Automated Reasoning for Equivalences in the Applied Pi Calculus with Barriers

International audienceObservational equivalence allows us to study important security properties such as anonymity. Unfortunately, the difficulty of proving observational equivalence hinders analysis. Blanchet, Abadi & Fournet simplify its proof by introducing a sufficient condition for observational equivalence , called diff-equivalence, which is a reachability condition that can be proved automatically by ProVerif. However, diff-equivalence is a very strong condition, which often does not hold even if observational equivalence does. In particular, when proving equivalence between processes that contain several parallel components, e.g., P | Q and P | Q , diff-equivalence requires that P is equivalent to P and Q is equivalent to Q. To relax this constraint, Delaune, Ryan & Smyth introduced the idea of swapping data between parallel processes P and Q at synchronisation points, without proving its soundness. We extend their work by formalising the semantics of synchronisation, formalising the definition of swapping, and proving its soundness. We also relax some restrictions they had on the processes to which swapping can be applied. Moreover, we have implemented our results in ProVerif. Hence, we extend the class of equivalences that can be proved automatically. We showcase our results by analysing privacy in election schemes by Fujioka, Okamoto & Ohta and Lee et al., and in the vehicular ad-hoc network by Freudiger et al

Causal Reasoning with Ancestral Graphs

Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate post-intervention probabilities to pre-intervention probabilities that are estimable from observational data. However, such causal diagrams are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on data-mining can only output an equivalence class of causal diagrams (rather than a single one). This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a (partial) ancestral graph. We present two main results. The first result extends Pearl (1995)'s celebrated do-calculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl's calculus---the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (1993)

Algorithms of causal inference for the analysis of effective connectivity among brain regions

In recent years, powerful general algorithms of causal inference have been developed. In particular, in the framework of Pearl’s causality, algorithms of inductive causation (IC and IC*) provide a procedure to determine which causal connections among nodes in a network can be inferred from empirical observations even in the presence of latent variables, indicating the limits of what can be learned without active manipulation of the system. These algorithms can in principle become important complements to established techniques such as Granger causality and Dynamic Causal Modeling (DCM) to analyze causal influences (effective connectivity) among brain regions. However, their application to dynamic processes has not been yet examined. Here we study how to apply these algorithms to time-varying signals such as electrophysiological or neuroimaging signals. We propose a new algorithm which combines the basic principles of the previous algorithms with Granger causality to obtain a representation of the causal relations suited to dynamic processes. Furthermore, we use graphical criteria to predict dynamic statistical dependencies between the signals from the causal structure. We show how some problems for causal inference from neural signals (e.g., measurement noise, hemodynamic responses, and time aggregation) can be understood in a general graphical approach. Focusing on the effect of spatial aggregation, we show that when causal inference is performed at a coarser scale than the one at which the neural sources interact, results strongly depend on the degree of integration of the neural sources aggregated in the signals, and thus characterize more the intra-areal properties than the interactions among regions. We finally discuss how the explicit consideration of latent processes contributes to understand Granger causality and DCM as well as to distinguish functional and effective connectivity

Implementation of classical communication in a quantum world

Observations of quantum systems carried out by finite observers who subsequently communicate their results using classical data structures can be described as "local operations, classical communication" (LOCC) observations. The implementation of LOCC observations by the Hamiltonian dynamics prescribed by minimal quantum mechanics is investigated. It is shown that LOCC observations cannot be described using decoherence considerations alone, but rather require the \textit{a priori} stipulation of a positive operator-valued measure (POVM) about which communicating observers agree. It is also shown that the transfer of classical information from system to observer can be described in terms of system-observer entanglement, raising the possibility that an apparatus implementing an appropriate POVM can reveal the entangled system-observer states that implement LOCC observations.Comment: 17 pages, 2 figures; final versio

Consistency of maximum likelihood estimation for some dynamical systems

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1259 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multiple Dark Matter as a self-regulating mechanism for dark sector interactions

(Abridged) Present cosmological constraints and the absence of a direct detection and identification of any dark matter particle candidate leave room to the possibility that the dark sector of the Universe be actually more complex than it is normally assumed. In particular, more than one new fundamental particle could be responsible for the observed dark matter density in the Universe, and possible new interactions between dark energy and dark matter might characterize the dark sector. In the present work, we investigate the possibility that two dark matter particles exist in nature, with identical physical properties except for the sign of their coupling constant to dark energy. Extending previous works on similar scenarios, we study the evolution of the background cosmology as well as the growth of linear density perturbations for a wide range of parameters of such model. Interestingly, our results show how the simple assumption that dark matter particles carry a "charge" with respect to their interaction with the dark energy field allows for new long-range scalar forces of gravitational strength in the dark sector without conflicting with present observations both at the background and linear levels. Our scenario does not introduce new parameters with respect to the case of a single dark matter species for which such strong dark interactions have been already ruled out.Comment: 18 pages, 1 table, 9 figures. Invited paper for the special issue of Annalen der Physik on "Dark Matter" (Ed. Matthias Bartelmann and Volker Springel