The surface/surface intersection problem by means of matrix based representations Evaluating the intersection of two rational parameterized algebraic surfaces is an important problem in solid modeling. In this paper, we make use of some generalized matrix based representations of parameterized surfaces in order to represent the intersection curve of two such surfaces as the zero set of a matrix determinant. As a consequence, we extend to a dramatically larger class of rational parameterized surfaces, the applicability of a general approach to the surface/surface intersection problem due to J. Canny and D. Manocha. In this way, we obtain compact and efficient representations of intersection curves allowing to reduce some geometric operations on such curves to matrix operations using results from linear algebra. Computing the intersection between two parameterized algebraic surfaces is a fundamental task in Computer Aided Geometric Design. Several methods and approaches have been developed for that purpose. Some of them are based on the use of matrix representations of the objects because they allow to transform geometric operations on the intersection curve into matrix operations. This approach seems to have been first introduced by J. Canny and D. Manocha in their paper [16] . Roughly speaking, it consists in representing the implicit equation of one of the two surfaces as the determinant of a certain matrix, necessarily square. Then, instead of using this implicit equation, the matrix itself is used as a representation of this first parameterized surface and then a matrix representation of the intersection curve is easily obtained by substituting the implicit variables with the parameterization of the second surface.. As far as we know, this matrix based approach and all its successive improvements (see e.g. [13, 18] ), have only been developed by using square matrices for representing parameterized surfaces. These matrices are obtained either as resultant matrices, which is the case for instance in [16] , or as matrices filled with some syzygies of a parameterization. This second class of matrices is known under the name of the moving quadrics method (see [19, 12, 9] ). It turns out that only some particular surface parameterizations, namely the parameterizations without base points (i.e. that are well defined over all their parameter space) can be represented by such matrices (with the exception of the matrices given in [9] ). This absence of base points is definitely a very strong constraint in the context of applications in solid modeling. It is hence the main limitation of applicability of the Canny-Manocha matrix based approach to the surface/surface intersection problem that is nevertheless an interesting compromise to provide an efficient, robust and accurate solution to this problem (see [16] ). The goal of this paper is to overcome this limitation.. Recently, new matrix representations of parameterized algebraic surfaces have been introduced in [11, 7, 6] . These matrices are filled with syzygies of a parameterization in the same spirit as the moving quadrics method, but with the difference that they are non-square matrices. However they are still representation matrices because they are generically full rank matrices and their rank drop exactly on the surface (this is a direct generalization of a matrix determinant to non-square matrices). The main advantage of using these representation matrices is that they exist for a significantly larger class of parameterizations, in particular for most of parameterizations having base points (see [11, 7, 8, 6] for details).. In this paper, we will introduce the use of these more general matrix representations in the context of the surface/ surface intersection problem. By doing this, a new difficulty appears because we will have to manipulate pencils of matrices 1 that are non-square, whereas in the classical Canny-Manocha approach the intersection curve is directly represented as a matrix determinant. It turns out that most techniques and algorithms that allow to determine the intersection curve with its exact topology need an implicit equation of this curve. Therefore, it is necessary to extract such an equation from a non-square matrix representation of this curve. For that purpose, instead of proceeding in a naive way by computing a greatest common divisor of several minors, we develop an algorithm based on matrix operations to extract from the non-square pencil of matrices all the information we need under the form of a pencil of square matrices. We will here follow the work of V. N. Kublanovskaya on what is called the ∆W − 1 decomposition algorithm [14] .. The paper is organized as follows. In Section 2, we briefly define and review the matrix representations of a parametrized surface that we will use in the sequel. In Section 3, we deal with the surface/surface intersection problem. In particular, we show how to reduce the computation of the intersection curve of two parameterized surfaces to the determination of the spectrum of a bivariate pencil of matrices. Then, in Section 4 we propose a method, based on the ∆W − 1 decomposition of V. N. Kublanovskaya , that allows us to extract the regular part corresponding to the one-dimensional eigenvalues of such a bivariate pencil of matrices. The paper ends with some illustrative examples.. This work is a follow-up of a more general research program whose goal is to show that non-square matrix representations of algebraic curves and surfaces can be used in the place of square matrix representations with the advantage of being available for a dramatically larger class of parameterizations. Thus, in [2] the curve/surface intersection problem has been addressed and the space curve/space curve intersection problem is treated in [5] . As a natural continuation, we deal with the surface/surface intersection problem in this paper. This work is part of the PhD thesis of the second author [1] .. For simplicity, throughout the paper the ground field will be an algebraically closed field, typically the field of complex numbers C. However, mention that most of the results in Section 2, notably the matrix-based representations of surfaces we will introduce, could be given over an arbitrary infinite field. Given two parameterized surfaces, this paper proposes a new method for computing an equation of a plane curve that is in correspondence with the intersection space curve of these two surfaces for very general parameterizations. This operation is the first step of the whole treatment of the intersection of two parameterized surfaces following an approach that has been introduced by Canny and Manocha [16] . Our results allow to remove the strong assumptions that was necessary to require on the surface parameterizations, making this approach applicable for two general surface parameterizations. In a future work, we plan to study the computational complexity of this algorithm which is difficult to determine because of the reduction of pencil of matrices based on Kublanovskaya decomposition.

