Path Similarity Evaluation Using Bloom Filters The performance of several Internet applications often relies on the measurability of path similarity between different participants. In particular, the performance of content distribution networks mainly relies on the awareness of content sources topology information. It is commonly admitted nowadays that, in order to ensure either path redundancy or efficient content replication, topological similarities between sources is evaluated by exchanging raw traceroute data, and by a hop by hop comparison of the IP topology observed from the sources to the several hundred or thousands of destinations.In this paper, based on real data we collected, we advocate that path similarity comparisons between different Internet entities can be much simplified using lossy coding techniques, such as Bloom filters, to exchange compressed topology information. The technique we introduce to evaluate path similarity enforces both scalability and data confidentiality while maintaining a high level of accuracy. In addition, we demonstrate that our technique is scalable as it requires a small amount of active probing and is not targets dependent. Intuitively, the path similarity between two nodes is defined as the IP paths overlap when those two nodes infer their paths towards an arbitrary third one. Two nodes are considered as being similar if they observe a large portion of overlapping paths (or path segments) towards a set of destinations.. Path similarity is very useful for many Internet applications, ranging from efficient distributed systems deployment to content location selection. In the context of Content Distribution Networks, for instance, providers could use path similarity to achieve both optimal performance path selection and path redundancy insurance, the path selection being obtained through similarity, while redundancy by non similarity.. Similarity and non similarity might find also a suitable usage in the deployment of large-scale measurement infrastructure. In particular, in the context of the Internet topology discovery [1] based on traceroute [2] , it is important that monitors are well diversified in the network. An infrastructure such as the recently introduced Archipelago [3] or the Internet monitoring project grenouille.com [?] would benefit from similarity/non similarity when deploying a new monitor. Indeed, if two vantage points share a large path similarity, it is obvious that they will collect redundant data, making their contribution marginal. On the contrary, if two monitors are quite non similar, data collected should lead to a broader view of the network. In the same way, monitoring distributed systems from a set of vantage points can benefit from path similarity information in order to diversify monitoring locations [4, 7, 17, 18] .. Finally, as previously mentioned by Hu and Steenkiste, path similarity might be used in the context of available bandwidth estimation [5] . Indeed, if several monitors are similar, it is very likely they will share the same bottleneck, and as most of the end-hosts encounter bottleneck at the first or the last four hops [6] , it would be sufficient to collect bandwidth information from a single of these monitors.. Path similarity between monitors is evaluated based on actively collected data. A monitor probes a portion of the Internet, using traceroute, and sends the discovered topology to other monitors in the system for comparison. It should however be noted that current "raw" paths comparison for route similarity only achieve desirable accuracy, reliability and sensitivity properties at the expense of scalability and high overhead issues [7, 5] . In other words, several monitors that would like to compare mutual similarities may need to exchange a huge amount of "raw" traceroute data, which can prove to be very onerous in terms of overhead, and may lead to severe under performances of the network, especially when considering thousands of monitors, probing millions of IP destinations.. Further, exchanging "raw" traceroute data reveals most, if not all, of the network topology information of monitors, that are often controlled by Content Distribution Networks (CDN) [8, 9] . Such an information is of primary economic and security importance for CDNs. Encryption could of course help with such confidentiality issue, but it does not solve any of the scalability issues.. Such non scalable and cumbersome properties are then a compelling case for a lossy coding technique that would be used to exchange compressed data while maintaining both accuracy and confidentiality about path similarity.. In this paper, we propose to apply Bloom filters [10] for allowing monitors to exchange path information. A Bloom filter is a lossy summary technique based on a bit vector and a set of hash functions. While, Bloom filters have found numerous usages, particularly in networking due to their bandwidth saving capabilities [11, 12] , our approach uses them for encoding links discovered by a monitor during its probing (i.e., tracerouting) phase. The compressed path information is then exchanged between monitors and the bit vectors are compared by each monitor for evaluating its similarity with others. Scalability is achieved through the exchange of much lower amount of data, while confidentiality is maintained without encryption, as hop by hop information that would reveal networks topology is hashed by the Bloom filter. We provide methods for comparing two Bloom filters and infer, from this comparison, the similarity level between monitors.. Nevertheless, if a Bloom filter has the advantage of compressing the information, it comes with the drawback of triggering false positives. It would be a matter of concern if the bandwidth advantages of Bloom filters would be overcome by those false positives. A tradeoff must thus be found between compression, false positives, and similarity accuracy.. In this paper, we tackle also issues related to such tradeoffs. Based on real traceroutes we collected from PlanetLab monitors towards sets of thousands of destinations 1 , we examine the benefits of applying Bloom filters, and compare the efficiency of similarity results obtained by exchanging compact traceroute data. We first demonstrate that our Bloom filter-based approach allows one to reduce bandwidth consumption by more than, at least, four order of magnitude in terms of exchanged information, compared to traditional proposals quantifying path similarity. We also examine the effects of the Bloom filter parameters on the similarity results, showing that, as long as we consider a reasonable compression ratio, we provide accurate similarity results. We finally demonstrate that our approach is scalable, reducing so the risk of the probing phase from various monitors to turn out into a distributed denialof-service (DDoS) attack. Indeed, we show that our technique is independent from the number of traceroutes performed, as well as from the overlapping of destinations (i.e., monitors in the system do not necessarily require to traceroute exactly the same destinations).. The remainder of this paper is organized as follows: Sec. 2 provides the required background on Bloom filters and explains how they can be applied to study Internet paths similarity; Sec. 3 formally describes the similarity metrics we introduce in this paper; Sec. 4 evaluates our lossy similarity technique; Sec. 5 positions this paper regarding the state of the art; finally, Sec. 6 concludes this paper by summarizing its main contributions and discussing future directions. In Sec. 4.3, we evaluated the behavior of our metrics for comparing several large sets of information encoded as Bloom filters. Those sets were made of topological data (i.e., links between routers) collected through traceroute.. During our analysis, we mostly focused on two planes: Bloom filters and destination sensitivity. For both planes, we showed that the metrics rH(·, ·) and rH(·, ·) provide globally better performance results than B(·, ·). Table 4 aims at highlighting the main lessons learned from Sec. 4.3. Regarding the Bloom filter plane, the number of hash functions does not impact the accuracy. On the contrary, the bit vector size, m, has some influence. A too high compression ratio would lead to bad performance. For the destination plane, it is sufficient to probe between 100 and 250 destinations, while the overlap of destinations sets between monitors does not influence the performance accuracy.. Despite, on average, 85% of the paths were incomplete in our data set, all above observations indicate that the data set used in this paper can plausibly represent a rich cross-section of the whole situation on today's Internet, and thus allow us to quantify path similarity with high accuracy. In this paper, we presented a Bloom filter-based approach to measure and exchange Internet path similarity between monitors. Our solution aims at considerably decreasing the amount of data sent through the network and ensuring the secrecy of topology information, while maintaining a high level of confidence in the measurability of path similarity.. It is based on compacting traceroute data through the use of Bloom filters, exchange those Bloom filters, and then compute similarities or dissimilarities based on a set of metrics to compare each pair of monitors' Bloom filters. Our approach does not rely on destination overlapping, and as such is unaffected by the choice of the set of destinations that the monitors can probe. In fact, we have shown that for different percentages of destinations overlaps, and for even an acceptable low number of probed destinations, our metrics still provide very good performance, distinguishing clearly between similar monitors paths.. To the best of