Simple Decision Forests for Multi-Relational Classification An important task in multi-relational data mining is link-based classification which takes advantage of attributes of links and linked entities, to predict the class label. The relational naive Bayes classifier exploits independence assumptions to achieve scalability. We introduce a weaker independence assumption to the e↵ect that information from di↵erent data tables is independent given the class label. The independence assumption entails a closed-form formula for combining probabilistic predictions based on decision trees learned on di↵erent database tables. Logistic regression learns di↵erent weights for information from di↵erent tables and prunes irrelevant tables. In experiments, learning was very fast with competitive accuracy. Most real-world structured data are stored in the relational format, with di↵erent types of entities and information about their attributes and links between the entities. Relational data classification is the problem of predicting a class label of a target entity given information about features (attributes) of the entity, of the related entities, and of the links. One of the issues that makes link-based classification di cult compared to single-table learning is the large number of di↵erent types of dependencies that a model may have to consider [1, 2] . A principled way to approach the complexity of correlation types is to consider model classes with explicitly stated independence assumptions. The aim is to make a good trade-o↵ between the expressive power of the model on the one hand, and the scalability of learning on the other. Multi-relational Naive Bayes net classifiers (NBCs) are a prominent example of this approach [3, 4, 5] . Naive Bayes Classifiers incorporate two di↵erent kinds of independence assumptions: (1) cross-table independence, roughly that information from di↵erent tables is independent given the target class label, and (2) within-table independence, that descriptive attributes from the same table are independent given the target class label. The approach of this paper is to maintain the first assumption, but to drop the second one. This allows us to capture and exploit complex dependencies among the attributes and the class label within each table.. The Classification Model. The target table is the table that contains the class attribute. Consider the set of tables that can be joined to the target table via a chain of foreign key links; we refer to the corresponding table joins as join tables. We define a cross-table Naive Bayes assumption, according to which di↵erent join tables are independent given the class label, and mathematically derive from it a novel log-linear classification formula. We extend the loglinear classification model to allow di↵erent join tables to contribute more or less strongly to the classification decision, with weights for the relative contributions learned by a logistic regression algorithm. Zero weights can be used to prune irrelevant tables.. Simple Decision Forests. We use a decision tree classifier as a base learner for dependencies within a single table, for the following reasons. (1) Decision tree learners are very fast. (2) There are well-researched methods for learning trees that provide class probability estimates in their leaves [6, 7, 8, 9] . Such trees are sometimes called probability estimation trees; in this paper, we use the simpler term decision tree. (3) Other multi-relational decision tree classifiers are available for comparison. (4) Decision trees easily handle continuous and categorical variables. (5) Decision trees support rule learning, and conversion to logic-based relational models, such as Markov Logic Networks [10] . (6) Decision trees are one of the most popular classifiers. Brydon and Gemino describe applications of decision trees in decision support and business intelligence [11] . An empirical comparison shows a large run-time advantage and a strong predictive performance, that is better than that of previous relational decision tree learners, and of a relational Naive Bayes classifier.. Contributions. The main novel contributions of our work are as follows.. 1. Use of naive Bayes assumption across tables but not within tables. 2. Use of logistic regression to assign weights for the contributions from di↵erent linked tables, including zero weights for pruning. 3. A new method, based on independence assumptions, for upgrading a single-table decision tree classifier for multi-relational classification. 4. An experimental evaluation on five real life databases, demonstrating that our method is very fast with good predictive accuracy.. Paper Organization. We first describe related work, review background material and define our notation. Then we formalize the independence assumptions for multi-relational learning and derive the classification formula. We describe the simple forest induction, use of logistic regression, and classification algorithms. The final section evaluates the classification performance of the di↵erent models on three benchmark datasets. If an object has a large number of links, the information from links contributes many more terms in Equation (5) than the target entity's attributes. For example if Jack has taken 6 courses, the information from attributes of Jack, like ranking, is overwhelmed by information about courses. Normalizing the total log-contribution from each table by its size puts the contribution from tables with di↵erent sizes on the same scale: This uses the average logcontribution from the rows in a table, rather than the sum total of the logcontributions over all rows in the table. Scaling factors have been previously used with log-linear models [10, 38] . A goal of relational classification is to make predictions that utilize information not only about the target table but also about related objects. Decisions trees are a well-established predictive method for propositional single table data. We proposed a new way of upgrading them for relational data classification. The basic idea is to independently learn di↵erent decision trees for di↵erent related tables, and then combine their contributions in a new log-linear model to predict class probabilities. The log-linear model is derived from an explicitly defined cross-table Naive Bayes independence assumption. Features that distinguish this method from other relational decision tree learners include the following. (1) Aggregation functions are not used, which avoids some information loss and allows for e cient learning. (2) Information from all links is considered in classification. (3) Logistic regression is used to weight information from di↵erent tables. Empirical evaluation on three datasets showed very fast runtimes, with improved predictive performance.. A natural variant of our approach, especially for continuous attributes, is to use logistic regression as the base probabilistic classifier, instead of decision trees. This would provide regression weights on attributes/features within each table in addition to the weights for each table we learned in our experiment. A promising direction for future work is to combine our log-linear model with propositionalization techniques. While a search for informative aggregate features is computationally expensive, when it succeeds, the new aggregate features can increase the predictive accuracy (e.g., [39, 12] ). There are several possibilities for a combined hybrid approach. (i) Once good aggregate features are found, they can be treated like other features and used in a decision tree. (ii) A simple decision forest is fast to learn and can establish a strong baseline for evaluating the information gain due to a candidate aggregate feature. (iii) The regression weights can be used to quickly prune uninformative join tables with 0 or small weights, which allows the search for aggregate features to focus on the most relevant link paths. We selectively describe relevant multi-relational classification approaches.. Feature Generation. Most of the work on relational upgrades of single-table classifiers uses a mechanism for relational feature generation. Feature generation is done by using aggregate functions to summarize the information in links [12, 13, 14, 15, 16] . Inductive Logic Programming (ILP) approaches use existentially quantified logical rules [17, 18] . Several recent systems combine both aggregation and logical conditions (e.g., [12, 15] ). Treeliker is a recent propositionalization system that uses monotonicity properties to generate non-redundant conjunctive features, with state-of-the-art e ciency performance [16] . The generated features can be used by any propositional learner. The