Combining frequency and time domain approaches to systems with multiple spike train input and output Abstract A frequency domain approach and a time domain approach have been combined in an investigation of the behaviour of the primary and secondary endings of an isolated muscle spindle in response to the activity of two static fusimotor axons when the parent muscle is held at a fixed length and when it is subjected to random length changes. The frequency domain analysis has an associated error process which provides a measure of how well the input processes can be used to predict the output processes and is also used to specify how the interactions between the recorded processes contribute to this error. Without assuming stationarity of the input, the time domain approach uses a sequence of probability models of increasing complexity in which the number of input processes to the model is progressively increased. This feature of the time domain approach was used to identify a preferred direction of interaction between the processes underlying the generation of the activity of the primary and secondary endings. In the presence of fusimotor activity and dynamic length changes imposed on the muscle, it was shown that the activity of the primary and secondary endings carried different information about the effects of the inputs imposed The behaviour of networks of neurons is commonly described in terms of the strength of association between pairs of neurons within the network, an assessment of their timing relations and the identification of those neurons which interact directly or are influenced by common inputs. Consistent with the view presented by Segundo (Cox et al. 1975) , what is required is an approach which characterises the behaviour of a network as a single object as opposed to that of pairwise measures.. Pepe Segundo, beginning with his work on aplysia (see, Moore this issue), worked at the interface between Neuroscience and Statistics and continued this type of work for the majority of his career. The work presented here contributes to that endeavour and at the same time illustrates that work of this kind will necessarily contribute to both fields. We shall outline two approaches for analysing the behaviour of networks of neurons based on a generalised linear model relating vectors of input and output processes in which the components of these vectors can be either continuous or point process signals.. The first model is formulated in terms of Fourier transforms, and its performance is described by how well it predicts output network behaviour. It is shown that the spectral density matrix of the output processes can be decomposed into a series of spectral density matrices. The sum of these matrices, each weighted by a factor which may be interpreted as a generalised coherence, forms the spectral density matrix of the error process for the network model. The measure of size of the error process is taken to be the largest eigenvalue (Hermitian norm) of the spectral density matrix of the output process. Departures of the Hermitian norm of the error process from its maximum value provides a measure of the adequacy of the linear model. The causes for these departures can be explained by the behaviour of the eigenvalues in the expansion of the spectrum of the error process. The structure of these eigenvalues reflects the influence of connectivity within the network.. The second model is based on the complete intensity function of the output processes given the history of the input and output processes. This model is an adaptation of that used in Brillinger and Segundo (1979) and Brillinger (1992) , but applied to the mammalian muscle spindle under conditions of multiple input and multiple output. The estimates of the parameters of this model are based on a likelihood function and therefore may be anticipated to be reasonably efficient. Further, these estimates may be expected to highlight different aspects of the system behaviour than those highlighted by the Fourier method. An advantage of the second approach is that the input can be nonstationary and other explanatory variables introduced directly.. Whereas the first model examines the global behaviour of the system, the second model characterises the interactions among the recorded processes by constructing a sequence of generalised linear models of increasing complexity progressing from single input single output to multiple input multiple output models in which the complete intensity function is now formulated in terms of vector-valued processes. The two approaches to network behaviour described here are illustrated by the analysis of an experiment on an isolated mammalian muscle spindle in which the data from two input point processes and two output point process are available for analysis. A particular feature of the analysis is that the association of the activity between primary and secondary muscle spindle endings is thought to be functionally important (Gladden and Matsuzaki 2002; Halliday et al. 1987) . For example, interneurons in di-synaptic excitatory and some inhibitory pathways from group I and group II afferents receive inputs from both primary and secondary muscle spindle axons (Edgley and Jankowska 1987; Jankowska 1992; Jankowska and Hammar 2002) . The effects that these interneurons exert on the α-motoneurons would be facilitated by associations induced between the activity of primary and secondary muscle spindle endings controlled by fusimotor activity and length changes imposed on the muscle spindle. The changes in correlation between the discharges of the primary and secondary endings can best be examined when these discharges are recorded from the same muscle spindle. In this case the effect of the controlling processes can be associated directly with the pattern of fusimotor innervation of the muscle spindle. A frequency domain approach and a time domain approach have been combined in an investigation of the behaviour of the primary and secondary endings of an isolated muscle spindle in response to the activity of two static fusimotor axons when the parent muscle is held at a fixed length and when it is subjected to random length changes.. The frequency domain analysis is based on a stationary input with the assumption referring only to the first and second order moments of the processes, and has been used to examine the properties of the muscle spindle by providing a measure of the error process associated with the linear model, and to specify how the interactions between the recorded processes contribute to this process. On the other hand the time domain approach involves a full probability model in which the inputs can be general processes which need not be stationary processes-a very important feature of this approach since in many experimental situations the input processes are not stationary. The construction of the time domain model allows new input processes to be included directly to the model in arbitrary combinations with existing input processes. A number of mathematical models of the muscle spindle have been developed (Mileusnic et al. 2006) . One application of the procedures developed in this article would be to apply them to assess the linear behaviour of these models using the frequency domain approach outlined in Sects. 3 and 3.2, and to examine the behaviour of the kernels derived from the time domain methods presented in Sect. 4.. The main feature of the time domain results is that they illustrate how the addition of further processes to the input interact with the effects of existing inputs. This property of the time domain approach was used to identify a preferred direction of interaction between the processes underlying the generation of the activity of the primary and secondary endings. By contrast, the frequency domain approach showed that the linear range of the model is extended when both input processes are present. By associating an error process with the linear model, it was shown that this model is reasonable at frequencies below 25 Hz in the absence of an imposed length change. The range of frequencies for which the model is adequate lie within the physiological range of naturally occurring frequencies at fixed lengths. On the other hand, in the presence of dynamic variations in the length of the parent muscle, the linear model did not give a satisfactory description of the behaviour of the input and output processes. However, this description may be improved by taking account of nonlinear behaviour in the manner proposed by Moore and Auriemma (1985) . The results presented in this work emphasise that the analysis of the behaviour of complex systems benefits from a combination of frequency and time domain methods.