our knowledge, this is the first such general method capable of providing accurate results while maintaining a very low overhead in exchanging traceroute information. Optionally, our method allows one to hide the network topology from monitors to the set of destinations they are monitoring. Since hops are hashed through the Bloom filters, topological information is then hidden and immune from any malicious data sniffing activity. Encryption of raw data provides also efficient confidentiality for data, but does not resolve the problem of overhead.. In practice, we introduced a simple way to study path similarity between monitors through compacted traceroute information. We choose to illustrate this study through traceroute information, which is at the very core of any Internet topology. This leads us to believe that our proposed similarity detection approach can effectively identify similar monitors in very many CDNs monitors deployment without any major software change. However, the way to code "raw" information and the metrics introduced to compare Bloom filters are generic enough to allow for their application on very many other topology characteristics information needed to be exchanged. We could, for instance, include information describing available bandwidth estimation for paths, as complementary to traceroute paths, and encode such an information into Bloom filters. Again, the gain in terms of reduced overhead would allow an easier and more practical information exchange among monitors. Note that, despite we performed measurement in an IPv4 environment, our technique is independent of the used IP version. This means that in a world where IPv6 would be largely deployed, our technique would present stronger interest in term of compression.. The measurements collected in this paper were deliberately tested on monitors and destinations chosen at random in the real Internet, with a realistic high percentage of non complete traceroute, although their similarities or dissimilarities increase with traceroute paths fullness. Despite the possible non optimal similarity measurements resulting from such a choice, the results obtained show the effectiveness of our method in characterizing path similarity with very low overhead. Nevertheless, given the gain afforded by our approach, one can envisage that CDNs may readily want to deploy monitors within their network to offer enhanced services to their customers, and to select well suited set of controlled destinations inside the core network. Such business driven strategic deployment can only improve the measurability of our similarity metrics and thus improve the path similarity accuracy, with much higher similarity detection rates than the lower bound reported in this paper. We have also shown that the false positive rates are very low, promising not considering monitors to be similar while it is not actually the case. This feature can be exploited when deploying redundant backup content servers. In this case, we insure (with very high confidence) that the backup server, if solicited, will continue to serve customers under the same conditions than the previous server.. The schemes presented in this paper are generic and might be applied in any context in which large sets of information must be exchanged and compared. Future work should reveal the efficiency of our techniques under those contexts. We further aim at evaluating them in a geolocalisation context. In this section, we evaluate the performance of our three metrics for retrieving path similarity information from Bloom filters. We first discuss our methodology, in particular how we actively collected data (Sec. 4.1). We next describe the performance metrics we use throughout this evaluation (Sec. 4.2). Sec. 4.3 discusses the results while Sec. 4.4 provides a summary of the main achievements of this section. In this section, we discuss the relevance of using Bloom filters for compacting path similarity information as well as the accuracy of our metrics for retrieving path similarity information from Bloom filters. We first show the advantage of Bloom filters in terms of compression (Sec. 4.3.1) and, next, evaluate factors that can influence the accuracy of our metrics for detecting compact path similarity. These factors are: the Bloom filter parameters (Sec. 4.3.2), the proportion of destinations overlap (Sec. 4.3.3), and the number of destinations probed by monitors (Sec. 4.3.3). In order to avoid biased statistical study, as these factors are interdependent, the factor being studied changes and the remaining are fixed. For example, evaluation of Bloom filter parameters may ignore changes in the overlapping proportion. Since the late 90's, the topology discovery has been an extensive research field [1] . This research activity focused mostly on developing efficient traceroutelike tool or on modeling the Internet topology. Although there are many potential applications, the problem of path similarity does not appear to have been the subject of much study. Only a few work has been done on path similarity or diversity.. For instance, Teixeira et al. evaluate the IP-level path diversity between Points of Presence (PoPs), i.e., a collection of routers owned by an AS in a specific location (city or suburb). Based on real ISP dataset, Teixeira et al. found that all pairs of PoPs have, at least, two disjoint paths between them. However, Teixeira et al. do not discuss if this diversity might be observed at the Internet scale, neither how a given application might use this diversity.. Hu and Steenkiste propose a metric, RSIM, for evaluating end-to-end path similarity. This metric is based on the number of common links between two monitors. A specificity of RSIM is that it is a bi-directional metric, i.e., it provides the similarity between monitor A and B, but also between B and A. An application of RSIM is for scalable bandwidth estimation [15] . However, it is not explained how this similarity information might be exchanged between monitors. Pathak et al. use path similarity at the AS and router level for evaluating the asymmetry of delay in the Internet [16] . Roughly, they propose a metric somewhat equivalent to RSIM but without taking into account the bi-directionality of links.. Works has also been done on identifying relays for alternative paths in large scale networks to increase route diversity [17, 18] . Indeed, multipath routing has been proposed to better reduce maximum load on nodes and congestion. The use of alternatives paths improves the quality of service of communications across the Internet. For instance, Agapi et al. seek to find good relay nodes by using path similarity-based synthetic coordinates [18] . The key idea is based on the assumption that if a relay is suitable for a given path, it is also likely to be good for other similar paths. They define path similarity between paths P 1 and P 2 as the probability that a relay that is good for P 1 is also good for P 2 . Note that a set of relay could be exchanged between nodes using Bloom filters. This has not been investigated by Agapi et al.. Bloom filters have been extensively studied, particularly in networking due to their capacities in bandwidth savings when membership information must be exchanged between monitors [11] . Recent works used Bloom filters for exchanging topology information between traceroute-like monitors [19,?] . However, authors do not investigate how these Bloom filters might be used to evaluate path similarity. For the purpose of our studies in this paper, we collected data using traceroute from 30 PlanetLab machines towards sets of 1,000 destinations. The measurement campaign was done between March 31 st , 2009 and April 5 th , 2009. All these experiments were run concurrently so as to experience the same network conditions. We used the native PlanetLab traceroute. Our dataset is freely available 2 . Regarding the geographical situation of PlanetLab monitors used during the probing phase, Europe was the most represented continent, with 25 monitors, followed by America (four monitors in the United States), and Asia (a single monitor in China).. The traceroute destinations were randomly selected within the Archipelago set of 3,000,000 destinations [3] . Archipelago is skitter' successor and has been deployed since September 2007. Destinations in Archipelago are selected from all routed /24's. As we will be, in the following, interested in the impact of overlapping destinations, i.e., monitors in the system share entirely the same set of destinations or a given proportion of destinations in their set of targets, we defined nine different destinations sets.. From our dataset, we removed one monitor, located in Europe (Italy), as it was unable to perform correctly the traceroutes: it stopped discovering interfaces after the second hop. Note that, for the rest of the monitors, on average, 85% of the paths were incomplete, i.e., did not terminate at the destination.. When tracerouting, some routers along the path might reply with invalid address, typically because of mis-configuration, or might not respond to probes. For our study, we chose to remove links containing at least one invalid address and links containing at least one non responding node. The addresses that we consider as invalid are a subset of the special-use IPv4 addresses described in RFC 3330 [13] . Specifically, we eliminate visits to the private IP address blocks 10.0.0./8, 172.16.0.0/12, and 192.168.0.0/16. We also remove the loopback address block 127.0.0.0/8. On average, 15% of links discovered by a monitor were categorized as invalid.. Regarding Bloom filters, the hashing was emulated with random numbers. We simulated randomness with the Mersenne Twister MT19937 pseudo-random number generator [14] .

