Blotto game-based low-complexity fair multiuser subcarrier allocation for uplink OFDMA networks This article presents a subcarrier allocation scheme based on a Blotto game (SABG) for orthogonal frequencydivision multiple access (OFDMA) networks where correlation between adjacent subcarriers is considered. In the proposed game, users simultaneously compete for subcarriers using a limited budget. In order to win as many good subcarriers as possible in this game, users are required to wisely allocate their budget. Efficient power and budget allocation strategies are derived for users for obtaining optimal throughput. By manipulating the total budget available for each user, competitive fairness can be enforced for the SABG. In addition, the conditions to ensure the existence and uniqueness of Nash equilibrium (NE) for the SABG are also established. An lowcomplexity algorithm that ensures convergence to NE is proposed. Simulation results show that the proposed lowcomplexity SABG can allocate resources fairly and efficiently for both uncorrelated and correlated fading channels. The need for more efficient spectrum utilization techniques in wireless networks is becoming increasingly important as the number of users continues to grow rapidly while the radio spectrum remains a scarce resource. Among the emerging broadband wireless access technologies, orthogonal frequency-division multiple access (OFDMA) is a promising technique for efficient utilization of the available spectrum. Owing to its several attractive features, OFDMA has been envisaged for possible implementation in future-generation wireless networks, e.g., 3GPP-long term evolution [1] , cognitive radio networks [2] , and IEEE 802.20 mobile broadband wireless access [3] .. By exploiting multiuser diversity, efficient subcarrier allocation (SA) mechanism can be designed to ensure quality of service provisioning of multimedia services in OFDMA systems. Some recent studies on SA schemes have been reported in [4] [5] [6] [7] . Nevertheless, most of the aforementioned SA schemes focus on throughput maximization and/or transmit power reduction subject to some constraints. The fairness issue, however, has largely been ignored. The deployment of such schemes naturally gives rise to the following problem: users with better channel conditions always dominate usage of resources, causing low throughput for users with poor channel conditions. Thus, the max-min fairness criterion is used in [8] to maximize the throughput of users with poor channel conditions, but this approach results in severe spectrum inefficiency. To resolve this conflict, Nash bargaining solution (NBS) [9] is applied where the system performance is maximized subject to the constraint that each user is guaranteed a portion of resources. Although the fairness and efficiency issues have been considered in the NBS scheme, however, the computational complexity remains prohibitive for practical mobile applications.. According to [10] , the aforementioned types of fairness that are artificially decided by the system are not truly fair from the users' perspective. Hence, competitive fairness is introduced in [10] using an auction method where each user competes for the resources and is responsible for its own action and resulting throughput. Nevertheless, auction-based spectrum sharing is not appropriate for multicarrier systems. Han et al. [11] proposed an enhanced auction-based SA method for OFDMA systems for achieving high spectrum utilization and ensure competitive fairness. However, previous studies on fairness [8] [9] [10] [11] do not take into account the correlation between adjacent subcarriers. In fact, spectrum unfairness is more significant in correlated OFDM channels because the subcarriers utilized by a user may experience deep fades simultaneously and the use of techniques proposed in [8] [9] [10] [11] may not lead to desired fairness in such scenarios.. In this study, we aim to develop an SA technique which can achieve a good trade-off performance among fairness, efficiency, and complexity for both correlated and uncorrelated OFDMA channels. Unlike the conventional auction method, we propose a multi-dimensional auction-based subcarrier allocation scheme based on a Blotto game (SABG) [12] where users simultaneously compete for subcarriers using a limited budget. In this game, users need to allocate power and budget wisely across the available subcarriers to win as many good subcarriers as possible. Subject to power and budget constraints, efficient power allocation (PA) and budget allocation (BA) strategies are derived. Next, we propose a low-complexity algorithm to guide the SABG to reach the unique Nash equilibrium (NE) where all the users can obtain optimal throughput fairly. Besides, by manipulating the amount of budget available for each user, the SABG can enjoy a good trade-off between throughput and spectrum fairness. It will be shown via simulation results that the SABG, which is a low-complexity SA scheme, can allocate more resources fairly and efficiently in both uncorrelated and correlated OFDM channels as compared to some existing SA techniques.. The rest of this article is organized as follows. In Section 2, we outline the system model. Section 3 formulates the SABG and investigates the conditions to ensure the existence and uniqueness of NE in SABG. An algorithm that guides the SABG to the unique NE is proposed in Section 4 and its complexity is analyzed. Simulation results and performance analysis are presented in Section 5. We end the article with some concluding remarks in Section 6. In this article, the SA problem in OFDMA networks has been studied in a realistic channel model which considers correlation between adjacent subcarriers. We have shown that spectrum unfairness is more severe in correlated fading channels than in uncorrelated ones. To enforce competitive fairness in correlated fading channels while attaining high spectral efficiency and maintaining low complexity, we have proposed the SABG in which all the users simultaneously compete for the available subcarriers using a limited budget. Efficient PA and BA strategies have been derived for users for obtaining optimal throughput fairly. By manipulating the amount of budget available for each user, the SABG can enjoy a good trade-off between spectral efficiency and spectrum fairness. If the BS allocates equal amounts of budget to all users, then the fairest spectrum sharing among users can be enforced at a minimal loss in total throughput. The SABG has been shown to be more favorable than the existing SA schemes because of its high efficiency, fairness assurance, and low complexity. Simulation results demonstrate that the SABG algorithm can converge rapidly to the unique NE where upon reaching this point, subcarriers can be allocated fairly and efficiently to every user. From Equations A3 and A4, we notice that the PA strategy can be modeled using the waterfilling algorithm [3] . Let μ k (t+1) = (μ k (t)-ξ(t)D k (t)) + be the subgradient update methods where ξ(t) > 0 are the update steps while D k (t) is. We can decouple the PA from BA by fixing b k while updating p k . Therefore, optimal PA can be obtained as . Without loss of generality, Equation A10 can be rearranged and represented using a general expression, i.e., The proposed BA strategy is thus obtained.

