In this paper we describe a method that estimates the motion of a calibrated camera (settled
on an experimental vehicle) and the tridimensional geometry of the environment. The only …

We give a complexity dichotomy theorem for the counting constraint satisfaction problem (#
CSP in short) with algebraic complex weights. To this end, we give three conditions for its …

We study the problem of approximating the partition function of the ferromagnetic Ising
model with both pairwise as well as higher order interactions (equivalently, in graphs as well …

Each symmetric matrix A over C defines a graph homomorphism function Z_\bfA(⋅) on
undirected graphs. The function Z_A(⋅) is also called the partition function from statistical …

We propose and explore a novel alternative framework to study the complexity of counting
problems, called Holant Problems. Compared to counting Constrained Satisfaction …

We prove a complexity dichotomy theorem for Holant problems over an arbitrary set of
complex-valued symmetric constraint functions {F} on Boolean variables. This extends and …

We prove a complexity dichotomy theorem for the most general form of Boolean# CSP
where every constraint function takes values in the field of complex numbers C. We first give …

We study the connection between the correlation decay property (more precisely, strong
spatial mixing) and the zero-freeness of the partition function of 2-spin systems on graphs of …

We prove a complexity dichotomy theorem for counting constraint satisfaction problems (#
CSPs) with nonnegative and algebraic weights. This caps a long series of important results …

We propose a new method to prove complexity dichotomy theorems. First we introduce
Fibonacci gates which provide a new class of polynomial time holographic algorithms. Then …