A LOOSELY COUPLED ASPECT LANGUAGE FOR SOA APPLICATIONS The aspect-oriented programming (AOP) paradigm offers software developers with powerful modularization abstractions to help them explicitly separate design concerns at the source code level. However, the impact of AOP in the service-oriented architecture (SOA) paradigm has been dwarfed by the fact that existing AOP solutions are tightly coupled to a particular programming language, middleware system or execution platform. Clearly, this not only restricts the implementation choices available to application developers, but it also clashes with the heterogeneous and loosely coupled nature of SOA. This paper presents the Web Service Aspect Language (WSAL) that seamlessly integrates AOP and SOA concepts, thus avoiding the drawbacks of existing solutions. In WSAL, aspects themselves are freely specified, implemented and executed as loosely coupled web services. This characteristic allows WSAL aspects to be easily woven into the message flow exchanged between service consumers and service providers, in a way that is completely independent from any particular implementation technology. The paper also reports on the implementation and preliminary evaluation of a prototype aspect weaver for WSAL, which is based on an existing web intermediary technology. Service-oriented computing (SOC) is emerging as a powerful software development paradigm in which services constitute the fundamental elements of design [1] . SOC applications follow a standard service-oriented architecture (SOA) in which one or more service providers declaratively describe their services' operations and invocation properties in a standard, machine-readable format, so that those services can be dynamically discovered, selected, and invoked using a suit of standard protocols [2] . The most popular manifestation of the SOC paradigm is in the form of a suite of non-proprietary XML-based technologies collectively known as web services [3] . These include three core technologies, namely SOAP [4] , a service invocation protocol, WSDL [5] , a language for describing service interfaces, and UDDI [6] , a service-based repository for dynamic service discovery and location. Other related technologies are also being developed to deal with non-functional SOA requirements, such as reliability, security and performance [7] .. The dynamic binding between service providers and service consumers makes SOA applications loosely-coupled in nature, allowing services to be provided and consumed independently of the client applications' programming language, execution platform, and transport protocol. This characteristic has the main benefit that it makes it easier to integrate independently developed SOA applications, even when they have not been developed with integration as a major design concern.. On the other hand, the distributed and loosely-coupled nature of SOA applications also raises a series of design concerns (typically associated with the provision of non-functional service properties) that must be properly addressed by application developers. These concerns tend to be very difficult (or even impossible) to be modularized using current SOA development technologies. The reason is that nonfunctional concerns usually affect both service providers and service consumers. As a consequence, their implementation becomes scattered across the implementation of several application components at both sides [8] . For example, to guarantee secure service interactions it is necessary to modify the implementation of both service providers and service consumers, so that both sides can put in place and use the appropriate security mechanisms [9] . Similarly, to allow dynamic service selection at the client side, it is necessary to change the implementation of service providers, so that they can announce their service' QoS properties using some sort of service broker [10] , and also to change the implementation of service consumers, so that they can discover and select the servers that best suit their needs, before invoking their required service operations [11] .. Another consequence of the lack of better modularization support for nonfunctional concerns in current SOA technologies is that, as the number of those concerns increases, implementing and, subsequently, maintaining them become exceedingly difficult. This problem exacerbates for applications that are implemented using different programming languages or executed over different execution platforms, a typical SOA scenario.. The fact that some design concerns, such as those discussed above, are inherently difficult to modularize using traditional (i.e., functional) decomposition techniques is the main motivation behind the aspect-oriented programming (AOP) paradigm [12] . AOP introduces a new type of abstraction -called aspect -which allows to explicitly separate design concerns that otherwise would have to be implemented as part of (and tangled with) the implementation of several application components. AOP also provides novel software composition mechanisms to weave the implementation of those concerns (called cross-cutting concerns) back into the implementation of application components at well-defined execution points (called join points).. In view of the current need for mechanisms to separate cross-cutting concerns in SOA applications, and of the powerful modularization constructs introduced by AOP, there is a natural demand for solutions that aim at integrating these two emerging software development paradigms. Even though there has been a number of works geared toward this direction recently [13, 14, 15, 16, 17] , all solutions proposed thus far suffer from the limitation of being tightly coupled to a particular programming language, middleware technology or execution platform. The high level of coupling associated with those solutions is undesirable for two main reasons: (i) it restricts the spectrum of technological choices available to application developers; and (ii) it clashes with the heterogeneous and loosely coupled nature of typical SOA applications. Therefore, any effective solution for integrating concepts from the SOA and AOP paradigms must provide technology independence as a core design principle [19] .. In our previous work [18, 19] , we have proposed a novel aspect model for SOA applications, in which services themselves provide the necessary abstractions to modularize cross-cutting concerns. In this paper, we present the Web Service Aspect Language (WSAL), which is a concrete realization of the concepts first introduced in that model. As such, WSAL seamlessly integrates fundamental AOP concepts, such as aspects, join points and advices [12] , into the SOA context. Differently from other existing solutions that attempt to integrate these two emerging software development paradigms, in WSAL aspects can be freely specified, implemented, deployed and executed as loosely coupled web services. This characteristic allows WSAL aspects to be easily woven into the message flow exchanged between service consumers and service providers, in a way that is completely independent from any particular implementation technology.. The rest of the paper is organized as follows. Sec. 2 describes the syntax and semantics of WSAL. Sec. 3 illustrates the use of WSAL through a series of examples. Sec. 4 reports on the implementation of a prototype aspect weaver for WSAL. Sec. 5 presents the results of a preliminary evaluation of our prototype in a controlled setting. Sec. 6 covers related work. Finally, Sec. 7 concludes the paper and suggests some directions for future research. This paper presented a novel aspect language, called Web Service Aspect Language (WSAL), which provides a natural mechanism for integrating aspect-oriented programming concepts into the context of service-oriented architectures. In WSAL, aspects are both implemented and deployed as loosely-coupled web services, which allow crosscutting concern implementations (or advices) to be dynamically woven into the SOAP traffic generated between service consumers and services providers. In contrast to most existing approaches that also aim at integrating these two emerging software development paradigms, the weaving process supported in WSAL is completely independent of any particular implementation technology. The paper also presented some details on the design and implementation of a prototype aspect A Loosely Coupled Aspect Language for SOA Applications 19 weaver for WSAL, which has been developed based on a existing HTTP intermediary framework. Results of a preliminary performance evaluation of the weaver in a controlled setting were finally presented and discussed.. As regards future work, we envision the following research lines:. • Developing new versions of the weaver using different intermediary technologies. The idea is to evaluate empirically the characteristics of reusability and intermediary platform independence of our proposed weaver architecture.. • Conducting a more systematic evaluation of our tools, in both controlled and production settings. This would help us in fine tuning their performance to meet the QoS requirements of industrial-strength SOA applications.. • Developing new tools to support the creation, deployment and monitoring of WSAL aspects. These tools are vital to improve the quality of the WSAL development process and to make it more accessible to SOA developers in general. It is worth noting that, because WSAL is an specification language, rather than an implementation one, all details pertaining the implementation of aspectual service operations are under the responsibility of their respective developers. Therefore, it is the developers' responsibility to guarantee that the implemented operations comply with their execution semantics, as required by the WSAL weaver.. On the other hand, by decoupling aspect specifications from their implementations, WSAL allows aspect implementations to be reused across applications developed using different implementation technologies. For example, the client authentication aspect (shown in Figure 3 ) could be reused to add credentials to SOAP request messages generated from client applications running in different network domains, independently of the their programming language, midlleware system or execution environment. Similar arguments also apply to the cache and billing aspects. Such level of reuse is simply not possible with existing solutions that also attempt to integrate the AOP and SOA paradigms.. A more detailed comparison between WSAL and a number of related approaches can be found in Section 6. Using SOAP intermediaries as a way to implement crosscutting SOA concerns is not a novel ideal. In fact, it has been part of the SOAP specification since its early versions [4] . In most existing web service frameworks, such as .NET [29] and JAX-WS [30] , such intermediaries are implemented as message handlers, which can be deployed at both the client and service sides. The weaving model supported by WSAL takes this idea one step ahead, by using SOAP intermediaries not as the technology to implement SOA concerns directly (which would bind concern implementations to a particular intermediary technology), but as the means to decouple, in a SOA context, concern composition (weaving) from concern implementation. A number of other approaches exist that aim at integrating concepts from the AOP and SOC paradigms [13, 17, 31] . However, those solutions all rely on an aspect weaving mechanism that is tightly bound to a specific programming language or development environment. For instance, the approaches by Verheecke and Cibrán [13] and Baligand and Monfort [31] rely on different weaving mechanisms specific to the Java platform, and thus require that both the aspects and their target applications be implemented in Java. Similarly, the approach by Verheecke et al. [17] relies on a weaving mechanism specific to .NET, and thus requires aspects and applications only to be implemented using that framework. In contrast to the above approaches, in WSAl aspects are implemented as loosely-coupled web services that can be weaved dynamically into SOAP-based interaction events captured over the network.. Two other related works follow a slightly different approach [14, 15] . They both integrate AOP and SOC concepts at the service composition level, and both extend BPEL4WS [32] , a web service-based process composition language. The extension includes creating new constructs for specifying process composition aspects, and a new composition mechanism for weaving the aspects back to the original BPEL4WS processes. By relying on a weaving mechanism that works at the service composition level, those two works, like our work on WSAL, also support aspect implementation and weaving in the form of loosely coupled web services. However, the weaving mechanism used in those approaches is more limited in scope, being restricted to dynamic join points expressed in terms of interaction events captured by the BPEL4WS execution engine at the service composition level. This feature has the drawback that it tightly couples aspect implementation in those approaches to the BPEL4WS language.. On the other hand, WSAL design is independent from SOAP engines and business process modeling languages. The prototype aspect weaver for WSAL described in this paper relies on the WBI framework for message interception. However, other weavers can be implemented using different SOAP engines or providing their own interception frameworks.