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


KCRC-LCD: Discriminative Kernel Collaborative Representation with Locality Constrained Dictionary for Visual Categorization We consider the image classification problem via kernel collaborative representation classification with locality constrained dictionary (KCRC-LCD). Specifically, we propose a kernel collaborative representation classification (KCRC) approach in which kernel method is used to improve the discrimination ability of collaborative representation classification (CRC). We then measure the similarities between the query and atoms in the global dictionary in order to construct a locality constrained dictionary (LCD) for KCRC. In addition, we discuss several similarity measure approaches in LCD and further present a simple yet effective unified similarity measure whose superiority is validated in experiments. There are several appealing aspects associated with LCD. First, LCD can be nicely incorporated under the framework of KCRC. The LCD similarity measure can be kernelized under KCRC, which theoretically links CRC and LCD under the kernel method. Second, KCRC-LCD becomes more scalable to both the training set size and the feature dimension. Example shows that KCRC is able to perfectly classify data with certain distribution, while conventional CRC fails completely. Comprehensive experiments on many public datasets also show that KCRC-LCD is a robust discriminative classifier with both excellent performance and good scalability, being comparable or outperforming many other state-of-the-art approaches. Recent years have witnessed the great success of the sparse representation techniques in a variety of problems in computer vision, including image restoration [1] , image denoising [2] as well as image classification [3, 4, 5] . Sparse representation is widely believed to bring many benefits to classification problems in terms of robustness and discriminativeness. Specifically, sparsity is a regularizer that can reduce the solution space under ill-conditioned problems, by seeking to represent a signal as a linear combination of only a few bases. These bases are called the "atoms" and the whole overcomplete collection of atoms together form what one call a "dictionary". Many natural signals such as image and audio indeed have sparse priors. Imposing sparsity not only returns a unique solution, but also helps to recover the true signal structure, giving more robust estimation against noise. In addition, the sparse representation of a signal often leads to better separation and decorrelation which benefits subsequent classification problems. Despite the fact that sparse optimization is a nonconvex problem, the l 1 -norm convex relaxation and its optimization techniques have been thoroughly studied.. Wright et al. [3] employed the entire set of the training samples as the dictionary and reported a discriminative sparse representation-based classification (SRC) with promising performance on face recognition. SRC approximates an input signal y with a linear combination of the atoms from an overcomplete dictionary D under the sparsity constraint and gives the predicted label by selecting the minimum reconstruction residuals. Despite the fact that SRC was widely used in various applications [6, 7, 8] , [9, 10, 11] still questioned the role that sparse representation plays in the image classification tasks.. Zhang et al. [11] further commented that it is unnecessary to enforce the sparse constraint with computationally expensive l 1 -norm if the feature dimension is high enough. Their work emphasized the importance of collaborative representation (CR) rather than the sparse representation, arguing that CR is the key to the improvement of classification accuracy, which was validated by their comparison experiments. They used the l 2 -norm regularization instead of l 1 -norm, further improving the classification accuracy while significantly reducing much computational cost. The corresponding proposed method is called collaborative representation classification (CRC).. Despite their robust performance, the linear nature of both SRC and CRC makes them perform poorly when the training data are distributed vector-like in one direction. Kernel function, proven useful in kernel principle component analysis (KPCA) [12] and support vector machine (SVM) [13] , was introduced to overcome such shortcoming for both SRC and CRC, leading to the kernel sparse representation-based classifi-cation (KSRC) [14] and the kernel collaborative representation classification (KCRC) [15] . In particular, a Mercer kernel implicitly defines a nonlinear mapping to map the data from the input space into a high or even infinite dimensional kernel space where features of the same class can be grouped together more easily and different classes become linear separable.. Besides summarizing the KCRC [15] , our major contribution in this paper lies in proposing a generalized framework for KCRC with locality constrained dictionary and unified similarity measure, giving both performance gain and significant reduction of computational cost. Due to the poor scalability of the global dictionary (GD) used in CR-based methods, classification becomes intractable in large database for KCRC with GD (KCRC-GD). To enable the scalability to large databases, we prune the dictionary via k-nearest neighbor (K-NN) classifier to enforce locality. Specifically, the nearest neighbors of a query serve to construct a locality constrained dictionary (LCD) for KCRC. Such strategy is both intuitively reasonable and mathematically appealing. Intuitively, LCD is well motivated by the psychological findings about human perception that visual categories are not defined by lists of features, but rather by similarity to prototypes [16] . In other word, coarse level matching, for which K-NN is used, plays an important role in human perception. Mathematically, LCD can be nicely incorporated under the framework of KCRC. First, the LCD similarity measure can also be kernelized under KCRC, which theoretically links CRC and LCD under the kernel method. Second, KCRC-LCD becomes more scalable to both the training set size and the feature dimension. The kernel gram matrix is now obtained from a subset of the global dictionary, while KCRC operates on the reduced kernel matrix without referring to original features.. The high level intuition of LCD is that local dictionary atoms are typically the most important and informative samples. Looking into these representative exemplars often brings even more gains than globally considering all samples together. It is not hard to see similar concepts and link the connections. For example, if the query is located near decision boundary, then these local atoms play the role similar to support vectors in an SVM, or in an extreme case, exemplars in an exemplar SVM [17] . In a model recommendation system, selecting the most responsive models instead of all models has been reported to give gains [15] . In fact, SRC also seeks to use only few exemplar atoms in the dictionary. Yet the proposed method is able to run much faster with even better performance. In the extreme scenario, if K equals the number of atoms, then the proposed KCRC-LCD degenerates to regular KCRC with global dictionary. If K equals 1, KCRC-LCD degenerates to the simplest nearest neighbor classifier.. In this paper, we specifically focus on the application of our proposed framework to the image classification/visual categorization problem, demonstrating its robust performance with a comprehensive series of image classification tasks. Image classification is among the most fundamental computer vision problems where each image is labeled with a certain or multiple categories/tags. Though great advance has been achieved, much is pending to be done since the current state-of-the-art approaches are far from being able to achieve human-level performance, particularly in handling cluttered, complicated scenarios and inferring abstract concepts. Such gap between the machine and human remains an open challenge, motivating us to exploit more discriminative and efficient image classifiers.. The outline of the paper is as follows. Section II discusses related work of KCRC-LCD and presents our main contributions. In Section III, necessary preliminaries are briefly introduced. Section IV elaborates the formulation of KCRC-LCD and discusses some important details. The locality constrained dictionary is proposed and discussed in Section V. Experimental results are provided and discussed in Section VI, followed by concluding remarks in Section VII. We elaborated the KCRC approach in which kernel technique is smoothly combined with CRC. KCRC enhances the discrimination ability of CRC, making the decision boundary more reasonable. Additionally, we present a locality constrained dictionary, of which the locality is exploited to further enhance the classification performance. KCRC and LCD are mathematically linked via distance kernelization. On one hand, LCD not only helps the classifier adaptive and scalable to large databases via pruning the dictionary, but also reduce the dimensionality in kernel space, enhancing both discrimination ability and efficiency. On the other hand, kernel function makes our approach discriminative and robust to more data distribution, i.e., the same direction distribution. Furthermore, the coarse-to-fine classification strategy of KCRC-LCD is similar to the human perception process, which makes the intuition of KCRC-LCD even more appealing.. We conduct comprehensive experiments to show the superiority of KCRC-LCD. Our approach yields very good classification results on various well-known public databases. While achieving high level discrimination ability, efficiency is one of the biggest merits of KCRC-LCD, which is validated in running time test. Moreover, we simulate the representation and construction of KCRC with different dimensionality reduction for kernel space, and further experiment these methods on public database. The simulation results show the discrimination ability of KCRC. Different distance metrics used in LCD are also compared to support the idea that discriminative distance metric can greatly improve the classification accuracy. We also create a toy data sets to show CRC suffers from data with the same direction distribution while KCRC perfectly overcomes such shortcoming. To sum up, tested by various experiments, KCRC is proven discriminative and efficient when combined with LCD.. Possible future work includes improving the unified similarity measure model and learning the most effective kernel for KCRC-LCD instead of selecting the fixed kernel. It can be predicted that KCRC-LCD will becomes more powerful when combined with kernel learning, or even multiple kernel learning. Pioneering work for combining kernel technique to SRC is proposed in [18, 14, 19] . Gao et al. first proposed the idea of kernel-based SRC with a promising experimental results. Zhang et al. [14] further unified the mathematical model [18] to a generic kernel framework and conducted more comprehensive experiments to evaluate the performance. To overcome the shortcoming of handling data with the same direction distribution, Liu et al. [15] addressed the problem of kernel collaborative representation. The authors presented a smooth formulation to incorporate kernel function into the CRC model. A practical application of kernel CRC in vehicle logo recognition was further discussed in [20] . We happened to notice that a very recent work [21] proposed a similar idea by combining the column-generation kernel to CRC for hyperspectral image classification. It should be pointed out, however, that both the formulations as well as the applications are significantly different when dealing with the high dimension in kernel space. In terms of application, [21] formulated the kernel collaborative representation on pixel-level tasks for hyperspectral images while our method focus on image-level classification. Significant differences also exist in the formulation: [21] incorporated the kernel function with column generation without considering dimensionality reduction in kernel space (possibly due to the characteristics of the hyperspectral classification task). On the contrary, our method combines the CRC with kernel function in a strategy similar to KPCA and kernel Fisher discriminant analysis (KFDA). Moreover, a series of dimensionality reduction approaches have been taken into account in our generalized formulation. In general, we aim at extending the idea of KCRC by further improving formulation details of KCRC and presenting specific methods to perform dimensionality reduction in kernel space.. We also noticed that [22] presented a similar idea of constructing locally adaptive dictionary, but such dictionary pruning strategy was only applied in the standard CRC framework instead of the kernel CRC framework. As one shall see, the proposed KCRC-LCD is not a trivial extension of CRC-LCD by combining KCRC with locality constrained dictionary, but a well-motivated and appealing framework in which LCD and KCRC are theoretically linked by kernelizing the distance used in LCD. In addition, the kernelization in conjunction with LCD not only brings scalability in terms of data set size, but also further extends its scalability to feature dimensionality. We will show that the locally adaptive dictionary in [22] is a special case of our proposed LCD.