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A novel hybrid intelligent system for multi-objective machine parameter optimization Abstract This multidisciplinary research presents a novel hybrid intelligent system to perform a multi-objective industrial parameter optimization process. The intelligent system is based on the application of evolutionary and neural computation in conjunction with identification systems, which makes it possible to optimize the implementation conditions in the manufacturing process of high precision parts, including finishing precision, while saving time, financial costs and/or energy. Empirical verification of the proposed hybrid intelligent system is performed in a real industrial domain, where a case study is defined and analyzed. The experiments are carried out based on real dental milling processes using a high precision machining centre with five axes, requiring high finishing precision of measures in micrometers with a large number of process factors to analyze. The results of the experiments which validate the performance of the proposed approach are presented in this study. Intelligent systems have been widely used for industrial process modelling. Recently, different paradigms of artificial intelligence have been applied to different industrial problems [1] [2] [3] .. System identification [4] [5] [6] has made it possible to model, simulate and predict the behavior of many industrial applications successfully and in different areas, such as control, robotics [7] , energy processes [8] , milling machine [9] , high precision [1] , power system security [10] , etc. A novel and economically advantageous application is the optimization process in the field of Medical Therapeutics (Odonto-Stomatology), a booming industry [9, [11] [12] [13] .. Prosthetic restorations must have a high marginal fit [14] . A bad marginal fit [15] affects fracture resistance and reduces the longevity of the restoration, resulting in higher risk of recurrent carious lesions and periodontal disease, as well as the dissolution of the cement [16] which allows entry of fluid and microorganisms between the tooth and the restoration, causing discoloration, pulpal irritation, secondary carious lesions and treatment failure [17] .. Disturbances or marginal discrepancies between 50 and 120 micrometers are considered clinically acceptable in relation to the longevity of the restorations [18, 19] .. Improved processing and optimization of parameters, such as processing time, temperature, accuracy, etc., for the development of pieces (such as dental-oral prostheses for partial crowns, inlays, onlays, etc., with application for rehabilitation and oral-dental restoration) are the focus of rigorous studies today [9] . The optimization process of machine parameters, such as the time parameter [20] , permits significant economic savings due to the high number of dental pieces produced daily by the same high precision dental milling machine centre. Another important factor in the milling process is the temperature of the tools, which can be expanded or fractured by an inappropriate feed rate or by the heating of the coolant. Maintaining a constant temperature during the manufacturing process will make it possible to produce dental pieces with suitable quality. This could significantly help to increase a company's efficiency, and substantially contribute to cost reductions in the preparation and setting of the machines processes.. One way to achieve this optimization is based on the hybridization [9, [21] [22] [23] [24] [25] of emerging and active techniques, such as neural [5, 25] and evolutionary computation [26, 27] , nature-inspired smart systems [28] , data mining and decision support systems [29] , information fusion [30] , ensemble models, visualization techniques [31] , cognitive and reactive distributed AI systems [32] , case-based reasoning [33] , among others.. This study is organized as follows. Section 2 describes hybrid intelligent systems. Section 3 introduces the unsupervised neural models applied for analyzing the data sets. Section 4 presents the system identification techniques used in the system modelling. Section 5 introduces the applied multi-objective genetic algorithm. Section 6 presents the hybrid intelligent system for the optimization of the process. Section 7 describes the industrial case study, a real dental milling process. The final section presents the different models that are used to solve the high precision dental milling optimization case study. At the end, the conclusions are set out and some comments on future research lines are presented. The novel hybrid intelligent system with a multi-objective optimization process described in this research can be successfully used to optimize machine parameters for industrial processes, based on the obtained results. The optimization process may increase a company's efficiency and substantially reduces the cost of preparing and setting machine processes. We have used this method for multi-objective optimization and adjustments during the manufacturing process of dental pieces, such as implants according to medical specifications for precise moldings.. The method proposed is based on the selection of the most important features in an initial step. ANNs are then trained for modelling the features and these can, thus, be used as two fitness functions in the multi-objective optimization. Finally, a NGSA-II and MOSA try to achieve the best conditions for manufacturing from the model. The data set collected in this real dental milling process presents an important manufacturing time error rate of about 26.8 %. This is due to the difference between the estimated time of the machine itself and the real production time. The obtained model is capable of modelling more than 82 % of the actual measurements in relation to the time error (modelling more than 96.1 % of real time work). This helps to reduce the error and the variability rate of manufacturing processes down to 4 %, compared to the initial 26.8 %, which is an acceptable error rate in planning work for dental milling. In addition, the difference of temperature between the beginning and the end of the dental manufacturing process has an increase of about 10.2 %. The obtained model is capable of modelling more than 99 % of the actual measurements in relation to the difference of temperature (modelling more than 99 % of real final temperature work).. The multi-objective optimization is able to find the best values for the feed rate X and Y from some fixed parameters, such as normal conditions of manufacturing and the multi-objective minimization of time errors, and the difference of temperature. Although, both the MOSA and the NSGA-II are valid to learn the models, the best resultsconsidering the 10 runs-are obtained in less time with NSGA-II; i.e., the solution can be obtained with less computational cost. Therefore, the milling process will be able to minimize the time errors and the difference of temperature to a value as close to zero as possible. Future lines of research will investigate the selection of the most suitable features using a wrapper feature