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


Noise reduction for magnetic resonance images via adaptive multiscale products thresholding Abstract-Edge-preserving denoising is of great interest in medical image processing. This paper presents a wavelet-based multiscale products thresholding scheme for noise suppression of magnetic resonance images. A Canny edge detector-like dyadic wavelet transform is employed. This results in the significant features in images evolving with high magnitude across wavelet scales, while noise decays rapidly. To exploit the wavelet interscale dependencies we multiply the adjacent wavelet subbands to enhance edge structures while weakening noise. In the multiscale products, edges can be effectively distinguished from noise. Thereafter, an adaptive threshold is calculated and imposed on the products, instead of on the wavelet coefficients, to identify important features. Experiments show that the proposed scheme better suppresses noise and preserves edges than other wavelet-thresholding denoising methods. This paper proposes an MRI image denoising scheme using an adaptive wavelet thresholding technique. Unlike many traditional schemes that directly threshold the wavelet coefficients, the proposed scheme multiplies the adjacent wavelet subbands to amplify the significant features and then applies the thresholding to the multiscale products to better differentiate edge structures from noise. The distribution of the products was analyzed and an adaptive threshold was formulated to remove most of the noise. Experiments on the MRI images show that the proposed scheme not only achieves high MSR and CNR measurements but also preserves more edge features. The is a cubic spline whose integral is equal to 1 and is a quadratic spline. In Fig. 12 , they are plotted and compared with a Gaussian function and its first derivative. It is noticed that the approximates closely to the Gaussian function. The wavelet transform behaves like a Canny edge detector [17] .. The discrete decomposition algorithms of 1-D and 2-D DWT are illustrated in Fig. 13 . Filter ( ) is the scale dilation of ( ) (putting zeros between each of the coefficients of ( )).. ( ) is the transpose of ( ). The coefficients of filters and are available in [4] . Suppose the input signal has samples, then at each scale the wavelet coefficients and also have samples. There are at most scales and the complexity of the decomposition algorithm is . It should be noted that in the discrete implementation, at each scale the wavelet coefficients should be sampled with a constant shift. For a 1-D signal, we denote the discrete sample sequence by