predictors in our model are not derived features, but the descriptive attributes as defined in the relational database schema. Relational feature generation is by far the most computationally demanding part of such approaches. (For an example, generating 100,000 features on the CiteSeer dataset, which is smaller than the databases we consider in this paper, can take several CPU days [15, Ch.16.1.2] ). Models that use independence assumptions rather than generated features to combine the information from di↵erent tables are orders of magnitude faster to learn, as our experiments confirm. At the end of the paper we discuss how our approach can be extended to support aggregate feature generation.. Relational Decision Trees. To our knowledge, all previous work on relational decision trees has followed the propositionalization/aggregation paradigm (e.g., [12, 19, 14] ). We do not utilize aggregate functions or existential quantification (which may be viewed as an aggregation mechanism). Instead, we consider each link independently and utilize all the information from them. Using aggregation/quantification implies loss of information [4] . FORF (First Order Random Forest) learns an ensemble of di↵erent decision trees, each of which is constructed using a random subset of the schema features [12] . Nodes of the trees are first-order logic queries. First order random forests can be categorized according to di↵erent levels of aggregation. FORF-NA is the simplest one with no aggregation function. FORF-SA uses simple aggregation, and FORF-RA employs refinements of aggregate queries. The final decision is made by averaging the results of trees. In contrast, in our model we learn di↵erent trees using all attributes of each table. Attributes within a table are typically more correlated than attributes from di↵erent tables, so it is advantageous to learn trees from each table's attributes jointly than on random subsets of features. We combine the results using the weights learned by logistic regression rather than plain averaging. TILDE (Top-down induction of first-order logical decision tree) is a prominent relational decision tree within the Inductive Logic Programming framework [19] . The nodes in TILDE trees test first-order conditions. The trees are learned with a divide and conquer algorithm similar to C4.5 [20] . The main di↵erence with our model is that Tilde uses the existential quantifier to build rules. Runtime e ciency is a challenge in Tilde, because it potentially generates many rules to find the best ones.. MRDT (Multi Relational Decision Tree) constructs the decision tree by using selection graphs as the nodes of the tree [21] . A selection graph is a directed graph which imposes a set of constraints on incorporating information from several tables. MRDT use the existential quantifier to aggregate information from di↵erent links. Guo et al in [22] speed up the MRDT algorithm by using id propagation to implement a virtual join operation that avoids the cost of physical joins.. Independence Assumptions. There are various proposals to apply Naive Bayes (NB) Assumptions and logistic regression (LR) to relational data. Logistic regression can be viewed as a discriminative version of the generative Naive Bayes Classifier model [23] . For single-table classification, the advantages of logistic regression over simple Naive Bayes Classifier have been studied in detail [23] , and similar results have been reported for single-relation classification [24] . Popescul and Unger combine logistic regression with an expressive feature generation language based on SQL queries [15] .. Much of the work on relational Naive Bayes Classifiers combines firstorder features defined by logical rules [25, 26, 17] . The nFOIL system utilizes the Naive Bayes assumption to learn existentially quantified first-order features. Neville et al. [3] investigate di↵erent functions for aggregating the influence of linked objects. Chen et al. discuss the pros and cons of using aggregation vs. independence assumptions, and argue that for a relational Naive Bayes Classifier, the use of aggregate function loses statistical information and is not necessary [4] . The multi-relational Naive Bayes Classifier assumes that all attributes in a database are independent, including attributes from the same table [4] . We use a weaker assumption by learning decision trees for attributes within the tables.. CrossMine [18] is an e cient ILP-style rule learner algorithm. It uses tuple ID propagation to virtually join tables, and randomly selects instances to overcome the skewness of datasets.. Structured logistic regression treats the influence on the class label of the target table and that of linked tables as independent [24] . Two independent logistic regressions are carried out, one on the target table and the other on the set of linked tables. Information from links is summarized using aggregate functions. The product of the results determines the class label. In our method we use a stronger assumption that links are independent of each other, and learn a model for each link separately. The predictors in our model are probabilities predicted based on local information rather than aggregates as in structured logistic regression.. The Heterogeneous Naive Bayes classifier [5] considers join tables conditionally independent, and combines the posterior results from the table classifiers applied separately to linked and target tables by a naive Bayes assumption. A key di↵erence is the classification model: We formally derive our classification formula, which normalizes the posterior probability from each linked table by the class prior. Also, we use decision trees, and we employ logistic regression to combine the contributions of di↵erent linked tables.. Ensemble Classifiers. Our model has some resemblance to ensemble/committee classifiers in that we combine the probabilistic outputs of di↵erent classifiers. The main di↵erences are as follows.. 1. Most ensemble methods grow the set of classifiers, e.g., a decision forest, dynamically in the course of learning. In a simple decision forest, the set of decision trees is fixed by the database schema, since each tree represents a classifier for a given relational pathway (chain of foreign key links). 2. In many ensemble models, gating functions are learned that assign di↵erent classifiers to di↵erent parts of the input feature space. In our simple decision forest, the partition of the input feature space is predetermined by the database schema. 3. There are potentially many methods for combining the predictions of a classifier ensemble [27, 28] . Our cross-table Naive Bayes independence assumption entails a log-linear combining method.. Graphical Models. Ideas from directed graphical models are used by Probabilistic Relational Models [29] , which learn a Bayesian network model of the data distribution, and use aggregate functions to specify conditional probability tables.. Unlike directed graphical models which impose an acyclicity constraint, undirected ones do not have a cyclicity problem and are widely used for LBC [30, 10, 31] . Two major formalisms are relational conditional Markov random fields [30] and Markov Logic Networks (MLNs) [10] . Relational Markov random fields are a general log-linear model that does not use aggregate functions nor independence assumptions [10] . The classification formula we derive from the cross-table Naive Bayes assumption is also a log-linear model, which shows that our model is a subclass of relational conditional random fields. This observation provides a probabilistic interpretation of our classification formulas in terms of a general graphical model. While compared to general Markov models, the expressive power of our log-linear model is restricted by independence assumptions, the trade-o↵ for the expressive power of more general log-linear models is higher complexity in learning; various studies have shown that scaleable learning is a major challenge for Markov model learning in the multi-relational setting [32, 33, 31] .. In practice one often needs to perform collective classification: predict the class label of several interrelated entities simultaneously. While collective classification has received much attention [30, 34] , our theoretical framework for multi-relational classification formulas is already quite rich, so our empirical evaluation focuses only on individual classification and leaves applications to collective classification for future work. A principled approach to collective classification is to convert decision forests to Markov Logic Networks, as described in Section 3.2, and then apply MLN techniques for collective classification [10] .

