SMCA: a general model for mining asynchronous periodic patterns in temporal databases Abstract-Mining periodic patterns in time series databases is an important data mining problem with many applications. Previous studies have considered synchronous periodic patterns where misaligned occurrences are not allowed. However, asynchronous periodic pattern mining has received less attention and only been discussed for a sequence of symbols where each time point contains one event. In this paper, we propose a more general model of asynchronous periodic patterns from a sequence of symbol sets where a time slot can contain multiple events. Three parameters min rep, max dis, and global rep are employed to specify the minimum number of repetitions required for a valid segment of nondisrupted pattern occurrences, the maximum allowed disturbance between two successive valid segments, and the total repetitions required for a valid sequence. A 4-phase algorithm is devised to discover periodic patterns from a time series database presented in vertical format. The experiments demonstrate good performance and scalability with large frequent patterns. P ATTERN mining plays an important role in data mining tasks. Various patterns have been introduced for different applications, e.g., frequent item sets [1] , [6] and sequential patterns [2] , [14] , [18] for transaction databases, frequent episodes [10] , [11] , [12] in event sequences, and frequent continuities [15] , [7] for intertransaction association. Periodic patterns are recurring patterns that have temporal regularities in time-series databases. Periodic patterns exist in many kinds of data. For example, tides, planet trajectories, somite formation, daily traffic patterns, and power consumptions all present certain periodic patterns. There are many emerging applications, including stock market price movement, earthquake prediction, telecommunication network fault analysis, repeat detection in DNA sequences and occurrences of recurrent illnesses, etc.. The discovery of patterns with periodicity has been studied in several works [3] , [4] , [5] , [9] , [13] . For example, Ozden et al. proposed the mining of cyclic association rules that reoccur in every cycle of the time span of the temporal database [13] . Han et al. considered imperfect periodic patterns that reoccur for at least minconf percent of the cycles [4] . Berberidis et al. further proposed an approximate periodicity detection algorithm [3] . However, these studies considered only synchronous periodic patterns and did not recognize the misaligned presence of patterns due to the intervention of random noise. For example, assume that a temporal database contains a periodic pattern, "Beer and Diaper," on Friday nights, from January to March. However, in April, the business has a big promotion for beer every Saturday. Therefore, many customers would buy beer on Saturday instead of Friday because of this promotion. In this case, it would be desirable if the pattern can still be recognized when the disturbance is within some reasonable threshold. Therefore, in [17] , Yang et al. extended the idea to find asynchronous periodic patterns.. Yang et al.'s asynchronous periodic pattern problem aims at mining the longest periodic subsequence which may contain a disturbance of length up to a certain threshold. Formally, a valid subsequence with respect to a pattern P in a sequence D is a set of nonoverlapping valid segments, where a valid segment has at least min rep contiguous matches of P and the distance between any two successive valid segments does not exceed a parameter max dis. A valid subsequence with the most overall repetitions of P is called its longest valid subsequence. However, this model has some problems.. . First, this model only focused on mining periodic patterns in temporal sequences of events. However, in real-world applications, we may find multiple events at one time slot in terms of various intervals (e.g., hour, day, week, etc.) as discussed in previous works [4] , [5] , [13] . We refer to such databases as sequences of event sets. . Second, this model only focused on mining the longest sequence of a pattern, which can only capture part of the system's behavior. For example, in the case when two successive, nonoverlapped segments with a disturbance larger than max dis, only the larger segment will be reported. Taking another example, as shown in Fig. 1a , it is possible that two overlapped subsequences, (S 1 ; S 3 ) and (S 2 ), are controlled by two network administrators. Therefore, reporting the longest subsequence will miss the other subsequence. . Third, in order to discover the longest subsequence, a longer segment can be broken into smaller segments when two segments overlap. Take Fig. 1a , for example. Suppose the min rep is 2, the longest subsequence for pattern ðA; Ã; ÃÞ which can be connected by segments:. , and (D 9 $ D 10 ) according to the definition in [17] . This, however, has to break a longer segment (both S 2 and S 3 ) into smaller segments to avoid overlapping. In fact, there can be several subsequences with the most overall repetitions, e.g., (. , and (D 8 $ D 10 ) is another subsequence with seven repetitions. We argue that a segment should be extended to its longest possibility and the overlapping of two segments should be considered as two separate sequences. . The final problem regards the definition of a segment's end position, which affects whether or not two segments overlap. Instead of using the pattern's last occurrence as the segment's end position, the end position of a segment is defined as the period's end for the last occurrence of the pattern. To illustrate this, the end position of segment S 1 in Fig. 1a is 9 according to the definition in [17] . Therefore, segment S 1 and S 2 overlap. If we use the pattern's last occurrence as the segment's end position, as shown in Fig. 1b , the end position for segment S 1 will be 7 and segment S 1 and S 2 will not overlap. This consideration is from the application of inventory replenishment where an event occurs ahead of time as addressed in [17] . In order to connect such occurrences, the end of a segment is better defined as the event's last occurrence. To address these problems, in this paper, we discuss asynchronous partial periodic patterns in eventset sequences where each time slot may contain multiple events.. Three parameters, namely, min rep, global rep, and max dis are employed to qualify valid patterns and the subsequence containing them, where this subsequence, in turn, can be viewed as a list of valid segments of perfect repetitions interleaved by a disturbance. Each valid segment is required to be of maximal and at least min rep contiguous matches of the pattern, and the distance of each piece of disturbance is allowed only up to max dis. A sequence is termed valid if and only if the overall repetitions of the pattern are greater than global rep. We propose a series of algorithms for mining asynchronous periodic patterns, proceeding from mining valid segments for 1-patterns to mining periodic segments for i-patterns. We first devise an algorithm (called SPMiner) to discover all valid segments for each single event from temporal database presented in vertical format. The idea is to trace p possible segments for period p. When examining a time slot T i for the given event, if T i minus the last position for the segment maintained in T i %p equals p, this segment is extended and its last position is updated. Then, two algorithms, MPMiner and CPMiner, are devised to discover valid segments for multievent 1-patterns and i-patterns. To avoid additional scans over the temporal database, we use the discovered valid segments and combine them using depth first enumeration, thus reducing redundant generation and testing. Finally, all valid segments with respect to a pattern can be combined to form an asynchronous subsequence by APMiner. In summary, this paper make the following contributions in this paper:. . A more general model of asynchronous periodic patterns is proposed to allow the mining of all patterns, not