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


An Algorithm for Gradual Patch Acceptance Detection in Open Source Software Repository Mining Passakorn PHANNACHITTA †a) , Nonmember, Akinori IHARA †b) , Member, Pijak JIRAPIWONG † †c) , Nonmember, Masao OHIRA †d) , and Ken-ichi MATSUMOTO †e) , MembersNowadays, software development societies have given more precedence to Open Source Software (OSS). There is much research aimed at understanding the OSS society to sustain the OSS product. To lead an OSS project to a successful conclusion, researchers study how developers change source codes called patches in project repositories. In existing studies, we found an argument in the conventional patch acceptance detection procedure. It was so simplified that it omitted important cases from the analysis, and would lead researchers to wrong conclusions. In this research, we propose an algorithm to overcome the problem. To prove out our algorithm, we constructed a framework and conducted two case studies. As a result, we came to a new and interesting understanding of patch activities. Open Source Software (OSS) has become critical throughout all software development societies. Software developers even from industries take more interest in OSS, because it helps them shorten their software development cycles. More research has been aimed at supporting OSS, which has elevated the variety of studies. Since OSS is a community-driven development, comprehensiveameliorated studies have become highly popular. There are supportive activities in OSS that enable everyone to collaborate their work efficiently, even they are geographically separated. Patch Submission is the key activity for the purpose. Although an OSS project's archives are manifestly open to everyone, only committers (i.e. core developers who can take the full control of a project) can make a permanent modification to the artifacts. A patch acts like a bridge that connects a gap between committers and non-committers. It enables non-committers to suggest ideas for modifying some parts of an OSS project.. A precise study of patch-related activities was intro- duced by Bird et al. [1] . They are the pioneers who proposed a method to collect and extract patches for further analysis. Later, there have been many studies following the Bird et al. method that analyzed OSS patch-related information to achieve a better understanding of OSS projects [2] - [5] .. Weißgerber et al. [6] have concluded that small size patches are more valuable and suggested the peer developers to submit small size patches for more possibilities of acceptance. However, it has been found that their analyzing procedure was not powerful enough to coverage sufficient cases. They count a patch as accepted if the whole of its record was committed into a revision at once. This led them to their mistaken conclusion that smaller size patches are preferable. This study is motivated by the studies of Bird et al. [1] and Weißgerber et al. [6] . We have found that their analytical grain may be too coarse to conclude the characteristic of acceptable patches (i.e. the preferred size of patches for acceptance). The question is what will happen if patch activities analysis is performed in finer grain? In this study, we devise a novel algorithm that divides patches into smallest meaningful grain, which is a line of source code (LOC). It led us to discover new dimensions of patch analysis. In our evaluation, we certify the preferable size of accepted patches. Our devised algorithm enables us to include the case in which only a portion of the source code was accepted gradually, which is more likely to be occurrence in practice. With further evaluation we try to explore a totally new finding that can be brought out only from our propose. We seek out an inconclusive conjecture that fine-grained patch acceptance analysis has a potential to elucidate it. We turn out that temporal-based patch submission analysis could explain OSS project evolution and can conclude an inconclusive belief from Nakakoji et al. proposed OSS evolution pattern [7] .. The remainder of the paper is organized as follows: Sect. 2 outlines background related to the analysis of patches submitting activities. Section 3 explains our proposed algorithm and its method of implementation. Section 4 demonstrates our case studies and elaborates the results. Section 5 discusses on our findings and validates our proposal, and Sect. 6 concludes the paper.. Copyright c 2012 The Institute of Electronics, Information and Communication Engineers We have invented a novel algorithm that fills the unexplored area of patch-related activities in OSS study. Our proposed algorithm can identify a portion and gradual patch accepted cases in the patch acceptance analysis. It will lead researchers to a better understanding of OSS project societies.. Recently, a study based on patch acceptance analysis has simplified the procedure improperly by omitting from the study both of the important cases mentioned here. This unfortunately led the researchers to a fallacious research conclusion, because the cases omitted always occur. To prove the potential of the algorithm, we constructed a patch analysis framework and perform two case studies using Apache HTTP Server, and Eclipse Platform. They are large and well-known OSS projects.. Our first case study brought many insights into patch acceptance study, which is improved by the utilization of our proposed algorithm. The experimental results from our analyzing framework are very interesting. They include larger size patches and are more likely to be accepted, a conclusion different from that of existing studies. We believe the reason is that the existing coarse-grained algorithm excludes the portion and gradual patch accepted cases that has generated a bias toward larger patches.. In our second case study, we found that exhaustive details of an OSS committer's openness (i.e. the level at which committers accept a suggestion from outside) can be elucidated by extending a temporal-based analysis from our patch acceptance identification algorithm. The analysis reveals two interesting identities of OSS committers' openness. The first is that a special event occurrence in an OSS project would affect the committers' openness level, and the second finding is that there exists a relationship between OSS committer's openness and OSS project evolution.. Both case studies are good examples that show the promise of our proposed algorithm. In continuing with this research, we would like to seek more criteria that have been overlooked or omitted from the existing patch-related activity studies. This will help researchers come to understand OSS societies better.