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


Changing learning with new interactive and media-rich instruction environments: virtual labs case study report Technology has created a new dimension for visual teaching and learning with web-delivered interactive media. The Virtual Labs Project has embraced this technology with instructional design and evaluation methodologies behind the simPHYSIO suite of simulationbased, online interactive teaching modules in physiology for the Stanford students. In addition, simPHYSIO provides the convenience of anytime web-access and a modular structure that allows for personalization and customization of the learning material. This innovative tool provides a solid delivery and pedagogical backbone that can be applied to developing an interactive simulation-based training tool for the use and management of the Picture Archiving and Communication System (PACS) image information system. The disparity in the knowledge between health and IT professionals can be bridged by providing convenient modular teaching tools to fill the gaps in knowledge. An innovative teaching method in the whole PACS is deemed necessary for its successful implementation and operation since it has become widely distributed with many interfaces, components, and customizations. This paper will discuss the techniques for developing an interactive-based teaching tool, a case study of its implementation, and a perspective for applying this approach to an online PACS training tool. q web design; Picture archiving and communication system training simulator 0895-6111/03/$ -see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 5 -6 1 1 1 ( 0 2 ) 0 0 0 8 9 -7 The PACS requires a diversity in personnel to interface with the intricate and complex system. To successfully implement PACS, a comprehensive education program would enable personnel to interleave all of its components seamlessly. SimPHYSIO's pedagogical design and methodologies can be applied to build an educational environment for all levels of personnel involved in integrated PACS. simPHYSIO is a suite of interactive online teaching media designed to integrate and dynamically teach complex systems using media-rich animations, real-time simulations, and virtual environments in physiology. The strength of simPHYSIO also includes internet distribution, scalability, and content customization. Integration of educational media into the curriculum becomes increasingly successful with the addition of relevant content and working closely with the course administration. Our interactive and visual teaching approach was one of the most salient features in helping a student learn physiology AND enjoy it in the process. "Move over, textbooks. Homework's not just reading in the Core anymore. Today's human biology students make hearts beat, experiment with surface tension, and stimulate neurons in visual signaling pathways. All of this and more is possible with the advent of the Virtual Labs, an ambitious project designed to bring custom-designed 'virtual' physiology experiments and experiences to students of the human biology core." (Newsletter 2000-2001) [11] .. There is a need for electronic learning tools to enhance existing teaching pedagogy and offer alternative learning situations. This kind of media becomes essential today-to widely distribute modular teaching content a convenient, effective, and engaging learning tool. The success of simPHYSIO in other curricula can have a major impact on biomedical science education programs. simPHYSIO can also have a much broader use-continuing education (industry, nursing, pharmaceutics, physical therapy, etc.); delivery to underprivileged institutions; 'refresher' resource for review; keeping up-to-date with current content. The pedagogical and design strategy of simPHYSIO is not limited to the biomedical sciences, it can be applied to teaching any topic. SimPHYSIO, also referred to as Virtual Labs, is an interactive educational website with modules in renal, cardiovascular, respiratory, gastrointestinal, and neuro systems that cover difficult concepts for physiologyrelated courses at Stanford University. The underlying pedagogy uses learner-centered design and motivational strategies to deliver an active learning atmosphere that is enjoyable and memorable for the students. An additional database website of student usage data was established for evaluation purposes. Last year, simPHYSIO introduced required online problem sets for each topic and a chat room used for online office hours, student forum, or discussion area ( Fig. 2 ).

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


Ontologies for Supporting Engineering Design Optimization This paper presents an optimization ontology and its implementation into a prototype computational knowledge-based tool dubbed ONTOP (ontology for optimization). Salient feature of ONTOP include a knowledge base that incorporates both standardized optimization terminology, formal method definitions, and often unrecorded optimization details, such as any idealizations and assumptions that may be made when creating an optimization model, as well as the model developer's rationale and justification behind these idealizations and assumptions. ONTOP was developed using Protégé, a Java-based, free open-source ontology development environment created by Stanford University. Two engineering design optimization case studies are presented. The first case study consists of the optimization of a structural beam element and demonstrates ONTOP 's ability to address the variations in an optimal solution that may arise when different techniques and approaches are used. A second case study, a more complex design problem that deals with the optimization of an impeller of a pediatric left ventricular heart assist device, demonstrates the wealth of knowledge ONTOP is able to capture. Together, these test beds help illustrate the potential value of an ontology in representing application-specific knowledge while facilitating both the sharing and exchanging of this knowledge in engineering design optimization. Optimization, most noticeably design optimization, has established itself as a mainstay in the field of engineering, becoming an integral part of engineering design process. The application of the field of optimization to engineering design has grown to involve a substantial number of terms, methods, and software programs. Consequently, an immense amount of knowledge is associated with optimization within engineering. The organization and availability of this knowledge can play a significant role when interpreting outcomes of a design optimization problem.. Solutions to optimization problems, as with results obtained in many other fields of engineering, depend heavily on initial assumptions and conditions. Optimization results, especially in complex problems such as nonlinear multivariate engineering problems, can vary widely depending on the type of approach or technique used when solving of a problem. A situation of multiple solutions is commonly encountered, as demonstrated later in the paper when optimizing a relatively simple cantilever I-beam. A reliable mechanism is needed for ensuring the integrity of a problem, the optimization process, and the resulting optimized solutions. This paper introduces the design and development of such an approach, using the instantiation of