Security model for a multi-agent marketplace A multi-agent marketplace, MAGNET (Multi AGent Negotiation Testbed), is a promising solution to conduct online combinatorial auctions. The trust model of MAGNET is somewhat different from other on-line auction systems: the mediated marketplace is a partially-trusted third party. In this paper, we identify the security vulnerabilities of MAG-NET and present a solution that overcomes these weaknesses. Our solution makes use of three different existing technologies with other standard cryptographic techniques: publish/subscribe systems that provide simple and more general messaging, time-release cryptography to provide guaranteed nondisclosure of the bids, and anonymous communication to hide the identity of the bidders until the end of the auction. By doing so, we successfully minimize the trust on the market as well as increase the security of the whole system. The protocol that we have developed can be adapted for use by other agent-based auction systems, which use a third party to mediate transactions. The business-to-business (B2B) e-commerce market is expected to expand rapidly in coming years, with the global market expected to exceed $7.29 trillion in 2004, according to Gartner Group research. Online marketplaces, as a meeting point for B2B businesses, offer benefits to both buyers and sellers. For buyers, a marketplace can significantly ease the process of searching for and comparing providers, while for sellers marketplaces provide access to much broader customer bases [10] . Sellers and buyers can maximize their interests by making use of auction-based marketplaces.. MAGNET and the supporting architecture provides support for complex agent interactions, such as in automated contracting, as well as other types of negotiation protocols [6] . MAGNET's auctions are reverse auctions, since the auctioneer pays instead of getting paid; first priced, since the bids selected are the lowest cost feasible bids; sealed bid, since the auctioneer is the only one who sees the bids; and combinatorial, since bids can include multiple tasks with a single price for the combination. Such an architecture can be used for carrying out contracting activities required in a B2B marketplace. However, in the absence of a secure architecture, its utilization in real world is still elusive.. When the original MAGNET system was designed, security was not a major concern. However, as the system has evolved, it has become clear to us that in order to be used on open networks, a security architecture needs to be in place. Specifically, MAGNET has problems with secrecy of bids, non-repudiation, early bid opening, and manipulation of bids. These problems are quiet common in auction systems. However, in MAGNET there exists a notion of a trusted third party: the market.. The presence of the market poses a unique challenge, that of ensuring the sanctity of the trust endowed in it. We came to realize that by ensuring this trust in the market we could overcome most of the existing security problems in MAG-NET. Our solution is achieved by a little bit of tweaking with the market architecture itself. The market will use a publish/subscribe system to notify other agents about its actions. By cross-checking the actions taken by the market, other agents can ensure that the market is acting properly. Thus our notion of trust is dependent on the vigilance of other agents. In a similar manner, we can ensure that other agents are acting in a proper manner. This paper is organized as follows. In Section 2 we examine the design of MAGNET and the resulting vulnerabilities. In Section 3 we present the security assumptions for MAGNET. We outline the proposed protocol in Section 4. In Section 5 we analyze the efficiency and security of the protocol that we presented. We compare our work with existing methods in Section 6. Finally, in Section 7 we present conclusions and talk about future work. In this paper we have presented ideas from recent work in security protocols for conducting secure electronic auctions and ideas for conducting agent-based electronic commerce. We have proposed a security architecture that would ensure the security of MAGNET and similar multi-agent marketplaces when used over public networks. Using various existing technologies, our protocol builds upon the trust model of the original marketplace and develops a system which has better methods of controlling fraud and deception.. We have begun implementing the proposed security model for use within MAGNET. Eventually we would like to release a secure version of the system to be used over the Internet. In the future we would also like to focus our work on establishing protocols for agent registration and payment collection in the execution phase once an auction has been closed. We would also like to include fault tolerance into the system so that the auction does not fail because of the failure of the entities involved. The majority of the work in the field of auction security has been done on sealed bid auctions in which the auction outcome is made public. Most of these protocols require m auctioneers out of which at least n should be trustworthy (threshold cryptography). Franklin and Reiter proposed one of these earlier systems in which using a variation of the secret sharing scheme algorithm they try to reduce the trust on the auctioneer [7] . In their system the value of n is a third of m. The resulting system requires exchange of numerous messages making it highly inefficient. This system cannot be applied to MAGNET as there exists only a single instance of the market (auctioneer). SAM [9] is a system in which the trust is shifted from the auctioneer to a hardware implemented secure co-processor [14] . The basic idea is to replace the auctioneer by a combination of hardware and software which can be trusted by all the parties involved in the auction mechanism. Any tampering of the hardware results in its self-destruction. The system is similar to MAGNET in the sense that only a single auctioneer exists in the system. However, the market in MAGNET is not absolutely trusted as SAM is supposed to be. Protocols in which the auctioneer is completely eliminated have also been proposed [1] . The idea behind such protocols is to let the bidders decide the winner themselves by splitting and distributing all the bids amongst all the bidders. Using a secret sharing scheme, the bids can be assembled only if all the bidders are willing to do so. As long as a single bidder does not collude with the other bidders, individual bids cannot be determined. In case all the bidders collude, the auction mechanism becomes an "open cry" auction. Once the bids are reassembled the winner can be determined by finding the highest bid. This system cannot be applied to MAGNET as the winner determination process is more complex than simply determining the highest bid [2] . A system which utilizes temporarily secret bid commitment has also been proposed [13] . However, none of the systems described above meet all the security requirements faced by multi-agent marketplaces like MAG-NET in the manner we have described.

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


A Multidimensional Positive Definite Remapping for Lagrangian Solutions of The Noh Problem A remapping based on the multidimensional positive definite advection transport algorithm (MPDATA), implemented for ALE methods, is used to model the Noh problem. Typical solutions in the Lagrangian reference frame contain heating errors which arise during the simulation of a shock reflection originating at a wall. The paper shows that the inherent properties of MPDATA can be exploited in the remapping to reduce wall heating errors. The resulting increase in accuracy and symmetry of solutions is demonstrated. A second-order accurate MPDATA remapping has been presented. The work builds upon developments of the algorithm for ALE calculations shown in [5] . The volume coordinate infinite gauge option is obtained by linearising the algorithm (4)- (9) around an arbitrarily large constant, see Section 4 in [9] for a detailed discussion of the process. In this way, the scalar or vector field is modified to be effectively non-negative, which in turn removes the need to exploit absolute values in derivatives. In practice, the basic algorithm is altered such that unity replaces each Ψ in the denominators of (7) and (8),. and in the fluxes of the corrective pass (9). To highlight the benefits of the infinite gauge option, a simple test is considered using the cyclic remapping mesh movement of [6] , with a scalar distribution given by ψ(x, y) = sin(2πx)sin(2πy) (A.1). remapped onto a series of meshes which are determined by a tensor product mesh movement, as described in [6] . The prescribed mesh movement has the effect of skewing an initially Cartesian mesh, before returning to the initial

