Proving the Turing Universality of Oritatami Co-Transcriptional Folding (Full Text)

We study the oritatami model for molecular co-transcriptional folding. In oritatami systems, the transcript (the "molecule") folds as it is synthesized (transcribed), according to a local energy optimisation process, which is similar to how actual biomolecules such as RNA fold into complex shapes and functions as they are transcribed. We prove that there is an oritatami system embedding universal computation in the folding process itself. Our result relies on the development of a generic toolbox, which is easily reusable for future work to design complex functions in oritatami systems. We develop "low-level" tools that allow to easily spread apart the encoding of different "functions" in the transcript, even if they are required to be applied at the same geometrical location in the folding. We build upon these low-level tools, a programming framework with increasing levels of abstraction, from encoding of instructions into the transcript to logical analysis. This framework is similar to the hardware-to-algorithm levels of abstractions in standard algorithm theory. These various levels of abstractions allow to separate the proof of correctness of the global behavior of our system, from the proof of correctness of its implementation. Thanks to this framework, we were able to computerize the proof of correctness of its implementation and produce certificates, in the form of a relatively small number of proof trees, compact and easily readable and checkable by human, while encapsulating huge case enumerations. We believe this particular type of certificates can be generalized to other discrete dynamical systems, where proofs involve large case enumerations as well

Communication Complexity and Intrinsic Universality in Cellular Automata

The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce necessary conditions for a cellular automaton to be "universal", according to a precise notion of simulation, related both to the dynamics of cellular automata and to their computational power. This notion of simulation relies on simple operations of space-time rescaling and it is intrinsic to the model of cellular automata. Intrinsinc universality, the derived notion, is stronger than Turing universality, but more uniform, and easier to define and study. Our approach builds upon the notion of communication complexity, which was primarily designed to study parallel programs, and thus is, as we show in this article, particulary well suited to the study of cellular automata: it allowed to show, by studying natural problems on the dynamics of cellular automata, that several classes of cellular automata, as well as many natural (elementary) examples, could not be intrinsically universal

Capacity decisions with demand fluctuations and carbon leakage

For carbon-intensive, internationally-traded industrial goods, a unilateral increase in the domestic CO2 price may result in the reduction of the domestic production but an increase of imports. In such sectors as electricity, cement or steel, the trade ows result more from short-term regional disequilibria between supply and demand than from international competition. This paper formalizes this empirical observation and characterizes its impact on leakage. Domestic fi rms invest in home plants under uncertainty; then, as uncertainty unfolds, they may source the home market from their home plants or from imports. We prove that there would be no leakage in the short-term (without capacity adaptation) but there would be in the long-term (with capacity adaption). Furthermore, the larger the uncertainty the larger the leakage is. We also characterize the impacts of uncertainty on the (short-term and long-term) pass-through rates. In the concluding section we discuss the implications of these results for the evaluation of climate policies

Pour un financement conditionnel des projets risqués bas carbone

Une critique récurrente des subventions aux technologies propres (énergies renouvelables, solaire, mécanismes de développement propre, voiture électrique, …) est l’existence d’effets d’aubaine : des investissements bénéficient de subventions dont ils n’ont pas besoin pour être rentables. Cette note formalise ce type de situation comme la sélection d’un portefeuille de projets par l’Etat dans un contexte d’asymétrie d’information. Il montre qu’une forme de garantie du financement, avec remboursement en cas de succès, permet de limiter les effets d’aubaines et les dépenses publiques tout en maximisant le bénéfice social en termes de réduction des émissions. La pertinence du mécanisme proposé est illustrée dans le cadre de subventions pour le déploiement des infrastructures pour les véhicules à hydrogène

Superconducting nano-mechanical diamond resonators

In this work we present the fabrication and characterization of superconducting nano-mechanical resonators made from nanocrystalline boron doped diamond (BDD). The oscillators can be driven and read out in their superconducting state and show quality factors as high as 40,000 at a resonance frequency of around 10 MHz. Mechanical damping is studied for magnetic fields up to 3 T where the resonators still show superconducting properties. Due to their simple fabrication procedure, the devices can easily be coupled to other superconducting circuits and their performance is comparable with state-of-the-art technology.Comment: 5 pages 6 figures, Accepted for publication in Carbo