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


Evaluating Supplier Performance Using DEA and Piecewise Triangular Fuzzy AHP Data envelopment analysis (DEA) In this paper, a novel method for evaluating alternative candidates in a multi-input and multi-output decision making problem is proposed, which was developed by combining the DEA, AHP, and fuzzy set theory through introducing a new concept of a controllable BTR. Figure 3 depicts the evolution flowchart of the new proposed model.. The piecewise triangular fuzzy set for the weighting priorities intuitively represents the redundancy and inconsistency of decision makers. With the introduction of the piecewise triangular fuzzy set and the BTR, which leaves a varying but restrained range of weighting for the evaluation criteria, both the subjective and objective ͑e.g., based on some collected data͒ views of candidates based on evaluation criteria of a decision maker can be taken into considerations in this decision support model. Moreover, the BTR provides the decision maker the flexibility to conveniently tighten or loosen the weighting restraint. Thus, the eligibly efficient suppliers would not only be sorted out but also be ranked according to the evaluation criteria. On the other hand, the introduction of the BTR alleviates the possible misjudgment because of the uncertain and inappropriate weighting factors, which may lead to exclude the potential eligibly efficient supplier out of the selection, who otherwise might be qualified under another weighting factors allocation.. It is sometimes troublesome and difficult to determine appropriate weights, although it has the flexibility. The difficulty of determining appropriate weights causes the possible misjudge from using the model. To overcome this difficulty or problem, the piecewise triangular fuzzy set and the BTR parameter are introduced in this paper to prevent the potential valuable suppliers from being pruned out. Fig. 3 Evolution of the proposed model

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A MULTI-OBJECTIVE GENETIC ALGORITHM FOR TUNING AND RULE SELECTION TO OBTAIN ACCURATE AND COMPACT LINGUISTIC FUZZY RULE-BASED SYSTEMS This work proposes the application of Multi-Objective Genetic Algorithms to obtain Fuzzy Rule-Based Systems with a better trade-off between interpretability and accuracy in linguistic fuzzy modelling problems. To do that, we present a new post-processing method that by considering selection of rules together with tuning of membership functions gets solutions only in the Pareto zone with the highest accuracy, i.e., containing solutions with the least number of possible rules but still presenting high accuracy. This method is based on the well-known SPEA2 algorithm, applying appropriate genetic operators and including some modifications to concentrate the search in the desired Pareto zone. One of the aims in focusing the research in the Linguistic Fuzzy Modelling area in recent years is the trade-off between interpretability and accuracy.. 1 Of course, the ideal thing would be to satisfy both criteria to a high degree, but since they are contradictory issues generally it is not possible.. A widely-used approach to improve the accuracy of linguistic Fuzzy Rule-Based Systems (FRBSs) is the tuning of Membership Functions (MFs), [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] which refines a previous definition of the Data Base (DB) once the rule base has been obtained. Although tuning usually improves the system performance, sometimes a large number of rules is used to reach an acceptable degree of accuracy. In this case, some works 1, 5 consider the selection of rules together with the tuning of MFs but only considering performance criteria.. In this contribution, we focus on this problem by using Genetic Algorithms as a tool for evolving the MFs parameters and rule base size and by coding all of them (rules and parameters) in the same chromosome. Since the problem presents multiobjective nature we could consider the use of Multi-Objective Genetic Algorithms (MOGAs) [11] [12] [13] [14] [15] to obtain a set of solutions with different degrees of accuracy and number of rules by using both characteristics as objectives.. Although there are some works in the literature using MOGAs to improve the difficult trade-off between interpretability and accuracy of FRBSs, [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] practically all these works were applied to classification problems trying to obtain the complete Pareto (set of non-dominated solutions with different trade-off) by selecting or learning the set of rules better representing the example data, i.e., improving the system classification ability and decreasing the system complexity but not considering learning or tuning of the fuzzy system parameters (which involves another type of Pareto front, a more complicated search space and therefore needs different considerations respect to the works in the existing literature).. In this way, our main interest is to design an appropriate MOGA for this type of problem due to the fact that standard MOGAs can present some problems. As said, MOGAs are generally based on obtaining a set of non-dominated solutions. However, in this case, there are solutions that are not interesting although they are in the Pareto frontier. For example, non-dominated solutions with a small number of rules and high error are not interesting since they have not the desired trade-off between accuracy and interpretability. Furthermore, the existence of these kinds of solutions favours the selection of solutions with very different number of rules and accuracy to apply the crossover operator, which gives results with poor accuracy (the tuning parameters would be very different and the crossover would not have any sense except for exploring new combinations of rules).. In our proposal, we concentrate the search in the Pareto zone with still accurate solutions trying to obtain the least number of possible rules. To do that, we propose a modification of the well-known SPEA2 26 (Strength Pareto Evolutionary Algorithm 2) that considering the rule selection together with the tuning of MFs concentrates the search in the Pareto zone having accurate solutions with the least number of possible rules, the Accuracy-Oriented SPEA2 (SPEA2 ACC ). Besides, we have performed the same modification and experiments with NSGA-II 27 (Nondominated Sorting Genetic Algorithm II), showing that this approach is not the most adequate for this problem.. This paper is arranged as follows. First, a brief summary of different proposals to improve the balance between interpretability and accuracy is presented, specially taking into account those considering MOGAs for this purpose. In section 3, we present a study of the estimated Pareto frontier for this problem (tuning and rule selection). SPEA2 ACC algorithm is introduced in Section 4 together with the modifications proposed on SPEA2 and the genetic operators considered. Section 5 shows an experimental study of the proposed methods in a real-world problem. Finally, Section 6 gives some conclusions. Taking into account the results showed in the previous section, we can conclude that the models obtained by the proposed method present a better trade-off between interpretability and accuracy than the remaining ones. By searching for a good configuration of rules (only removing rules with little importance) and by tuning the parameter for a small set of rules, the proposed algorithm has obtained models even with a better accuracy than those obtained by methods only guided by measures of accuracy. In this way, the results obtained have shown that the use of MOEAs can represent a way to obtain even more accurate and simpler linguistic models than those obtained by only considering performance measures.. On the other hand, the proposed algorithm (SPEA2 ACC ) could be of interest in problems that, although presenting a multi-objective nature, need as solution not all the Pareto frontier but only a specific area of it. To evaluate the usefulness of the method proposed, SPEA2 ACC , we have considered a real-world problem 49 with 4 input variables that consists of estimating the maintenance costs of medium voltage lines in a town. The methods considered for the experiments are briefly described in Table 1 . WM 47 method is considered to obtain the initial rule base to be tuned. T and S methods perform the tuning of parameters and rule selection respectively. TS indicates tuning together with rule selection in the same algorithm. All of them consider the accuracy of the model as the sole objective. The remaining are MOGAs with and without the proposed modifications (all of them perform rule selection with tuning of parameters considering two objectives, accuracy and number of rules). However, we have to highlight that all of them consider the same population initialization, i.e., they start considering all the candidate rules for the initial individuals in order to see better the influence of the changes applied on the original SPEA2.. The linguistic partitions are comprised by five linguistic terms with triangular shape. The values of the input parameters considered by all the MOGAs studied are presented as follows: population size of 200, external population size of 61 (in the case of SPEA2 and SPEA2 ACC ), 50,000 evaluations and 0.2 as mutation probability per chromosome.

