This article presents a review of the state of the art of the Wind Farm Design and
Optimization (WFDO) problem. The WFDO problem refers to a set of advanced planning …

We prove that multilinear (tensor) analogues of many efficiently computable problems in
numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a …

We discuss the geometry of orbit closures and the asymptotic behavior of Kronecker
coefficients in the context of the geometric complexity theory program to prove a variant of …

A model of quantum computation based on unitary matrix operations was introduced by
Feynman and Deutsch. It has been asked whether the power of this model exceeds that of …

Complexity theory is built fundamentally on the notion of efficient reduction among
computational problems. Classical reductions involve gadgets that map solution fragments …

The classical Feferman–Vaught Theorem for First Order Logic explains how to compute the
truth value of a first order sentence in a generalized product of first order structures by …

We discuss the parametrized complexity of counting and evaluation problems on graphs
where the range of counting is definable in monadic second-order logic (MSOL). We show …

We study two quite different approaches to understanding the complexity of fundamental
problems in numerical analysis:(a) the Blum–Shub–Smale model of computation over the …

The book introduces new techniques that imply rigorous lower bounds on the com plexity of
some number-theoretic and cryptographic problems. It also establishes certain attractive …

In their paper on the “chasm at depth four”, Agrawal and Vinay have shown that polynomials
in m variables of degree O (m) which admit arithmetic circuits of size 2o (m) also admit …