An approach to computing downward closures

The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes. This work presents a simple general method for computing downward closures. For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be reduced to checking a certain unboundedness property. This result is used to prove that downward closures are computable for (i) every language class with effectively semilinear Parikh images that are closed under rational transductions, (ii) matrix languages, and (iii) indexed languages (equivalently, languages accepted by higher-order pushdown automata of order 2).Comment: Full version of contribution to ICALP 2015. Comments welcom

A Characterization for Decidable Separability by Piecewise Testable Languages

The separability problem for word languages of a class $\mathcal{C}$ by languages of a class $\mathcal{S}$ asks, for two given languages $I$ and $E$ from $\mathcal{C}$, whether there exists a language $S$ from $\mathcal{S}$ that includes $I$ and excludes $E$, that is, $I \subseteq S$ and $S\cap E = \emptyset$. In this work, we assume some mild closure properties for $\mathcal{C}$ and study for which such classes separability by a piecewise testable language (PTL) is decidable. We characterize these classes in terms of decidability of (two variants of) an unboundedness problem. From this, we deduce that separability by PTL is decidable for a number of language classes, such as the context-free languages and languages of labeled vector addition systems. Furthermore, it follows that separability by PTL is decidable if and only if one can compute for any language of the class its downward closure wrt. the scattered substring ordering (i.e., if the set of scattered substrings of any language of the class is effectively regular). The obtained decidability results contrast some undecidability results. In fact, for all (non-regular) language classes that we present as examples with decidable separability, it is undecidable whether a given language is a PTL itself. Our characterization involves a result of independent interest, which states that for any kind of languages $I$ and $E$, non-separability by PTL is equivalent to the existence of common patterns in $I$ and $E$

Collective Dynamics of Dark Web Marketplaces

Dark markets are commercial websites that use Bitcoin to sell or broker transactions involving drugs, weapons, and other illicit goods. Being illegal, they do not offer any user protection, and several police raids and scams have caused large losses to both customers and vendors over the past years. However, this uncertainty has not prevented a steady growth of the dark market phenomenon and a proliferation of new markets. The origin of this resilience have remained unclear so far, also due to the difficulty of identifying relevant Bitcoin transaction data. Here, we investigate how the dark market ecosystem re-organises following the disappearance of a market, due to factors including raids and scams. To do so, we analyse 24 episodes of unexpected market closure through a novel datasets of 133 million Bitcoin transactions involving 31 dark markets and their users, totalling 4 billion USD. We show that coordinated user migration from the closed market to coexisting markets guarantees overall systemic resilience beyond the intrinsic fragility of individual markets. The migration is swift, efficient and common to all market closures. We find that migrants are on average more active users in comparison to non-migrants and move preferentially towards the coexisting market with the highest trading volume. Our findings shed light on the resilience of the dark market ecosystem and we anticipate that they may inform future research on the self-organisation of emerging online markets

Characteristics of stratified flows of Newtonian/non-Newtonian shear-thinning fluids

Exact solutions for laminar stratified flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined channels are presented. An iterative algorithm is proposed to compute the laminar solution for the general case of a Carreau non-Newtonian fluid. The exact solution is used to study the effect of the rheology of the shear-thinning liquid on two-phase flow characteristics considering both gas/liquid and liquid/liquid systems. Concurrent and counter-current inclined systems are investigated, including the mapping of multiple solution boundaries. Aspects relevant to practical applications are discussed, such as the insitu hold-up, or lubrication effects achieved by adding a less viscous phase. A characteristic of this family of systems is that, even if the liquid has a complex rheology (Carreau fluid), the two-phase stratified flow can behave like the liquid is Newtonian for a wide range of operational conditions. The capability of the two-fluid model to yield satisfactory predictions in the presence of shear-thinning liquids is tested, and an algorithm is proposed to a priori predict if the Newtonian (zero shear rate viscosity) behaviour arises for a given operational conditions in order to avoid large errors in the predictions of flow characteristics when the power-law is considered for modelling the shear-thinning behaviour. Two-fluid model closures implied by the exact solution and the effect of a turbulent gas layer are also addressed.Comment: 36 pages, 27 Figure