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


A fast method for calculating reliable event supports in tree reconciliations via Pareto optimality Background: Given a gene and a species tree, reconciliation methods attempt to retrieve the macro-evolutionary events that best explain the discrepancies between the two tree topologies. The DTL parsimonious approach searches for a most parsimonious reconciliation between a gene tree and a (dated) species tree, considering four possible macro-evolutionary events (speciation, duplication, transfer, and loss) with specific costs. Unfortunately, many events are erroneously predicted due to errors in the input trees, inappropriate input cost values or because of the existence of several equally parsimonious scenarios. It is thus crucial to provide a measure of the reliability for predicted events. It has been recently proposed that the reliability of an event can be estimated via its frequency in the set of most parsimonious reconciliations obtained using a variety of reasonable input cost vectors. To compute such a support, a straightforward but time-consuming approach is to generate the costs slightly departing from the original ones, independently compute the set of all most parsimonious reconciliations for each vector, and combine these sets a posteriori. Another proposed approach uses Pareto-optimality to partition cost values into regions which induce reconciliations with the same number of DTL events. The support of an event is then defined as its frequency in the set of regions. However, often, the number of regions is not large enough to provide reliable supports. Results: We present here a method to compute efficiently event supports via a polynomial-sized graph, which can represent all reconciliations for several different costs. Moreover, two methods are proposed to take into account alternative input costs: either explicitly providing an input cost range or allowing a tolerance for the over cost of a reconciliation. Our methods are faster than the region based method, substantially faster than the sampling-costs approach, and have a higher event-prediction accuracy on simulated data. Conclusions: We propose a new approach to improve the accuracy of event supports for parsimonious reconciliation methods to account for uncertainty in the input costs. Furthermore, because of their speed, our methods can be used on large gene families. Our algorithms are implemented in the ecceTERA program, freely available from http://mbb.univ-montp2.fr/MBB/. In a parsimony framework, the choice of the costs for basic events may have a strong impact on the set of predicted events. In this paper, we provide a new tool dealing with this problem, which both improves the accuracy of D, T, L events predicted by parsimonious reconciliation methods and scales up to handle the larger set of gene trees used in phylogenomic studies nowadays. This work combines the complementary ideas of the methods presented in [8] and [10] into new strategies that combine their strengths: speed and reliability. To deal with the inherent uncertainty of the input cost vectors, two approaches have been proposed and tested: explicitly providing an input cost range (strategy s3), or considering non-optimal reconciliations up to a fixed over-cost (strategies s4 and s5). Our approaches and models are flexible so that one can choose the strategy that fits the data better: considering either only parsimonious reconciliations or nearly optimal ones, choosing acceptable cost ranges, the over-cost, and even providing some-user defined additional constraints to filter the event count vectors list (see strategy s5). Our tests on simulated data demonstrate that models using dated (or partially dated) species trees seem to provide more accurate event predictions than those using undated species trees. Moreover, in our experiments, using median reconciliations is more effective than picking a random one, and better than taking the list of all events, confirming the findings of [8] . Furthermore, our approaches are faster and more accurate than both methods in [8] and [10] . Finally, this work emphasizes the benefits of using the reconciliation graph to manage the space of reconciliations efficiently. Many other tools could be developed by using this graph, for example calculating the reconciliation whose average of the supports is maximized.. This work confirms that erroneously inferred events can be, at least in part, filtered out. This filtering could probably be further improved by also taking into account reconciliations of close alternative gene tree/species tree topologies. Yet, taking such alternative reconciliations into account is challenging, as the reconciliation graph solution [7] , proposed to efficiently handle alternative reconciliations, was not designed to handle reconciliations between different gene/species trees. The evolutionary history of a gene family often differs from the history of the species containing those genes due to macro-evolutionary events other than speciation. Reconciliation methods compare gene trees with a species tree in order to recover these events. The DTL reconciliation model [1] [2] [3] [4] accounts for three types of events: gene duplications (D), losses (L), and transfers (T). This model is typically used in a parsimony framework, which searches for the reconciliations that minimize the overall cost, given a cost vector specifying the costs for D, T and L events. Unfortunately, ensuring the time-consistency of gene transfers, i.e., satisfying the chronological constraints among nodes of the species tree that are involved in transfer events, is NP-hard [4, 5] . However, if the internal nodes of the species tree are ordered, i.e. using a dated species tree, the problem can be efficiently solved [1, 6] . Although there can be an exponential number of optimal reconciliations for a given cost vector, the DTL-graph can be used to represent them compactly [7] .. Some of the events predicted by reconciliations methods may not be reliable due to potential inaccuracies in the input trees and the inherent imprecision of the input costs. Thus, it is necessary to estimate confidence values, or supports, for each predicted event. Supports can be defined, for example, as the frequency of an event over a space of alternative solutions.. In [7] [8] [9] , the support of an event is defined as the frequency of the reconciliations containing it over all reconciliations in the solution space. In [7, 8] , the DTL-graph was used to compute event supports in this sense over the set of all parsimonious solutions (for one cost vector in [7] and for several ones in [8] ). Moreover, in [8] , the authors used these event supports to identify the median reconciliation, that is the reconciliation that minimizes the sum of event-based distances between itself and all other parsimonious alternatives (here, the event-based distance between two reconciliations is defined as the number of events contained in one but not in the other). Bansal et al. [9] presented another way to address the problem, suitable for non-dated species trees as well as dated ones: they designed a method which samples the space of parsimonious reconciliations uniformly at random and then counts the frequency of each event within all sampled solutions.. However, the approaches presented in [7, 9] only focus on one cost vector; though, it is often difficult to know the appropriate cost vector, and the solutions can be very sensitive to the input costs. In [8] , the authors used a time-consuming approach that samples the space of cost vectors around the input one and then apply the algorithm presented in [7] to compute a DTL-graph for each sample. Libeskind-Hadas et al. [10] presented a method to estimate the sensibility of a parsimonious reconciliation with respect to the input costs. They use Pareto-optimal event count vectors to partition the cost space into regions such that the costs in the same region induce reconciliations with the same number of DTL events. These regions are then used to compute events supports, defined as the fraction of regions having an event in all (or one of, depending on the option used) their reconciliations. However, for the support measure to be reliable, the events should be recovered using biologically realistic costs, which can vary with respect to the phylum we are interested in (e.g., in Mammalian, duplications are much more frequent than transfers, whilst transfers are predominant in the evolution of Bacteria).. But, when analyzing a realistic cost space with the method in [10] , we observe that, often, a small number of regions, e.g. in many cases only one, is returned; thus, the corresponding supports can only be either 0 or 1 and are almost useless to filter out events. On the other hand, a larger cost space can account for more regions, but the event supports may be unreliable since they consider events retrieved using unrealistic costs (we will see in the Results section that this is indeed the case). Moreover, the method in [10] does not generate median reconciliations. It was shown in [8] that the median reconciliation has better event predictions than random ones.. Here, we use the definition of an event support given in [7, 8] and extend the work in [7] by taking into account several cost vectors. Rather than using the timeconsuming sampling method in [8] , we construct the space of all solutions corresponding to the input cost range and then compute the event supports over this space. As we shall see, our algorithm also makes use of Pareto-optimal reconciliations, which are efficiently computed via an extended version of the DTL-graph. This has the advantage of efficiently taking into account all relevant parsimonious reconciliations -even those that are parsimonious for very few event cost combinations and that are thus unlikely to be discovered by an ad hoc choice or a random sampling of event costs [10] .. The approaches presented in [7] [8] [9] only consider optimal parsimonious reconciliations, even though the real gene evolution might not be optimal. In this paper, we also present a method for computing near optimal reconciliations that allows a tolerance for the overall reconciliation cost. Our methods are faster than the one presented in [10] , substantially faster than the sampling-costs approach presented in [8] , and have a higher event prediction accuracy on simulated data than both methods. In this section, we will show how to compute all event count vectors of Pareto-optimal reconciliations (see Algorithm 1). This list of vectors is cleaned to keep either reconciliations that are parsimonious with respect to the given cost range (for solving Problem 1), or those having cost at most cost m (G, S , c) + (for solving Problem 2). Each of the returned lists is then used to construct the corresponding graph (Algorithm S1 in the Additional file 1) that represents all the solutions for the associated problem. Using this graph, we can compute supports for events, as well as median reconciliations.