an ontology to serve as a formal method for capturing and retaining domain-specific knowledge in an explicit, easy-to-follow, and comprehensive manner. The ontology implementation ONTOP ͑ontology for optimization͒ will address the critical information gap in the engineering design optimization process. This information gap includes the complications created through inconsistent optimization lexicons, the large number of optimization methods that have been created, and the lack of communication between existing optimization tools.. A substantial, yet widely overlooked problem in engineering, the absence of an ability to represent abstract design-related knowledge, will be one of the main focuses of the ontology for optimization. The ontology will provide methods for both capturing and sharing this often neglected higher-level knowledge. The capturing of abstract knowledge is also the next step in improving design optimization techniques and one of the major tasks accomplished in ONTOP. The representation of this abstract engineering design optimization modeling knowledge by ONTOP will greatly facilitate the development of robust design optimization models for modified and similar products. As industry continues to redesign and optimize products and processes, optimization knowledge becomes ever more valuable. This process will reduce time once spent in recreating models from scratch as well as facilitate the elimination of costly trial and error approaches. ONTOP will overall improve the ability to manage optimization knowledge.. ONTOP is able to identify multiple design optimization models created under a single optimization type as well as multiple model revisions created using a single method. This detailed compilation of knowledge allows engineers to track the progression of solutions to a single design optimization model. ONTOP also affords engineers the ability to approach design optimization problems within an established optimization knowledge base using welldefined techniques. The knowledge from a specific optimization problem can then be stored through a class instance, each instance specifically defined by the attributes of the design being optimized. ONTOP can provide an engineer a method for quickly identifying feasible optimization techniques for a given design optimization problem while capturing the knowledge within the problem and help ensure the integrity and quality of the optimization process. While ample work has been done on ONTOP, there is still room for further advancement. As Gruber states, "In short, a commitment to a common ontology is a guarantee of consistency, but not completeness, with respect to queries and assertions using the vocabulary defined in the ontology" ͓31͔. This statement acknowledges that while ontologies can guarantee consistency, they cannot guarantee completeness. The optimization knowledge stored within the ontology still has considerable room for additional methods and techniques, though there does exist a trade-off between ontology complexity and ease of use. The slots used to define the ontology may still be refined to capture further information that may be important for other optimization models. As additional properties are added within Protégé, the amount of the knowledge stored increases, as does its complexity. However, it must be recognized that there is a limit to the practicality of ON-TOP, and that there is a price to pay as the complexity of the ontology increases. This price is reflected in the time taken in storing and sharing the knowledge.. Methods for sharing the knowledge must still be explored, as there is no "best" way to share the knowledge, and many options are available. The Protégé program incorporates the ability to share knowledge through commonly accepted methods. Protégé provides the ability to generate HTML files from the knowledge stored within the ontology. Protégé also provides the option to export the knowledge into OWL ͑web ontology language͒ ͓32͔ and XML ͓33͔ formats. OWL is based on XML and has become a web standard as well as a widely accepted language in the computer programing field.. The ability to export the knowledge stored in Protégé into standard formats is a major advantage to using the program as an ontological tool, along with its easy-to-use graphical interface. It is recognized that there alternate methods for creating and sharing ontologies, and ONTOP implementation will not be restricted to Protégé. Using its open source code and plug-in capabilities, methods are currently being created with the ability to extract knowledge from a Protégé ontology and automatically create a technical report. This ability will allow an engineer to recapture time once used in creating technical report and apply it to the instantiation of an optimization model in the ontological knowledge base. The ability to automatically create a technical report will justify the time spent in instantiation of a knowledge instance within ONTOP. This technical report method is in its final stages of development, and is currently capable of creating a rough report from the knowledge instances contained in the ONTOP knowledge base. When completed, the technical-report generator will be available as a method that operates on the ONTOP knowledge base to create a well-detailed, easy-to-read technical report.. Currently OTNOP provides the ability to capture abstract knowledge in "string" format as well as more specific optimization knowledge. Through this knowledge, others are able to better understand a problem, and what changes may have been made from earlier versions. As the ONTOP continues to be developed, domain knowledge is becoming more explicit when capturing both higherand lower-level knowledge. This explicitness will eventually lead to the ability to operate on the captured knowledge base using logical reasoning. This logical reasoning could then be used to guide and facilitate the knowledge-capturing process.. ONTOP was successfully employed during the optimization of the PVAD impeller. It was able to capture and store all the knowledge used in the optimization of the PVAD impeller, as well as successfully share it with others. ONTOP allowed the number of optimization runs to be tracked, as well as the solution of each run. The abstract knowledge involved in the optimization of the PVAD was successfully passed as well. The images and details stored in the ontology proved very useful in understanding the optimization problem at hand.. Although the ONTOP test beds demonstrated its ability to capture significant amounts of model information, it also revealed a major shortcoming, its inability to distinguish between optimization, analysis, and geometric properties. This shortcoming can be addressed by expanding the scope of ONTOP beyond optimization. A new, revised, ontology is currently in the process of being created through its incorporation with ON-TEAM. Incorporation of ONTOP with the existing ON-TEAM structure will provide a more complete ontology for engineering design. The new ontology has incorporated and linked optimization models, analysis models, and geometric models. Links created between these models will lead to a much greater understanding of the individual models as well as their properties. Eventually, full product design knowledge and development knowledge with be easily stored and readily accessible using ontologies.

