In this paper the problem of univariate polynomial evaluation is considered. When both polynomial coefficients and the evaluation "point" are integers, unbalanced multiplications (one factor having many more digits than the other one) in classical Ruffini-Horner rule do not let computations completely benefit of sub quadratic methods, like Karatsuba, Toom-Cook and Schonhage-Strassen's. We face this problem by applying an approach originally proposed by Estrin to augment parallelism exploitation in computation. We show that it is also effective in the sequential case, whenever data dimensions grow, e.g. in the long integer case. We add some adjustments to Estrin's proposal obtaining a smoother behavior around corner cases, and to avoid performance degradation when most of the coefficients are zero. This way, a new general algorithm is obtained, improving both theoretical complexity and actual performance. The algorithm itself is very simple, and its use can be usefully extended to evaluation of polynomials on rationals or on polynomials (polynomial composition). Some tests, results and comparisons obtained with PARI/GP are also presented, for both dense and "sparse" polynomials.
{"title":"Long Integers and Polynomial Evaluation with Estrin's Scheme","authors":"Marco Bodrato, A. Zanoni","doi":"10.1109/SYNASC.2011.17","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.17","url":null,"abstract":"In this paper the problem of univariate polynomial evaluation is considered. When both polynomial coefficients and the evaluation \"point\" are integers, unbalanced multiplications (one factor having many more digits than the other one) in classical Ruffini-Horner rule do not let computations completely benefit of sub quadratic methods, like Karatsuba, Toom-Cook and Schonhage-Strassen's. We face this problem by applying an approach originally proposed by Estrin to augment parallelism exploitation in computation. We show that it is also effective in the sequential case, whenever data dimensions grow, e.g. in the long integer case. We add some adjustments to Estrin's proposal obtaining a smoother behavior around corner cases, and to avoid performance degradation when most of the coefficients are zero. This way, a new general algorithm is obtained, improving both theoretical complexity and actual performance. The algorithm itself is very simple, and its use can be usefully extended to evaluation of polynomials on rationals or on polynomials (polynomial composition). Some tests, results and comparisons obtained with PARI/GP are also presented, for both dense and \"sparse\" polynomials.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"12 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":"116928843","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}
Research collaboration has always been important and has recently become even more so. I wish therefore to address a topic I believe to require attention now, and that is software support for mathematical collaboration.
{"title":"Computational Tools for Mathematical Collaboration","authors":"S. Watt","doi":"10.1109/SYNASC.2011.64","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.64","url":null,"abstract":"Research collaboration has always been important and has recently become even more so. I wish therefore to address a topic I believe to require attention now, and that is software support for mathematical collaboration.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"81 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":"132656155","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}
Recommender systems can increase the sales by suggesting to users additional products, that were selected by their preferences. Availability of efficient mechanisms for generating the adequate products and for capturing the eligible information are the most important challenges of Web users. The Apriori algorithm is the best-known association rules mining algorithm, whose objective is to find all co-occurrence relationships between data items. In order to obtain a well defined information in an open standard format, we propose, an ontology-based recommender system, which describes the item features in terms of semantic concepts. In this paper, a methodology that combines the Apriori algorithm with a domain-specific ontology is proposed. The proposed model transfers the association rules on custom OWLIM rules, and by using OWLIM semantic repositories the detected associations will become public and can be interconnected with other information from the Internet. In this way, new facts can be deduced, therefore new relationships and rules between product items will be generated.
