Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with precisely $k$ non-zero entries per row and let $y\in F_q^m$ be a random vector chosen independently of $A$. We identify the threshold $m/n$ up to which the linear system $A x=y$ has a solution with high probability and analyse the geometry of the set of solutions. In the special case $q=2$, known as the random $k$-XORSAT pr...

Variable selection in linear models is essential for improved inference and interpretation, an activity which has become even more critical for high dimensional data. In this article, we provide a selective review of some classical methods including Akaike information criterion, Bayesian information criterion, Mallow’s Cp and risk inflation criterion, as well as regularization methods including...

We present a block cipher that has the best performance of all 64-bit block ciphers with the smallest proven di erential/linear probability 2 62 using the structure proposed by Matsui. One of features of his methodology is to use some power functions in GF (2 n ) with di erent n that are resistant to di erential and linear attacks. In this paper we discuss how to combine power functions x k in ...

We consider a model of medium-term commodity contracts management. Randomness takes place only in the prices on which the commodities are exchanged, whilst state variable is multi-dimensional, and decision variable is integer. In [7], we proposed an algorithm based on the quantization of random process and a dual dynamic programming type approach to solve the continuous relaxation problem. In t...