Reducing Buyers' Uncertainty About Taste-Related Product Attributes AbstractIt is becoming increasingly important for firms to know when to take steps to reduce buyers Today's firms use new technological means to reduce consumers' uncertainty about product characteristics and performance, and doing so may appear to be a strategic necessity [16] , since today's consumers are using information to guide purchasing decisions more heavily than ever before. This is true for consumer purchases both online and offline, as evidenced by the increasing percentage of online and offline purchases that are preceded by online search for descriptive product information [1, 40] . Not all mechanisms for reducing consumer uncertainty are equally effective, and sometimes the process of reducing uncertainty can be quite expensive; consequently, the question of when to reduce buyers' uncertainty is becoming increasingly important.. Traditionally, firms have had a limited number of options regarding investing in reducing buyers' uncertainty about their offerings. Firms can engage in any or all of the following:. � thorough product testing [22, 39] and making the favorable results of the tests easily available � better organizing and presenting product information, so that consumers become educated about different features and can assess the importance of these features to them [24, 31] � supporting certification intermediaries that act as trusted third parties [2] , in providing product samples and free returns � training their sales force so that it can better communicate the advantage of each product to prospective customers [50] .. Other methods, like providing discounts for initial purchase (promotional discounts) and giving away free samples (sampling) have also been used extensively in markets for fast moving consumer goods, where buyers will be expected to make frequent repeat purchases. These are far too expensive to use in markets for expensive technology products and manufactured durable goods, where repeat purchases are unlikely. Sampling is also far too expensive to use in niche markets, where only a tiny fraction of the population provided with samples might be expected to become repeat purchasers.. In recent years, technology has offered firms new ways to increase consumers' knowledge about their offerings. Data analytics allow firms to target even traditional methods to more receptive audiences; for example, Netflix shows different trailers for the same TV-series to different audience segments, based on each segment's viewing preferences [8] . Vendors can now provide interactive Working Paper -Please do not cite applications to help buyers find their perfect product fit. It is now possible to use rich, interactive media [33] to allow buyers to sample products electronically and thus to evaluate the experience of owning the actual product [42] . Sellers can now allow consumers to view a video clip, listen to a snippet of a song, or download the first chapter of a book before making purchase decisions. Indeed, many PC-games feature playable demo versions, while high-end clothing and apparel retailers have begun to offer virtual try-ons and 3D tours of their products. The ability to engage in informative advertising has also been significantly improved with technologies like QR code, which allows vendors to supplement their magazine ads with QR codes that enable readers to explore specific product features using mobile phones and tablets, even while they continue to read their magazine.. Even as firms that wish to reduce buyer uncertainty have more investment options than ever before, these investments are themselves becoming increasingly important. Indeed, a large and continuously growing portion of electronic commerce (e-Commerce) involves active information acquisition on the part of consumers. In 2009 in the USA 10-15% of retail sales that involve the Internet (including Research Online-Purchase Offline, or ROPO) were the direct result of a consumer actively engaging in search for feature information [40] . These sales added up to a $57-67 billion market, about evenly split between online and offline purchases [40] . The number of people who perform such searches before purchasing continues to grow. Accenture reported in 2007 that of consumers they surveyed, more than two thirds explored product features online, and found that this was a rising trend [1] . The e-tailing group [51] reported an increase in the number of people who value retailers' efforts to reducing their uncertainty: the percentage of consumers who think product comparison capabilities are important grew from 67% in 2007 to 70% in 2008 , and the percentage of those who appreciate informative product videos climbed from 25% to 31%. Consumers' use of information may or may not result in increased total category sales or to an increase in market size, but failure to provide consumers with precisely the information they want almost certainly represents lost sales for firms that do not learn how to provide information to consumers effectively.. Firms' increasing need to know when to invest and reduce buyer uncertainty is even more pronounced for information about product attributes that are related to differences among consumers' tastes, rather than to differences in product quality. These are product attributes for which consumers Working Paper -Please do not cite do not generally agree on what is better when they try to compare them. Examples of such tasterelated attributes abound and are often related to aspects of design, personal preferences, size, etc.. Taste-related attributes contrast with attributes that are related to product quality and for which consumers generally agree when they compare them. While consumers may not agree on whether the iPhone design is better than that of a Samsung Android phone, and they may not agree on whether a Belgian strong ale is better than an American double IPA, most generally agree that customer service for an Infiniti FX 37 is better than customer service for the almost identical Nissan Murano.. Taste-related product attributes have always been important, as almost all products and services incorporate them. Today, their relative importance is increasing, for three reasons:. � Increasingly, consumers purchase what they want, rather than what they merely need. This is explained in Trading Up, in The Long Tail [3] , and in numerous references on the shift from merely satisfying basic needs towards self-indulgent delight.. � Increasingly, firms can deliver products tailored at smaller and smaller market niches [46] . � And increasingly, consumers are able to find and use the information they need to guide their purchasing decisions and find their ideal product selections. This is in large measure due to the rising popularity of social commerce platforms [26] , and the increased availability of recommendation technologies [44] , such as collaborative filtering [6] 1 . Indeed, companies like Facebook, Pinterest, and LivingSocial connect like-minded shoppers and encourage consumers to search for products and services based on their own idiosyncratic preferences. At the same time, intelligent shopping recommendations, based on collative filtering techniques, allow people to focus on subjective and idiosyncratic measures of product fit, rather than objective and universal measures of product performance and absolute quality.. Social commerce and recommendation technologies are especially suited to communicate tasterelated attributes. The first generation of e-Commerce websites allowed people to sort products based on quality attributes (e.g., sorting of digital cameras based on megapixel count), but could not make intelligent recommendations based on consumers' personal tastes. Yet, while we all prefer more Working Paper -Please do not cite pixels rather than fewer, a greater zoom range rather than a more limited one, and a lighter camera to a bulkier one, we do not all make the same tradeoffs among these attributes when selecting a single camera. Today's social platforms and intelligent online tools support far more sophisticated analyses before making purchasing decisions. Consumers today can choose to "follow" the design-based handbag recommendations of a like-minded shopper in Pinterest, or receive restaurant suggestions when they visit a new country, based solely on their favorite restaurants back home.. In Table 1 , we show examples of different information disclosure investments for different products, also highlighting a taste-related attribute for each product. This article showed that firms should account for the heterogeneity or homogeneity of consumer preferences when making investments that are designed to reduce consumers' uncertainty about their products. If a firm believes that its product is offered in a sweet spot -in a part of the product space with a large concentration of buyers with the same preferences -then investments in information disclosure are highly desirable. We also explained that a firm whose product receives buyer reviews with low variance should view this as a signal that it has hit a sweet spot in the product attribute space, and that it is likely to benefit greatly from investing in information disclosure about to its taste-Working Paper -Please do not cite related attributes. We showed that the mean of buyer reviews is not as informative as the variance, because it mostly caries information about the product's quality attributes rather than information about its position in the attribute space. The ubiquity of buyer reviews today and consumers' growing reliance upon acquiring information before purchase make our recommendations easy to follow, and managerially important. Finally, our results' applicability is further improved by the fact that they are independent of the way by which consumers estimate product quality from previous buyers' reviews.. There are many possible extensions for this line of research. An interesting extension would be to use information about the structure of the product space, embedded within consumer reviews, to inform not only information investment decisions, but also decisions regarding how many products to offer and also if some of these products should allow for customizations that would cover a range, rather than a spot in the product space [20] . The prospect of studying the actual disclosures more closely is also appealing. Ideally we would like to be able