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


Towards an accurate performance modeling of parallel sparse factorization We present a simulation-based performance model to analyze a parallel sparse LU factorization algorithm on modern cached-based, high-end parallel architectures. We consider supernodal right-looking parallel factorization on a bi-dimensional grid of processors, that uses static pivoting. Our model characterizes the algorithmic behavior by taking into account the underlying processor speed, memory system performance, as well as the interconnect speed. The model is validated using the implementation in the SuperLU_DIST linear system solver, the sparse matrices from real application, and an IBM POWER3 parallel machine. Our modeling methodology can be adapted to study performance of other types of sparse factorizations, such as Cholesky or QR, and on different parallel machines. We developed a simulation-based performance model to analyze a parallel sparse LU factorization algorithm on modern cached-based, high-end parallel architectures. Our model characterizes the algorithmic behavior by taking into account the underlying processor speed, memory system performance, as well as the interconnect speed. The simulation-based model differs from our previously developed analytical model [6] in that it actually simulates the execution of the parallel algorithm. When comparing the predicted runtime with the results of SuperLU_DIST, we noticed that the old analytical model failed to predict accurately the parallel execution time with increasing number of processors.. Unlike Level 2 sparse BLAS operations, such as sparse matrix-vector multiply or sparse triangular solution, where performance is usually solely dominated by memory system performance, the sparse factorization algorithms usually contain a mixture of Level 2 and Level 3 BLAS routines. Depending on the sparsity of the matrix, which changes at different stages of factorization, the kernels can be either memory-bound or flops-bound. We have taken into account this feature in our analysis, and our new model is more accurate in predicting performance.. Another improvement over the previous work is to use different bandwidth values to model interconnect communication speed for different message sizes. This is very important for sparse factorization algorithms, because throughout factorization, the message sizes can differ by several orders of magnitudes.. We have validated our model using SuperLU_DIST on an IBM POWER3 parallel machine, and showed that the simulated runtime is close to the measured runtime. In the future, we plan to validate the model on different parallel architectures. After this validation phase, we will be able to use the model realistically for predicting code performance on newly designed architectures and for new matrices. Furthermore, our model reveals that the loss of parallel efficiency on a large number of processors is due to load imbalance and communication cost. This points to possible future work to improve the code. For example, we can use better matrix distribution scheme to reduce load imbalance. We can use a higher level of look-ahead scheme to increase the overlap of communication with computation.. Finally, our modeling methodology can be adapted to study performance of other types of sparse factorizations, such as Cholesky or QR. This remains future work. Algorithm 1 presents a right-looking algorithm that factorizes a sparse unsymmetric n × n matrix A into the product of a unit lower triangular matrix L and an upper triangular matrix U. The matrix is partitioned into N × N blocks of submatrices using unsymmetric supernodes (columns of L with the same nonzero structure). The algorithm loops over N supernodes. At the kth step, the first k − 1 block columns of L and block rows of U are already computed. Now, the block column L(k : N, k) is factored, the triangular solves are performed to compute U(k, k + 1 : N), and the trailing matrix is updated using L(k + 1 : N, k) and U(k, k + 1 : N). The last step requires most of the work and also exhibits most of the parallelism in the right-looking approach.

O O O B I 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


Hierarchical Approaches to Understanding Consciousness There has been much discussion of what a scientific theory of consciousness would look like, and even whether such a theory is possible. Some common misunderstandings of the nature of theories (e.g., in the physical sciences) have confused the discussion of theories concerning consciousness. Theories in the physical sciences establish hierarchies of descriptions that relate high-level descriptions of macro-level phenomena to detailed-level descriptions at a micro level. Detailed descriptions are usually more accurate but information-dense and therefore often beyond human comprehensibility (unless limited to tiny segments of a macrolevel phenomenon). High-level descriptions are usually much less information-dense but more approximate. The ability to map between levels of description, and in particular the understanding of when a shift from a higher-level to a more detailed description is needed to achieve a desired degree of accuracy, is fundamental to an effective theory in any field. The form of such a theory of consciousness is sketched, and the limitations of some alternative approaches described.There are a range of possible approaches aimed at understanding consciousness. At one extreme, there has been debate over whether a scientific theory of consciousness is possible in principle [e.g. Chalmers 1995] . Another type of approach has been the creation of models that describe cognitive operations regarded as being conscious, but with limited consideration for how physiology could support the processes required by the model. Computer implementations of some of these models have been attempted [e.g. Franklin et al 1999 , Sun 1999 ]. Yet another approach has been to look for physiological activity that discriminates between conscious and unconscious states, the so-called "neural correlates of consciousness" [e.g. Rees et al, 2002 , Crick et al 1998 ]. Lamme [2006] claimed that neural activity occurred in different structures depending on the type of conscious or unconscious behaviour, and argued that the presence of neural activity should be part of the definition of whether consciousness was present, independent of cognitive measures. Yet another approach has been to claim that understanding of consciousness is only possible with reference to quantum mechanics [Penrose 1994] . Furthermore, there have been extensive debates over what phenomena should actually be labeled "conscious" [e.g. Block 1995] . The end result has been considerable meta-theoretical confusion.For several centuries, the physical sciences have been regarded as the paradigm for valid scientific theories. We believe that much of the confusion over scientific understanding of There are a range of possible approaches aimed at understanding consciousness. At one extreme, there has been debate over whether a scientific theory of consciousness is possible in principle [e.g. Chalmers 1995] . Another type of approach has been the creation of models that describe cognitive operations regarded as being conscious, but with limited consideration for how physiology could support the processes required by the model. Computer implementations of some of these models have been attempted [e.g. Franklin et al 1999 , Sun 1999 ]. Yet another approach has been to look for physiological activity that discriminates between conscious and unconscious states, the so-called "neural correlates of consciousness" [e.g. Rees et al, 2002 , Crick et al 1998 ]. Lamme [2006] claimed that neural activity occurred in different structures depending on the type of conscious or unconscious behaviour, and argued that the presence of neural activity should be part of the definition of whether consciousness was present, independent of cognitive measures. Yet another approach has been to claim that understanding of consciousness is only possible with reference to quantum mechanics [Penrose 1994 ]. Furthermore, there have been extensive debates over what phenomena should actually be labeled "conscious" [e.g. Block 1995] . The end result has been considerable meta-theoretical confusion.. For several centuries, the physical sciences have been regarded as the paradigm for valid scientific theories. We believe that much of the confusion over scientific understanding of consciousness derives from misunderstanding of what theories in the physical sciences actually deliver, and once these misunderstandings are cleared away, the form which a theory of consciousness must take becomes clearer. There are some good questions about whether a scientific theory of consciousness is possible, but these questions are in fact more empirical than philosophical, and relate to whether the brain is organized in such a way that understanding can occur within the limits of human information handling capabilities.. There are some significant similarities between theories in the physical sciences and the theoretical techniques by which the understanding of a complex computational system is achieved and maintained. Although there are minimal direct resemblances between brains and complex computational systems, natural selection pressures on brains have tended to have architectural effects which make these techniques relevant and applicable (Coward 2005) , thus providing a basis for a scientific theory of consciousness. The general form which such a theory would take can therefore be sketched. An argument has been made here that a scientific theory of consciousness analogous with theories in the physical sciences is likely to be possible, but the form of that science may be different from some existing (and often widespread) expectations because of the misunderstanding of what a theory in the physical sciences actually delivers. The rough general form of an eventual theory of consciousness has been outlined (to a very limited extent, of course), and issues with a few of the many approaches to understanding consciousness briefly identified.