selection method, in which Genetic Algorithms and ANNs are hybridized. Finally, an algorithm will be developed to automatically identify the best operating conditions: minor time errors for the manufacturing of dental pieces and minor differences of temperature. Moreover, the resulting model would be applied to different metals used in prosthetic dentistry and in other industrial processes, such as the automotive sector.. Castilla y León]. The authors would also like to thank to ESTUDIO PREVIO (Madrid-Spain) for its collaboration in this research. This multidisciplinary research initially analyzed the data set to obtain the variables/characteristics that are most closely related to manufacturing time errors and difference of temperature in the machine.. In the first step, several unsupervised models were applied for the sake of comparison. In this case, neural versions of PCA and CMLHL were applied as powerful techniques for identifying internal data set structures. In order to analyze the two main parameters to be estimated (the time error for manufacturing and the difference of temperature in the machine) the initial data set was divided into two data sets: one with the time error and another with the difference of temperature.. The axes forming the projections (Figs. 3a, b, 4a , b) represent combinations of the variables contained in the original data sets. In the case of PCA, the model is looking for those directions with the biggest variance, while CMLHL is looking for the kurtosis (directions which are as little Gaussian as possible) [38, 42] .. In relation to time error, (see Fig. 3 ), both methods, PCA (Fig. 3a) and CMLHL (Fig. 3b) , are able to find a clear internal structure in the data set by identifying several clusters (see Tables 2, 3 ). Both methods also identified feed rate X and Y as relevant variables. It is clear that CMLHL provides a sparser representation than PCA, and that CMLHL projections provide more clear information identifying parameters, such as type of work and time error as other important variables.. An analysis of the results obtained with the CMLHL model (Fig. 3b) leads to the conclusion that this method has identified several different clusters ordered by feed rate X and Y and the type of work. Inside each cluster, there are further classifications by 'time error' and the data set can be said to have an interesting internal structure based on the clusters identified.. In relation to the difference of temperature, (see Fig. 4 ), both methods, PCA (Fig. 4a) and CMLHL (Fig. 4b) , found a clear internal structure in the data set by identifying several clusters (see Tables 4, 5 ). It is clear that CMLHL provides a sparser representation than that obtained by PCA, and that CMLHL projections provide more clear information identifying parameters, such as the type of work, feed rate X and Y, initial temperature and difference of temperature as important variables.. An analysis of the results obtained with the CMLHL model (Fig. 4b) leads to the conclusion that this method has identified several different clusters ordered by the and 'initial temperature' and the data set can be said to have an interesting internal structure based on the clusters identified.. When the data set is considered sufficiently informative, as in this case, the next step is to model the relationship between inputs and production time errors, and between inputs and the difference of temperature in the process, which is accomplished by applying several artificial neural network modelling systems.. Two multilayer perceptron networks (MLP) (feedforward network) were used to monitor time error and the difference of temperature in the manufacturing of dental pieces. The data set is pre-processed from the input and output normalization step, and the reduction of the input vectors dimension (the data set gathered in the previous step). The MLP is trained from the most widely used training algorithms, such as the Levenberg-Marquardt algorithm [54] , quasi-Newton methods [55] , resilient backpropagation algorithm [56] , and escalated conjugate gradient algorithm [57] , using the criteria of normal stopping, early stopping, and Bayesian regularization techniques [58] .. The features for the two best MLPs proposed and its indexes are stated below: The feedforward network-called f 1 -to predict the time error has 30 hyperbolic tangent units (layer 1), 25 hidden hyperbolic tangent units (layer 2), 25 hidden hyperbolic tangent units (layer 3), 4 hidden hyperbolic tangent units (layer 4), and 1 linear output unit. The parameters in the network were estimated using the Levenberg-Marquardt algorithm with normal stopping criterion. Normalizing the minimum and maximum values of data set to [- 1 1] .. The feedforward network-called f 2 -to predict the difference of temperature has 30 hyperbolic tangent units (layer 1), 20 hidden hyperbolic tangent units (layer 2), 5 hidden hyperbolic tangent units (layer 3), and 1 linear output unit. The parameters in the network were estimated using the Levenberg-Marquardt algorithm with Bayesian regularized criterion. Normalizing the data set to media null and variance 1. These models (f 1 and f 2 ) do not only present the lowest V (0.001 and 5.25E-5) and NSSE (0.013 and 0.12E-3), but also a higher system representation index value FIT1 (82.45 and 99.87 %) and a small k(0.1E-4 and 1.32E-9). From these indicators, it may be concluded that the ANNs selected are able to simulate and predict the behavior of time errors and the difference of temperature for manufacturing dental pieces (as a consequence of the production process). The models of time error (f 1 ) and difference of temperature (f 2 ) obtained may be used as two fitness functions in the next step to determine the best operating conditions for the dental milling processes, i.e., to choose the values of feed rate X and feed rate Y with the least possible time error and the least change of temperature in the process. Table 6 and in the boxplot of Fig. 6 . In Table 6 , the 11 experiments are compared for the best individual error found and for the individual closest to the origin. Although some differences have been found, both the MOSA and the NSGA-II are valid to learn the models. Nevertheless, the NSGA-II presents a worst behavior in the MSE of time error in some experiments.. Besides, in Fig. 7 is depicted one of the multi-optimization experiments accomplished and shown in the Table 6 , concretely the experiment number five. The X-axis shows the feed rate X (mm per min) and the Y-axis represents feed rate Y (mm per min), for from 0 to 3,000. The features fixed are 29°C for initial temperature and 900 s for estimated work time. In Fig. 7a , the Z-axis represents the output variable range (time error) from -3,000 to 1,000 s. This value is also shown on the vertical bar. In Fig. 7c , the Z-axis represents the output variable range (difference of temperature) from -8 to 4°C. The difference in temperature is also shown on the vertical bar. Figure 7b , d presents the final value got for the feed rate X and Y with a value close to zero in the two outputs optimized (the black point in the interior of circle).