only in a sequences of events, but also in a temporal database of event sets. . A dynamic hash-based validation mechanism is devised to discover all patterns using a single scan of the temporal database. . There is no candidate pattern generation, as required for Apriori-like algorithms. . Finally, the complexity analysis and experiments of the proposed algorithm show great scalability with large data sets. The remaining parts of the paper are organized as follows: We summarize some related research in Section 2. In Section 3, we define the problem of asynchronous periodic pattern mining for temporal database. Section 4 presents our algorithm for mining asynchronous periodic patterns from temporal database and Section 5 compares the proposed algorithm with that in [17] . Experiments and performances of the algorithm study are reported in Section 6, and our conclusion are presented in Section 7. In this paper, a general model for asynchronous periodic pattern mining is defined. A four-phase algorithm which includes singular periodic pattern mining (SPMiner), multievent periodic pattern mining (MPMiner), complex periodic pattern mining (CPMiner), and asynchronous sequence mining (APMiner) is devised to solve the problem. One of the main contributions of this paper is that SMCA is devised to discover all patterns via two scans of the temporal database. Transforming horizontal database into their vertical formats can be done in a straightforward way. Also, SMCA can be modified for incremental mining with proper management of the mining results (both final and intermediate). Maintaining a maximal patterns can also save additional time for unnecessary mining. More works will be reported in the near future.. Kuo-Yu Huang is currently a PhD student of computer science information engineering at National Central University, Taiwan, ROC. He is also a member of the Database Laboratory. His research interests include the design of efficient, scalable, and flexible algorithms for various data mining techniques such as intratransaction rule, intertransaction rule, and temporal data mining. He has published more than 10 books on computer programming language in Chinese.. Chia-Hui Chang received the BS degree in computer science and information engineering from National Taiwan University, Taiwan, in 1993 and received the PhD degree in the same department in January 1999. She is an assistant professor in the Department of Computer Science and Information Engineering, National Central University in Taiwan. She worked as a postdoctoral in Chun-Nan Hsu's group after graduation, then joined National Central University from August 1999. Her research interests include information retrieval, knowledge discovery from databases, machine learning, and Web related research. She is a member of the IEEE Computer Society.. . For more information on this or any other computing topic, please visit our Digital Library at www.computer.org/publications/dlib. In this section, we compare the mining procedure of our proposed algorithm, SMCA, with the LSI algorithm proposed in [17] . Furthermore, we discuss the solution when the data is too long/large to fit in memory space. There have been a number of recent studies in periodic pattern mining. For example, cyclic association rules proposed by Ozden et al. [13] , partial periodic patterns by Han et al. [4] , [5] , and asynchronous periodic patterns by Yang et al. [16] , [17] . However, each of these studies has a different definition for periodicity. Special terms like partial versus full, perfect versus imperfect, and synchronous versus asynchronous are used and need to be clarified.. The so called full periodicity specifies the behavior of the time series at all points in the period, while partial periodicity specifies the behavior at some but not all points in time. Partial periodicity is a looser kind of periodicity than full periodicity and its application is more general because of the mixture of periodic events and nonperiodic events in real-world data. Full periodicity search has been studied for time series of numerical values, while partial periodicity search is mainly applied for symbolic patterns. For example, Ozden et al. define the problem of discovering cyclic association rules that display regular cyclic variation over time [13] . This motivation is based on the observation that an association rule may not have the user-specified minimum confidence or support over the entire time spectrum, but its confidence and support may be above the minimum threshold within certain time intervals. In this work, a periodic pattern is expressed as c ¼ ðp; l; oÞ, where a pattern p occurs in every l time unit starting at the oth time unit (o l). Note that what Ozden et al. considered are partial periodic patterns with perfect periodicity in the sense that the pattern reoccurs in every cycle, with 100 percent confidence. By studying the interaction between association rules and time, they applied three heuristics: cycle pruning, cycle skipping, and cycle elimination to find cyclic association rules in transactional databases.. Since real-life patterns are usually imperfect, Han et al. [4] , [5] presented several algorithms to efficiently mine partial and imperfect periodic patterns by exploring some interesting properties related to partial periodicity, such as the Apriori property and the max-subpattern hit set property, and by shared mining of multiple periods. In order to tame the restriction cyclic association rule, Han et al. used confidence to measure how significant a periodic pattern is. The confidence of a pattern was defined as the occurrence count of the pattern over the maximum number of periods of the pattern length in the temporal database. For example, ða; Ã; bÞ is a partial pattern of period 3 (The character "*" is a "don't care" character, which can match any single set of events); its occurrence count in the event series "a{b,c}baebaced" is 2; and its confidence is 2/3, where 3 is the maximum number of periods of length 3.. Nevertheless, the proposed mining model works only for synchronous periodic pattern mining.. Therefore, Yang et al. [16] , [17] proposed to mine for asynchronous periodic patterns that are significant using a subsequence of symbols. Two parameters, min rep and max dis, are employed to qualify valid patterns. The intuition is that a pattern needs to repeat itself at least a certain number (min rep) of times to demonstrate its significance and periodicity. On the other hand, the disturbance between two valid segments has to be within some reasonable bound (max dis). Otherwise, it would be more appropriate to treat such a disturbance as a signal of "change of system behavior" instead of random noise injected into some persistent behavior. A two-step algorithm is devised to first generate potential periods by distance-based pruning, followed by an iterative procedure to derive and validate candidate patterns and locate the longest valid subsequence for 1-patterns (called LSI). For patterns satisfying min rep and max dis requirements, their model will return the subsequence with the maximum overall repetitions. The second step then applies an Apriorilike algorithm (called level-wise search) to generate the subsequences of i-patterns based on valid subsequences of all ði À 1Þ-patterns with the same period length. As argued above, this model considers only sequences of symbols, and the longest subsequences can only capture part of the system's behavior. Therefore, a more general model is proposed in this paper. In this section, we report on a performance study of the algorithms proposed in this paper and an application of periodic pattern mining in a real data set. We first investigate the performance of SPMiner for singular patterns and compare the result with the LSI (Longest Sequence Identifier) algorithm proposed in [17] using synthetic data. We also compare two multievent pattern mining algorithms, TBE and SBE. Then, complex pattern mining using CPMiner is also evaluated. Finally, the algorithms are applied to real data for periodic pattern mining.