to also prescribe the kind of disclosure investment that would be more appropriate for each firm, given the structure of published consumer reviews.. Detailed empirical and experimental investigation is also required to verify the applicability of the article's theoretical recommendations. Investments could be observed in any of the forms that we discussed (from playable game demos of computer games, to the use of technology-enabled informative advertising) and causally linked to the mean and especially the variance of consumer ratings. Our own preliminary results in the PC-game market appear highly promising.. We believe that the line of research that uses higher moments of the ratings distribution to improve managerial decisions will prove to be highly fruitful. Learning to interpret as much as possible of the information embedded in buyer reviews will help firms to improve their decisions regarding investment in reducing consumer uncertainty, as this article has argued. It should also improve decisions on other competitive actions such as potential product line extension opportunities, product customization strategies, and prospects for price discrimination. Consequently, the firms that do a better job than their competitors in extracting useful and actionable information from higher moments of consumer reviews will gain a competitive edge. Working Paper -Please do not cite. The information in buyer review should be used far more fully than it is today, and requires far more analysis than has been completed to date. Indeed, it is still very much an open research question as to what information is encoded in the mean, variance, skewness and curtosis of the distribution of buyer reviews, and under what conditions.. The increasing availability of ratings information, combined with the increased importance of the kind of managerial decisions that ratings information can potentially support, virtually guarantee that these questions will continue to attract interest among members of our research community. Working Paper -Please do not cite. This is because at this location, even the buyer who, due to uncertainty, has the most pessimistic view possible about the product, would still gain positive utility from purchasing it. It is easy to show that beyond distance � � the probability that buyers will purchase the product decreases linearly until it reaches zero at distance � � . The distance � � is the distance from the product of the furthermost buyer who has a nonzero probability of purchasing the product. This distance is given by. This is because at this location, even the buyer who, due to uncertainty, has the most optimistic view possible about the product, would still gain no utility from purchasing it. Thus, the demand generated on one side is given by �1 � �� �� � � � � �

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


Gene selection for cancer identification: a decision tree model empowered by particle swarm optimization algorithm Background: In the application of microarray data, how to select a small number of informative genes from thousands of genes that may contribute to the occurrence of cancers is an important issue. Many researchers use various computational intelligence methods to analyzed gene expression data. Results: To achieve efficient gene selection from thousands of candidate genes that can contribute in identifying cancers, this study aims at developing a novel method utilizing particle swarm optimization combined with a decision tree as the classifier. This study also compares the performance of our proposed method with other well-known benchmark classification methods (support vector machine, self-organizing map, back propagation neural network, C4.5 decision tree, Naive Bayes, CART decision tree, and artificial immune recognition system) and conducts experiments on 11 gene expression cancer datasets.Conclusion: Based on statistical analysis, our proposed method outperforms other popular classifiers for all test datasets, and is compatible to SVM for certain specific datasets. Further, the housekeeping genes with various expression patterns and tissue-specific genes are identified. These genes provide a high discrimination power on cancer classification. We proposed a novel method to identify tissue-specific genes as well as housekeeping genes with altered expression patterns that provide a high discrimination power on cancer classification. These genes may play as an important role in diagnosis and/or pathogenesis of various types of tumors. Eleven cancer datasets were used to test the performance of the proposed method, and a five-fold cross-validation method was used to justify the performance of our proposed method. Our proposed approach achieved a higher accuracy as compared with all the other methods. This proposed method has integrated with the nonlinear search capability of PSO and linearly separable advantage of DT to apply to microarray cancer datasets for gene selection. Hawse have identified representative cancer genes (453 genes) from numerous microarray data (65,000 genes) that can reduce costs. In addition, we compared our proposed method with four well-known algorithms using a variety of datasets (diverse sizes and numbers of classes and features). Consequently, our proposed method outperformed all the other benchmark methods and is compatible to SVM for certain specific datasets.. Further studies to be further conducted are suggested as follows. First, PSO may result in better solutions by optimizing parameter settings; therefore, self-adaptation parameters of particle size, number of iterations, and constant weight factors are worth developing. Second, adding hybrid search algorithms in PSO algorithm may improve its performance; for example, swarms with mixed particles may further enhance the effectiveness. Third, the improvement in the execution time for large-sized data sets could be treated as a research subject in the future. Researchers have tried to analyze thousands of genes simultaneously by microarray technology to obtain important information about specific cellular functions of gene(s) which can be used in cancer diagnosis and prognosis [1] . The gene selection from gene expression data are challenging due to the properties of small sample size, high dimension and high noise. A method is needed for choosing the important subset of genes with high classification accuracy. Such method would not only enable doctors to identify a small subset of biologically relevant genes for cancers, but will also save computational costs [2] .. The gene selection method can be divided into three classes, the wrapper, the filter, and the embedded approaches. Wrappers utilize learning machine and search for the best features in the space of all feature subsets. Despite their simplicity and often having the best performance results, wrappers highly depend on the inductive principle of the learning model and may suffer from excessive computational complexity because the learning machine has to be retrained for each feature subset considered [3] . The wrapper method is usually superior to the filter one since it involves intercorrelation of individual genes in a multivariate manner, and can automatically determine the optimal number of feature genes for a particular classifier. The filter approach usually employs statistical methods to collect the intrinsic characteristics of genes in discriminating the targeted phenotype class, such as statistical tests, Wilcoxon's rank test and mutual information, to directly select feature genes [4] . This approach is easily implemented, but ignores the complex interaction among genes. Finally, the embedded method is a catch-all group technique which performs feature selection as part of the model construction process. It is similar to the wrapper method, while multiple algorithms can be combined in the embedded method to perform feature subset selection [5, 6] . Genetic algorithms (GAs) [7] are generally used as the search engine for feature subset in the embedded method, while other classification methods, such as estimation of distribution algorithm (EDA) with SVM [8] [9] [10] [11] [12] [13] , K nearest neighbors/ genetic algorithms (KNN/GA) [14] , genetic algorithmssupport vector machine (GA-SVM) [15] and so forth, are used to select feature subset.. Particle Swarm Optimization (PSO), developed by Kennedy and Eberhart [16] , is a population-based metaheuristic on the basis of stochastic optimization, inspired by the social behavior of flocks of birds or schools of fish [17] . PSO has been widely applied in many fields to solve various optimization problems, including gene selection [1, 2, [18] [19] [20] . A swarm of particles with randomly initialized positions would move toward the optimal position along the search path that is iteratively updated on the basis of the best particle position and velocity in PSO. The potential solutions, called particles, are used to represent a candidate solution for the problem. Among the classifiers given a specific search algorithm, C4.5 is a decision tree-based classifier listed in the top 10 most influential data-mining algorithms [21] . Decision trees are a linear method which is easy to interpret and understand.. This paper presents a PSO-based algorithm to address the problem of gene selection. The proposed approach is an integration of PSO searching algorithm and C4.5 decision tree classifier, called PSODT. Combining PSO with C4.5 classifier has rarely been investigated by previous researchers. The performance of our proposed method will be evaluated by 11 microarray datasets, which consist of 1 dataset from cancer patients of the M 2 DB in Taiwan [22] and 10 from the Gene Expression Model Selector [23]. In addition, the performance of our proposed method will be compared with other well-known classifier algorithms, such as self-organizing map (SOM), C4.5, back propagation neural network (BPNN), SVM, NaivaBayes (NB), CART decision tree, and artificial immune recognition system (AIRS). Statistical test will be employed to discriminate the difference of all the algorithms in terms of classification accuracy. We integrated PSO algorithm with the C4.5 classifier to address the gene selection problem (refer to Appendix 1 & 2 at [34] ). The important genes were proposed using PSO algorithm, and then C4.5 was employed as a fitness function of the PSO algorithm to verify the efficiency of the selected genes.

