Many data applications have certain invariant constraints due to practical needs. Data curators who employ differential privacy need respect such on the sanitized product as a primary utility requirement. Invariants challenge formulation, implementation, and interpretation of guarantees. We propose subspace privacy, honestly characterize dependence output confidential aspects data. discuss two ...

We consider maximal operators associated to singular averages along finite subsets Σ of the Grassmannian Gr(d,n) d-dimensional subspaces Rn. The well studied d=1 case corresponds directional function with respect arbitrary Gr(1,n)=Sn−1. provide a systematic study all cases 1≤d<n and prove essentially sharp L2(Rn) bounds for subspace averaging operator in terms cardinality Σ, no assumption on st...

In the context of constant-dimension subspace codes, an important problem is to determine largest possible size $ A_q(n, d; k) codes whose codewords are k $-subspaces {\mathbb F}_q^n with minimum distance d $. Here in order obtain improved constructions, we investigate several approaches combine codes. This allow us present improvements on lower bounds for many parameters, including A_q(10, 4; ...

a new guideline for proper allocation of multipoles in the multiple multipole method (mmp) is proposed. in an ‘a posteriori’ approach, subspace fitting (ssf) is used to find the best location of multipole expansions for the two dimensional dielectric scattering problem. it is shown that the best location of multipole expansions (regarding their global approximating power) coincides with the med...