Prefix computations on symmetric multiprocessors We introduce a new optimal prefix computation algorithm on linked lists which builds upon the sparse ruling set approach of Reid-Miller and Prefix computations on linked structures are basic operations used for the manipulation of lists, trees, and graph data structures. However, beyond their obvious utility, the computational tasks involved are well-known to defy practical parallel implementation on coarse grain architectures, especially for a relatively small number of processors. The source of the difficulty lies in the fact that there is no obvious way to estimate the relative proximity of two list elements except by essentially solving the overall problem. Thus, there is no way to partition the list elements amongst the various processors that will avoid either irregular communication or memory access patterns. To make matters worse, there is very little computation with which to mask these costs. Finally, any parallel solution must compete against the obvious sequential solution, which is extremely simple with very small constants.. In this paper, we introduce a new prefix computation algorithm which builds upon the sparse ruling set approach of Reid-Miller and Blelloch [7] . Unlike the original algorithm, we choose the ruling set in such a way as to avoid the need for conflict resolution. Besides making the algorithm simpler, this change allows us to achieve a stronger bound on the complexity. Whereas Reid-Miller and Blelloch claim an expected complexity of O n p for n p ,. we claim a complexity with high probability of O n p for n p 2 ln n. At the same time, our algorithm incurs approximately half the memory costs of their algorithm, which we believe to be the smallest of any parallel algorithm we are aware of. Finally, whereas Reid-Miller and Blelloch targeted their algorithm for implementation on a vector multiprocessor architecture, we develop our algorithm for implementation on the symmetric multiprocessor architecture (SMP). The advantage of vector multiprocessors is the high global communication bandwidth and the pipelined memory access. Indeed, as long as there are no memory bank conflicts, the network can service one memory request per clock cycle for each memory pipe. However, despite this advantage, recent trends in multiprocessor architecture have placed in question the future of these vector machines. By contrast, symmetric multiprocessors dominate the high-end server market and are currently the primary candidate for constructing large scale multiprocessor systems. Our prefix computation algorithm was implemented in C using POSIX threads and run on four symmetric multiprocessors -the IBM SP-2 (High Node), the HP-Convex Exemplar (S-Class), the Silicon Graphics Power Challenge, and the DEC AlphaServer. We ran our code using a variety of benchmarks which we identified to examine the dependence of our algorithm on memory access patterns. For some problems, our algorithm actually matched or exceeded the performance of the sequential solution using only a single thread. Moreover, in spite of the fact that the processors must compete for access to main memory, our algorithm still yielded scalable performance with up to 16 processors, which was the largest platform available to us.. The organization of our paper is as follows. Section 2 presents our computational model for analyzing algorithms for this class of problems on symmetric multiprocessors. Section 3 describes in detail our prefix computation algorithm for this platform. Finally, Section 4 describes the experimental performance of our prefix computation algorithm.

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


Object Class Recognition and Localization Using Sparse Features with Limited Receptive Fields We investigate the role of sparsity and localized features in a biologically-inspired model of visual object classification. As in the model of Serre, Wolf, and Poggio, we first apply Gabor filters at all positions and scales; feature complexity and position/scale invariance are then built up by alternating template matching and max pooling operations. We refine the approach in several biologically plausible ways. Sparsity is increased by constraining the number of feature inputs, lateral inhibition, and feature selection. We also demonstrate the value of retaining some position and scale information above the intermediate feature level. Our final model is competitive with current computer vision algorithms on several standard datasets, including the Caltech 101 object categories and the UIUC car localization task. The results further the case for biologically-motivated approaches to object classification. The problem of recognizing multiple object classes in natural images has proven to be a difficult challenge for computer vision. Given the vastly superior performance of human vision on this task, it is reasonable to look to biology for inspiration. Recent work by used a computational model based on our knowledge of visual cortex to obtain promising results on some of the standard classification datasets. Our paper builds on their approach by incorporating some additional biologically-motivated properties, specifically, sparsity and localized intermediate-level features. We show that these modifications further improve classification performance, strengthening our understanding of the computational constraints facing both biological and computer vision systems.. Within machine learning, it has been found that increasing the sparsity of basis functions (Figueiredo 2003; Krishnapuram et al. 2005 ) (equivalent to reducing the capacity of the classifier) plays an important role in improving generalization performance. Similarly, within computational neuroscience, it has been found that adding a sparsity constraint is critical for learning biologically plausible models from the statistics of natural images (Olshausen and Field 1996) . In our object classification model, one way we have found to increase sparsity is to use a lateral inhibition step that eliminates weaker responses that disagree with the locally dominant ones. We further enhance this approach by matching only the dominant orientation at each position within a feature rather than comparing all orientation responses. We also increase sparsity during final classification by discarding features with low weights and using only those that are found most effective. We show that each of these changes provides a significant boost in generalization performance.. While some current successful methods for object classification learn and apply quite precise geometric constraints on feature locations (Fergus et al. 2003; Bouchard and Triggs 2005) , others ignore geometry and use a "bag of features" approach that ignores the locations of individual features (Csurka et al. 2005; Opelt et al. 2006) . Intermediate approaches retain some coarsely-coded location information (Agarwal et al. 2004) or record the locations of features relative to the object center (Leibe et al. 2004; Berg et al. 2005) . According to models of object recognition in cortex (Riesenhuber and Poggio 1999) , the brain uses a hierarchical approach, in which simple, low-level features having high position and scale specificity are pooled and combined into more complex, higher-level features having greater location invariance. At higher levels, spatial structure becomes implicitly encoded into the features themselves, which may overlap, while explicit spatial information is coded more coarsely. The question becomes one of identifying the level at which features have become complex enough that explicit spatial information can be discarded. We investigate retaining some degree of position and scale sensitivity up to the level of object detection, and show that this provides a significant improvement in final classification performance.. We test these improvements on the large Caltech dataset of images from 101 object categories (Fei-Fei et al. 2004 ). Our results show that there are significant improvements to classification performance from each of the changes. Further tests on the UIUC car database (Agarwal et al. 2004 ) and the Graz-02 datasets (Opelt et al. 2006 ) demonstrate that the resulting system can also perform well on object localization. Our results further strengthen the case for incorporating concepts from biological vision into the design of computer vision systems.

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


Interval Neutrosophic Sets and Topology Abstract: On 2005, F. Smarandache generalized the Atanassov's intuitionistic fuzzy setsto neutrosophic sets. Also, this author and some co-workers introduced the notion of interval neutrosophic set, which is an instance of neutrosophic set and studied various properties. The notion of neutro-sophic topology on the non-standard interval is also due to Smarandache. We study in this paper relations between interval neutrosophic sets and topology. In various recent papers, F. Smarandache generalizes intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs)... The notion of intuitionistic fuzzy set defined by K.T. Atanassov (1983 Atanassov ( , 1986 ) has been applied by Ç oker (1997) for study intuitionistic fuzzy topological spaces. This concept has been developed by many authors (specially Ç oker and co-workers, 1997; Hanafy; Hur, Kim and Ryou; Lee and Lee; and Lupiáñez) .. F. Smarandache also defined the notion of neutrosophic topology on the non-standard interval (Sm1).. One can expect some relation between the intuitionistic fuzzy topology on an IFS and the neutrosophic topology. We show in (Lupiáñez 2008 ) that this is false. Indeed, an intuitionistic fuzzy topology is not necessarilly a neutrosophic topology.. Also, (Wang, Smarandache, Zhang, and Sunderraman, 2005) introduced the notion of interval neutrosophic set, which is an instance of neutrosophic set and studied various properties. We study in this paper relations between interval neutrosophic sets and topology.