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


Spatiotemporal correspondence as a metric for human-like robot motion Coupled degrees-of-freedom exhibit correspondence, in that their trajectories influence each other. In this paper we add evidence to the hypothesis that spatiotemporal correspondence (STC) of distributed actuators is a component of human-like motion. We demonstrate a method for making robot motion more human-like, by optimizing with respect to a nonlinear STC metric. Quantitative evaluation of STC between coordinated robot motion, human motion capture data, and retargeted human motion capture data projected onto an anthropomorphic robot suggests that coordinating robot motion with respect to the STC metric makes the motion more human-like. A user study based on mimicking shows that STC-optimized motion is (1) more often recognized as a common human motion, (2) more accurately identified as the originally intended motion, and (3) mimicked more accurately than a non-optimized version. We conclude that coordinating robot motion with respect to the STC metric makes the motion more human-like. Finally, we present and discuss data on potential reasons why coordinating motion increases recognition and ability to mimic. When social robots interact with humans by communicating in a manner that is socially relevant and familiar 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. HRI '11, March 6-9, 2011 , Lausanne, Switzerland. Copyright 2011 ACM 978-1-4503-0561-7/11/03 ...$10.00.. to their human partners, the benefits are increased transparency; improved teammate synchronization; and reduced training cost for collaborative robots due to increased "userfriendliness." This has been called "natural human-robot interaction," and requires believable behavior to establish appropriate social expectations [6] . Furthermore, display of appropriate non-verbal communication behavior increases perception of agent realism [4] . Our work addresses this overall problem of how to generate believable or human-like motion for an anthropomorphic robot.. We hypothesize that spatiotemporal correspondence (STC) of distributed actuators (i.e. motor coordination) is a component of human-like motion. We present motion optimized with respect to a nonlinear STC metric based on KolmogorovSinai entropy as both a synthesis and evaluation tool, and validate our results using a user study based on mimicking. The results show that STC-optimized motion is (1) more often recognized as a common human motion, (2) more accurately identified as the originally intended motion, and (3) mimicked more accurately than an unmodified version of human motion retargeted to the robot. We conclude that coordinating robot motion with respect to the STC metric makes it more human-like. Finally, we present and discuss potential reasons why coordinating motion increases recognition and the human ability to mimic. In the experiment, participants are shown a video of a motion and then asked to mimic it. The OR and OC motion trajectories were videotaped on the Simon hardware from multiple angles for the study. Similarly, the original human motion was visualized on a simplified virtual human character ( Fig. 1(a) ); also recorded from multiple angles.. Forty-one participants (17 women and 24 men), ranging in ages from 20-26 were recruited for the study. Each participant saw a set of twelve motions from the possible set of twenty, randomly selected for each participant in such a way that each participant received four OH, four OR, and four OC motions each. This provided us with a set of 492 mimicked motions total (i.e. 164 motions from each of three groups, with 8-9 mimicked examples for each of 20 motions). We have demonstrated a metric that can be used to synthesize and evaluate motion. If the goal of anthropomorphic robots is to communicate with humans as humans communicate with each other, then robot motion can be improved with this metric to create more human-like motion.. We presented spatial and temporal correspondence (i.e motor coordination) as an quantitative metric for humanlike motion. We also presented objective and subjective data to support our claims that motion optimized with respect to STC is more human-like and easier to recognize, and therefore has benefits for human-robot interaction. Our metric is useful as both a tool for human-like motion synthesis for anthropomorphic robots and as a measurement instrument for the evaluation of human-like motion. The spatiotemporal correspondence problem has already been heavily studied and analyzed mathematically for a pair of trajectory sets, where there is a one-to-one correspondence between trajectories in each set (e.g. two human bodies, both of which have completely defined and completely identical kinematic hierarchies and dynamic properties) [7, 10] . Given two trajectories x(t) and y(t), correspondence entails determining the combination of sets of spatial (a(t)) and temporal (b(t)) shifts that map two trajectories onto each other. In the absence of constraints, the temporal and spatial shifts satisfy the equations in 1, where reference trajectory x(t) is being mapped onto y(t).. where, ( ) = first reference trajectory ( ) = second reference or output trajectory ( ) = set of time-dependent spatial shifts ( ) = set of time-dependent temporal shifts = time ′ = temporally shifted time variable. The correspondence problem is ill-posed, meaning that the set of spatial and temporal shifts is not unique. Therefore, a metric is often used to define a unique set of shifts.. Spatial-only metrics, which constitute the majority of "distance" metrics, are insufficient when data includes spatial and temporal relationships. Spatiotemporal-Isomap (STIsomap) is a common algorithm that takes advantage of STC in data to reduce dimensionality. However, the geodesic distance-based algorithm at the core of ST-Isomap was not selected as the candidate metric due to manual tuning of thresholds and operator input required to cleanly establish correspondence [9] . Another critical requirement for a metric is nonlinearity, since human motion data is nonlinear.. Prokopenko et. al. used 2 as a metric for STC for modular reconfigurable robots to identify optimal configurations that overcome environmental constraints on motion [17, 16] . We take advantage of their temporally extended version of the 2 metric, which is nonlinear and an upper bound of Kolmogorov-Sinai entropy (KSE). In short, KSE describes rate of system state information loss as a function of time. Therefore, a lower value of 2 is more optimal, since it indicates higher retention of system state information over time.

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


Building Roadmaps of Minima and Transitions in Visual Models Abstract. Becoming trapped in suboptimal local minima is a perennial problem when optimizing visual models, particularly in applications like monocular human body tracking where complicated parametric models are repeatedly fitted to ambiguous image measurements. We show that trapping can be significantly reduced by building 'roadmaps' of nearby minima linked by transition pathways-paths leading over low 'mountain passes' in the cost surface-found by locating the transition state (codimension-1 saddle point) at the top of the pass and then sliding downhill to the next minimum. We present two families of transition-state-finding algorithms based on local optimization. In eigenvector tracking, unconstrained Newton minimization is modified to climb uphill towards a transition state, while in hypersurface sweeping, a moving hypersurface is swept through the space and moving local minima within it are tracked using a constrained Newton method. These widely applicable numerical methods, which appear not to be known in vision and optimization, generalize methods from computational chemistry where finding transition states is critical for predicting reaction parameters. Experiments on the challenging problem of estimating 3D human pose from monocular images show that our algorithms find nearby transition states and minima very efficiently, but also underline the disturbingly large numbers of minima that can exist in this and similar model based vision problems. Many visual modeling problems can be reduced to cost minimization in a high dimensional parameter space. Local minimization is usually feasible, but practical cost functions often have large numbers of local minima and it can be very difficult to ensure that the desired one is found. Exhaustive search is seldom feasible in more than about 2-3 dimensions, so global optimizers are typically built around heuristics for finding 'good places to look next'. This includes both deterministic methods like branch-and-bound and pattern search, and stochastic importance samplers like simulated annealing (Kirkpatrick et al., 1983) , genetic algorithms and tabu search (Glover, 1990) .. Unfortunately, global optimization remains expensive with any of these methods. In this paper we develop an alternative strategy based on building 1-D 'roadmaps' linking the salient nearby minima. Each local minimum has a basin of attraction within which local optimization converges to it. Roughly speaking, our strategy is to start from a given minimum and to search for low lying 'mountain passes' that lead away from its basin of attraction, finding the new minima they lead to by sliding downhill using local optimization. The procedure is repeated recursively to build up a roadmap linking the neighboring minima. More precisely, any minimum-peak-cost path connecting two minima passes through a special state at its highest point, at which the path crosses the brow of the pass and begins to descend. Such "transition states" are saddle points (the gradient of the cost function vanishes there) at which the cost has a local maximum in the direction of the path and a local minimum in all orthogonal directions. Technically, transition states are "codimension 1" saddle points-ones with one negative and (in n dimensions) n − 1 positive principal curvatures (Hessian eigenvalues). At the heart of our approach are two families of efficient numerical methods for locating the transition states surrounding a given local minimum (see, for instance Fig. 4 ).. Although there are many algorithms for finding local minima, it seems that finding transition states has generally been considered to be intractable, and we know of little previous work in the vision or optimization communities on methods for this. However such methods do exist in the computational chemistry/solid state physics community, where transition states are central to the theory of chemical reactions.. 1 Both of our classes of transition-state-locating algorithms have roots in chemistry, and both are based on modified forms of local Newton minimization. Eigenvector tracking redefines a standard damped Newton minimization to converge uphill to a saddle point of the desired signature, while hypersurface sweeping sweeps a moving hypersurface through the space, using a constrained Sequential Quadratic Programming like iteration to track moving local minima within it. These methods should be useful in many visual modeling problems where local minima cause difficulties. Examples include model based tracking, reconstruction under correspondence ambiguities, and various classes of camera pose and calibration problems. In this paper, we present experimental results on monocular model based human pose estimation.. Contents: Section 2 describes our motivation and overall strategy. Section 3 discusses related trajectory methods in computational chemistry and global optimization. Section 4 introduces damped Newton methods for locating transition states, and discusses their relation to local minimization algorithms. Sections 5 and 6 detail our Eigenvector Tracking and Hypersurface Sweeping algorithms. Section 7 illustrates the methods on a 2D toy problem. Section 8 presents our main experiments on locating minima during monocular reconstruction and tracking of 3D human body pose. Section 9 concludes the paper and discusses possible directions for future research.