O O O O O O O O O O O O O O O O O O O O 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 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 B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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A High-Order Fast Direct Solver for Singular Poisson Equations We present a fourth order numerical solution method for the singular Neumann boundary problem of Poisson equations. Such problems arise in the solution process of incompressible Navier-Stokes equations and in the time-harmonic wave propagation in the frequence space with the zero wavenumber. The equation is first discretized with a fourth order modified Collatz difference scheme, producing a singular discrete equation. Then an efficient singular value decomposition (SVD) method modified from a fast Poisson solver is employed to project the discrete singular equation into the orthogonal complement of the null space of the singular matrix. In the complement of the null space, the projected equation is uniquely solvable and its solution is proven to be a solution of the original singular discrete equation when the original equation has a solution. Analytical and experimental results show that this newly proposed singular equation solver is efficient while retaining the accuracy of the high order discretization. In this paper, we consider high-order solutions for the Poisson equation on a rectangular domain with Neumann boundary condition dp dn = b(x, y) on ∂ , (1.2) where ∂ is the boundary of the rectangular domain , n is the normal vector of the boundary of the computational domain, and and in acoustics, elastics, and electromagnetics in the time-harmonic wave propagation in the frequency space [1, 12] with the zero wavenumber. It is well known [3, 11, 19] that the Neumann problem of the Poisson equation is singular. A singular linear system is solvable if and only if its right hand side is orthogonal to the null space of the singular matrix [3, 11] . The condition number 1 of a singular matrix is infinity. Thus in general, singular problems are difficult to solve efficiently and accurately. For the singular Neumann problem of the Poisson equation, however, there exist several efficient solvers, including Schumann and Sweet's cyclic reduction [19] , Golub, Huang, Simon and Tang's generalized eigen-decomposition [11] , Bialecki and Remington's Fast Poisson solver-based eigen-decomposition [3] , and the Kaczmarz projection method that Tanabe introduced for singular systems [24] .. The cyclic reduction is fast and has a complexity of O(n 2 log n) on a square grid of size n × n. But Schumann and Sweet did not discuss how the singularity is treated and how cyclic reduction affects the accuracy of the solution of the discrete system. The generalized eigen-decomposition employed by Golub et al. has a complexity of O(n 3 ); however, it singles out the null space of the singular matrix, successfully avoiding error enlargement and thus retaining the discretization accuracy. Their method also allows non-uniform meshes and hence is applicable to more general singular problems. The method of Bialecki and Remington is also an eigen-decomposition method, which is a modification of Hochney's fast Poisson solver with the singularity singled out for special treatment. Their method thus retains accuracy of discretization and also achieves a high efficiency of O(n 2 log n). The Kaczmarz projection method is an iterative method that keeps the solution component in the null space of the matrix fixed for each iteration. Thus, it is also a decomposition method which iteratively decomposes the equation into singular and non-singular problems. The Kaczmarz method was later combined with multigrid procedures [7] to improve its convergence (efficiency of the multigrid Kaczmarz method was analyzed by Shapira [20] ).. The singular solver proposed in this paper is similar to that of Bialecki and Remington in utilizing FFT for efficient matrix decomposition but with a reduced programming complexity for singularity treatment. In Bialecki and Remington's method, the original discrete singular equation is first perturbed by adding a term to the right hand side of the equation to ensure the solvability of the perturbed equation. They proved that the solution of the perturbed equation is a least square solution of the original singular problem. Our method differs from their method in two places. First, we do not perturb the singular discrete equation. We project the singular equation into the orthogonal complement of the null space of the singular matrix. In the orthogonal complement of the null space, the projected equation is non-singular and always uniquely solvable regardless of the solvability of the original singular discrete system. The second difference (see Section 3) is that we ignore the projected equation in the null space and only solve the projected equation in the orthogonal complement of the null space. We have proven that the solution of the projected equation in the complement of the null space is a solution of the original singular discrete equation when the original is solvable, and is a least-squares solution of the original equation when the original equation is not solvable. Thus, comparing with Bialecki and Remington's method, our method does not compute the perturbation to ensure the solvability, and also has avoided a process to determine a solution of the projected equation in the null space.. High-order discretization methods for the Laplace operator have been investigated for a long time. Collatz studied several finite difference methods for the 2-D Laplace operator in 1960 [10] . One of the fourth-order methods Collatz studied is a square stencil nine-point scheme which is a popular choice for the Dirichlet problem of Possion equations. In 1975, Lynch and Rice introduced a systematic procedure called HODIE [16] for calculating the coefficients of finite difference discretization formulas for general elliptic equations for almost "any" numerical order. The HODIE procedure was employed by Boisvert in 1981 to discretize the Helmholtz equations [5] and was applied in 1985 to the Neumann problem of the Helmholtz equation (see [18, pp. 199-200] ). Another finite difference method for obtaining high-order discretization of the Laplace operator is the Padé-type high-order approximation of Singer and Turkel [21] . A different approach to high-order discretization is the finite element type schemes, among which are Kaufman and Warner's [14] RayleighRitz-Galerkin method with tensor product B-splines and Bialecki and Fairweather's highorder orthogonal spline collocation method [2] .. In this paper we modify the Collatz's popular nine-point scheme for Neumann problems and obtain a fourth order formula which is more general than both the Collatz formula and Boisvert's formula given in ( [18, pp. 199-200] ).. While our discussion of the singular Poisson solver is restricted to Poisson equations, it is readily extendible to singular Helmholtz equations with either Dirichlet or Neumann boundary conditions. For a Helmholtz equation arising in the time harmonic wave propagation, when the square of the wavenumber happens to be equal to an eigenvalue of the Laplace operator in magnitude, the equation becomes singular. With the proposed singular treatment modified for the non-zero wavenumber cases, singular Helmholtz equations can be solved efficiently and accurately on rectangular domains with uniform meshes chosen, or combined with domain decomposition methods [8, 17] to produce fast and accurate subdomain solvers. This paper is organized as follows. Fourth order discretizations of the equation and the Neumann boundary condition are presented in Section 2. A decomposition, projection, and solution method for the singular discrete equation are discussed in Section 3. Section 4 contains an error analysis and an efficiency comparison with second order methods. Finally, testing results are presented in Section 5. Section 6 gives the conclusion. We present a fourth order fast solver for the singular Neumann boundary problem of Poisson equations on a rectangular domain. A modified Collatz finite difference scheme is used to discretize the Laplace operator. This discretization produces a singular discrete equation which is projected into the orthogonal complement of the null space of the singular matrix and solved in the complement of the null space. It is proven that the solution of the projected equation is a solution of the original singular discrete equation when the original equation is solvable. The projection of the singular equation into the complement of the null space utilizes the fast Fourier transform whose application to Poisson equations was pioneered by Hockney. As both analytical and testing results show, our proposed SVD keeps the accuracy obtained from the high-order discretization while maintaining high efficiency.