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A generic formalism for the semantic modeling and representation of architectural elements Abstract This article presents a methodological approach to the semantic description of architectural elements based both on theoretical reflections and research experiences. To develop this approach, a first process of extraction and formalization of architectural knowledge on the basis of the analysis of architectural treaties is proposed. Then, the identified features are used to produce a template shape library dedicated to buildings surveying. Finally, the problem of the overall model structuring and organization using semantic information is addressed for user handling purposes. Studies on architectural heritage can be supported today by three-dimensional reconstructions of real buildings. The 3D digital model can bring an effective support to documenting the current state of historical buildings and also to create resources for the researchers who lead analyses on their historical evolution. With the purpose of confirming this assumption, several problems must be approached. As a result of using instruments such as the laser scanner for the building documentation, making the 3D models of architectural elements focuses on automatic procedures of reconstruction which consist primarily in a geometrical interpolation of metric data [27] . However, the objective of an architectural representation is to lead a semantic reading of the recorded data through the geometrical interpretation of the shape it describes. So, in order to attain these objectives, the process of threedimensional restitution of an observed reality must necessarily refer to a universe of knowledge. It is thus necessary to reaffirm the historical distinction between the acquisition phase and the data interpretation phase [28] while taking into account the relations of dependence that exist between these two stages. To give an example, many patrimonial buildings testify an intensive use by their builders of the concept of moulding. The importance of this concept is, for the architectural theory, largely established: it is described there initially as an essential tool in the composition of the shapes, but also as the means by which the shape gathers sense, by which the shape adds to its geometry properties of significant expression -softening, underlining, etc. In this direction, the coherence of the procedures of digital processing compared to the codes of the architectural representation constitutes an important issue we will address. In this article, we present an approach and the tools we have developed for the geometrical and semantic description of classical architecture elements. This approach guides the development of two applications: 1 a tool for the three-dimensional reconstruction of buildings, starting from a joint acquisition by laser scanning and photography, and a system for consulting on the Internet of the surveying and of the representations. This article is organized as follows: Section 2 presents the basic concepts for the understanding of geometrical nature of elements of classical language. Section 3 describes a generic formalism for geometrical and semantic description of profiled elements while Sect. 4 tackles the problem of the semantic structuring of the model with the aim of exploiting the description model for multiple objectives of analysis.. 2 Basic concepts to understand the geometrical nature of the elements of classical architecture The problems tackled in this article relates to an approach to understanding, reconstructing, structuring and representing architectural elements. This approach suggests an-swers to a certain number of problems in the field of the architectural representation, but it presents some gaps that must be analyzed. Indeed, even if the restitution of the shape based on a priori models can appear as an interesting solution for the dimensional comparison of repetitive elements, its implementation presents problems not yet solved. The positioning of the architectural primitive in the point-cloud is currently based on arbitrary estimations of the user. With an aim of making this procedure more robust it will be necessary to implement best-fit techniques according to various aspects: surfaces [7] , characteristic profiles [22] or construction history [25] . In the Fig. 29 . Ideal models (in wireframe) instantiated on the archaeological rests (reconstructed) of the Roman theater in Arles same spirit, the methods using graph grammar for the automatic rebuilding of shapes [10] could be taken into account. The principle introduced for the description of the building was tested only on buildings of classical language whose architectural composition is characterized by a clear organization of the composing elements. Other stylistic currents are likely to be studied by a formalization of this type. In the same way, it is necessary to hold into account the composition relations, which rest on a set of rules controlling the relative positioning and the dimensioning of elements in a general geometrical layout. This aspect may, in the same time, appear relevant to understanding the architectural composition that characterizes an existing building and to the development of restitution assumptions of a partially or totally destroyed building. The problem consists of formalizing the proportion systems that interest the buildings of a great part of the history of architecture [30] . This type of reasoning may for example be applied to the representation of restitution assumptions resulting from a comparison between ideal models and reconstructed fragments [3] (see Fig. 29 ). In this direction, the concept of multi-representation could play an important role: to organize around the description of the building a set of representations corresponding to the various levels of its hypothetical restitution. LIVIO

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Property-Preserving Data Reconstruction We initiate a new line of investigation into online property-preserving data reconstruction. Consider a dataset which is assumed to satisfy various (known) structural properties; e.g., it may consist of sorted numbers, or points on a manifold, or vectors in a polyhedral cone, or codewords from an error-correcting code. Because of noise and errors, however, an (unknown) fraction of the data is deemed unsound, i.e., in violation with the expected structural properties. Can one still query into the dataset in an online fashion and be provided data that is always sound? In other words, can one design a filter which, when given a query to any item I in the dataset, returns a sound item J that, although not necessarily in the dataset, differs from I as infrequently as possible. No preprocessing should be allowed and queries should be answered online.We consider the case of a monotone function. Specifically, the dataset encodes a function f : {1, . . . , n} → R that is at (unknown) distance ε from monotone, meaning that f can-and must-be modified at εn places to become monotone.Our main result is a randomized filter that can answer any query in O(log 2 n log log n) time while modifying the function f at only O(εn) places. The amortized time over n function evaluations is O(log n). The filter works as stated with probability arbitrarily close to 1. We provide an alternative filter with O(log n) worst case

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Maximum thick paths in static and dynamic environments We consider the problem of finding a maximum number of disjoint paths for unit disks moving amidst static or dynamic obstacles. For the static case we give efficient exact algorithms, based on adapting the "continuous uppermost path" paradigm. As a by-product, we establish a continuous analogue of Menger's Theorem. (In this extended abstract we only state these results.)Next we study the dynamic problem in which the obstacles may move, appear and disappear, and otherwise change with time in a known manner; in addition, the disks are required to enter/exit the domain during prescribed time intervals. We observe that (unless P=NP), for any α, β > 0, one cannot decide in polynomial time whether there exist ⌈αK⌉ paths for disks of radius βR, where K is the maximum number of paths for radius-R disks. The problem is hard even if the obstacles are static, and only the entry/exit time intervals are specified for the disks. This motivates studying "dual" approximations, compromising on the radius of the disks and on the maximum speed of motion.Our main result is a pseudopolynomial-time dual-approximation algorithm: if K unit disks, each with unit bound on the speed, may be routed through an environment, our algorithm finds (at least) K paths for disks of radius Ω(1) moving with speed O(1). The algorithm computes a maxflow with "forbidden pairs" in an "adaptive" grid, laid out in spacetime. Although (as we show) in general finding even an approximation to the maxflow with forbidden pairs is not possible (unless P=NP), a careful choice of time discetization and a non-uniform grid of "way-points" allows us to give provable approximation guarantees on the quality of the solution produced by the algorithm. paths for translational motion of arbitrary-shape objects. Path planning in geometric domains is an important computational geometry subject with applications in robotics, VLSI routing, air traffic management (ATM), sensor networks, etc. In many applications it is of interest to find multiple disjoint paths for non-point objects avoiding moving obstacles. This is the problem studied in this paper.. The input to the problem is specified by a polygonal domain, with two edges of the outer polygon designated as the "source" and the "sink". The holes/obstacles in the domain move along known trajectories. Also given are the entry and exit time intervals. The goal is to find a maximum number of trajectories for equal-radii disks, moving with bounded speed, entering (resp., exiting) the domain through the source (resp., sink) during the entry (resp., exit) interval, never intersecting each other, nor the obstacles.. Specifying entry/exit times is not crucial for the problem's (in)tractability: one may just introduce obstacles that cover the source/sink during the times that are infeasible for entry/exit. We opted to retain the entry/exit time constraints in our formulation for two reasons. First, our algorithm is capable of addressing them; moreover, it can also respect given bounds on the total number of disks entering/exiting the domain within any set of multiple time intervals. This is important in ATM-our motivating application-since it allows one to bound the workload of air traffic controllers for a given sector of airspace during any specified set of time periods. Second, ATM often involves putting aircraft into "holding patterns" due to congestion at an airport or in an adjacent sector. Even if an aircraft may pass through an airspace quickly, it may be necessary to introduce delay (through path maneuvers or speed control). Monitoring aircraft in holding patterns adds significantly to the workload for a human controller; it is preferable to monitor aircraft that move as directly as possible through an airspace sector. Finding a maximum number of source-sink paths in graphs is equivalent to computing maxflow. Three classical graphtheoretic results related to the equivalence are the MaxFlowMinCut, the Flow Decomposition, and Menger's Theorem.. The extensions of the theorems to (static) geometric domains are developed in [13, 15, 22] , and this paper, respectively. Real-data implementation of the algorithm, based on our Continuous Menger's Theorem, is reported in [8, 9, 16] .. A lot of research has been done on computing fastest paths amidst moving/morphing obstacles for a point object, possibly with nonholonomic motion constraints, both in 2D and 3D [1, 2, [5] [6] [7] 17, 21, [23] [24] [25] [27] [28] [29] . See the books [11, 12] , Section 4.4 in the survey [14] , and references therein for details.. To the best of our knowledge, no algorithm with provable approximation guarantees has been known previously for finding a maximum number of paths in the presence of moving obstacles. The approaches for planning paths for multiple objects fall into two major categories: prioritized, when the paths are routed one-by-one, and coordinated, ranging from centralized to roadmap-based to decoupled (the classification is taken from [26] , where a more detailed discussion of the approaches may be found). Existing algorithms are heuristics, many of them are based on laying a regular grid in time-space and searching it for paths. In ATM applications, the possibly leading methods are the heuristics implemented in the Flow-Based Route Planner (FBRP) [19] . The FBRP searches the grid for the paths greedily and iteratively: each computed (thick) path becomes a constraint (obstacle) in space-time for subsequent paths. Although examples exist for which arbitrarily many paths may be routed, while the FBRP produces only one, the planner performs very well in practical situations [8-10, 19, 20] .