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Complexity and mathematical tools toward the modelling of multicellular growing systems This paper deals with a multiscale modelling approach to complex biological systems constituted by several interacting entities. The methodology is based on mathematical kinetic theory for active particles and is focused on the modelling of complex multicellular systems under therapeutic actions at the cellular level and mutations with onset of new populations. Asymptotic hyperbolic methods are developed to derive models at the macroscopic scale of tissues from the underlying description at the level of cells for a open system with variable number of populations. The aim of this paper is to deal with the development of mathematical tools for the modelling of complex biological systems constituted by diverse entities such as genes or cells, which have the ability of expressing heterogeneously different functions and that interact, in vivo, under external actions. The contents are focused on theoretical issues, pursuing the hints posed in [1, 2] . In this framework it is relevant to consider that the different cells cohabit taking into account short and long range interactions between them. On the other hand, the influence on the different cell populations of some possible therapies as well as how these therapies modify the dynamical behavior and those of the immune system are one of the objectives of this paper. Regarding these effects, it is possible to consider the influence of different kind of therapies. Those more aggressive, as in tumor growth, could be the chemo-and radio-therapies, or others whose objective is to control the information between cells through the proteins pathways. The problem when such number of populations is considered (cells, therapies, biochemical interactions, gens, . . . ) is to manage with the resulting system of equations. The idea of this paper is to deduce a hydrodynamical limit of hyperbolic type (we try to skip diffusive phenomena) in order to propose new macroscopic models when studying these kind of problems.. The above objective is pursued by the mathematical methods of the kinetic theory for active particles [3] (KTAP), which has been applied to model various complex systems in life sciences, for instance social systems [4, 5] , behavioral economy [6] or epidemics with gene mutations [7] . This theory is here properly developed to describe, by mathematical equations, multicellular systems according to a multiscale approach where the dynamics of cells is determined by the dynamics at the molecular scale, while models at tissue level are derived from the underlying description at the cellular scale.. The main difficulty consists in taking into account the different complexity sources that characterize living systems. Specifically, their ability to organize the dynamics following specific strategies rather than rules of classical mechanics. These systems are complex considering that the dynamics of a few entities does not generate straightforwardly the dynamics of the whole system. Emerging collective behaviors do not appear to be related to the individual dynamics and not even to the dynamics of a few entities. The above mentioned strategy developed by the interacting individuals depends on their density and topological distribution.. The contents are focused on mathematical aspects with the aim of covering the whole path from the lower scale to the higher macroscopic of tissues. The final aim consists of contributing to a background for a mathematical theory of complex biological system. This challenging objective means that such a theory should be valid for a broader variety of systems rather than for specific systems only. This paper is organized through three more sections that follow this introduction. Section 2 analyzes some common features of the class of biological systems under consideration viewed as a complex system. Several sources of complexity are considered: the ability to express a strategy which modifies laws of classical mechanics, the ability to adapt such a strategy to the presence and localization of other cells of different populations, Darwinian evolution due to adaptation to the mutating environmental conditions, competition for survival followed by proliferative and destructive actions, and so on. All these characteristics represent a target for the development of mathematical tools. In other words, the mathematical approach is required to possess the ability to describe all the above characteristics. Section 3 deals with the derivation of the mathematical tools first for closed systems in absence of external actions, and subsequently for open systems. The first step consists in the decomposition of the overall systems, to reduce its complexity, into functional subsystems by a suitable development of the theory of functional modules by Hartwell [8] revisited in [2] . The second step is the modelling of interactions at the individual level of active particles, where the output is determined by stochastic games. Subsequently, a mathematical framework is derived, using the modelling of microscopic interactions, by a suitable balance equation in the elementary space of microscopic states. The third step is modelling open systems. The final objective consists in the derivation of suitable frameworks which act as background paradigm for the derivation of specific models. Section 4 applies the mathematical frameworks offered by the preceding section to modelling some specific phenomena of interest in biological sciences. After a preliminary analysis on the modelling multicellular systems, onset of pathological states and competitions with the immune system under the specific action of external therapeutic actions, the contents are focused on the derivation of macroscopic models of biological growing and progressing tissues from the underlying description at the cellular scale.

