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Multi-degree Bounds on the Betti Numbers of Real Varieties and Semi-algebraic Sets and Applications
Discrete & Computational Geometry, 2015We prove new bounds on the Betti numbers of real varieties and semi-algebraic sets that have a more refined dependence on the degrees of the polynomials defining them than results known before.
S. Basu, Anthony Rizzie
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Testing real-time constraints in a process algebraic setting
Proceedings of the 17th international conference on Software engineering - ICSE '95, 1995Verifying timing properties of real-time systems by traditional approaches that depend on the exploration of the entire system state space is impractical for large systems. In contrast, testing allows the search for violations of a property to be narrowed to a relatively small portion of the overall state space, based on assumptions regarding the ...
Duncan Clarke, Insup Lee
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Algebra: Real-Life Investigations in a Lab Setting
Mathematics Teaching in the Middle School, 1997How will we make algebra accessible to all students? In the past, we have taught algebra as an abstract course involving manipulation of variables and numbers, which are symbolic representations. We have neglected to make a strong connection between the symbolic algebra and the underlying concrete relationships.
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Full Rank Representation of Real Algebraic Sets and Applications
Computer Algebra in Scientific Computing, 2017Changbo Chen, Wenyuan Wu, Yong Feng
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An overview of real‐world data sources for oncology and considerations for research
Ca-A Cancer Journal for Clinicians, 2022Lynne Penberthy +2 more
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Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets
International Congress on Mathematical Software, 2014Daniel A. Brake +5 more
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Algebraic computations on the set of real intervals
2014The set of closed intervals of R is provided with a semigroup structure. We complete this semigroup to obtain a 2-dimensional vector space. But neither associative nor nonassociative algebra structure satisfying a natural property on the product of intervals can be defined on this vector space.
Goze, Michel +2 more
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Circulating tumor DNA in advanced solid tumors: Clinical relevance and future directions
Ca-A Cancer Journal for Clinicians, 2021Michael L Cheng +2 more
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