In this paper we describe, formalize, implement, and experimentally evaluate a novel transaction re-identification attack against official foreigntrade statistics releases in Brazil. The attack’s goal is to re-identify the importers of foreign-trade transactions (by revealing the identity of the company performing that transaction), which consequently violates those importers’ fiscal secrecy (by revealing sensitive information: the value and volume of traded goods). We provide a mathematical formalization of this fiscal secrecy problem using principles from the framework of quantitative information flow (QIF), then carefully identify the main sources of imprecision in the official data releases used as auxiliary information in the attack, and model transaction re-construction as a linear optimization problem solvable through integer linear programming (ILP). We show that this problem is NP-complete, and provide a methodology to identify tractable instances. We exemplify the feasibility of our attack by performing 2,003 transaction re-identifications that in total amount to more than $137M, and affect 348 Brazilian companies. Further, since similar statistics are produced by other statistical agencies, our attack is of broader concern.

The notion of duality is a key element in understanding the interplay between the stability and chromatic numbers of a graph. This notion is a central aspect in the celebrated theory of perfect graphs and is further and deeply developed in the context of the Lovász theta function and its equivalent characterizations and variants. The main achievement of this paper is the introduction of a new family of norms, providing upper bounds for the stability number, that are obtained through duality from the norms motivated by Hoffman's lower bound for the chromatic number, and which achieve the (complementary) Lovász theta function at their optimum. As a consequence, our norms make it formal that Hoffman's bound for the chromatic number and the Delsarte--Hoffman ratio bound for the stability number are indeed dual. Further, we show that our new bounds strengthen the convex quadratic bounds for the stability number studied by Luz and Schrijver, and which achieve the Lovász theta function at their optimum. One of the key observations regarding weighted versions of these bounds is that, for any upper bound for the stability number of a graph which is a positive definite monotone gauge function, its gauge dual is a lower bound on the fractional chromatic number, and conversely. Our presentation is elementary and accessible to a wide audience.

We consider a system of qubits coupled via nearest-neighbor interaction governed by the Heisenberg Hamiltonian. We further suppose that all coupling constants are equal to 1. We are interested in determining which graphs allow for a transfer of quantum state with fidelity equal to 1. To answer this question, it is enough to consider the action of the Laplacian matrix of the graph in a vector space of suitable dimension. Our main result is that if the underlying graph is a tree with more than two vertices, then perfect state transfer does not happen. We also explore related questions, such as what happens in bipartite graphs and graphs with an odd number of spanning trees. Finally, we consider the model based on the $XY$-Hamiltonian, whose action is equivalent to the action of the adjacency matrix of the graph. In this case, we conjecture that perfect state transfer does not happen in trees with more than three vertices.