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


Dynamic 3-D Visualization of Vocal Tract Shaping During Speech Noninvasive imaging is widely used in speech research as a means to investigate the shaping and dynamics of the vocal tract during speech production. 3-D dynamic MRI would be a major advance, as it would provide 3-D dynamic visualization of the entire vocal tract. We present a novel method for the creation of 3-D dynamic movies of vocal tract shaping based on the acquisition of 2-D dynamic data from parallel slices and temporal alignment of the image sequences using audio information. Multiple sagittal 2-D real-time movies with synchronized audio recordings are acquired for English vowel-consonant-vowel stimuli /ala/, /ara/, /asa/, and /a∫a/. Audio data are aligned using mel-frequency cepstral coefficients (MFCC) extracted from windowed intervals of the speech signal. Sagittal image sequences acquired from all slices are then aligned using dynamic time warping (DTW). The aligned image sequences enable dynamic 3-D visualization by creating synthesized movies of the moving airway in the coronal planes, visualizing desired tissue surfaces and tube-shaped vocal tract airway after manual segmentation of targeted articulators and smoothing. The resulting volumes allow for dynamic 3-D visualization of salient aspects of lingual articulation, including the formation of tongue grooves and sublingual cavities, with a temporal resolution of 78 ms. T HE VOCAL tract is the universal human instrument, played with great dexterity and skill in the production of spoken language. Speech researchers are interested in characterizing the relationship between articulation and acoustics, and understanding critically-controlled aspects of vocal tract shaping during speech. Visualization of the movements of the lips, tongue, and velum can provide important information about the spatiotemporal properties of speech gestures. This paper has supplementary downloadable material available at http://ieeexplore.ieee.org, provided by the authors. *Y. Zhu is with the Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089 USA (e-mail: yinghuaz@usc.edu).. Y.-C. Kim, S. S. Narayanan, and K. S. Nayak are with the Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089 USA.. M. I. Proctor is with the Department of Linguistics, University of Western Sydney, Milperra, NSW 2214 Australia.. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.. Digital Object Identifier 10.1109/TMI.2012. 2230017 Several techniques have been utilized to visualize tongue shaping during speech, including computed tomography (CT) [1] , electromagnetic articulography (EMA) [2] , X-ray [3] , [4] , X-ray microbeam [5] , [6] , ultrasound [7] , and magnetic resonance imaging (MRI) [8] - [19] . However, each of these approaches has important limitations. Both CT and X-ray expose subjects to radiation. In addition, X-ray averages the entire vocal tract volume into a 2-D image from one projection. EMA provides 3-D data with high temporal resolution, but the EMA sensors are spatially sparse and difficult to attach to pharyngeal structures. Ultrasound is safe and noninvasive, but it detects only the first air-tissue boundary, and typically does not image either the tongue tip or lower pharyngeal articulation. Furthermore, the ultrasound transducer probe is typically in contact with the jaw and may affect the speech production. Although MRI has provided relatively lower spatial and temporal resolution, it has the unique advantage that it can produce complete views, and quantitative measurements, of the entire vocal tract including the velum, posterior oral cavity, and pharyngeal portions. Phonetic data from these regions are not easily acquired using other modalities, but can be safely and noninvasively imaged with MRI, making it a promising tool for speech research. A critical discussion of various techniques can be found in [20] .. MRI of the upper airway for speech research has been limited by slow acquisition speed. A number of the early MRI acquisition techniques for speech have been based on imaging of multiple 2-D slices [8] - [12] with long scan times in the order of minutes, typically requiring multiple sustained repetitions of the utterance under investigation. The recent introduction of 3-D-encoded MRI techniques combined with either compressed sensing or parallel imaging has accelerated the acquisition speed within the duration (typically 6-10 s) of a single sustained sound production [13] , [14] . Compared with 2-D multislice MRI, 3-D-encoded MRI can provide higher acceleration with pseudo-random undersampling available in 2-D -space, and also has the potential for thinner slices and higher signal-tonoise ratio (SNR).. More recently, dynamic MRI methods have been used to provide information about changes in vocal tract shaping during speech. Cine-MRI enables obtaining a set of images by repeatedly scanning the vocal tract while subjects produce (hopefully) identical repetitions of the same utterance. During each repetition, part of the -space (e.g., one row) is acquired sequentially [15] - [17] . In order to construct images from these data, cine-MRI usually requires synchronization in data acquisition and image reconstruction. Moreover, cine-MRI fills the -space in a predetermined pattern, which assumes that different repetitions of production have the same pace and duration. Realtime MRI, on the other hand, does not involve the synchro-0278-0062/$31.00 © 2012 IEEE nization of -space acquisition and motions of the soft tissue (e.g., tongue motion, ventricular motion of the beating heart), and captures the motion using fast image acquisition techniques. Demolin et al. demonstrated real-time MRI of speech using turbo spin echo sequence (TSE) with 4 fps on a single slice [18] . Narayanan et al. proposed real-time MRI of vocal tract dynamics with 20-24 fps using a spiral gradient echo sequence and sliding window reconstruction, which is sufficient to capture the underlying motion and physiology of interest during the production of speech [19] .. Dynamic imaging of the full 3-D vocal tract with high spatial and temporal resolution is, however, more desirable than just a single plane view for a proper understanding of articulation during fluent speech. Current MRI systems do not meet the requirements for capturing 3-D vocal tract dynamics in real-time. Interesting engineering, but compromised, solutions have included model-fitting methods and multi-planar imaging in separate operations. Several approaches (including non-MRI ones) have been proposed. Engwall established a 3-D parametric tongue model using static MRI and electropalatography (EPG), and estimated parameters for tongue movements using EMA [21] . Video data acquired from pellets marked on the human face were combined with 3-D static MRI data to linearly model the articulators [22] . Yang and Stone reconstructed 3-D tongue surface motions by temporal registration of ultrasound images from multiple scan locations [23] . Takemoto et al. demonstrated a 3-D cine-MRI technique that measures the shaping of the vocal tract using multi-planar 2-D cine-MRI [24] . The success of cine-MRI depends crucially on synchronization between speech production and MRI acquisition. This can be challenging to speakers who are not trained to repeat the utterances at the same speech rate. Inspired by multi-planar 2-D imaging techniques, in this paper, we propose a novel approach to reconstruct 3-D dynamics from multi-planar real-time MRI.. The proposed method constructs 3-D movies of the tongue shape and vocal tract dynamics by temporal alignment of parallel 2-D MRI data of overlapping sagittal slices covering the entire vocal tract. We briefly introduced the approach and demonstrated the preliminary results first in [25] . The remainder of this paper is organized as follows. We first briefly review real-time MRI of speech, acoustic features mel-frequency cepstral coefficients (MFCC), and a well-known algorithm to measure sequence similarity, called dynamic time warping (DTW). We then describe a systematic approach of parameter selection for extracting MFCCs and evaluation of the performance of different methods of parameterization. Following which, we demonstrate the in vivo results of audio alignment, synthesized coronal images, and 3-D dynamic visualization of tongue and vocal tract shaping during fluent speech. Finally, we critically discuss the current approach, and propose potential future directions for this work. We presented a novel method for 3-D dynamic imaging of human vocal tract airway shaping (and of the associated articulators, notably, the tongue) based on 2-D real-time MRI of parallel sagittal slices that are independently acquired from repetitions of the same speech corpus. The technique applies DTW to comparable series of audio MFCC feature vectors to compensate for the temporal mismatches of the videos resulting from varied speech rates. With this technique, we were able to reconstruct 3-D vocal tract movies with 2.4 mm 2.4 mm 3 mm spatial resolution and 78 ms temporal resolution, from which we successfully visualized lingual features of several tested utterances. The proposed method can give improved insights into the goals of speech production, since it can provide high temporal resolution information about the changing geometry of the entire vocal tract-data which are not available from conventional 2-D/3-D MRI techniques. To our knowledge, the proposed method is the first demonstration of dynamic 3-D visualization of the vocal tract shaping using real-time MRI and synchronized audio recordings. Since the proposed method relies on 2-D real-time MRI data, it inherits the image quality problems of 2-D real-time MRI. Significantly low SNR due to poor coil sensitivities of our current receiver coil array was observed in the middle to lower neck. This made it difficult to observe the dynamics of the vocal cord, which is another region of interest for the application of the proposed approach. In addition, the proposed technique requires finer slice resolution than 6 mm to improve visualization of coronal-slice tongue shape, but the image SNR is unacceptable with the slice thickness thinner than 6 mm in our current 2-D real-time MRI of speech. Together 6 mm thickness and 3 mm overlap result in a volume covering the entire vocal tract with reasonable pixel resolution and data fidelity in the cross-plane direction, since a 2-D image is a projection of tissue slice. We made trade-offs among image quality, data fidelity and scan time. Midsagittal plane is most commonly used in speech research to get a full view of the vocal tract from the lip opening to the glottic region, and acquisition of contiguous parallel sagittal planes is more time-efficient in covering the entire vocal tract than acquisition of stack of axial or coronal planes, because vocal tract has much smaller dimension alone R-L direction than A-P or superior-inferior (S-I) direction. If we prescribe axial or coronal plane, more slices are required for covering the entire vocal tract, leading to more repetitions of the speech corpus for subjects.. We have performed our experiment on three subjects using different stimuli including VCV utterances, long English words, and English sentences. Experiments involving English sentences require multiple separate scans to acquire data for all the sagittal slices covering the entire vocal tract, because of scan time limitations. Nevertheless, the MFCC-DTW technique successfully aligned separately-acquired data to a similar level in all cases (more than ten). We demonstrate manually-segmented results of four short, representative VCV utterances in Fig. 7 and the supplemental dynamic 3-D movies, which demonstrate 3-D features of interest.. The number of triangular filters used in MFCC extraction, 24-40, is widely accepted in audio signal processing community [29] , and for speech processing applications, the first 13 out of 24 MFCCs are commonly used [29] . We tried different values within the range, and observed little differences in the alignment results. Fig. 3 shows that the minimum-distance warping path is a nondecreasing, discontinuous curve constrained by the monotonicity criterion. The curve verifies the abilities of MFCC-DTW alignment to align two productions where the speech rates are unstable, and to align two MFCC sequences of different lengths because one-to-many and many-to-one mappings are both allowed. The drawbacks of DTW include quadratic time complexity and memory requirement. DTW is a dynamic programming algorithm using a cost matrix whose size is proportional to the product of the lengths of two time series [32] . This puts practical limits on the usage of DTW for aligning extremely long acquisitions or using extremely small shift sizes. Other groups have accelerated traditional DTW and improved memory occupancy efficiency by sacrificing minor accuracy. Following Salvador and Chan's classification [32] , established approaches fall into three categories: 1) Constraints which limit the number of cells in the cost matrix to be evaluated, such as Sakoe-Chiba Band [33] and Itakura Parallelogram [34] ; 2) Data Abstraction which reduces the sizes of time series as DTW input [35] ; and 3) Indexing which prunes out the number of times DTW runs using lower-bounding functions [36] .. Our results indicate that the performance of long-to-short alignment is superior to that of short-to-long alignment. We believe this is because when a subject intentionally produces short utterances, most acoustic features are shortened, and some may be discarded. When a subject intentionally prolongs utterances, he appears to preserve all the acoustic features, or even adds some abnormal acoustic features. The MFCC-DTW algorithm simply discards additional features by mapping multiple entries to a single entry in the test audio in long-to-short alignment, such as period 1.6-1.9 s in Fig. 3 . But when the algorithm aligns a short utterance to a long utterance, misalignments may occur when the algorithm aligns normal acoustic features to abnormal ones due to artificial elongation of the utterance. Since experimental audio recordings for utterances collected to date have a mean of 1.1 s/utterance and a variance of s/utterance, this suggests that short-to-long alignment is not a concern in real audio alignment.. There is no universal optimal value of frame width or shift size for short-time audio processing, such as MFCC extraction. We observed that 100 minimum-error parameter settings cluster in a small area, and thus we averaged them for our estimate.. The resulting 36 ms frame width falls into the typical range conventionally used in speech processing (5-100 ms, [30] ), and is very close to that of 40 ms used in [29] , but the shift size is only 2/9 of the frame width, smaller than the suggested 1/3 of the frame width [30] .. Coronal views derived from the reconstructed data using this technique are a good example of the type of arbitrary reformatting that can only be done with 3-D data, and provide a clear method by which to examine the synthesized 3-D vocal tract data. Poor alignment leads to asymmetry of reconstructed tongue and jagged surfaces (i.e., stair-step artifact), which are evident in linear and equal-time alignment results, but are greatly mitigated in MFCC-DTW alignment results. The results from the rms error plots show that DTW-MFCC alignment invariably outperforms the other two alignment methods, and confirm the observations of qualitative evaluations. The rms errors of linear and equal-time alignments from anterior slice are significantly higher than from middle and posterior slices (see Fig. 6 ), because the vocal tract constriction of / / and / / is located between the tongue tip and alveolar ridge, and lasts for a very short period (about 100-200 ms), so that any misalignment would be manifest as stair-step artifact. In addition, linear and equal-time alignments tend to be very sensitive to the duration, the start and end of segmented data, to which MFCC-DTW alignment exhibits the robustness. Therefore, the careful data/audio segmentation of single short utterances by mutual inspection of video/audio in the preprocessing improves accuracy of the linear and equal-time alignments.. From a temporal perspective, MFCC-DTW alignment has poorer results at the start and the end of each utterance, compared with the medial data portions. The likely reason is that MFCC-DTW alignment relies on audio information, but there are no clearly identifiable acoustic landmarks to support proper alignment at the start and end of the utterance, corresponding to points in time when the articulators just leave from or move back to rest positions (without producing sound). In spite of these limitations, the intervals of most interest for linguistic research are focused on periods of more active articulation, when acousticarticulatory alignment is more easily achieved, and slight mismatches at the start and the end of each utterance are therefore less problematic.. The 3-D movies generated using this technique successfully allowed for the dynamic visualization of many of the salient articulatory features anticipated in these stimuli. However, one important limitation of the method at this stage of development is the presence of minor surface irregularities in the reconstructed object. Several possible reasons are as follows. 1) Image quality problems: off-resonance and motion artifacts could blur the air-tissue boundaries, resulting in contour tracking errors. 2) Slice thickness: the shape of the tongue changes along the R-L direction, especially at both ends of the tongue, where steep changes exist. 3) Gross head motion: some head movement is inevitable during multiple repetitions, despite the limiting effect of having subjects' heads immobilized using foam paddings. 4) Varying degrees of jaw opening: subjects could not precisely repeat the same degree of jaw opening in different repetitions. 5) Manual segmentation errors: manual segmentation currently outperforms any automatic segmentation methods, but can be weakened by shortcomings including reproducibility errors, operator fatigue and bias.. Finally, it is worth noting that high temporal resolution 3-D vocal tract data is valuable not only to linguistic studies, but could also be useful for clinical research, including the investigation of articulatory differences between the pre-and post-operative vocal tracts in glossectomy patients [37] .