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


A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three-dimensional, unsteady, and nonlinear water waves generated by a ship hull advancing in water.The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-differential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via implicit Backward Differentiation Formulas (BDF) with adaptive step size and variable order.When the velocity of the advancing ship hull is non-negligible, the semiLagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free-surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method.The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on a Wigley hull advancing in calm water with fixed sink and trim. The use of computational tools to predict hydrodynamic performances of ships has gained a lot of popularity in recent years. Models based on potential flow theory have historically been among the most successful to assess the wave pattern around a ship hull in presence of a forward ship motion.. In this framework, the assumptions of irrotational flow and inviscid fluid reduce the Navier Stokes incompressibility constraint and momentum balance equations to the Laplace's and Bernoulli's equations, defined on a moving and a-priori unknown domain.. This boundary value problem is tackled with a Mixed Eulerian-Lagrangian approach, in which the Eulerian field equations are solved to obtain the fluid velocities, which are then used to displace in a Lagrangian way the free-surface, and update the corresponding potential field values [24] . In this framework, the Eulerian problem is expressed in boundary integral form, and it is typically discretized using the Boundary Element Method (BEM). The velocity field and Bernoulli's equation provide a kinematic boundary condition for the Lagrangian evolution of the free-surface, and a dynamic boundary condition for the evolution of the potential field.. Numerical treatment of the Lagrangian step usually relies on accurate reconstructions of the position vector and of potential field gradients. In presence of a forward motion, these reconstructions may lead to instability in the time advancing scheme for the free-surface discretization, as well as for the corresponding potential field values. A smoothing technique is often adopted to reduce the sensitivity of the discretization on the reconstruction of the full velocity field, at the cost of introducing an artificial viscosity in the system.. An alternative cure was presented by Grilli et al. [13] who developed a high order iso-parametric BEM discretization of a Numerical Wave Tank to simulate overturning waves up to the breaking point on arbitrarily shaped bottoms. The use of a high order discretization bypasses the problem of reconstructing the gradients, and is very reliable when the numerical evolution of the free-surface is done in a purely Lagrangian way.. Ship hydrodynamics simulations, however, are typically carried out in a frame of reference attached to the boat, requiring the presence of a water current in the simulations. In this case a fully Lagrangian approach leads to downstream transportation of the free-surface nodes, or to their clustering around stagnation points, ultimately resulting in blowup of the simulations (see, for example, [22] ).. Beck [4] proposed alternative semi-Lagrangian free surface boundary conditions, under the assumption that the surface elevation function is single-valued. Employing such conditions, it is possible to prescribe arbitrarily the horizontal velocity of the free surface nodes, while preserving the physical shape of the free-surface itself.. However, if there is a significant difference between the water current speed and the horizontal nodes speed, stability issues may arise [22] , [21] . For this reason, the semi-Lagrangian free-surface boundary conditions proposed by Beck have been in most cases employed imposing nodes longitudinal speeds equal to the water current ones [22] , thus reducing the instability at the cost of more complex algorithms for mesh management.. More recently, Sung and Grilli [23] applied an alternative method, combining semi-Lagrangian and Lagrangian free surface boundary conditions to the problem of a pressure perturbation moving on the water surface. The semiLagrangian free-surface boundary conditions were used also in the work of Kjellberg, Contento and Jansson [18] , where free-surface instabilities are avoided by choosing an earth-fixed reference frame, in which no current speed is needed.. The drawback of this choice is that in such frame the ship moves with a specified horizontal speed, and the computational grid needs to be constantly regenerated to cover the region surrounding the hull with an adequate number of cells.. The purpose of this work is to present a new stabilized semi-Lagrangian potential model for the simulation of three dimensional unsteady nonlinear water waves generated by a ship hull advancing in calm water. The resulting integro-differential boundary value problem is discretized to a system of nonlinear differential-algebraic equations, in which the unknowns are the positions of the nodes of the computational grid, along with the corresponding values of the potential and of its normal derivative.. Time advancing of the nonlinear differential-algebraic system is performed using implicit Backward Differentiation Formulas (BDF) with variable step size and variable order, implemented in the framework of the open source library SUNDIALS [15] . The collocated and iso-parametric BEM discretization of the Laplace's equation has been implemented using the open source C++ library deal.II [3] .. The computational grid, composed by quadrilateral cells of arbitrary order, is adapted in a geometrically consistent way (see [6] ) via an a-posteriori error estimator based on the jump of the solution gradient along the cell internal boundaries. Even when low order boundary elements are used, accurate estimations of the position vector and potential gradients on the free-surface are recovered by a Streamwise Upwind Petrov-Galerkin (SUPG) projection, which is used to stabilize the transport dominated terms. The SUPG projection is strongly consistent, and does not introduce numerical dissipation in the equations. This allows the use of robust unstructured grids, which can be generated and managed on arbitrary hull geometries in a relatively simple way.. The test case considered in this paper is that of a Wigley hull advancing at constant speed in calm water. The simulations have been performed using bilinear elements. The arbitrary horizontal velocity specified in the semi-Lagrangian free-surface boundary condition is chosen so the nodes have null longitudinal velocity with respect to the hull. The numerical results obtained imposing six different Froude numbers are finally compared with experimental results reported in [20] , to assess the accuracy of the model. An accurate and efficient boundary element method for the simulation of unsteady and fully nonlinear potential waves past surging ships was developed, implemented and tested. Compared to existing algorithms, the method presents several innovative features which try to address some of the most CPU intensive aspects of this kind of computations.. The most innovative idea behind the proposed method is the fact that the equations are studied on a fixed reference domain, which is deformed through an arbitrary Lagrangian Eulerian map that keeps track of the physical shape of the water domain around the ship. Some aspects of this approach resemble the semi-Lagrangian formulation of the potential wave equations, but here they are takled using powerful differential geometry tools, combined with finite element techniques for arbitrary surfaces.. This reformulation in terms of a fixed reference domain presents severe stability issues in presence of a forward ship motion, or in presence of an incident stream velocity. Stabilization is achieved via a weighted SUPG projection, which allows the use of fully unstructured meshes, and guarantees an accurate reconstruction of the velocity fields on the mesh nodes, also when low order finite dimensional spaces are used for the numerical discretization.. To the best of the authors' knowledge, such formulation has never been successfully used in ship hydrodynamic problems in presence of a non zero stream velocity, due to the free-surface instabilities.. With respect to existing methods, the combination of the semi-Lagrangian approach with the SUPG stabilization eliminates the need for periodic remeshing of the computational domain, and opens up the possibility to exploit local adaptivity tools, typical of finite element discretizations. We exploit these ideas by employing simple a-posteriori error estimates to refine adaptively the computational mesh. Accurate results are obtained even when using a very limited number of degrees of freedom.. Implicit BDF methods with variable order and variable step size are also employed, which render the final computational tool very attractive in terms of robustness.. A direct interface with standard CAD file formats is currently under development, and our preliminary results indicate that the final tool could be used to study the unsteady interaction between arbitrary hull shapes and nonlinear water waves in a robust and automated way.. The authors gratefully acknowledge the Italian/Slovenian cross-border cooperation eXact-Lab/Arctur for the processing power that was made available on the Arctur cluster.. while, given an Eulerian field q : Ω(t) × R → R, its Lagrangian representation would beq (x, t) := q(p(x, t), t), ∀x ∈Ω.. A similar structure is valid for ALE fields:. The fluid particle velocity v which appears in Problem (1) is the Eulerian representation of the particles velocity. In a similar way, we define the Eulerian representation of the domain velocity, or ALE velocity the field w such that. Time variations of physical quantities associated with material particles are computed at fixedx, generating the usual material derivative Dq(x, t) Dt := ∂q(p(x, t), t) ∂t. In a similar fashion, if we compute quantities at fixed ALE pointx, we obtain the ALE time derivative, wich we will denote as δq(x, t) δt := ∂q(p(x, t), t) ∂t. The ALE deformation allows one to define the equations of motions in Problem (1) in terms of the fixed ALE reference domainΩ, while still solving the same physical problem. On the free-surface part of the boundary, the ALE motion needs to follow the evolution of the fluid particles in order to maintain the correct shape of the domain Ω(t), in particular the minimum requirement for the ALE motion on the free-surface is given by the free-surface kinematic boundary condition. which complements the dynamic boundary condition (1c), and provides an evolution equation for the normal part of the ALE motion on the boundary Γ w (t). In terms of the ALE motion, the above condition reads ∂p ∂t (x, t) · n = v(p(x, t), t) · n on Γ w (t). (A.12). Equations (1c) and (A.11) are usually referred to as the free-surface dynamic and kinematic boundary conditions, since they represent the physical condition applied to the free-surface (equilibrium of the pressure on the water surface) and its evolution equation (the shape of the free-surface follows the velocity field of the flow).