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Technology Trends in Survey Data Collection This article reviews recent and emerging technology developments in survey research. Recent developments include computer-assisted self-interviewing (CASI) methods using audio and/or video, automated telephone interviewing systems (interactive voice response), and the World Wide Web. These developments are already having a profound effect on survey data collection. Newer technological challenges include wireless applications (mobile web) and portable digital devices. These technologies offer many opportunities to expand the way we think of survey data collection, increasing the ways we can interact with survey respondents and expanding the range of stimulus material that can be used. The implications of many of these new developments for survey data quality are yet to be fully understood. This article reviews the state of the field with regard to emerging data collection technologies, and their implications for survey research.

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Distributing expressional faces in 2-D emotional space Facial expressions are often classified into one of several basic emotion categories. This categorical approach seems improper to treat faces with blended emotion, as well as hard to measure the intensity of an emotion. In this paper facial expressions are evaluated with dimensional approach of affect that was originally introduced by psycho-physiologic study. An expressional face can be represented as a point in a two-dimensional (2-D) emotional space characterized by arousal and valence factors. To link low-level face features with emotional factors, we propose a simple method that builds an emotional mapping by a coarse labeling on Cohn-Kanade database and a linear fitting on the labeled data. Our preliminary experimental result shows that the proposed emotional mapping can be used to visualize the distribution of affective content in a large face set and further retrieval expressional face images or relevant video shots by specifying a region in the 2-D emotional space. Nowadays more and more digital images and videos become available. With expanding data, there is also growing requirement of effective indexing and browsing the multimedia content. Facial expression can be one of important contents to index, since emotional expressions generally correspond to interesting events and highlights for video summarization and retrieval. Automatic facial expression analysis has been a hot research topic for years [11, 22] . This technique can be used to help user to search face images with specific expressions in large database, or retrieval exciting shots in long video.. Facial expressions are often evaluated by classifying face images into six basic emotion categories, i.e., happiness, sadness, anger, fear, surprise and disgust, which is based on a cross-culture study made by Ekman and Friesen in 1971 [9] . Limiting the evaluation of facial expression into predefined categories, however, may raise several problems. First, some expression can reflect multiple emotions, e.g., raised eyebrows and smiling mouth reveals a blend of surprise and happiness [22] . It is improper to classify such an expression as one of predefined basic emotions. Second, the intensity of an emotion is intrinsically ignored by the classification task itself. In this case, a small variation on face due to emotion may still be regarded as neutral face. Although, some recognition algorithm provides posterior probability of emotions [27, 8] that can be used as an intensity measurement. Third, facial expressions may not reflect any emotion at all, as they are simply facial actions. Considering this, some research [29, 30] analyzes facial expression by recognizing Action Units (AUs) [10] , the visually observable facial muscle actions.. Besides categorical approach, dimensional approach has also been used in emotion evaluation, which can easily represent blended emotion and measure the intensity of emotion. One powerful emotional space is represented in terms of the three affective attributes, i.e., valence, arousal and control, which is known as 3-D VAC coordinate space [24] . Dietz and Lang [7] use this emotional space to develop an affective agent that serves as mediators between the computer and user. Yeasin et al. [32] use a similar 3-D space to analyze facial expression and measure levels of interest from video content. When Grimm et al. [13] study spontaneous facial expressions, they perform the evaluation of emotions both in basic emotion categories and in a 2-D emotional space (arousal vs. valence). Hanjalic and Xu [15] represent the affective video content as "affect curve" by linking emotional dimensions with low-level audio feature and the motion feature between consecutive video frames. Following them, Chan and Jones [2] explored a similar method for affective content retrieval in video. Note that in everyday interactions, people do not describe facial expressions as couple of real numbers. In the scenario of face image retrieval with computer, however, this quantitative representation becomes quite useful when taking into account on varied intensity and mixed categories of human emotion.. In comparison with category-based representation, relatively fewer works of emotion modeling have been done with dimensional representation. Apart from seeking effective feature that reflects affective factors, the main difficulty comes from the labeling of ground-truth data. Normally, subjects' affective responses to stimuli are quantified either by computing the average of subjective Self-Assessment Manikin [13] or by measuring physiological functions that are considered related to particular affective factors [6] .. In this paper, we propose a simple and effective strategy to build an emotional mapping that links the low-level face feature with semantic affective dimensions. To build the mapping, we utilize the Cohn-Kanade database [17] and label face images by a coarse manual classification and a linear interpolation on each image sequence. After this, the emotional mapping can be built by linear fitting on the labeled data. In spite of the simplicity, our preliminary experimental result shows that the derived emotional mapping can be used to visualize the distribution of affective content of a large face set and further retrieval expressional face images or relevant video shots by specifying a region in the 2-D emotional space. In this paper, we proposed a simple method to build a mapping that links low-level face feature to emotional dimensions. The emotional mapping was built by a coarse data labeling on Cohn-Kanade database and a simple linear fitting on labeled data. The mapping can be used for arbitrary person and a group of face images can be represented as a distribution of points in the 2-D emotional space characterized by the arousal and valence. We tested the performance of emotional mapping on JAFFE database as well as on a clip of real video. Our preliminary experiment shows that the affective content of face images can be well distributed in the 2-D emotional space. While building the emotional mapping, we explored several face features to adapt different situation, such as using LBP-based mapping for frontal faces, using SHP feature for non-frontal faces in real video. Proper facial feature may make the emotional mapping more effective, which is a future research direction. With current experimental result, we also discussed the possibility of building an interactive interface based on the emotional plane where user is able to navigate throughout the video according to affective content.