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


On

the

Complexity

of

Sparse

Exon

Assembly

Abstract.

Gene

structure

prediction

is

one

of

the

most

important

problems

in

computational

molecular

biology.

A

combinatorial

approach

to

the

problem,

denoted

Gene

Prediction

via

Spliced

Alignment,

was

introduced

by

Gelfand,

Mironov

and

Pevzner

The

method

works

by

finding

a

set

of

blocks

in

a

source

genomic

sequence

S

whose

concatenation

(splicing)

fits

a

target

gene

T

belonging

to

a

homologous

species.

Let

S,T

and

the

candidate

exons

be

sequences

of

size

O(n).

The

innovative

algorithm

described

in

yields

an

O(n

result

for

spliced

alignment,

regardless

of

filtration

mode.

In

this

paper

we

suggest

a

new

algorithm

which

targets

the

case

where

filtering

has

been

applied

to

the

data,

resulting

in

a

set

of

O(n)

candidate

exon

blocks.

Our

algorithm

yields

an

O(n

n)

solution

for

this

case.

Recognition

of

genes

in

eukaryotic

DNA

is

seriously

complicated

by

noisy

regions

(introns)

that

interrupt

the

coding

regions

(exons)

of

genes.

The

gene-prediction

via

spliced

alignment

approach,

due

to

Gelfand,

Mironov

and

Pevzner

incorporates

similarity

analysis

into

gene

prediction

by

attempting

to

find

a

set

of

potential

exons

in

a

genomic

sequence

whose

concatenation

is

highly

similar

to

one

of

the

already

known

gene

sequences

in

the

database..