{"title":"Integration of Association Rule Detection with Rule-Based Ontological Support for Product Recommendation","authors":"Anita Hejja, R. Buchmann, A. Szekely","doi":"10.1109/SYNASC.2011.50","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.50","url":null,"abstract":"Recommender systems can increase the sales by suggesting to users additional products, that were selected by their preferences. Availability of efficient mechanisms for generating the adequate products and for capturing the eligible information are the most important challenges of Web users. The Apriori algorithm is the best-known association rules mining algorithm, whose objective is to find all co-occurrence relationships between data items. In order to obtain a well defined information in an open standard format, we propose, an ontology-based recommender system, which describes the item features in terms of semantic concepts. In this paper, a methodology that combines the Apriori algorithm with a domain-specific ontology is proposed. The proposed model transfers the association rules on custom OWLIM rules, and by using OWLIM semantic repositories the detected associations will become public and can be interconnected with other information from the Internet. In this way, new facts can be deduced, therefore new relationships and rules between product items will be generated.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"11 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":"125410454","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 the context of constructive synthesis of sorting algorithms, starting from the specification of the problem (input and output conditions), the proof of existence of a sorted tuple is performed inductively and we design, implement, and experiment with different proof techniques: First we use a back-chaining mechanism similar to a Prolog engine for first order logic, in which meta-variables are used for finding the existential witnesses. In order to overcome the search space explosion, we introduce various specific prove-solve methods for the theory of tuples. For instance, the equivalence relation on tuples "have same elements'' can be treated using a normal form based on multisets -- this leads to a very efficient inference rule for rewriting. When reasoning about sorting, we also have an ordering relation between elements. We extend this to an ordering between an element and a tuple, and even between tuples. Ordering relations create specific problems in Prolog style reasoning, because of transitivity and reflexivity. We demonstrate that ordering can be treated very efficiently by decomposing atomic statements into simpler ones (containing only symbols instead of terms), both for goals (backward reasoning) as well as for assumptions (forward reasoning). This leads to an interesting combination of backward and forward inferences which goes beyond and complements Prolog style reasoning. Finally, we develop a solving mechanism for finding sorted tuples, which performs the proof more efficiently, by combining relatively simple inference rules and small searches with goal directed solving rules. The techniques are implemented in the Theorem a system and are able to produce automatically proofs and algorithms for various problems: Insertion Sort, Insertion, Merge Sort, and Merge. Besides the special proof techniques, this work also gives useful hints about finding appropriate induction principles for tuples, as well as for the construction of appropriate collections of properties of tuples which are necessary for reasoning about sorting.
{"title":"Proof Techniques for Synthesis of Sorting Algorithms","authors":"I. Dramnesc, T. Jebelean","doi":"10.1109/SYNASC.2011.23","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.23","url":null,"abstract":"In the context of constructive synthesis of sorting algorithms, starting from the specification of the problem (input and output conditions), the proof of existence of a sorted tuple is performed inductively and we design, implement, and experiment with different proof techniques: First we use a back-chaining mechanism similar to a Prolog engine for first order logic, in which meta-variables are used for finding the existential witnesses. In order to overcome the search space explosion, we introduce various specific prove-solve methods for the theory of tuples. For instance, the equivalence relation on tuples \"have same elements'' can be treated using a normal form based on multisets -- this leads to a very efficient inference rule for rewriting. When reasoning about sorting, we also have an ordering relation between elements. We extend this to an ordering between an element and a tuple, and even between tuples. Ordering relations create specific problems in Prolog style reasoning, because of transitivity and reflexivity. We demonstrate that ordering can be treated very efficiently by decomposing atomic statements into simpler ones (containing only symbols instead of terms), both for goals (backward reasoning) as well as for assumptions (forward reasoning). This leads to an interesting combination of backward and forward inferences which goes beyond and complements Prolog style reasoning. Finally, we develop a solving mechanism for finding sorted tuples, which performs the proof more efficiently, by combining relatively simple inference rules and small searches with goal directed solving rules. The techniques are implemented in the Theorem a system and are able to produce automatically proofs and algorithms for various problems: Insertion Sort, Insertion, Merge Sort, and Merge. Besides the special proof techniques, this work also gives useful hints about finding appropriate induction principles for tuples, as well as for the construction of appropriate collections of properties of tuples which are necessary for reasoning about sorting.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"16 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":"126439941","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 concept of a checking test is of prime interest to the study of a variant of exact identification problem, in which the learner is given a hint about the unknown object. A graph F is said to be a checking test for a co graph G iff for any other co graph H there exists an edge in F distinguishing G and H, that is, contained in exactly one of the graphs G and H. It is known that for any co graph G there exists a unique irredundant checking test, the number of edges in which is called the checking test complexity of G. We show that almost all co graphs on n vertices have relatively small checking test complexity of O(n log n). Using this result, we obtain an upper bound on the checking test complexity of almost all read-once Boolean functions over the basis of disjunction and parity functions.