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


Semantic distance of concepts within a unified framework in the biomedical domain This paper presents a cross-ontology approach, as an extension of the Cluster-Based approach, to measure semantic distance between concepts within single ontology or between concepts dispersed in multiple ontologies in a unified framework in the biomedical domain. The experimental results (with ~0.81 correlation with human scores) confirmed that the proposed approach is effective and has great potential in measuring semantic distance using multiple ontologies in a unified framework. Ontology-based semantic distance (inverse of semantic similarity) techniques, also called similarity measures, can estimate the semantic similarity between two terms/concepts according to a given ontology or taxonomy. The pure ontology-based semantic distance/similarity measures use IS-A relations in ontology as the primary information source to determine the semantic similarity between concepts [1] .. The Metathesaurus in UMLS (Unified Medical Language System) [3] is built from the electronic versions of various thesauri, classifications, code sets, and lists of controlled terms used in patient care, health services billing, public health statistics, indexing and cataloging of biomedical literature. These are referred to as the "source vocabularies" of the Metathesaurus. The control vocabularies or terminologies in these resources are expressed hierarchically with the major relations between concepts are IS-A relations, therefore, these sources are also called ontology, taxonomy, etc.. In this paper, we propose an ontology-based semantic distance approach that can measure semantic distance in single ontology as well as in cross-ontology in UMLS framework. The proposed measure is adapted from (and is an extension of) the ClusterBased approach proposed by Al-Mubaid & Nguyen [2] which was developed to compute the semantic distance/similarity between two terms across multiple clusters within a single ontology . We have presented a cross-ontology semantic distance approach in a unified framework. For example, in biomedical IR, there is a great need for measuring the semantic similarity between biomedical terms/concepts and documents and there are several potential ontologies. The experimental results show that the approach is very promising in computing semantic distance/similarity of concepts dispersed in multiple ontologies.

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


Stability of parallel algorithms to evaluate Chebyshev series Abstract--In this paper, we present rounding error bounds of recent parallel versions of Forsythe's and Clenshaw's algorithms for the evaluation of finite series of Chebyshev polynomials of-the first and second kind. The backward errors are studied by using the matrix formulation of the algorithm, whereas the forward error is also studied by means of a more direct approach that permits us to obtain sharper bounds. The bounds show an almost stable behavior as in the sequential algorithms. This fact is illustrated with several numerical tests. (~) Polynomial evaluation is one of the most common problems in scientific computing. Therefore, this problem has attracted the attention of many researchers and several algorithms suitable for parallel evaluation of power series have been proposed [1] [2] [3] [4] [5] . For the particular case of finite series of Chebyshev polynomials, a parallel algorithm was presented recently [6, 7] that permits their efficient evaluation.. The error analysis for the evaluation of polynomials has received a great deal of attention in the literature. Backward and forward error analysis for Homer's rule was first given by Wilkinson [8] . The behavior of the evaluation of Chebyshev representations of a polynomial is studied in [9] [10] [11] [12] [13] [14] [15] , where one can find an error analysis of the evaluation of a Chebyshev series using Clenshaw's algorithm and variations of it. However, for the parallel algorithms, there is no theoretical analysis. It is known that, in general, the parallel algorithms can be much more unstable than the sequential algorithms [16] , but in some particular problems, the parallel algorithms are as stable as the sequential algorithms [17, 18] . Therefore, it is interesting to analyze the behavior of the recently proposed parallel algorithms to evaluate a Chebyshev series. In the analysis, we have used a matrix formulation that is equivalent to the algorithms given in [6, 7] . This formulation permits us to use the classical rounding error techniques for linear systems. Also, we present an alternative forward error bound analysis based on a direct method [12, 13, 19] . From these bounds, it is established that the parallel algorithms are almost as stable as the sequential ones.. Helpful comments and suggestions from an anonymous referee are gratefully acknowledged. The author was supported in part by the Spanish Ministry of Education and Science (Project #ESP99-1074-CO2-01) and by the Centre National d'l~tudes Spatiales at Toulouse (France). The parallel bounds are similar to those of the sequential algorithms, although new points where the rounding error can grow appear in the parallel algorithms.. The paper is organized as follows. In Section 2, we review the sequential and parallel Forsythe and Clenshaw algorithms for the evaluation of a Chebyshev series. In Section 3, we introduce the stability analysis of the parallel algorithms and, in Section 4, we show some numerical tests to compare the theoretical bounds and the simulated rounding errors. From the numerical tests and the theoretical rounding error bounds, we conclude that the parallel algorithms are almost as stable as the sequential ones, but at some points, the rounding errors increase slightly. Note that these points are not random inside the interval, their position is well known, which is the relative extrema of Tp(x) when we use p processors.