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


Joint time-frequency domain cyclostationarity-based approach to blind estimation of OFDM transmission parameters Blind estimation of the transmission parameters of orthogonal frequency division multiplexing (OFDM) signal is an important issue for various civilian and military applications. This paper presents a new cyclostationarity-based approach to blind estimation of OFDM signal parameters. Analytical expression for extracting transmission parameters from second-order cyclic cumulant (CC) of OFDM signal is derived first, with the consideration of the effects of time dispersion and consistent estimator errors on CC. The approach exploits the cyclostationarity of OFDM both in time delay domain and cyclic frequency domain; a statistic hypothesis testing framework was formulated to determine the threshold for detecting the presence of cycles of OFDM signal. The simulation results reveal that the proposed approach is robust for both previous synchronization and channel condition concurrently. Blind estimation of communication signal parameters plays a key role in various civilian and military applications, such as cognitive radio (CR) and noncooperative communication [1, 2] . The cognitive radio aims at improving the spectrum utilization by allowing the secondary user to sense and use the licensed spectrum, which needs to have the intelligence of dynamically changing its parameters. Therefore, it is necessary for the blind parameter estimation for CR to efficiently demodulate the signals in hostile wireless channel. In noncooperative communication, hostile communication signal must be detected, estimated, and recognized by its transmission parameters, which are vital for decisions involving electronic warfare operations and other tactical actions. Over the recent decades, orthogonal frequency division multiplexing (OFDM) has been widely employed in many wireless communication systems, owing to the advantages of high spectral efficiency and robustness against channel fading. OFDM is also a good alternative transmission scheme for underwater communication that both remedies the problem of ISI and provides low complexity solutions. For the OFDM signal, the recognized parameters include the symbol periodic, subcarrier spacing, subcarrier number, and cyclic prefix (CP) length.. The cyclostationarity properties of OFDM signal was widely exploited for various purposes: signal detection, classification [3] [4] [5] [6] , synchronization [7] [8] [9] , and parameter estimation [10] [11] [12] [13] , in which the blind estimation of OFDM parameters have been investigated only in recent years, and these literatures generally achieved the estimation parameters by finding the cycles present in the cyclic statistics of OFDM signal. The algorithm proposed in [10] is based on the signal empirical distribution function. In [11] , the cyclic correlation of OFDM signal is used to estimate the sampling frequency and CP length. A blind parameter estimation algorithm exploits the cyclostationary property of OFDM while considering the effect of time-dispersive channel [12] . The work in [13] pursues more accurate blindly estimated results by processing the candidate set of cyclic frequencies with average idea. However, in all of these literatures, the detection procedure is overly empirical and not rigorous for estimation accuracy, e.g., by checking the cycle presence based on a predefined threshold. In addition, the exploitation of cyclic statistics only applied in single domain (time or frequency) does not make full use of the cyclostationarity properties of OFDM signal [14] . This paper presents a cyclostationarity-based approach to the blind estimation of OFDM transmission parameters, which derives the estimated parameters from both time (delay) and frequency domain using the second-order cyclic cumulant (CC) in a similar way as [14] . It is shown that detection and estimation in two domains can improve the accuracy probability of estimating evidently. To ensure the preciseness of the approach, a statistic hypothesis testing was developed to determine the threshold for detecting the presence of cycles of OFDM signal, by which the theoretical relation between the threshold value and constant false alarm rate (CFAR) was derived. Another contribution of this paper is that it derived the analytical expression of second-order CC of OFDM signal in both additive white Gaussian noise (AWGN) and multipath channel, and consequently, the condition of estimating the parameters from second-order CC are achieved with the consideration of the effects of time dispersion and consistent estimator errors.. The paper is organized as follows: we first give the OFDM signal model in AWGN and multipath channels in Section 2. In Section 3, the analytical expression of second-order CC of OFDM signal and the condition of estimating the parameters are derived. The proposed cyclostationarity-based approach to the blind estimation of OFDM transmission parameters is given in Section 4. Simulation results are presented in Section 5, and finally, conclusions are drawn in Section 6. This paper has investigated the blind estimation of OFDM parameters based on the signal's cyclostationarity. Firstly, the possibility of extracting the transmission parameters from second-order CC is derived theoretically, which analyzes both the continuous and discrete signal models under the AWGN channel and multipath channel, respectively. The proposed estimation approach jointly exploits the delay and cyclic frequency domain properties of second-order CC and develops a CFAR-based statistic hypothesis testing framework to detect the presence of CP-introduced cyclostationarity. The approach only assumes that the OFDM signal have the cyclic prefix and does not require any priori condition, so it can be easily extended to most cases that need blind estimation of OFDM parameters.

