the advent of emerging information and communication technologies, such as RFID, small size sensors and sensor networks, has made accessible a huge amount of information that requires sophisticated and efficient searc...
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ISBN:
(纸本)9781538626269
the advent of emerging information and communication technologies, such as RFID, small size sensors and sensor networks, has made accessible a huge amount of information that requires sophisticated and efficient search algorithms to support queries on that data. In this paper we focus on the problem of aggregating data collected from these devices to efficiently support queries, inferences or statistics on them. In general, data aggregation techniques are necessary to efficiently collect information in a compact and cost-effective way. Some current solutions try to meet the above criteria, by exploiting different data aggregation techniques, for instance BitVector or Q_Digest. In this manuscript, we exploit the mathematical wavelet structure to define a sophisticated data aggregation technique for information collected from different nodes. the aggregated data is then exploited for solving multidimensional range queries. Experimental results based on simulations of a real dataset show the effectiveness of our approach with respect to other aggregation strategies.
As in any other scientific field, the quality control (by peer reviewing), archiving and distribution of knowledge in mathematics is organized by journals. Currently, mathematical journals represent huge chunks of kno...
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ISBN:
(纸本)9780769530789
As in any other scientific field, the quality control (by peer reviewing), archiving and distribution of knowledge in mathematics is organized by journals. Currently, mathematical journals represent huge chunks of knowledge that sit passively on a shelf and wait for a human user to read or query them. In contrast, what we want to achieve in this project is the transformation of the knowledge contained in mathematical journals into formal mathematical knowledge bases that behave as active reasoning agents.
We review our recent results concerning several computer algebra aspects of determining canonical forms, performing a decomposition and deciding the isomorphism question for matrix problems. We consider them in the la...
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ISBN:
(纸本)9780769549347;9781467350266
We review our recent results concerning several computer algebra aspects of determining canonical forms, performing a decomposition and deciding the isomorphism question for matrix problems. We consider them in the language of finite dimensional modules over algebra and the language of square block matrices with an action of elements from some subalgebra of the full matrix algebra. We present an efficient (polynomial-time) improvement of classical Bongartz's algorithm for determining a maximal common direct summand of modules, and its application to solving the isomorphism problem. the improved algorithm recently became a part of QPA package ver. 1.07 for GAP. We also study the behaviour of Belitskii's algorithm for determining certain canonical form on a class of square block matrices, especially for matrix problems associated with a poset. Both problems can be considered as a highly generalized classical Jordan problem for square matrices.
Verifying arithmetic circuits is an important problem which still requires considerable manual effort. For instance multipliers are considered difficult to verify. the currently most effective approach for arithmetic ...
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ISBN:
(纸本)9781538626269
Verifying arithmetic circuits is an important problem which still requires considerable manual effort. For instance multipliers are considered difficult to verify. the currently most effective approach for arithmetic circuit verification uses computer algebra. In this approach the circuit is modeled as a set of pseudo-boolean polynomials and it is checked if the given word-level specification is implied by the circuit polynomials. For this purpose the theory of Grobner bases is used. In this paper we give a summary of two recent papers on this work. We reword the theory and illustrate the results of these papers by examples. We also present a new technical theorem which allows to rewrite local parts of the Grobner basis. Rewriting the Grobner basis has tremendous effect on computation time.
the growing availability of distributed and cloud computing frameworks makes it possible to face complex computational problems in a more effective and convenient way. A notable example is state-space exploration of d...
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ISBN:
(纸本)9780769549347;9781467350266
the growing availability of distributed and cloud computing frameworks makes it possible to face complex computational problems in a more effective and convenient way. A notable example is state-space exploration of discrete-event systems specified in a formal way. the exponential complexity of this task is a major limitation to the usage of consolidated analysis techniques and tools. Several techniques for addressing the state space explosion problem within this context have been studied in the literature. One of these is to use distributed memory and computation to deal withthe state space explosion problem. In this paper we study and compare two different approaches, relying on distributed and cloud frameworks, respectively. these approaches were designed and implemented following the same computational schema, a sort of map & fold. they are applied on symbolic state-space exploration of real-time systems specified by (a timed extension of) Petri Nets, by re-adapting a sequential algorithm implemented as a command-line Java tool. the outcome of several tests performed on a benchmarking specification are presented, thus showing the convenience of distributed approaches.