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


Shielding against design flaws with field repairable control logic Correctness is a paramount attribute of any microprocessor design; however, without novel technologies to tame the increasing complexity of design verification, the amount of bugs that escape into silicon will only grow in the future. In this paper, we propose a novel hardware patching mechanism that can detect design errors which escaped the verification process, and can correct them directly in the field. We accomplish this goal through a simple fieldprogrammable state matcher, which can identify erroneous configurations in the processor's control state and switch the processor into formally-verified degraded performance mode, once a "match" occurs. When the instructions exposing the design flaw are committed, the processor is switched back to normal mode. We show that our approach can detect and correct infrequently-occurring errors with almost no performance impact and has approximately 2% area overhead. End-users of microprocessor-based products rely on the hardware to function correctly at all times. To meet this expectation, microprocessor design houses perform extensive validation of their designs before production and release to the marketplace. The success of this process is crucial to the survival of the company, as the financial impact of microprocessor bugs can be devastating (e.g., the infamous Pentium FDIV bug, which cost Intel $475 million).. Designers address correctness concerns through verification, the process of extensively validating all the functionalities of a circuit throughout the development process. Simulation-based techniques are central to this process: they exercise a design with relevant test sequences trying to expose latent bugs. However, this approach is often incapable of fully exercising the design space of modern processors. For example, the simple out-of-order core that we use in the experiments for this work has a total of 2 10441 distinct states, each with up to 2 128 outgoing edges. In contrast, the verification of the Pentium 4, which used a pool of 6,000 workstations, was only able to test as many as 2 37 states prior to tape-out [4] . It is obvious, that engineers must be very selective in the configurations that they choose to validate.. Formal verification techniques have grown to address the non-exhaustive nature of simulation-based methods. Formal methods utilize mechanisms such as theorem proving and model checking to show that a component violates or upholds a certain property. The primary drawback of formal techniques, however, is that they do not scale to the complexity of modern designs, constraining their use to only a few components within the processor. For example, the verification of the Pentium 4 heavily utilized formal verification techniques, but their use was limited to proving properties of the floating-point execution units, the instruction decoders, and the dynamic scheduler [5] .. Unfortunately, the situation is deteriorating with exponentially increasing design complexity and slower growth rate in the capabilities of design verification tools. Thus, without better verification solutions, or techniques to shield the system from design errors, we can only expect future designs to be more and more flawed.. In this paper, we introduce an expressive, reliable and lowcost control logic patching mechanism that allows a wide range of control-logic design bugs in a processor pipeline to be fixed in the field after manufacturing.. Our approach employs a control state matching mechanism, the state matcher, that identifies when the processor has entered a control state associated with a design bug. Once a match occurs, the pipeline is flushed and forced into a degraded performance mode of operation to execute the next instruction. We formally verified the correctness of the system in this mode of execution, guaranteeing correct forward progress past the occurrence of the flawed configuration by running in degraded mode. We specifically designed the control state matcher to detect multiple design errors with minimal false-positive triggering.. In the experimental result section we show that the area and performance impact of our solution are minimal. When multiple design errors must be corrected, we show that our state matcher can effectively trade-off area for false positive rate. Our solution goes beyond instruction and microcode patching because it can effectively address design errors that relate to a particular instruction, combination of instructions, and even errors that are not associated with any specific instruction, for instance a non-maskable interrupt.. The remainder of the paper is organized as follows. Section 2 makes a case for repairable control logic, by examining types of bugs that escape verification. Section 3 details our approach to field-repairable control logic and Section 4 evaluates its performance and area overhead. Finally, we present our conclusions in Section 5. In this paper we introduced the concept of field-repairable control logic, and presented a design that can detect when a processor enters a bug state and switch to a low-complexity reliable execution mode until the bug is bypassed. We described a low-cost CAM-based state matching mechanism to detect and recover from bugs. With moderate size matchers we can ensure highly accurate detection of bug states, as nearly all of our experiments demonstrate a specificity of 1. We found the area cost of the technique to be about or below 2%. Finally, we found that if the bug matching frequency is less than one recovery per 100 instructions, performance impacts are negligible.

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


Skeptical Notes on a Physics of Passage ABSTRACT: This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question of the paper is whether the existing representation of time is adequate, or whether it can or should be supplemented: especially, do we need a physics incorporating some kind of 'dynamical passage' of time? The paper argues that the existing mathematical framework is resistant to such changes, and might have to be rejected by anyone seeking a physics of passage. Then it rebuts two common arguments for incorporating passage into physics, especially the claim that it is an element of experience. Finally the paper investigates whether, as has been claimed, 'causal set theory' provides a physics of passage.The papers in this volume are based on talks given at a meeting Cape Town, in response to the question, 'do we need a physics of passage?' First, let's take it that the question asks whether we need a new physics, incorporating passage in a way that existing physics does not -especially, does a quantum theory of gravity require passage? Second, we are asking about a physics of passage, so the question is about the possible need for a mathematical representation of passage.'Passage' does not have an unequivocal meaning, so there is a different question for each meaning; however, my answer will be largely negative for each of the senses that I 1 I hope that I have explicated some of the important ways in which time, and especially passage already appear in our theories -and how the very mathematical framework resists one kind of program for developing a richer physics for passage. I've also indicated how certain intuitive pulls towards passage can be resisted: there's nothing actually wrong with the existing mathematics. Finally, in a somewhat more positive vein, I have sketched a different approach to passage; but even here the demands of relativity at least constrain progress when one thinks carefully about what passage means.

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Convex Programming Upper Bounds on the Capacity of 2-D Constraints Abstract-The capacity of 1-D constraints is given by the entropy of a corresponding stationary maxentropic Markov chain. Namely, the entropy is maximized over a set of probability distributions, which is defined by some linear equalities and inequalities. In this paper, certain aspects of this characterization are extended to 2-D constraints. The result is a method for calculating an upper bound on the capacity of 2-D constraints. The key steps are as follows: The maxentropic stationary probability distribution on square configurations is considered; set of linear equalities and inequalities is derived from this stationarity; the result is then a convex program, which can be easily solved numerically. Our method improves upon previous upper bounds for the capacity of the 2-D "no isolated bits" constraint, as well as certain 2-D RLL constraints.