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Exact and heuristic solution approaches for the mixed integer setup knapsack problem We consider a class of knapsack problems that include setup costs for families of items. An individual item can be loaded into the knapsack only if a setup cost is incurred for the family to which it belongs. A mixed integer programming formulation for the problem is provided along with exact and heuristic solution methods. The exact algorithm uses cross decomposition. The proposed heuristic gives fast and tight bounds. In addition, a Benders decomposition algorithm is presented to solve the continuous relaxation of the problem. This method for solving the continuous relaxation can be used to improve the performance of a branch and bound algorithm for solving the integer problem. Computational performance of the algorithms are reported and compared to CPLEX. Knapsack problems are widely studied due to their ability to closely represent real world problems and their frequent appearance as subproblems in more complex models. Martello and Toth (1990) and Kellerer et al. (2004) provide extensive reviews of the major classes of knapsack problems, theoretical results, and solution algorithms. Lin (1998) surveyed well-known non-standard knapsack problems and identified the setup knapsack problem (SKP) as worthy of further investigation. The objective of the SKP is to select specific items, which belong to mutually exclusive product family sets, for placement in a capacitated knapsack while either maximizing its value or minimizing its cost. However, an item can only be selected if a setup charge for placing the family of items in the knapsack is incurred.. The SKP has been identified as a significant subproblem for the solution of capacitated scheduling problems. Guignard (1993) proposed a Lagrangean Decomposition scheme for finding a lower bound on the optimal makespan of a scheduling problem 0377-2217/$ -see front matter Ó 2007 Elsevier B.V. All rights reserved. doi: 10.1016/j.ejor.2007.07.003 with parallel unrelated machines with setups. A series of 0-1 programming SKPs, one for each capacitated machine, is solved each iteration of a subgradient algorithm. Chajakis and Guignard (1994) presented a dynamic programming algorithm and two versions of a two-phase enumerative scheme, which solve the SKP in pseudo-polynomial time. However, due to the relatively large storage requirements of dynamic programming, they emphasized the importance of designing good upper bounding schemes and heuristics to be embedded in efficient branch and bound algorithms.. In addition to appearing as a subproblem in scheduling capacitated machines, SKP by itself can model a variety of resource allocation problems. Consider a freight consolidation problem in which a capacitated transport vehicle can carry several different product families as defined by commodity type, shipper, or destination. The decision problem objective is to select the product families and quantities of items to ship in order to maximize the value of the line haul. However, each family requires a setup cost (e.g. a pickup or delivery charge, or specialized freight services such as dunning, refrigeration, or government inspection) before any items in its family can be included in the shipment.. Product category management, where a supplier is allocated limited retail shelf capacity and must determine the mix of product families and items to stock, provides a second example. Each product family included in the lineup has a fixed setup cost for administration, inventory maintenance, and billing, while associated with each item and stocking quantity is an expected profit contribution. The decision is to select the mix of families and items that maximizes the expected value of the product category. Other potential applications are in portfolio management where each investment opportunity is associated with an account setup, subscription or membership cost and expected return. The objective is to select the mix of investments and quantity of each to maximize the expected return of the portfolio.. Recently, Akinc (2006) developed a variety of algorithmic components to improve the efficiency of branch and bound to solve the SKP. The first component solves the LP relaxation of the problem by a non-iterative procedure similar to the one described in Section 4.1. Akinc reported that the LP relaxation of SKP is very tight, with at most a 1.7% gap. The second component he developed is geared towards finding good feasible solutions to accelerate fathoming branch and bound nodes. One approach mentioned simply involved rounding the fractional setup variables up or down to obtain two feasible solutions. Then the better of the two solutions was used for fathoming. The second approach Akinc presented reallocated total capacity by solving a traditional knapsack problem for all the individual items for which a setup is incurred in the LP solution. The last component Akinc developed to improve the efficiency of branch and bound consists of a set of rules to peg the setup variables to zero or one. The three approaches described above reportedly improved the performance of the branch and bound, although no computational times were reported.. In this paper, we focus on a variant of the SKP where fractions of individual items are allowed to load into the knapsack. This mixed-integer setup knapsack problem (MISKP) is equivalent to a continuous relaxation of the binary constraints on items in the SKP of Chajakis and Guignard (1994) . However, MISKP allows multiple units of each item to be included in the knapsack and they are continuously divisible (e.g. dollars in an investment fund, weight/volume in assignment to a transportation vehicle, units in a production schedule). Another difference is that in MISKP, family setups do not consume any of the limited resource. The problem appears as a subproblem of the capacitated coordinated replenishment problem (Robinson and Lawrence, 2004) . MISKP plays a critical role in developing efficient solution approaches to the capacitated coordinated replenishment problem but has not received much attention in the literature. With this paper we provide the first comprehensive study of this problem.. The contribution of the paper is threefold. First, we present a mixed-integer programming model and investigate the potential of using an exact solution algorithm based on Van Roy's (1983) cross decomposition procedure. Secondly, we propose an efficient upper bounding heuristic and develop a Benders decomposition based approach to obtain the lower bound as an alternative to the method described in Akinc (2006) . The development of efficient exact solution approaches to MISKP makes solving large problems possible. Good heuristics to generate tight bounds and efficient methods to solve the LP-relaxation of the problem promotes the development of algorithms for more complex decision problems that utilize MISKP as subproblems. Lastly, the contributions of the paper draw from better understanding of the problem. We designed an experiment to investigate what makes the problem difficult to solve, and how effective is the state-of-the-art commercially available software.. In the next section, we define the notation and formulate the problem. In Section 3 we describe the cross decomposition algorithm. Section 4 focuses on generating upper and lower bounds. Section 5 discusses experimental design and presents the results of the computational experiments. Section 6 concludes the manuscript. We presented two variants of the Setup Knapsack Problem, namely the Mixed Integer Setup Knapsack Problem and its LP-relaxation, which have important implications for solving capacitated scheduling problems, as well as potential applications in freight consolidation and portfolio management. A cross decomposition based exact algorithm was developed and its performance compared against CPLEX linear optimization software. Computational experiments indicate that the proposed algorithm has great potential in solving the MISKP. A major factor limiting the algorithm's computational efficiency is solving the primal master problem. Improvements on the solution algorithm for the master problem could improve overall solution times significantly.. Our computational results also showed that the proposed upper bounding heuristic is effective and provides a higher quality upper bound than the one associated with CPLEX for every experimental factor setting. We also developed a Benders Decomposition based procedure to solve the LP-relaxation of MISKP. This procedure was, on average, eight times faster than CPLEX, offering an improved lower bounding procedure for LP relaxation based branch and bound methods.. Finally, the experimental design and analysis provides a comprehensive set of test problems that identify the factors driving problem difficulty from both a heuristic and optimization perspective. Both optimization approaches experience significant challenge solving problems with higher numbers of families, demand/cost correlation, and lower setup costs. When applying cross decomposition and CPLEX as heuristics, higher levels of capacity utilization and demand/cost correlation and lower levels of product families and setup cost result in lower quality lower and upper bounds. These results suggest the need for additional heuristic and optimizationbased research on this important problem class.

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Electronic Trading Systems: Strategic Implications of Market Design Choices Modern financial markets compete aggressively for trading activity and investor interest.Information technology, once a crucial element in streamlining paper flows andoperations, is now a strategic resource used in attracting or retaining market liquidity.Established exchanges introduce technology to enhance their markets. New marketvenues challenge the status quo and rely on technology to offer diverse services toincreasingly sophisticated investors. In this paper, we examine the strategic designdecisions embedded in these new electronic trading systems. Design decisions arecritical, as they determine the market microstructure which influences investingstrategies, patterns of trade, liquidity and volatility. We propose a taxonomy of designalternatives based on six major dimensions: market structure, type of orders, orderexecution priority rules, price discovery rules, time stamping, and transparency. Usingexamples of existing systems, we discuss the potential impact of the various alternativeson the eventual attractiveness of the market to the investors.

