Large deviations principle for Curie-Weiss models with random fields

In this article we consider an extension of the classical Curie-Weiss model in which the global and deterministic external magnetic field is replaced by local and random external fields which interact with each spin of the system. We prove a Large Deviations Principle for the so-called {\it magnetization per spin} $S_n/n$ with respect to the associated Gibbs measure, where $S_n/n$ is the scaled partial sum of spins. In particular, we obtain an explicit expression for the LDP rate function, which enables an extensive study of the phase diagram in some examples. It is worth mentioning that the model considered in this article covers, in particular, both the case of i.\,i.\,d.\ random external fields (also known under the name of random field Curie-Weiss models) and the case of dependent random external fields generated by e.\,g.\ Markov chains or dynamical systems.Comment: 11 page

Quantum Mechanical Aspects of Cell Microtubules: Science Fiction or Realistic Possibility?

Recent experimental research with marine algae points towards quantum entanglement at ambient temperature, with correlations between essential biological units separated by distances as long as 20 Angstr\"oms. The associated decoherence times, due to environmental influences, are found to be of order 400 fs. This prompted some authors to connect such findings with the possibility of some kind of quantum computation taking place in these biological entities: within the decoherence time scales, the cell "quantum calculates" the optimal "path" along which energy and signal would be transported more efficiently. Prompted by these experimental results, in this talk I remind the audience of a related topic proposed several years ago in connection with the possible r\^ole of quantum mechanics and/or field theory on dissipation-free energy transfer in microtubules (MT), which constitute fundamental cell substructures. Quantum entanglement between tubulin dimers was argued to be possible, provided there exists sufficient isolation from other environmental cell effects. The model was based on certain ferroelectric aspects of MT. In the talk I review the model and the associated experimental tests so far and discuss future directions, especially in view of the algae photo-experiments.Comment: 31 pages latex, 11 pdf figures, uses special macros, Invited Plenary Talk at DICE2010, Castello Pasquini, Castiglioncello (Italy), September 13-18 201

Membraneless channels sieve cations in ammonia-oxidizing marine archaea

Nitrosopumilus maritimus is an ammonia-oxidizing archaeon that is crucial to the global nitrogen cycle1, 2. A critical step for nitrogen oxidation is the entrapment of ammonium ions from a dilute marine environment at the cell surface and their subsequent channelling to the cell membrane of N. maritimus. Here we elucidate the structure of the molecular machinery responsible for this process, comprising the surface layer (S-layer), using electron cryotomography and subtomogram averaging from cells. We supplemented our in situ structure of the ammonium-binding S-layer array with a single-particle electron cryomicroscopy structure, revealing detailed features of this immunoglobulin-rich and glycan-decorated S-layer. Biochemical analyses showed strong ammonium binding by the cell surface, which was lost after S-layer disassembly. Sensitive bioinformatic analyses identified similar S-layers in many ammonia-oxidizing archaea, with conserved sequence and structural characteristics. Moreover, molecular simulations and structure determination of ammonium-enriched specimens enabled us to examine the cation-binding properties of the S-layer, revealing how it concentrates ammonium ions on its cell-facing side, effectively acting as a multichannel sieve on the cell membrane. This in situ structural study illuminates the biogeochemically essential process of ammonium binding and channelling, common to many marine microorganisms that are fundamental to the nitrogen cycle

Rate Equations for Graphs

In this paper, we combine ideas from two different scientific traditions: 1) graph transformation systems (GTSs) stemming from the theory of formal languages and concurrency, and 2) mean field approximations (MFAs), a collection of approximation techniques ubiquitous in the study of complex dynamics. Using existing tools from algebraic graph rewriting, as well as new ones, we build a framework which generates rate equations for stochastic GTSs and from which one can derive MFAs of any order (no longer limited to the humanly computable). The procedure for deriving rate equations and their approximations can be automated. An implementation and example models are available online at https://rhz.github.io/fragger. We apply our techniques and tools to derive an expression for the mean velocity of a two-legged walker protein on DNA.Comment: to be presented at the 18th International Conference on Computational Methods in Systems Biology (CMSB 2020

Möglichkeitsdenken. Utopie und Dystopie in der Gegenwart

Utopien denken Möglichkeiten von Zukunft. Mit Beginn der historischen Moderne, in der die Erwartung an die Zukunft die Erfahrung der Vergangenheit übersteigt, entstehen in der je aktuellen Gegenwart Entwürfe, die Utopien genannt werden können. Die Temporalisierung der Erfahrung macht Projektionen in die Zukunft möglich (Reinhart Koselleck). Diese sind nie eindeutig. Sie liefern mehrdeutige Wunsch- und Schreckbilder auch in eigentümlichen Verschränkungen. Die Einsicht in diese Dialektik nimmt mit dem Grad der Selbstreferentialität von Zukunftsentwürfen zu; Utopie und Dystopie bedingen sich wechselseitig. – Gegenwärtig leben wir mit außerordentlich unsicheren Zukunftsperspektiven. Haben Utopien nur in Dystopien überlebt? Nach dem Ende des Utopismus-Verdachts am Beginn der 90er Jahre geht es heute um eine Bestandsaufnahme von Zukunftspotentialen, um Diskussionen von Denkformen des Hypothetisch-Möglichen. Bietet die Tradition des utopischen Denkens Anknüpfungspunkte für aktuelle, positiv oder negativ konnotierte Zukunftsbeschreibungen? Wunsch- oder Warnbilder sind noch immer jenem utopischen Impuls verpflichtet, der den Blick aus der Gegenwart in die Zukunft richten will. Die Frage nach der Zukunft utopischen Denkens stellt somit in den Möglichkeiten temporalen, visionären und konjunktivischen Denkens zugleich die Frage nach dem Ort des Gesellschaftlichen und der Gesellschaft heute – und damit die Frage nach der Verbindlichkeit von Tradition, und das heißt auch: nach Traditionen des Utopischen

Proving termination and memory safety for programs with Pointer Arithmetic

Proving termination automatically for programs with explicit pointer arithmetic is still an open problem. To close this gap, we introduce a novel abstract domain that can track allocated memory in detail. We use it to automatically construct a symbolic execution graph that represents all possible runs of the program and that can be used to prove memory safety. This graph is then transformed into an integer transition system, whose termination can be proved by standard techniques. We implemented this approach in the automated termination prover AProVE and demonstrate its capability of analyzing C programs with pointer arithmetic that existing tools cannot handle