Multi-scale Arithmetization of Linear Transformations

Arithmetization of distributions and linear goal programming

Linear goal programming can be used as a complementary technique when local moment matching method up to the second moment gives some negative mass. This could happen when manipulating a discrete or mixed type severity distribution. In that case we can avoid a simple retreat to the first moment and look for an arithmetic distribution with equal mean and the second moment closest to that of the ...

Omega-Arithmetization: A Discrete Multi-resolution Representation of Real Functions

Multi-resolution analysis and numerical precisions problems are very important subjects in fields like image analysis or geometrical modeling. In the continuation of previous works of the authors, we expose in this article a new method called the Ω-arithmetization. It is a process to obtain a multi-scale discretization of a continuous function that is a solution of a differential equation. The ...

On One-Sided Ideals of Rings of Linear Transformations

Shorter arithmetization of nondeterministic computations

Arithmetizing computation is a crucial component of many fundamental results in complexity theory, including results that gave insight into the power of interactive proofs, multi-prover interactive proofs, and probabilistically-checkable proofs. Informally, an arithmetization is a way to encode a machine’s computation so that its correctness can be easily verified via few probabilistic algebrai...

Ω-Arithmetization of Ellipses

Multi-resolution analysis and numerical precision problems are very important subjects in fields like image analysis or geometrical modeling. In the continuation of our previous works, we propose to apply the method of Ω-arithmetization to ellipses. We obtain a discrete multi-resolution representation of arcs of ellipses. The corresponding algorithms are completely constructive and thus, can be...