Extracting Semantic Frames from Thai Medical-Symptom Unstructured Text with Unknown Target-Phrase Boundaries †a) , Student Member, Ekawit NANTAJEEWARAWAT †b) , and Thanaruk THEERAMUNKONG †c) , Members SUMMARY Due to the limitations of language-processing tools for the Thai language, pattern-based information extraction from Thai documents requires supplementary techniques. Based on sliding-window rule application and extraction filtering, we present a framework for extracting semantic information from medical-symptom phrases with unknown boundaries in Thai unstructured-text information entries. A supervised rule learning algorithm is employed for automatic construction of information extraction rules from hand-tagged training symptom phrases. Two filtering components are introduced: one uses a classification model to predict rule application across a symptom-phrase boundary based on instantiation features of rule internal wildcards, the other uses weighted classification confidence to resolve conflicts arising from overlapping extractions. In our experimental study, we focus our attention on two basic types of symptom phrasal descriptions: one is concerned with abnormal characteristics of some observable entities and the other with human-body locations at which primitive symptoms appear. The experimental results show that the filtering components improve precision while preserving recall satisfactorily. Standard knowledge representation languages for the Semantic Web, such as RDF [1] and OWL [2] , have been recently developed and are now in place. A crucial question still remains: how will we feed machines with the relevant knowledge in an application domain? In this article, we present an information extraction (IE) framework towards bridging the gap between medical-symptom descriptions in Thai text and the world of concepts, which represent abstractions of human thoughts. IE techniques usually involve linguistic patterns and domain-specific lexicons, coupled with a conceptual description of an application domain, i.e., a domain ontology. While an ideal domain ontology is possibly language-independent, linguistic patterns and lexicons rely heavily on the language in use. Due to languagestructure differences, when an IE framework that works well in one language is applied to a different language, supplementary components are often necessary.. As part of a broader-scope project on constructing a large-scale medical-related knowledge base in Thailand from information sources available on the Internet [3] , we aim to develop a system for extracting semantic information from unstructured-text (free-text) symptom descriptions in Thai and representing the extracted results in a form of machine-processable frames. IE based on linguistic analysis of Thai text is not currently feasible due to the lack of basic supporting language-processing tools. Not to mention a full parser for Thai sentences, neither a shallow-parsing (chunking) tool nor a fairly accurate part-of-speech analyzer is currently available, much owing to the high ambiguity of the structure of written Thai. However, by incorporation of ontology-based semantic annotations and appropriate extraction filtering techniques, it is expected that IE based on patterns of triggering class tags and triggering plain words can be realized for Thai documents without part-of-speech tagging and text chunking. We focus on two types of symptom descriptions: one is concerned with abnormal characteristics of some observable entities and the other with human-body locations at which primitive symptoms appear. A well-known supervised rule learning algorithm, called WHISK [4] , is used as the core algorithm for constructing IE rules automatically from a set of hand-tagged training symptom phrases. The technical challenges we address in this paper are twofold: From a set of manually collected symptom phrases, IE rules are created using our implementation of WHISK. To apply the obtained rules to unstructured-text information entries without predetermining symptom-phrase boundaries, rule application using sliding windows is introduced. Filtering techniques are proposed for the removal of false positives resulting from rule application across symptom-phrase boundaries and those resulting from overlapping extractions. The experimental results show that these techniques improve extraction precision while satisfactorily preserving high recall of sliding-window rule application. When the window size is sufficiently large, the performance of the proposed framework appears to be fairly close to that of rule application with manually located target phrases. Further works include extension of the types of target phrases and in-depth analysis of how the ontology-based semantic frames extracted from symptom phrases facilitate logic-based medical diagnosis reasoning. Application of WHISK to IE tasks in medical-related domains was reported in [23] and [24] -the former is concerned with information on biomedical events and the latter with drug treatment information. Both of them take English documents as information sources and use linguistic tools, such as part-of-speech taggers and chunk parsers, along with ontology-based semantic tagging for text preprocessing. While a preliminary investigation was given in [24] without introducing any supplementary technique, an extraction verification module was proposed in [23] for removing incorrectly extracted biomedical events based on a maximum entropy (ME) classification method. The verification module in [23] employs a learned ME classifier to predict a class of the an extracted slot filler, and removes an extracted frame whose components contradict the class assigned by the classifier. By contrast, the WIF module in our framework uses a classifier to predict rule application across a symptom-phrase boundary, compensating for the unavailability of a phrase boundary analyzer.. Very few works on IE from Thai text were reported in the literature. Sukhahuta and Smith [25] proposed strategies for Thai-text IE using corpus-based syntactic surface analysis based on predefined context-free grammar rules. The extraction precision of their developed system is still rela-tively low; as pointed out in [25] itself, one main cause of errors comes from the ambiguity of the sentence structure, due to which a parser is unable to determine sentence boundaries, resulting in parse-tree construction failure, in particular, when constituents such as subject or verb do not appear in a sentence as expected in the grammar rules. Only handcrafted triggering-term patterns were considered in [25] ; extraction-pattern learning was not discussed. Narupiyakul et al. [26] introduced a method for automated Thai-text IE in a housing advertisement corpus by using rule-based syllable segmentation for text preprocessing and applying Hidden Markov Models, with the Viterbi algorithm, to extract individual target fields independently. Target fields along with their prefixes and suffixes are tagged in the level of syllables, which are far less meaningful than words and semantic classes. Moreover, individual-field extraction, such as that in [26] , has a serious limitation for a significant number of applications, in particular, when an information entry contains fillers of more than one frame, e.g., it cannot relate a particular person with his address when an information entry contains several person names and addresses.

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


NCBO Technology: Powering semantically aware applications As new biomedical technologies are developed, the amount of publically available biomedical data continues to increase. To help manage these vast and disparate data sources, researchers have turned to the Semantic Web. Specifically, ontologies are used in data annotation, natural language processing, information retrieval, clinical decision support, and data integration tasks. The development of software applications to perform these tasks requires the integration of Web services to incorporate the wide variety of ontologies used in the health care and life sciences. The National Center for Biomedical Ontology, a National Center for Biomedical Computing created under the NIH Roadmap, developed BioPortal, which provides access to one of the largest repositories of biomedical ontologies. The NCBO Web services provide programmtic access to these ontologies and can be grouped into four categories; Ontology, Mapping, Annotation, and Data Access. The Ontology Web services provide access to ontologies, their metadata, ontology versions, downloads, navigation of the class hierarchy (parents, children, siblings) and details of each term. The Mapping Web services provide access to the millions of ontology mappings published in BioPortal. The NCBO Annotator Web service "tags" text automatically with terms from ontologies in BioPortal, and the NCBO Resource Index Web services provides access to an ontology-based index of public, online data resources. The NCBO Widgets package the Ontology Web services for use directly in Web sites. The functionality of the NCBO Web services and widgets are incorporated into semantically aware applications for ontology development and visualization, data annotation, and data integration. This overview will describe these classes of applications, discuss a few examples of each type, and which NCBO Web services are used by these applications.BioPortal is an open repository of biomedical ontologies that stores ontologies developed in various formats, such as OWL, OBO format, Protégé frames, and the Rich release format, and provides access to this content via Web browsers and Web services [1, 2] . The BioPortal Web interface allows users to browse the list of ontologies, search and comment on terms in ontologies, annotate text with ontology terms, and search an ontology-based index of biomedical resources. The BioPortal architecture currently includes both LexEVS

