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Graph embedding is a transformation of nodes of a graph into a set of vectors. A good embedding should capture the graph topology, node-to-node relationship and other relevant information about the graph, its subgraphs and nodes. ...
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Graph embedding is a transformation of nodes of a graph into a set of vectors. A good embedding should capture the graph topology, node-to-node relationship and other relevant information about the graph, its subgraphs and nodes. If these objectives are achieved, an embedding is a meaningful, understandable, compressed representations of a network that can be used for other machine learning tools such as node classification, community detection or link prediction. In this article, we do a series of extensive experiments with selected graph embedding algorithms, both on real-world networks as well as artificially generated ones. Based on those experiments, we formulate the following general conclusions. First, we confirm the main problem of node embeddings that is rather well-known to practitioners but less documented in the literature. There exist many algorithms available to choose from which use different techniques and have various parameters that may be tuned, the dimension being one of them. One needs to ensure that embeddings describe the properties of the underlying graphs well but, as our experiments confirm, it highly depends on properties of the network at hand and the given application in mind. As a result, selecting the best embedding is a challenging task and very often requires domain experts. Since investigating embeddings in a supervised manner is computationally expensive, there is a need for an unsupervised tool that is able to select a handful of promising embeddings for future (supervised) investigation. A general framework, introduced recently in the literature and easily available on GitHub repository, provides one of the very first tools for an unsupervised graph embedding comparison by assigning the ‘divergence score’ to embeddings with a goal of distinguishing good from bad ones. We show that the divergence score strongly correlates with the quality of embeddings by investigating three main applications of node embeddings: node classification, community detection and link prediction.
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Truncation in digit-precision is a very important and common operation in embedded system design for bounding the required finite precision and for area-time-power savings. In this paper, we present the use of online arithmetic to...
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Truncation in digit-precision is a very important and common operation in embedded system design for bounding the required finite precision and for area-time-power savings. In this paper, we present the use of online arithmetic to provide truncated computations with communication systems as one of the applications. In contrast to truncation in conventional arithmetic, online arithmetic can truncate dynamically and produce both area and time benefits due to the digit-serial nature of computations. This is of great advantage in communication systems where the precision requirements can change dynamically with the environment. While truncation in conventional arithmetic can have significant truncation errors, especially when the output precision is less than the input precision, the redundancy and most significant digit first nature of online arithmetic restricts the truncation error to only the least significant digit of the truncated result. As an application that uses significant truncation in precision, a code matched filter detector for wireless systems is designed using truncated online arithmetic. The detector can provide both hard decisions and soft(er) decisions dynamically as well as interface with other conventional arithmetic circuits or act as a DSP coprocessor. Thus, optimized communication receivers with coexisting conventional arithmetic for saturation and online arithmetic for truncation can now be built. The truncated online arithmetic detector was also verified with a VLSI implementation in an AMI 0.5 mu MOSIS tiny chip process.
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System-level diagnosis aims at the identification of faulty units in a system by the analysis of the system syndrome, that is, the outcomes of a set of interunit tests. For any given syndrome, it is possible to produce a correct (...
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System-level diagnosis aims at the identification of faulty units in a system by the analysis of the system syndrome, that is, the outcomes of a set of interunit tests. For any given syndrome, it is possible to produce a correct (although possibly incomplete) diagnosis of the system if the number of faults is below a syndrome-dependent bound and the degree of diagnosis completeness, that is, the number of correctly diagnosed units, is also dependent on the actual syndrome sigma. The worst-case diagnosis completeness is a syndrome-independent bound that represents the minimum number of units that the diagnosis algorithm correctly diagnoses for any syndrome. This paper provides a lower bound to the worst-case diagnosis completeness for regular graphs for which vertex-isoperimetric inequalities are known and it shows how this bound can be applied to toroidal grids. These results prove a previous hypothesis about the influence of two topological parameters of the diagnostic graph, that is, the bisection width and the diameter, on the degree of diagnosis completeness.
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We describe methods for the computation of Galois groups of univariate polynomials over the rationals which we have implemented up to degree 15. These methods are based on Stauduhar's algorithm. All computations are done in unrami...
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We describe methods for the computation of Galois groups of univariate polynomials over the rationals which we have implemented up to degree 15. These methods are based on Stauduhar's algorithm. All computations are done in unramified p-adic extensions. For imprimitive groups we give an improvement using subfields. In the primitive case we use known subgroups of the Galois group together with a combination of Stauduhar's method and the absolute resolvent method.
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This paper presents our experiences of parallelizing the sequential implementation of NAS benchmarks using compiler directives on SGI Origin 2000 distributed shared memory (DSM) system. Porting existing applications to new high pe...