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Locomotion analysis and its applications in neurological disorders detection: state-of-art review Abstract Driven by the need of non-invasive diagnosis in clinical practice, behavioral screening and tests have attracted more and more research interests recently. Locomotion analysis, as an important division of behavioral tests, has been widely used in diagnostic decision making, comparative biomechanics, biometric identification and forensics, etc. Plenty of instruments and approaches for locomotion analysis have been developed in both academic and industrial fields to detect diseases clinically, especially neurological disorders. Thus, it is crucial to summarize the methodology and applications of locomotion analysis to help researchers better understand this field. In this review, we focus on describing some recently developed locomotion instruments and their applications in detecting neurological disorders. We also discuss the recent progress of locomotion studies and their pros and cons. Early diagnosis of diseases is the best protection against their effects. Thus, an efficient and smart approach to detect some specific diseases early is a key to protect people. What kind of approaches can be called efficient and smart? There are several criteria to follow. First of all, the detected results should be accurate. Second, the detection approach should be simple, minor or non-invasive. Third, the cost should be low. Driven by the demands of these criteria, many detecting approaches have been developed, such as specimen tests, computed tomography (CT), magnetic resonance imaging (MRI), behavioral screening and tests, etc. A particular disease may have one or more appropriate options. Locomotion analysis, a division of behavioral tests, has attracted increasing research interests (Thomsen et al. 2012; Wu et al. 2012; Reiner et al. 2012; Suresh Babu et al. 2012; Young et al. 2012) , and it is potentially the best early detection solution for some particular diseases.. Locomotion analysis, also called gait analysis mostly, is a technology that aims to extract useful information by studying the motions of animal models or human subjects. Moreover, locomotion analysis matches the three criteria perfectly as an efficient, non-invasive, and economical approach. The technology has been used since the seventeenth century, and its development has accelerated recently with the advent of computer technology (for a review see Morris and Lawson 2009) . The utility of locomotion analysis is broad now, and has been used in the detection of limps in dairy cows (Liu et al. 2009a) , aging research (Woollacott and Shumway-Cook 2002) , neurological disorders detection (Tang et al. 2012 ), etc. Toro et al. (2002 published a review of observational gait assessment in clinical practice, and the report focused on the approaches to perform gait analysis, such as ''naked eye'' observation of gait and video-based observational gait assessment. Gait assessment is an everyday responsibility for some practicing therapists. Visual assessment, which is universally used for this purpose, has been shown to be unreliable. Thus, measurement of the temporal and spatial factors of gait objectively has been found to be clinically meaningful (Wall and Brunt 1996) . Moreover, locomotion analysis has been rapidly expanding in the past few years and its impact on the diagnosis of neurological disorders has been rapidly increased. Locomotion analysis has become an important approach for the diagnosis of many neurological disorders (Tien et al. 2010) . As a result, it is necessary to review the recent progress of locomotion studies and their applications in detecting neurological disorders.. A system of locomotion analysis commonly consists of two components: an instrument which collects data and a computational model which generates reliable detection results based on the data set collected. The rest of this review article is organized as follows: an introduction to the instruments, the data generated by the instruments, and approaches used to analyze the locomotion data will be presented in Sect. 2, including laboratory prototypes and commercially available instruments, for animal models as well as human beings; Sect. 3 will describe the applications of locomotion analysis in the detection of neurological disorders and their performance. Discussion and conclusion will be delivered in Sects. 4 and 5, respectively. Locomotion measurements can be classified to kinetic and kinematic measurements. In addition, different locomotion instruments have different experimental subjects, i.e., animal models and human subjects. Thus, the locomotion analysis instruments listed above can be classified as in Table 3 , according to their corresponding measurement approaches and subjects. Among the gait instruments introduced above, the systems developed by Full and Tu (1990) and GaitShoe et al. (2008) This review summarized the recent development in the field of locomotion analysis, including locomotion analysis instruments and their applications in detecting neurological disorders. The experimental subjects of locomotion analysis consisted of animal models and human beings.. Locomotion analysis, a subgenre study of motion analysis as well as an important division of behavioral research, is usually used as a non-invasive approach to clinical diagnosis. It is impossible to fully summarize locomotion study in one paper. However, this review focused on creating a rough picture of locomotion analysis in detection of neurological disorders according to the authors' experience in the field. The materials provided here is to the authors' best knowledge. A major advantage of locomotion analysis is its non-invasive characteristics, compared to other available clinical tests. This is extremely important for some specific diseases, such as neurological diseases. In addition, locomotion analysis systems are simple to implement, carry a Fig. 9 Height of the body center of mass plotted against time for control animals (a; n = 6) and striatal dopaminergic (DA)-depleted animals (b; n = 5). Solid and hatched bars demonstrate the duration of ground contact for each limb. Note that the center of mass oscillates evenly twice during each stride in control animals, but oscillates unevenly during each stride in animals with DA depletion (adapted from Muir and Whishaw 1999b) Fig. 10 Summed GRFs in the vertical direction for control (a) and DA depleted animal model (b). Notice the two peaks in vertical force produced during contact of the good hindlimb and bad forelimb (asterisk in b) (adapted from Muir and Whishaw 1999b) low cost, and reduce the risk of complication. Therefore, they have been widely used to detect neurological diseases (Hamers et al. 2001; Koopmans et al. 2006; Neumann et al. 2009 ).. Locomotion analysis instruments make the gait measurements objective. There is a definite need for objective measurement of gaits. Without it, the quality of treatment decisions is reduced due to subjective and often unreliable assessments. Objective measurements must also be employed if one is to demonstrate the efficacy of a treatment protocol (Wall and Brunt 1996) .. Gait patterns can be affected by many factors, such as emotional and environmental factors. Thus, the challenge of locomotion analysis is how to prove the gait abnormalities measured are caused by the target disorders rather than other factors. In other words, the challenge is how to eliminate false positives. One solution for this is to validate the results of locomotion analysis by using other diagnostic approaches, such as image-processing-based clinical decision support (Zillner and Sonntag 2012) and genomic data integration (Zhou et al. 2012) .