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Personalized retrieval in social bookmarking Users of social bookmarking systems take advantage of pivot browsing, an interaction technique allowing them to easily refine lists of bookmarks through the selection of filter terms. However, social bookmarking systems use one-size-fits-all ranking metrics to order refined lists. These generic rankings ignore past user interactions that may be useful in determining the relevance of bookmarks. In this work we describe a personalized ordering algorithm that leverages the fact that refinding, rather than discovery (finding a bookmark for the first time), makes up the majority of bookmark accesses. The algorithm examines useraccess histories and promotes bookmarks that a user has previously visited. We investigate the potential of our algorithm using interaction logs from an enterprise social bookmarking system, the results show that our personalized algorithm would lead to improved bookmark rankings. Social bookmarking systems have become popular applications for people to store, retrieve and share personal bookmarks. Bookmarks are uploaded to a bookmarking service, annotated with keywords (called tags), and shared for all users to see. While users of bookmarking systems have varied goals for their contributions, which can include community building and publishing [11] , the primary reason for a user to contribute content to a bookmarking system is to facilitate refinding at a later time, using the tags as hooks for recalling bookmarks [9] . Studies of web browsing behaviours have reported that between 50% [2] and 80% [10] of webpage visits are to pages previously visited by a user. Here we present, for the first time, results that show a conservative estimate of refinding in the social bookmarking domain is 59%.. Pivot browsing characterizes the lightweight interactions that are common for exploration and discovery in social bookmarking systems. It allows users to "reorient" their view of bookmark lists, by clicking on different tag artifacts [9] . Pivot browsing in effect is equivalent to providing a text-based filter or query refinement, but allows users to more quickly explore the information-space by alleviating the need to recall and correctly type a tag or username. Users can see not only their own tags but tags entered by other users, so pivot browsing also supports discovery by following the tag links created by other users. However, this technique encourages users to enter queries one piece at time (by clicking on a single tag link), resulting in several refinement steps in order to complete a single query. Further, the result lists returned after each refinement step are ordered in generic ways that do not take into account the possible relevance of bookmarks for the user.. Our research investigates an area that has received little attention in the past: improving ordering algorithms to assist users in finding content in social bookmarking systems. We present a technique that exploits the viewing actions of a searcher as a means of judging relevance; thus the probability the searcher will select a bookmark. Our ordering algorithm coupled with the pivot browsing model can reduce the effort required by users to refind bookmarks. We demonstrate this using the logs of an enterprise social bookmarking system, Dogear [9] , and report on the savings in terms of reduced browsing steps and improved result list positioning. We have presented new evidence that helps to characterize social bookmarking system usage. We have incorporated these results into a simple, yet effective, personalized ordering algorithm and our initial evaluation clearly shows its strong potential. Overall, there is a substantial improvement in bookmark ordering, leading to a target bookmark being shown both higher in a list, and being presented after fewer refinement steps. These improvements occur despite the conservative approach of the algorithm, which incorporates all query types and user purposes, and does not consider other possible factors such as contributor and time frame. Our algorithm has potential to improve the user experience using the popular pivot browsing mechanism by improving bookmark orderings, thus reducing the number of query term refinements needed to find a bookmark of interest. Further analysis of the actual implications of our technique would require a live user trial.. A major advantage of our algorithm is its simplicity: It leverages data that can be easily captured and applied in social bookmarking systems. We believe that this provides designers of social bookmarking systems several new options in presenting personalized bookmark lists: by providing a new option for ordering any bookmark list in addition to date and popularity based orderings; and, perhaps, in a new support widget that provides users with a list of their most frequently visited sites.. We will investigate the effects of including additional features to improve the current algorithm performance. For example, the relevancy of a bookmark could also incorporate whether or not the searcher has it in their collection. A bias toward older bookmarks exists in the current algorithm, as older bookmarks may have an increased chance to accrue selections. This bias could be alleviated through the use of a simple decay model. Our analysis shows that refinding is common in social bookmark information accesses with at least 59% of selections being a repeated selection. However, this also means that 41% of selections are to new content. Our technique works best when users are refinding. If we could identify in the initial steps of query refinement a user's intention (whether a user is refinding or looking to discover new bookmarks) we could more intelligently decide when it is appropriate to use our technique and when another metric may be more appropriate.. Finally, despite the lack of success we have had incorporating the influence of group interactions we believe there are still potential insights to be gained from groups of users. An algorithm incorporating group influence would help when a user is looking to discover new information; by identifying a pool of similar users the searcher could be guided by their group's access patterns. Further, it could help overcome the cold start problem, when new users have no history profile for use by relevance algorithms. Our first metric for determining the effectiveness of our algorithm relates to the position of the target bookmark (the selected bookmark) in each of the result lists. Overall (see Figure 2a) , the default date-based ordering had an average rank for the userselected bookmark of 37.8 and a median rank of 5. We were surprised to find that in many sessions (72%) the target bookmark was presented to the user in the initial result list (after the initial filter), however, the user continued to refine their query through pivot browsing. We hypothesize that the result was not ranked highly enough in the lists of bookmarks to grab the user's attention (lists were of length of 10, 25 or 50, based on a user-set preference). Our personalized ordering improved the average position of a target selection by 16.2 positions, bringing the target bookmark to a higher average position of 21.6 and median of 3. Overall, the personalized ordering metric decreased the median position for selected results by 2 positions over the default datebased ordering. Reducing the mean by 2 might seem like a small change, however, when we consider this in terms of selection bias in search engine results the improvement is sizeable. By increasing the ranking of a target bookmark we increase the likelihood that the bookmark is seen and selected by a user. The figures discussed in the remainder of this section will concentrate on the medians, because the sample set is highly skewed.. Our second metric for determining success was based on how many times the target bookmark appeared in a result list during a query session. Figure 2b shows the percentage of times that the target bookmark was presented to the user, over all refinement steps in a query session. Recall that the date-based orderings presented the target bookmark 72% of the time (18,965 results lists), whereas our personalized ranking metric made a 9.8% relative increase in presenting the target bookmark (20,818 lists). In order to get a better idea of the circumstances under which our technique best performed, we decomposed our results by type of filter event. Table 1 presents the results by each type of query filter used, for each of the ordering metrics. We see that our algorithm outperforms or equals the date-based ordering in all cases. In general the size of improvement seems to be proportional to the size of the result lists. As previously mentioned social tagging systems suffer from limited and converging vocabularies, resulting in large numbers of bookmarks being associated with individual tags. Therefore, when a user initiates a query using only a single tag they are often presented with a large result list. We see that for query refinements using a single tag, the median rank of the selected bookmark is 29. Meaning most users would need to navigate from the first page of results to find a target bookmark (the default list size is 25 results per page). The personalized ranking algorithm reports a much lower median of 19 (a 33% reduction) reducing the median by 10 and placing the result on the first page. We see that when users use more than one tag in their queries our algorithm is not as effective, returning identical medians. This is due to the smaller result list sizes, and the fact that users have already completed at least one refinement step. When users view their personal bookmark collections we see another large ranking improvement, with the median rank dropping from 10 to 6. This is logical, as a user will go to their own profile when they are refinding a bookmark.. In the last two cases we see an increase in rank of only one position, which when compared to the other larger position increases seems to be disappointing. However, when the position of the increase is examined we see an increase in rank from 3 to 2 when people are searching over other people's contributed content and from 2 to the, all important, top result when people are searching others content with a tag in their refinement. This highlights an encouraging detail in that the personalized algorithm; it performs well when users view the profiles of other users. This also provides evidence that users are refinding bookmarks within the collections of others -whether the bookmark is in the collection of the searcher or not. This is an interesting finding, given that there are links allowing users to very quickly add a new bookmark to their collection or discover if the bookmark already exists in their collection.