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


Using ghost edges for classification in sparsely labeled networks We address the problem of classification in partially labeled networks (a.k.a. within-network classification) where observed class labels are sparse. Techniques for statistical relational learning have been shown to perform well on network classification tasks by exploiting dependencies between class labels of neighboring nodes. However, relational classifiers can fail when unlabeled nodes have too few labeled neighbors to support learning (during training phase) and/or inference (during testing phase). This situation arises in realworld problems when observed labels are sparse.In this paper, we propose a novel approach to within-network classification that combines aspects of statistical relational learning and semi-supervised learning to improve classification performance in sparse networks. Our approach works by adding "ghost edges" to a network, which enable the flow of information from labeled to unlabeled nodes. Through experiments on real-world data sets, we demonstrate that our approach performs well across a range of conditions where existing approaches, such as collective classification and semi-supervised learning, fail. On all tasks, our approach improves area under the ROC curve (AUC) by up to 15 points over existing approaches. Furthermore, we demonstrate that our approach runs in time proportional to L · E, where L is the number of labeled nodes and E is the number of edges. We address the problem of within-network classification in sparsely labeled networks. Given a network of both labeled and unlabeled nodes, our goal is to provide labels for the unlabeled nodes. Here, labeling simply means assigning each node a class from among a set of possible classes (see Figure 1 Generate "ghost edges" for node i to existing labeled nodes Figure 1 : Problem definition and our solution. We address the problem of label sparsity in network classification by creating "ghost edges" using random walks with restarts. These ghost edges connect an unlabeled node to the most relevant labeled nodes.. Suppose we want to identify fraudulent users of a cell phone network. In this case, our set of possible classes for users is {fraud, legit}. If a user is known to be involved in fraud, we assign a label of "fraud." If a user is known to not be involved in fraud, we assign a label of "legit." Otherwise, we leave the node unlabeled. Our goal is then to assign labels ("fraud" or "legit") to the unlabeled users.. Cell phone fraud is an example where networks are often very sparsely labeled. We have a handful of known fraudsters and legitimate users, but the labels are unknown for the vast majority of users. For such applications, it is reasonable to expect that we have access to labels for fewer than 10%, 5%, or even 1% of the nodes.. In addition to being sparsely labeled, cell phone networks are generally anonymized. That is, the nodes often contain no attributes besides class labels. These sparsely labeled, anonymized networks are the focus of this study. Put another way, our work focuses on univariate within-network classification in sparsely labeled networks.. Techniques for statistical relational learning (SRL) have been shown to perform well on network classification tasks because of their ability to exploit dependencies between labels of related nodes [18] . These techniques use labeled data to learn a model of the dependencies between labels of neighboring nodes. The labels of unlabeled nodes can then be inferred by propagating information from labeled nodes throughout the network, according to this learned dependency model (i.e., collective classification). Unfortunately, sparse labels cause a number of problems for relational classifiers. First, collective classification techniques can fail without sufficiently many labels to seed the inference process [15] . Second, fewer labeled nodes means fewer training examples from which to learn dependencies. Finally, even when a node is labeled, many of its neighbors will not be. This is equivalent to having many missing attribute values in a traditional supervised learning setting. The result is that it is very difficult to learn an accurate model of the dependencies present in the data.. Within-network classification can also be viewed as a graphbased semi-supervised learning problem since we have both labeled and unlabeled data available at training time. Although semisupervised learning (SSL) is generally applied to non-network data, graph-based SSL approaches can be applied to within-network classification, as we show. SSL techniques have the advantage that they do not rely as heavily on labeled training data and can make use of unlabeled data as well. However, graph-based SSL approaches generally do not learn dependencies from data, but instead assume local label consistency (i.e., that nearby points tend to have the same label). If the label consistency assumption is not met, SSL techniques can perform extremely poorly. Figure 2 provides a preview of our results. It plots classifier performance (measured by area under the ROC curve, a.k.a. AUC) versus data set ID. The data sets are ordered according to their local consistency (a.k.a. homophily score). 1 Notice that the two proposed ghostEdge methods are consistently at the top, while the competing methods may perform very poorly depending on the data set's local consistency.. In this paper, we explore a novel approach to within-network classification that capitalizes on the strengths of both statistical relational learning (SRL) and semi-supervised learning (SSL), to produce a classifier that is robust in the face of both sparse labeling and low label consistency. Our contributions are as follows:. • We propose a novel approach to within-network classification, based on the creation of "ghost edges" that enable the propagation of information from labeled to unlabeled nodes.. • We demonstrate that our approach is robust to both sparse labeling and low label consistency, performing well consistently across a range of real world classification tasks where collective classification or semi-supervised learning fail.. • We demonstrate the scalability of our approach. Specifically, we show that our methods run in time proportional to L · E where L is the number of labeled nodes and E is the number of edges in our graph.. The rest of the paper is organized as follows. In Section 2, we review related work. We present our proposed methods in Section 3. Sections 4 and 5 describe our experimental methodology and results. Finally, we offer conclusions in Section 6. 1 Note that throughout this paper, we use the terms 'homophily', 'positive auto-correlation', 'local consistency' and 'smoothness' interchangeably. We also use the terms 'inverse relationship', 'negative auto-correlation' and 'lack of homophily' interchangeably. Local Consistency (lower) (higher) Figure 2 : A preview of our results: classification performance of various approaches when half of the nodes in a graph data set are unlabeled. The solid blue (square icon) and red (circle icon) lines on the top represent our ghostEdge approaches, which perform consistently well regardless of the degree of local consistency in the data set. We focus on the problem of predicting node labels in a large graph, when (a) there are few labeled nodes and (b) local consistency (a.k.a. homophily) does not necessarily hold. To address the first problem, we introduce 'ghost edges', by judiciously adding edges between nodes, according to RWR proximity. To address the second problem, we propose to bypass all the activation-spreading methods (which implicitly assume homophily), and instead we use a classifier on a carefully chosen set of features from observed, as well as 'ghost-edge' neighbors. A subtle, but vital point is that we consider RWR not on the original matrix, but on its square. This change makes our method robust, regardless of the degree of homophily. In other words, our method does well even when the local consistency assumption is not met. We performed experiments on several real, publicly available data sets, measuring the AUC. The competitors were carefully chosen to be the state of the art. Our method is very robust, performing as well as or better than the best competitor across tasks. All other classifiers we evaluated perform poorly in some cases, depending on the degree of homophily. We also showed that the complexity of our approach is O(L · E), where L is the number of labeled nodes and E is the number of edges. Therefore, the approach is suitable for large data sets, provided that known labels and edges are sufficiently sparse. In recent years, there has been a great deal of work on models for learning and inference in relational data [7, 10, 11, 16, 18] . For within-network classification tasks where we have sparse labels, we categorize the previous work into two main groups: collective classification and graph-based semi-supervised learning.. Collective classification. Collective classification deals with label sparsity by simultaneously labelling a set of related nodes, allowing estimates of neighboring labels to influence one another. Representative work in this line started with the seminal paper of Chakrabarti et al. on using hyperlinks to for hypertext classification [2] . Sen et al. [17] provide a careful empirical study of the various procedures for collective inference. Macskassy and Provost [12] provide a nice case-study of previous work in learning attributes of networked data. McDowell et al. [14] demonstrate that "cautious" collective classification procedures produce better classification performance than "aggressive" ones. They recommend only propagating information about the top-k most confidently predicted labels. One of the major advantages of collective classification lies in its powerful ability to learn various kinds of dependency structures (positive vs. negative auto-correlation, different degrees of correlation, etc). However, as pointed out in [15] , when the labeled data is very sparse, which is quite common in the sparsely labeled networks that we are particularly interested in, the performance of collective classification might be largely degraded due to the lack of sufficient neighbors. This is exactly one major advantage of the proposed method, -we incorporate informative "ghost edges" into the networks to deal with sparsity issues. From this point of view, our method shares the similar spirit as the work by Macskassy [13] . However, in [13] , the additional edges are calculated based on attribute-similarity (specifically, text similarity). If such information is not available (which is quite common in many real applications and which is the case we are interested in), the method in [13] is not applicable. On the other hand, we can always leverage our "ghost edges" since they are based on the intrinsic structure of the networks. Lastly, the algorithm proposed in [13] does not learn the weights, instead it combines the weights through a heuristic.. Graph-based semi-supervised learning. The problem of withinnetwork classification can also be thought of as the graph-based semi-supervised learning problem. Here, the basic idea is to estimate a function on the graph which satisfies two kinds of constrains: (1) the consistency with the label information and (2) the smoothness over the whole graph. The methods in this area mainly vary in the different ways to balance these two constraints. For example, Zhu's Gaussian random field (GRF) method [23] puts a hard constraint on the label consistency and then achieves the smoothness by the harmonic function. Zhou's global and local consistency method [21] combines the two kinds constraints by a regularization parameter and solves a quadratic optimization problem. For more on graph-based semi-supervised learning, we refer the reader to an excellent survey by Zhu [22] . By exploring the global structure (i.e. smoothness) over the whole graph, graph-based semi-supervised learning methods usually outperform the traditional methods, particularly when there are very few labeled nodes in the networks. However, the constraint on smoothness implicitly assumes positive auto-correlation in the graph, that is nearby nodes tend to share the same class labels (i.e., homophily). When such an underlying assumption does not hold (negative auto-correlation, the degree of auto-correlation being small, etc), the performance might be largely affected. This is another advantage of our "ghost edge" method, -it leverages the additional learning stage to recover the intrinsic correlation structure.