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


Evaluating the dynamic properties of recommendation algorithms Collaborative recommendation algorithms are typically evaluated on a static matrix of user rating data. However, when users experience a recommender system, it is dynamic, constantly evolving as new items and new users arrive. The dynamic properties of collaborative recommendation have become important as prediction algorithms based on the interactions of rating histories have been proposed, and as researchers seek to understand problems of robustness and maintenance in rating databases. This paper proposes a new evaluation method for the dynamic aspects of collaborative algorithms, the "temporal leave-one-out" approach, which can provide insight into both user-specific and system-level evolution of recommendation behavior. As a case study, the methodology is applied to the Influence Limiter algorithm [12] , showing that its robustness to attack comes at a high accuracy cost. Collaborative recommender systems are essential tools for web personalization and e-commerce, and they can be found throughout the information ecology from the World-Wide Web to mobile environments and consumer devices [13] . The user experience of a recommender system is inherently dynamic. New items arrive constantly, possibly triggering waves of user activity, as in a popular new movie. In a thriving recommender system, new users are also adding themselves to the mix, uploading new opinions that may reshape the peer neighborhoods on which recommendations rest. In Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. addition, there is a strongly mixed-initiative flavor to the interplay between ratings users provide and the recommendations systems give. A user will be more likely to experience and thus rate an item that the system has recommended [2] .. However, the dynamic properties of recommender systems have received scant notice in the research literature and are poorly captured by the evaluation methodologies typical of research practice. The standard research methodology coalesces the rating stream into a ratings matrix, which is further decomposed into training and test sets, and algorithmic performance in this static environment has become the gold standard for collaborative recommendation algorithms [4] . Even researchers who are making use of temporal aspects of the rating database [5, 7] are not evaluating the properties of their algorithms over time.. Researchers interested in "cold-start" phenomena, such as [11, 14] , approach the problem by selecting some users or items with shorter profiles and looking at system performance on this subset, or by artificially degrading profiles by eliminating ratings. Applying accuracy or ranking metrics then gives a picture of the performance of the system on some users or items with sparse histories, but it does not give an overview of how performance changes over the history of a user and, depending on how ratings are eliminated, may not give a valid picture of the evolution of an algorithm's performance in the wild.. Two exceptions are evident. One is the "scouts, promoters, and connectors" work by Mohan, Keller and Ramakrishnan [9] that examines the roles that ratings play over time in a graph-based model of recommendation. Another example can be found in the recent work of Lathia, Hailes and Capra [6] in which a variant of kNN with adaptive neighborhoods is proposed. Such an algorithm can only be evaluated in a dynamic manner, and Lathia et al. use a more coarse-grained version of the technique proposed here.. The limitations of the static methodology have come to the fore in work on recommender systems robustness. In particular, some researchers have proposed maintenance processes for ratings databases, in which the collection of user profiles is periodically swept for evidence of attackers [1] . Others have proposed dynamic algorithms based on the evolution and propagation of trust relationships. In particular, the Influence Limiter algorithm of Resnick and Sami [12] is a collaborative technique with provable limits on the amount of power that a potential attacker can exert to influence others. Researchers have been accustomed to a static view of collaborative recommender systems, a by-product of evaluation methodologies that use a static rating matrix as their starting point. However, recent research has resulted in the development of algorithms that cannot be evaluated in this static way, but depend rather on the dynamic properties of the rating database. This paper has put forward an evaluation methodology suited to the exploration of the temporal aspects of collaborative recommendation. Application of this methodology reveals phenomena not previously observed in the well-known MovieLens data set, in particular the diminishing returns to a user for adding ratings. In addition, this work has enabled the evaluation of the Influence Limiter algorithm, demonstrating that its robustness to attack comes at a severe cost to prediction accuracy and showing that its requirement of consistency in neighbors is too strict.. This work represents an initial foray into the application of these ideas and as such leaves many questions unanswered. There are of course many proposed algorithms for collaborative recommendation and while some have been extensively evaluated statically, their dynamic properties are largely unknown. In this preliminary study, the temporal leave-one-out technique is applied to two algorithms: the well-studied user-based collaborative filtering technique [3] and the Influence Limiter algorithm [12] proposed by Resnick and Sahmi. The version of the user-based algorithm here uses a co-rate weighting of 50, a neighborhood size of 20 and a similarity threshold of 0.0. 1 Of course, the number of users at each size k is different since not all profiles are of the same length, a fact which must be taken into account in analyzing the results.