{"title":"An Upper Bound on Checking Test Complexity for Almost All Cographs","authors":"O. V. Zubkov, D. Chistikov, A. A. Voronenko","doi":"10.1109/SYNASC.2011.44","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.44","url":null,"abstract":"The concept of a checking test is of prime interest to the study of a variant of exact identification problem, in which the learner is given a hint about the unknown object. A graph F is said to be a checking test for a co graph G iff for any other co graph H there exists an edge in F distinguishing G and H, that is, contained in exactly one of the graphs G and H. It is known that for any co graph G there exists a unique irredundant checking test, the number of edges in which is called the checking test complexity of G. We show that almost all co graphs on n vertices have relatively small checking test complexity of O(n log n). Using this result, we obtain an upper bound on the checking test complexity of almost all read-once Boolean functions over the basis of disjunction and parity functions.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"23 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":"133842152","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}
A lot of different environmental simulations use computational fluid dynamics for detailed airflow computation and pollution transportation. Unfortunately, a multi-scale computational fluid dynamics simulation is very time consuming and computational intensive, as a high geometric discretisation has to be chosen in order to capture all required physical phenomena, so that without any parallelisation strategies, these computations tend to be impossible to perform. In this paper, we will discuss communication schemes using the message passing paradigm implemented in a previously validated fluid simulation code. Advantages and disadvantages of the current implementation will be discussed and improvements will be proposed.
{"title":"Communication Schemes of a Parallel Fluid Solver for Multi-scale Environmental Simulations","authors":"J. Frisch, R. Mundani, E. Rank","doi":"10.1109/SYNASC.2011.7","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.7","url":null,"abstract":"A lot of different environmental simulations use computational fluid dynamics for detailed airflow computation and pollution transportation. Unfortunately, a multi-scale computational fluid dynamics simulation is very time consuming and computational intensive, as a high geometric discretisation has to be chosen in order to capture all required physical phenomena, so that without any parallelisation strategies, these computations tend to be impossible to perform. In this paper, we will discuss communication schemes using the message passing paradigm implemented in a previously validated fluid simulation code. Advantages and disadvantages of the current implementation will be discussed and improvements will be proposed.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"67 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":"131385981","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 CAD, constraint solvers allow a user to describe a figure or an object with a set of constraints like distances, angles, tangencies, incidences and so on. Geometric solvers proceed in two stages. First, a symbolic construction plan is provided from the set of constraints. Then, the dimensions of constraints are used in a numerical stage to evaluate the construction plan. However, construction plans can not be easily provided for many problems in 3D. A classic idea consists in removing and adding some constraints in order to make the problem solvable by a geometric method. This leads to a numerical problem in which numerical values for the added constraints have to be computed in order to find the values of the added dimensions that validate the removed dimensions. Finding these values is usually done by sampling which is very time-consuming when there are more than 2 variables to sample. In this paper we address the numerical stage by adapting a path-tracking method. This allows to find several solutions and this method is efficient when the number of values is greater than 2.
{"title":"Tracking Method for Reparametrized Geometrical Constraint Systems","authors":"Rémi Imbach, P. Mathis, P. Schreck","doi":"10.1109/SYNASC.2011.26","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.26","url":null,"abstract":"In CAD, constraint solvers allow a user to describe a figure or an object with a set of constraints like distances, angles, tangencies, incidences and so on. Geometric solvers proceed in two stages. First, a symbolic construction plan is provided from the set of constraints. Then, the dimensions of constraints are used in a numerical stage to evaluate the construction plan. However, construction plans can not be easily provided for many problems in 3D. A classic idea consists in removing and adding some constraints in order to make the problem solvable by a geometric method. This leads to a numerical problem in which numerical values for the added constraints have to be computed in order to find the values of the added dimensions that validate the removed dimensions. Finding these values is usually done by sampling which is very time-consuming when there are more than 2 variables to sample. In this paper we address the numerical stage by adapting a path-tracking method. This allows to find several solutions and this method is efficient when the number of values is greater than 2.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"35 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":"123930158","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}
Fraud is a recurring phenomenon at online actions sites like eBay. The enormous amount of transaction data public ally available offers a good opportunity for fraud prevention based on learning methods. However, online auction sites usually neither confirm nor deny fraudulent behavior: they simply suspend seller accounts and publicize feedback information supplied by buyers. While some cases receive media attention, most of them are hidden in the site's database. This limits the possibility of developing and testing new learning methods for fraud prevention, due to the scarcity of fraud samples. In order to overcome this limitation, we designed a system based on supervised learning to recognize in the textual comments left by buyers some common statements regarding seller behavior. Combining the type and frequency of those statements with other public ally available data, we can build a set of sellers who can arguably be considered fraudsters. We implemented a prototype of the system and evaluated it using data extracted from a major online auction site.