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Day-Ahead Price Forecasting in Asia's First Liberalized Electricity Market using Artificial Neural Networks This paper proposes a comparative model for the day-ahead electricity price forecasting that could be realized using multi-layer neural network (MLNN) with levenberg-marquardt (LM) algorithm, generalized regression neural network (GRNN) and cascade-forward neural network (CFNN). In this work applications of various models were applied to national electricity market of Singapore (NEMS), i.e. Asia's first liberalized electricity market. The individual price of year 2006 is very volatile with a very wide range. Therefore, accurate forecasting models are required for Singapore electricity market company (EMC) to maximize their profits and for consumers to maximize their utilities. Hence the year 2006 has been taken for forecasting the uniform Singapore electricity price (USEP). The mean absolute percentage error (MAPE) results show that the proposed CFNN model possess better forecasting abilities than the other models and its performance was least affected by the volatility.Keywords: Price forecasting, Levenberg-marquardt (LM) algorithm, Generalized regression neural network (GRNN), Cascade-forward neural network (CFNN), National electricity market of singapore (NEMS), Uniform singapore energy price (USEP). In a de-regulated electric power industry, the electricity prices play a key role for market participants. The main objective of market participants is to ensure a transparent, professional and cost-effective market. Since the beginning of floating electricity prices, electricity price forecasting has become one of the main endeavors for researchers and practitioners in energy market. 1 The daily load curves have similar load patterns, whereas the electricity price movement shows very great volatility among all commodities. 2 Electricity price can rise to tens of or even hundreds of times its normal values at some periods. Sometimes, it may drop to zero or even to negative values at other periods. 3, 4 A good price forecasting tool in deregulated markets should be able to capture the uncertainty associated with those prices. Some of the key uncertainties are fuel prices, future addition of generation and transmission capacity, regulatory structure and rules, future demand growth, plant operations and climate changes. 5 From these many factors are impacting electricity price, in which some factors are more important than others. Besides, the factors, which impact price, they consider are very limited, just including historical price and system load. 6 Therefore, price forecasting tools are essential for all market participants for their survival under new deregulated environment. 7 Seeing the importance of the price-forecasting problem several techniques have been tried out in this paper. In general, hard and soft computing techniques could be used to predict electricity prices. 5 Prediction under hard-computing models, such as autoregressive integrated moving average (ARIMA) and generalized auto-regressive conditional heteroskedastic (GARCH) are used. This approach can be very accurate, but it requires a lot of information, and the computational cost is very high. 3 Prediction under soft-computing models, such as artificial neural network (ANN) and other intelligent algorithms are used. In particular, neural networks have been used to solve problems such as load/price predictions, component and system fault diagnosis, security assessment, unit commitment etc. The ANN is a simple, powerful and flexible tool for forecasting, providing better solution to model complex non-linear relationships. 8 The considered hard computing models are linear predictors, 13 while electricity price is generally a nonlinear. The proposed ANN soft computing approach works on complex nonlinear relationships than the traditional linear models. Moreover, there is no hard computing approach with satisfactory performance in dealing with the spikes. 8 Hence, compared to hard computing, an important advantage of the proposed soft computing approach is, it learns well the nonlinear training pattern. It effectively encounters even large prediction errors in the test phase. The soft computing models are fast in execution. The hard computing models are time consuming. 5 The superiority of the soft computing model is on the robustness, particularly in the easy interpretability of the models. Some electricity market price forecasting models using a multi-layer neural network (MLNN), training by levenberg-marquardt (LM) algorithm, 5, 14, 15 and generalized regression neural network (GRNN) with principal component analysis (PCA) 12 There is a need to make more research efforts in other markets as well; this will help in interpreting and understanding the price evolution in different electricity markets in a better perspective. 7 So, this paper mainly focuses on several half-hour ahead electricity prices using historical data from the Singapore's power system. The Singapore's electricity pool, an Asia's first liberalized electricity market; a new legal and regulatory framework was introduced that formed the basis for a new electricity day-ahead market. The electricity market company (EMC) implemented the wholesale market systems, rules and business that would underpin the new market.. The national electricity market of Singapore (NEMS) opened for trading, placing Singapore's at the forefront of a global movement to liberalize the electricity industry. All of Singapore's electricity is bought and sold through EMC in the NEMS. The EMC is the exchange for wholesale electricity trading, providing a transparent and competitive trading platform and the governance for the market. Generation companies offer every half-hour to sell electricity into the wholesale electricity market. All sales and purchases of electricity through the wholesale market are settled through EMC. Generators and retailers or major users can enter into financial bilateral agreements outside the wholesale market. 9 In Singapore's electricity market, the price of electricity varies every half-hour, so generators, retailers and consumers require some expectation of future electricity prices to aid them in optimizing their business strategies. Among the different techniques of price forecasting, application of ANN technology has been adopted in this paper because of its ability to learn complex and non-linear relationships that are difficult to model with conventional techniques. 2 In this study, a comparative electricity price forecasting was realized by using MLNN with LM algorithm, GRNN and proposed cascade-forward neural network (CFNN). The electricity price dataset were prepared by using singapore's daily trading reports, presented on a monthly basis. The CFNN are capable of recasting price efficiently than the other neural network structures, expecting a better mean absolute percentage error (MAPE).. To determine the effect of the proposed CFNN, different ANN models (MLNN with LM algorithm and GRNN) are trained. The remaining neural network models supported by the MATLAB are not able to learn the proposed electricity price dataset. Hence the above three models were taken. The rest of the paper is organized as follows. The section 2 presents data source and the different neural network structures to forecast electricity price using their dataset. Section 3 presents the numerical results of various neural network structures from a real-world case study based on the electricity market of Singapore. Finally, conclusions are presented in section 4. This paper presented several ANN models for dayahead price forecasting in Asia's first liberalized electricity market (NEMS). The important factors impacting electricity price forecasting historical price factors and demand factors are discussed. Past 42 days were trained and the next seven days were forecasted. In the first approach, an MLNN with LM model is used for price forecast. Then, different neural network structures were tested. Network types that have been tested include GRNN and CFNN. All of the neural network structures comprise 33 neurons in the input and one neuron in the output. Prediction results corresponding to the market of Singapore for the four weeks of the year 2006 is reported, yielding an average weekly MAPE which is close to 11.78% for MLNN with LM, 11.94% for GRNN, and 11.22% for CFNN respectively. In this research work, a CFNN has been proposed for price prediction. The simulation results from the comparisons clearly shows that the CFNN model is effective than other forecast models while the average computation time is 19 ms. Results show that the proposed CFNN approach is good in forecasting accuracy and less computation time than other ANN models. The research work is underway in order to develop better feature selection algorithm for different power markets and forecast models. This section describes the data source and different neural network structure for day-ahead price forecasting in Asia's first liberalized electricity market.