The

task

of

gene

prediction

is

generally

divided

into

two

stages.

The

first

task

is

that

of

finding

candidate

exons

in

a

long

DNA

sequence

believed

to

contain

a

gene.

A

candidate

exon

is

a

sequence

fragment

whose

left

boundary

is

an

acceptor

site

or

a

start

codon,

and

the

right

boundary

is

a

donor

site

or

a

stop

codon.

The

nucleotide

sequence

in

Figure

contains

marked

sites

where

a

candidate

exon

may

begin

and

end.

Uppercase

A-E

mark

identified

sites

where

an

exon

is

likely

to

begin

(start/acceptor

sites),

and

lowercase

f-j

mark

sites

where

exons

are

likely

to

end

(stop/donor

sites).

Candidate

exons

are

A-f,

A-g,

A-h,

A-i,

A-j,

B-f,

B-g,

B-h,

B-i,

B-j,

C-g,

etc.

The

second

task

is

that

of

selecting

the

best

subset

of

non

overlapping

candidate

exons

to

cover

the

sequence

of

the

predicted

gene.

An

interesting

combinatorial

approach,

using

network

dynamic

programming,

which

explores

all

possible

exon

assemblies

in

polynomial

time,

is

described

in

Assuming

that

S

and

T

as

well

as

the

sizes

of

the

candidate

exons

is

O(n),

this

algorithm

yields

an

O(n

solution

for

Sparse

Spliced

Alignment.

Good

filtration

is

crucial

for

exon

assembly,

especially

if

targets

from

distant

taxa

are

used.

In

the

authors

studied

the

performance

of

the

spliced

alignment

algorithm

for

different

targets

on

a

complete

set

of

human

genomic

sequences

with

known

relatives

and

demonstrated

that

the

average

performance

of

the

method

remains

high

even

for

distant

targets.

The

authors

analyzed

several

filtration

procedures

of

varying

strength

and

demonstrated

that

weak

filtration

provides

better

results

with

mammalian

targets.

In

the

case

of

distant

targets,

the

stronger

filtering

was

more

useful

than

in

the

case

of

close

targets,

and

sometimes

it

was

shown

to

significantly

improve

the

prediction

quality.

Furthermore,

it

was

also

explicitly

shown

(see

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 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 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


Rapid

screening

for

phenotype-genotype

associations

by

linear

transformations

of

genomic

evaluations

Background:

Currently,

association

studies

are

analysed

using

statistical

mixed

models,

with

marker

effects

estimated

by

a

linear

transformation

of

genomic

breeding

values.

The

variances

of

marker

effects

are

needed

when

performing

the

tests

of

association.

However,

approaches

used

to

estimate

the

parameters

rely

on

a

prior

variance

or

on

a

constant

estimate

of

the

additive

variance.

Alternatively,

we

propose

a

standardized

test

of

association

using

the

variance

of

each

marker

effect,

which

generally

differ

among

each

other.

Random

breeding

values

from

a

mixed

model

including

fixed

effects

and

a

genomic

covariance

matrix

are

linearly

transformed

to

estimate

the

marker

effects.Results:

The

standardized

test

was

neither

conservative

nor

liberal

with

respect

to

type

I

error

rate

(false-positives),

compared

to

a

similar

test

using

Predictor

Error

Variance,

a

method

that

was

too

conservative.

Furthermore,

genomic

predictions

are

solved

efficiently

by

the

procedure,

and

the

p-values

are

virtually

identical

to

those

calculated

from

tests

for

one

marker

effect

at

a

time.

Moreover,

the

standardized

test

reduces

computing

time

and

memory

requirements.

The

following

steps

are

used

to

locate

genome

segments

displaying

strong

association.

The

marker

with

the

highest

log(p-value)

in

each

chromosome

is

selected,

and

the

segment

is

expanded

one

Mb

upstream

and

one

Mb

downstream

of

the

marker.

A

genomic

matrix

is

calculated

using

the

information

from

those

markers

only,

which

is

used

as

the

variance-covariance

of

the

segment

effects

in

a

model

that

also

includes

fixed

effects

and

random

genomic

breeding

values.

The

likelihood

ratio

is

then

calculated

to

test

for

the

effect

in

every

chromosome

against

a

reduced

model

with

fixed

effects

and

genomic

breeding

values.

In

a

case

study

with

pigs,

a

significant

segment

from

chromosome

explained

of

total

genetic

variance.The

standardized

test

of

marker

effects

using

their

own

variance

helps

in

detecting

specific

genomic

regions

involved

in

the

additive

variance,

and

in

reducing

false

positives.

Moreover,

genome

scanning

of

candidate

segments

can

be

used

in

meta-analyses

of

genome-wide

association

studies,

as

it

enables

the

detection

of

specific

genome

regions

that

affect

an

economically

relevant

trait

when

using

multiple

populations.

Fast

genome

screening

of

SNP

effects

linearly

transformed

from

genomic

breeding

values

is

advantageous,

as

a

byproduct

of

genomic

evaluations

for

different

species

of

farm

animals.

Moreover,

the

standardized

tests

of

SNP

effects

using

their

own

variance

Varĝ

j

developed

in

this

study

helps

in

detecting

specific

genomic

regions

involved

in

the

additive

variation

of

the

trait

and

reducing

false

positive

locations

using

less

computing

time.

Additionally,

genome

segments

of

about

Mb

formed

by

surrounding

the

SNP

with

the

smallest

p-values

on

each

chromosome,

and

tested

with

a

standardized

test

involving

Varĝ

j

and

with

the

Bonferroni

correction,

could

detect

genome

regions

responsible

for

sizeable

fractions

of

the

trait

genetic

variance.

This

methodology

involving

genome

scan

and

candidate

segment

approach

is

a

useful

method

for

meta-analyses

of

genome-wide

association

studies,

as

it

enables

the

detection

of

specific

genome

regions

that

affect

an

economically

relevant

trait

when

using

multiple

populations.

Code

and

data

to

obtain

and

reproduce

the

results

presented

is

publicly

available

at

The

main

goal

of

this

research

was

to

develop

a

novel

procedure

to

perform

a

rapid

genome

scan,

or

GWAS

analysis,

from

a

genomic

evaluation.

Moreover,

the

sufficient

statistics

of

our

methodology

are:

the

Best

Linear

Unbiased

Prediction

(BLUP)

of

the

breeding

values

from

an

animal

model,

G

as

the

covariance

matrix

(or

H

for

a

single

step

evaluation

Z

as

the

standardized

marker

effects

matrix,

variance

components,

and

C

aa

This

setting

makes

the

implementation

extremely

feasible

after

the

genomic

evaluation

has

been

performed

as

discussed

by

Legarra

et

al.