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


On Feasible Cases of Checking Multi-Agent Systems Behavior The complexity of multi-agent systems behavior properties is studied. The behavior properties are formulated using classical temporal logic languages and are checked relative to the transition system induced by the multi-agent system definition. We show that there are deterministic or nondeterministic polynomial time check algorithms under some realistic structural and semantic restrictions on agent programs and actions. Emerging in the late 80ies, the terms 'Intelligent Agent' (IA) and 'Multi-Agent System' (MA-system) refer to a new and generic metaphor of an artificial intelligence based computing technology. The range of IA applications extends from operating system interfaces, processing of satellite imaging data and WEB navigation to air traffic control, business process management and electronic commerce. This is the reason why there is no unified reading of the terms. We address the reader to the book [26] and several publications [29, 15, 18, 19, 23, 22] discussing their different readings and definitions. Meanwhile, the intuitive appeal of the term 'Intelligent Agent' is quite clear :. -an IA is autonomous, i.e. it can function by itself in predetermined environments; -it is reactive, i.e. it is capable of perceiving and responding to the stimuli of other agents or of its medium; -it is intelligent, i.e. its actions are determined by a certain logic and estimation of its environment; -and it is goal oriented, i.e. even if its functioning is continuous, it is oriented on reaching states with some predetermined properties.. Concrete realizations of these properties determine particular agent architectures. Agent's intelligence capacity can vary from finite state control structures or IF-THEN rules to logic programs, non monotone belief based systems or deontic logics (see [26] for a discussion and references).. In this paper, we study the complexity of recognizing properties of behavior of MA-systems. The research of this kind is rather scarce (besides the cited book [26] , see [9, 10, 14, 28] ). The reason for this lacuna is the difference in orientations of MA-system architecture definitions and of logical or complexity analysis of behavior properties. The former are oriented to higher expressivity and adequacy relative to applications. The latter, on the contrary, needs abstraction from details and substantial simplifications of analyzed models. So one of the problems is that of finding an adequate abstraction level. ¿From many known agent architectures, we have chosen the so called IMPACT architecture described in detail in the book [26] . This very elaborated architecture is neatly formalized in terms of state transition systems and carefully studied. In particular, the complexity bounds of several aspects of decision making are established in [26] (chapter 11), which partially characterize the complexity of one-step state transition. This complexity being rather high (from N P and F N P to Π P 3 -complete), we simplify this architecture leaving only the agent features concerning actions, decision policies and communication. We express behavior properties of deterministic and nondeterministic MA-systems as the properties of trajectories (i.e. finite or infinite paths) in the state transition systems they define. This allows the use of classical temporal logics as behavior properties description languages. The "MA-BEHAVIOR" problem we consider in this paper, consists in verifying that a temporal logic formula Φ holds on the tree of trajectories of a given MA-system. So it is a model checking type problem. Model checking has been extensively studied since the early 80ies (see [6, 20, 16, 24, 27, 25, 8, 11, 12, 7] ). There is however a substantial difference between the classical problem statement and that of this paper. Traditionally, the complexity results are established for explicitly presented transition diagrams or else for some their fixed representation (by a finite automata, by OBDD).. Meanwhile, we establish the complexity bounds with respect to MA-systems whose operational semantics is presented in the form of transition systems. MA-systems constitute a compact representation of the corresponding transition system. For example, even for a ground (i.e. variable-free) MA-system A, the transition system T (A) describing its trajectories may have the size exponential in |A|, because it can occur that it has O(2 |A| ) states. So the lower bounds may be (and they are) more pessimistic as compared with the classical ones for the same classes of logics. This being so, we nevertheless establish in this paper interesting classes of MA-systems, in which the MA-BEHAVIOR problem turns out to be decidable in deterministic or nondeterministic polynomial time. And this is due to a new possibility of formulating natural constraints in terms of structural parameters of MA-systems.. 2 Agent and MA-system architecture An intelligent agent (IA) a, as it shows up in this paper, has its internal state, which is a finite set of ground atoms in the signature P e a , communicates other agents through messages, which are ground message atoms in the signature P m a , held in its message box, is capable of performing a number of parameterized actions in the signature P act a , constituting its action base AB a , is controlled by a program P a , whose semantics determines the set of executable actions and uses its one-step semantics Act a in order to select the actions to execute. A multi-agent system (MA-system) A = {a 1 , ..., a n } serves as a common frame for interacting IA a 1 , ..., a n . It fixes some finite extensional signature P e , message signature P m , and intensional actions signature P act such that P e a ⊆ P e , P m a ⊆ P m , P act a ⊆ P act for a ∈ A. We adopt a domain closure assumption fixing some finite set of constants C denoting the domain objects and considering a set Π of polynomial time computable built-in predicates and operations (e.g., the standard arithmetical operations over numbers).. Hereafter, by A e , A m , A act and L e , L m , L act we denote the sets of atoms and literals in the corresponding predicate signatures, using constants in C and variables in some countable set V. By B e , B m , and B act we denote the corresponding sets of ground atoms, and by LB e , LB m , and LB act we denote the corresponding sets of ground literals.. The message box of an agent a, denoted M sgBox a can hold messages received from other agents, i.e. pairs of the form (Sender agent, M essage), where M essage is a ground atom in the signature P m a . We call local states the pairs IM a = (I a , M sgBox a ) consisting of the current individual state I a and the current message box contents M sgBox a . Action base AB a is a finite set of actions specified by expressions (α(X 1 , ..., X l ), ADD(α), DEL(α), SEN D(α)), in which the atom α(X 1 , ..., X l ) (uniquely) determines the action's name and parameter list, ADD(α) and DEL(α) are lists of atoms to add to (respectively, remove from) the state, and SEN D(α) is a set of messages to send to indicated agents. Atoms in ADD(α), DEL(α) and messages in SEN D(α)) may share parameters X 1 , ..., X l . So each ground substitution τ binding the parameters fixes the corresponding action instance τ (α). An action α is expanding if DEL(α) = ∅. Agent a is expanding if it has only expanding actions. Program P a defines the agent's action policy. It is a logic program with the clauses of the form H ← L 1 , ..., L n , where n ≥ 0, the head H = α(t 1 , ..., t l ) is an (intensional) action atom in A act such that (α(X 1 , ..., X l ), ADD(α), DEL(α), SEN D(α)) ∈ AB a , literals L i in its body are either action literals over L act , or (extensional) state literals in LB e , or message literals of the form Received(Source agent, M essage), or their negations ¬Received(Source agent, M essage) with M essage ∈ A m , or atoms q(t) with built-in predicates q ∈ Π. An agent's program is positive if there are no negations in it's clauses. An agent with positive program is also called positive.. We suppose that the clauses are safe in the sense that all variables in the head H occur positively in the body L 1 , ..., L n , and that the program P state a. Program semantics determines the set of actions which in principle can be executed by the agent in its current local state. As it is well known (see [2] IA and MA-system architectures published within the past few years are dissimilar and diversified because they represent various application domains of this new software technology. Technically, our study concerns one such specific architecture. However, it illustrates the way in which penetrating deeply in a complex MA-system architecture permits in some cases to understand more deeply the behavior properties and in this way, to discover interesting classes of MA-systems with with efficiently checked behavior properties.