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


Perfect periodic scheduling for three basic cycles This is the published version of the paper.This version of the publication may differ from the final published version. Abstract Periodic scheduling has many attractions for wireless telecommunications. It offers energy saving where equipment can be turned off between transmissions, and high-quality reception through the elimination of jitter, caused by irregularity of reception. However, perfect periodic schedules, in which each (of n) client is serviced at regular, prespecified intervals, are notoriously difficult to construct. The problem is known to be NP-hard even when service times are identical. This paper focuses on cases of up to three distinct periodicities, with unit service times. Our contribution is to derive a O(n 4 ) test for the existence of a feasible schedule, and a method of constructing a feasible schedule if one exists, for the given combination of client periodicities. We also indicate why schedules with a higher number of periodicities are unlikely to be useful in practice. This methodology can be used to support perfect periodic scheduling in a wide range in real world settings, including machine maintenance service, wireless mesh networks and various other telecommunication networks transmitting packet size data.Permanent repository link: In this paper, we explore the construction of schedules for clients who are serviced on a periodic basis, where clients receive identical service durations but at different intervals. An immediate practical problem motivates our research, namely local transmission of data in Wireless Mesh Networks (WMN) which is of increasingly importance for communication worldwide (Akyildiz et al. 2005) . In wireless networks, data are transmitted in packets, and this feature can be exploited to extract considerable energy saving of a factor of 5 to 10 through efficient algorithms for packet scheduling (Quintas and Friderikos 2012) . Wireless Mesh Networks represent a technology that economically increases the geographical area within which mobile clients may access broadband communication.. Mesh routers facilitate multi-hop wireless transmission to relay data over extended distances without the cost, delay and disruption of installing cabled access points. The routers also act as local access points for devices or clients (e.g. for WiFi access). The routers typically have a fixed location and can be mounted on buildings, street lamps, etc. It is the provision of local access (i.e. devices connecting to the access point) that is of relevance in this paper. Local access is governed by a star topology with all devices connecting to the local access point. Bandwidth must be scheduled so that at any point in time, an access point is servicing at most one client. In this scenario, perfect periodic scheduling provides numerous benefits associated with predictability of activity time. A schedule is perfect periodic when each client is itself serviced regularly at a fixed interval, known as its periodicity. The duration and periodicity of service for each client is given. In classic machine scheduling context, processing of a job is synonymous with servicing of a client, and processing time with duration. We will use these two paradigms interchangeably throughout. The predictability allows the total power consumption of the network to be minimised and the interference from competing simultaneous transmissions to be reduced or even eliminated.. Several studies have been undertaken on perfect periodic scheduling problems. The problem of finding a feasible perfect periodic schedule has been proved by Bar-Noy et al. (2002a) to be NP-hard in general. However, there are some special cases for which simple closed form expressions offer a polynomial time solution method. For three products with three distinct periodicities, Glass (1992) derives a simple test for existence of a feasible schedule, and a method of constructing feasible schedules if one exists. In addition, Glass (1994) and Glass et al. (1994) study the feasibility problem in the context of the Economic Lot Scheduling Problem where several products with different durations are produced periodically so as to minimise holding and set up costs. For two (three) products with two (three) distinct periodicities, they develop a simple necessary and sufficient condition for the feasibility test and construction of a feasible schedule.. Due to the difficulty of finding a feasible perfect periodic schedule for any given periodicities, called as request periodicity, heuristics are therefore used to allocated close values, called as allocated periodicity, using specific criteria. study perfect periodic scheduling for multiple servers, with the objective is to minimise the maximum ratio of the allocated periodicity and requested periodicity. They develop some approximation algorithms for the problem. Patil and Garg (2006) propose an adaptive algorithm, called Adapmin. They find a worst case performance bound on the quality of schedules produced by Adaptmin and compare Adapmin to the algorithm of Brakerski et al.. Chen and Huang (2008) propose an efficient algorithm of requested periodicities with high density and large variance.. For perfect periodic scheduling with identical processing times, Bar-Noy et al. (2004) consider two objective measures of maximum and weighted average ratios between the allocated periodicity and requested periodicity. They present a few efficient heuristic algorithms using a methodology, called tree scheduling, based on an hierarchical round-robin approach, where the hierarchy is a form of tree. Bar-Noy et al. (2002b) develop tree-based approximation algorithms for perfect periodic scheduling with the objective of minimising weighted average ratios between the allocated periodicity and requested periodicity. Brakerski et al. (2003) study the question of dispatching in a perfect periodic schedule, namely how to find the next item to schedule, assuming that the schedule is already given somehow.. All of the above approaches to finding a perfect periodic schedule are limited in the range of schedules which they consider. For example, tree scheduling algorithms (Bar-Noy et al. 2002b; Brakerski et al. 2003) restrict their solution space to a set of periodicities with a non-trivial greatest common divisor. Moreover, , Patil and Garg (2006) , and Chen and Huang (2008) constrain solutions to those for which the ratio between any pair of two allocated periodicities is a power of 2. Thus, further improvements in heuristics depend upon being able to establish perfect periodic schedules with a wider range of periodicities. Additional motivation for developing our understanding of perfect period scheduling, arises in the context of wireless mesh networks where the response time variability in transmissions, known as jitter, is an important issue. Jitter relates to quality of reception and is measured by total response time variation as well as the "bottleneck metric," of maximum deviation from an ideal interval, identified by Steiner and Yeomans (1993) . Corominas et al. (2007) provide effective heuristics for measures which prove to be optimal for the case of two tasks. However, they avoid attempts to find solutions with no interval variation, which are perfectly periodic, because of "the serious practical disadvantage . . . that there may not be a feasible solution.". The aim of this paper is to address the issue of feasibility for perfect periodic scheduling problem on a single resource. We restrict our attention to problems with identical task durations and at most three distinct periodicities in total. Observe that the focus on tasks with identical durations is generally no limitation in the packet scheduling environment of wireless networks. Current practice is to use a common cycle time to co-ordinate packet scheduling (Quintas and Friderikos 2012) . Thus, any methodology which facilitates variety in periodicities infers enhanced flexibility and thus potential additional energy savings for network operators. In the context of a wireless network with homogeneous link bandwidth, transmission time for a data packet is uniform throughout the network, and time may thus be divided into unit slots accordingly for scheduling purposes. Our dual contributions are to provide a test of feasibility and a method for constructing a feasible schedule (when one exists).. This article contributes to a broader programme of research into energy efficient scheduling for WMNs using time slot models. A complementary algorithm for coordinating given periodic schedules at mesh nodes with data transmission through the routing tree of the access network is provided by Allen et al. (2012a) , and demonstrated on simple networks. Then, for routing trees with a binary structure, Kim and Glass (2012) develop a perfect periodic scheduling methodology for efficiently transmitting data through the access network, while providing the local clients at a mesh node with a common scheduling cycle. For a general routing tree, Allen et al. (2012b) introduce an integer programming formulation to describe an optimised schedule with time slots, and a fast heuristic approximation which produces The only possible, infeasible, schedule for two clients with periodicities 2 and 3, respectively near-optimal solutions. They additionally explore the potential for increasing throughput in a wireless mesh network by varying transmission rates at individual links, taking account of signal interference.. The remainder of the paper is structured as follows. The problem itself is formulated in purely mathematical terms in the next section. Our results rely only upon classic properties in modulo arithmetic, which are included for completeness. We then analyse the case of two distinct periodicities in Sect. 3. We establish a closed form test for the existence of a perfect periodic schedule, and in doing so indicate the structure of a feasible solution. Section 4 provides similar results for the case of three periodicities. Various cases are analysed, resulting in a test for feasibility which runs in O(n 4 ) time, where n is the total number of clients, in the last subsection. The construction of a feasible solution itself, where one exists, is presented explicitly in Sect. 6. A few concluding remarks are then offered in Sect. 7. For convenience, the remainder of the paper is framed in the telecommunications context of "service" to "clients," and not in the alternative machine scheduling terminology of "processing" of "jobs." This paper examines the perfect periodic scheduling problem with unit service time. We have extended the range of perfect periodic scheduling problem which are amenable to polynomial time algorithms from one periodicity to three distinct periodicities. The extent of such special cases is likely to be limited since the existence of perfect periodic schedule problem for the general case is NP-hard. The only models commonly used in the literature are based upon a single common periodicity: either the single periodicity itself, its powers (eg. power of 2), or based upon repeated divisibility (depicted as a tree structure).. We have presented an algorithm for testing for the existence of a feasible schedule for any combination of clients Fig. 7 The structure of each -set in the feasible schedule for Example 3, as a -partition with up to three distinct periodicities, which runs in O(n 4 ). In addition, we have provided the construction of a feasible schedule where one exists. We have thus extended the range of feasible perfect periodic schedules available for operating Wireless Mesh Networks beyond those with a common factor.. The next obvious step is to embed these algorithms within heuristics for meeting the requests of mobile telecommunication clients, according to different service level quality measures, see Bar-Noy et al. (2004) , Brakerski and PattShamir (2006) . There is potential for accommodating a wide range of combinations of periodicities, by incorporating multiples of the three basic periodicities in particular power of 2. The addition of a fourth distinct periodicity might be investigated. However, it is unlikely to be an attractive option due to the large number of idle time slots imposed in the schedule. Future research will evaluate the advantage of the wider solution spaces made accessible through the current article. In particular, efficient methodologies will be sought for combining perfect periodic schedules for local clients at mesh nodes, with approaches to data transmission through a routing tree, such as Allen et al. (2012a,b) , as is applicable for Internet access through Wireless Mesh Networks. Proof By symmetry, it is sufficient to show that Statement 1 implies Statement 2. Take an integer x satisfying the inequalities, (31), (32) and (33). Let y = n 3 /(g 23 − x) . Observe that 1 ≤ y ≤ g 31 − 1 from (32). Then, n 3 /(g 23 − x) ≤ y, and hence 1 ≤ x ≤ g 23 − n 3 /y which implies that the inequality (34) Thus, the inequality (36) holds. Moreover, since n 2 > 0 and the inequalities (34) and (36) hold, 0 < g 12 − n 1 /(g 31 − y) , which implies that the inequality (35) also holds completing the proof.. the periodicity of q 1 , q 2 and q 3 , respectively, fit into a singleμ 3 ≤ g 31 −