The

availability

of

high

density

genotypes

of

single

nucleotide

polymorphism

(SNP)

markers

for

plants

and

livestock

species,

in

conjunction

with

phenotypic

data

for

complex

traits,

allows

the

calculation

of:

estimates

of

genomic

breeding

values

(GEBVs)

for

genomic

evaluation

and

estimates

of

the

effects

of

genomic

regions

associated

with

the

genetic

variability

in

genome

wide

association

studies

(GWAS)

There

is

an

increasing

number

of

GWAS

data

sets

analyzed

by

mixed

models

and

multiple

testing

procedures

after

fitting

all

individual

effects

of

genomic

regions

into

the

model

The

model

may

be

difficult

to

fit

when

both,

the

number

of

individuals

and

SNP

effects,

are

large.

We

propose

to

use

a

linear

transformation

of

genomic

breeding

values

to

estimate

the

marker

effects

from

a

simpler

equivalent

mixed

model,

and

then

testing

those

effects

using

a

standardized

test

statistic

that

employs

the

variance

(rather

than

prediction

error

variance)

of

the

same

effects..

The

method

of

genomic

selection

proposed

by

Meuwissen

et

al.

to

estimate

GEBVs

starts

by

fitting

the

SNP

effects

to

a

given

data

set.

Next

is

to

estimate

GEBV

of

any

individual

using

its

genotype

(SNP),

by

adding

across

the

entire

genome

those

solutions

corresponding

to

the

individual's

SNP.

The

mixed

model

employed

conveys

vectors

of

fixed

effects,

and

random

effects

of

markers

or

SNPs

g

assumed

to

be

normally

distributed

with

mean

and

a

covariance

matrix

proportional

to

the

identity

matrix

times

the

variance

of

SNP

effects

I

σ

g.

Errors

are

assumed

to

be

Gaussian,

independent

and

identically

distributed

with

mean

and

covariance

matrix

I

σ

e

An

equivalent

mixed

model

discussed

by

Garrick

and

Stranden

is

fitted

after

the

linear

transformation

a

Z

g

where

a

is

a

random

vector

of

breeding

values,

and

Z

an

incidence

matrix

that

relates

elements

in

a

to

those

in

g.

Each

column

of

Z

is

associated

with

a

given

SNP

and

the

elements

are

standardized

by

functions

of

SNP

allele

frequencies

and

by

the

total

number

of

SNP.

It

is

worth

noting

that

the

same

Z

is

used

in

our

implementation

of

the

model

of

Meuwissen

et

al.

to

relate

the

vector

of

marker

effects

in

g

to

the

data

phenotypes.

Moreover,

GEBVs

in

the

equivalent

model

have

variance-covariance

matrix

G

σ

A

¼

Z

Z

σ

g

The

procedure

requires

that

the

variances

are

equal,

i.e.

σ

A

¼

σ

g

Once

the

equivalent

model

is

fit,

SNP

effects

are

calculated

by

the

transformation

g

Z

G

a,

and

individual

SNP

effects

in

g

are

divided

by

the

square

root

of

its

variance

(Var(

g

j

to

get

the

so

called

SNP

ej

test

statistics.

We

also

provide

a

formula

to

calculate

Var(

g

j

without

having

to

fit

the

model

with

SNP

effects.

The

next

step

is

to

select

genome

segments

that

may

be

highly

associated

with

the

genetic

variability

of

the

trait

for

each

chromosome.

In

doing

so,

we

look

for

the

SNP

having

the

highest

value

of

minus

the

logarithm

of

the

p-value

throughout

the

chromosome.

Once

the

SNP

is

located,

a

segment

of

one

Mb

to

the

left

and

one

to

the

right

is

defined,

and

a

relationship

matrix

is

calculated

using

only

the

information

from

those

markers.

The

relationship

matrix

is

used

as

the

proportional

variance-covariance

of

the

segment

effects

in

a

model

that

also

includes

fixed

effects

and

random

GEBVs.

In

a

final

step,

the

likelihood

ratio

is

calculated

to

test

the

significance

of

the

largest

effect

segment

of

each

chromosome

by

comparing

against

a

reduced

model

with

fixed

effects

and

GEBVs.

The

critical

value

(size

of

the

test)

is

adjusted

by

the

Bonferroni

correction.

The

algorithm

not

only

delivers

genome

wide

associations

and

genomic

predictions

efficiently,

but

it

also

minimizes

computing

time

and

memory

requirements.

Moreover,

the

specific

variance

of

the

SNP

effects

is

used

in

calculating

the

test,

thus

taking

into

account

the

amount

of

information

of

any

given

marker.

Instead,

other

testing

approaches

rely

on

a

prior

variance

or

a

constant

estimate

of

the

additive

variance.

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


Analysis of traffic data from a hybrid satellite-terrestrial network Satellite data networks provide broadband access for areas not served by traditional broadband technologies. In this paper, we describe a collection of traffic data (billing records and tcpdump traces) from a satellite Internet service provider in China. We use the billing records to investigate the uploaded and downloaded traffic volume and the aggregate user behavior. We examine daily and weekly cycles and effects of holidays on traffic patterns. Analysis of the tcpdump traces indicates that Transmission Control Protocol (TCP) accounts for the majority of data transfers. The analysis also includes the detection of anomalies such as invalid TCP flag combinations, port scans, and anomalies in traffic volume.