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Modeling NASA swarm-based systems: using agent-oriented software engineering and formal methods The need to collect new data and perform new science is causing the complexity of NASA missions to continually increase. This complexity needs to be controlled via new technological advancements and balanced with a reduction in mission and operation costs. Planned and hypothesized missions involve self-management, biologicalinspiration based on swarms, and autonomous operation as a means of achieving these goals. We consider a tailored software engineering approach to developing such systems based on agent-oriented software engineering and formal methods. NASA is investigating new concepts for future space exploration to conduct new science and reduce costs. Potential new mission concepts include the use of multiple spacecraft, unmanned autonomous vehicles (UAVs) and armies of robots, operating like swarms in nature [3] , to explore harsh remote environments. Such missions will be necessarily unmanned and highly autonomous, exhibiting the properties of autonomic systems, being self-protecting, selfhealing, self-configuring, and self-optimizing [16] .. Swarms [1, 5] consist of a large number of simple agents that have local interactions (between each other and the environment). There is no central controller directing the swarm and no one agent has a global view; they are self-organizing based on the emergent behaviors of the simple interactions.. This kind of system has many advantages since complex behaviors emerge from the definition of simple individual behaviors, thus reducing the design effort. Its unpredictability, however, represents a problem since unexpected behaviors may cause the failure of a mission.. Formal methods can provide guidance in determining possible emergent behaviors that must be considered. They may be used to propose certain properties that might or might not hold, or certain emergent behaviors that may arise [14] . Verifying emergent behavior has been little addressed by the formal methods community, though there has been work by computer scientists on analyzing biological systems [7, 15] .. Complexity is a particular problem in developing such swarm-based mission. To address this, we have been investigating an approach based on formal methods and AgentOriented Software Engineering (AOSE). A promising means of achieving ambitious goals for conducting new science in future NASA missions is based on the use of biological inspiration from swarms in nature. When tackling any system development, and particularly something as complex and ambitious as the NASA ANTS concept mission, complexity can quickly become unmanageable, negating the value of new technologies, such as self-management. Our experience of modeling swarm-based systems has been that a combination of UML-based tailored models and formal methods augurs much promise. While promising results have been achieved to date, we are continuing to improve the integration of these approaches and to improve the support tools that we have been developing.

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Computing optimal strategies to commit to in extensive-form games Computing optimal strategies to commit to in general normal-form or Bayesian games is a topic that has recently been gaining attention, in part due to the application of such algorithms in various security and law enforcement scenarios. In this paper, we extend this line of work to the more general case of commitment in extensiveform games. We show that in some cases, the optimal strategy can be computed in polynomial time; in others, computing it is NPhard. Game theory defines solution concepts for strategic situations, in which multiple self-interested agents interact in the same environment. Perhaps the best-known solution concept is that of Nash equilibrium [13] . A Nash equilibrium prescribes a strategy for every player, in such a way that no individual player has an incentive to change her strategy. If strategies are allowed to be mixed-a mixed strategy is a probability distribution over pure strategiesthen it is known that every finite game has at least one Nash equilibrium. Some games have more than one equilibrium, leading to the equilibrium selection problem.. Perhaps the most basic representation of a game is the normal form. In the normal-form representation, every player's pure strategies are explicitly listed, and for every combination of pure strategies, every player's utility is explicitly listed.. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. EC '10, June 7-11, 2010 , Cambridge, Massachusetts, USA. Copyright 2010 ACM 978-1-60558-822-3/10/06 ...$10.00.. The problem of computing Nash equilibria of a normal-form game has received a large amount of attention in recent years. Finding a Nash equilibrium is PPAD-complete [5, 1] . Finding an optimal equilibrium (for just about any reasonable definition of "optimal"-for instance, maximizing the sum of the players' utilities) is NP-hard [6, 3] ; moreover, it is not even possible to find an equilibrium that is approximately optimal in polynomial time, unless P=NP [3] . This holds even for two-player games.. However, one can argue about whether Nash equilibrium is always the right solution concept. In some settings, one player can credibly commit to a strategy, and communicate this to the other player, before the other player can make a decision. To see how this can affect the outcome of a game, consider the following game (which is often used as an example of this). Figure 1 . For the case where the players move simultaneously (no ability to commit), the unique Nash equilibrium is (U, L): U strictly dominates D, so that the game is solvable by iterated strict dominance. So, player 1 (the row player) receives utility 1. However, now suppose that player 1 has the ability to commit. Then, she is better off committing to play D, which will incentivize player 2 to play R, resulting in a utility of 2 for player 1. The situation gets even better for player 1 if she can commit to a mixed strategy: in this case, she can commit to the mixed strategy (.5 − ǫ, .5 + ǫ), which still incentivizes player 2 to play R, but now player 1 receives an expected utility of 2.5 − ǫ. To ensure the existence of optimal strategies, we assume (as is commonly done and for which good justifications can be given [2, 14] ) that player 2 breaks ties in player 1's favor, so that the optimal strategy for player 1 to commit to is (.5, .5), resulting in a utility of 2.5 A summary of our results appears in Figure 8 , in the form of a decision tree. (This is the only tree in this paper that does not correspond to a game.). No Chance Perfect Info.