{"title":"A Supervised Learning Process to Elicit Fraud Cases in Online Auction Sites","authors":"Vinicius Almendra, D. Enachescu","doi":"10.1109/SYNASC.2011.15","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.15","url":null,"abstract":"Fraud is a recurring phenomenon at online actions sites like eBay. The enormous amount of transaction data public ally available offers a good opportunity for fraud prevention based on learning methods. However, online auction sites usually neither confirm nor deny fraudulent behavior: they simply suspend seller accounts and publicize feedback information supplied by buyers. While some cases receive media attention, most of them are hidden in the site's database. This limits the possibility of developing and testing new learning methods for fraud prevention, due to the scarcity of fraud samples. In order to overcome this limitation, we designed a system based on supervised learning to recognize in the textual comments left by buyers some common statements regarding seller behavior. Combining the type and frequency of those statements with other public ally available data, we can build a set of sellers who can arguably be considered fraudsters. We implemented a prototype of the system and evaluated it using data extracted from a major online auction site.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"174 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":"122052534","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}
Automatic understanding of the intended meaning of computer programs is a very hard problem, requiring intelligence and reasoning. In this abstract we discuss a new method for program analysis, called symbol elimination. Symbol elimination uses first-order theorem proving techniques to automatically discover non-trivial program properties, such as loop invariants and loop bounds. Moreover, symbol elimination can be used as an alternative to interpolation for software verification.
{"title":"Symbol Elimination in Program Analysis","authors":"Laura Kov´cs","doi":"10.1109/SYNASC.2011.60","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.60","url":null,"abstract":"Automatic understanding of the intended meaning of computer programs is a very hard problem, requiring intelligence and reasoning. In this abstract we discuss a new method for program analysis, called symbol elimination. Symbol elimination uses first-order theorem proving techniques to automatically discover non-trivial program properties, such as loop invariants and loop bounds. Moreover, symbol elimination can be used as an alternative to interpolation for software verification.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"16 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":"123282014","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 starting point of this research was the observation that object oriented classification mostly reflects one particular perspective which is ascribed to all the objects in the system. It was considered that this is an important limitation when trying to add autonomy to the objects in order to progress towards an agent oriented paradigm. In particular, we consider that agents may have the ability of classifying the external world instead of only relying on the classification being imposed. Therefore this paper proposes a way to add a new type of classification elements into an OO language such as the objects reason about other objects when providing/executing services based on what we call subjective classification.
{"title":"Enhancing Objects' Autonomy through the Classification of Objects' Interactions","authors":"C. Sandru","doi":"10.1109/SYNASC.2011.38","DOIUrl":"https://doi.org/10.1109/SYNASC.2011.38","url":null,"abstract":"The starting point of this research was the observation that object oriented classification mostly reflects one particular perspective which is ascribed to all the objects in the system. It was considered that this is an important limitation when trying to add autonomy to the objects in order to progress towards an agent oriented paradigm. In particular, we consider that agents may have the ability of classifying the external world instead of only relying on the classification being imposed. Therefore this paper proposes a way to add a new type of classification elements into an OO language such as the objects reason about other objects when providing/executing services based on what we call subjective classification.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"35 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":"131666341","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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