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


Classification Tree for Risk Assessment in Patients Suffering From Congestive Heart Failure via Long-Term Heart Rate Variability Abstract-This study aims to develop an automatic classifier for risk assessment in patients suffering from congestive heart failure (CHF). The proposed classifier separates lower risk patients from higher risk ones, using standard long-term heart rate variability (HRV) measures. Patients are labeled as lower or higher risk according to the New York Heart Association classification (NYHA). A retrospective analysis on two public Holter databases was performed, analyzing the data of 12 patients suffering from mild CHF (NYHA I and II), labeled as lower risk, and 32 suffering from severe CHF (NYHA III and IV), labeled as higher risk. Only patients with a fraction of total heartbeats intervals (RR) classified as normal-to-normal (NN) intervals (NN/RR) higher than 80% were selected as eligible in order to have a satisfactory signal quality. Classification and regression tree (CART) was employed to develop the classifiers. A total of 30 higher risk and 11 lower risk patients were included in the analysis. The proposed classification trees achieved a sensitivity and a specificity rate of 93.3% and 63.6%, respectively, in identifying higher risk patients. Finally, the rules obtained by CART are comprehensible and consistent with the consensus showed by previous studies that depressed HRV is a useful tool for risk assessment in patients suffering from CHF.Index Terms-Congestive heart failure (CHF), data mining, decision tree, heart rate variability (HRV). In this study, we developed a classification tree based on standard long-term HRV for risk assessment in patients suffering from CHF.. The classifiers based on the combinations of standard longterm HRV measures "TOTPWR, pNN10, pNN50, SDNNIDX" and "ULF, TOTPWR, PNN50" enable distinguishing HRPs from LRPs with an accuracy rate of 85.4%, a sensitivity rate of 93.3%, and a specificity rate of 63.6% (tenfold cross-validation estimates). The existence of these two best combinations can be explained by the high correlation between HRV measures [5] , [38] .. The selection of pNN10 in the best combination would confirm its discrimination power proved by Mietus et al. [7] , even if the differences in pNN10 values between the two groups were lower than those of other measures, as shown by the statistical analysis performed in the current study. As concerns pNN50, Mietus et al. [7] showed that pNN50 failed to distinguish the LRPs and HRPs, while pNN50 is used in the BSTs (see Fig. 1 node 2 and Fig. 2 node 4) . This apparent inconsistency may be explained by considering that pNN50 could have a discriminative power only for the subgroups of patients which had high value of TOTPWR (TOTPWR > 11080.25 ms 2 ), consistent with the absence of statically significant differences between the two patient groups.. The sets of rules of both the models are clinically consistent, even if CART does not use any medical priori knowledge. In fact, the main clinical result of this research is that terminal node classifying as HRPs are on the left, thereby revealing lower values of the splitting features for severe CHF patients (with the only exception of pNN50). This is coherent with the statistical analysis performed in the current study and with the results showed by Casolo et al. [18] , Panina [6] and Arbolishvili [12] . It should be emphasized that the findings of Casolo et al. [18] , Panina et al. [6] , and Arbolishvili et al. [12] were obtained adopting different methods for PSD estimation. Several methods were proposed in literature in order to estimate PSD of RR intervals [4] , [5] . Particularly, many PSD estimators are based on the hypothesis that the signal under examination is uniformly sampled [36] . In contrast, the RR series is unevenly sampled and requires resampling before PSD estimation. In this paper, LS periodogram [35] was chosen as it estimates PSD of unevenly sampled signals without the requisite of resampling and its estimation has been proven to be more accurate than fast Fourier transform (FFT)-based method for RR data [40] .. In relation to the methodology, the exhaustive research for feature selection improved the classification performance compared to CART model obtained using all the features. Moreover, as the study dataset is imbalanced, we compared the performance of the proposed method with SMOTE, an approach based on oversampling to handle the class-imbalance problem and with other two widely used decision-tree methods. The proposed method achieved the highest performance in terms of accuracy rate and F 1 , which is one of the most suitable metrics for rare class problems [41] . Compared to our previous studies, based on short-term measures [22] , the classifier proposed in the current studies achieved an higher accuracy and sensitivity (85.4% versus 79.3% and 93.3% versus 82.4%, respectively), even if with a lower specificity (75.0% versus 63.6%). This result leaded us to consider long-term HRV measures more effective for the individuation of higher risk patients than short-term ones.. As regards the other classifier proposed in literature for CHF assessment, Guidi [23] compared different algorithms to automatically classify CHF patients in three groups (mild, moderate, and severe) and achieved an accuracy of 86% (independent set estimate; sensitivity and sensibility are not reported) by using neural network. Yang et al. [24] proposed a classifier based on support-vector machine, which achieved an accuracy of 74% (tenfold cross-validation estimate) in discriminating between mild CHF (NYHA I) and moderate/severe CHF patients (NYHA II and III). We underline that the classifier proposed by Guidi [23] was based on anamnestic and instrumental data (not including HRV measures), and the one by Yang et al. [24] was based on 12 parameters, including LF/HF and other parameters from clinical tests (blood test, echocardiography test, electrocardiography test, chest radiography test, and 6-min walk distance test). For that reason, some parameters needed by the automatic classifier proposed by Guidi [23] or Yang et al. [24] should be entered by physicians, while the adoption of only HRV measures, as in the current study, enables a completely automatic assessment.. Our study had the following limitations related to the employed Holter databases: 1) a small and unbalanced dataset; 2) the differences in the sampling frequency of ECG recordings; and 3) the different extraction procedures of NN intervals (for instance, some recordings were not manually reviewed and incorrect RR detections due to artifact may occur).. The small sample size could result in biased cross-validated performance estimates, even if we adopted strategies (feature selection and tree pruning) to avoid overfitting and to increase the generalization ability. A study with a larger dataset would be useful to confirm the generalization of our findings. Unfortunately, to the best of the authors' knowledge, a larger public dataset is not available and the choice of only public databases (and freely available HRV software) enables other researchers to reproduce our results and compare different classification methods.. As regards the imbalanced dataset problem, we adopted a standard approach (oversampling) as a benchmark to compare the proposed method, as previously described.. As regards the sampling frequency of ECG, it should be remembered that finite sampling frequency introduces an error in the RR interval measurement, as previously shown by Merri et al. [42] . However, a sampling rate of 128 Hz, which is the lowest sampling rate of the recordings used in this paper, has been found to be accurate enough to locate the R-peaks and, hence, compute HRV [5] . Finally, in order to handle unreliable RR interval measurements due to artifacts, following previous studies, the automated outlier removal provided by the adopted software was performed and a measure of data reliability (NN/RR) was adopted to discard unreliable results, as described in Section II. In the future research, we are planning to develop a similar study on a larger (although nonpublic) dataset of ECG recordings digitalized at the same sampling frequency and annotated with a stated procedure, i.e., the database of Regione Campania Network [43] . Moreover, nonlinear [44] , [45] and/or point process time-frequency [46] analysis could provide additional useful measures for automatic classification. Finally, the classification algorithms could be integrated in portable sensing devices [47] - [49] .. We conclude that the long-term HRV measures enable higher risk patients to be distinguished from lower risk ones. The classification trees developed achieved an accuracy rate of 85.4%, a sensitivity rate of 93.3% and a specificity rate of 63.6% (tenfold cross-validation estimates) using the combination of features "TOTPWR, pNN10, pNN50, SDNNIDX" and "ULF, TOTPWR, PNN50." Finally, our results are consistent with the consensus that depressed HRV values are associated with higher cardiovascular risk.

