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Murat Pasa Uysal
2018 Figshare  
In this paper, a software practice mapping method is proposed, which adopts and employs Concept Algebra principles in a Scrum case.  ...  The results are promising, however, more empirical evidences are needed to support the solution.  ...  In this study, the relational operations are used for comparing and mapping the corresponding abstract concepts of a SE practice to the semantic context of EF (Θ).  ... 
doi:10.6084/m9.figshare.7187948.v1 fatcat:6h3gm6lt6zgtpfmzqstpgiixta

Longer bars for bigger numbers? children's usage and understanding of graphical representations of algebraic problems

Kerry Lee, Kiat Hui Khng, Swee Fong Ng, Jeremy Lan Kong Ng
2013 Frontline Learning Research  
Primary 5 students who showed more abstract appreciations in the validation task were less likely to use the bar diagrams in a concrete fashion in the production task.  ...  In Singapore, primary school students are taught to use bar diagrams to represent known and unknown values in algebraic word problems.  ...  Acknowledgements The work was supported by grants from the Centre for Research in Pedagogy and Practice (#CRP 9/05 KL).  ... 
doi:10.14786/flr.v1i1.49 fatcat:zhfhnwlexrdyndbevsdwz4xjn4

A Formal Method for Mapping Software Engineering Practices to Essence

Murat Pasa Uysal
2018 Zenodo  
The results are promising and they differ from the ones exist in the current EF related literature.  ...  The formal method employs an algorithm based on Concept Algebra and it is applied in a Scrum case study.  ...  In this study, the relational operations are used for comparing and mapping the corresponding abstract concepts of a SE practice to the semantic context of EF (Θ).  ... 
doi:10.5281/zenodo.1880455 fatcat:7y7yljww5bc57oqi5ikatrtj5q

Numeric domains meet algebraic data types

Santiago Bautista, Thomas Jensen, Benoît Montagu
2020 Proceedings of the 9th ACM SIGPLAN International Workshop on Numerical and Symbolic Abstract Domains  
The construction employs projection paths on algebraic values, and in particular projections on variant cases, whose sound treatment is subtle due to mutual exclusiveness.  ...  We report on the design and formalization of a novel abstract domain, called numeric path relations (NPRs), that combines numeric relational domains with algebraic data types.  ...  Taking the reduced product of correlations and NPRs would allow to combine the expressiveness of both approaches.  ... 
doi:10.1145/3427762.3430178 fatcat:yo2yc7xve5acvmmy5ti65xmiwe

Image analysis method for overcoming source distortion using algebraic invariant methods

Boris Kovalerchuk, Richard Chase, Sylvia S. Shen, Paul E. Lewis
2005 Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XI  
In addition to geometric shapes and topological data, features and images can also be compared algebraically.  ...  Deriving a method that is invariant to disproportional scaling that is based on an algebraic invariant method is a new approach to solving this problem and represents a new mathematical language for the  ...  The main idea of this approach is assigning matching labels to features from two images 13 .  ... 
doi:10.1117/12.602955 fatcat:snenh4qmfrfrdjy6ggb2gptf6i

Bridging the gap

Andreas Kunft, Alexander Alexandrov, Asterios Katsifodimos, Volker Markl
2016 Proceedings of the 3rd ACM SIGMOD Workshop on Algorithms and Systems for MapReduce and Beyond - BeyondMR '16  
Programs written in Lara are compiled to an intermediate representation (IR) which enables optimizations across linear and relational algebra.  ...  Second, it aims to enable joint optimizations over both relational and linear algebra.  ...  For this task, we have to gather data from various log files residing in different production plants and join them in order to get all measurements of a mixer throughout its production.  ... 
doi:10.1145/2926534.2926540 dblp:conf/sigmod/KunftAKM16 fatcat:4zusweokhbda5hxc64i6hr4nb4

Control interpretations of products in the Hopf algebra

Matthias Kawski
2009 Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference  
series, including the antipode and two convolution products.  ...  Families of differential operators, like those defining affine, generally nonlinear, control systems are known to have natural Hopf algebra structures.  ...  Many open questions remain -but the main observation is that the two Hopf algebra structures with their two convolution products correspond to different points of view that consider the points in the state  ... 
doi:10.1109/cdc.2009.5400441 dblp:conf/cdc/Kawski09 fatcat:uxhskyf2pfcbhjqpz32bevrbua

Foundations for a Combination of Heterogeneous Specification Components

Gwen Salaün, Michel Allemand, Christian Attiogbé
2002 Electronical Notes in Theoretical Computer Science  
In this paper, we advocate an approach to combine formal specification components.  ...  A case study about a vending machine is specified to illustrate how this approach could be practically used.  ...  Compared with related works, our approach presents many interests.  ... 
doi:10.1016/s1571-0661(04)80453-5 fatcat:eprygsealbfk3bs47uf6x4n7fi