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


Intelligent data analysis and model interpretation with spectral analysis fuzzy symbolic modeling This paper proposes fuzzy symbolic modeling as a framework for intelligent data analysis and model interpretation in classification and regression problems. The fuzzy symbolic modeling approach is based on the eigenstructure analysis of the data similarity matrix to define the number of fuzzy rules in the model. Each fuzzy rule is associated with a symbol and is defined by a Gaussian membership function. The prototypes for the rules are computed by a clustering algorithm, and the model output parameters are computed as the solutions of a bounded quadratic optimization problem. In classification problems, the rules' parameters are interpreted as the rules' confidence. In regression problems, the rules' parameters are used to derive rules' confidences for classes that represent ranges of output variable values. The resulting model is evaluated based on a set of benchmark datasets for classification and regression problems. Nonparametric statistical tests were performed on the benchmark results, showing that the proposed approach produces compact fuzzy models with accuracy comparable to models produced by the standard modeling approaches. The resulting model is also exploited from the interpretability point of view, showing how the rule weights provide additional information to help in data and model understanding, such that it can be used as a decision support tool for the prediction of new data. One of the most widely used models in soft computing, which has been developed within many different modeling frameworks, is written as:. where x 2 R p is the vector of the input variables; g i (x, X i ), i = 1,. . ., n are the basis functions, each of which is parameterized by the set of parameters X i , and h = [h 1 , . . ., h n ] is the output parameters vector. Usually, the interpolation function g(x, X) is the Gaussian function:. The set of parameters X i = {x i , r i }, where x i 2 R p is the center of the Gaussian function and r i is the width parameter. The model defined by Eqs. (1) and (2) has been extensively studied in supervised (or prediction) learning problems in many classification (or pattern recognition) and regression (or function approximation) applications. This model is described as a radial basis function (RBF) neural network [1, 2] , which is equivalent to the (unbiased) support vector machine (SVM) [3, 4] . These two models have also been recognized to be equivalent to certain types of fuzzy rule-based systems, both in the RBF neural network framework [5, 6] and, more recently, in the SVM framework [7] [8] [9] .. Several methods and algorithms have been described in the literature for the estimation of parameters given a training set of input-output data samples. Most of these methods differ in how to define the dimension of the feature space that is spawned by the set of the interpolation functions (2), i.e., the number n of interpolating functions that should be used in the model (1) . There are several strategies for estimating the number of radial basis functions in the RBF neural network framework including orthogonal least squares (OLS) methods [16, 17] , genetic algorithms (GA) [18] [19] [20] , and hybrid methods [21, 22] . Using the structural risk minimization paradigm, a tolerance for the error of the model is fixed and the model structure is minimized [4] , obtaining the number of support vectors as a byproduct.. In the fuzzy systems framework, the feature space dimension is related to the number of rules. In the earlier approaches, the number of rules was defined a priori based on expert advice [5] . Some approaches have also been proposed based on reducing the rule base through orthogonal transforms [23, 24] . Since the mid 1990s, the structure optimization of fuzzy systems using GA-based strategies has being a very active research area [25] [26] [27] . More recently, some approaches for the design of fuzzy systems based on the SVM algorithm have also been proposed [7] [8] [9] . The numerical accuracy of the results is more often emphasized, but the interpretability of the rule base has recently been brought to attention [10] [11] [12] [13] [14] [15] , especially when using the genetic fuzzy systems approach [28] [29] [30] [31] [32] [33] [34] .. A fuzzy rule described by a multidimensional Gaussian membership function (2) cannot be directly translated into a linguistic expression such as a fuzzy rule written as a set of variable-value pairs. According to the terminology proposed by Zou and Gan [12] , multidimensional fuzzy rules can achieve only high-level interpretability, whereas fuzzy rules written as a set of variable-value pairs can have both high-and low-level interpretability. On the other hand, in many real world problems, the fuzzy model needs a large number of rules that relate several variable-value pairs on the premise in order to achieve the desired accuracy and, consequently, the model becomes very difficult to interpret linguistically [14, 15] .. The interpretability of fuzzy rules should not be regarded as an end in itself, but as a means for human experts to develop insight into complex problems. The model and the modeling methodology must be considered as a whole in the task of problem understanding. The analysis of the weights of the fuzzy rules for model interpretation can partially overcome the drawback of the lack of linguistic interpretability of multidimensional fuzzy rules. Moreover, the graphical visualization of data provides a rough interpretation of the problem that allows the analyst to obtain insight into the problem, supporting future decision making in the analysis of new data.. In this work, a methodology for design and interpretation of fuzzy models in the form (1) and (2) is proposed. The main contribution of this work is on the interpretation framework based on assigning the interpolation functions (2) to symbols that are related to prototype values. A learning methodology, compatible with the proposed interpretation framework, is also presented. The resulting model is expressed by a compact but accurate fuzzy rule base. The analysis of the weights of the fuzzy rules and the graphical visualization of the data and rules provide additional information for human experts to guide the prediction of new data.. The learning procedure is based on spectral analysis [32] to determine the number of multidimensional rules, as described by the Gaussian membership function (2) . The model identification is performed in two steps: rule induction and parameter estimation. In the rule induction task, the number of relevant fuzzy rules is computed by spectral analysis, and a clustering algorithm computes the positions of their centers. In the parameter estimation task, the output parameters of the rules are computed by solving a bounded quadratic optimization problem. This paper is organized as follows. In the next section, the symbolic approach for fuzzy modeling is introduced to set up the notation and to present the parameters that should be estimated by the identification algorithm. Section 3 presents the spectral analysis used to determine the number of rules in the model. Section 4 presents the rule induction algorithm and the formulation of the optimization problem for parameter estimation. Section 5 presents the interpretation of the model and graphical visualization. In Section 6, the performance results in classification and regression benchmark problems are presented and evaluated using nonparametric statistical tests. The interpretation and exploitation of the model is also discussed in Section 6. Concluding remarks and the directions for future research are presented in Section 7. This work has presented a semantic, coherent and organized set of known methods to obtain a conceptual framework for data understanding and approximate reasoning in complex systems modeling. In the proposed framework (which can be employed in classification or regression learning tasks), the number of interpolation functions of the model (Eqs. (1) and (2)) is computed using spectral analysis. Each interpolation function is associated with a symbol to generate a fuzzy rule. Each symbol is related to a center or prototype that is computed using a clustering algorithm and that can be used to interpret the model in the context of an application. The model parameters are optimized by solving a bounded quadratic programming problem and then interpreted as rule confidences. Graphic visualization of the rule confidences and projecting the data into a two-dimensional space spawned by the principal components have also been proposed, and these may help the user to understand the data and the model. The user can then use it a tool for decision support in the prediction of new data.. Numerical results obtained for the classification and regression benchmark datasets show that the selection of the model through cross-validation allows an accurate model to be found. The statistical tests have shown that the performance of the proposed approach is similar to that of the standard methods used to design the model (1) . The solution of the bounded quadratic problem has shown to be effective at controlling the model capacity while preserving accuracy in classification and regression problems. Moreover, the default design with no free parameters to be set has obtained similar performance results to those of the LibSVM models in classification and regression problems. Nevertheless, the spectral analysis in the default design has resulted in a smaller number of interpolating functions to represent the model and is consequently more interesting for model interpretation and exploitation than SVM models.. The main focus of the proposed method is on the interpretability rather than the accuracy of the resulting model. This interpretability is achieved by the compact model obtained by the spectral analysis and quadratic programming parameter optimization. The graphical visualization of the rules' weights and the 2D linear projection of the data and the rules' centers enable the model interpretation for a better understanding of the problem. The main drawback of the method is the high computational cost for the solution of the spectral analysis, which can be a hurdle for problems with a huge number of records. Nevertheless, advances in multi-core hardware platforms and parallel implementation of numerical algorithms can deal with this handicap. Moreover, the more difficult problems are usually those with a low number of records, while those with a huge number of records can always be treated using sampling methods to obtain a more compact dataset.. The future direction of this research is to deeply explore the number of rules generated by the variation of the dispersion parameter in the affinity matrix in spectral analysis, so that it can be used as a tool for understanding data. Model interpretation using this set of models could also be improved in a hierarchical structure, thereby allowing a multi-modeling approach with multiple levels of representation.