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


Online reconstruction of 3D objects from arbitrary cross-sections We describe a simple algorithm to reconstruct the surface of smooth threedimensional multilabeled objects from sampled planar cross-sections of arbitrary orientation. The algorithm has the unique ability to handle crosssections in which regions are classified as being inside the object, outside the object, or unknown. This is achieved by constructing a scalar function on R 3 , whose zero set is the desired surface. The function is constructed independently inside every cell of the arrangement of the cross-section planes using transfinite interpolation techniques based on barycentric coordinates. These guarantee that the function is smooth, and its zero set interpolates the cross-sections. The algorithm is highly parallelizable and may be implemented as an incremental update as each new cross-section is introduced. This leads to an efficient online version, performed on a GPU, which is suitable for interactive medical applications. The reconstruction of a surface from a set of planar cross-sections S (also called slices), such that the surface interpolates, or approximates, S in the planes, has been thoroughly studied in the past decades. This problem arises mainly in the fields of medical Authors' addresses: A. Bermano, A. Vaxman (corresponding author), and C. Gotsman, Computer Science Department, Technion -Israel Institute of Technology, Israel; email: avaxman@cs.technion.ac.il. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. c 2011 ACM 0730-0301/2011/10-ART113 $10. 00 DOI 10.1145 00 DOI 10. /2019627.2019632 http://doi.acm.org/10.1145 imaging (MRI, CT, ultrasound, etc.) and geographical information systems (for terrain reconstruction). The input is assumed to have been segmented in a preprocessing step, to create a set of closed two-dimensional contours, separating the "inside" and "outside" of the object on each slice. A reconstruction algorithm typically creates a surface, enclosing a solid volume, which interpolates these contours and is consistent with the given inside/outside information. See Figure 1 for an illustration of the scenario.. The prior art related to this problem typically assumes that entire cross-sections are available and that the contour information in them is complete (i.e., a set of closed contours) and segmented correctly. However, in most practical cases, the input images are noisy, so there might be regions of uncertainty (see Figure 1 ) which cannot be reliably segmented. Thus, instead of a complete inside/outside classification per cross-section, there will also be regions which are unclassified. We deal with this general scenario.. The algorithm we describe constructs a signed "distance function," whose zero set is the surface. It consists of two steps: completing the regions of unknown information on the cross-section planes, and then using these to define a function on R 3 , from which it extracts a zero set. Our construction is based on the definition of near-binary functions on the individual planes and their interpolation onto R 3 using transfinite interpolation methods based on barycentric coordinates.. Our algorithm solves the most general version of the problem, with every setting of cross-sections and contours, as well as the multilabeled contour problem (i.e., the contours within each plane may belong to separate components of the object, and are labeled accordingly). The resulting surface, obtained as the zero set of a smooth function, is naturally smooth. To the best of our knowledge, the only method that attempts to solve this problem at this level of generality is that of Barequet and Vaxman [2009] , which, as we will see later, takes an entirely different, more complicated approach. Our algorithm handles all cases of noise and completion of crosssections in a simple and uniform manner, without extra complexity due to irregular topologies. The resulting surfaces are smooth and well-behaved, requiring minimal postprocessing.. In addition, we deal with the online variant of the problem, in which the slices are not all available at reconstruction time, rather given individually over time, and the reconstruction is to be updated after receiving the new slice. This online reconstruction problem is typical of freehand ultrasound scanning applications, where the physician scans a patient and sees the anatomy build up as s/he scans more and more. Our algorithm easily adapts to this scenario, as we explain in Section 7. The input to our algorithm is a set of planar cross-sections (along with the orientation parameters of the planes). Each such plane is partitioned into labeled polygonal regions, with exactly one region having infinite area. The regions are labeled as follows.. (1) Outside (indicating the null material).. (2) The ID of a material (indicating that this region is in the interior of a specific three-dimensional object). (3) Unknown (indicating that there is no reliable information as to whether the region is inside or outside an object).. In a nutshell, the algorithm proceeds as follows (see Figure 1 ).. (1) Assign a binary indicator function value to the vertices and half-edges of contours within each slice, indicating the type of regions they bound (inside or outside). Figure 2 illustrates a two-dimensional version of our algorithm. We begin by describing our method for the simplest special case of reconstruction of a single-material object, when there are no unknown regions on any of the planes. In Section 5 we describe the extension of this algorithm to cross-sections containing unknown regions, and in Section 6 its generalization to multilabeled contours. The output is a triangulated manifold mesh which represents the boundary of the object whose planar cross-sections agree with the input. Following Barequet and Vaxman [2009] , we call the crosssection planes "slices," and the regions bounded by the contours on each slice "images." We have described an algorithm which introduces barycentric interpolation to the problem of reconstruction from slices, and produces a smooth interpolating surface corresponding to a set of either unicolored or segmented cross-sections, even when the labeling of some regions is unknown. The algorithm also allows for an efficient online version. This solves the problem of reconstruction from arbitrarily oriented cross-sections at a new level of generality. The algorithm is intuitive and quite easy to implement. Our unknown region completion is a simple extension of the same mean-value transfinite interpolation. Our algorithm is also numerically robust in comparison to previous geometric tiling approaches, since small errors in the mean-value function evaluation only perturb the indicator function slightly, which does not