Neighbours of Einstein's Equations: Connections and Curvatures

Once the action for Einstein's equations is rewritten as a functional of an SO(3,C) connection and a conformal factor of the metric, it admits a family of ``neighbours'' having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in general very complicated. The Einstein case is distinguished by the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the general case the theory is bimetric on the fibers.Comment: 16 pages, LaTe

Performance bounds for particle filters using the optimal proposal

Particle filters may suffer from degeneracy of the particle weights. For the simplest "bootstrap" filter, it is known that avoiding degeneracy in large systems requires that the ensemble size must increase exponentially with the variance of the observation log-likelihood. The present article shows first that a similar result applies to particle filters using sequential importance sampling and the optimal proposal distribution and, second, that the optimal proposal yields minimal degeneracy when compared to any other proposal distribution that depends only on the previous state and the most recent observations. Thus, the optimal proposal provides performance bounds for filters using sequential importance sampling and any such proposal. An example with independent and identically distributed degrees of freedom illustrates both the need for exponentially large ensemble size with the optimal proposal as the system dimension increases and the potentially dramatic advantages of the optimal proposal relative to simpler proposals. Those advantages depend crucially on the magnitude of the system noise

TarTar: A Timed Automata Repair Tool

We present TarTar, an automatic repair analysis tool that, given a timed diagnostic trace (TDT) obtained during the model checking of a timed automaton model, suggests possible syntactic repairs of the analyzed model. The suggested repairs include modified values for clock bounds in location invariants and transition guards, adding or removing clock resets, etc. The proposed repairs are guaranteed to eliminate executability of the given TDT, while preserving the overall functional behavior of the system. We give insights into the design and architecture of TarTar, and show that it can successfully repair 69% of the seeded errors in system models taken from a diverse suite of case studies.Comment: 15 pages, 7 figure

Galois Unitaries, Mutually Unbiased Bases, and MUB-balanced states

A Galois unitary is a generalization of the notion of anti-unitary operators. They act only on those vectors in Hilbert space whose entries belong to some chosen number field. For Mutually Unbiased Bases the relevant number field is a cyclotomic field. By including Galois unitaries we are able to remove a mismatch between the finite projective group acting on the bases on the one hand, and the set of those permutations of the bases that can be implemented as transformations in Hilbert space on the other hand. In particular we show that there exist transformations that cycle through all the bases in every dimension which is an odd power of an odd prime. (For even primes unitary MUB-cyclers exist.) These transformations have eigenvectors, which are MUB-balanced states (i.e. rotationally symmetric states in the original terminology of Wootters and Sussman) if and only if d = 3 modulo 4. We conjecture that this construction yields all such states in odd prime power dimension.Comment: 32 pages, 2 figures, AMS Latex. Version 2: minor improvements plus a few additional reference

Causal structure and degenerate phase boundaries

Timelike and null hypersurfaces in the degenerate space-times in the Ashtekar theory are defined in the light of the degenerate causal structure proposed by Matschull. Using the new definition of null hypersufaces, the conjecture that the "phase boundary" separating the degenerate space-time region from the non-degenerate one in Ashtekar's gravity is always null is proved under certain circumstances.Comment: 13 pages, Revte

Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation

Quantum correlations have fundamental and technological interest, and hence many measures have been introduced to quantify them. Some hierarchical orderings of these measures have been established, e.g., discord is bigger than entanglement, and we present a class of bipartite states, called premeasurement states, for which several of these hierarchies collapse to a single value. Because premeasurement states are the kind of states produced when a system interacts with a measurement device, the hierarchy collapse implies that the uncertainty of an observable is quantitatively connected to the quantum correlations (entanglement, discord, etc.) produced when that observable is measured. This fascinating connection between uncertainty and quantum correlations leads to a reinterpretation of entropic formulations of the uncertainty principle, so-called entropic uncertainty relations, including ones that allow for quantum memory. These relations can be thought of as lower-bounds on the entanglement created when incompatible observables are measured. Hence, we find that entanglement creation exhibits complementarity, a concept that should encourage exploration into "entanglement complementarity relations".Comment: 19 pages, 2 figures. Added Figure 1 and various remarks to improve clarity of presentatio

Screening of organically based fungicides for apple scab (Venturia inaequalis) control and a histopathological study of the mode of action of a resistance inducer.

A range of possible substitutes for copper-based fungicides for control of apple scab (Venturia inaequalis) in organic growing were tested in laboratory and growth chamber experiments in the Danish project StopScab (2002-2004). Eighteen crude plant extracts, 19 commercial plant-based products and 6 miscellaneous compounds were tested for their ability to reduce scab symptoms on apple seedlings. Most of the compounds were also tested for their effect on conidium germination on glass slides. Fourteen of the crude plant extracts, 13 of the commercial plant products and 5 of the miscellaneous compounds showed promising control efficacies when used either preventively or curatively in the plant assay. A histopathological study was carried out on the mode of action of the resistance inducer, acibenzolar-S-methyl (ASM), which reduced scab severity and sporulation on apple seedlings in several plant assays when applied as preventive treatment. The effect of the inducer on key pre- and post-penetration events of V. inaequalis was studied and compared to these events in water-treated control leaves. The histopathological study showed that the inducer had its strongest effect on post-penetration events indicated by delayed infection and reduced stroma development. In addition, a small but significant inhibition of conidial germination and a stimulation of germ tube length were observed. This investigation provides new histopathological evidence for the mode of action of ASM against V. inaequalis and serves as a model for evaluation of the mechanisms by which the organically based fungicides reduce infection of V. inaequalis

Finite-size effects in the dynamics of few bosons in a ring potential

We study the temporal evolution of a small number $N$ of ultra-cold bosonic atoms confined in a ring potential. Assuming that initially the system is in a solitary-wave solution of the corresponding mean-field problem, we identify significant differences in the time evolution of the density distribution of the atoms when it instead is evaluated with the many-body Schr\"odinger equation. Three characteristic timescales are derived: the first is the period of rotation of the wave around the ring, the second is associated with a "decay" of the density variation, and the third is associated with periodic "collapses" and "revivals" of the density variations, with a factor of $\sqrt N$ separating each of them. The last two timescales tend to infinity in the appropriate limit of large $N$, in agreement with the mean-field approximation. These findings are based on the assumption of the initial state being a mean-field state. We confirm this behavior by comparison to the exact solutions for a few-body system stirred by an external potential. We find that the exact solutions of the driven system exhibit similar dynamical features.Comment: To appear in Journal of Physics

A study of separability criteria for mixed three-qubit states

We study the noisy GHZ-W mixture. We demonstrate some necessary but not sufficient criteria for different classes of separability of these states. It turns out that the partial transposition criterion of Peres and the criteria of G\"uhne and Seevinck dealing with matrix elements are the strongest ones for different separability classes of this 2 parameter state. As a new result we determine a set of entangled states of positive partial transpose.Comment: 18 pages, 10 figures, PRA styl