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On the impact of far-away interference on evaluations of wireless multihop networks It is common practice in wireless multihop network evaluations to ignore interfering signals below a certain signal strength threshold. This paper investigates the thesis that this produces highly inaccurate evaluations in many cases. We start by defining a bounded version of the physical interference model, in which interference generated by transmitters located beyond a certain distance s from a receiver is ignored. We then derive a lower bound on neglected interference and show that it is approximately two orders of magnitude greater than the noise floor for typical parameter values and a surprisingly small number of nodes. We next evaluate the effect of neglected interference through extensive simulations done with a widely-used packet-level simulator (GTNetS), considering 802.11 MAC with both CBR and TCP traffic in networks of varying size and topology. The results of these simulations show very large evaluation errors when neglecting far-away interference: errors in evaluating aggregate throughput when using the default interference model reached up to 210% with 100 nodes, and errors in individual flow throughputs were far greater. In wireless network evaluations, interference has been traditionally modeled as a binary, pair-wise phenomenon. By binary, we mean that interference either totally eliminates the ability to communicate or is non-existent, and by pairwise, we mean that interference is considered only between pairs of nodes or links. In reality, whether a communication is successful depends on whether signal power exceeds the sum of the interference powers plus noise by a threshold that is a property of the physical layer design. This SINR (signal to interference plus noise ratio)-based model is known as the physical interference model [4] . The complexity here is that interference is neither binary nor pairwise; aggregated interference from all communicating nodes must be considered to decide whether a communication is successful.. While physical interference models that account for all possible transmissions throughout the network are the most accurate, such models are very complex. As a result, several approximations are made in packet-level network simulators [12, 14, 17 ] to prevent simulation times from being slowed down by large factors. All major simulators (ns2, GTNetS, and Glomosim/QualNet) ignore individual interference contributions below a certain threshold (this can be implemented in different ways but can be thought of as an "interference range" beyond which interference is ignored). Inside the considered interference range, the simulators either accumulate all interference (Glomosim/QualNet) or consider only single interferers for a given transmission (ns2 and GTNetS). One of the main goals of this paper is to study the effects of these approximate interference models and to evaluate how much slowdown in simulation execution can be expected if more accurate models are used.. First, we concentrate on analytically evaluating the impact of the limited interference range assumption. We prove that, if the interference range is set to be a constant (independent of the number of nodes n), the neglected interference is large enough to cause significant errors in the accuracy of the model. This corresponds to the standard assumption in the literature and in all network simulators we are aware of. For a constant transmitter density, we also prove that, if the interference range is an arbitrary unbounded increasing function of n, the neglected interference vanishes as n → ∞, meaning that the approximate interference model approaches the accuracy of the true interference model asymptotically.. Next, we present simulation results from a packet-level simulator (GTNetS), which we modified to accumulate interference inside the interference range, while keeping the exact range as a tunable parameter. This allowed us both to validate our analytical results and to investigate trade-offs between simulation accuracy and simulation time by varying the interference range. The results demonstrate very large errors in evaluation of both packet delivery time and throughput for the commonly used interference models under several scenarios with 802.11 MAC and both CBR and TCP flows. Errors are considerable for CBR flows and even larger for TCP flows, reaching 200% in some cases. In terms of simulation time, using the most accurate model does have a significant negative impact. There is a roughly two orders of magnitude increase in simulation time for CBR flows and a roughly one order of magnitude increase for TCP flows. The main contribution of this paper is an in-depth investigation of the accuracy of approximate, bounded interference models in estimating relevant performance metrics of wireless multihop networks, and of the tradeoff between simulation accuracy and running time. Summarizing, our results suggest that ignoring far-away interference leads to highly inaccurate simulation results, but the price to pay for this accuracy is a one-two orders of magnitude increase in simulation running time.. Overall, the issue of how to address the fundamental tradeoff between simulation accuracy and running time is the main problem left open by this paper. We believe optimally addressing this tradeoff is a very difficult task, since it depends on the specific network setting at hand, the type of transport-layer traffic, and so on. A promising research direction is deriving analytical/stastical methods to accurately estimate aggregate interference generated by far-away interferers, so that relatively accurate estimates of the SINR values at single receivers can be obtained without actually computing each far-away interference signal level. An interesting first step in this direction is [13] , where the authors introduce a Markov-chain based interference model which is fed by testbed measurement. While the idea of measurement driven interference model is interesting, the approach of [13] considers only 1-hop flows, and is based on Markov chains with a number of states exponential in the number of nodes (and is thus not scalable). Hence, further work is needed to derive scalable approaches that account also for multi-hop flows. In this section, we formally prove that, under some conditions on transmitter deployment, the aggregate far-away interference converges to 0 as n → ∞. Due to lack of space, the results are presented without proofs, which are reported in the full version of the paper [1] . The results are valid under the two following assumptions: a1. Radio signal propagation obeys the log-distance path loss model, with path loss exponent α > 2; and, a2. All nodes use the same transmit power P , which is such that the resulting transmission range r (in absence of interference) is at least 1. Theorem 1. Assume a constant density of transmitter nodes, and let u be an arbitrary node in the network which is at the receiver end of a communication link; the interference generated by nodes located at distance d > s from u, where s ≥ 2r is the interference range, is upper bounded by. where ρ is an upper bound to the transmitter density per unit area.. If the interference range s is chosen in such a way that s = f (n), where f (n) is an arbitrary unbounded increasing function of n, then the total interference at an arbitrary receiver node u due to nodes located at distance greater than s from u converges to 0 as n → ∞.. In [1] , it is shown that condition s = f (n) is not only sufficient, but also necessary for asymptotic accuracy of the BPI model. In particular, it is shown that if s is set to an arbitrary constant, aggregate far-away interference is order of magnitude larger than the noise floor (e.g., at least −55dBm for typical 802.11a/b/g parameter settings). Furthermore, it is shown that similar results hold when nodes are distributed uniformly at random in the unit square.