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


Progressive Transmission of Images using MAP Detection over Channels with Memory We propose a new Maximum A Posteriori (MAP) detector, without the need for explicit channel coding, to lessen the impact of communication channel errors on compressed image sources. The MAP detector exploits the spatial correlation in the compressed bit-stream as well as the temporal memory in the channel to correct channel errors. We rst present a technique for computing the residual redundancy inherent in a compressed greyscale image (compressed using VQ). The performance of the proposed MAP detector is compared to that of a memoryless MAP detector. We also investigate the dependence of the performance on memory characteristics of the Gilbert-Elliott channel as well as average channel error rate. Finally, we study the robustness of the proposed MAP detector's performance to estimation errors. Traditionally, bit errors caused by a noisy communication channel have been dealt with by inserting redundancy into the transmitted bit stream via channel coding. Shannon's source-channel separation theorem 1, 2] shows that a source code and a channel code can be designed separately and used in tandem without loss of optimality. However, in the presence of delay/complexity constraints, joint source-channel coding outperforms tandem coding 3, 4, 5] and minimizes the transmission bandwidth 6, 7] .. In many practical situations, delay constraints as well as imperfect knowledge about the source statistics result in a suboptimal source coder. This suboptimality is re ected in the fact that the source encoder does not eliminate all the redundancy in the source. The remaining redundancy in the coded bit stream is referred to as its residual redundancy 8] . Reduction in the redundancy of the source results in increased sensitivity to channel noise, necessitating techniques to correct channel errors. Standard channel coding techniques, which attempt to correct channel errors by reinserting some redundancy into the coded symbol stream, result in an increase in the number of bits transmitted across the channel. An alternative technique uses Maximum A Posteriori (MAP) detection to exploit the residual redundancy after source coding without the overhead of channel coding 8, 9, 10].. Several MAP-based channel error correction techniques for memoryless channels have been studied in recent work 9, 11, 12, 13] . In contrast to memoryless channels which are characterized by uncorrelated errors, many real-world channels, such as wireless channels, tend to have errors occuring in clusters separated by relatively long error-free gaps 14] . This tendency of a channel to generate clusters of errors is referred to as its \memory." Among the causes of channel memory are slow fading, natural phenomena such as lightning strikes, and switching transients. MAP detection for channels with memory has been recently investigated in 6, 15] using a Polya contagion urn based model for channel memory and in 10] using a Gilbert channel model.. Progressive transmission (PT) of images enables rapid recognition of the image content at the receiver as well as early interruption of transmission (if the image being sent is not desired) resulting in savings in transmission bandwidth 16, 17] . Data encoded by full-search vector quantization (VQ) can be transmitted progressively using a full-search VQ progressive transmission tree (also called a PT tree). The PT tree is designed by organizing the codebook using one of several alternative techniques including Principal Component Partitioning (PCP) 18]. PCP-based codebook organization reorders the residual redundancy in the codeword bit-planes thus enabling error correction using MAP techniques and helps reduce the impact of noise on VQ 13] .. This paper considers the impact of burst errors generated by a Gilbert-Elliott channel 19, 20] , a commonly used model for channels with memory, on VQ distortion performance for progressive image transmission. The proposed coding scheme, combining PCP-based VQ coding and MAP decoding, can be viewed as a joint source-channel coding scheme, since the VQ encoder reduces the source entropy (thus corresponding to source coding) while the encoder output retains some residual redundancy (corresponding to channel coding). Note that, while the MAP detector can be considered as a channel decoder, the system does not have an explicit channel encoder. We investigate the dependence of the proposed MAP detector's error correction performance on channel memory and on average error rate. In addition, we examine the performance gain achieved by exploiting the channel memory relative to a memoryless MAP detector used on an interleaved channel.. The paper is organized as follows. We describe the Gilbert-Elliot channel model, and de ne some important channel parameters in Section 2. We then quantify residual redundancy and suggest a way to compute it for real images in Section 3. We describe the concept of interleaving, a commonly used technique for eliminating the temporal memory of a channel, in Section 4. The MAP detection technique for channels with memory is formulated in Section 5. Experimental results on the dependence of the MAP detector's performance on channel parameters and on the robustness of the MAP detector to estimation errors are presented in Section 6. Finally, our conclusions are presented in Section 7. In this paper we have presented a joint source-channel coding scheme for the transmission of grayscale images over channels with memory such as the Gilbert-Elliott channel. Taking advantage of both temporal correlation due to channel memory and spatial correlation in the form of residual redundancy in the encoded bit-stream due to the suboptimality of the source code, a MAP detector, referred to as a spatio-temporal MAP (ST-MAP) detector, has been proposed. The ST-MAP detector exploits the memory of the channel to provide superior results to that achieved by a S-MAP (memoryless) detector. This improvement is achieved by the ST-MAP detector as a consequence of its ability to correct a greater number of errors while introducing a smaller number of new errors due to channel state misestimation. The ST-MAP detector incorporates channel state information in the Viterbi algorithm and thus takes advantage of channel memory despite the use of interleaving. Additionally, non-causal source distributions, characteristic of most real world images and better able to represent image statistics, have been incorporated in this work. The dependence of the MAP detector's performance on the channel memory (as well as ) has been studied. Finally, the sensitivity of the MAP detector to errors in estimating channel statistics has been investigated. The major conclusion of this paper is that signi cant performance bene ts can be obtained by exploiting both the temporal and spatial correlation in image transmission. The spatial correlation, due to dependencies on neighboring pixels, helps the decoder in estimating the transmitted bits. More surprisingly, temporal correlation, due to the presence of memory in the channel, can also be taken advantage of by properly modifying the receiver structure. The resulting performance improvement can be dramatic, both qualitatively and quantitatively. Joint source-channel coding techniques for more complex burst error channel models as well as for video sources are currently being investigated. Figure 1 : Gilbert-Elliott channel model with GOOD state error probability = and BAD state error probability = . Also, P GB =Pr(BjG) and P BG =Pr(GjB). In the simpler Gilbert model, = 0.

