Solving Large-Scale Optimization Problems Related to Bell's Theorem

Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth description of a method of testing the existence of such models, which involves two levels of optimization: a higher-level non-linear task and a lower-level linear programming (LP) task. The article compares the performances of the existing implementation of the method, where the LPs are solved with the simplex method, and our new implementation, where the LPs are solved with a matrix-free interior point method. We describe in detail how the latter can be applied to our problem, discuss the basic scenario and possible improvements and how they impact on overall performance. Significant performance advantage of the matrix-free interior point method over the simplex method is confirmed by extensive computational results. The new method is able to solve problems which are orders of magnitude larger. Consequently, the noise resistance of the non-classicality of correlations of several types of quantum states, which has never been computed before, can now be efficiently determined. An extensive set of data in the form of tables and graphics is presented and discussed. The article is intended for all audiences, no quantum-mechanical background is necessary.Comment: 19 pages, 7 tables, 1 figur

Integer iobj, Integer ncolh,

e04nkc nag opt sparse convex qp (e04nkc

A tRNA world

Knowledge about the kinetics of chemical reactions in cells is important for an understanding of signaling pathways and regulation. Even though there are many kinetic measurements of in vitro reactions in literature, methods for in vivo measurements are sparse. With help of Temperature Oscillation Optical Lock-in (TOOL) microscopy we measure the kinetics of DNA hybridization inside cells and detect signicant acceleration or deceleration compared to in vitro measurements, dependent on the DNA sample. The dierences can not be explained by molecular crowding eects. Only models that take the background interactions with genomic DNA and RNA as well as the activity of single stranded and double stranded binding proteins into account, can be tted to data. The results imply that the biological relevance of kinetic rates measured in vitro has to be rejudged carefully. The RNA world hypothesis predicts catalytic molecules based on RNA, as for example early replicators, as precursor of modern biology. But how can a pool of appropriate RNA molecules arise under early earth conditions? In a Gillespie-model, we observe the length distribution, secondary structure and sequences of a pool of RNA molecules in porous rocks like they appear near sites of volcanic activity. We assume a monomer in ux, a length dependent out ux, a random, non-templated polymerisation and a degradation that is much stronger for single stranded than for double stranded RNA. After equilibrium is reached, the pool is populated with many hairpin-like structures due to the selection pressure for hybridized strands that can be bricks for RNA machines. Once sequence motifs and their complements appear in the reactor, they protect each other and are present longer than statistically expected. This "protection by hybridization" has the same ngerprint as a weak replication. As a consequence, the pool does not cover the full sequence space but includes more similar sequences, which is an important condition for chemical reactions. Replication of genetic information by RNA molecules is considered to be a key process in the beginning of evolution. It is so crucial that traces of this early replication are expected to be present in key processes of modern biology. We present a replication scheme based on hairpins derived from the sequence of tRNA that replicates the genetic information about a succession of sequence snippets. The replication is driven by temperature oscillations as they occur naturally inside of porous rocks in presence of temperature gradients, and independent on external chemical energy sources. It is selective for correct information and shows exponential growth rates with doubling times in the range of seconds to minutes and is thereby the fastest early replicator in the literature. The replication scheme can naturally be expanded to longer successions by using double hairpins derived from full tRNA sequences by only few mutations. By charging double hairpins with amino acids or peptides, the proposed replication bridges the gap from the RNA world to modern biology by oering a rudimentary translation mechanism, that sorts amino acids to chains according to genetic information

High temperature supercapacitors

The scientific objective of this research program was to determine the feasibility of manufacturing an ionic liquid-based supercapacitor that could operate at temperatures up to 220 °C. A secondary objective was to determine the compatibility of ionic liquids with other cell components (e.g. current collectors) at high temperature and, if required, consider means of mitigating any problems. The industrial motivation for the present work was to develop a supercapacitor capable of working in the harsh environment of deep offshore boreholes. If successful, this technology would allow down-hole telemetry under conditions of mechanical vibration and high temperature. The obstacles, however, were many. All supercapacitor components had to be stable against thermal decomposition up to T ≥ 220 °C. Volatile components had to be eliminated. If possible, the finished device should be able to withstand voltages greater than 4 V, in order to maximise the amount of stored energy. The internal resistance should be as low as possible. Side reactions, particularly faradaic reactions, should be eliminated or suppressed. All liquid components should be gelled to minimise leakage in the event of cell damage. Finally, any emergent problems should be identified. [Continues.