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Adaptive sequential Monte Carlo by means of mixture of experts Abstract: Appropriately designing the proposal kernel of particle filters is an issue of significant importance, since a bad choice may lead to deterioration of the particle sample and, consequently, waste of computational power. In this paper we introduce a novel algorithm adaptively approximating the socalled optimal proposal kernel by a mixture of integrated curved exponential distributions with logistic weights. This family of distributions, referred to as mixtures of experts, is broad enough to be used in the presence of multi-modality or strongly skewed distributions. The mixtures are fitted, via online-EM methods, to the optimal kernel through minimisation of the Kullback-Leibler divergence between the auxiliary target and instrumental distributions of the particle filter. At each iteration of the particle filter, the algorithm is required to solve only a single optimisation problem for the whole particle sample, yielding an algorithm with only linear complexity. In addition, we illustrate in a simulation study how the method can be successfully applied to optimal filtering in nonlinear state-space models. During the last decade, sequential Monte Carlo (SMC) methods have developed from being a tool for solving specific problems, such as the optimal filtering problem in general state-space models or simulation of rare events (these topics are abundantly covered in Liu, 2001; Doucet et al., 2001; Ristic et al., 2004; Cappé et al., 2005; Del Moral et al., 2006 , and the references therein). The high flexibility of these methods makes it possible to use them for efficiently executing key steps of composite algorithms tackling very complex problems, e.g., as in particle Markov chain Monte Carlo (MCMC) methods for joint inference on static and dynamic variables (see Andrieu et al., 2010) .. However, while there has been abundant work on adaptation of MCMC methods, from the early algorithms of Haario et al. (2001) to the mathematical study of disminishing adaptation established in Andrieu and Moulines (2006) and Roberts and Rosenthal (2009) , adaptive methods for SMC are still in their infancy. This article, which sets out from a theoretical framework for adaptive SMC presented in Cornebise et al. (2008) , is part of the effort to fill this gap-which is required to achieve maximum efficiency and user-friendliness. A mathematically less detailed pre-version of the present paper appeared as part of the Ph. D. dissertation by Cornebise (2009) .. Such adaptive methods are especially suited to cope with the rising complexity of state-space models (SSMs) in recent applications. While simple unidimensional filtering problems will rarely justify even a slight computational overhead of adaptive methods over plain SMC methods (such as the bootstrap particle filter ; see Section 3.1), the situation is reversed for many state-of-the-art SSMs, where forward simulation may require costly physical emulators or the evaluation of computationally expensive transition densities. This occurs, e.g., as soon as the model involves differential equations and numeric solutions of the same. Recent examples range from health sciences (see e.g. Korotsil et al., 2012 , for a study of the epidemiology of human papillomavirus infections) to environmental sciences (see e.g. Robins et al., 2009 , who studied data assimilation for atmospheric dispersion of hazardous airborne biological material).. In the SMC framework, the objective is to approximate a sequence of target densities, defined on a sequence of state spaces as follows. Given a density µ on some state space Ξ, the next densityμ in the sequence is defined bỹ µ(x) := µ(x)l(x,x) dx µ(x)l(x,x) dx dx ,x ∈Ξ,. (1.1) whereΞ is some other state space and l : Ξ ×Ξ → R + is an un-normalised transition density. Here the dimensions ofΞ and Ξ typically differ. This framework encompasses, inter alia, the classical problem of optimal filtering in SSMs recalled in Section 6 (see in particular Equation (6.4)).. SMC methods approximate online the densities generated by (1.1) by a recursively updated set of random particles {X i } N i=1 and associated importance weights. . At each iteration of the algorithm, the weighted particle sample {(X i , ω i )} N i=1 approximates the corresponding target density µ in the sense that N i=1 ω i f (X i )/Ω, with Ω := N =1 ω , approximates E µ [f (X)] := f (x)µ(x) dx (this will be our generic notation for expectations) for all bounded measurable functions f on the corresponding state space Ξ. All SMC methods have two main operations in common: a mutation step and a selection step. In the former, the particles are randomly scattered in the state space by means of a proposal transition density r : Ξ ×Ξ → R + ; more specifically, the mutation operation generates a set of new,Ξ-valued particles by moving the particles according to the transition density r and assigning each mutated particle an updated importance weight proportional to l/r; consequently, each weight reflects the relevance of the corresponding particle as measured by the likelihood ratio. In general, the mutated particles are conditionally independent given the ancestor particles. In the selection step, the particles are duplicated or eliminated with probabilities depending on the importance weights. This is typically done by multinomially resampling the particles with probabilities proportional to the corresponding weights. In the auxiliary particle filter (proposed by Pitt and Shephard, 1999 ) the particles are resampled according to weights that are modified by a factor determined by an adjustment multiplier function a : Ξ → R + . Introducing adjustment multipliers makes it possible to, by using some convenient lookahead strategy, increase the weight of those particles that will most likely contribute significantly to the approximation of the subsequent target distribution after having been selected. In this way computational power is directed toward zones of the state space where the mass of the subsequent target density is located.. The choice of the adjustment weight function a and the proposal density r affects significantly the quality of the generated sample, and in this paper we focus on adaptive design of the latter. Letting r(x,x) = l(x,x)/ l(x,x) dx is appealing as the particles in this case are propagated according to a dynamics that is closely related to that of the recursion (1.1). Indeed, by combining this choice of proposal kernel with the adjustment multiplier function a(x) = l(x,x) dx yields perfectly uniform importance weights. In this case the SMC algorithm is referred to as fully adapted. However, this so-called optimal proposal kernel and adjustment multiplier weight function can be expressed on closed-form only in a few cases and one is in general referred to approximations of these quantities.. There is a large literature dealing with the problem of approximating the optimal proposal kernel. When using SMC for optimal filtering in SSMs, suggest approximating each function l(x, ·) by a Gaussian density whose mean and covariance are obtained using the extended Kalman filter. A similar approach based on the unscented Kalman filter was proposed by Van der Merwe et al. (2000) (see also Van der Merwe and Wan, 2003) . This technique presupposes that the model under consideration can be well approximated by a nonlinear Gaussian SSM with linear measurement equation; however, this far from always the case, and careless linearisation (e.g. in cases where the local likelihood is multimodal) may boomerang and cause severe deterioration of the particle sample. Cappé et al. (2005, Section 7 .2.2.4) make a form of Laplace approximation of l(x, ·) by simply locating the mode of the function in question and centering a Gaussian density or the density of a student's t-distribution around the same. This technique, which goes back to Pitt and Shephard (1999) , is appro-priate when the function is log-concave (or strongly unimodal); nevertheless, as the mode of each l(x, ·) is a function of x, this approach involves solving one optimisation problem per particle. Thus, in spite of this intense recent activity in the field, the state-of-the-art algorithms have met only mitigated success as they implicitly assume that the functions l(x, ·) have a single mode.. A common practice (see e.g. Oh and Berger, 1993) for designing proposal distributions in standard (non-sequential) importance sampling is to consider a parametric family of proposal distributions and then identify a parameter that minimizes some measure of discrepancy between the target and the proposal distributions. Common choices are the widely used squared coefficient of variation of the importance weights or the negated Shannon entropy (see e.g. Cappé et al., 2005, p. 235 , for definitions of these quantities) of the same. Both are maximal when the sample is completely degenerated, i.e. when one single particle carries all the weight, and minimal when all the importance weights are equal. The coefficient of variation often appears in a transformed form as the effective sample size (we refer again to Cappé et al., 2005 , for a definition). The