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Towards automatic feature vector optimization for multimedia applications We systematically evaluate a recently proposed method for unsupervised discrimination power analysis for feature selection and optimization in multimedia applications. A series of experiments using real and synthetic benchmark data is conducted, the results of which indicate the suitability of the method for unsupervised feature selection and optimization. We present an approach for generating synthetic feature spaces of varying discrimination power, modeling main characteristics from real world feature vector extractors. A simple, yet powerful visualization is used to communicate the results of the automatic analysis to the user. We evaluated an automatic, unsupervised method for estimation of discrimination power in competing FV spaces. Systematic experiments on real and synthetic benchmark data showed that the unsupervised estimator based on distributions of distances in compressed FV space is able to closely resemble supervised benchmarking analysis. The method was shown to be robust w.r.t. main parameter settings. It is proposed as a valuable tool supporting and complementing the data-dependent and expensive supervised benchmarking approach to FV selection and optimization in multimedia applications.. Future work involves refining the method by including more sophisticated statistical distribution tests, experimenting with additional estimator functions, and evaluating the approach on additional benchmark data.

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A Testbed for MANETs: Implementation, Experiences and Learned Lessons Abstract-In this paper, we present the implementation, experiences and lessons learned of our tesbed for Ad-hoc networks and Mobile Ad hoc Networks (MANETs). We used OLSR protocol for real experimental evaluation. We investigate the effect of mobility and topology changing in the throughput of a MANET. We study the impact of best-effort traffic for Mesh Topology and Linear Topology. In this work, we consider eight experimental models and we assess the performance of our testbed in terms of throughput, round trip time and packet loss. We found that some of the OLSR's problems can be solved, for instance the routing loop, but this protocol still has the self-interference problem. Also, there is an intricate interdependence between MAC layer and routing layer. We carried out the experiments considering stationary nodes of an Ad-hoc network and the node mobility of MANETs. We found that throughput of TCP was improved by reducing Link Quality Window Size (LQWS). For TCP data flow, we got better results when the LQWS value was 10. Moreover, we found that the node join and leave operations increase the packet loss. The OLSR protocol has a good performance when the source node is moving. However, the performance is not good when the relay nodes are moving. In this paper, we presented the implementation, experiences and lessons learned of our tesbed for Ad-hoc networks and MANETs. We used OLSR protocol for real experimental evaluation. We considered three parameters for performance evaluation: throughput, RTT and packet loss. In our experiments, we considered eight models: STA, MV1, MV2, MV3, MV4, MV5, MV6, and MV7.. From the experiments, we found the following results. We proved that while some of the OLSR's problems can be solved, for instance the routing loop, this protocol still have the self-in- terference problem. There is an intricate interdependence between MAC layer and routing layer, which can lead the experimenter to misunderstand the results of the experiments. For example, the horizon is not caused only by IEEE 802.11 Distributed Coordination Function (DCF), but also by the routing protocol. We carried out the experiments considering stationary nodes of an ad-hoc network and the node mobility of MANETs. We found that throughput of TCP were improved by reducing Link Quality Window Size (LQWS), but there were packet loss because of experimental environment and traffic interference. For TCP data flow, we got better results when the LQWS value was 10. Moreover, we found that the node join and leave operations increase the packet loss. The OLSR protocol has a good performance when the source node is moving. However, the performance is not good when the relay nodes are moving. There are some oscillations in MV3, MV5 and MV6 models. This is because of node movement.. Our experimental results will shed light for the real implementation of Ad-hoc and MANETs.. The experiments where performed using a single flow through the network. In the future, we would like to consider the effect of multiple flows on the routing and increase the number of nodes. Moreover, we would like to extend our testbed. In [4] , the authors analyze the performance of an outdoor ad-hoc network, but their study is limited to reactive protocols such as Ad hoc On Demand Distance Vector (AODV) and Dynamic Source Routing (DSR). The authors of [5] , performs outdoor experiments of non standard proactive protocols. Other ad-hoc experiments are limited to identify MAC problems, by providing insights on the one-hop MAC dynamics as shown in [6] .. The closest work to ours is that in [7] . However, the authors did not care about the routing protocol. In [8] , the disadvantage of using hysteresis routing metric is presented through simulation and indoor measurements. Our experiments are concerned with the interaction of transport protocols and routing protocol, for instance OLSR. Furthermore, we compare the performance of the testbed for eight scenarios.. In [9] , the authors present an experimental comparison of OLSR using the standard hysteresis routing metric and the Expected Transmission Count (ETX) metric in a 7 7 grid of closely spaced Wi-Fi nodes to obtain more realistic results. The throughput results are similar to our previous work and are effected by hop distance [10] .