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IP Packet Size Entropy-Based Scheme for Detection of DoS/DDoS Attacks SUMMARY Denial of service (DoS) attacks have become one of the most serious threats to the Internet. Enabling detection of attacks in network traffic is an important and challenging task. However, most existing volume-based schemes can not detect short-term attacks that have a minor effect on traffic volume. On the other hand, feature-based schemes are not suitable for real-time detection because of their complicated calculations. In this paper, we develop an IP packet size entropy (IPSE)-based DoS/DDoS detection scheme in which the entropy is markedly changed when traffic is affected by an attack. Through our analysis, we find that the IPSE-based scheme is capable of detecting not only long-term attacks but also short-term attacks that are beyond the volume-based schemes' ability to detect. Moreover, we test our proposal using two typical Internet traffic data sets from DARPA and SINET, and the test results show that the IPSEbased detection scheme can provide detection of DoS/DDoS attacks not only in a local area network (DARPA) and but also in academic backbone network (SINET). key words: denial of service attack, network security, attack detection With the explosive growth of the global Internet, people enjoying the network services with worldwide connectivity are at risk of attacks from other malicious users. In recent years, denial of service (DoS) [1] attacks have caused significant financial loss and have become one of the most serious security threats to the Internet. In a DoS attack, a malicious user often cripples a victim by simply flooding the target with many legitimate-looking requests. A sophisticated version of DoS is known as a distributed denial of service (DDoS) attack in which an attack is launched by multiple coordinated computers under an attacker's control. Launching a DoS/DDoS attack is very easy by using some attack tools such as Tribe Flood Network (TFN), TFN2K, and Trinity, which are available on the Internet [2]. But detection is still an open issue because of the complex nature of network traffic.. The current approaches of DoS/DDoS detection can be divided into two types: volume-based and feature-based. In a volume-based detection scheme, attacks are detected by identifying abrupt changes in traffic volume. In [3], J. Haggerty et al. proposed a real-time anomaly detection scheme to identify TCP SYN flooding attacks by analyzing the daily maximum arrival rate. In [6] , the anomalies were detected with a wavelet-based signal analysis system. Although these A feature-based detection scheme detects attacks by inspecting changes in the distributional aspects of packet header fields. H. Wang et al. [7] proposed a statistics-based mechanism to detect TCP SYN flooding attacks by checking the ratio of SYN/FIN packets. In [5] , a DDoS attack was detected when it caused the destination addresses to be concentrated on the victim address while the source addresses were spoofed. Although feature-based detection schemes can detect even small-volume attack traffic [5] , [7] , [11] , inspecting the header fields of every packet to collect and analyze the features is too exhausting a method to detect attacks in real time.. In this paper, considering that different application traffic has different packet size distributions and that this distribution changes during DoS/DDoS attacks, we propose an IP packet size entropy (IPSE)-based scheme in which the attacks are detected by observing time series of packet size entropy. A spike in the time series indicates that a possible DoS/DDoS attack is under way. We provide two methods to distinguish DoS traffic and DDoS traffic from legitimate traffic at the detected possible attack points. Different from existing volume-based and feature-based methods, our research studies DoS/DDoS traffic characteristics from the perspective of the IP packet size distribution, which has not been used in attack detection yet.. The main contribution of this paper is that our proposal not only detects long-term attack traffic, but also detects short-term attack traffic which does not cause detectable changes in traffic volume. The second contribution is that our proposal can provide a means of detection of DDoS attacks before they cripple the target. Compared with featurebased methods, our proposal does not need to inspect the header fields of each packet. This makes it simpler and more practical for real-time implementation.. Finally, our proposal can work in both local area network (LAN) (such as DARPA [12] ) and backbone network (such as SINET [15] ) environments.. The rest of the paper is organized as follows. Section 2 elaborates on the utility of the IPSE-based scheme for detecting DoS/DDoS attacks and introduces two methods for distinguishing attack traffic from legitimate traffic. Section 3 discusses the performance of our proposal with a traditional volume-based scheme in experiments using real traffic-trace data sets. We use DARPA data as LAN traffic, and SINET data as backbone network traffic for investigating proposed IPSE-based attack detection scheme. Section 4 concludes our proposal and outlines our future work. In this paper, we described an IP packet size entropy (IPSE)- based DoS/DDoS detection scheme, which was capable of detect not only long-term attacks but also short-term attacks which did not cause abrupt changes in traffic volume by observing the time series of the entropy of packet size.. Although our proposal can not detect all attacks completely (actually no scheme can), it is a novel approach with a simple implementation for DoS/DDoS detection. If a wily attacker knows our detection scheme and modifies his strategy, there is still a possibility to find new differences between the packet size distributions of the humanparticipating legitimate traffic and the machine-automating attack traffic. Our future work is to detect more stealthy attacks.

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SMIS members: a membership analysis This article discusses the results of a survey of SMIS members. Members were asked to respond to questions regarding demographics, their satisfaction with SMIS services, and the importance of eighteen management issues which MIS management might address. The article presents percentage results of individual questions and interprets the results of those questions. No attempt is made to use any bivariate statistics in this article. All questions asked on the survey are presented in this article. The survey reported in this article represents the first attempt to study the characteristics of the membership of SMIS, what needs and issues they face, and the direction that SMIS should follow in the future. The data collected is rich in information content and we are just now beginning to fully analyze it. In addition to the numerical data presented here, over 300 written comments appeared on the survey forms which are, of course, more difficult to analyze but potentially of more value to determining the direction of SMIS.. Future work with this data will be concentrated on analyzing the needs and issues of members categorized according to various demographics. For instance, it might be interesting to see if there is a difference in needs and issues when the data is divided by industry group, size of the organization, or class of SMIS membership. Other demographic divisions might also be interesting to review.. This, then, is a preliminary view of this survey. Yet, the information content is important. For example, we have learned that members are part of very large organizations with control over substantial resources. Also, the members are well-educated and spend a considerable amount of time and effort in professional development activities. They are particularly concerned with management issues and have a strong need to do more long range planning and to be able to measure the effectiveness of the organizations that they manage.. In brief, SMIS is an organization for top information systems managers. It would appear that the programs that they provide are satisfying their members. We hope that this study will assist them to continue in that direction.