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


Low-connectivity and full-coverage three dimensional wireless sensor networks Low-connectivity and full-coverage three dimensional Wireless Sensor Networks (WSNs) have many real-world applications. By low connectivity, we mean there are at least k disjoint paths between any two sensor nodes in a WSN, where k ≤ 4. In this paper, we design a set of patterns for these networks. In particular, we design and prove the optimality of 1-and 2-connectivity patterns under any value of the ratio of communication range rc over sensing range rs, among regular lattice deployment patterns. We further propose a set of patterns to achieve 3-and 4-connectivity patterns and investigate the evolutions among all the proposed low-connectivity patterns. Finally, we study the proposed patterns under several practical settings. In this paper, we study the problem of how to construct a three dimensional (3D) Wireless Sensor Network (WSN) that Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. achieves low-connectivity and full-coverage by using the least number of sensors. By low connectivity, we mean there are at least k disjoint paths between any two sensors, where k ≤ 4. In this paper, we have designed a set of patterns for lowconnectivity (k ≤ 4) and full-coverage WSNs in 3D space. We have proved the optimality of 1 and 2 connectivity patterns under any value of the ratio of rc/rs among the right lattice deployment patterns. We have investigated the evolutions among all the proposed low-connectivity patterns. The proposed patterns can save a significant number of sensor nodes, and provide insights for further pattern optimality exploration in 3D WSNs.. We are to explore the optimal deployment patterns to achieve full-coverage and multiple-connectivity in 3D space among more general regular patterns. Extending our research to more practical scenarios is also one of our future directions. Any opinions, findings, conclusions, and recommendations in this paper are those of the authors and do not necessarily reflect the views of the funding agencies. Our research on the above problem is motivated by the following two important facts. There are two sets of work related to the low-connectivity and full-coverage deployment problem in WSNs.. − Sphere Covering and Packing in Discrete Computational Geometry One closely related problem in discrete computational geometry is covering problem, especially sphere covering in 3D Euclidean space. In 1887, Lord Kelvin provided a conjectured answer to the problem of "What is the optimal way to fill a three dimensional space with cells of equal volume, so that the surface area (interface area) is minimum?". His answer states that the Voronoi polyhedrons in the optimal covering strategy are 14-sided truncated octahedrons [8] . To date, the proof for Kelvin's conjecture remains open. However, there are valuable efforts on the covering problem under certain conditions. One important condition is the spheres are placed following certain regularity. In [9] , R. Bambah first proved that the least covering density of a 3D space by identical spheres is 5 √ 5π/24 (the definition of covering density will be given later). E. Barnes in [10] and L. Few in [11] proved the same result in different ways. Another closely related problem in discrete computational geometry is sphere packing in 3D Euclidean space. Sphere packing considers arrangements of non-overlapping identical spheres filling a space. There have been several works on the packing problem [14] . One of the most famous results is known as Kepler's conjecture. In 1611, Johannes Kepler conjectured the maximum possible density for sphere packing is π/ √ 18. There is no rigorous proof until 2005. T. C. Hales in [15] accomplished the proof showing that no packing of identical spheres in 3D Euclidean space can have density greater than π/ √ 18, which is the density of the face-centered cubic packing [15] , [16] , [17] . None of the above efforts considers connectivity in 3D Euclidean space.. − Connectivity and Coverage in WSN Deployment S. Alam and Z. Haas in [21] suggested the sensor deployment pattern that creates the Voronoi tessellation of truncated octahedral cells in 3D space. The suggestion is directly from Kelvin's conjecture. The numerical data in [21] illustrates truncated octahedron tessellation is better than the tessellations of cube, hexagonal prism, and rhombic dodecahedron. However, the optimality proof for truncated octahedron tessellation is untouched. Besides the efforts focused on the optimal deployment strategy, there are some works in 3D sensor deployment addressing other issues related to coverage. In [22] , a deployment algorithm is proposed to "repair" coverage holes once they are discovered in a 3D volume. In [23] , some sufficient conditions are presented for sensors in a given deployment to check if every points in a 3D volume is covered by at least k sensors. None of these two provides any lead towards the optimality of deployment patterns in 3D WSNs. We notice there are many valuable efforts on 3D routing and localization, e.g., [24] , [25] , [7] , [26] , etc. Our research can act as a complement to them by providing new network topologies as a carrier for their algorithms and protocols. In 2D WSNs, X. Bai et al. in [18] , [19] , and [20] studied several optimal deployment patterns to achieve multiple connectivity and full coverage in 2D WSNs. The optimality of the proposed patterns in [20] is proved under the constraints of regularity. X. Bai et al. have made an attempt to further the exploration of optimal lattice patterns into three dimensional space, and some results on high connectivity are presented in [31] .

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High-Order Quadratures for the Solution of Scattering Problems in Two Dimensions We construct an iterative algorithm for the solution of forward scattering problems in two dimensions. The scheme is based on the combination of high-order quadrature formulae, fast application of integral operators in Lippmann-Schwinger equations, and the stabilized biconjugate gradient method (BI-CGSTAB). While the FFT-based fast application of integral operators and the BI-CGSTAB for the solution of linear systems are fairly standard, a large part of this paper is devoted to constructing a class of high-order quadrature formulae applicable to a wide range of singular functions in two and three dimensions; these are used to obtain rapidly convergent discretizations of Lippmann-Schwinger equations. The performance of the algorithm is illustrated with several numerical examples. Forward scattering has been an active field of research in science, mathematics, and engineering over the past several decades (see e.g. [3] , [4] ). The most straightforward method for the solution of a forward scattering problem is to discretize the