
Constructing Faithful Homomorphisms over Fields of Finite Characteristic
We study the question of algebraic rank or transcendence degree preservi...
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Semigraphoids Are TwoAntecedental Approximations of Stochastic Conditional Independence Models
The semigraphoid closure of every couple of CIstatements (GI=conditiona...
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Incidence geometry in the projective plane via almostprincipal minors of symmetric matrices
We present an encoding of a polynomial system into vanishing and nonvan...
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On the relative power of algebraic approximations of graph isomorphism
We compare the capabilities of two approaches to approximating graph iso...
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Regular matroids have polynomial extension complexity
We prove that the extension complexity of the independence polytope of e...
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Foundations of regular coinduction
Inference systems are a widespread framework used to define possibly rec...
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Stable Independance and Complexity of Representation
The representation of independence relations generally builds upon the w...
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Gaussoids are twoantecedental approximations of Gaussian conditional independence structures
The gaussoid axioms are conditional independence inference rules which characterize regular Gaussian CI structures over a threeelement ground set. It is known that no finite set of inference rules completely describes regular Gaussian CI as the ground set grows. In this article we show that the gaussoid axioms logically imply every inference rule of at most two antecedents which is valid for regular Gaussians over any ground set. The proof is accomplished by exhibiting for each inclusionminimal gaussoid extension of at most two CI statements a regular Gaussian realization. Moreover we prove that all those gaussoids have rational positivedefinite realizations inside every εball around the identity matrix. For the proof we introduce the concept of algebraic Gaussians over arbitrary fields and of positive Gaussians over ordered fields and obtain the same twoantecedental completeness of the gaussoid axioms for algebraic and positive Gaussians over all fields of characteristic zero as a byproduct.
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