The space of compatible full conditionals is a unimodular toric variety
نویسندگان
چکیده
The set of all m-tuples of compatible full conditional distributions on discrete random variables is an algebraic set whose defining ideal is a unimodular toric ideal. We identify the defining polynomials of these ideals with closed walks on a bipartite graph. Our algebraic characterization provides a natural generalization of the requirement that compatible conditionals have identical odds ratios and holds regardless of the patterns of zeros in the conditional arrays.
منابع مشابه
Projective Toric Varieties as Fine Moduli Spaces of Quiver Representations
This paper proves that every projective toric variety is the fine moduli space for stable representations of an appropriate bound quiver. To accomplish this, we study the quiver Q with relations R corresponding to the finite-dimensional algebra End (⊕ r i=0 Li ) where L := (OX , L1, . . . , Lr) is a list of line bundles on a projective toric variety X . The quiver Q defines a unimodular, projec...
متن کاملNon-compact Symplectic Toric Manifolds
The paradigmatic result in symplectic toric geometry is the paper of Delzant that classifies compact connected symplectic manifolds with effective completely integrable torus actions, the so called (compact) symplectic toric manifolds. The moment map induces an embedding of the quotient of the manifold by the torus action into the dual of the Lie algebra of the torus; its image is a simple unim...
متن کاملKähler Geometry of Toric Manifolds in Symplectic Coordinates
A theorem of Delzant states that any symplectic manifold (M,ω) of dimension 2n, equipped with an effective Hamiltonian action of the standard n-torus Tn = Rn/2πZn, is a smooth projective toric variety completely determined (as a Hamiltonian Tn-space) by the image of the moment map φ : M → Rn, a convex polytope P = φ(M) ⊂ Rn. In this paper we show, using symplectic (action-angle) coordinates on ...
متن کاملMixed Toric Residues and Tropical Degenerations
This paper is a follow-up to our paper [19], where we prove a conjecture of Batyrev and Materov, the Toric Residue Mirror Conjecture (TRMC). Here we extend our results, and show that they imply a generalization of this conjecture, the Mixed Toric Residue Mirror Conjecture (MTRMC), which is also due to Batyrev and Materov [3]. Roughly, these conjectures state that the generating function of cert...
متن کاملNo conformal anomaly in unimodular gravity
The conformal invariance of unimodular gravity survives quantum corrections, even in the presence of conformal matter. Unimodular gravity can actually be understood as a certain truncation of the full Einstein-Hilbert theory, where in the Einstein frame the metric tensor has unit determinant. Our result is compatible with the idea that the corresponding restriction in the functional integral is...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 41 شماره
صفحات -
تاریخ انتشار 2006