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


Controllable Adiabatic Manipulation of the Qubit State We propose a scheme which implements a controllable change of the state of the target spin qubit in such a way that both the control and the target spin qubits remain in their ground states. The interaction between the two spins is mediated by an auxiliary spin, which can transfer to its excited state. Our scheme suggests a possible relationship between the gate and adiabatic quantum computation. .) Unlike the traditional (gate) quantum computer, the adiabatic quantum computer is based on a slow change of the Hamiltonian describing the quantum system. The basic idea behind adiabatic quantum computation is the following: in order to find a complicated ground state of an Ising system in a longitudinal external magnetic field, one starts from the simple ground state of the non-interacting spins in an external transverse magnetic field. Then, one adiabatically changes the initial Hamiltonian to the Ising one, so that, finally, the system exhibits the complicated ground state of the Ising Hamiltonian. In the process of evolution, the adiabatic quantum computer remains in its ground state. This approach promises to solve important combinatorial and graph theory NP-hard problems. One example is the MAX CLIQUE problem. In graph theory, a clique is a subset of vertices, such that every pair of vertices is connected by an edge. In some cases, the MAX CLIQUE problem is equivalent to finding the ground state of the Ising system [2] . Adiabatic quantum computation has been implemented recently by D-wave Systems Inc. using superconducting flux qubits, whose evolution can be described by effective Ising Hamiltonian with the controllable interaction constants [4] .A "traditional" quantum computer is based on quantum logic gates, which change the state of a quantum system. (See, for example, [5] .) Before and after the action of the gates the quantum system is described by the same Hamiltonian. At first sight, an adiabatic quantum computer is completely different from a gate quantum computer. Indeed, while a gate quantum computer utilizes quantum superposition, entanglement and interference in order to "sample" all possible "numbers", an adiabatic quantum computer utilizes quantum tunneling in order to approach the true ground state.In this paper we investigate a possible bridge between the adiabatic and gate approaches to quantum computation. Namely, we set the simplest problem: how can one change the state of a target spin qubit conditional on the state of a control spin qubit if both the control and the target qubits remain in their ground states? One way to achieve this objective is to use an auxiliary spin, which mediates the interaction between the control and target spin qubits. As an example, the first control qubit (an electron spin S 1 ) experiences a large local magnetic field B 1 and always points opposite to this field (as the electron gyromagnetic ratio is negative). An auxiliary spin S 3 experiences a local magnetic field B 3 and a rf rotating field B rf . It also interacts with both the control spin S 1 and the target spin S 2 (e. g. a ferromagnetic exchange interaction with constants J 13 and J 23 ). The effective exchange field J 13 S 3 (in frequency units) acting on the spin S 1 must be much smaller than B 1 (in the same units). The effective exchange fields J 13 S 1 and J 23 S 2 must be much smaller than B 3 . In this case one can use the resonant rf field B rf on the auxiliary spin in order to manipulate its direction, conditional on the direction of the control spin. The target spin S 2 experiences only the exchange field J 23 S 3 produced by the auxiliary spin and should evolve adiabatically, changing its direction together with the direction of the auxiliary spin. Thus, the target spin will change its direction conditional on the direction of the control spin remaining in the ground state. The only spin which does not remain in the ground state is the auxiliary one.The greatest challenge in this proposed scheme is associated with the adiabatic motion of the target spin. Indeed, the exchange field produced by the target spin on the auxiliary spin must be small compared to the exchange field produced by the control spin. However, in this case the exchange field J 23 S 3 produced by the auxiliary spin on the target one (which determines the Larmor frequency of precession of the target spin) is small compared to the field B 3 acting on the auxiliary spin. The

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


Intrusion

detection

model

based

on

selective

packet

sampling

Recent

experimental

work

by

Androulidakis

and

Papavassiliou

(IET

Commun

IEEE

Netw

has

shown

that

it

is

possible

to

maintain

a

high

level

of

network

security

while

selectively

inspecting

packets

for

the

existence

of

intrusive

activity,

thereby

resulting

in

a

minimal

amount

of

processing

overhead.

In

this

paper,

a

statistical

approach

for

the

modeling

of

network

intrusions

as

Markov

processes

is

introduced.