same quantities have been widely used also within the framework of SMC, but until recently only for triggering selection and not as a tool for adaptive design of the instrumental distribution. The key result of Cornebise et al. (2008, Theorems 1 and 2) was to relate the Shannon entropy to the Kullback-Leibler divergence (KLD; see Equation (3.6)) between the instrumental and proposal distributions of the particle filter. More specifically, when selection is carried through using multinomial resampling, each particle cloud update (selection followed by resampling) can be viewed as standard importance sampling where a weighted mixture of N stratas-the ith stratum being proportional to ω i l(X i , ·)-approximatingμ is targeted using a mixture proposal π comprising N stratas proportional to {ω i r(X i , ·)} N i=1 . As the number of particles tends to infinity, one may prove that the KLD between these two mixtures tends to the KLD between two distributions having densities µ * (x,x) ∝ l(x,x)µ(x) and π * (x,x) ∝ a(x)r(x,x)µ(x), which can be viewed as "asymptotic" target and proposal distributions on the product space Ξ ×Ξ. In addition, one may prove that the Shannon entropy has the same limit. (Cornebise et al. (2008) established a similar relation between the coefficient of variation of the particle weights and the chi-square divergence between the same distributions.) This gives a sound theoretical support for using the Shannon entropy of the importance weights for measuring the quality of the particle sample. In addition, it suggests that the KLD between the target mixture and π could be used in lieu of the Shannon entropy for all purposes, especially adaptation. As a matter of fact, in the context of adaptive design of SMC methods, the KLD is (as pointed out by Cornebise et al., 2008 , Section 2.3) highly practical since it decouples the adaptation of the adjustment weight function a and that of the proposal kernel r; see the next section.. Henceforth, in the present article we extend and implement fully the methodology indicated and sketched by Cornebise et al. (2008) and select the auxiliary proposal distribution π from a family {π θ ; θ ∈ Θ} of candidate distributions by picking θ * such that the KLD between the target mixture and π θ * is minimal and letting π = π θ * . On the one hand, the chosen parametric family should be flexible enough to approximate complex transition kernels; on the other hand, sampling from π θ should be easy. Finally, the parameterisation should be done in such a way that the problem of estimating the parameters is as simple as possible. In this article, we suggest modeling the proposal π θ as a mixture of integrated curved exponential distributions. By letting the mixture weights of the chosen proposal depend on the ancestor particles {X i } N i=1 , we allow for partitioning of the input space into regions corresponding to a specialised kernel. Each component of the mixture belongs to a family of integrated curved exponential distributions, whose two most known members are the multivariate Gaussian distribution and the Student's t-distribution. Also the parameters of the mixture depend on the ancestors. . This parameterisation of the proposal distribution is closely related to the (hierarchical) mixture of experts appearing in the machine learning community and described in (Jordan and Jacobs, 1994; Jordan and Xu, 1995) . The flexibility of our approach allows for efficient approximation of the optimal kernel for a large class of intricate (nonlinear nonGaussian) models. Unlike typical EM-type parameter estimation procedures, which are in general run iteratively until stabilisation, our adaptive SMC algorithm only requires a decrease of the KLD, not an exact minimum.. As illustrated in our examples in Section 6, such a gain typically occurs already at early iterations of the algorithm (a characteristic of EM-type algorithms), impliying the need of only very few EM iterations and therefore a minimal computational overhead.. The paper is organized as follows. In the next section we introduce some matrix notation and list the most common notation used throughout the paper. Section 3 describes, in a nutshell, auxiliary SMC methods as well as a KLD-based approach to adaptation of these methods that is used in the paper. Section 4 recalls mixtures of experts and Section 5 treats optimisation of the mixture parameters by means of stochastic approximation methods; the latter section is the core of the paper and contains our main results. In Section 6 we illustrate the efficiency of the method on several simulation-based examples and Section A contains some proofs.

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


Motion sequence analysis in the presence of figural cues The perception of 3-D structure in dynamic sequences is believed to be subserved primarily through the use of motion cues. However, real-world sequences contain many figural shape cues besides the dynamic ones. We hypothesize that if figural cues are perceptually significant during sequence analysis, then inconsistencies in these cues over time would lead to percepts of non-rigidity in sequences showing physically rigid objects in motion. We develop an experimental paradigm to test this hypothesis and present results with two patients with impairments in motion perception due to focal neurological damage, as well as two control subjects. Consistent with our hypothesis, the data suggest that figural cues strongly influence the perception of structure in motion sequences, even to the extent of inducing non-rigid percepts in sequences where motion information alone would yield rigid structures. Beyond helping to probe the issue of shape perception, our experimental paradigm might also serve as a possible perceptual assessment tool in a clinical setting. Motion of objects in the environment induces complex transformations in their images. The human visual system can recover the 3-D structure of the viewed objects and their motion in space by interpreting these image transformations [4, 34] . As early as 1953, Wallach and O'Connell demonstrated humans' capacity to interpret structure from motion while studying what they termed the 'kinetic depth effect' [39] . In their experiments, an unfamiliar object was rotated behind a translucent screen with its shadow being observed from the other side of the screen. In most cases, the viewers were able to describe correctly the 3-D shape of the hidden object and its motion, even when each static shadow projection of the object was unrecognizable and contained no 3-D information.. Any vision system that attempts to compute 3-D structure from motion must contend with the problem that the recovery of structure is under-constrained; there are infinitely many 3-D structures consistent with a given pattern of motion in the changing 2-D image. Additional constraint is required to establish a unique interpretation. Computational studies have used the rigidity assumption to derive a unique 3-D structure and motion; they assume that if it is possible to interpret the changing 2-D image as the projection of a rigid 3-D object in motion, then such an interpretation should be chosen [2, 6, 10, 13, 17, [21] [22] [23] [24] [25] [33] [34] [35] 43] . The rigidity assumption was suggested by perceptual studies that described a tendency for the human visual system to choose a rigid interpretation of moving elements [8, 14, 15, 39] .. The rigidity assumption has proven to be a powerful constraint, one that appears sufficient to explain how the human visual system solves the structure from motion problem in general settings. However, some interesting perceptual effects suggest that this notion of sufficiency might need to be revisited, at least insofar as modeling human performance is concerned. According to the rigidity assumption, a rigid object in motion should necessarily be perceived as rigid. But, a few studies have reported instances where displays of rigid objects in motion can give rise to the perception of distorting objects [3, 5, 9, 40, 44] . As detailed below, we suggest that these breakdowns of rigidity perception hint at a significant contribution from figural shape cues in the perceptual analysis of dynamic sequences. In this paper, we develop the hypothesis of a role for figural cues in sequence analysis, and present experiments designed to test this hypothesis.. The remainder of this paper is organized as follows: we first briefly review the current state of research related to the recovery of 3-D structure from motion and static image attributes; subsequently we present a hypothesis regarding interactions between shape information derived using motion and that derived from figural cues; and in Section 2 we describe the psychophysical experiment and in Section 3 we present evidence from normal observers as well as stroke patients with perceptual impairments in support of the basic thesis of this paper. We have considered the perceptual analysis of dynamic sequences that provide not merely motion information of a few feature points, but also figural information in each frame. We hypothesized that the figural cues would contribute to the eventual percept experienced by an observer. The