In this paper, we treat polynomials with coefficients of floating-point numbers. The conventional concept of ideal breaks down for such polynomials, and we first define a concept of "approximate ideal''. Then, introducing "accuracy-guarding reductions'', we define approximate Groebner bases and give an algorithm for computing the approximate Groebner bases. We prove several theorems showing basic properties of approximate Groebner bases. The algorithm has been implemented, and we explain the approximate Groebner bases concretely by instructive examples.
{"title":"A Theory and an Algorithm of Approximate Gröbner Bases","authors":"Tateaki Sasaki","doi":"10.1109/SYNASC.2011.12","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.12","url":null,"abstract":"In this paper, we treat polynomials with coefficients of floating-point numbers. The conventional concept of ideal breaks down for such polynomials, and we first define a concept of \"approximate ideal''. Then, introducing \"accuracy-guarding reductions'', we define approximate Groebner bases and give an algorithm for computing the approximate Groebner bases. We prove several theorems showing basic properties of approximate Groebner bases. The algorithm has been implemented, and we explain the approximate Groebner bases concretely by instructive examples.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131872581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The trigonometric interpolation polynomial with an arbitrary even number of nodes is computed in connection with other well known results.
结合其他已知结果，计算了具有任意偶数节点的三角插值多项式。
{"title":"On the Interpolation Trigonometric Polynomial with an Arbitrary Even Number of Nodes","authors":"E. Scheiber","doi":"10.1109/SYNASC.2011.13","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.13","url":null,"abstract":"The trigonometric interpolation polynomial with an arbitrary even number of nodes is computed in connection with other well known results.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121718440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. The main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting.
{"title":"On Kahan's Rules for Determining Branch Cuts","authors":"F. Chyzak, J. Davenport, C. Koutschan, B. Salvy","doi":"10.1109/SYNASC.2011.51","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.51","url":null,"abstract":"In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. The main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124715307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents the general architecture of a system which creates a map of semantic information around a named entity (Person, Organization, etc.). Thus, after the user specifies a named entity, the system searches on the web and returns the first 200 web pages containing the specified entity, applies semantic roles on the returned paragraphs, and extracts a map of related actions involving the searched entity. This map of actions can then be chronologically ordered, thus illustrating the actions a certain entity has performed in a specific time frame (or at least the way it is reflected by the online world).
{"title":"Towards Extracting Semantic Information from Texts","authors":"Diana Trandabat","doi":"10.1109/SYNASC.2011.47","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.47","url":null,"abstract":"This paper presents the general architecture of a system which creates a map of semantic information around a named entity (Person, Organization, etc.). Thus, after the user specifies a named entity, the system searches on the web and returns the first 200 web pages containing the specified entity, applies semantic roles on the returned paragraphs, and extracts a map of related actions involving the searched entity. This map of actions can then be chronologically ordered, thus illustrating the actions a certain entity has performed in a specific time frame (or at least the way it is reflected by the online world).","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131093793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The ever-increasing size, variety and complexity of distributed systems necessitate the development of highly automated and intelligent solutions for monitoring system parameters. In the context of Large Scale Distributed Systems, automatically detecting events and activity patterns will provide self-organization abilities and increase the dependability of these systems. We present in this paper a model for representing a wide variety of patterns in the parallel time series describing the distributed system parameters and states. Based on this model, we outline an application architecture for a system that employs advanced machine learning techniques for detecting and learning patterns in a distributed system with only minimal user input. The application is implemented as an add-on to the highly successful MonALISA monitoring framework for distributed systems. We test and validate the proposed model in real-time using the large amount of monitoring data provided by the MonALISA system. The novelty of this solution consists of the expressiveness of the model and the advanced automated data analysis for pattern learning and recognition in a long-time monitored system.
{"title":"Pattern Detection Model for Monitoring Distributed Systems","authors":"Cristian-Mircea Dinu, Florin Pop, V. Cristea","doi":"10.1109/SYNASC.2011.22","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.22","url":null,"abstract":"The ever-increasing size, variety and complexity of distributed systems necessitate the development of highly automated and intelligent solutions for monitoring system parameters. In the context of Large Scale Distributed Systems, automatically detecting events and activity patterns will provide self-organization abilities and increase the dependability of these systems. We present in this paper a model for representing a wide variety of patterns in the parallel time series describing the distributed system parameters and states. Based on this model, we outline an application architecture for a system that employs advanced machine learning techniques for detecting and learning patterns in a distributed system with only minimal user input. The application is implemented as an add-on to the highly successful MonALISA monitoring framework for distributed systems. We test and validate the proposed model in real-time using the large amount of monitoring data provided by the MonALISA system. The novelty of this solution consists of the expressiveness of the model and the advanced automated data analysis for pattern learning and recognition in a long-time monitored system.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"657 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116095204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a technique for reach ability analysis of Time-Basic (TB) Petri nets, a powerful formalism for real time systems where time constraints are expressed as intervals, representing possible transition firing times, whose bounds are functions of marking's time description. The technique consists of building a symbolic reach ability graph relying on a sort of time coverage, and overcomes the limitations of the only available analyzer for TB nets, based in turn on a time-bounded inspection of a (possibly infinite) tree-tree. The graph construction algorithm has been automated by a tool-set, briefly described in the paper together with its main functionality and analysis capability. A running example is used throughout the paper to sketch the symbolic graph construction. A use case describing a small real system - that the running example is an excerpt from - has been employed to benchmark the technique and the tool-set. The main outcome of this test are also presented in the paper. Ongoing work, in the perspective of integrating with a model-checking engine, is shortly discussed.
{"title":"Reachability Analysis of Time Basic Petri Nets: A Time Coverage Approach","authors":"C. Bellettini, L. Capra","doi":"10.1109/SYNASC.2011.16","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.16","url":null,"abstract":"We introduce a technique for reach ability analysis of Time-Basic (TB) Petri nets, a powerful formalism for real time systems where time constraints are expressed as intervals, representing possible transition firing times, whose bounds are functions of marking's time description. The technique consists of building a symbolic reach ability graph relying on a sort of time coverage, and overcomes the limitations of the only available analyzer for TB nets, based in turn on a time-bounded inspection of a (possibly infinite) tree-tree. The graph construction algorithm has been automated by a tool-set, briefly described in the paper together with its main functionality and analysis capability. A running example is used throughout the paper to sketch the symbolic graph construction. A use case describing a small real system - that the running example is an excerpt from - has been employed to benchmark the technique and the tool-set. The main outcome of this test are also presented in the paper. Ongoing work, in the perspective of integrating with a model-checking engine, is shortly discussed.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120839440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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