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


Two-level mortar domain decomposition preconditioners for heterogeneous elliptic problems We consider a second order elliptic problem with a heterogeneous coefficient, which models, for example, single phase flow through a porous medium. We write this problem in mixed form and approximate it for parallel computation using the multiscale mortar domain decomposition mixed finite element method, which gives rise to a saddle point linear system. We use a relatively fine mortar space, which allows us to enforce continuity of the normal velocity flux, or nearly so in the case of nonmatching meshes. To solve the Schur complement linear system for the mortar unknowns, we propose a two-level preconditioner based on the interfaces between subdomains. The coarse preconditioner also uses the multiscale mortar domain decomposition method, but with instead a very coarse mortar space. We show that the prolongation operator of the coarse mortar to the fine is defined uniquely by the condition that the L 2 -projection of a coarse mortar agrees with its projection onto the space of normal velocity fluxes, i.e., no energy is introduced when changing mortar scales. The local smoothing preconditioner is based on block Jacobi, using blocks defined by the interfaces. We use restrictive smoothing domains that are smaller normal to the interfaces, and overlapping in the directions tangential to the interfaces. In the simplest case, the condition number of the preconditioned interface operator is bounded by a multiple of (log(1 + H/h)) 2 . We show several numerical examples involving strongly heterogeneous porous media to demonstrate the efficiency and robustness of the preconditioner. We see that it is often desirable, and sometimes necessary, to use a piecewise linear or higher order coarse mortar space to achieve good convergence for heterogeneous problems. On a domain Ω ⊂ R d , d = 2 or 3, we consider the second order elliptic problem. wherein ν is the outer unit normal vector to the domain, which is written in mixed form, i.e., as a system of two first order equations plus the boundary condition. The equation arises from minimizing the functional F(u, p) = 1 2 E(u) + Ω (∇ · u − f ) p dx, where E(u) = Ω a −1 |u| 2 dx is the energy of the system and p enforces the divergence constraint. We target applications involving flow in porous media [1, 2] , in which case p is the fluid pressure, u is the (Darcy) velocity, and the coefficient a is the permeability. The permeability is often highly anisotropic and heterogeneous, varying by many orders of magnitude from point to point. In fact, often the permeability has narrow channels within which the flow is concentrated. These channels are high in permeability and correlated for great distances in some directions but not in others (see, e.g., [3] ).. Understanding and predicting fluid flow processes is critical in many subsurface applications, such as CO 2 sequestration, nuclear waste storage, and oil and natural gas production. Furthermore, the flow problem is one of the most time-consuming parts of these simulations. With the development of reservoir characterization methods and geostatistical modeling techniques, the description of reservoir properties can be detailed at multiple scales, from core scales (centimeters) to geological scales (kilometers). A typical reservoir or aquifer is extremely large, and so the geocellular model may have billions of mesh elements. Subsurface processes often last hundreds of years, as in the case of CO 2 migration, or even millions of years for nuclear contaminants. Therefore, we can only simulate these processes using massively parallel supercomputers.. One way of tackling this problem is to reduce its size through upscaling or multiscale techniques [4] . However, the accuracy of the upscaled solution can deteriorate with increasing channel correlation length. Moreover, the flow solution is often coupled to a transport problem, which can magnify errors associated to the flow (see Sec. 2.2 below). Our goal is to solve the system on a fine-scale and use multiscale ideas to design effective and robust two-level preconditioners that are suitable for parallel computing when combined with a Krylov accelerator. It is not a new idea to use multiscale ideas to design preconditioners (see, e.g., [5, 6, 7] ), multigrid methods (e.g., [8, 9] ), and other iterative procedures (e.g., [10] ).. Our approach is to use domain decomposition methods to increase parallelism. In pioneering work, Glowinski and Wheeler [11] defined a nonoverlapping domain decomposition approach to solve the mixed system (1)- (3) . We base our work on this method, as modified later to incorporate a general mortar space [12] , which became the multiscale mortar mixed method [13, 14] . This method fully resolves the problem within the subdomains and glues them together with a mortar finite element space. A multiscale solution is obtained when the mortar uses only a few degrees of freedom per interface between subdomains. We use a relatively fine scale mortar space to obtain a fine-scale solution, and a coarse mortar space to define the coarse level preconditioner. The key is to define the extension operator R T 0 from the coarse to the fine mortar space. In fact, we will 2. show that it is uniquely defined by the energy minimizing condition (16) that the L 2 -projection of a coarse mortar agree with the projection of its extension, where the projection is onto the space of traces of the normal component of the velocity on the interfaces between subdomains.. The local, smoothing part of the two-level preconditioner is based on the block Jacobi method, where the block is determined by the unknowns on each interface between subdomains. We advocate using a nonsymmetric, overlapping smoother [15, 16, 17, 18, 19, 20, 21, 22] .. There is a vast literature on the subject of preconditioners for elliptic problems [22, 23] . We mention only a few closely related works that apply to mixed or saddle point systems. The balancing domain decomposition (BDD) [24, 25] and BDD with constrains (BDDC) [26] approaches are very similar. These two base their coarse and local preconditioners on single subdomain problems rather than on the interfaces between adjacent subdomains. The method in [27] shares many similarities in terms using domain decomposition and multiscale preconditioners. Solving the interface system using multigrid has been proposed in [28, 29] . In the simplest case, our preconditioner has a bounded condition number; the proof (not given here) is related to well-developed theory for similar methods [30, 18, 24, 31, 19, 22] .. Numerical examples show that the convergence performance of our preconditioners is not very sensitive to the ratio of the highest to smallest permeability in a high contrast medium (at least when appearing in a checkerboard arrangement). Problems involving heterogeneous porous media, such as the permeability fields from the SPE10 benchmark problem [3] , show that the preconditioned system has a low condition number and eigenvalues clustered around 1, and that our preconditioner is relatively efficient and robust for these types of problems.. In the sequel, Section 2 describes the general mortar domain decomposition methods used and shows why a fine-scale solution is desired for the coupled flow-transport system of two-phase flow in porous media. Section 3 introduces the fine and coarse multiscale mortar domain decomposition methods. The coarse and local preconditioners are defined in Sections 4-5, and these are combined into two-level preconditioners in Section 6. The bound on the condition number is given in Section 7. Numerical results are presented in Section 8, and a summary and conclusions are given in the last section. We defined domain decomposition, two-level, additive, multiplicative, and hybrid iterative preconditioners (33)-(34) for elliptic problems in mixed form, most likely to be used within a Krylov accelerator such as PCG or GMRES. These two-level preconditioners incorporate a coarse preconditioner based on subdomain interfaces using the multiscale mortar method [14, 35, 36] and a local smoothing preconditioner based on block Jacobi (BJ), blocked by subdomain interfaces.. Given mixed finite element and fine scale mortar spaces for the discretization of the elliptic problem (4)-(6), we provided a framework for defining the coarse mortar space and thereby the coarse preconditioners. We need the technical assumption (10) for unique solvability, and the assumption (13) , that the projection P onto the space of normal fluxes of the coarse mortar space is contained in the projection of the fine mortar space. In terms of the coarse Schur complement matrix S 0 , the coarse preconditioner M 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 projection P of a coarse mortar agree with the projection of the extension (i.e., (16) ). Application of R 0 can be simplified in the matching and nonmatching mesh cases. We use local smoothers M −1 loc based on BJ that arise from solving the local problem (27)-(29) on a domainΩ i j ⊃ Γ i j . We use one of the full smoothing domainΩ i j = Ω i j (BJ), a restrictive domainΩ i j Ω i j (RBJ), an overlapping domainΩ i j Ω i j (OBJ), or a domain restricted normal to Γ i j and overlapping in the tangential directions (ROBJ). Generally, RBJ or ROBJ are the most efficient. The overlapping smoothers lead to an nonsymmetric local, and therefore also two-level, preconditioner.. The simplest additive two-level preconditioner that uses piecewise constant coarse mortars on matching grids has a preconditioned matrix with a condition number bounded by a multiple of (log(H/h)) 2 (Theorem 7.1), which is the same as in the classic BDD [18, 24] and BDDC [26] two-level preconditioners, which are based on subdomains rather than interfaces.. Finally, we showed some numerical examples that demonstrate the convergence performance of the preconditioners. We observed that the two-level preconditioners are not very sensitive to the ratio of the highest to smallest permeability in a high contrast medium (at least when appearing in a checkerboard arrangement). We considered problems involving heterogeneous porous media, such as the permeability fields from the SPE10 benchmark problem. We observed that the preconditioned system has a low condition number and eigenvalues clustered around 1. We also found that it is often desirable, and even necessary, to use at least piecewise linear instead of piecewise constant coarse mortar spaces to achieve convergence and efficiency. Moreover, the use of restrictive local smoothers improved efficiency significantly, without increasing much the number of iterations to converge. Errors often accumulate around the corners of the subdomains, so the use of the nonsymmetric restrictive overlapping preconditioner (ROBJ) could result in a faster and more robust algorithm. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