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The M/M/1 queue with inventory, lost sale, and general lead times We consider an M/M/1 queueing system with inventory under the (r, Q) policy and with lost sales, in which demands occur according to a Poisson process and service times are exponentially distributed. All arriving customers during stockout are lost. We derive the stationary distributions of the joint queue length (number of customers in the system) and on-hand inventory when lead times are random variables and can take various distributions. The derived stationary distributions are used to formulate long-run average performance measures and cost functions in some numerical examples. In classical inventory models, arriving demands are satisfied immediately if there is enough on-hand inventory. Most of these models consider optimization problems which chooses the optimal policy or optimal value of decision variables without computing the stationary distribution of inventory states. Nevertheless there are some studies that have derived stationary distributions to formulate long-run average cost functions which are used for optimization. Sahin [6] considered (s, S) inventory system and general random demand process with fixed lead time and backordering. He derived time dependent and stationary distribution to derive approximations for optimal control policy.. Focusing on lost sale problems, let us take a brief look at some of these studies. Mohebbi and Posner [4] considered a continuous-review inventory system with compound Poisson demand, Erlang as well as hyper-exponentially distributed lead time and lost sales. They derived the stationary distribution of inventory level for the purpose of formulating long-run average cost functions with/without a service level constraint. Mohebbi and Hao [5] considered inventory system with compound Poisson demand, Erlang-distributed lead times, random supply interruptions and derived the stationary distribution of the inventory level under an (r, Q)-type control policy.. Many recent studies deal with complex integrated production-inventory systems or service-inventory systems. In these models satisfying each demand needs on hand-inventory and involves a process or service that takes some time. Productioninventory or service-inventory systems can be discussed in connection with integrated supply chain management. In these systems, an important issue is the reaction of inventory management to queueing of demands. Interaction of production/service processes with attached inventories can be described by queueing systems with inventories. Queueing systems with inventory in comparison with previous inventory models are more general and realistic. Also in a supply chain, every segment can be adequately described by a queueing system with inventory.. An early contribution is [9] where a light traffic heuristic was derived for an M/G/1 queue with an attached inventory. A few analytical models in this field have been developed up to now. Berman and Kim [2] considered a service system with an attached inventory, with Poisson customer arrival process, exponential service times and Erlang distribution of replenishment. Their formulation was a Markov decision problem to characterize an optimal inventory policy as a monotonic threshold structure which minimizes system costs. Berman and Kim [3] presented an extension where revenue is generated upon the service. They found an optimal policy which maximizes the profit.. Schwarz and Daduna [7] considered an M/M/1 queue with inventory under continuous-review with backordering when lead times are exponentially distributed. They computed performance measures and derived optimality conditions under different order policies. For evaluating performance measures and steady state probabilities they presented an approximation scheme. Also Schwarz et al. [8] considered a similar model with lost sales of customers that arrive during stockout and different inventory management policies. They derived stationary distributions of the joint queue length and inventory processes in explicit product form.. In the last two models mentioned above, lead times are supposed to be exponentially distributed. It is obvious that removing this assumption would provide more generality. In this paper, we consider an M/M/1 queueing system with inventory with infinite waiting room and lost sales when lead times can take any probability distribution or can have fixed values. The aim of our research is to derive joint stationary distributions of joint queue length and inventory processes. These distributions are used to provide long-run average cost functions which can be used for optimization problem to find optimal values of the decision variables. In a queueing system with an attached inventory, customers arrive one by one and require service. In the M/M/1/∞ queue with inventory, customers arrive according to a Poisson process with arrival rate λ. There is a single server with unlimited waiting room and an inventory with unlimited capacity of items. Service times are exponentially distributed with parameter µ.. In our present model, during the period that there are some on-hand inventory, arriving demands join the queue and if there is no customer in the system the 2 arriving demand directly takes service. But customers, who arrive during a period when the server waits for the replenishment order, are rejected and lost. Each customer needs exactly one item from the inventory for service, and the on-hand inventory and number of customers in system decreases by one at the moment of service completion. When the on-hand inventory reaches zero, customers in the queue wait for the next replenishment and the server will serve the customer which is at the head of the line at the instant when the next replenishment arrives at the inventory. Replenishment lead times are random variables with known probability distribution (which could be degenerate at one point) and independent of on-hand inventory and number of customers in system.

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New materials in high voltage technology Assets in high voltage technology have to meet harsh service conditions over long lifetimes of 40 years or more. Due to environmental concerns, substitution of conventional insulating materials becomes a necessity. Because robustness and sustainability are serious requirements, only few new materials are really breaking through. At present some promising material technologies emerge with great potential applicability in high voltage engineering. This paper discusses especially nanocomposites and high temperature superconductors. In high voltage technology the assets have to meet harsh service conditions over long lifetimes of 40 years or more. Moreover, due to environmental concerns, substitution of conventional insulating materials becomes a necessity. For instance cross linked polymers, mineral oil and SF 6 are becoming considered non-sustainable solutions in the near future. Currently, these insulating materials are the cornerstone of many high voltage components. Because robustness and sustainability are serious requirements, only few new materials are breaking through. In general, in HV constructions new material inventions require interfacial matching with existing materials. For example for paper/oil insulation in submarine HVDC cables new polymeric insulation formulations are upcoming. However, interfaces with semiconducting layers influence the threshold field for space charge accumulation. This kind of complexity implies much longer development times than usual, notwithstanding the fact that at present some promising material technologies emerge with great potential applicability in high voltage engineering. To elucidate this some recent progress will be discussed. The topics are nanodielectrics, nanofluids, high temperature superconductors and electroactive polymers. Nanocomposites show great potential for high voltage engineering. With the right material combination, significant improvements of DC breakdown strength, PD resistance and space charge behavior are possible. The higher time to breakdown and increased resistance to electrical ageing that can be observed in nanocomposites also means more reliable systems. However, the properties of nanostructured insulation material have to be considered at the design of high voltage components, in order to get the most out of this novel material.. The increasing and intermittent load flows in future grid scenarios supersede the possibilities of many existing designs. To accommodate all high level requirements we arrive at the design limits of HV equipment. Nano and micro meter particles and layers help to expand the limits. Moreover, adding high temperature superconductors to the HV design makes possible higher power capacity, lower AC losses, intrinsic fault current limitation, better power flow control, smaller footprint and less emissions.

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An object-based approach for detecting small brain lesions: application to Virchow-Robin spaces This paper is concerned with the detection of multiple small brain lesions from magnetic resonance imaging (MRI) data. A model based on the marked point process framework is designed to detect Virchow-Robin spaces (VRSs). These tubular shaped spaces are due to retraction of the brain parenchyma from its supplying arteries. VRS are described by simple geometrical objects that are introduced as small tubular structures. Their radiometric properties are embedded in a data term. A prior model includes interactions describing the clustering property of VRS. A Reversible Jump Markov Chain Monte Carlo algorithm (RJMCMC) optimizes the proposed model, obtained by multiplying the prior and the data model. Example results are shown on T/sub 1/-weighted MRI datasets of elderly subjects. We applied a marked point process framework to derive a model for multiple small brain lesions detection that was optimized by a RJMCMC algorithm. A special feature of this approach is the object based modeling. In our application example, VRS are not considered at a voxel level but as geometrical shapes. This induces robustness with respect to noise and, thus, a good detection sensitivity. The sensitivity is further improved by the prior model which embeds specific interactions. The clustering interaction appears to be well adapted to VRS. Future work will consist of improving the specificity further by removing false positives.. The proposed model involves several parameters. The parameters defining the data term are derived from the intensity statistics of the dataset provided that a segmentation into the compartments CSF, WM, and GM is available. The prior model parameters and the hyper-parameters weighting the prior model and the data term were calibrated. Estimating these weights would be an improvement toward a fully automatic approach. However, using the same parameter values for all the datasets yielded satisfactory results which proves the robustness of the approach with respect to the parameters involved. Parameters of the prior model are relatively data independent. Therefore, spending extra computation time for parameter estimation appears unnecessary here.. The usual drawback of MCMC algorithms is the computation time necessary for model optimization, which may become critical in this 3-D case. Therefore, we have reduced the volume by using the filters defining the data term. Depending on the number of detected VRS, the computation time varies between 10 min and 2 hours on a personal computer (Intel 750-MHz processor). The optimal choice of the weighting between the different moves in the RJMCMC algorithm is considered an open issue.. Future work is twofold: we will study the correlation of VRS with clinical variables to address their significance for the process of aging. Second, this model may be modified for similar problems, such as detecting small lesions in Multiple Sclerosis. Our approach is quite general and suitable for detecting multiple lesions. However, for other lesion types, the object geometry and object relations in space must be revised and adapted to the target application. The target application of the algorithm described above is the detection of VRS in MRI brain data sets. Since VRS are a typical sign of an aged brain, we selected a random subsample of datasets acquired in a clinical study of minimal cognitive dysfunction in a population of elderly subjects [27] .. All 3-D datasets were acquired on a Siemens Vision 1.5-T scanner using a -weighted MPRAGE protocol (TR 11.4 ms, TE 4.4 ms, 128 sagittal slices, matrix 256 256, voxel size 0.9 0.9 1.5 mm). An affine transformation using b-spline interpolation [25] was applied to yield a dataset aligned with the stereotactical coordinate system [16] at an isotropical resolution of 1 mm.. For all experiments, we used the same parameters: , , , , , and . The huge value of parameter is used to forbid overlapping segments in the result. Other parameters were set by trials on a single dataset.