We present a logic-based verification method for imperative loops (including ones with abrupt termination) and the automatic proof of its soundness. the verification method consists in generating verification conditio...
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ISBN:
(纸本)9780769549347;9781467350266
We present a logic-based verification method for imperative loops (including ones with abrupt termination) and the automatic proof of its soundness. the verification method consists in generating verification conditions for total correctness of an imperative loop annotated with an invariant. We realized, in the theorema system (***), the automatic proof of the soundness of verification method: if the verification conditions hold, then the imperative loop is totally correct with respect to its given invariant. the approach is simpler than the others because it is based on functional semantics (no additional theory of program execution is necessary) and produces verification conditions in the object theory of the program. the computer-supported proofs reveal the minimal collection of logical assumptions (some from natural number theory) and logical inferences (including induction) which are necessary for the soundness of the verification technique.
Parallel code design is a challenging task especially when addressing petascale systems for massive parallel processing (MPP), i.e. parallel computations on several hundreds of thousands of cores. An in-house computat...
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ISBN:
(纸本)9781509004614
Parallel code design is a challenging task especially when addressing petascale systems for massive parallel processing (MPP), i.e. parallel computations on several hundreds of thousands of cores. An in-house computational fluid dynamics code, developed by our group, was designed for such high-fidelity runs in order to exhibit excellent scalability values. Basis for this code is an adaptive hierarchical data structure together with an efficient communication and (numerical) computation scheme that supports MPP. For a detailled scalability analysis, we performed several experiments on two of Germany's national supercomputers up to 140,000 processes. In this paper, we will show the results of those experiments and discuss any bottlenecks that could be observed while solving engineering-based problems such as porous media flows or thermal comfort assessments for problem sizes up to several hundred billion degrees of freedom.
Transformation-Interaction-Rational is a representation for symbolic Regression created withthe intent to constrain the search space of mathematical expressions with only simple models. In short, this representation ...
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ISBN:
(纸本)9781665465458
Transformation-Interaction-Rational is a representation for symbolic Regression created withthe intent to constrain the search space of mathematical expressions with only simple models. In short, this representation is a rational of two linear models with transformed variables. Even though the representation makes the model nonlinear w.r.t. its numerical parameters, it is possible to rewrite the expression such that the parameters become linear and, thus, can be adjusted using the Ordinary Least Squares method, that guarantees the global optima solution. But, when we are working with a noisy data set, the reparametrization procedure may skew the noise distribution leading to an incorrect value for the numerical parameters. In this work, we test and compare the use of Ordinary Least Square and a non-linear optimization in simulated benchmarks withthe presence of noise. the results show evidence that OLS is robust to noise and always returns a similar solution to the non-linear optimization algorithm.
the computation of self-intersection loci of parametrized surfaces is needed for constructing trimmed parametrizations and describing the topology of the considered surfaces in real settings. this paper presents two g...
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ISBN:
(纸本)9780769539645
the computation of self-intersection loci of parametrized surfaces is needed for constructing trimmed parametrizations and describing the topology of the considered surfaces in real settings. this paper presents two general and efficient methods for determining self-intersection loci of rationally parametrized surfaces. One of the methods, based on regular systems, is capable of computingthe exact parametric locus of self-intersection of a given surface and the other, based on Grobner bases, can compute the minimal variety passing through the exact parametric locus. the relation between the results computed by the two methods is established and two algorithms for computing parametric loci of self-intersection are described. Experimental results and comparisons with some existing methods show that our algorithms have a good performance for parametrized surfaces.
Web usage mining attempts to discover useful knowledge from the secondary data obtained from the interactions of the users withthe Web. Web usage mining has become very critical for effective Web site management, cre...
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ISBN:
(纸本)0769524532
Web usage mining attempts to discover useful knowledge from the secondary data obtained from the interactions of the users withthe Web. Web usage mining has become very critical for effective Web site management, creating adaptive Web sites, business and support services, personalization, network traffic flow analysis and so on. this paper introduces the various ingredients of natural computation and further presents the important concepts of Web usage mining and its various practical applications.
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