A one-to-one correspondence maps maximal LDP channels under the Blackwell order to vertices of a finite-dimensional polytope, making optimal privacy-utility trade-offs computable via linear programming or vertex enumeration for general problems.
Graduate Texts in Mathematics, 152
7 Pith papers cite this work. Polarity classification is still indexing.
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Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
Frobenius identities for the volume map on Cohen-Macaulay rings give sufficient conditions for anisotropy and Hard Lefschetz in Gorenstein quotients and deduce the g-theorem for simplicial spheres plus the Ohsugi-Hibi conjecture.
A complete linear inequality description and volume formula are derived for the convex hull of the graph of a monomial on a nonnegative box with at most one positive lower bound.
An analog of Cauchy's surface area formula is established for Funk geometry on a convex body K using Holmes-Thompson area and central projections, reducing to a weighted vertex sum for polytopes and yielding a generalized Crofton formula.
c-Birkhoff polytopes are unimodularly equivalent to the order polytopes of the heap posets of the c-sorting words of the longest permutation.
Adjacency Sampling reproduces all known Bell inequality classes in solved cases and generates over 129 million classes for the L_{3,3,3,3} scenario plus millions more for larger ones.
citing papers explorer
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Optimal Privacy-Utility Trade-Offs in LDP: Functional and Geometric Perspectives
A one-to-one correspondence maps maximal LDP channels under the Blackwell order to vertices of a finite-dimensional polytope, making optimal privacy-utility trade-offs computable via linear programming or vertex enumeration for general problems.
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Copositive Matrices with Ordered Off-Diagonal Entries
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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Frobenius identities for the volume map on Cohen--Macaulay rings
Frobenius identities for the volume map on Cohen-Macaulay rings give sufficient conditions for anisotropy and Hard Lefschetz in Gorenstein quotients and deduce the g-theorem for simplicial spheres plus the Ohsugi-Hibi conjecture.
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On the convex hull of the graph of a simple monomial
A complete linear inequality description and volume formula are derived for the convex hull of the graph of a monomial on a nonnegative box with at most one positive lower bound.
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Cauchy's Surface Area Formula in the Funk Geometry
An analog of Cauchy's surface area formula is established for Funk geometry on a convex body K using Holmes-Thompson area and central projections, reducing to a weighted vertex sum for polytopes and yielding a generalized Crofton formula.
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$c$-Birkhoff polytopes
c-Birkhoff polytopes are unimodularly equivalent to the order polytopes of the heap posets of the c-sorting words of the longest permutation.
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Bell Inequalities from Polyhedral Sampling
Adjacency Sampling reproduces all known Bell inequality classes in solved cases and generates over 129 million classes for the L_{3,3,3,3} scenario plus millions more for larger ones.