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


Empirical distribution of k-word matches in biological sequences This study focuses on an alignment-free sequence comparison method: the number of words of length k shared between two sequences, also known as the D 2 statistic. The advantages of the use of this statistic over alignment-based methods are firstly that it does not assume that homologous segments are contiguous, and secondly that the algorithm is computationally extremely fast, the runtime being proportional to the size of the sequence under scrutiny. Existing applications of the D 2 statistic include the clustering of related sequences in large EST databases such as the STACK database. Such applications have typically relied on heuristics without any statistical basis. Rigorous statistical characterisations of the distribution of D 2 have subsequently been undertaken, but have focussed on the distribution's asymptotic behaviour, leaving the distribution of D 2 uncharacterised for most practical cases. The work presented here bridges these two worlds to give usable approximations of the distribution of D 2 for ranges of parameters most frequently encountered in the study of biological sequences. The accelerating rate of accumulation of molecular sequences in public databases has triggered the development of a number of sequence comparison algorithms.. The most popular algorithms, such as FASTA, BLAST or BLAT, rely on sequence alignment, and assume contiguity between homologous segments. This assumption is, however, often broken in molecular sequences, due to events such as transposition, unequal crossing over or alternative splicing. To address this issue, a number of alignment-free sequence comparison methods have been developed. Amongst them, the count of words of length k letters matching between two sequences, also known as the D 2 statistic, has found some successful applications, due to its simplicity and its speed. The algorithm to calculate the D 2 statistic between two sequences runs as a linear function of the sequences' lengths, whereas alignmentbased sequence comparison methods typically have a worst case runtime quadratic in the sequences' lengths. The first applications of the D 2 statistic relied on heuristics to decide whether sequences are significantly similar, but did not have any statistical basis.. A rigorous examination of the distribution of D 2 led to the characterisation of asymptotic distributions, but the behaviour of D 2 in practical cases remains unknown. In a previous study, we characterized D 2 optimal word sizes for a range of sequence sizes. The goal of the present study is to find approximations of the distribution of D 2 for word sizes close to optimal, and for the sequence sizes most frequently encountered in molecular databases. This study introduces practical approximations to the distribution of the D 2 statistic and to the extreme value distribution of D 2 . For sequences of intermediate length (around 800 base pairs, close to the average size of ESTs and sequencing traces) and for p-values between 5% and 0.1%, the Gamma distribution closely approximates the distribution of D 2 . The Gamma distribution not only outperforms the normal distribution, but unlike the latter, it slightly overestimates the p-values, and thus would result in fewer false positives.. All the approximations presented here deteriorate as one moves further to the right hand of the tail (for smaller p-values). This is not, however, a major problem for any practical use of these approximations, where very small p-values would just have an indicative value.. Finally, our results show, that for longer sequences, such as genome assembly contigs, the normal approximation itself would be appropriate, even for very small p-values. . To simplfy the notation from here on we set u = (i, j), v = (i ′ , j ′ ). The first term in Eq. 8 depends only on. where p t is defined in Eq. 3. Thus To calculate the covariances in the second term of Eq. 8, it is convenient to use the notation and terminology of [8] , Chapter 11. Let J u = {v = (i ′ , j ′ ) : |i ′ − i| < k or |j ′ − j| < k} be the dependency neighbourhood of Y u . It can be decomposed into two parts, accordion and crabgrass, J u = J a u ∪ J c u , where . where we have used the fact that word matches occur simultaneously at u and v if and only if the first k letters of (A i , . . . , A i+k+t−1 ) are repeated at (B j , . . . , B j+k−1 ) and the final k letters are repeated at (B j ′ , . . . , B j ′ +k−1 ). This gives. Extending the argument to all −k + 1 ≤ t ≤ k − 1 gives. By symmetry of the covariance function, the same result applies to the sub-case v = (i ′ , j + t) where |i − i ′ | ≥ k and |t| ≤ k − 1. The crabgrass contribution to the sum over covariance terms in Eq. 8 is then Case 3: v is on the main diagonal of J a u . That is, v = (i + t, j + t), where −k < t < k and t = 0 (see Fig. 7 ). In this case,. and. The contribution to the sum over covariance terms in Eq. 8 from Case 3 is then. Case 4: v ∈ one of the subregions I, II, III or IV of J a u in Fig. 7 . That is, v = (i + t, j + s), where. Consider subregion I first. The word matches corresponding to the event "Y u = 1, Y v = 1" are illustrated in Fig. 8. For such a situation to occur, the t + s letters a 1 , . . . , a s , b 1 , . . . , b s and c 1 , . . . , c t−s can be specified independently, and the remaining 2k letters within the four words must be repeats of c 1 , . . . , c t−s as shown. The sequence c 1 , . . . , c t−s is repeated ν = ⌊(k − s)/(t − s)⌋ complete times in sequence B and ν + 1 complete times in sequence A, where ⌊ ⌋ indicates the integer part. At the right hand end of these repeats, the sequence c 1 , . . . , c ρ occurs once in Sequence A and once in Sequence B, where ρ = (k − s) mod (t − s).. Then. and. It is straightforward to check that similar results apply to subregions II, III and IV, giving the contribution to the sum over covariances in Eq. 8 from Case 4 as. where R = I ∪ II ∪ III ∪ IV is the union of the four subregions of Case 4 and. Case 5: v ∈ one of the subregions V or VI of J a u in Fig. 7 . That is, v = (i+t, j+s), where If the letters a 1 , . . . , a s , b 1 , . . . , b s and c 1 , . . . , c t−s are specified, the remaining letters within the four words must be repeats of c 1 , . . . , c t−s as shown, the final repeat being truncated at the same point in both Sequence A and Sequence B. If the letters a 1 , . . . , a t , b 1 , . . . , b r are specified, the remaining letters within the four words must be repeats of a 1 , . . . , b r in Sequence A and b 1 , . . . , a t in sequence B, the final repeat being truncated at the (k +t)th or (k +r)th position respectively.. Consider subregion V first. The word matches corresponding to the event "Y u = 1, Y v = 1" are illustrated in Fig. 9 . Set r = −s. For the event to occur, the affected block of length t + k in Sequence A must