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Ensemble Learning Based Segmentation of Metastatic Liver Tumours in Contrast-Enhanced Computed Tomography This paper presents an ensemble learning algorithm for liver tumour segmentation from a CT volume in the form of U-Boost and extends the loss functions to improve performance. Five segmentation algorithms trained by the ensemble learning algorithm with different loss functions are compared in terms of error rate and Jaccard Index between the extracted regions and true ones. Segmentation of metastatic liver tumours from a contrastenhanced computed tomography (CT) volume is a crucial process for computer-aided surgery and diagnosis. A number of algorithms for liver tumour extraction have been proposed [1] - [5] ; some of them were pitted against each other in the competition at the Medical Image Computing and Computer-Assisted Intervention (MICCAI) workshop held in 2008 [5] , in which ensemble learning based segmentation (ELBS) trained by AdaBoost [6] presented the best automated segmentation [7] . A segmentation algorithm consists of several hundred weak classifiers (or hypotheses) [4] , [7] - [9] , called weak segmentation processes in this paper. In a series of training rounds, an AdaBoost algorithm repeatedly calls a weak segmentation process and combines the called processes into one to construct a strong segmentation algorithm with a minimised loss function. The best algorithm in the MICCAI competition combined two ELBS algorithms, one of which was trained using tumours whose mean radius is larger than 24 mm and the other by smaller tumours, by a logical sum operation. Because characteristics of CT value distribution differ according to tumour size. This paper also adopts the same procedure.. Although ELBS has excellent features that can deal with large variations in CT values, some false positives and false negatives occur in the resultant images when compared to manually labelled boundaries set by human observers. One possible reason for such errors is outliers of input feature vectors; another is mislabelling of tumours used for training. AdaBoost is known to be incapable of managing outlier and mislabelling problems appropriately because of its exponential loss function [10] - [12] . Several improved ensemble learning algorithms have been proposed [10] - [13] , such as modified AdaBoost (MadaBoost) [10] and Most B-robust η-Boost (MBRη-Boost) [11] , known to be robust against outliers of feature vectors and/or mislabelling of tumours. Each algorithm has a different loss function, leading to different characteristics in segmentation. The best loss function depends on the specific application. Although a comparative study of loss functions is important, there is no report regarding liver tumour segmentation. Additionally, the outlier and mislabelling problems might occur more often around tumour boundaries than in other locations, but this is not taken into account in the existing ensemble learning algorithms.. The contributions of this paper are three-fold. First, we present an ensemble learning algorithm in the form of U-Boost [12] , which is a class of ensemble learning algorithms including not only AdaBoost but also MadaBoost and MBRη-Boost. The definition in the form of U-Boost makes the differences in algorithms clear, because the differences can be summarised in terms of the differences in the loss functions. Second, extensions of the loss functions of MadaBoost and MBRη-Boost are proposed to improve segmentation performance. Third, we compare the five ELBS algorithms for metastatic liver tumour segmentation trained by the five ensemble learning algorithms, or AdaBoost, Modified AdaBoost (MadaBoost), Most B-robust η-Boost (MBRη-Boost) and extensions of the MadaBoost and MBRη-Boost, to show the difference between AdaBoost and the other algorithms, the effectiveness of the proposed extension and determine the optimal algorithms. The five different loss functions for ensemble learning based liver tumour segmentation were presented in the form of U-Boost. The performance of segmentation algorithms trained by the different loss functions were compared and optimal one was determined for each tumour group, or small tumour group and large one. The performance of the five ELBS algorithms trained by AdaBoost, MadaBoost, MBRη-Boost, cost-sensitive MadaBoost (CS-MadaBoost) and modified MBRη-Boost (M-MBRη-Boost) were evaluated by a 10-fold CV test for each group, the large tumour and small tumour groups. The maximum number of weak segmentation processes was set to 200 for the large tumour group, and 1,000 or 1,500 for the small tumour group, σ of the Gaussian for η(x) was 1.8 mm, η for MBRη-Boost was an average of η(x) used in its extended version, or 0.0331 for large tumours and 0.0512 for small tumours, and minimisation in the computation process of confidence α t of step 3 in Fig. 1 was performed using the Brent algorithm [16] . Figure 3 (a) shows the transition of error rates for large tumours evaluated by 10-fold CV. The minimum error rates are marked by red circles. AdaBoost is inferior to MadaBoost and MBRη-Boost, whose performances are comparable to each other. The two extensions proposed in this paper yielded different results. M-MBRη-Boost failed to reduce its error due to a local minimum of the loss function, resulting in a high error rate, while CS-MadaBoost was confirmed as the best, slightly better than its original ensemble learning algorithm; it achieved the minimum error among all the algorithms. Figure 4 presents the regions extracted by AdaBoost, MadaBoost and CS-MadaBoost, where the number of weak segmentation processes was set to an optimal level, according to the red circles labelled a, b and c in Fig. 3 (a) . Semitransparent coloured regions correspond to the extracted re- gions, and manually defined true boundaries are shown in white. A difference was observed in the region indicated by yellow arrows, where false positives were eliminated by MadaBoost and CS-MadaBoost.. To evaluate the segmentation performance quantitatively, we computed the Jaccard Index (JI) between an extracted region and a true region, which was manually labelled by an author and approved by a radiologist. The JI of AdaBoost was improved by 1.2 pt with MadaBoost and 2.8 pt with CS-MadaBoost. The average improvement in JI for all materials was 0.092 pt by MadaBoost and 0.51 pt by CS-MadaBoost. Figure 3 (b) presents the transition of error rates for small tumours evaluated by 10-fold CV. Minimum error rates were achieved at the positions marked by red circles. This figure shows that AdaBoost is the worst, while the extension of MBRη-Boost is better than its original version and achieved the best performance. Figure 5 demonstrates that MBRη-Boost and M-MBRη-Boost could extract a tumour missed by AdaBoost when the number of weak segmentation processes was set as optimal. The JI of AdaBoost was greatly improved by MBRη-Boost and M-MBRη-Boost. The average improvement in JI for all materials was 2.0 pt by MBRη-Boost and 2.9 pt by M-MBRη-Boost, respectively.. We focus on AdaBoost as well as the best ensemble learning algorithm for each type of tumours and its original version, whose minimum error rates are annotated by a, b and c in the Fig. 3 . A Wilcoxon test was carried out to evaluate the difference in performance statistically. The null hypothesis H 0 is that no significant difference exists between the two distributions of error in a CT volume. In the large tumour group, the results told us that the difference between AdaBoost and MadaBoost, and that between AdaBoost and CS-MadaBoost were statistically significant with risk p < 0.01. A possible reason for their superiority to AdaBoost is their robustness against outliers and/or mislabelling of tumours. It was also found that extending the loss functions could boost segmentation performance, due mainly to the fact that outliers and/or mislabelling tend to happen more often around tumour boundaries than in other positions.. Similar findings were also observed in the small tumour group. The difference between AdaBoost and MBRη-Boost, and that between AdaBoost and M-MBRη-Boost whose error was minimum were statistically significant with risk p < 0.01 tested by a Wilcoxon test. Moreover, the difference between the JI values of MBRη-Boost and M-MBRη-Boost was statistically significant with risk p < 0.05. The result suggests that extending the loss function has the potential to improve the performance, particularly in small tumours.

