution

of

non-French

groups

to

the

current

population

population

structure

drug

intolerance

for

an

inherited

disorder

in

multigenerational

pedigree

and

patterns

of

genetic

sharing

relatively

to

expected

sharing

from

genealogical

information

We

have

extended

and

implemented

GENLIB

in

R

to

provide

a

freely

accessible

version

of

the

software

within

a

user-friendly

and

flexible

environment

and

to

allow

a

more

efficient

and

easier

integration

of

different

types

of

data

and

analytical

methods,

also

facilitating

future

developments.

Such

flexibility

is

especially

important

in

the

context

of

integrating

large-scale

genomic

data

and

genealogical

data.

While

other

pedigree

software

exist,

few

are

comprehensive,

free

and

specific

to

extended

genealogical

databases.

For

example,

the

PedHunter

and

PEDSYS

software

include

many

functions

to

describe

and

analyze

genealogical

data

but

do

not

provide

gene-dropping

simulation

functions.

In

this

article,

we

present

most

of

the

functions

in

the

GENLIB

package.

Using

these

functions,

we

perform

a

detailed

description

of

a

large

genealogical

corpus

including

individuals

provided

as

an

example

dataset

in

the

R

package.

Then

we

show

an

example

of

gene-dropping

simulations,

a

procedure

in

which

hypothetical

alleles,

or

chromosomal

segments,

are

assigned

to

ancestors

and

dropped

down

the

whole

genealogical

tree

Overview

GENLIB

was

originally

written

in

the

S

programming

language,

integrating

C++

functions

to

accelerate

and

extend

S

programming.

We

started

with

the

same

C++

functions

in

the

translation

of

GENLIB

into

an

R

package

and

we

extended

both

the

C++

and

R

translation

of

the

S

code.

Interaction

between

R

and

C++

is

well

supported

and

high

quality

R

libraries

are

available

to

help

implement

such

packages.

The

package

is

portable

across

Linux-like

and

Windows

operating

systems,

and

benefits

from

the

advantages

of

the

R

environment,

such

as

being

open-source,

available

online

under

the

GNU

General

Public

License,

and

offering

a

wide

range

of

complementary

functions.

All

code

has

been

tested

using

version

of

R

Version

of

the

GENLIB

package

presented

in

this

paper

includes

over

functions.

GENLIB

is

included

in

the

CRAN

packages

repository

and

is

also

available

on

the

BALSAC

website

By

installing

the

package,

users

also

have

access

to

the

genealogical

data

described

in

this

paper.

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