consist of repeats of a sequence (a 1 , . . . , a t , b 1 , . . . , b r ) where a 1 , . . . , a t and b 1 , . . . , b r are independently specified letters. The final repeat is truncated at the (k + t)th letter. The affected block in sequence B must consist of repeats of the sequence (b 1 , . . . , b r , a 1 , . . . , a t ) , the final repeat being truncated at the (k + r)th letter.. Let l i , i = 1, . . . , t be the total number of times the letter a i occurs and m j , j = 1, . . . , r be the total number of times the letter b j occurs in the two blocks in Fig. 9 . By noting that the stretches of length k not including the first t letters of the A-block or not including the first r letters of the B-block each contain ⌊k/(r + t)⌋ complete repeats of all s+t independent letters plus a final k mod (r+t) remaining letters at the right hand end, we arrive at. where. Then. and. A similar result holds for subregion VI. The contribution to the sum over covariances in Eq. 8 from Case 5 is then. where S = V ∪ VI is the union of the two subregions of Case 5 and l i and m j are given by Eq. 22. Finally, by Eq. 8, the variance of D 2 is given by the sum of the right hand sides of Eqs. 10, 14, 17, 20 and 26.. II. Consequences of failing to pre-specify parameters in the Kolmogorov-Smirnov test Given a random sample of observations X 1 , X 2 , . . . , X N sample , the KolmogorovSmirnov test [3] gives p-values for the null hypothesis that the observations are associated with pre-specified distribution function F hyp . The two-sided version of the test considered here uses as a test statistic sup i |F hyp (X i ) − S(X i )|, where S is the empirical cumulative distribution function based on the observations. Under the null hypothesis the p-values obtained are uniformly distributed on the interval [0, 1].. Importantly, if the hypothesised distribution F hyp is not fully pre-specified, but relies on estimates from the sample, the reported p-values will not be uniformly distributed under the null hypothesis. To illustrate this, we have generated a set of 10,000 independent samples of N sample = 2500 random numbers from a standard normal distribution, and applied the two-sided Kolmogorov-Smirnov test to each sample using the R function ks.test. Histograms of the p-values obtained are shown in Fig. 10 . In the first plot each sample was tested against the standard normal N (0, 1), whereas in the second plot each sample was tested against a normal distribution whose mean and variance was estimated from the sample. We see that in this situation, where the null hypothesis is true, but the Kolmogorov-Smirnov test is applied incorrectly, p-values are skewed heavily towards 1.. In a second test to see whether incorrect use of the Kolmogorov-Smirnov test can lead to an overly optimistic indication of agreement with a hypothesised distribution, we generated a set of 10,000 independent samples of N sample = 2500 random numbers from a Gamma distribution with mean 10 and variance 1. This distribution is close to, but not identical with, the normal distribution N (10, 1). The third and fourth histograms in Fig. 10 are of p-values obtained from application of the Kolmogorov-Smirnov test against a pre-specified N (10, 1), and against a normal distribution with mean and variance estimated from the sample respectively. The third plot is an indication the distribution of p-values that will result if the Kolmogorov-Smirnov test for normality is applied correctly to this non-normal Figure 10 : Histograms of p-values obtained from the Kolmogorov-Smirnov test applied to artificially generated data tested against a normal distribution. From top to bottom the plots are (i) standard normal data, parameters of the hypothesised distribution pre-specified; (ii) standard normal data, parameters of the hypothesised distribution estimated from the data; (iii) gamma distributed data with mean 10 and variance 1, parameters of the hypothesised distribution pre-specified; and (iv) gamma distributed data with mean 10 and variance 1, parameters of the hypothesised distribution estimated from the data.. data. Again we see that p-values are overestimated in the fourth plot when the test is used incorrectly. The D 2 statistic is defined to be the number of exact word matches of length k between sequences A = (A 1 , . . . , A m ) and B = (B 1 , . . . , B n ), with A i and B j belonging to a given alphabet A. For mathematical convenience we will impose periodic boundary conditions on both sequences, that is, the letter in the first position in sequence A is assumed to follow the letter in the mth position, and the letter in the first position in sequence B is assumed to follow the letter in the nth position. For k << m, n we do not expect our results to differ significantly from the usual case of free boundary conditions.. Defining the indicator variables Y (ij) for a word match between the k-word at position i in A and the word at position j in B by. the D 2 statistic is given by. where. For the case of free boundary conditions the index set is replaced by. We are interested in the distributional properties of D 2 under the null hypothesis that A and B are Bernoulli texts, meaning that each letter, A i or B j , is independently and identically (i.i.d.) distributed. Let the probability of occurrence of letter a ∈ A be f a , and define. The mean of D 2 is then [7] :. An exact value for the variance of D 2 has recently been given for the case of free boundary conditions in [6] . In Appendix I we derive a similar formula for the variance for the algebraically simpler case of periodic boundary conditions. From here on, to simplify matters we set m = n. Rigorous results exist for the limiting distribution of D 2 as n → ∞ in certain regimes. For pairs of Bernoulli texts with non-uniform letter distributions, the limiting distribution is compound Poisson in the regime k > 2 log b n + const. [7] , and normal in the regime k < 1/2 log b n + const [2] . Here b = p 2 −1 .. In earlier numerical analyses [4] , we tested the accuracy with which k-word matches are able to measure the relatedness of artificially evolved sequences. Calculations of the optimum word size k for a range of sequence lengths n, showed that optimum word sizes generally fall between the two parameter regimes for which the asymptotic behaviour of D 2 is known. Our purpose here is to perform numerical experiments to fill in the gap in the biologically relevant parameter regime between the asymptotically normal and compound Poisson asymptotic behaviours, and to find accurate and practical approximations to the distribution of D 2 in this parameter region. In particular, we are concerned with accurately reproducing the region of the tail corresponding to classical significance levels (0.001%, 0.01%, . . . ), both for the distribution of D 2 , and for its extreme value distribution that is used for determining p-values in database searches.