The

theoretical

findings

presented

here

confirm

the

earlier

experimental

results

of

Androulidakis

and

Papavassiliou.

A

common

notion

about

network

intrusion

detection

systems

is

that

every

packet

arriving

into

a

network

must

be

inspected

in

order

to

prevent

intrusions.

This

investigation,

together

with

the

earlier

experimental

results,

disproves

that

notion.

Additional

experimental

testing

of

a

corporate

local

area

network

is

reported.

Network

intrusion

detection

systems

(IDS)

perform

a

vital

role

in

protecting

networks

connected

to

the

World

Wide

Web

from

malicious

attacks.

Traditionally,

IDS

software

products

such

as

SNORT

SecureNet

and

Hogwash

work

by

monitoring

traffic

at

the

network

choke-point,

where

every

incoming

IP

packet

is

analyzed

for

suspicious

patterns

that

may

indicate

hostile

activity.

Because

those

software

systems

must

match

packets

against

thousands

of

known

ominous

patterns,

they

must

work

extremely

fast.

Under

heavy

traffic,

however,

the

IDS

is

usually

forced

to

drop

packets

so

that

the

IDS

itself

will

not

become

the

bottleneck

of

the

network,

of

course

at

the

risk

of

allowing

an

attack

to

go

undetected.

Because

of

this

deficiency,

host-based

IDS

solutions

have

been

introduced

Host-based

IDS

products

run

on

a

server

rather

than

at

the

network

gateway.

Unfortunately,

however,

host-based

solutions

can

slow

down

the

server

considerably

under

heavy

traffic

conditions.

Because

of

the

inherent

limitations

of

all

software

solutions,

hardware

solutions

were

finally

introduced.

The

state-of-the-art

hardware

solution

is

a

field

programmable

gate

array

(FPGA)

that

performs

the

same

IDS

function

at

substantially

higher

speeds

There

are

serious

other

problems,

however,

to

contend

with

when

hardware

solutions

are

implemented

The

purpose

of

this

paper

is

to

introduce

an

analytic

and

statistical

model

for

the

process

of

network

intrusion

and

to

demonstrate

that

the

common

notion

of

the

necessity

of

having

the

content

of

every

IP

packet

inspected

is

flawed.

In

the

past,

numerous

research

articles

that

addressed

the

problem

of

network

intrusion

modeling

have

appeared

in

the

literature

Kephart

and

White

published

the

first

analytical

work

on

the

modeling

of

the

propagation

of

viruses

and

worms.

More

recently,

Wang

and

Wang

guided

by

the

analysis

of

Kephart

and

White,

recognized

that

the

problem

of

network

intrusion

can

be

modeled

after

the

popular

"birth

and

death"

epidemiological

model.

Wang

and

Wang

(WW),

however,

did

not

develop

such

a

model

analytically,

as

the

problem

is

mathematically

challenging.

Very

recently,

an

important

experimental

discovery

was

made

by

Androulidakis

and

Papavassiliou

(AP)

when

they

demonstrated

experimentally

that

the

selective

inspection

of

packets

for

the

purpose

of

detecting

network

intrusion

can

be

as

effective

as

the

full

inspection

of

all

packets.

In

this

paper,

it

will

be

demonstrated

that

the

seemingly

unrelated

discoveries

of

WW

and

AP

do

in

fact

stem

from

the

same

mathematical

origin.

More

specifically,

the

WW

hypothesis

that

the

process

of

network

intrusion

can

be

modeled

after

the

"birth

and

death"

epidemiological

model

will

be

developed

analytically

for

the

first

time.

The

results

are

surprising

and

essentially

confirm

the

experimental

findings

of

AP.

The

main

conclusion

is

that

it

is

possible

to

selectively

inspect

packets

from

only

certain

packet

flows,

thereby

eliminating

the

speed

bottleneck

problem

and

the

necessity

to

drop

packets

at

high

bit

rates,

while

simultaneously

maintaining

a

high

degree

of

network

security..

Actual

testing

by

the

author

that

involved

a

corporate

local

area

network

has

confirmed

the

theoretical

findings.

Additional

testing

of

an

optimized

SNORT

software

package-in

combination

with

a

traffic

generator

and

an

Agilent

network

analyzer-has

further

confirmed

the

theoretical

findings.

The

implication

of

these

theoretical

and

experimental

results

to

the

structure

and

the

design

of

future

IDS

will

be

quite

substantial.

The

analysis

of

network

intrusions

as

Markov

chains

disproves

the

common

notion

that

it

is

necessary

to

fully

inspect

every

packet

entering

a

network

in

order

to

ensure

security.

The

results

shown

here

fully

support

the

experimental

results

that

were

published

recently

by

Androulidakis

and

Papavassiliou

The

analysis,

together

with

the

testing

data,

demonstrates

that

it

is

sufficient

to

inspect

only

a

small

number

of

packets

sampled

predominantly

from

small

flows,

as

long

as

the

probability

of

occurrence

of

intrusion

P

H

is

below

a

critical

threshold

Bakhoum

EURASIP

Journal

on

Information

Security

that

is

determined

from

Eq.

and

calculated

in

real

time

from

Eq.

The

implications

of

the

research

presented

here

for

software

IDS

solutions

such

as

SNORT

are

substantial,

as

the

selective

inspection

of

packets

allows

the

IDS

to

handle

high

speed

links

without

dropping

any

packets.

Hence,

it

is

essentially

possible

for

most

of

the

time

to

eliminate

the

speed

bottleneck

problem

without

compromising

security..

EndNotes

a

Here,

it

is

important

to

point

out

that

a

"process",

as

defined

in

the

previous

section,

can

be

started

with

one

or

more

packets.

The

procedure

for

calculating

P

H

however,

will

be

based

on

the

direct

inspection

of

packets.

b

It

can

be

argued

that

the

relationship

between

P

H

and

H(normalized)

should

be

a

proportionality

relationship,

not

an

exact

equality

as

shown

in

Eq.

However,

the

Figure

Test

of

Snort

in

the

regular

mode

inspection).

Snort

drops

packets

at

an

increasing

rate

as

the

link

speed

is

increased.

Figure

The

percentage

of

hostile

packets

that

slipped

through

Snort

as

a

function

of

P

H

for

link

speeds

ranging

from

Mbps

to

Gb/s.

objective

of

this

work

is

to

obtain

a

reasonable

estimate

for

the

likelihood

of

the

occurrence

of

intrusion,

not

to

seek

idealized,

precise

mathematical

relationships.

In

reality,

due

to

the

nature

of

the

problem,

the

mathematical

framework

presented

here

is

not

meant

to

be

highly

precise,

but

it

can

be

made

sufficiently

precise

with

the

inclusion

of

experimental

data.

c

It

is

to

be

pointed

out

that

DoS

attacks

can

be

identified

only

from

the

packet

headers.

d

SNORT

is

a

registered

trademark

of

Sourcefire,

Inc.

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