significantly affect the results.. The main drawback of our algorithm is the need to evaluate the interpolated indicator function at a large number of points in space during iso-surface extraction, which can be quite expensive in a regular CPU computation. This bottleneck is alleviated using a natural GPU implementation, which is possible due to the parallel nature of the mean-value function evaluation, and which allows for 113:12. a fast offline and online zero-set extraction. Better results can be achieved by parallelizing the mesh generator, and allowing it to only update the surface in the affected zone.. Another drawback that our algorithm shares with the other stateof-the-art algorithms solving this problem is the use of arrangements, which makes this stage of the algorithm cumbersome for large numbers of slices (i.e., more than 150). Moreover, we are not able to control the topology of the resulting surface, nor provide any theoretical guarantee for the outcome, even though empirically we obtain quite nice results.. In addition, even though the results are smooth and consistent, there is an apparent loss of detail when slicing an object with crosssections and then reconstructing (as seen in Figure 16 ) from them. This is common to all cross-section reconstruction methods, as far as we know. An interesting next step would be to create detailpreserving reconstructions, which might reproduce certain surfaces (e.g., sweep surfaces sampled by cross-sections parallel to the base), and incorporate the reconstruction of sharp features.. Finally, our choice of mean-value interpolation was motivated by the closed-form equations that fit our problem well. An interesting direction for future research is generalization of the barycentric method on an arrangement to any type of transfinite barycentric interpolation, for example, harmonic functions, and theoretical investigation of their properties. The first generation of work on the topic of reconstruction from contours (e.g., Batnitzky et al. [1981] , Fix and Ladner [1998] , Fuchs et al. [1977] , Ganapathy and Dennehy [1982] , , , Keppel [1975] , Sloan and Painter [1988] , Wang and Aggarwal [1986] , and Welzl and Wolfers [1994] ) studied the problem of interpolation between parallel cross-sections of a single object. Some (e.g., Choi and Park [1994] , Christiansen and Sederberg [1978] , Ekoule et al. [1991] , Meyers et al. [1991] , Shantz [1981] , and Zyda et al. [1987] ) even restrict the problem to scenarios where only a single contour is present in every input slice. Most early algorithms fail on complex inputs, such as multiple branching, or frequently create unacceptable self-intersecting solutions. More recent works [Bajaj et al. 1996; Barequet and Sharir 1996; Boissonnat 1988; Barequet et al. 2004; Boissonnat and Geiger 1992; Cheng and Dey 1999; Felkel and Obdržálek 1999; Ju et al. 2005b; Oliva et al. 1996] address the problem of reconstruction of a single object from parallel slices without imposing any constraints on the contours, their geometries, or their containment hierarchies. They all focus on creating a portion of the surface between two adjacent slices, and concatenating the boundary surface from the set of created layers. Only a few (e.g., Bogush et al. [2004] , Boissonnat and Memari [2007] , Dance and Prager [1997] , Liu et al. [2008] , and Payne and Toga [1994] ) have attempted to solve the problem for non-parallel, possibly intersecting slices.. The approach of most cross-section reconstruction algorithms is geometric, in which a correspondence is constructed between the vertices and edges of the polygonal input contours, forming triangulated surfaces, usually by projecting contours onto each other and solving the correspondence problem in two dimensions. The two most recent methods [Barequet and Vaxman 2009; Liu et al. 2008] form the arrangement of cross-section planes, and project the contours from the faces of each cell onto the faces of the straight skeleton or medial axis of the cell. They then erect "walls" between the original contours and the projections to create portions of the boundary surface. Albeit solving the problem in full generality, these methods create jagged surfaces with bad triangulations, which must then be improved using smoothing and/or remeshing in a postprocess. These geometric methods have the advantage of being fast and efficient for most reasonable inputs. However, both the medial axis and the straight skeleton have nonrational coordinates even for arrangements with rational coordinates, thus these methods are not numerically robust. This is further aggravated by the fact that the algorithms have zero error tolerance, as small errors in the computation of the skeleton might lead to self-intersecting surfaces, or surfaces with holes.. A completely different family of algorithms, to which our algorithm belongs, involves the use of distance functions (e.g., Turk and O'Brien [1999] , and Csebfalvi et al. [2002] ), commonly used in point cloud reconstruction algorithms. These scalar functions on R 3 are typically defined so that their zero set contains the given planar contours, and their absolute value increases with distance from the contour. However, these methods have been applied usually to the case of parallel, or at least ordered, slices (in which the ordering of the slices affects the solution). One might apply a traditional Radial-Basis Function (RBF) solution to our problem, interpolating the vertices (or some sampling) of the contours, but the sparsity of the data will typically result in the zero set having many spurious components.. In order to deal with partial information, Barequet and Vaxman [2009] remove the parts of the plane which are unknown, compute the arrangement of partial planes and its three-dimensional straightskeleton, and provide an extension to the algorithm of Liu et al. [2008] , dealing with nonconvex cells in order to reconstruct the surface. This technique also allows the user to insert patches of planes inside cells, to better control the result. The complexity of the straight skeleton and the arrangement then grow at least cubically with the complexity of the unknown regions (see [Barequet et al. 2008] ), which makes this algorithm prohibitive for complex noise patterns.. Finally, a few recent works [Ju et al. 2005b , Liu et al. 2008 , Barequet and Vaxman 2009 , Bajaj and Edwards 2010 addressed the more general problem of reconstruction from multilabeled contours (i.e., the contours within each plane may belong to separate components of the object). The main challenge here is to simultaneously reconstruct several nonintersecting surfaces. This is important in medical applications, where acquired images have been segmented to multiple organs. Our algorithm deals with multilabeled contours in a natural way.