underlying PDEs directly, replace the derivatives with finite differences, and solve numerically the resulting system of linear algebraic equations. However, discretization of differential equations leads to matrices with high condition numbers, with the attendant loss of accuracy, deterioration in the performance of iterative methods, etc. Another approach is to convert the underlying PDEs into integral equations of the second kind (normally referred to as the Lippmann-Schwinger equation), discretize the latter via appropriate quadrature formulae, and deal numerically with the resulting linear systems. This paper constructs a class of high-order quadrature formulae applicable to the Lippmann-Schwinger equation in two and three dimensions. A number of algorithms exist for the modeling of acoustic scattering; since we are interested in frequency domain results, we have concentrated on frequency domain (as opposed to timedomain) models. The usual approach to such problems is to convert the scattering problem into the Lippmann-Schwinger equation, and solve the latter iteratively (integral equations of the second kind being much more amenable to iterative techniques than the straightforward discretizations of underlying partial differential equations (PDEs)). In addition, the use of the Lippmann-Schwinger equation obviates the need to impose the radiation (Sommerfeld) condition at the boundary of the grid, since the "background" Green's function (11) imposes the Sommerfeld condition automatically.. Historically, there have been two problems associated with the numerical use of integral equations in scattering calculations. First, the kernels of Lippmann-Schwinger equations are dense, except when the background is extremely attenuating; since iterative techniques require application of the matrix of the discretized integral operator to a sequence of recursively generated vectors, the cost of the procedure is prohibitive, except for extremely small-scale problems. This difficulty was overcome almost 40 years ago via the observation that the free-space Green's function for the Helmholtz equation is translation invariant; appropriately chosen discretizations of Lippmann-Schwinger equations result in Toeplitz matrices, and the latter can be rapidly applied to arbitrary vectors via the FFT (Fast Fourier Transform), resulting in algorithms with CPU time requirements proportional to N · log(N), with N the number of nodes in the discretization of the problem. Various forms of this approach have been widely used in electrical engineering and other fields, under the name "k-space" methods; some of the existing codes are quite fast, even for discretizations involving hundreds of millions of nodes. However, the resulting solvers for the underlying PDEs are usually not very accurate, due to the problem discussed in the following paragraph.. The second difficulty associated with numerical use of Lippmann-Schwinger equations is due to the singular character of the Green's function for the Helmholtz equation; in two dimensions, the principal term of the singularity is of the form log(r), and in three dimensions, it is of the form 1/r. As a result, kernels of Lippmann-Schwinger equations are singular; the singularities are located on the diagonal, and in two dimensions are of the form. with P, Q two smooth functions, and P (x, x) = 0 for all x ∈ R 2 ; the corresponding form in three dimensions is. It is important to observe that in most cases, we do not have access to each of the functions P, Q separately, but can only evaluate the whole kernel K given a pair of points (x, y). In other words, standard integration techniques (such as product integration, etc.) can not be used efficiently. The standard procedure in the literature (referred to as the "singularity extraction") is to subtract the principal singularity and treat it analytically, and apply the trapezoidal quadrature rule to the remaining function. Since the latter is not smooth (having infinite derivatives at x = y), the procedure converges slowly, normally behaving like a second order scheme. We introduce a class of quadrature formulae for functions of the form (13) in two dimensions and (14) in three dimensions. The approach is somewhat related to the Ewald summation [6] , and leads to quadratures that can be viewed as a version of the corrected trapezoidal rule; it is easily combined with the FFT to obtain fast algorithms. While in principle corrections of arbitrarily high order could be constructed, in practice both the complexity of derivation and the number of corrections grow rapidly with the order. We have designed corrections of orders 4, 6, 8, and 10; they require 1, 5, 13, and 25 corrected nodes respectively.. The paper is organized as follows. In Section 2, we summarize several well-known mathematical facts to be used in the paper. In Section 3, we introduce analytical tools to be used in the construction of the algorithm. Section 4 describes the algorithm in detail, and contains a complexity analysis. In Section 5, several numerical examples are used to illustrate the performance of the algorithm. Finally, Section 6 contains generalizations and conclusions. In this paper, we construct an iterative algorithm for the solution of two-dimensional forward scattering problems. The scheme is based on the combination of high-order quadrature formulae, rapid numerical application of the integral operator in the Lippmann-Schwinger equation, and the stabilized bi-conjugate gradient method (BI-CGSTAB). As illustrated via several numerical examples, the scheme is (2p + 4) th (p = 0, 1, 2, 3, ...) order convergent; the computational complexity of the algorithm is O(N iter · N 2 log N), where N iter is the number of iterations used by the iterative solver, and N 2 is the total number of discretization points. The approach we use for the design of high order center-corrected quadrature formulae introduced in this paper is not limited to functions of the form (13) in two dimensions; it is also applicable to functions of the form (14) in three dimensions, as well as many similar situations. Furthermore, the method does not require access to each of the functions P , Q separately in (13) and (14); it only requires the evaluation of the whole kernel K given a pair of points (x, y). Quadrature formulae of order higher than 10 can also be constructed, though the derivations become more tedious. . with (i, j) = { (3, 1), (5, 1), (3, 3), (7, 1), (5, 3) }. The proofs are straightforward and tedious, and use the help of Mathematica.. Lemma 6.1 For any k ∈ C + and h > 0, . where r, α 1 , α 2 , x 1 , x 2 , y 1 , y 2 , z 1 , z 2 are defined by (88), (89), and (93)-(95). . and r, α 1 , α 2 , x 1 , x 2 , y 1 , y 2 , z 1 , z 2 are defined by (88), (89) and (93) . where r, α 1 , α 2 , x 1 , x 2 , y 1 , y 2 , z 1 , z 2 , w 1 , w 2 , u 1 , u 2 are defined by (88), (89), (93)-(95), (127) and (128).