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This paper presents our experiences of parallelizing the sequential implementation of NAS benchmarks using compiler directives on SGI Origin 2000 distributed shared memory (DSM) system. Porting existing applications to new high performance parallel and distributed computing platforms is a challenging task. Ideally, a user develops a sequential version of the application, leaving the task of porting the code to parallelization tools and compilers. Due to the simplicity of programming shared-memory multiprocessors, compiler developers have provided various facilities to allow the users to exploit parallelism. Native compilers on SIG Origin2000 support multiprocessing directives to allow users to exploit loop-level parallelism in their programs. additionally, supporting tools can accomplish this process atomatically . We experimented with these compiler directives and supporting tools can accomplish this process atomatically. We experimented with these compile redirectives and supporting tools by parallelizing sequential implementation of NAS benchmarks. Results reported in this paper indicate that with minimal effort, the performance gain is comparable with the hand-parallelized, carefully optimized, message-passing implementations of the same benchmarks.
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Bell-type inequalities, used in mathematical physics as a criterion to check whether a physical situation allows description in terms of classical (Kolmogrovian) or quantum probability calculus are applied to various fuzzy probabi...
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Bell-type inequalities, used in mathematical physics as a criterion to check whether a physical situation allows description in terms of classical (Kolmogrovian) or quantum probability calculus are applied to various fuzzy probability models. It occurs that the standard set of Bell-type inequalities does not allow to distinguish Kolmogorovian probabilities from fuzzy probabilities base don the most frequently sued Zadeh inter- section or probabilistic atersection, but it allows to distinguish all thee models from fuzzy probability models base don Giles (Lukasiewicz) intersection. It is proved that if we use fuzzy set intersections pointwisely generated by Frank's fundamental triangular norms T_s(x,y), then the borderline between fuzzy probability models that can be dis- tinguished form Kolmogrovian ones and these fuzzy probability models that cannot be distinguished is for s=9+4/5.
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In this paper, we introduce the general architecture of an image-search engine based on pre-attentive similarities. Local features are computed in key points to represent local properties of the images. Th location of key points, ...
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In this paper, we introduce the general architecture of an image-search engine based on pre-attentive similarities. Local features are computed in key points to represent local properties of the images. Th location of key points, where local features are computed, is discussed. We present two new key point detectors designed for image retrieval, both based on multi-resolution: the contrast-based point detector, and the wavelet-based point detector. Four different local features are used in our system: differential invariants, texture, shape and colour.
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A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular and annular plates with nonlinear thickness variation along the radial direction. Unlike c...
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A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular and annular plates with nonlinear thickness variation along the radial direction. Unlike conventional plate theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u_s, u_z, and u_0 in the radial, thickness, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the s and z directions. Potential (strain) and kinetic energies of the plates are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the plates. Numerical results are presented for completely free, annular and circular plates with uniform, linear, and quadratic variations in thickness. Comparisons are also made between results obtained from the present 3-D and previously published thin plate (2-D) data.
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This paper investigates the effect of prior feature selection in Support Vector Machine (SVM) text categorization. The input space was gradually increased by using mutual in- formation (MI) filtering and part-of-speech (POS) filte...
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This paper investigates the effect of prior feature selection in Support Vector Machine (SVM) text categorization. The input space was gradually increased by using mutual in- formation (MI) filtering and part-of-speech (POS) filtering, which determine the portion of words that are appropriate for SVM learning from the information-theoretic and the linguistic perspectives, respectively. The experimental results are that 1) the optimal number of features differed completely across categories, and 2) the average performance for all categories was best when all of the words were used. In addition, a comparison of the two experiments clarified that POS filtering consistently outperformed MI filtering, which indicates that SVMs cannot find irrelevant parts of speech. These results suggest a simple strategy for using a full number of words found through a rough filtering technique like part-of-speech tagging.
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A biophysical model of an insect olfactory sensillum in steady-state conditions is presented. The model has two distinguishing features. Firstly, it describes analytically the extracellularly Recorded potential, thus closing forma...
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A biophysical model of an insect olfactory sensillum in steady-state conditions is presented. The model has two distinguishing features. Firstly, it describes analytically the extracellularly Recorded potential, thus closing formally the gap between theoretical modes and experimental Results. Secondly, it integrates in a single description two extreme models previously investi- gated: that of the classical neuron located in a homogeneous environment and that of the neuron surrounded with auxillary cells. The generalized model presented gives the opportunity Of studying the response properties of the neuron to odors at various concentrations in A broader context.
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