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


Structured translation for cross-language information retrieval The paper introduces a query translation model that reflects the structure of the cross-language information retrieval task. The model is based on a structured bilingual dictionary in which the translations of each term are clustered into groups with distinct meanings. Query translation is modeled as a two-stage process, with the system first determining the intended meaning of a query term and then selecting translations appropriate to that meaning that might appear in the document collection. An implementation of structured translation based on automatic dictionary clustering is described and evaluated by using Chinese queries to retrieve English documents. Structured translation achieved an average precision that was statistically indistinguishable from Pirkola's technique for very short queries, but Pirkola's technique outperformed structured translation on long queries. The paper concludes with some observations on future work to improve retrieval effectiveness and on other potential uses of structured translation in interactive cross-language retrieval applications. Cross-language Information Retrieval (CLIR) is the task of finding documents that are written in one language (e.g., English) using queries that are expressed in another (e.g., Chinese). One common approach, known as "query translation," is to translate each query term and then perform monolingnal retrieval in the language of the document [11] . Bilingual dictionaries have proven to be a useful source for potential translations, and methods for selecting the appropriate translation(s) for each *Work by the first author was performed while at the University of Maryland Computer Science Department.. Permission to make digital or hard copies of all or part of this work for personal or classroom use ts granted without fee provided that copies are not made or distributed for profzt or commercial advantage and that copies bear this notice and the full cltataon on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SIGIR 2000 7/00 Athens, Greece © 2000 ACM 1-58113-226-3/00/0007... $5.00 term have been the subject of extensive research. Two fundamental approaches to this problem of translation selection have emerged, techniques guided by encoded linguistic knowledge and/or statistics that characterize term usage in large collections of text (cf., [8, 9] ) and techniques that treat each known translation as an equally valid alternative [14] . In this paper we introduce structured translation, a framework for query translation in which we assume that the dictionary employed has the target language translations grouped into distinct concepts. We use the first approach to select among alternative concepts that a query-language term might represent and then apply the second approach to accommodate the range of document-language terms that might be chosen to express that concept. We present a technique that transforms an unstructured bilingual dictionary into a structured one, and experimental results obtained using that technique. We have introduced the idea of structured translation and explored ways in which structured translation can be applied in a CLIR system. Although our experiments did not demonstrate better retrieval effectiveness than Pirkola's method, we believe that this may result from weaknesses in our present cluster weighting algorithm. Our experience with manual dictionary clustering has clarified the need for task-based measures of clustering effectiveness, and we plan to explore that issue further through user studies and additional retrieval experiments. The clustering algorithm used in our experiments builds on existing work in monolingnal applications, but bilingual dictionaries also offer the potential for iterative refinement, first clustering in one language and then the other. We are interested in exploring that possibility as a way of improving cluster assignments. We also plan to explore clustering techniques that exploit additional sources of evidence, such as the use of derivational morphology and the crosspart-of-speech links in EuroWordNet.. Although we introduced structured translation from the perspective of query translation, the retrieval problem is symmetric--it is equally useful to think of selecting an indexing vocabulary for documents that searchers are likely to choose. Incorporation of these ideas in a CLIR approach based on document translation should thus be quite straightforward. The results that we have focused on in our analysis have generally been statistically significant, but differences of the magnitude we have observed (typically less than 20%) might be of little conse-quence in a real application. This automated processing is, however, generally only a part of some larger crosslanguage search process. As we mentioned in Section 2, structured translation might find its most important application in other parts of that process. For interactive retrieval, Oard and Resnik suggested that displaying as many as three translations, one for each possible meanings of a term, might help users recognize promising documents through a "pop out" effect in which the context reinforces the user's perception of the appropriate translation [12] . User-assisted query translation might also benefit from structured translation. Ogden et al., for example, displayed all known back-translations for each candidate translation to provide monolingual users with a basis for making such a selection [13] . Fewer such decisions would be needed if alternate translations were grouped by meaning. Structured translation back into the query language might also be helpful since alternatives could then be displayed in semantically related groups.. Ultimately, the value of structured translation rests on the degree to which the model depicted in Figure 1 represents the structure of the task at hand. The common feature of the tasks that we have identified---crosslanguage retrieval, gloss translation for browsing, and query refinement using retranslation--is that techniques are known that can tolerate some degree unresolvable ambiguity. Structured translation offers a principled way of using the available evidence in an appropriate manner without making inappropriate choices in cases where sufficient evidence is not available. Our hypothesis was that within-cluster term selection should be handled differently from across-cluster term selection. For our initial experiments, we compared four techniques for using the belief values of alternative translations within a cluster. To do this, we treated every known translation as a single cluster and formed queries in five ways. Examples for each of are shown using a the very short query for TREC Topic 358 "bloodalcohol fatalities" that was manually translated to 'bcue3ye4jiu3jinglsi3wanglshi4gu4" and then automatically segmented to "xue3ye4 jiu3jingl si3wangl shi4gu4." The corresponding dictionary entries are {blood bloodstream}, {ethanol alcohol spiritns}, {death demise deadly doom (to die) abosis}, and {trouble accident mishap}. SU Single Unstructured. For each Chinese term, include every known translation. ~sum(blood bloodstream ethanol alcohol spiritus death demise deadly doom #uw2(to die) abosis trouble accident mishap);. SP Single Pirloka. The query is structured using Pirkola's method [14] . #sum(#syn(blood bloodstream) #syn (ethanol alcohol spiritus) ~syn(death demise deadly doom #uw2(to die) abosis) #syn(trouble accident mishap)); SO Single Or. For each Chinese terra, combine belief values for each alternative translation using a probabilistic or operator. #sum(#or(bloodbloodstream) #or(ethanol alcohol spiritus) ~or(death demise deadly doom #uw2(to die) abosis) #or( trouble accident mishap));

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