Chasing Individuation: Mathematical Description of Physical Systems [article]

Federico Zalamea
2016 arXiv   pre-print
The question becomes then to understand the precise articulation between these two roles.  ...  The "Chase for Individuation" is the analysis of different mathematical techniques which attempt to overcome this tension. In particular, we discuss how group theory furnishes a partial solution.  ...  (z 1 , . . . , z n−1 , x) ∈ R ←→ (z 1 , . . . , z n−1 , y) ∈ R If no relation can perceive the difference between two places-in other terms, if two places are relationally indiscernible-then, these places  ... 
arXiv:1612.02959v1 fatcat:a2qsxtgt4bc2dnb7nzvdlcatna

A metaprogramming approach to generating optimized code for algorithms in linear algebra

Najaf A. Shah, Anthony Skjellum
2005 Proceedings of the 43rd annual southeast regional conference on - ACM-SE 43  
This is an extended abstract for a poster that presents a new approach that employs metaprogramming to generate optimized code for algorithms in Linear Algebra.  ...  We propose a simple approach that uses metaprogramming to quickly compare the tradeoffs between different parameter values.  ...  We propose an alternative approach that enables programmers to quickly compare the tradeoffs between different parameter values.  ... 
doi:10.1145/1167350.1167399 dblp:conf/ACMse/ShahS05 fatcat:77nu6yrjlvcbdiclf73l6o6lai

Object-oriented programming for linear algebra

J. A. McDonald
1989 SIGPLAN notices  
To show how straightforward application of object-oriented design to standard algorithms in numerical linear algebra improves clarity and expressiveness, without sacrificing speed or accuracy, I describe  ...  parts of Cactus, a system for numerical linear algebra and constrained optimization, implemented in Common Lisp and CLOS.  ...  Abstractions Undergraduate mathematics courses in linear algebra tend to come in two styles: a relatively concrete version often called "Matrix Algebra!'  ... 
doi:10.1145/74878.74896 fatcat:vs277svxdrbt7kufnbaw7wwnnq

The development of studients' algebraic thinking in earlier grades:

Jinfa Cai, Hee Chan Lew, Anne Morris, John C. Moyer, Swee Fong Ng, Jean Schmittau
2005 Zentralblatt für Didaktik der Mathematik  
Based on the analyses of the five curricula, we discuss four issues related to the development of algebraic thinking in earlier grades: (1) To what extent do curricula expect students in early grades to  ...  In all five curricula, the main goal for learning algebraic concepts is to deepen students' understanding of quantitative relationships, but the emphases and approaches to helping students deepen their  ...  Success in algebra depends on the ability to think in a variety of powerful ways that foster productive algebraic performance.  ... 
doi:10.1007/bf02655892 fatcat:5puykb3ds5hg3entttkb2eszfi

Introducing Geometric Algebra to Geometric Computing Software Developers: A Computational Thinking Approach [article]

Ahmad Hosny Eid
2017 arXiv   pre-print
In particular, successfully introducing GA to software engineers requires quite different approaches from introducing GA to mathematicians or physicists.  ...  Without the presence of a unifying algebraic system to describe geometric models, the use of software abstractions alone can result in many design and maintenance problems.  ...  bigger subspace, and to reflect one subspace on another. • To compare two subspaces having different attitudes in space.  ... 
arXiv:1705.06668v1 fatcat:x7ytgeyqyjdpjap7w2xthpm7ge

Induction and recursion on datatypes [chapter]

Henk Doornbos, Roland Backhouse
1995 Lecture Notes in Computer Science  
Z-like Formal Development in Classical Set Theory John Staples 13 We begin by comparing the exploitation of abstraction in formal development methods with the use of abstraction in mathematics.  ...  The whole exercise was presented here as an example of application of relation algebra to a different field.  ...  Here, in contrast, an algebra of formal languages and relations is used to derive graph algorithms.  ... 
doi:10.1007/3-540-60117-1_14 fatcat:namzjvik6vapne363qzzvaqdlu

An Algebraic Baseline for Automatic Transformations in MDA

Artur Boronat, José Á. Carsí, Isidro Ramos
2005 Electronical Notes in Theoretical Computer Science  
The model-based software development approach allows the application of a more abstract process of software evolution, in accordance with the OMG's MDA initiative.  ...  Our model transformation approach is based on the algebraic specification of models and benefits from mature term rewriting system technology to perform model transformation using rewriting logic.  ...  There are two kinds of equivalence mappings that can be expressed in this language: (a) Simple mappings, which define a simple correspondence between two concepts that belong to different metamodels; for  ... 
doi:10.1016/j.entcs.2004.08.031 fatcat:i2olhdelxnc67hn77r562xwyhu
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