results from experiments with normal and neurologically impaired subjects support this hypothesis. They suggest that figural cues can overwhelm motion cues, even to the extent of over-riding the rigidity bias, resulting in objects that are physically rigid being perceived as non-rigid by observers. Furthermore, even participants whose neurological damage impaired their motion perception skills, reported percepts of non-rigidity, suggesting that the percepts were likely being engendered by figural analysis. Based on these results, we have outlined an admittedly oversimplified theoretical account of shape recovery in motion sequences.. Several important questions remain open. Primary among these is a finer grained analysis of interactions between motion-based and figural-based 3-D shape recovery processes. Investigating this issue will require a way to parametrically change the strengths of these two types of cues, and assessing the effects of these changes on the eventual percept. This study has contributed evidence showing that such interactions do exist and that the analysis of motion sequences involves a significant contribution from figural cues. Using a combination of experimental and computational modeling techniques, research in Prof. Sinha's laboratory focuses on understanding how the human brain learns to recognize objects through visual experience and how objects are encoded in memory. Prof. Sinha's experimental work on these issues involves studying healthy individuals and also those with neurological disorders such as autism. The goal is not only to derive clues regarding the nature and development of high-level visual skills, but also to create better therapeutic routines to help children overcome visual impairments. Prof. Sinha founded Project Prakash in 2005 with the twin objectives of providing treatment to children with disabilities and also understanding mechanisms of learning and plasticity in the brain. Project Prakash, which is a collaboration between MIT researchers and ophthalmologists in India, has provided insights into some fundamental questions about brain function while also transforming the lives of many blind children by bringing them the gift of sight.. Prof. Sinha is a recipient of the PECASE -the highest US Government award for young scientists, the Alfred P. Sloan Foundation Fellowship in Neuroscience, the John Merck Scholars Award for research on developmental disorders, the Jeptha and Emily Wade Award for creative research, the Troland Award from the National Academies, and the Distinguished Alumnus Award from IIT Delhi.. Prof. Sinha has served on the program committees for prominent scientific conferences on object and face recognition and is currently a member of the editorial board of ACM's Journal of Applied Perception. He is a founder of Imagen Inc., a company that applies insights regarding human image processing to challenging real-world machine vision problems. Imagen was the winner of the MIT $50K Entrepreneurship competition. Prof. Sinha was named a Global Indus Technovator, and was also inducted into the Guinness Book of World Records for creating the world's smallest reproduction of a printed book.. Lucia Maria Vaina is a professor of biomedical engineering and she is a clinical and computational research faculty at Harvard University and Massachusetts Institute of Technology. She received her Ph.D. in mathematics from the Sorbonne University, Paris, France, and her M.D.Ph.D. at Toulouse.. Using a combination of experimental, computational and magnetoencephalography approaches she studies visual-cognitive functions in the normal and damaged human brain in order to provide an explanatory model of the spatiotemporal orchestration of high level sensory brain functions and to understand how they fail as a result of focal brain lesions due to stroke. Professor Lucia Maria Vaina is a fellow of the American Institute for Medicine and Biomedical Engineering. In 2005, she received a Doctorate Honoris Causa from the University V. Goldis for her contributions to medical science. She received the Alfred Sloan Foundation award, and the Ford Foundation Award for postdoctoral studies that she carried out at University of California, at Berkeley, Stanford University and Massachusetts Institute of Technology.. Professor Vaina serves as a charter member on the Perception and Cognition study section of the National Institute of Health, and she also served as an ad hoc member on many NIH and NSF study sections, including the Panel reviewing the 'Human Connectome Project'. She serves on the editorial board of several journals, among which 'Synthese', 'Journal of Neurophysiological and Neurological Disorders', 'Medical Science Monitor', and the 'American Journal of Case reports'. The experimental results suggest that, when available, figural information plays a significant role in the analysis of dynamic sequences. This is in contrast to conventional theories of structure from motion, wherein motion cues are used exclusively for structure recovery in sequences [33, 34] . Recent evidence from other research groups also highlights the role of figural information in the analysis of motion sequences [1, 20] . In the light of these results, we now discuss a revised theoretical formulation of the processes responsible for the perception of 3-D structure in dynamic sequences. figure) illustrates the level of the slices shown from the lowest to the highest, and 'z' refers to the axial slice number in the Talaraich coordinates. MR images were obtained with a Magnetom 1.5 T unit (6 mm thick slices, with 1.2 mm gap). (a) Patient's AMG lesion is in the left hemisphere and it extends laterally by the margins of the occipital horns of the lateral ventricle into the lateral portion of the occipital lobe; (b) patient JT has a large infarction of the left hemisphere, extending from the occipital pole to the temporal pole with a significant involvement of the occipital lobe. The medial temporal lobe, however, is preserved to a great extent, although the parahippocampal gyrus is likely involved in the lesion. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.). Conceptually, we can assume that two processes operate concurrently -one concerned with 3-D shape recovery from dynamic cues and the other from figural ones. The 3-D estimates they produce as outputs need to be combined in order to produce the eventual percept. Exactly how this combination is accomplished is currently unknown. The results of the experiments presented here suggest that when strong figural cues are available, they can over-ride the motion derived shape estimates. However, our experiments leave open the issue of the combination rules when the figural cues are weakened, for instance by having unfamiliar shapes which are not associated with any specific 3-D structures. Confining our attention to the case where the figural cues are strongly evocative of specific 3-D geometries, we can outline a simple processing strategy for the analysis of dynamic sequences. The strategy involves verifying whether the figuraly derived shape at different time instants is the same. A rigid object is expected to maintain the same shape at all times. Changes (over time) in the figuraly derived 3-D shapes would suggest nonrigidity even though the structure-from-motion (SFM) process might recover a rigid structure. Although adequate to account for our present experimental results, this is probably an oversimplification. Both the static and dynamic shape recovery processes are likely to be important for the analysis of arbitrary motion sequences. Briefly, the simple model these results suggest requires determining the 3-D shape of the object seen in the motion sequence from static image attributes at frequent intervals. Depending on the constancy (or lack thereof) of the recovered shape at different times, the model predicts whether the object would be perceived as rigid by human observers. Relative scores of perceived non-rigidity were obtained as described in Section 2.2. The results from the healthy observers and the patients are shown in Fig. 6 . They are plotted as perceived non-rigidity scores as a function of amount of depth noise added. For all of the plotted points, we determined the coefficients of correlation (between amount of depth-distortion and perceived non-rigidity score) and their statistical significance. Healthy observers exhibited an increased percept of non-rigidity with higher levels of added noise when the sequences included figural cues (i.e. objects were presented with line segments). The correlation between these two variables was high and statistically significant. However, no statistically significant correlation was evident when the objects were presented only as collections of vertices. Patients AMG and JT also failed on the 3-D-structure from the motion test. Similar to other motion impaired patients, who in separate tests had been found to be highly compromised on their structure from motion abilities [36, 37] also exhibited the same pattern of resultsa strong positive correlation between added noise and perceived non-rigidity in the presence of figural cues, but not without them.

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