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


Improved Model- and View-Dependent Pruning of Large Botanical Scenes Abstract Rendering of natural scenes with vegetation as rich as in the real world has been a motivation of computer graphics research ever since. The complex visual appearance and the inhomogeneous structure of botanical objects makes real-time rendering of large scenes a challenging task that extends to this day. The obvious main reason is the tremendous amount of geometry that is needed to represent trees and plants. Storing as well as rendering such objects with full detail is beyond the capabilities even of modern graphics hardware. However, even if processing and rendering the data were possible, then the small sub-pixel details due to the complex geometry can still cause aliasing artefacts.. Many different approaches have been presented to render trees in real-time. Most often simple billboards or impostors [SSK96] are used, or automatically generated billboard clouds [DDSD03, GSSK05] which are sets of billboards that better preserve occlusion and parallax effects. However, these representations are well suited for distant objects and trees, but they are typically over simplified and close views reveal the low quality. It is also not possible to achieve coherent shading of the scene or to adapt the level of detail smoothly and without noticeable artefacts due to the planar nature of billboards [LEST06] .. In this paper we present a rendering technique for complex botanical scenes based on pruning. Pruning techniques (stochastically) reduce geometry by simply excluding some parts of the model, for example leaves, from the rendering and correcting contrast and the total rendered area by scaling the remaining leaves [CHPR07] . We improve upon previous methods in several respects:. • We describe a view-optimized pruning instead of purely stochastic simplification of the geometry. This allows us to account for global scene information, for example thick and sparse forest and occlusion from neighbouring trees.. • We show that scaling of geometry after pruning should not be inversely proportional to the geometry reduction.. • We formalize this by introducing Precision and Recall as a measure of rendering quality. Our measure does not consider pixel colours, but whether the right pixels of a rendered object are set. We also validate this by conducting a user-study where subjects had to manually adjust the preferred scaling value. In this paper, we introduced Precision and Recall as a measure of quality for rendering complex geometry with pruning. We further improved on previous methods by applying model-specific geometry reduction and optimized scaling as well as view-optimized pruning. We evaluated our method by means of a user study that indicates a considerable improvement compared to naive and purely stochastic pruning. However, our work also raises new questions. One interesting direction of future research is to consider more than just correct and incorrect pixels in PR, for example by accounting for deviations in the normals, measuring contrast and colour differences, or to evaluate how visible differences predictors can improve the measure and whether their use amortizes. Since the very beginning of computer graphics, rendering algorithms have been high consumers of computational resources and memory. In general, level of detail (LOD) methods aim at cutting down the rendering cost, mainly by reducing model detail or shading cost. Covering the huge body of work in this field is beyond the scope of this paper. Here we focus on geometry reduction techniques closely related to our work. There exists a variety of texture-based techniques, most notably impostors [SSK96] and billboard clouds [DDSD03] , which have been tailored for tree rendering [GSSK05, LEST06] . These techniques generate discrete levels of detail which require special treatment to avoid distracting popping artefacts when adapting the detail, for example using [SW08] . Decaudin and Neyret [DN04] use 3D textures representing parts of a dense forest and aperiodic tiling to render large scenes by volume slicing. However, this method only allows distant views, for example as used in flight simulators. They further extended this approach to volumetric impostors [DN09] , but this method shares the drawback of high memory consumption with the other texturebased techniques. Rebollo et al. [RRCR06] describe a GPUfriendly rendering technique for foliage using a multiresolution representation obtained from split and collapse operations, and Gumbau et al. [GCRR11] extend this idea by a view-dependent measure. Both however, require additional memory for storing the multiresolution model.. Because of the aforementioned limitations of these approaches, we base our method on pruning techniques. Especially the simple and efficient idea of stochastically removing geometry makes such approaches extremely simple to use and implement. Stochastic simplification can be easily used with geometry representations that do not require topology information, such as point rendering methods. The QSplat algorithm [RL00] and sequential point trees [DVS03] adapt the size of pre-positioned splats (rendered point primitives) to the required sampling density. Point samples can also be created on the fly, for example distributed randomly onto surfaces [WFP * 01], stratified [WS02] or adaptively [SD01] . All these methods have in common that-when using fewer samplesthey preserve the total area by scaling the rendered remaining primitives. Klein et al. [KKF * 04] used a stochastic simplification for polygonal scenes, however, the scene elements are only discarded, not altered, and thus this method is only suitable for coarse previews. Deussen et al. [DCSD02] applied stochastic simplification to rendering complex ecosystems. For reducing geometry they replaced the original triangles successively by lines and then points. Cook et al. [CHPR07] transfer this idea to complex geometry not restricted to point representations. They demonstrate simplification by pruning and scaling adapting not only to an object's screen size, but also to motion blur and depth of field. Their work is closely related to ours, however, we show that the rendering quality can be improved by cleverer scaling. An overview over various further techniques for rendering vegetation, such as fractalbased or space partitioning methods, is given by Zhang and Pang [ZP08] .

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


Anisotropic Field-of-Views in Radial Imaging Abstract-Radial imaging techniques, such as projection-reconstruction (PR), are used in magnetic resonance imaging (MRI) for dynamic imaging, angiography, and short-2 imaging. They are robust to flow and motion, have diffuse aliasing patterns, and support short readouts and echo times. One drawback is that standard implementations do not support anisotropic field-of-view ( We have introduced a new method that designs projections for anisotropic FOVs in radial imaging. These FOVs can be precisely tailored to noncircular objects or regions-of-interest in 2-D and 3-D imaging. This allows for scan time reductions without introducing aliasing artifacts. For undersampled applications, this method allows for reduction of aliasing artifacts.. Algorithms have been presented for the design of 2-D and 3-D PR trajectories, as well as 3-D cones. There is no loss in FOV area efficiency when using anisotropic FOVs. The algorithms are very simple and fast, allowing them to be computed on-the-fly. They also support variable trajectory extents which can be used in MRI to favor certain gradients or relax gradient constraints in 3-D cones. The algorithms presented are designed with fully-sampled FOV parameters, but will also be beneficial for undersampled radial imaging applications, as demonstrated in Fig. 15 . For undersampled applications like VIPR [7] , the desired FOV shape and size should be a scaled down version of the region-of-interest for equivalent undersampling factors in every dimension. The anisotropic FOV projections can also be applied to the highly constrained backprojection (HYPR) method for time-resolved MRI [24] because they can be reconstructed by filtered backprojection. Exam-specific FOVs can be used in all applications because the computation time of the design algorithms is small. Using an initial localizing scan, the desired FOV could be drawn or automatically detected and the acquisition tailored appropriately.. For some FOV and shapes, the resulting PSFs have low-level aliasing within the desired FOV. This is due to the finite width of the aliasing lobes, as shown in Fig. 1(b) , which is not accounted for in our design algorithms. The projection angles are designed based on the peak at the center of these aliasing lobes, leaving the potential for up to half of the lobe to overlap inside the FOV. Overlap is more likely to occur as the radial separation of neighboring lobes increases, and thus is correlated with . The online animations of the PSFs show how the origin of the low-level aliasing is primarily along the longer edges where this derivative is the largest. No aliasing originates from minima or maxima of the FOV where the angular derivative is zero.. Narrower shapes, which have a larger angular derivative, have more desirable efficiency curves in Fig. 7 because they have more low-level aliasing within the FOV. For the shapes in Fig. 7 , the total low-level aliasing power is approximately 0.60% and 1.3% of the main lobe power for the 1.5:1 and 2:1 ellipses, respectively, and 0.67%, 0.91%, and 1.2% for the 1:1, 1.5:1, and 2:1 rectangles. This confirms that narrower shapes have more low-level aliasing and that, in general, this aliasing is small. There is no low-level aliasing in the dual shape sampling patterns seen in Fig. 8(b)-(d) . This suggests that the low-level aliasing may be more correctly correlated with the derivative of , which is zero for the dual shapes. This derivative is very large for the FOV and shapes in Fig. 8(e) , which has significant aliasing inside the desired FOV. Another observation is that dual ellipse sampling can be formed by scaling an isotropic sampling pattern along one axis. By Fourier theory, this transformation scales the PSF along the corresponding axis by the inverse and introduces no low-level aliasing. It is possible that the other shapes may be formed by some transformation of isotropic case. We have found no derivation confirming this suggested low-level aliasing correlation or any general transformation starting with isotropic sampling.. With our method, it is possible to use 3-D radial imaging trajectories to image thin slabs with isotropic resolution, as demonstrated in Figs. 14 and 15. Previously, this was achieved by using stacks of projections [6] , [9] , which lacks some of the benefits of a true 3-D radial acquisition, such as ultra-short TEs. Stacking the projections also results in a coherent aliasing streak along the stacking direction, similar to the streak resulting from the cones-based design (see Fig. 10 ), which may be related to artifacts reported in the stacking dimension with contrast enhancement [7] . Both methods support one dimension of variable resolution, and stacks of 2-D anisotropic FOV projections are also possible.. This projection design can also be applied to other centricbased k-space trajectories. It can be directly applied to twisting radial-line (TwiRL) trajectories [25] by specifying the angular spacing of the different acquisitions. Anisotropic resolution can also be incorporated by adjusting the twist in the radial line to match . Interleaved spiral acquisitions can also be adjusted for anisotropic FOVs. The angular spacing of adjacent interleaves can be determined by our algorithm, and spirals with many interleaves will benefit the most from this adjustment. This could also be combined with the previous anisotropic FOV spiral method [26] which describes the design of the spirals themselves.