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An analytic solution approach for the economic order quantity model with Weibull ameliorating items While deterioration models consider the gradual reduction in quality and quantity of products over time, amelioration models assume the opposite. This paper is based on an earlier work by Hwang for finding an optimal economic order quantity solution for items subject to amelioration in a Weibull distribution. Hwang solved the problem with a graphical procedure. In this paper, a rigorous analytical solution approach is derived for cases with different shape parameters. A detailed numerical example is also presented to illustrate the optimality of the derived solution. In view of the significant number of deterioration phenomena of inventory items in practice, much research has been performed to develop various deterioration models. Inventory models were proposed to deal with deteriorating items where the amount of stock decreases gradually over time [2] [3] [4] [5] [6] [7] [8] . A contrasting phenomenon, amelioration, has recently been proposed and studied [1, 9] . Without considering the influence of demand, the definition for ameliorating items is that the amount of stock increases gradually during their holding period. Amelioration phenomena do exist in industries such as farming, fisheries, and poultry farming. Fast growing livestock such as ducks, pigs, broiler in poultry farms, hybrid fish in ponds and the culture of vegetables, fruits on farms are some examples. The phenomenon of amelioration is the opposite of deterioration and the modeling of it deserves an in-depth study.. Since a Weibull distribution can be used to effectively describe the life-span of a product by varying parameter values, it has been applied to the modeling of the product life cycle for inventory management in recent years. Jalan et al. In Hwang's [1] EOQ model, instead of deriving an exact analytic solution, he used a graphical procedure of Gupta [11] to estimate the optimal cycle time. Contrary to his approach, an analytical framework is established in this paper to derive an optimal solution for the EOQ model. Finally, the same numerical example from Hwang [1] is adopted to illustrate the correctness of the proposed approach and to show the error in Hwang's solution.

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The SROV program for data analysis and regression model identification A new stepwise regression program (SROV) for the construction of optimal (stable and of highest possible accuracy) regression models comprised of linear combination of independent variables and their non-linear functions is described. The program uses for regression QR decomposition based on Gram Á/Schmidth orthogonalization, which is highly resilient to numerical error propagation. Variables are selected to enter the regression model according to their level of correlation with the dependent variable and they are removed from further consideration when their residual information gets below the noise level. The use of this program is demonstrated in two examples. In both examples the program identifies an optimal and stable regression model and several sub-optimal models. The existence of sub-optimal models provides additional insight regarding the relationships that exist between the explanatory variables, between the explanatory variables and the dependent variable and information on model related uncertainties caused by sample size and experimental error. # Precise analysis, modeling and regression of experimental data are key requirements for realistic and accurate modeling and simulation of physical phenomena. As model based simulation, design, control and optimization of chemical processes become increasingly more widespread, the requirements for more precise regression models for representing input data (e.g. physical and transport properties, phase equilibrium) become increasingly more severe.. Regression models can be partially theory based or completely empirical. In both cases, it is not known apriori how many explanatory variables (independent variables, and/or their functions) and parameters should be included in the model for obtaining an optimal regression model. An insufficient number of explanatory variables result in an inaccurate model, which is characterized by a large variance. Some independent variables, which may have critical effects on the dependent variable under certain circumstances, may be left out of the correlation. On the other hand, including non-influential variables and/or variables which are collinear, renders an unstable model. The instability is characterized by typical ill effects, whereby adding or removing an experimental point from the data set may drastically change the parameter values. Also, the derivatives of the dependent variable are not represented correctly and extrapolation outside the region, where the measurements were taken, yields absurd results even for a small range of extrapolation. Shacham and Brauner (1997) , Brauner and Shacham (1998a,b) provide several examples where regression models published in the chemical engineering literature are grossly inaccurate and/or unstable.. Over the years, many procedures have been introduced for selection of the optimal model in linear regression (for detailed reviews, see for example Daniel & Wood, 1980; Neter, Wasserman & Kutner, 1990) . Wagner (1973) and Setzmann and Wagner (1989) have applied such procedures extensively to models of physicochemical and thermodynamic properties. In those procedures, various statistical tests, such as the F -test, t-test, R p 2 -criterion, C p -criterion, PRESS p -criterion, residual plot and other diagnostic plots are used to compare between different models and to decide which of the explanatory variables should be included or removed from the model in order to arrive at the 'best' subset of explanatory variables. (For details of the various statistical tests used, see for example, pp. 433 Á/470 in Neter et al., 1990) . Those tests may be applied while considering all possible combinations of the explanatory variables or in the framework of a stepwise regression procedure (such as forward stepwise regression, backward elimination, ridge regression, see for example Marquardt & Snee, 1975) .. Stepwise regression programs that use statistical tests do not take advantage of the information concerning the signal to noise ratio in the data. This information is usually available when working with experimental data, but it is less common in observational data that statisticians usually work with. Shacham and Brauner (1999a,b) have described the principles and the algorithm of a new stepwise regression procedure with orthogonal variables (SROV), which uses indicators based on 'signal-to-noise' ratio. They have also demonstrated some of the potential applications and the advantages of the use of this procedure (Shacham & Brauner, 1999a,b; . Experience in using the SROV algorithm for solving a wide range of problems has identified some necessary modifications of the algorithm.. In this paper the modified and extended SROV algorithm is presented. The algorithm has also been implemented as a MATLAB 1 program and it has become available on the Internet for downloading. The use of this new program is demonstrated in the paper.. In the next section two motivating examples that demonstrate the need for using stepwise regression, are presented. In Section 3, the revised and extended SROV algorithm is described while Section 4 includes details of the SROV program implementation and use. In Section 5, the motivating examples are solved using SROV. Finally some conclusions regarding the benefits in using SROV are presented.. The computations reported in the paper were carried out with MATLAB 5.3 and POLYMATH 2 5.1 The use of the SROV program for solving regression and data analysis problems involving linear, polynomial and quadratic models has been demonstrated. It has been shown that if the components of the model (the explanatory variables) cannot be determined a priory, using a stepwise regression procedure (such as SROV) is a must. Including non-influential or collinear explanatory variables in the model may lead to an unstable model where, for example, there is uncertainty regarding the direction of the change of the dependent variable due to changes in some of the explanatory variables.. In the examples presented, the SROV has identified the optimal model (a stable model with minimal variance) and identified also several sub-optimal models. The sub-optimal models help to discriminate between non-influential and collinear variables. Noninfluential variables do not show up in any of the suboptimal models and they can be safely removed from any further consideration. Variables that show up in some sub-optimal models and do not show up in others, are associated with a certain level of colinearity. In such cases and with a limited sample size, the distinction between the optimal and sub-optimal models may be sample dependent. A regression model, which seems optimal for one particular sample may not be the optimal for a different sample of the same accuracy level, of the same or a different size. Additional user considerations may dictate replacement of the optimal model by one of the sub-optimal models.. It can be concluded that in addition to providing an optimal and stable solution, the SROV program provides also insight regarding the relationships that exist between the explanatory variables, between the explanatory variables and the dependent variable and information on model related uncertainties caused by sample size and experimental errors.