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


The Use of a Computerized Brain Atlas to Support Knowledge-based Training in Radiology Trainers of radiologists face the particular challenges of teaching normal and abnormal appearance for a variety of imaging modalities, providing access to a large appropriatelyindexed case library, and teaching a consistent approach to the reporting of cases. The computer has the potential to address these issues, to supplement conventional teaching of radiology by providing case-based tutoring and diagnostic support based on a large library of images of normal and abnormal anatomy, fully described in a consistent terminology. This paper presents a new approach to computer-based training in radiology that combines a knowledge-based tutor with an on-line medical atlas. It describes two existing computer systems, The MR Tutor and ATLAS, and discusses the medical, computational, epistemic, and pedagogic issues involved in developing a combined Atlas-Tutor. Integrating an atlas with a training system could significantly improve the teaching and support offered, but practical difficulties include the need to merge knowledge representations and to incorporate techniques for registering atlas plates on images that exhibit abnormalities. The paper addresses these problems, and concludes by indicating how the Atlas-Tutor might be employed in practical radiology training. A recent study of medical training in the United Kingdom (Towle 1991 ) identified many problems with current teaching methods and proposed a curriculum that would include: a greater emphasis on developing skills rather than communicating facts; introduction of selfdirected and problem-based learning; decentralised teaching; fair and objective assessment. Trainers of radiologists face not only this general need to reform the medical curriculum, but also the particular challenges of teaching normal and abnormal appearance for a variety of imaging modalities, providing access to a large indexed case library, and teaching a consistent approach to the reporting of cases.. Two separate teams, in the UK and in France, are addressing these issues by developing, respectively, a computer-based training system for MRI neuroradiology [Sharples, 1995 #422; Sharples, 1997 #435] and an on-line atlas of the brain (Montabord, Gibaud et al. 1993 ). These systems have been developed to prototype stage and are currently being evaluated for medical use. A general aim of both these research groups is to provide an environment that supports active learning and enquiry, that can adapt to the user's needs and abilities and can cover a range of radiological tasks including image interpretation, diagnosis, and surgery planning. This paper discusses the benefits to be gained by merging the two approaches, to provide a computerised brain atlas in support of radiology training. The paper reviews existing training systems for radiology and presents the need for a case-based training and diagnostic support system. It describes the current MR Tutor system and concludes that while it is able to offer flexible training and support, it could be enhanced by the addition of an integrated atlas of the brain. The paper then surveys computer-based atlases and describes the Atlas project to develop a knowledge-based brain atlas as part of a medical decision support system. Integrating such an atlas with a training system could significantly improve the teaching and support offered, but practical difficulties include the need to merge knowledge representations and to develop new techniques for registering atlas plates on images that exhibit abnormalities. The paper addresses these problems and discusses how the combined Atlas-Tutor might be deployed in radiology training and some practical problems of integrating the two technologies. This paper has set out a new approach to computer-based training in radiology that combines a knowledge-based tutor with a medical atlas. There is no guarantee that such a system will be accepted by radiologists as a supplement to human teaching. However, each team has taken a user-centred approach to software design, with each prototype undergoing extensive testing both for usability and educational effectiveness. For the MR Tutor the MEDIATE team is carrying out a series of workplace studies to determine current practice in radiology training and to investigate how a computer-based training can fit into the working patterns of trainee radiologists [Sharples, 1997 #435] . This will inform the design of future versions.. An Atlas-Tutor offers the promise of combining training and diagnostic support within a single package, providing training on demand through a user-friendly multimedia system, and teaching a systematic approach to radiological reporting, supplemented by extensive atlas-based tools for defining and identifying anatomical structure. This can be done across the spectrum from initial medical education to specialist support.. Designing an Atlas-Tutor training system requires further investigation of knowledge representation, warping models and human computer interaction. It is necessary to design teaching strategies, dynamic student models, and tools for spatial reasoning. Conceptual knowledge of the appearance of abnormal images, in terms of lesion types, shapes, geometric qualifiers, intensities and associated signs needs to be acquired through techniques of knowledge engineering. Then this knowledge must be supplemented by biomedical knowledge. At present warping models are only suitable for case images of normal brains, but we believe that they could be adapted for images exhibiting abnormalities, as a step towards partially automated interpretation of MR images. These sources of knowledge need to be combined to determine appropriate teaching actions, according to the learner's knowledge and context. This must all be incorporated in an adaptive hypermedia system that can determine the relevant information, computations and teaching actions and then communicate with the user by means of a teaching context.

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 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 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