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


Distinct Multicolored Region Descriptors for Object Recognition Abstract-The problem of object recognition has been considered here. Color descriptions from distinct regions covering multiple segments are considered for object representation. Distinct multicolored regions are detected using edge maps and clustering. Performance of the proposed methodologies has been evaluated on three data sets and the results are found to be better than existing methods when a small number of training views is considered. THE challenges involved in object recognition are mainly the efficient representation and then the comparison of two objects through their representations. Broadly speaking, there are two types of approaches to object representation. While the first utilizes the knowledge gained from the spatial arrangements of the "shape features" such as the edge elements, boundaries, corners, and junctions, the other uses the brightness or color features obtained more directly from the object images [1] . But, there are limitations to any algorithm which uses only either shape features or color features. The representation scheme should carry the color information and its pattern of appearance on the object surface. This study proposes a scheme to describe an object in such a way that the description contains the color information as well as the patterns of colors on the object surface. Note that, in most of the cases, wherever there is shape or structural information in the object, the corresponding patterns in the image possess discontinuities in colors. Thus, extraction of information regarding patterns of colors automatically leads to extracting shape and structural information of the object.. There are several approaches to object representation such as histogram-based, eigenspace-based, edge and corner-based, graphbased representations, etc. Among histogram-based methods, the work by Swain and Ballard [2] is one of the earliest works which used color as a primal cue for object recognition and image retrieval. Stricker [3] introduced an indexing technique based on the boundary histogram of multicolored objects. The histogrambased approach is an attractive method for object recognition because of its simplicity, speed, and robustness [4] . Although it is simple, the main drawbacks of this approach are its inability to encode shape and structural information of the objects and the use of only color information for distinguishing the objects.. The standard procedure in eigenspace-based methods is to represent an object by considering the whole image as a vector and projecting it over a set of eigenvectors to achieve data compression and reduction of redundant information. Generally, the eigenvectors corresponding to the dominant eigenvalues are found using Principal Component Analysis (PCA). Some of the earliest works on object recognition using eigenspace-based representation are by Murase and Nayar [5] , [6] and Turk and Pentland [7] . These methods are effective when eigenspace captures the characteristics of the whole database, for example, when all the object images have a uniform known background. If there is a large variation in the images, performance of the methods can deteriorate. Such methods are best suited for recognition of an object that constitutes a complete image [8] .. In graph-based representation, generally, regions with their corresponding feature vector and the geometric relationship between these regions are encoded in the form of a graph. Tu et al. [8] proposed a method which segments the image into regions of approximately constant color and the geometric relationship of the segmented colored regions is represented by an attributed graph. Object matching, then, is formulated as an approximate graphmatching problem. Methods such as Color Adjacency Graph (CAG) [9] , Attributed Relational Graph (ARG) [10] , and Shock graph [11] are prominent in this approach. Kostin et al. [12] proposed an object recognition scheme using graph matching. One advantage of graphbased representation is that the geometric relationship can be used to encode certain shape information of the object and any subgraph matching algorithm can be used to identify a single as well as multiple objects in query images. However, matching two such representations becomes a complicated process. Some of the issues in this regard are discussed in [12] .. Support Vector Machine (SVM)-based methods are used to classify both globally and locally obtained feature vectors of the objects [13] , [14] . Roth et al. [15] proposed a view-based algorithm for 3D object recognition using a network of linear units. The sparse Network of Winnows (SNoW) learning architecture is used to learn the representations of objects. Two experiments are carried out by them using pixel-based representation and edge-based representation of the objects separately.. In general, the above discussed methods use representation schemes which are global in nature. The global representation schemes have certain shortcomings. These shortcomings can be overcome using local representations. In local representation schemes, generally, information from several regions of the images are encoded. Some of the local representation schemes are Local Affine Frames (LAF) [16] , "Scale Invariant Feature Transform (SIFT)" [17] , "Shape Context" [1] , and "Multimodal Neighborhood Signature (MNS)." However, SIFT and Shape Context are designed for gray-scale images. Marée et al. [18] have proposed a generic approach to image classification based on decision tree ensembles and local subwindows and improvements upon this method are reported in [19] . They have tested the performance on gray scale as well as color images.. Two methods are proposed in this paper for object recognition. Section 2 describes the motivation of the work. Section 3 contains a representation scheme to represent an object image using the descriptions of different regions of interest. Two different schemes are proposed to extract the regions of interest. Section 4 has two dissimilarity measures, one is to compare two regions of interest and the other is to compare two object images through their descriptors. Section 5 contains a brief description of the data sets used and comparisons with the existing methods. This paper is concluded with a discussion on the proposed methodology in Section 6.