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Some consistent finite element formulations of 1-D beam models: a comparative study A consistent Finite Element formulation was developed for fou r classical 1-D beam models. This fo rmu lation is based upon the solutio n of the homogeneous differential equation (or equations) associated with each mode l. Results such as the shape functions, stjffness matrices and consistent force vectors for the constant section beam were found. Some of these results were compared wilh the corTespood ing ones obta ined by the standard Finite Element Method (i.e. using polynom ial expansions for the fie ld variables).Some of the diffic ulties reported in the literature concerning some of these models may be avo ided by this technique and some numerical sensitivity analysis on this subject are presented. An alternative to the earlier described approach is to transform tbe corresponding boundary value equations into weak fotms that are suitable for appljcation of the FEM. In this case the following results are reached:. Sti ffness matrix for Navier-Bernoulli and Timoshenko beam models: ln the case of the Navier-Bemoulli beam and in the beam-column model, the expressions for matrices ll and J2 can he written as follows:. For the Timoshenko beam and the beam-colwnn model with shear strain the expressions for the earlier mentioned matrices become:. If the shape functions H. correspond to the ones obtained in the previous sections for the beam of constant section and are used in eqns (25) and (26), then the results forK and f~q are identical to those presented in Appendix B. However these shape functions can be introduced in the fomlUla even for the cases of beams with variable section and the result obtained then represents a good approximation of the exact solution, which in many cases cannot be analytically found.. In order to estimate the accuracy of this type of approximation, the stiffness matrix of some constant section beam models wi ll be computed using eqns. (25) w ith shape functions corresponding to different and simpler beam models. Namely, two cases wi ll be analysed:. (a) Beam-column model using Hennitian polynomials as shape functions. (b) Beam-colum n mode l with shear strain using the shape functions of the Timoshenko beam model. The use of shape functions derived from the solutions of the homogeneous differential equations governing a given beam model in the FEM (these functions are not necessarily polynom ials), leads to results that are much more accurate than those obtained with the standard polynomial ft.mctions of the FEM when one element is used. The consistent formulation avoids some of the inconsistencies reported in the literature concerning the use of finite elements to model beams with shear strain.. The consistent shape functions determined may also be used to obtain the vectors and matrices of elements with longitudinal variation of the cross sections using the Finite Element technique. The results found in this way, although approximate, would be more accurate than those obtained with the standard polynomial shape functions.. However, the determination of the consistent shape functions demands an important programming and computing effort for each one of the different beam models considered, un like standard polynomial functi ons which are much more versatile.

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Gene regulated car driving: using a gene regulatory network to drive a virtual car Abstract This paper presents a virtual racing car controller based on an artificial gene regulatory network. Usually used to control virtual cells in developmental models, recent works showed that gene regulatory networks are also capable to control various kinds of agents such as foraging agents, pole cart, swarm robots, etc. This paper details how a gene regulatory network is evolved to drive on any track through a three-stages incremental evolution. To do so, the inputs and outputs of the network are directly mapped to the car sensors and actuators. To make this controller a competitive racer, we have distorted its inputs online to make it drive faster and to avoid opponents. Another interesting property emerges from this approach: the regulatory network is naturally resistant to noise. To evaluate this approach, we participated in the 2013 simulated racing car competition against eight other evolutionary and scripted approaches. After its first participation, this approach finished in third place in the competition. The simulated racing car competition (SRC) aims to design a controller in order to race competitors on various unknown tracks. This competition is based on the open-source racing car simulator (TORCS 1 ). Both scripted and evolutionary approaches can be used to control the virtual car. Within the frame of this competition, we have proposed a new approach based on gene regulation evolved with a genetic algorithm to produce a virtual car controller. Gene regulatory networks are bio-inspired approaches usually used to control virtual cells in developmental models. However, over the past few years, they have been found to be competitive approaches to control agents that have to deal with uncertainty. To our knowledge, this work is the first attempt to use such a controller to drive a virtual car. The competition offers a very unique frame to compare this approach to other ones within a common benchmark. The remainder of this section presents the existing approaches based on an evolutionary process. Further details about them, and about other fully hand scripted, supervised learning or imitation based controllers can be found in [23, 24] Amongst the existing controllers for virtual car racing games that use an evolutionary process to optimize the driver behavior, we can broadly consider two kind of controllers. The first kind are indirect controllers where the inputs are not directly linked to the outputs of the virtual racing car. The inputs, such as track sensors, angle sensors, and speed sensors, are computed and transmitted to driving policies based on hand-coded rules or heuristics that manage steering and throttle controls. Usually, these controllers already know how to drive but an evolutionary algorithm is used to improve and tune the driving policies in order to obtain a competitive driver. They learn how, or are evolved, to drive better than their initial design. The driver presented in [5] , COBOSTAR, is such a controller. It is based on two hand coded driving strategies, one for on-track driving and the other for offtrack driving. The parameters of these strategies are then optimized with CMA-ES. The controllers Autopia in [26] and Mr. Driver in [29, 30] are both based on a modular architecture. The modules are hand-coded heuristics or sets of rules in charge of the basic control of the car (gear, steering wheel, opponents management, etc.). A learning module then detects the segments of the track and adapts the target speed of the car to drive as fast as possible. These kind of controllers are efficient and they have been at the top of the SRC competition since 2009.. The second kind of controllers are direct controllers where sensors are directly mapped to the car effectors. These direct controllers actually learn how to drive the car using its sensors and actuators. These direct controllers can be based on evolved artificial neural networks [2, 34] , genetic programming [1] or the NEAT algorithm [6, 8, 32, 33] . These methods have produced controllers that are specialized and efficient on one specific track. The one in [32] approaches curves from the outside and then cuts inside to reach the curve apex and maximize its speed. However, they can also produce more generalized controllers that drive on most of the tracks but on a safer race line rather than on the optimal race line of the tracks [6] . Because evolving a direct controller from scratch that can drive on-track and manage all car controls and race events is difficult, these controllers are sometimes mixed with hand-coded policies that modify the controller outputs to handle crash recovery or opponents, or that manage specific controls such as gear handling.. The controller we present in this paper is a direct controller. Instead of designing complex hand-coded heuristics, we prefer to evolve the controller to drive the car by using a standard genetic algorithm. In this work, the controller is based on a Gene Regulatory Network (GRN). In order to optimize this GRN, we have used an incremental evolution (as in [5, 34] ) based on different fitnesses that gradually refine the controller's behavior. The experiments presented in this paper show that this controller is able to drive on every kind of track. The performance of the GRN has also been improved by the means of hand-coded contextual modifications of its inputs to make it drive faster and overtake opponents.. The paper is organized as follows. Section 2 presents gene regulatory networks in general, describing the existing computational models and the problems they are currently handling. This section also introduces the computational model we have used in this work. Section 3 describes how the GRN is connected to the car sensors and actuators and how the GRN is incrementally trained with a genetic algorithm to produce a basic driver. This section also demonstrates the capacity of the GRN to naturally handle noisy sensors without any noise filter in-between the GRN and the sensors. Then, Sect. 4 shows how we biased the GRN's inputs to improve its capacity to drive fast and avoid opponents. A comparitive study follows, showing how the GRN performs in comparison to other approaches involved in the past years competition. A discussion about how the obtained GRN works and about the advantages and the weaknesses of our approach is provided in Sect. 6. Finally, the paper concludes how this approach could be improved to produce a more efficient car controller and how the GRNs are becoming a competitive alternative to other common evolutionary approaches. In this paper, we have showed how to used a gene regulatory network to drive a virtual car. The connections between the car and the GRN have been kept as simple as possible. The GRN has been naturally resistant to sensor noise: the impact of noise on the GRN's capacity to drive the car is very low. Moreover, the GRN is able to generalize a behavior learned on asphalt tracks to other types of surfaces such as sandy and rocky tracks. The GRN evolved through a 3-steps evolutionary process has been found to be a safe driver. To make it become a real racer, we have distorded the GRN inputs to make it more aggressive with the break and accelerator and to create multiple trajectories in order to make it overtake or avoid other cars. A recovery procedure has also been implemented in order to put the car back on track when the GRN fails to handle a complex situation.. To improve this work, multiple options have to been investigated. Our goal is to design a driver with as much automatic learning as possible. First, the use of the GRN as a racing driver requires the design of a track learning method to speed up the wise GRNs we generally obtain by evolution. We would like to teach the GRN to go faster by the use of a hierarchical architecture: a second GRN, pre-optimized on multiple tracks and reoptimized during the warm-up stage, could modify the inputs and/or the outputs of the driving GRN according to the current car state. The specialization capacity of the GRN observed in the first evolutionary step could be helpful during this warm-up stage.. This GRN must also be improved in order to correctly handle opponents. For now, the perception of the GRN is modified by a hand-written script in order to overtake or avoid an opponent detected too close to the car. This approach is innovative in comparison to most other approaches because they usually directly impact the car actuators. Modifying the inputs instead of the output keeps the controller as the center piece of the algorithm. However, we want the GRN to learn to handle this move by itself because most overruns are currently due to this script. Having all the information the car can detect and letting the GRN decide the best move could reduce this issue.. A full detailed study on how the GRN actually handles noise could be interesting to conduct. Our first hypothesis is that the granularity between the protein affinities helps the network to compensate for input distortions. Studying this phenomenon precisely could help us to better understand the dynamics of the evolved GRNs and possibly to prove their capacity to handle noisy inputs.. According to past experiences using the GRN as an agent controller (in developmental models, foraging agents, pole carts, etc.), we believe this approach is now ready to be used in a wide range of agent-based problems. This method can handle uncertainty because of the kinetics of the network. The GRN is thus easy to plug to any kind of agent; the only requirement is being able to convert the input and output signals into normalized concentration values. The strength of the GRN is also in handling cooperative and conflicting behavior within the same network. In our opinion, this method can compete with neural networks, genetic programming, and other evolutionary approaches on multiple domains.