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


The Complexity of Boolean Functions in Different Characteristics Abstract. Every Boolean function on n variables can be expressed as a unique multivariate polynomial modulo p for every prime p. In this work, we study how the degree of a function in one characteristic affects its complexity in other characteristics. We establish the following general principle: functions with low degree modulo p must have high complexity in every other characteristic q. More precisely, we show the following results about Boolean functions f : {0, 1} n → {0, 1} which depend on all n variables, and distinct primes p, q:• If f has degree o(log n) modulo p, then it must have degree Ω(n 1−o(1) ) modulo q. Thus a Boolean function has degree o(log n) in at most one characteristic. This result is essentially tight as there exist functions that have degree log n in every characteristic.• If f has degree d = o(log n) modulo p, then it cannot be computed correctly on more than 1 − p −O(d) fraction of the hypercube by polynomials of degree n 1 2 − modulo q. As a corollary of the above results it follows that if f has degree o(log n) modulo p, then it requires super-polynomial size AC 0 [q] circuits. This gives a lower bound for a broad and natural class of functions.

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Combining UCT and Nested Monte Carlo Search for Single-Player General Game Playing Abstract-Monte G ENERAL GAME PLAYING (GGP) tries to address the shortcomings of current specialized game playing programs that cannot adapt to other domains than the game they were programmed for. The goal is to find general algorithms for games, or to automatically classify games according to the algorithms that play them well. In GGP, the programs are required to have more general intelligence than game-specific programs.. Programs play games that they have never seen before. They are given the rules of a game, and after an initial autonomous analysis performed in a predefined time, they play the game. A specificity of GGP is that programs are given the rules of the game explicitly, in the game description language (GDL), hence they can analyze and manipulate these rules.. GGP addresses single-player, two-player, and multiplayer games with simultaneous or turn taking moves. Games may be zero sum or not. GGP does not currently address incomplete information games and infinite games. The Stanford Logic Group organizes an annual GGP competition between GGP players at the AAAI Conference on Artificial Intelligence.. In this paper, we focus on Monte Carlo tree search (MCTS) algorithms. The basis of MCTS is to play random games called playouts. Using the results of the previous playouts in order to improve the future playouts was shown by Coulom to be very efficient in the game of Go [10] . A simple and related algorithm named upper confidence bounds for trees (UCT) was published the same year [16] and is now widely used as a basis for MCTS algorithms, even though some of the best programs do not use the UCT formula anymore [6] , [7] , [17] . Improvements on the basic UCT algorithm came from learning patterns to direct the search and to bias the playouts [11] and from biasing the choice of moves in the tree with statistics on the results of the previous playouts where a move was played [13] . Building on these successes in two-player games, MCTS algorithm was also recently used in single-player games [4] , [5] , [20] . In single-player GGP, other approaches such as answer set programming are also possible [22] . In this paper, we address single-player GGP. Section II is about the GDL. Section III deals with UCT. Section IV deals with nested Monte Carlo (NMC) search. Section V details the structure of Ary. Section VI details experimental results. We have compared four different algorithms for 20 single-player games of the previous GGP competitions: UCT-T, UCT+T, NMC search, and a simple combination of UCT+T and NMC search (MAX).. On these games, UCT+T always gets better or equivalent results to UCT-T.. UCT+T works better in some games than NMC while it is the contrary in other games. On average, NMC works slightly better.. The evolution of the scores of UCT+T and NMC with time is shown to be problem dependent. On some problems, one algorithm is always better than the other, while on the other problems, one algorithm starts worse and gets better than the other within a longer period of time.. MAX gets the performances of both algorithms by taking at each step the move with the best independent evaluation.. We combined UCT+T and NMC in the most simple way, spending equal time for both algorithms. It could also be interesting to use different ratios of the time spent for UCT+T and NMC, for example, 30% for UCT+T and 70% for NMC, or other ratios.

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


Multimodal authentication based on random projections and source coding In this paper, we consider an authentication framework for independent modalities based on binary hypothesis testing using source coding jointly with the random projections. The source coding ensures the multimodal signals reconstruction at the decoder based on the authentication data. The random projections are used to cope with the security, privacy, robustness and complexity issues. Finally, the authentication performance is investigated for both direct and random projections domains. The asymptotic performance approximation is derived and compared with the exact solutions. The impact of modality fusion on the authentication system performance is demonstrated. Recently, reproduction technologies have performed an impressive evolution allowing to reproduce not only two-dimensional (2D) graphics but also three-dimensional (3D) relief structures, synthesize voice, images, 3D shapes and even recreate human facial expressions. Besides the obvious advantages, these tools offer at the same time unprecedent possibilities for the people targeting illegal actions ranging from the gaining access to various services, facilities and infrastructures to the counterfeiting of legal documents, certificates, IDs or even physical items such as luxury goods, art objects etc.. 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. The classical protection mechanisms are based either on proprietary techniques (material science), which use added features that are either rare in nature or difficult to clone, or shared secret (password, pin, key) or accompanying ID documents that all together do not completely satisfy the requirements to the reliability and security. The proprietary technology secrets are often relatively quickly become outdated due to the technological development, can be disclosed, guessed, reversely engineered or maliciously intercepted in various protocols while the ID documents can be stolen, lost or sometimes relatively easily faked. The attempts to apply classical crypto-based techniques to the protection of humans and physical items fail due to the inherently noisy nature of measurements. In this paper, we have investigated the impact of additional modality presence on the authentication performance in terms of ROC and average probability of error. To avoid the information loss, the authentication setup was based on the raw data fusion. Even in the case of statistically independent modalities belonging to the same object, we observed the reduction of the corresponding error probabilities computed according to the exact formulas for the Gaussian assumptions and generic error exponent bounds for any distributions. In the same line, we also investigated the impact of dimensionality reduction performed using random orthoprojectors and proposed the corresponding approximations using the Jonhnson-Lindenstrauss lemma. It was established that the orthoprojectors reduce the vector and distribution distances proportionally to the ratio of the vector lengths after and before projection. These findings might be of interest for the design of practical authentication systems. In future, we plan to consider the security of the presented setup and study possible attacks.

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


On the Weight Distribution of Terminated Convolutional Codes Abstract-In this correspondence, the low-weight terms of the weight distribution of the block code obtained by terminating a convolutional code after x information blocks are expressed as a function of x. It is shown that this function is linear in x for codes with noncatastrophic encoders, but quadratic in x for codes with catastrophic encoders. These results are useful to explain the poor performance of convolutional codes with a catastrophic encoder at low-to-medium signal-to-noise ratios. Any binary rate k=n convolutional code with constraint length L (or memory order L 01) whose associated trellis diagram terminates with a zero tail after encoding x blocks of k information bits into x blocks of n transmitted symbols generates an (n(x + L 0 1); kx) binary block code. In this correspondence, for each such (n(x + L 0 function is linear in x for codes with noncatastrophic encoders, but quadratic in x for codes with catastrophic encoders. This fact helps to explain why convolutional codes generated by a catastrophic encoder perform poorly. These results can be viewed as a simpler method than the one derived in [1] to obtain the low-weight terms of the weight distribution of a zero-tail terminated convolutional code. These results are also useful in deriving a good approximation of the union upper bound on the bit error probability for maximum-likelihood decoding (MLD) of convolutional codes with a noncatastrophic encoder by applying standard bounding techniques for block codes. Finally, since the weight distribution of a block code is independent of the mapping between information bits and codewords, these results are valid for terminated convolutional codes with encoder realizations in feedforward as well as in feedback forms. In this correspondence, the union bounding techniques for error control codes with limited interleaving over block fading Rician channels were considered. The traditional union bounding technique, which sums averaged pairwise error probabilities, was shown to yield very loose results especially for low Rician factors (a block fading Rayleigh channel). A modified union bounding technique was presented which limits the conditional union bound before averaging over the fading process and thus avoids the "explosion" of the union bound for low SNR. This modified bounding technique provides much tighter, and hence useful, numerical results, but requires L-fold numerical integration where L is the number of diversity subchannels. Examples were shown for terminated convolutional codes but the necessity for optimization before averaging in the block fading channels can be extended to other block codes as well. This was also clearly shown for random coding techniques in [5] .