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


Learning full pairwise affinities for spectral segmentation Abstract Unsupervised image segmentation is a fundamental but challenging problem in computer vision. It automatically partitions an image into coherent groups without any prior knowledge. Recently, the main research directions are focused on deterministic annealing [21] , stochastic clustering [13] [26] , mode-seeking methods like mean shift [5] [4] , mixture model [23] [24] , rate distortion [22] , graph theoretic approaches [27] [9] [33] , and other variational methods [20] [8] . Most studies generally defined the segmentation problem as finding the labeling of an image that minimizes a specific energy function. However simple appearance based methods like the mean shift image segmentation algorithm [5] are still generally used to make the over-segmentations with detailed boundaries. [27] , MNCut [6] , and our algorithm with the boundaries drawn in red, respectively.. Several problems make unsupervised image segmentation difficult in natural images, such as finding the faint object boundaries and separating the highly cluttered background. To solve these problems, several recent works focused on integration of local grouping cues across long ranges of spatial connections between pairwise pixels and produced impressive segmentation results. Since using the full range connections would require a great computational cost, two conventional approaches to propagate local grouping cues across larger image areas recently became popular. The first approach is a multi-scale image segmentation [25] [1] [31] [10] [6] to combine both coarse-and finelevel details. The multi-scale frameworks give efficient approximation to incorporate long-range connections with low complexity. However they typically fail to detect fine-level details along object boundaries due to coarsening error. The second approach is to define the segmentation as the grouping of non-overlapping regions, instead of pixels [29] [22] . It is inspired by the hard constraint whereby pixels in a particular region should have the same label. This region-based segmentation has the benefit of using more informative features extracted from the pixels inside the regions, as well as transferring local information to a larger image area with connections across regions. If, however, the regions are not consistent with the object boundaries, there are radical difficulties in obtaining the exact solutions. In fact, such situations often arise in natural images.. Unlike these conventional approaches, we propose a new segmentation algorithm to directly incorporate a full range of pairwise affinities in the spectral framework. The key contributions of our algorithm are as follows.. 1. We introduce a new affinity model for image segmentation. Unlike the conventional affinity models learnt from a large database with manually segmented images [11] , or from only local properties of the neighboring pixels [16] [6], we propose to use the relevance scores, learnt from the test image by semi-supervised learning [3] [34] [19] , as graph affinities. We first construct a multi-layer graph with pixels and regions generated by the mean shift algorithm [5] . After we assign each node and all other nodes as labeled and unlabeled data respectively, the affinities are efficiently estimated by applying the semi-supervised strategy to this graph. Fig. 1 shows that compared with the general affinity model [6] , which heuristically unifies region and boundary information, our proposed affinity model intuitively gives better scores in the highly textured images. In this paper, the segmentation algorithm based on spectral clustering is proposed. Our work is novel in that it sheds understanding on the full affinities gained in integrating local grouping cues by using semi-supervised learning. Since these well-defined full pairwise affinities are directly used in the multi-layer spectral segmentation framework, our algorithm produces high-quality segmentation results with object details in natural images. Further, our algorithm is computationally very efficient. Our future work is to automatically estimate the number of segments K.