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


Leader Election in Oriented Star Graphs Leader election in a network plays an important role in the area of distributed algorithm design. Structural properties of the network as well as presence of direction on the edges of the network greatly affects the complexity of the leader election problem which is primarily measure by the message complexity of the protocol. Our purpose in the present paper is to adapt the existing distributed match making concepts to design a linear time leader election algorithm for star graphs. Star graphs have been extensively studied as attractive alternative for the well known hypercubes for network design. Linear election algorithms for oriented hypercubes is known; no such algorithm exist for oriented star graphs. Leader election in a network is one of the most important problems in the area of distributed algorithm design. Consider any network of N nodes; a leader node is defined to be any node of the network unambiguously identified by some characteristics (unique from all other nodes). A leader election process is defined to be a uniform algorithm (code) executed at each node of the network; at the end of the algorithm execution, exactly one node is elected the leader and all other nodes are in the non-leader state. Gallager et. al. [1] have developed a leader election algorithm for arbitrary networks whose message complexity is O(N log N + E) where N is the number of nodes and E is the number of edges in the network. Santoro in [2] has studied how the knowledge of topology of the network and the orientation of the links in the network affect the message complexity of leader election algorithms in networks. Subsequently, many authors have studied leader election algorithms for various kinds of networks with or without link orientations. Existence of orientation of the links have been shown not to improve the message complexity of leader election for either rings or tori [3] , while that helps for cliques; the lower bound on message complexity of leader election in oriented cliques is O(N ) [4] and that for unoriented cliques is Ω(N log N ) [5] . Authors in [4] have considered complete networks with a sense of direction.. Authors in [6, 7] has developed leader election for oriented hypercubes whose message complexity is linear in the number of nodes. Research in leader election in both unoriented and oriented graphs have continued [8, 9, 10] .. Another very efficient interconnection topology, called star graphs [11, 12] , has been extensively investigated in the literature [13, 14] since these graphs seem to enjoy most of the desirable properties of the hypercubes at considerably less cost; they accommodate more nodes with less interconnection hardware and less communication delay. In this paper, our purpose is to propose an election algorithm for the oriented star graphs that uses O(N ) messages. As far as we know, no leader election algorithm exists for these star graphs although the straightforward application of existing algorithms would give a leader election algorithm for unoriented star graphs with O(N log N ) message complexity. It is not clear if one can design a linear election algorithm for unoriented stars. We have proposed an election algorithm in oriented star graph networks that has a message complexity linear in the number of nodes in the network. It would be interesting to study election algorithms in unoriented star graphs and to find if orientation of links helps in star graphs helps or we can come up with a linear election algorithm in star graphs as was reported for hypercubes in [9] .

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An approach for QoS-aware service composition based on genetic algorithms Web services are rapidly changing the landscape of software engineering. One of the most interesting challenges introduced by web services is represented by Quality Of Service (QoS)-aware composition and late-binding. This allows to bind, at run-time, a service-oriented system with a set of services that, among those providing the required features, meet some non-functional constraints, and optimize criteria such as the overall cost or response time. In other words, QoS-aware composition can be modeled as an optimization problem.We propose to adopt Genetic Algorithms to this aim. Genetic Algorithms, while being slower than integer programming, represent a more scalable choice, and are more suitable to handle generic QoS attributes. The paper describes our approach and its applicability, advantages and weaknesses, discussing results of some numerical simulations. The rapid diffusion of web services and of service-oriented systems constitutes an important step towards a radical change in the software development process. ServiceOriented software engineering represents a natural evolution of Component-Based Software Engineering (CBSE). In Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. CBSE, a component integrator searches for reusable components and then physically integrates them into a new system using some glue code. A web service exports a piece of functionality on a network server. Web services are used by (remotely) invoking service operations. Thus, there is no need to integrate the service with the application under development. Service interface publication, service discovery and service invocation are performed using XML-based standards, known as WSDL, UDDI and SOAP [16] . In particular, SOAP is a XML-encoded RPC protocol built over well-known TCP/IP application protocols such as HTTP or SMTP. A service oriented system is therefore composed of some service invocations, orchestrated using glue code [14] or some specific web service orchestration language (e.g., BPEL4WS [2] or WSCI [15] ).. One of the biggest promises of service-oriented systems is the use of late-binding mechanisms. Given a specific feature needed in a service orchestration (this feature will be hereby referred to as an abstract service), several services (referred to as concrete services) realizing such a feature may be available. In Figure 1 , circles represent an orchestration of abstract services, while the corresponding concrete services are represented as rectangles.. All concrete services corresponding to an abstract service are functionally equivalent and thus are replaceable by each other. The choice between them can be dictated by nonfunctional properties, referred to as Quality of Service (QoS) attributes. One may decide to choose the cheapest service, the fastest, or maybe a compromise between the two. According to Std. ISO 8402 [11] and ITU [12] , QoS may be defined in terms of attributes such as price, response time, availability, reputation (further details can be found in Cardoso's PhD thesis [3] ). Moreover, it may be possible to have some domain-specific QoS attributes (e.g., a temperature service could have QoS attributes such as precision or refresh frequency). Finally, an user may specify constraints on the values of some attributes (e.g., the price cannot be greater than a given value), which could influence the choice. On the other hand, the service provider can estimate ranges for the QoS attribute values as part of the contract with potential