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


Fast spectral solution of the generalized Enskog equation for dense gases We propose a fast spectral method for solving the generalized Enskog equation for dense gases. For elastic collisions, the method solves the Enskog collision operator with a computational cost of O (M d−1 N d log N), where d is the dimension of the velocity space, and M d−1 and N d are the number of solid angle and velocity space discretizations, respectively. For inelastic collisions, the cost is N times higher. The accuracy of this fast spectral method is assessed by comparing our numerical results with analytical solutions of the spatially-homogeneous relaxation of heated granular gases. We also compare our results for force-driven Poiseuille flow and Fourier flow with those from molecular dynamics and Monte Carlo simulations. Although it is phenomenological, the generalized Enskog equation is capable of capturing the flow dynamics of dense granular gases, and the fast spectral method is accurate and efficient. As example applications, Fourier and Couette flows of a dense granular gas are investigated. In addition to the temperature profile, both the density and the high-energy tails in the velocity distribution functions are found to be strongly influenced by the restitution coefficient. When the gas molecular mean free path (MFP) is comparable to the characteristic flow length, the Navier-Stokes equations based on the continuum-fluid assumption fail, and the Boltzmann equation is needed to study the rarefied gas dynamics [1] . Since in most situations the MFP is much larger than the molecular dimension, the binary collision modeled by the Boltzmann collision operator is localized in space. However, the collision is delocalized when the gas is compressed to such a density that the ratio of the molecular dimension to the MFP becomes appreciable; yet the continuum-fluid assumption is still inappropriate because of the small characteristic flow system size. This situation occurs, for instance, in gas flow in ultra-tight shale strata. For these dense gases, the Boltzmann equation is extended to the Enskog equation for hard-sphere molecules:. where f (t, x, v) is the velocity distribution function (VDF) of molecular velocity v at spatial location x and time t, and a is the external acceleration. The right-hand side of Eq. (1) is the Enskog collision operator (ECO), where σ is the molecular diameter, d is the dimension of the velocity space, k is a unit vector associated with the relative position of two molecules at the time of their impact, and u = v − v * is the relative pre-collision velocity of two colliding molecules. The post-collision velocities v and v * are related to the pre-collision molecular velocities v and v * through v = v − (u · k)k and v * = v * + (u · k)k. Finally, the nonlocal collision is characterized by the product of the VDF and a pair correlation function at different locations:. (2). The velocity-independent pair correlation function χ is a given function of gas density. In the standard Enskog theory, χ coincides with the pair correction function in a state of uniform equilibrium evaluated at the contact point, while in the revised Enskog theory it is evaluated as the local equilibrium value in a nonuniform state [2] . In this paper, the former is adopted and the detailed expressions for the pair correlation function will be given below. The ECO has been extended to dense granular gases (i.e. materials composed of many small discrete grains), where the kinetic energy is not conserved during collisions [3] [4] [5] . A restitution coefficient 0 ≤ α ≤ 1, which is a function of the normal relative pre-collision velocity |u · k|, is introduced to characterize the loss of kinetic energy. Neglecting rotational degrees of freedom, the generalized Enskog collision operator (GECO) becomes:. where ṽ and ṽ * are the pre-collision velocities producing post-collision ones v and v * after collision, and J is the Jacobian of the transformation from (ṽ, ṽ * ) into (v, v * ).. The generalized Enskog equation has applications ranging from astrophysics (e.g. stellar cloud formation) to industrial processes (e.g. fluidized beds and transport lines, handling of pharmaceuticals, and shale gas exploitation). The Enskog-Vlasov equation with the mean-field potential is even able to describe both liquid and vapor phases, and automatically capture liquid-vapor and fluid-solid interfaces [6, 7] , which has potential applications to multiphase flows in micro/nanoelectromechanical systems.. While various numerical methods have been proposed for the Boltzmann equation, there are only a few for the Enskog equation, let alone for the generalized equation. The most difficult part is the numerical solution of the collision operator. For elastic collisions, the ECO was first solved using a Monte Carlo quadrature method [8] , and the study of shock propagation in a dense hard-sphere gas indicated that the Enskog equation can produce exact solutions comparable to molecular dynamics (MD) simulations [9] . Later, inspired by direct simulation Monte Carlo (DSMC) methods for the Boltzmann equation [10, 11] , several particle schemes were proposed for the simulation of dense gases [12] [13] [14] [15] , as well as the MD-DSMC hybrid method [16] . For inelastic collisions, the GECO has been solved by the DSMC [17, 18] and spectral [19] methods for spatially-homogeneous relaxation problems.. As is well-known, the DSMC method has a computational cost proportional to the number of simulated particles (which may be far fewer than the actual number of molecules). However, particle-based methods are vulnerable to noise when macroscopic flow quantities are much smaller than the corresponding characteristic values (for example, when the flow velocity is much smaller than the sound speed). On the other hand, the spectral method is a deterministic numerical approach which solves the GECO with a computational cost O (N 2d ), where N is the number of discretized velocities in each direction [19] . It is good at resolving small flow signals (e.g. it can easily capture the high-energy tail of the VDF in a heated granular gas [19] ) but has greater computational complexity than the DSMC method. A deterministic numerical method with high accuracy but small computational cost would be in strong demand.. Recently, a fast spectral method (FSM) with a computational cost of O (N d log N) has been proposed for solving the Boltzmann equation with spectral accuracy [20] [21] [22] . It has been successfully applied to many challenging cases for which the DSMC method is extremely time-consuming [23] [24] [25] . In this paper, we investigate the applicability of the FSM for solving the generalized Enskog equation.. This paper is organized as follows. The weak form of the GECO is expressed in the Carleman representation in Section 2, and is approximated by the FSM in Section 3. In Section 4, the accuracy of the FSM is assessed in several numerical tests. In Section 5, Fourier and Couette flows of a dense granular gas are investigated. Finally, concluding remarks are made in Section 6. Based on the Carleman representation of the collision operator in its weak form, and a Fourier-Galerkin discretization of velocity space, we have developed a fast spectral method to solve the generalized Enskog collision operator for dense granular gases. This method has a computational cost of O (M d−1 N d+1 log N), and works for any form of the intermolecular potential. In particular, the computational cost reduces to O (M d−1 N d log N) for elastic collisions with special collision kernels such as those of hard-disk and hard-sphere gases. The accuracy of the proposed method has been demonstrated through several numerical tests. To our knowledge, this is the first time that the generalized Enskog collision operator has been solved by a deterministic numerical method with both high accuracy and high efficiency.. The Fourier and Couette flows of dense granular gases have also been investigated. We found that the restitution coefficient has a strong influence on the molecular density and high-energy tail of the velocity distribution functions. Generally speaking, the smaller the restitution coefficient, the more molecules concentrate around the central region of the channel and the more molecules there are with high velocities.. The fast spectral method can be extended straightforwardly to gas mixtures, which could then help reveal the abundant exotic phenomena in dense granular gases. For granular flows with small values of the restitution coefficient, the temperature decreases drastically from the energy source due to the large dissipation, and thus a large number of discretized velocities is needed. In this case, velocity rescaling may be incorporated to improve the computational efficiency [43] .

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


Simulated

unbound

structures

for

benchmarking

of

protein

docking

in

the

Dockground

resource

Background:

Proteins

play

an

important

role

in

biological

processes

in

living

organisms.

Many

protein

functions

are

based

on

interaction

with

other

proteins.

The

structural

information

is

important

for

adequate

description

of

these

interactions.

Sets

of

protein

structures

determined

in

both

bound

and

unbound

states

are

essential

for

benchmarking

of

the

docking

procedures.

However,

the

number

of

such

proteins

in

PDB

is

relatively

small.

A

radical

expansion

of

such

sets

is

possible

if

the

unbound

structures

are

computationally

simulated.

Results:

The

DOCKGROUND

public

resource

provides

data

to

improve

our

understanding

of

protein-protein

interactions

and

to

assist

in

the

development

of

better

tools

for

structural

modeling

of

protein

complexes,

such

as

docking

algorithms

and

scoring

functions.

A

large

set

of

simulated

unbound

protein

structures

was

generated

from

the

bound

structures.

The

modeling

protocol

was

based

on

ns

Langevin

dynamics

simulation.

The

simulated

structures

were

validated

on

the

ensemble

of

experimentally

determined

unbound

and

bound

structures.

The

set

is

intended

for

large

scale

benchmarking

of

docking

algorithms

and

scoring

functions.

Conclusions:

A

radical

expansion

of

the

unbound

protein

docking

benchmark

set

was

achieved

by

simulating

the

unbound

structures.

The

simulated

unbound

structures

were

selected

according

to

criteria

from

systematic

comparison

of

experimentally

determined

bound

and

unbound

structures.

The

set

is

publicly

available

at

The

DOCKGROUND

public

resource

provides

data

to

improve

our

understanding

of

protein-protein

interactions

and

to

assist

in

development

of

docking

algorithms

and

scoring

functions.

Sets

of

protein

structures

determined

in

both

bound

and

unbound

states

are

essential

for

benchmarking

docking

procedures.

However,

the

number

of

such

proteins

in

PDB

is

relatively

small.

A

radical

expansion

of

such

sets

is

possible

if

the

unbound

structures

are

computationally

simulated.

Such

simulated

unbound

protein

set

was

generated

for

the

DOCK-GROUND

resource.

The

modeling

protocol

was

based

on

ns

Langevin

dynamics

simulation.

Simulated

unbound

structure

was

selected

according

to

criteria

from

systematic

comparison

of

experimentally

determined

bound

and

unbound

structures.

The

set

is

publicly

available

at

Proteins

play

an

important

role

in

biological

processes

in

living

organisms.

Many

protein

functions

are

based

on

interaction

with

other

proteins.

The

structural

information

is

essential

for

adequate

description

of

these

interactions.