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Estimating the depth of anesthesia using fuzzy soft computation applied to EEG features Abstract. Estimating the depth of anesthesia (DOA) is still a challenging area in anesthesia research. The objective of this study was to design a fuzzy rule based system which integrates electroencephalogram (EEG) features to quantitatively estimate the DOA.The proposed method is based on the analysis of single-channel EEG using frequency and time domain methods. A clinical study was conducted on 22 patients to construct subsets of reference data corresponding to four well-defined anesthetic states: awake, moderate anesthesia, surgical anesthesia and isoelectric.Statistical analysis of features was used to design input membership functions (MFs). The input space was partitioned with respect to the derived MFs and the training data was used to label the partitions and extract efficient fuzzy if-then rules. Consequently, the fuzzy rule-base index (FRI) is derived between 0 (isoelectric) to 100 (fully awake) using fuzzy inference engine and designed output MFs.We also applied the same features to an adaptive network-based fuzzy inference system (ANFIS) derived without any prior knowledge. The results show that FRI correlates more with the clinically accepted DOA index, CSI TM (CSM, Danmeter, Denmark). In addition to this achievement the main idea behind this study is to simplify the mutual knowledge exchange between the human expert and the machine, leading to enhance both interpretability of the results and performance of the system. Depth of anesthesia assessment has remained a challenging problem for several decades. It is because none of the parameters used to this aim has satisfactorily described the complexity of the system. Patient hemodynamics like blood pressure, heart rate, tearing and sweating can not avoid awareness and movement during surgery. Neither plasma nor the effect site concentrations of the drugs are direct measures of clinical effect. Solving this problem the Central Nervous System, the main target for anesthetic agents, has received a great deal of attention and EEG-based methods have been widely used for estimating the anesthetic depth.. Various types of features have been extracted from the electroencephalogram to predict depth of anesthesia. Early studies have used spectral edge frequency (SEF), median frequency and the relative and total power in the classical frequency bands [1] [2] [3] . Using parameters based on bispectrum made a progress in EEG-based anesthesia monitoring [4] [5] [6] . The bispectrum power is said to indicate the presence of quadratic phase-coupling between different frequencies within the signal. Recently some researchers have used EEG entropy measures as an indicator of depth of anesthesia [7] [8] [9] [10] . The concept behind this is that EEG becomes more regular as the anesthetic depth increases. Also Lempel-Ziv complexity of EEG has shown good correlation with increasing the anesthetic depth [11] .. Although these parameters can distinguish well between awake and anesthetized states, they don't behave monotonically during transition between wakefulness and deep isoelectric states [2] . So we can't utilize them individually to continuously monitor anesthetic state changes during different phases of anesthesia and it is essential to utilize an efficient system to integrate these features.. Computational intelligence methods comprising fuzzy logic, neural networks and evolutionary computing have shown a promising prospective to make a suitable decision according to combination of features. In depth of anesthesia studies some efforts have been made to combine EEG features using neural networks and neuro-fuzzy inference systems [8, 12, 13] , however the lack of interpretability in these systems led us to use a fuzzy knowledge based model.. Fuzzy logic, which is known as the oldest and most reported soft computing area, provides an effective tool for describing the characteristics of a system that is too complex or ill-defined to admit precise mathematical analysis. This theory is based on approximate reasoning which plays a major role in human thought process. Roughly, the aim of fuzzy logic is to build a flexible information processing system which provides soft decision strategy resembling human decision making [14] .. The concept of fuzzy sets can be used at both the feature and classification levels. At feature level, it can be applied to represent input data as an array of membership values signifying the degree of possession of certain properties and also to represent linguistically phrased input features. At the classification level, it can be used for representing multiclass membership of objects, and for providing an estimate (or representation) of missing information in terms of membership values. In other words, fuzzy set theory provides a concept of embedding; we find a better solution to a crisp problem by looking in a large space at first, which has different (usually less) constraints and therefore allows the algorithm more freedom to avoid errors forced by commission to hard answers in intermediate stages [14, 15] .. Two trends can be observed in development of anesthesia monitors. Some algorithms put more emphasis on some advanced parameters like bispectrum or entropy, while the others (like CSM, Cerebral State Monitor) combine some well-known spectral ratios and time domain characteristic of EEG applying them to a classification algorithm. CSM (Danmeter, Denmark) is a recently developed depth of anesthesia monitor having good correlation with clinical assessments [16, 17] . It uses 3 later defined spectral ratios: alpha-ratio, beta-ratio and difference between them, which is called theta ratio in this paper, accompany with burst-suppression, a time domain feature relating to deep iso-electric states. Each of these components are affecting in a specific range of anesthetic level where they perform best. Adaptive Neural Fuzzy Inference System (ANFIS) is used to calculate the CSI which is a scalar index changing between 0 and 100.. In this study we utilized features used in calculating CSI in conjunction with a FIS. To design input memberships of the fuzzy system, histogram analysis of these features have been done over 4 defined anesthetic states. Also we have used genetic algorithm to tune the MFs and to reduce the number of rules. Eventually we compared our proposed index naming FRI with CSI recorded from the CSM monitor and an ANFIS derived index using the same features. In this study four database of distinct anesthetic states, comprising awake, moderate anesthesia, surgical anesthesia and isoelectric, were constructed. Spectral and time domain features from the raw EEG were extracted. In contrast with prior studies in which distributions of features in just two states of anesthesia (awake and anesthetized) is taken into account, here we investigated them over four defined states that led us to well tune initial fuzzy MFs. The proposed fuzzy rule based system has following advantages: 1) Classification results are so improved in comparison with LDA and ANFIS classifiers; 2) Assigning appropriate output MFs based on intuitive insight of different anesthetic levels makes the transition between continuous levels gradually rather than abrupt. It is essential in the operation room to prevent patient awareness during surgery.. Needless to say, such an index can help the anesthesiologist to monitor the anesthetic depth continuously, thus preventing the patient from being conscious; 3) It is easy to fuse and extract knowledge to and from the system. Because it was first initialized by the human expert and final rules are just 5 rules. 4) Independence from subject to test; 5) predictive for the appearance of clinical signs of inadequate anesthesia like movement.. The performance of proposed fuzzy rule based system for assessment of DOA varies with input features. The most useful parameters which are derived from the EEG are dependent upon the signal processing technique used. To extract more robust features further works must be done on the signal artifact rejection and denoising of the raw EEG. For future we intend to add some other features and examine different combination of them as an input to the fuzzy system.. Although EEG has sufficient information of DOA but it can't monitor the whole complexity of the anesthesia. So combining EEG features with hemodynamics information and also measurements of muscle relaxation may result to more confident indices of depth of anesthesia. We pursued two different goals in this study. Firstly to find out how can single features or different combinations of features discriminate between distinct stages of anesthesia. Another purpose of this paper was to define a unitless index, witch can measure DOA continuously.

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A pedagogically targeted logic design and simulation tool AbstractJLS is a GUI-based digital logic simulation tool specif- Choosing a logic simulation tool for introductory courses in logic design and computer organization is problematic. On the one hand there are industrial strength tools that are Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. expensive, have steep learning curves, and are generally used by experienced designers. Many of these tools use textual, as opposed to graphical, input.. On the other hand there are many free tools. Most are (very) limited in functionality. Few will work on multiple platforms.. JLS is a portable powerful digital logic simulation tool created primarily for educational use that addresses the problems listed above. It is written in Java and has been tested on many platforms. It is free. It consists of a simple to use yet powerful graphical editor that allows users to create and modify logic circuits, and a simulator that will show (in multiple ways) the operation of the circuit over a period of time. Circuits as simple as a few logic gates or as complex as complete CPU microarchitectures with embedded subcircuits have been created and simulated in JLS.. Logic circuits can contain the standard gate types: AND, OR, NOT, NAND, NOR, XOR, tri-state buffer and logically neutral time delay element; composite elements: decoder, multiplexor, and adder; memory elements: registers, SRAM, and ROM; a clock and various mechanisms for connecting gates and elements via wires and wiring elements. State machines can be created by using JLS's state machine editor. Combinational circuitry specified by a truth table can be generated by using JLS's truth table editor. Complex, synchronized multi-signal inputs can be specified. Circuits can include copies of other circuits (subcircuits), nested to an arbitrary depth. Circuits can be printed or exported as image (JPEG) files.. JLS has many features that are useful for classroom instruction, student use, and for the grading of students' circuit assignments. These include simple and intuitive drawing and editing, comprehensive error checking/reporting and extensive on-line help and undo/redo. This paper discusses the pedagogical requirements of a digital logical simulation tool. It then describes JLS and, in particular, its features that address those requirements. Finally it compares JLS with other available tools.

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