O O O O O O B I 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 B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I 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 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Artificial boundary conditions for the numerical simulation of unsteady acoustic waves A central characteristic feature of an important class of hyperbolic PDEs in odddimension spaces is the presence of lacunae, i.e., sharp aft fronts of the waves, in their solutions. This feature, which is often associated with the Huygens' principle, is employed to construct accurate non-local artificial boundary conditions (ABCs) for the Maxwell equations. The setup includes the propagation of electromagnetic waves from moving sources over unbounded domains. For the purpose of obtaining a finite numerical approximation the domain is truncated, and the ABCs guarantee that the outer boundary be completely transparent for all the outgoing waves. The lacunae-based approach has earlier been used for the scalar wave equation, as well as for acoustics. In the current paper, we emphasize the key distinctions between those previously studied models and the Maxwell equations of electrodynamics, as they manifest themselves in the context of lacunae-based integration. The extent of temporal nonlocality of the proposed ABCs is fixed and limited, and this is not a result of any approximation, it is rather an immediate implication of the existence of lacunae. The ABCs can be applied to any numerical scheme that is used to integrate the Maxwell equations. They do not require any geometric adaptation, and they guarantee that the accuracy of the boundary treatment will not deteriorate even on long time intervals. The paper presents a number of numerical demonstrations that corroborate the theoretical design features of the boundary conditions. Key words: Electromagnetic waves, Maxwell's equations, unsteady propagation, unbounded domains, truncation, finite computational domain, lacunae, non-deteriorating method, long-term numerical integration.Email address: tsynkov@math.ncsu.edu (S. V. Tsynkov). URL: http://www.math.ncsu.edu/∼stsynkov (S. V. Tsynkov). Sharp aft fronts of the waves, or lacunae, is a unique feature of certain hyperbolic solutions in odd-dimension spaces. The corresponding class of PDEs includes the Maxwell equations of electrodynamics studied in the current paper, along with the acoustics system (linearized Euler equations) and the scalar wave equation, that have been analyzed previously, see [1] [2] [3] . The key idea of using lacunae for computations is very simple. If the sources of waves are compactly supported in space and time, and if the domain of interest has finite size, then it will completely fall inside the lacuna once a certain time interval has elapsed since the inception of the sources. This interval can be easily evaluated ahead of time, and for all subsequent moments of time the solution on the domain of interest will be zero, as this domain will already be behind the aft front of the waves. Therefore, no computation will need to be run any further, which puts a cap on the long-term error build-up. Moreover, during this predetermined finite interval no wave can travel more than a certain distance away in space from the domain of interest. Consequently, a finite auxiliary computational domain can be set up, which facilitates construction of artificial boundary conditions (ABCs). In general, the term "ABCs" is associated with a fairly large group of methods employed for solving infinite-domain problems on the computer. For the purpose of obtaining a finite numerical approximation the original domain is truncated, and the ABCs provide a required closure for the resulting truncated formulation. The literature on the subject of ABCs is broad, and we refer the reader to the review papers [4] [5] [6] .. It is generally known that highly accurate ABCs are nonlocal. In particular, exact ABCs are always nonlocal in multidimensional settings. For unsteady problems, this also implies nonlocality in time. Nonlocal ABCs may incur high computational costs and require elaborate implementation strategies. As such, local alternatives obtained either independently or as an approximation of nonlocal ABCs conditions, becomes viable. These ABCs are usually inexpensive and easy to implement, but may often lack computational accuracy.. The ABCs for the Maxwell equations that we propose hereafter are nonlocal, and their accuracy can always match that of the interior discretization. However, the extent of their temporal nonlocality is limited, and does not increase as the time elapses. The bound on temporal nonlocality comes as a consequence of the presence of lacunae, i.e., sharp aft fronts of the waves, in the corresponding solutions. In the literature, existence of the lacunae is often referred to in connection with the Huygens' principle.. The lacunae-based ABCs are not limited to the aforementioned case of the compactly supported sources of waves. The case of continuously operating sources, or in general, that of a certain process/phenomenon confined to a bounded region that manifests itself by radiation of electromagnetic waves in the far field, is treated by employing special partitions along the time axis.. Several other nonlocal ABCs' methodologies for unsteady waves have recently been put forward, most notably [7] [8] [9] [10] [11] [12] [13] [14] ; see also the survey [15] . In comparison, our approach has a number of distinctive characteristics, besides the restricted temporal nonlocality that does not come at a cost of accuracy. The lacunaebased ABCs are obtained directly for the discretization, and can supplement any consistent and stable scheme. In other words, they bypass the common stage of deriving the continuous ABCs and subsequently approximating them, see [5] . The lacunae-based ABCs withstand long-term numerical integration with no deterioration of accuracy and are not restricted geometrically to any particular shape of the external artificial boundary. They also allow one to analyze a variety of cases, including the one of moving sources of waves.. Even though the current ABCs for electromagnetics are related to those developed previously for the scalar wave equation [1, 2] and for acoustics [3] , there are not only similarities but also very important differences between the respective models. Foremost, the source terms that drive the Maxwell equations are not independent, they are related via the continuity equation. The latter must be enforced on all stages of building the lacunae-based algorithm. In general, the current ABCs' approach fits into the universal framework of [16] .. The scope of numerical demonstrations that we present is limited to the transverse magnetic (TM) mode with cylindrical symmetry. This allows us to take advantage of the three-dimensional effects in a two-dimensional setting. We have constructed and tested the algorithm for setting highly-accurate global artificial boundary conditions for the computation of time-dependent electromagnetic waves. This work extends our previous approach that applies to the scalar wave equation [2] , and is also similar to the ABCs that we have recently developed for unsteady acoustics [3] . The algorithm is based on the presence of lacunae (aft fronts of the waves) in the three-dimensional wavetype solutions. The ABCs are obtained directly for the discrete formulation of the problem and can complement any consistent and stable finite-difference scheme. In so doing, neither a rational approximation of non-reflecting kernels, nor discretization of the continuous boundary conditions is required, see the review [5] . The extent of temporal nonlocality of the new ABCs appears fixed and limited, and this is not a result of any approximation but rather a direct consequence of the fundamental properties of the solution. The proposed ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed. Besides, they possess a unique capability of being able to handle boundaries of moving computational domains, including the case of accelerated motion.. The key idea of using lacunae for computations is straightforward: One should not continue the computation inside the lacuna once the solution has become zero there due to "natural causes." Otherwise the error may unwarrantably build up on one hand, and on the other hand, the extent of the required temporal pre-history of the solution may grow un-justifiably high.. Of course, there are many technical issues that need to be addressed before this idea can actually be implemented in practice. Those relate primarily to what to do with the waves outside, rather than inside, the domain of interest. In the framework of the previous analysis, we simply allow them to propagate a certain distance away till they get reflected, and then set up the auxiliary domain so that the reflected waves do not reach the domain of interest before it completely falls inside the lacuna. This, however, is by no means the only possible option. In fact, any treatment of the outgoing waves that would prevent the reflections from re-entering the domain of interest before it falls into the lacuna will be appropriate. At the same time, introducing an alternative to the approach described above may be beneficial from the standpoint of the overall computational cost. For example, a treatment of the sponge layer type that slows down the outgoing waves, see, e.g., [27, 28] , may allow to reduce the size of the auxiliary domain. Alternatively, the lacunae-based approach can be combined with a PML-based treatment for the waves outside the domain of interest, see, e.g., the survey papers [29, 30] .. The scope of numerical demonstrations presented in the current paper is limited to the cylindrically symmetric case. The reason for that is two-fold. On one hand, by doing so we can take advantage of the fundamentally important three-dimensional effects in an essentially two-dimensional computational setting. We have, in fact, followed this strategy in our previous work on acoustics [3] and on the scalar wave equation [2] . On the other hand, cylindrically symmetric TM mode helps us guarantee that the partitioned auxiliary sources will satisfy the correct continuity equation, see the beginning of Section 6. For that purpose we also need to use a particular method of obtaining the auxiliary sources that involves reconstruction of the potential component A θ . Reconstruction of A θ in the context of electromagnetics is similar to reconstruction of the velocity potential that we have used in acoustics, see [3] . In electromagnetics, however, it is needed to ensure the solvability the auxiliary sub-problems with the partitioned RHSs (27b), whereas in acoustics existence of the potential implies existence of the lacunae in the solutions of the auxiliary problem. We should note that in the full-fledged electromagnetics context that involves all six field components (as opposed to the TM subsystem that governs only three components) there will be both the magnetic continuity equation and the electric continuity equation for the RHSs that will need to be enforced once the sources are partitioned in time. At this moment of time, the question of how it may be achieved for the electric part remains open. To some extent, this presents an obstacle for constructing the lacunae-based ABCs for the Maxwell equations in the most general case. Of course, this obstacle can be easily overcome by simply reducing the system to a collection of six individual wave equations for the field components, and treating each equation independently from the others according to the methodology of [2] . This always remains a "fail-safe" option; it may, however, be more expensive than obtaining the ABCs in the framework of one first-order system. As such, implementation for the full three-dimensional Maxwell system will be in the focus of the future study.. For the current cylindrically symmetric case, numerical experiments conducted in the paper fully corroborate the theoretical design properties of the method. Besides, when a key parameter of the algorithm, the width of the transition region, changes so that to reduce the overall memory requirements, the performance of the ABCs deteriorates in an expected way. However, on fine grids this deterioration is considerably slower than that on coarse grids. Therefore, for those practical problems, for which typical integration times are sufficiently long but not excessively long, this deterioration my go almost unnoticed.