users (i.e., the Service Level Agreement (SLA)).. As it will be detailed in Section 3, given an orchestration, a relevant problem is to determine the set of concretizations (i.e., bindings between abstract and concrete services) that satisfy the QoS constraints imposed by the SLA, and optimize some fitness criteria chosen by the service integra- tor (e.g., minimize the cost). Finding the solution of such a problem, known as QoS-aware composition, is NP-hard. Some approaches, mostly based on linear integer programming, have been proposed in literature (e.g., the approach of Zeng et al. [17] ).. It is particularly important for the QoS aware composition to be fast. Especially for interactive systems, long delays may be unacceptable. For example, the user of a booking ticket system might not want to wait for a long time while the system searches for candidate services offering flight tickets with the lowest booking fare. Gaining a few cents after several minutes of waiting may make the user disappointed.. A fast composition is also required to replan a service composition during the execution, because the actual QoS deviates from the estimated one and this could cause constraint violation, or simply because some services might not be available. In this case the composition time influences the overall service response time, thus it should be kept as low as possible.. This paper proposes to tackle the QoS-aware composition problem using Genetic Algorithms (GAs). Advantages and weaknesses of GAs will be compared with those of linear integer programming, that is the most widely adopted approach.. The remainder of this paper is organized as follows. After a review of the literature in Section 2, Section 3 details the proposed approach. In particular, after the QoS composition rules are shown, the evolutionary approach for QoS-aware composition is described. Section 4 reports and discusses results obtained in the simulations. Finally, Section 5 concludes. This paper proposed a GA-based approach for QoS-aware service composition, i.e., to determine a set of concrete services to be bound to abstract services contained in a orchestration to meet a set of constraints and to optimize a fitness criterion on QoS attributes. Compared with linear Integer Programming, the most widely adopted approached, GA permits to deal with QoS attributes having non-linear aggregation functions. Also, GA is able to scale-up when the number of concretizations increases. Finally, to deal with constraints, it is possible to adopt a fitness function with both static or dynamic penalty, even if we did not experience a significant difference, at least for our case studies and calibration mechanisms.. Future work will aim to apply the proposed approach to some large-scale service-oriented system, and to perform a thorough comparison of GA with other non-linear technique, such as non-linear integer programming. Multi-objective fitness functions will also be considered as an alternative to single-objective fitness functions where factors are aggregated using a weighted sum. Dynamic service discovery and QoS-aware service composition offer interesting applications of constraint handling methods and search strategies from operational research or artificial intelligence. In fact, in service-oriented architectures, constraint sets are used to express functional and non-functional properties of the services to search for or to monitor, and the service may be selected according to some QoS optimum criteria ( [4] , [5] , [13] ).. More challenging is the case of composite services whose structures are described by abstract processes, i.e, processes containing abstract services, where the aim is to find the best combination of concrete services, from the QoS point of view, at run time. This combination may change during execution due to the dynamic nature of the web services environment, therefore one important requirement is that a feasible, SLA-compliant solution should be found in a short time. Integer programming (IP) solutions to this problem have been proposed in some recent papers ( [1] , [17] ). Both works assume linearity of the constraints and of the objective function, whose expression is similar to that described in Sub-section 3.4. In fact, Zeng et al. [17] essentially focus on the cost, response time, availability and reliability attributes, where logarithmic reductions are used for the multiplicative aggregation functions, and the model is claimed to be extensible with respect to other similarly behaving attributes. The need to deal with more general constraint criteria, such as service dependencies or user preferences, is strengthened in the work of Aggarwal et al. [1] . However, they do not explain how the optimization problem could be solved. In this paper, we advocate the use of GAs instead, as any kind of constraint could be handled, and provide some empirical data to assess the performance of our method against the (linear) integer programming solution in the service composition setting. An alternative to GAs could be to use nonlinear integer programming techniques, but the maturity of the available tools is questionable, and the application of these methods in our setting requires fur-ther investigation. A survey of some nonlinear techniques is contained in a paper by Grossmann [9] .. GAs are unconstrained procedures by their nature, and so it is necessary to find ways to integrate constraint-handling techniques during the search process. Usually, this is achieved through penalty functions, i.e., constraints are incorporated in the fitness function so that their satisfaction is guaranteed for the optimal solution. An extensive survey of the constraint-handling techniques proposed in literature in the context of evolutionary algorithms is contained in a paper by Coello Coello [6] . In particular, several kinds of penalty functions are listed in the paper, together with an analysis of advantages/disadvantages for each of them. To solve our problem, we have used a simple distance-based penalty approach, that has turned successful also in scheduling problems presented in a work by Fang [8] . More complex dynamic or adaptive functions cited in the survey are not really worth in our case where the amount of constraints is usually small and so extra computational costs can be avoided.. Another approach for constraint handling derives from Artificial Intelligence, namely Constraint Logic Programming (CLP). CLP has the advantage of a richer modeling capability, but providing a good model for the problem at hand has implications on the performance of the approach. The peculiarity of CLP is constraint propagation, i.e., constraints are used to identify allowed subdomains for the variable values, which is continuously applied during the search. Obviously, this approach can lead to a more efficient search but it is expensive itself. Again, as the priority here is optimization, while constraints are expected to be few and rather simple, we think that a GAs-based approach is more appropriate. Comparative studies of all these approaches on some specific problems are described, for example, in papers by Craenen et al. [7] , and by Helm et al. [10] .

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