Protein

interaction

is

characterized

by

structural

and

physicochemical

recognition

factors

and

conformational

changes

upon

binding

Computational

approaches

to

the

structural

modeling

of

protein

interactions

are

important,

given

the

limitations

of

experimental

techniques

A

significant

progress

in

the

computational

prediction

of

protein-protein

complexes

(protein-protein

docking)

has

been

reflected

in

the

community-wide

assessment

The

original

steric

complementaritybased

algorithms

paved

the

way

to

knowledge-based

approaches

including

those

based

on

similarity

to

existing

co-crystallized

complexes,

low-resolution

(coarse-grained)

techniques,

and

proteome-wide

applications

The

docking

algorithms

are

generally

based

on

the

concept

of

structure

complementarity,

observed

in

experimentally

determined

complexes.

Thus,

most

docking

procedures

perform

better

when

the

bound

(co-crystallized)

protein

structures

are

used,

assuring

the

perfect

match

between

the

structures.

Such

bound

docking

allows

one

to

neglect

the

internal

degrees

of

freedom

(structural

flexibility),

providing

for

an

effective

search

of

the

six-dimensional

rigid-body

space

of

the

external

coordinates.

However,

in

the

real-case

scenario,

the

bound

structures

of

the

participating

proteins

are

unknown,

and

one

has

to

rely

on

the

unbound

(e.g.

crystallized

separately)

proteins.

Because

of

the

huge

number

of

potentially

relevant

internal

degrees

of

freedom,

the

problem

of

unbound

docking

is

far

from

being

solved..

The

rigid-body

docking

of

unbound

proteins

results

in

structural

mismatches

at

the

putative

interfaces.

Thus,

one

approach

to

the

unbound

docking

lowers

the

resolution

of

the

structures,

alleviating

the

difference

between

unbound

and

bound

structures,

and

decreasing

the

structural

overlap

The

downside

of

such

an

approach

is

a

lesser

(low-resolution)

precision

of

the

predicted

structure

of

the

complex.

An

alternative

paradigm

is

to

use

sophisticated

scoring

schemes

to

evaluate

a

large

number

(e.g.

hundreds

of

thousands)

of

high-resolution

rigid-body

predictions,

in

anticipation

that

it

would

capture

the

native

interface

containing

structural

mismatches

(thus

having

high

energy)

Docking

approaches

that

explicitly

search

the

internal

coordinates

are

being

developed

However,

their

success

in

the

unbound

docking

is

still

limited

Template-based

docking

approaches

(structure

or

sequence-based)

generally

are

based

on

the

backbone

alignment

(followed

by

the

repacking

of

the

side

chains

for

the

final

prediction).

Thus,

in

principle,

they

should

not

depend

on

the

bound/unbound

difference

in

the

side

chains

conformations.

However,

the

difference

in

the

backbone

may

affect

the

performance

of

the

procedure..

For

the

development

of

docking

techniques

applicable

to

the

unbound

proteins,

it

is

essential

to

learn

the

experimentally

determined

difference

between

bound

and

unbound

states.

A

number

of

proteins

have

structures

experimentally

determined

in

both

unbound

and

bound

states

In

most

proteins

of

complexes)

conformational

change

upon

binding

is

Å

all

atoms

RMSD

A

significant

number

of

complexes

with

larger

RMSD

have

a

domain

shift,

where

conformational

changes

in

the

domains

themselves

are

small.

Still,

the

other

cases

of

large

RMSD

involve

interface

loops,

which

change

conformation

significantly

upon

binding.

Thus,

our

ability

to

adequately

address

conformational

changes

in

docking

is

important..

The

utility

of

the

unbound

docking

approaches

is

tested

in

the

CAPRI

blind

experiment

To

provide

consistent

sets

for

validation

of

docking

and

scoring

procedures,

benchmark

sets

of

protein-protein

complexes

were

compiled

However,

the

number

of

known

representative

protein

pairs

with

experimentally

determined

structures

in

both

bound

and

unbound

states

is

relatively

small

(e.g.,

in

the

Weng's

Benchmark

At

the

same

time,

the

number

of

co-crystallized

complexes

is

much

larger.

A

key

feature

in

the

DOCKGROUND

resource

is

flexibility,

which

allows

users

to

build

the

datasets

according

to

their

own

requirements.

Such

datasets

can

involve

thousands

of

complexes

and

thus

can

be

used

for

truly

large-scale

benchmarking

of

docking

methodologies.

Simulating

the

unbound

structure

from

the

bound

one

provides

such

an

opportunity.

Our

earlier

set

of

simulated

unbound

structures

based

on

an

older

version

of

DOCKGROUND,

was

generated

by

changing

the

side

chain

conformations

according

to

the

rotamer

library

In

the

current

paper

we

describe

a

much

larger

set

obtained

by

Langevin

dynamics

simulation

and

based

on

a

systematic

analysis

of

the

experimentally

determined

bound/unbound

structural

differences.

The

set

is

a

valuable

resource

for

benchmarking

docking

procedures

and

development

of

docking

methodologies.

Protein

complexes

were

selected

from

the

Bound

part

of

DOCKGROUND

with

the

following

criteria:

mean

area

buried

Å

include

alternative

binding

modes,

homo/hetero

n-mers,

and

oligomers,

and

the

redundancy

cutoff

The

resulting

set

contained

proteinprotein

complexes.

Program

Profix

from

the

Jackal

package

php/Software)

was

used

to

build

the

disordered

residues

and

missing

atoms..

It

was

expected

that

dynamic

simulation

of

separate

bound

protein

structures,

without

the

interacting

partner,

would

relax

interface

side-chain

conformations

constrained

by

the

interacting

partner

and

thus

approximate

the

unbound

form

of

the

protein.

To

speed

up

the

calculations,

we

chose

the

Langevin

Dynamics

(LD)

simulation

in

CHARMM

force

field),

with

electrostatics

by

Generalized

Born

approximation,

performed

on

each

bound

structure

without

its

interacting

partner.

Prior

to

LD

simulation,

the

initial

structures

from

PDB

files

were

minimized

(by

steps

of

steepest

descent

minimization

followed

by

steps

of

adopted

basis

Newton-Raphson

minimization)..

In

the

simulation,

the

backbone

atoms

of

helices

and

strands

were

constrained

with

a

force

constant

of

kcal/

mol,

the

temperature

was

set

to

K,

the

bond

lengths

were

fixed

using

shake

with

tolerance

the

friction

force

fbeta

was

and

the

time

of

simulation

was

ns,

with

snapshots

saved..

Protein

structures

that

crashed

during

the

simulation

were

removed.

The

simulation

yielded

protein

structures.

The

number

of

resulting

complexes

with

both

proteins

simulated

was

In

complexes

only

one

partner

was

simulated.

The

structure

with

the

largest

all

atoms

RMSD

from

the

bound

structure

was

designated

as

the

simulated

unbound

structure.