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


Lipid Rafts and Apical Membrane Traffic ABSTRACT: Lipid rafts are dynamic assemblies floating freely in the surrounding membranes of living cells. This membrane heterogeneity provides a useful concept for understanding processes as diverse as cell polarity, signal transduction, and membrane sorting. Individual rafts are small entities containing thousands of lipids but only a few proteins. Regulation of raft association and size is an elementary feature of interactions at the molecular level. By clustering small rafts into a bigger platform, proteins are brought together for modification. Oligomerization might transform a monomeric weakly raft-associated protein into an assembly with higher raft affinity. Lectins are multivalent glycoprotein-binding proteins and are likely to be key players in mediating the clustering of rafts in vivo. Glycosylation-dependent surface delivery in a polarized fashion is a feature conserved across evolution, and we expect lectins to be at the heart of the molecular machinery responsible for lipid raft delivery to the cell surface. Currently, we are evaluating candidate proteins by affinity chromatography, proteomics, and RNA interference.Lipid rafts are dynamic microdomains in the membranes of living cells, composed of cholesterol and sphingolipids. Cholesterol and sphingolipids carrying saturated hydrocarbon chains assemble to form tightly packed subdomains corresponding to liquid-ordered phases biophysically characterized in model membranes. 1,2 These lipid rafts float freely in the surrounding membrane which is more fluid and analogous to the liquid-disordered phase. At the molecular level, the higher fluidity is the consequence of the high surface area occupied by unsaturated phospholipids compared to the dense packing of the sphingolipid-cholesterol assemblies. Cholesterol also condenses monounsaturated phospholipids but leaves them in the liquid-disordered phase. 3 Proteins strongly associating with lipid rafts include glycosylphosphatidylinositol (GPI)-anchored proteins, doubly acylated proteins, and several transmembrane proteins, especially palmitoylated ones. The concept of lipid raft microdomains builds a framework to incorporate seemingly unrelated processes such as cell polarity, signal transduction, and membrane sorting in a coherent fashion. Crucial to this concept is the regulation of raft association and size. By clustering small individual rafts together into a larger platform, efficient interaction of raft-associated proteins is realized. Weak raft affinities of individual proteins are strengthened by oligomerization. Apart from classic ligands and cytoskeletal scaffolds, we believe that lectin-mediated clustering of glycoproteins is an important way for cells to regulate lipid rafts in vivo (FIG. 4) .

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Oscillation of certain third-order difference equations We establish some new criteria for the oscillation of third-order difference equations of the form ∆((1/a 2 (n))(∆(1/a 1 (n))(∆x(n)) α1 ) α2 ) + δq(n) f (x[g(n)]) = 0, where ∆ is the forward difference operator defined by ∆x(n) = x(n + 1) − x(n). In this paper, we are concerned with the oscillatory behavior of the third-order difference equation. (1.1;δ) where δ = ±1, n ∈ N = {0, 1,2,...},. (

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


TIME ACCURATE FAST THREE-STEP WAVELET-GALERKIN METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS We introduce the concept of three-step wavelet-Galerkin method based on the Taylor series expansion in time. Unlike the Taylor-Galerkin methods, the present scheme does not contain any new higher-order derivatives which makes it suitable for solving nonlinear problems. Numerical schemes taking advantage of the wavelet bases capabilities to compress the operators and sparse representation of functions which are smooth, except for localized regions, up to any given accuracy are presented. Here numerical experiments deal with advection equation with the spiky solution in one dimension, two dimensions and nonlinear equation with a shock in solution in two dimensions. Numerical results indicate the versatility and effectiveness of the proposed scheme. Wavelets method is a new numerical tool for solving partial differential equations (PDEs). Wavelet analysis assumed significance due to successful applications in signal and image processing during the eighties. Compactly supported wavelets which are differentiable were introduced by Daubechies in her celebrated paper, 1 which has had applications in a number of areas. Since these functions combine orthogonality with localization and scaling properties, it has been a natural idea to attempt to use these functions for the numerical approximation to solutions to partial differential equations (PDEs). There have been a number of papers in this direction including studies of Burgers' equation 2, 3 as well as two-dimensional flow. [4] [5] [6] Glowinski et al. 7 considered wavelet-based variational methods to solve one-dimension linear and nonlinear ordinary differential equations. Where multiresolution analysis and their associated scale function bases are used as alternative bases in Galerkin methods.. Thus, such methods have convergence properties similar to the ones of spectral methods, and simultaneously, partial derivative operators discretize similarly as the finite-difference methods.. In the literature, many tentatives have been performed, often based on Galerkin or Petrov-Galerkin methods which use the compression properties of wavelet bases, and contain specific wavelet methods for PDEs. Some of them take advantage of the wavelet compression of the solution, 2 others use instead the wavelet compression of the operator. 8 The aim of this paper is to introduce fast three-step wavelet-Galerkin method which has the benefit of both these properties.. In the conventional numerical approach to transient problems, the accuracy gained in using the high-order spatial discretization is partially lost due to the use of low-order time discretization schemes. Here, usually spatial approximation precedes the temporal discretization. On the contrary, the reversed order of discretization can lead to better time accurate schemes with improved stability properties. The fundamental idea behind the Taylor-Galerkin approach 9 is the substitution of space derivatives for the time derivatives in the Taylor series, as used in derivation of the Lax-Wendroff method, 10 the only modification being that the procedure is carried out to third order. However, its applications are mainly for hyperbolic problems and some convection diffusion equations, because too many terms are introduced in the third-order time derivative term, especially for nonlinear multidimensional equations, and treatment of the boundary integrations arising from high-order time derivative terms are too complicated. A three-step finite element method based on a Taylor series expansion in time is proposed in Ref. 11 . This scheme involves neither complicated expression nor higher-order derivatives like the Taylor-Galerkin method 9 but the advantage has not been taken of sparsity of matrices which are in evolutionary problems. Time accurate solution of Korteweg-de Vries equation using the wavelet-Galerkin method is also developed in Ref. 12 and wavelet multilayer Taylor-Galerkin schemes for hyperbolic and parabolic problems are introduced in Ref. 13 . Our three-step wavelet-Galerkin method is based on fast algorithms like matrix vector product in wavelet bases and wavelet compression property of smooth data. Solutions to PDEs often behave differently in different areas. In fluid dynamics, we have shocks, boundary layers and turbulence. In acoustics, an example of PDEs is a low-frequency wave, with a localized high-frequency burst. For these examples, the solution can be smooth in most of the solution domain, with small areas where the solution changes quickly. Where the discretization in space (correlatively in time) ought to handle a huge number of degrees-of-freedom. The aim of the present paper is to examine the feasibility of applying fast three-step waveletGalerkin method to such types of PDEs which require the advantage of wavelet compression. A combination of such a time-marching scheme with wavelet approximation in space can lead to simple higher-order space and time accurate numerical methods. In the three-step wavelet-Galerkin method, the precedence of time discretization to space discretization in conjunction with wavelet bases for expressing spatial terms renders robustness to the proposed schemes and makes them space and time accurate. The three-step wavelet-Galerkin method retains the third-order accuracy and stability property of the Taylor-Galerkin method. The concepts are introduced through linear advection equation and Burgers' equation where we can show the power of wavelet compression as well as time accurate schemes. Since no new higherorder derivative term occurs in the numerical formulations, the present method is suitable for nonlinear problems. Further, the method can be directly extended to three-dimensional problems. The numerical results show that the present method is computationally efficient.

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