More specifically, we use Theorem B.1 from (Sheffet, 2015) that states that given a matrix A whose all of its singular values at greater than T ( , δ) where T ( , δ) = 2B (√ 2r ln(4/δ) + 2 ln(4/δ) ) , publishing RA is ( , δ)differentially private for a r-row matrix R whose entries sampled are i.i.d normal Gaussians. Since we have that all of the singular values of A′ are greater than w (as spec...

An astonishing fact was established by Lee A. Rubel in 81: there exists a fixed non-trivial fourthorder polynomial differential algebraic equation (DAE) such that for any positive continuous function φ on the reals, and for any positive continuous function (t), it has a C∞ solution with |y(t) − φ(t)| < (t) for all t. Lee A. Rubel provided an explicit example of such a polynomial DAE. Other exam...

Let R be the universal deformation ring of a residual representation of a local Galois group. Kisin showed that many loci in MaxSpec(R[1/p]) of interest are Zariski closed, and gave a way to study the generic fiber of the corresponding quotient of R. However, his method gives little information about the quotient ring before inverting p. We give a method for studying this quotient in certain ca...

The Poisson process is a stochastic counting process that arises naturally in a large variety of daily-life situations. We present a few definitions of the Poisson process and discuss several properties as well as relations to some well-known probability distributions. We further briefly discuss the compound Poisson process.

We present a Cournot model that compares the critical threshold of collusion in Duopoly and Oligopoly Markets where the actors are private, mixed or public. We assume that the incentive critical threshold for collusion depends on the interconnection fees. The different threshold values calculated in each Market structure are then estimated, using the OLS method, with variables related to the Tu...