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


Noninvasive Clinical Assessment of Trunk Deformities Associated With Scoliosis Abstract-Besides the spinal deformity, scoliosis modifies notably the general appearance of the trunk resulting in trunk rotation, imbalance, and asymmetries that constitutes patients' major concern. Existing classifications of scoliosis, based on the type of spinal curve as depicted on radiographs, are currently used to guide treatment strategies. Unfortunately, even though a perfect correction of the spinal curve is achieved, some trunk deformities remain, making patients dissatisfied with the treatment received. The purpose of this study is to identify possible shape patterns of trunk surface deformity associated with scoliosis. First, trunk surface is represented by a multivariate functional trunk shape descriptor based on 3-D clinical measurements computed on cross sections of the trunk. Then, the classical formulation of hierarchical clustering is adapted to the case of multivariate functional data and applied to a set of 236 trunk surface 3-D reconstructions. The highest internal validity is obtained when considering 11 clusters that explain up to 65% of the variance in our dataset. Our clustering result shows a concordance with the radiographic classification of spinal curves in 68% of the cases. As opposed to radiographic evaluation, the trunk descriptor is 3-D and its functional nature offers a compact and elegant description of not only the type, but also the severity and extent of the trunk surface deformity along the trunk length. In future work, new management strategies based on the resulting trunk shape patterns could be thought of in order to improve the esthetic outcome after treatment, and thus patients satisfaction. In this paper, we propose a clustering method based on functional data analysis to group scoliosis patients' trunks according to their surface deformities. Results show that a classification into 11 clusters provides good consistency and homogeneity inside each cluster and that the differences between clusters explain up to 65% of the whole variance in the dataset. Between clusters differences are attributed to the amplitude, the level, and the extent of the deformations in the frontal and axial planes, and the modification of the trunk balance in the sagittal plane. In addition, the resulting clusters show no significant differences in terms of subjects' age and corpulence.. This study is the first to apply functional data analysis into a shape analysis problem such as the clustering of trunk surface reconstructions. Functional cluster analysis has proved to be valuable for depicting similarities and differences between trunk measurements. The trunk shape is described as a combination of multilevel measurements computed in the transverse (BSR), coronal (X G ), and sagittal (Z G ) planes. This multivariate functional representation offers a way of synthesizing information across the three distinct measurements. Moreover, functional data analysis allows taking into consideration the dependence of the deformities to trunk levels, as opposed to taking only the measurements at the most deformed level [21] , [22] . This representation assesses not only the amplitude of the deformations but also its location and extent along the trunk.. In this novel trunk shape analysis approach, the trunk is described as a vertically elongated volume that can be deformed in three possible ways: axial sections of the volume can be rotated around the vertical axis and translated along the two other axes. This description is not information preserving [40] , meaning that it does not allow for an accurate reconstruction of the trunk shape from its descriptor. Thus, we might be missing other local deformations. Nevertheless, the three deformations accounted for in our representation describe well the real major deformations associated with scoliosis. Moreover, in the particular case of scoliosis assessment, clinicians are used to a single measurement-the Cobb angle-, to quantify the whole spinal deformity. Thus, to make the assessment more accessible and intuitive in a clinical context, it is important to limit the number of measurements as much as possible, at the expense of losing some information.. The main difficulty in this study resides in the interpretation and validation of the clustering since no reference classification of trunk deformities exists to compare our results with. To overcome this limitation, we evaluated the agreement between the resulting clustering and the radiographic spinal deformity classification even though the two classifications refer to different components of the scoliosis deformity. Despite the fact, that the relationship between the surface deformity and the underlying spinal curve is not well documented, we found that the two classifications are related, to some extent. Particularly, there is an excellent distinction between thoracic curves (RX 1) and lumbar curves (RX 3). However, trunks corresponding to double major curves (RX 2) and normal spinal curves (RX 0) are gathered into the same clusters (clusters 8 to 10). In fact, the presence of two major curves along the spine leads to compensation between the deformities of the lower and upper parts of the trunk, resulting in a less deformed trunk shape. To address this point, a larger dataset with more healthy subjects might widen the gap between normal and double major spinal curves.. The lack of a perfect concordance with the radiographic classification can be explained first, by the fact that while the common classifications of scoliosis are essentially based on the type of spinal curvature, our clustering goes a step further in differentiating trunk shapes not only in terms of underlying spinal curve's type but also according to the severity of the deformations in the three anatomical planes. Moreover, the trunk shape offers 3-D information while the radiographic spinal classification is based on a 2-D radiograph, thus there is no information about the deformation in other planes, such as the axial rotation causing the hump. The case study presented in the Section III illustrates well how two trunks with the same type of underlying spinal curvature differ in 3-D, and how the same spinal correction induces different corrections in terms aesthetical outcome, mainly at reducing the hump on the back. We believe that aside the radiographic evaluation of the spinal deformity, consideration of this aesthetic difference into treatment planning might increase the success rate in terms of trunk appearance, and thus patients' satisfaction.. Another novelty in this study is that an unsupervised classification is favored. The clustering algorithm uses only the information provided by our trunk shape features. Radiographic information about the spinal deformity is only used a posteriori for ends of comparison and interpretation. Thus, we can say that, as opposed to previous scoliosis trunk or back shape classifications that were built to concord with radiographic information (Cobb angle or spinal curve type) [16] , [18] , [19] , our classification is neutral. The spine and the trunk deformities are considered in this paper as two distinct components of scoliosis deformity. Both are related to a certain degree (Rand index = 0.68) but they are not completely redundant.. Furthermore, it is the first time that such a large dataset of trunk surface reconstructions is collected and analyzed. Previous studies aiming at characterizing trunk surface deformities made use of less than 150 full trunk reconstructions [17] , [19] , [22] . A cluster analysis is only feasible when a large dataset is available. With a set of 236 trunk reconstructions, we were able to identify distinct and consistent patterns of trunk deformities associated with scoliosis.. At the light of this study, we can conclude that our multivariate functional descriptor of trunk shape is not only reliable [23] , but also allows to distinguish between different types of scoliosis trunk deformities. These two criteria being validated, it can be concluded that our multivariate functional descriptor of trunk shape satisfies the principles of optimality [20] and can be considered as an optimal index for the noninvasive assessment of trunk deformities in scoliosis. It represents a promising tool in scoliosis clinic for two major reasons. First, it provides clinicians a new sight on scoliosis deformity, an automatic and reliable way to examine trunk deformities that constitutes patients' major concern. At the light of our clustering results, new treatment strategies could be thought of in order to improve the esthetic outcome after surgery. Second, the noninvasive acquisition and reconstruction of the trunk surface makes it possible to follow up scoliosis patients more frequently. Future work will be now oriented toward the evaluation of the changes in trunk deformities over time for each cluster in order to predict eventual scoliosis progression.

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