Variational Bayesian sparse additive matrix factorization Abstract Principal component analysis (PCA) approximates a data matrix with a low-rank one by imposing sparsity on its singular values. Its robust variant can cope with spiky noise by introducing an element-wise sparse term. In this paper, we extend such sparse matrix learning methods, and propose a novel framework called sparse additive matrix factorization (SAMF). SAMF systematically induces various types of sparsity by a Bayesian regularization effect, called model-induced regularization. Although group LASSO also allows us to design arbitrary types of sparsity on a matrix, SAMF, which is based on the Bayesian framework, provides inference without any requirement for manual parameter tuning. We propose an efficient iterative algorithm called the mean update (MU) for the variational Bayesian approximation to SAMF, which gives the global optimal solution for a large subset of parameters in each step. We demonstrate the usefulness of our method on benchmark datasets and a foreground/background video separation problem. Principal component analysis (PCA) (Hotelling 1933 ) is a classical method for obtaining low-dimensional expression of data. PCA can be regarded as approximating a data matrix with a low-rank one by imposing sparsity on its singular values. A robust variant of PCA further copes with sparse spiky noise included in observations (Candès et al. 2011; Ding et al. 2011; Babacan et al. 2012) .. In this paper, we extend the idea of robust PCA, and propose a more general framework called sparse additive matrix factorization (SAMF). The proposed SAMF can handle various types of sparse noise such as row-wise and column-wise sparsity, in addition to element-wise sparsity (spiky noise) and low-rank sparsity (low-dimensional expression); furthermore, their arbitrary additive combination is also allowed. In the context of robust PCA, row-wise and column-wise sparsity can capture noise observed when some sensors are broken and their outputs are always unreliable, or some accident disturbs all sensor outputs at a time.. Flexibility of SAMF in sparsity design allows us to incorporate side information more efficiently. We show such an example in foreground/background video separation, where sparsity is induced based on image segmentation. Although group LASSO (Yuan and Lin 2006; Raman et al. 2009 ) also allows arbitrary sparsity design on matrix entries, SAMF, which is based on the Bayesian framework, enables us to estimate all unknowns from observations, and allows us to enjoy inference without manual parameter tuning.. Technically, our approach induces sparsity by the so-called model-induced regularization (MIR) (Nakajima and Sugiyama 2011) . MIR is an implicit regularization property of the Bayesian approach, which is based on one-to-many (i.e., redundant) mapping of parameters and outcomes (Watanabe 2009 ). In the case of matrix factorization, an observed matrix is decomposed into two redundant matrices, which was shown to induce sparsity in the singular values under the variational Bayesian approximation (Nakajima and Sugiyama 2011) .. We show that MIR in SAMF can be interpreted as automatic relevance determination (ARD) (Neal 1996) , which is a popular Bayesian approach to inducing sparsity. Nevertheless, we argue that the MIR formulation is more preferable since it allows us to derive a practically useful algorithm called the mean update (MU) from a recent theoretical result (Nakajima et al. 2013) : The MU algorithm is based on the variational Bayesian approximation, and gives the global optimal solution for a large subset of parameters in each step. Through experiments, we show that the MU algorithm compares favorably with a standard iterative algorithm for variational Bayesian inference. In this paper, we proposed a sparse additive matrix factorization (SAMF) model, which allows us to design various forms of factorization that induce various types of sparsity. We then proposed a variational Bayesian (VB) algorithm called the mean update (MU), which gives the global optimal solution for a large subset of parameters in each step. Through experiments, we showed that the MU algorithm compares favorably with the standard VB iteration. We also demonstrated the usefulness of the flexibility of SAMF in a real-world foreground/background video separation experiment, where image segmentation is used for automatically designing an SMF term.. Future work is to overcome the limitations discussed in Sect. 4.4. Analysis of convergence properties of the MU algorithm, and theoretical elucidation of the reason why the MU algorithm tends to give a better solution than the standard VB algorithm are also our important future work.. Proposition 1 (Bishop 1999; Lim and Teh 2007) In this section, we first relate MIR to ARD. Then, we introduce the standard VB iteration for SAMF, which is used as a baseline in the experiments. After that, we discuss related previous work, and the limitation of the current work. As widely known, traditional PCA is sensitive to outliers in data and generally fails in their presence. Robust PCA (Candès et al. 2011 ) was developed to cope with large outliers that are not modeled within the traditional PCA. Unlike methods based on robust statistics ( (9)). This model can also be applied to applications where the task is to estimate the elementwise sparse term itself (as opposed to discarding it as noise). A typical such application is foreground/background video separation (Fig. 3) .. The original formulation of robust PCA is non-Bayesian, and the sparsity is induced by the 1 -norm regularization. Although its solution can be efficiently obtained via the augmented Lagrange multiplier (ALM) method (Lin et al. 2009 ), there are unknown algorithmic parameters that should be carefully tuned to obtain its best performance. Employing a Bayesian formulation addresses this issue: A sampling-based method (Ding et al. 2011 ) and a VB method were proposed, where all unknown parameters are estimated from the observation. Babacan et al. (2012) conducted an extensive experimental comparison between their VB method, called a VB robust PCA, and other methods. They reported that the ALM method (Lin et al. 2009 ) requires careful tuning of its algorithmic parameters, and the Bayesian sampling method (Ding et al. 2011 ) has high computational complexity that can be prohibitive in large-scale applications. Compared to these methods, the VB robust PCA is favorable both in terms of computational complexity and estimation performance.. Our SAMF framework contains the robust PCA model as a special case where the observed matrix is modeled as the sum of a low-rank and an element-wise sparse terms. The VB algorithm used in Babacan et al. (2012) is the same as the standard VB iteration introduced in Sect. 4.2, except a slight difference in the hyperprior setting. Accordingly, our proposal in this paper is an extension of the VB robust PCA in two ways-more variation in sparsity with different types of factorization and higher accuracy with the MU algorithm. In Sect. 5, we experimentally show advantages of these extensions. In our experiment, we use a SAMF counterpart of the VB robust PCA, named 'LE'-SAMF in Sect. 5.1, with the standard VB iteration as a baseline method for comparison.. Group LASSO (Yuan and Lin 2006 ) also provides a framework for arbitrary sparsity design, where the sparsity is induced by the 1 -regularization. Although the convexity of the group LASSO problem is attractive, it typically requires careful tuning of regularization parameters, as the ALM method for robust PCA. On the other hand, group-sparsity is induced by model-induced regularization in SAMF, and all unknown parameters can be estimated, based on the Bayesian framework.. Another typical application of MF is collaborative filtering, where the observed matrix has missing entries. Fitting the observed entries with a low-rank matrix enables us to predict the missing entries. Convex optimization methods with the trace-norm penalty (i.e., singular values are regularized by the 1 -penalty) have been extensively studied Rennie and Srebro 2005; Cai et al. 2010; Ji and Ye 2009; Tomioka et al. 2010) .. Bayesian approaches to MF have also been actively explored. A maximum a posteriori (MAP) estimation, which computes the mode of the posterior distributions, was shown to be equivalent to the 1 -MF when Gaussian priors are imposed on factorized matrices ). Salakhutdinov and Mnih (2008) applied the Markov chain Monte Carlo method to MF for the fully-Bayesian treatment. The VB approximation (Attias 1999; Bishop 2006) has also been applied to MF (Bishop 1999; Lim and Teh 2007; Ilin and Raiko 2010) , and it was shown to perform well in experiments. Its theoretical properties, including the modelinduced regularization, have been investigated in Nakajima and Sugiyama (2011) .

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


A dynamic programming algorithm for constructing optimal "1"-ended binary prefix-free codes Abstract -We discuss the problem of efficiently constructing minimum-cost b i n a r y prefix-free codes having the p r o p e r t y that each codeword ends w i t h a L L l " . A code is a set of binary words C = {wl, w2, . . . , w,} c {0,1}*. A code C is prefix-free if for all pairs w, w' E C, w is not a prefix of 20'. Let P = {PI, p 2 , p3, . . . , p , } be a discrete probability distribution. The cost of code C with distribution P is Cost(C, P ) = xi 1wi( .pi where lzul is the length of word w. Finding a minimum cost code for a given distribution can be efficiently done in O ( n ) time using the standard Huffman encoding algorithm (when the pi are sorted) [5).. In 1990, T. Berger and R. W. Yeung [l] introduced a new variant of this problem. They defined a feasible or 1-ended code to be a prefix-free code in which every word is restricted to end with a "1". Such codes are used, for example, in the design of self-synchronizing codes [2] . Given P, their problem was to find a minimum-cost 1-ended code.. As an example let P = {$, $, $, $, i, $}. and consider the two codes C1 and C2 : C1 is an optimal prefix-free code for P but not an optimal 1-ended one since it contains words that end with "0". C2 is an optimal 1-ended prefix-free code for P. Berger and Yeung derived properties of such codes, such as the relationship of a min-cost feasible code to the entropy of P, and then described an exponential (in n ) time algorithm for constructing them. A few years later Capocelli, De Santis and Persiano [3] gave another more efficient, but still exponential time construction algorithm.. In this note we describe an O ( n 3 ) time algorithm for ca'nstructing such a code.

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Improving resource location with locally precomputed partial random walks Abstract Random walks can be used to search complex networks for a desired resource. To reduce search lengths, we propose a mechanism based on building random walks connecting together partial walks (PW) previously computed at each network node. Resources found in each PW are registered. Searches can then jump over PWs where the resource is not located. However, we assume that perfect recording of resources may be costly, and hence, probabilistic structures like Bloom filters are used. Then, unnecessary hops may come from false positives at the Bloom filters. Two variations of this mechanism have been considered, depending on whether we first choose a PW in the current node and then check it for the resource, or we first check all PWs and then choose one. In addition, PWs can be either simple random walks or self-avoiding random walks. Analytical models are provided to predict expected search lengths and other magnitudes of the resulting four mechanisms. Simulation experiments validate these predictions and allow us to compare these techniques with simple random walk searches, finding very large reductions of expected search lengths. The proposed resource location mechanisms could be improved with new strategies to choose from the PWs available at the nodes. Smarter (and more costly) variants of RWs could be used as PWs. It would be interesting to compare their application to unstructured P2P networks with algorithms for structured overlays like DHT or quorum systems.

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