Entanglement detection for electrons via witness operators

We discuss an implementation of the entanglement witness, a method to detect entanglement with few local measurements, in systems where entangled electrons are generated both in the spin and orbital degrees of freedom. We address the efficiency of this method in various setups, including two different particle-hole entanglement structures, and we demonstrate that it can also be used to infer information on the possible dephasing afflicting the devices.Comment: 12 pages, 5 figures; published versio

An efficient and principled method for detecting communities in networks

A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based on a principled statistical approach using generative network models. We show how the method can be implemented using a fast, closed-form expectation-maximization algorithm that allows us to analyze networks of millions of nodes in reasonable running times. We test the method both on real-world networks and on synthetic benchmarks and find that it gives results competitive with previous methods. We also show that the same approach can be used to extract nonoverlapping community divisions via a relaxation method, and demonstrate that the algorithm is competitively fast and accurate for the nonoverlapping problem.Comment: 14 pages, 5 figures, 1 tabl

A critical test of the mode-coupling theory of the glass transition

The mode-coupling theory of the glass transition predicts the time evolution of the intermediate scattering functions in viscous liquids on the sole basis of the structural information encoded in two-point density correlations. We provide a critical test of this property and show that the theory fails to describe the qualitatively distinct dynamical behavior obtained in two model liquids characterized by very similar pair correlation functions. Because we use `exact' static information provided by numerical simulations, our results are a direct proof that some important information about the dynamics of viscous liquids is not captured by pair correlations, and is thus not described by the mode-coupling theory, even in the temperature regime where the theory is usually applied.Comment: 7 pages, 5 figures

Border Basis relaxation for polynomial optimization

A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic closed semi algebraic set. A new stopping criterion is given to detect when the relaxation sequence reaches the minimum, using a sparse flat extension criterion. We also provide a new algorithm to reconstruct a finite sum of weighted Dirac measures from a truncated sequence of moments, which can be applied to other sparse reconstruction problems. As an application, we obtain a new algorithm to compute zero-dimensional minimizer ideals and the minimizer points or zero-dimensional G-radical ideals. Experimentations show the impact of this new method on significant benchmarks.Comment: Accepted for publication in Journal of Symbolic Computatio