Among

the

simulated

proteins

there

were

non-obligate

and

obligate

complexes,

according

to

NOXClass

procedure

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


Using the minimum description length principle to reduce the rate of false positives of best-fit algorithms The inference of gene regulatory networks is a core problem in systems biology. Many inference algorithms have been proposed and all suffer from false positives. In this paper, we use the minimum description length (MDL) principle to reduce the rate of false positives for best-fit algorithms. The performance of these algorithms is evaluated via two metrics: the normalized-edge Hamming distance and the steady-state distribution distance. Results for synthetic networks and a well-studied budding-yeast cell cycle network show that MDL-based filtering is more effective than filtering based on conditional mutual information (CMI). In addition, MDL-based filtering provides better inference than the MDL algorithm itself. A key goal in systems biology is to characterize the molecular mechanisms that govern specific cellular behavior and processes. Models of gene regulatory networks run the gamut from coarse-grained discrete networks to detailed descriptions of such networks by stochastic differential equations [1] . Boolean networks and the more general class of probabilistic Boolean networks are among the most popular approaches for modeling gene networks because they provide a structured way to study biological phenomena (e.g., the cell cycle) and diseases (e.g., cancer), ultimately leading to systems-based therapeutic strategies. The inference of gene networks from high-throughput genomic data is an ill-posed problem known as reverse engineering. It is particularly challenging when dealing with small sample sizes because the number of variables in the system (e.g., the number of genes) typically is much greater than the number of observations [2] . Many inference algorithms have been proposed to elucidate the regulatory relationships between genes, such as Reveal [3] , ARACNE [4] , the minimum description length principle (MDL) [5] [6] [7] [8] [9] , the coefficient of determination (CoD) [10, 11] , and the best-fit extension [12, 13] .. False positives are a common problem in inference, especially when dealing with small sample sizes and noisy conditions. In fact, false positives are a kind of structural redundancy. Given three genes, x 1 , x 2 , and x 3 , they may interact in a chain-like manner, such as x 1 → x 2 → x 3 or x 1 ← x 2 ← x 3 ; or in a hub-based way, such as x 1 → x 2 ← x 3 or x 1 ← x 2 → x 3 . Indirect interactions between two genes may produce some correlation in their expression data, which can lead to a false regulation detection by inference algorithms. The data-processing inequality (DPI) was first used in ARACNE, which aims to reduce the false positives produced by chain interaction [4] . Later, conditional mutual information (CMI) was proposed to tackle the false positives produced by both the chain-like and hub-based interactions [14] . Because the conditioning gene, x 2 , is usually not known, a greedy search strategy was adopted to check if the CMI between x 1 and x 3 conditioned on some other genes was below a given threshold. To check the CMI on other unrelated genes is problematic. Not only is it computationally burdensome, it also suffers from an enormous multiplecomparisons problem. Moreover, since the interaction strength between genes generally varies a lot, their being both strong and weak interactions, how to set an appropriate threshold is a key problem.. A recent study shows that the best-fit algorithm appears to give the best results for recovering regulatory relationships in comparison to the aforementioned algorithms [15] . In the present paper, we propose to reduce the false positives of the best-fit algorithm by using the MDL principle. Simulation results show that it is more effective than the CMI-based method and can reduce the false positives in the MDL algorithm in [5] . In effect, the false-positive reducing procedure acts as a filter for removing false positives.. The aim of filtering in the present framework is to reduce the number of false positive connections. As with any false-positive reducing algorithm, this will invariably increase the number of false negatives, meaning more missing connections. Thus, two questions must be addressed. First, what benefits accrue from reducing the number of false positives? Second, does the increase in false negatives significantly impact inference performance?. A salient problem in translational genomics is the utilization of gene regulatory networks in determining therapeutic intervention strategies [2, 16, 17] . A big obstacle in deriving optimal treatment strategies from networks is the computational complexity arising directly from network complexity. Hence, significant effort has been focused on network reduction [18, 19] . As with any compression scheme, reduction methods sacrifice information in return for computational tractability. Because genes are removed from the network based upon their regulatory relations with other genes, false positives are particularly troublesome. First, they increase the amount of reduction necessary and second, they compete with true positive connections for retention in the reduced network. While it is true that an increase in false negatives is not beneficial, a missing connection creates no additional computational burden (in fact, reduces computation) and plays no role in the reduction procedure. Now, for the caveat, all of this is fine, so long as the accuracy of the original inference algorithm is not adversely impacted. Practically, this means that, relative to some distance function between a ground-truth network and an inferred network (which quantifies inference accuracy), the distance is not increased when using the modified false-positive reducing algorithm in place of the original algorithm. In this paper, we will consider two distance functions, one based on the hamming distance between the ground-truth and inferred networks and the other based on the difference between the steady-state distributions of the ground-truth and inferred networks. This paper is organized as follows: Background information and necessary definitions are given in Section 2. The implementation of MDL, the best-fit algorithm, and CMI-and MDL-based filtering is then introduced in Reducing the rate of false positives is an important issue in network inference. In this paper, we address this question by using the minimum description length (MDL) principle. Specifically, we apply the MDL measurement technique proposed by Zhao et al. to filter the model obtained by two best-fit algorithms (best-fit-I and best-fit-II). We compare the performance of MDL, best-fit-I, and best-fit-II filtered by CMI and MDL both on simulated networks and on an artificial model of budding yeast. The results show that, as determined by the distance metrics μ e ham and μ ssd , MDL-based filtering does not degrade inference performance, can improve inference performance, and is more effective than CMIbased filtering. Moreover, the combination of MDL filtering with the best-fit algorithm can even outperform the MDL algorithm alone. Additionally, applying MDLbased filtering is computationally less burdensome than using the MDL algorithm alone because calculating the data-coding length L D is more complex than calculating the error estimate of the best-fit algorithm, and the complexity of the calculation increases dramatically as the sample size m increases. Last but not the least, MDL-based filtering can also be applied to the results of other minimal error algorithms such as CoD. Based on the common assumption that genetic regulatory networks are sparsely connected, we restrict simulated Boolean networks to a scale-free topology with maximal connectivity K = 4 and average connectivity k = 2. The best-fit algorithm searches for the best-fit function for each gene by exhaustively searching for all combinations of potential regulator sets. The search space grows exponentially with the number of genes. In practice, the limit k i ≤ 3 is generally applied to mitigate model complexity. In this paper, we restrict best-fit-algorithm searches to combinations of 1, 2, or 3 possible regulators. The combinatorial set with the smallest error is then selected as the regulatory set. We call this best-fit-I. In practice, the minimal error predictor set may not unique. We employ the heuristic that each of them can be viewed as fitting the target gene in a different way and if one gene occurs frequently in those sets, then it is highly likely to be a true regulatory gene. Thus, we can determine the regulatory set by applying the majority rule in these sets. Here, we refer to this algorithm as best-fit-II.. Then CMI and MDL criteria are used to filter falsepositive connections. For each regulatory connection, if the CMI for one of the remaining genes is less than 0.005, then the gene is deleted; otherwise, it remains. The MDL criterion is applied to each target gene x i . Given its parent set, Pa(x i ), we delete the regulatory gene x j ∈ Pa(x i ) that can maximally reduce its coding length L i for each point in time, repeating this process until the deletion of one regulatory gene causes L i to increase. We implement an MDL inference algorithm by directly searching the combination of 1, 2, or 3 possible regulators with minimal coding length L i . The free parameter τ in Equation 6 is set to 0.2.. We have analyzed CMI-and MDL-based filtering by using both synthetic networks as well as the well-studied cell-cycle model known as the budding-yeast network. We compare them with the ground-truth network according to the following two distances [15, 23] :. (1) The normalized-edge Hamming distance:. where FN and FP represent the number of false-negative and false-positive wires, respectively, and P represents the total number of positive wires. This Hamming distance reflects the accuracy of the recovered regulatory relationships.. (2) The steady-state distribution distance:. where π k and π ′ k are the steady-state probabilities state x k in the ground-truth and inferred network, respectively. The steady-state distribution distance reflects the degree to which an inferred network approximates the long-run behavior of the ground-truth network.

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