O O B I 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 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 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 B I O O O O O 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 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 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


Local search with edge weighting and configuration checking heuristics for minimum vertex cover The Minimum Vertex Cover (MVC) problem is a well-known combinatorial optimization problem of great importance in theory and applications. In recent years, local search has been shown to be an effective and promising approach to solve hard problems, such as MVC. In this paper, we introduce two new local search algorithms for MVC, called EWLS (Edge Weighting Local Search) and EWCC (Edge Weighting Configuration Checking). The first algorithm EWLS is an iterated local search algorithm that works with a partial vertex cover, and utilizes an edge weighting scheme which updates edge weights when getting stuck in local optima. Nevertheless, EWLS has an instance-dependent parameter. Further, we propose a strategy called Configuration Checking for handling the cycling problem in local search. This is used in designing a more efficient algorithm that has no instance-dependent parameters, which is referred to as EWCC. Unlike previous vertex-based heuristics, the configuration checking strategy considers the induced subgraph configurations when selecting a vertex to add into the current candidate solution. A detailed experimental study is carried out using the well-known DIMACS and BHOSLIB benchmarks. The experimental results conclude that EWLS and EWCC are largely competitive on DIMACS benchmarks, where they outperform other current best heuristic algorithms on most hard instances, and dominate on the hard random BHOSLIB benchmarks. Moreover, EWCC makes a significant improvement over EWLS, while both EWLS and EWCC set a new record on a twenty-year challenge instance. Further, EWCC performs quite well even on structured instances in comparison to the best exact algorithm we know. We also study the run-time behavior of EWLS and EWCC which shows interesting properties of both algorithms. In this paper, we studied stochastic local search approaches to a challenging problem in graph theory that has a wide range of applications in AI and computer science. We have proposed two novel search strategies EW (Edge Weighting) and CC (Configuration Checking) to address the well known NP-hard MVC problem. We employed these two strategies in the development of two new local search algorithms which we call as EWLS and EWCC. The EWCC is an extension of EWLS. This was achieved by integrating the configuration checking strategy within EWLS. The EWCC not only significantly outperforms EWLS, but also it does not require instance-dependent parameters as EWLS does. Thus, it makes a worthwhile advancement to the state-of-the-art on local search algorithms for MVC.. The EW strategy we proposed is in some way inspired by the clause weighting technique in SAT solving [30, 31, 43, 53, 54] . It is a novel idea for solving the MVC problem. The EW strategy associates a weight to each edge and increases the cost of local optima it meets. This means the algorithm may find good candidate solutions hidden behind local optima. It is important to note that our EW strategy is rather different from the strategy adopted in the COVER algorithm which also makes use of edge weights. While COVER is an iterative best improvement algorithm that updates edge weights in each step, the EW strategy in EWLS updates edge weights only when the search being stuck in local optima.. The CC strategy we proposed is to handle the cycling problem in local search. It takes the induced subgraph configuration into account when selecting vertices to add into the current candidate solution, in order to prevent a vertex from getting into the circumstance it just leaves; and hence reduces cycling steps. This novel strategy is essentially different from previous heuristics on MVC, MIS and MC problems, which usually refer to the vertex information but neglect its circumstance in making decisions. It is exciting that the CC strategy is surprisingly effective while being conceptually simple; indeed, EWCC dramatically improves EWLS just by adopting the CC strategy instead of using the standard tabu mechanism as in EWLS. We believe that it also provides an interesting alternative to the standard use of the tabu mechanism to avoid the cycling phenomenon in other combinatorial search problems.. We have carried out experiments on two important benchmark sets, DIMACS and BHOSLIB. Compared with the current best heuristic algorithms, EWLS and EWCC are largely competitive on DIMACS benchmarks and outperform them on most hard instances, and dominate on the hard random BHOSLIB benchmarks. Moreover, EWCC makes a significant improvement over EWLS, particularly on the BHOSLIB benchmarks, where EWCC delivers the best results which significantly improve existing ones. Further, they perform quite well even on structured instances in comparison to the best exact MC algorithm. Notably, both EWLS and EWCC set a new record to the twenty year challenging instance frb100-40. In this sense, this work takes a promising step towards solving hard instances of MVC, MIS and MC problems.. Furthermore, we have shown that EWLS and EWCC are characterized by exponential RTD and RLD, which means they are robust w.r.t. the cutoff parameters and the number of random restarts, and hence have close-to-optimal parallelization speedup [28, 29] . We also perform some further investigations to illustrate the effectiveness of the underlying mechanisms in these two algorithms.. A significant future direction is to apply the configuration checking heuristic to various combinatorial search problems. The CC strategy is very simple and the notions (such as neighbors and state of solution components) it uses are common in combinatorial problems. From its ability to incorporate and guide another procedure, in amended form as a subroutine, the CC strategy may be viewed as a meta-strategy for combinatorial problem solving. Given the success of the CC strategy and its generality, we believe it is also effective for solving other hard combinatorial search problems. Also, based on the discussions in Section 6.5, it would be a valuable work to implement the CC strategy accurately with low time price to handle the cycling problem better. Proof. In this proof, E(G) is the universal set. u ∈ C and v / ∈ C . Let E 0 = {e | e is not covered by C }, E 1 = e e is not covered by C \{u} , E 2 = e e is covered by u and not covered by C \{u} . In this section, we perform additional empirical analysis to gain a deeper understanding of the run-time behavior of our two algorithms and the efficacy of their underlying mechanisms. Specifically, we explore the variability in run-time between multiple independent runs on the same problem instance; the effectiveness of the edge weighting scheme; the impact of the delta parameter on the performance of EWLS; the efficacy of the old-to-young strategy; and more insights into the configuration checking strategy.

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