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Emotional remapping of music to facial animation We propose a method to extract the emotional data from a piece of music and then use that data via a remapping algorithm to automatically animate an emotional 3D face sequence. The method is based on studies of the emotional aspect of music and our parametric-based behavioral head model for face animation. We address the issue of affective communication remapping in general, i.e. translation of affective content (eg. emotions, and mood) from one communication form to another. We report on the results of our MusicFace system, which use these techniques to automatically create emotional facial animations from multiinstrument polyphonic music scores in MIDI format and a remapping rule set. Human beings communicate their feelings, sensations, and ideas through a variety of channels. Such channels are, usually, designed to be aesthetically appealing to make the communication more attractive and pleasant. Although some might argue that artistic creativity, primarily, serves the creative needs of the artist, it is reasonable to say that, almost always, a motion picture, a painting, a piece of music, and any other aesthetic creation share a common theme that we call "affective communication". They express and/or cause different emotional states [Levinson et al 1999] . Affective communication complements (and frequently overlaps with) "literal communication" which is essentially based on storytelling (through audio, visual, or textual means). They both map content to certain elements and structures, but while the former is concerned with the expression of feelings and sensations, the latter is mainly related to describing events and making statements.. Although translation, as remapping some content from one form to another, has long been used for literal communication, its application to affective communication has been studied only recently, after the secrets of emotions themselves have been revealed by psychology and cognitive science [Ekman 2003 , Levinson et al 1999 . A motion picture made based on a novel, and a document translated to a new language, are examples of the operation that remaps communication material from one domain to another. It is possible because the material (events, statements, etc) which were primarily mapped to structural elements of source communication medium, can later be remapped to a target medium. In other terms, this possibility is due to the fact that the content, communication media, and their relation are well-known.. Emotions and the way we express them through body/facial actions [Ekman 2003 , Levinson et al 1999 and external media such as music [Juslin and Sloboda 2001, Krumhansl 2002] are the subject of a growing research. This increasing knowledge has also motivated "affective computing", i.e. computer systems such as software agents that can work with affective processes, for instance recognize and express emotions. In this paper, we introduce the concept of "affective communication remapping". Our knowledge about affective issues (emotions, moods, and the way they are expressed and perceived through different communication channels) enables us to extract affective information from source channels and express them in a target channel, as shown in Figure 2 .. Emotional remapping is based on the idea that each affective communication consists of a medium-dependent form and a "general" or "abstract" affective or sentic form [Clynes 1992 ]. The remapping is done by relating affective forms of source medium to the affective forms of the target. Although some researchers have argued that these affective forms are independent of communication channels and remain unchanged [Clynes 1992 ], but due to the different nature of two media, the relation is not necessarily a one-to-one correspondence, and might need user interaction to select desired mapping. To demonstrate affective communication remapping, we have developed a music-driven emotionally expressive face animation system called MusicFace. We use emotional aspects of a given piece of music, provided in MIDI or audio data, to animate a face. Based on designer's interaction, the animation system can illustrate the emotional states expressed in music, simulate the possible emotional responses, or demonstrate a free "facial choreography" based on the piece of music. This is part of our Interactive Face Animation -Comprehensive Environment (iFACE) project that aims at developing a framework for "face objects" and "facespaces" [Arya and DiPaola 2004, DiPaola 2002] . Face object is a software component that represents human faces with a variety of functionality (talking, moving expressions, etc) through interfaces that can be accessed by users or other applications (web pages, GUI programs, etc). Facespace is a multi-dimensional space that holds different states and variations of a face object. iFACE allows programming face object and navigating through the facespace. Music-driven Emotionally Expressive Face (MusicFace) is a sample iFACE client that controls the face object and creates a "facial choreography" or "moving along a path in facespace" driven by musical input. In addition to artistic values, MusicFace can be used for creating visual effects in movies and animations, and also realistic characters in computer games and virtual worlds. But most important aspect of MusicFace is to provide an example and prototype for more complicated applications of affective communication remapping between media such as music, dance, animation, and painting. MusicFace starts by receiving the input music in MIDI format (or Audio format that provides extra information about the music). Structure and expressive cues such as tempo, loudness, and timing are combined with emotion color cues from extracting harmonic tension and rhythm, which then can be translated into emotional states based on the associations defined by our observations and other existing studies. A fuzzy rule-based system, using a two dimensional mood model, is responsible for deciding on facial emotions and actions (e.g. blinking). The requested facial actions are then sent to iFACE framework components in order to create the visual effects.. To create visual content, MusicFace mainly uses a parameterized 3D head model, provided by iFACE framework. This model has a multi-layer parameter space that allows control of the head movements and facial actions at low (vertex), medium (facial feature), and high (feature group) levels, combined with parameters for mood and personality. Extensions to MusicFace (and iFACE) involves non-photo-realistic animation or "moving paintings" where the emotions are applied to a painting rather than a photograph or computer model (Figure 6a b: Stills from test animation where the mouth, blinks, eye brows, and head nods were automatically controlled by different tracks of the musical score using simple (pre-emotional) rules such as "nod on beat" and "eyebrow up on pitch". c: Stills (top and bottom) of our second generation MusicFace system where 3D shape distortion and color/image effects were also automatically driven by the music score's emotional content via the remapping rules. This piece was shown in art galleries in NYC and LA on a 6 foot internally projected sphere (inset). Figure 1 and 6 show some typical facial actions driven by music features, generated by MusicFace system taken from our simple test music score (Figure 6b ), from the multimedia piece "Concerto for Virtual Strings and Faces" (Figure 1 and 6a) and from the art installation piece "insideOut" (Figure 6b ). MusicFace has been used in several art animation based projects including Vancouver's NewForms Festival and in New York City's A.I.R. Gallery in a piece called "insideOut" which was displayed on a 6 foot projected globe. In both cases a simple rule set was created by the artist. All animation was generated by the MusicFace system via the music in MIDI format and a rule set. A subset of rules discussed in this paper were used, but were musically associated with beat, volume, note length, melody and tonality. One rule created by the artist had the face close it's eyes and lean back contemplatively for a length of time when the score's note pitches were higher than average for a short sustained sequence and were generally harmonic. This rule would fire whenever this musical condition occurred additively with other rules creating a very natural mapping from music to face animation. Although human emotions and affective behaviours have long been subjects of psychological and physiological studies [Darwin 1872 , Ekman 2003 , Levinson, Ponzetti and Jorgensen 1999 , emotions and especially their facial expression are still active research topics [Ekman 2003 ]. During the 1980s, several models for emotional states and moods were proposed which were mainly based on two-dimensional mood classification. Among them Russell's circumplex model of emotion [Russell 1980 ] and Thayer's mood model [Thayer 1989 ] can be mentioned, illustrated in Figure 3 . The former is based on activation and pleasure as two dimensions, and the latter energy and stress (two different types of activation). More than a hundred years after Charles Darwin proposed the idea of universal human expressions, Ekman and Friesen [1978] showed that basic human emotions and their facial expressions are universal among different cultures, and defined Facial Action Coding System (FACS) to represent major facial expressions and actions. In computer graphics and animation, FACS has been used to create emotionally expressive characters [Arya and DiPaola 2004] , and acted as the conceptual foundation for Motion Picture Expert Group (MPEG) Face Animation Parameters (FAPs) in MPEG-4 standard [Ostermann 1998 ]. Figure 3 . Emotion Models. Russell [1980] (top) and Thayer [1989] (bottom).. Emotional aspects of music have also been studied for a long time [Farnsworth 1958 , Hevner 1936 , Juslin and Sloboda 2001 . Despite the well-established body of knowledge about musical structures especially for western music [Lerdahl 2001 , Temperley 2001 , the effect of musical structure and performance on listeners' emotional response and perception is still a challenging research area [Juslin and Sloboda 2001] . Hevner [1936] grouped listeners' emotional response to pieces of music by asking them to write adjectives describing the music, and then clustering these adjectives. Fransworth [1958] refined and regrouped these adjectives into ten groups. Extracting audio features and classifying music based on these adjective groups is used to detect emotional states of music pieces [Li and Ogihara 2003 ]. Other researchers have used two dimensional mood models to achieve emotion detection in music. Liu et al. [2003] use music intensity to represent the energy dimension of Thayer model, and timbre and rhythm for stress. While psychologists and music therapist [Juslin and Sloboda 2001, Krumhansl 2002] have associated different structural aspects of music to certain emotions through experiments, some have focused more on performance-dependent aspects. Juslin [2000] considers tempo, sound level, frequency spectrum (as a representative of timbre), and articulation as performance cues and relate them to intended and perceived emotions.

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