Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence
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DOI: 10.1007/s10469-017-9449-2
Abstract: The present paper is one in our series of works on algebraic geometry over arbitrary algebraic structures, which focuses on the concept of geometrical equivalence. This concept signifies that for two geometrically equivalent algebraic structures… read more here.
Keywords: geometrical equivalence; algebraic structures; algebraic geometry; equivalence ... See more keywords
Quantum codes from a new construction of self-orthogonal algebraic geometry codes
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DOI: 10.1007/s11128-020-2616-8
Abstract: We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes. These results… read more here.
Keywords: geometry codes; self orthogonal; algebraic geometry; quantum codes ... See more keywords
Convex Polytopes, Algebraic Geometry, and Combinatorics
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DOI: 10.1090/noti2137
Abstract: In the last several decades, convex geometry methods have proven very useful in algebraic geometry specifically to understand discrete invariants of algebraic varieties. An approach to study algebraic varieties is to assign to a family… read more here.
Keywords: algebraic geometry; polytopes algebraic; geometry combinatorics; geometry ... See more keywords
Algebraic Geometry Tools in Systems Biology
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DOI: 10.1090/noti2188
Abstract: Many models in the sciences and engineering are expressed as solution sets to systems of polynomial equations, that is, as affine algebraic varieties. This is a basic notion in algebraic geometry, a vibrant area of… read more here.
Keywords: mathematics; algebraic geometry; geometry tools; geometry ... See more keywords
Anomaly-free model building with algebraic geometry
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DOI: 10.1103/physrevd.100.055032
Abstract: We present a method to find anomaly-free gauged Froggatt-Nielsen type models using results from algebraic geometry. These methods should be of general interest for model building beyond the Standard Model (SM) when rational charges are… read more here.
Keywords: algebraic geometry; neutral heavy; model building; geometry ... See more keywords
The loss surface of deep linear networks viewed through the algebraic geometry lens
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DOI: 10.1109/tpami.2021.3071289
Abstract: By using the viewpoint of modern computational algebraic geometry, we explore properties of the optimization landscapes of the deep linear neural network models. After clarifying on the various definitions of "flat" minima, we show that… read more here.
Keywords: algebraic geometry; number; linear networks; minima ... See more keywords
Identifiability and numerical algebraic geometry
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DOI: 10.1371/journal.pone.0226299
Abstract: A common problem when analyzing models, such as mathematical modeling of a biological process, is to determine if the unknown parameters of the model can be determined from given input-output data. Identifiable models are models… read more here.
Keywords: numerical algebraic; algebraic geometry; identifiability; model ... See more keywords