Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

A novel suite of cyclotides from Viola odorata: sequence variation and the implications for structure, function and stability

Cyclotides are a fascinating family of plant-derived peptides characterized by their head-to-tail cyclized backbone and knotted arrangement of three disulfide bonds. This conserved structural architecture, termed the CCK (cyclic cystine knot), is responsible for their exceptional resistance to thermal, chemical and enzymatic degradation. Cyclotides have a variety of biological activities, but their insecticidal activities suggest that their primary function is in plant defence. In the present study, we determined the cyclotide content of the sweet violet Viola odorata, a member of the Violaceae family. We identified 30 cyclotides from the aerial parts and roots of this plant, 13 of which are novel sequences. The new sequences provide information about the natural diversity of cyclotides and the role of particular residues in defining structure and function. As many of the biological activities of cyclotides appear to be associated with membrane interactions, we used haemolytic activity as a marker of bioactivity for a selection of the new cyclotides. The new cyclotides were tested for their ability to resist proteolysis by a range of enzymes and, in common with other cyclotides, were completely resistant to trypsin, pepsin and thermolysin. The results show that while biological activity varies with the sequence, the proteolytic stability of the framework does not, and appears to be an inherent feature of the cyclotide framework. The structure of one of the new cyclotides, cycloviolacin O14, was determined and shown to contain the CCK motif. This study confirms that cyclotides may be regarded as a natural combinatorial template that displays a variety of peptide epitopes most likely targeted to a range of plant pests and pathogens.

Methicillin-resistant Staphylococcus aureus genotyping using a small set of polymorphisms

The aim of this study was to identify a set of genetic polymorphisms that efficiently divides methicillin-resistant Staphylococcus aureus (MRSA) strains into groups consistent with the population structure. The rationale was that such polymorphisms could underpin rapid real-time PCR or low-density array-based methods for monitoring MRSA dissemination in a cost-effective manner. Previously, the authors devised a computerized method for identifying sets of single nucleoticle polymorphisms (SNPs) with high resolving power that are defined by multilocus sequence typing (MLST) databases, and also developed a real-time PCR method for interrogating a seven-member SNP set for genotyping S. aureus. Here, it is shown that these seven SNPs efficiently resolve the major MRSA lineages and define 27 genotypes. The SNP-based genotypes are consistent with the MRSA population structure as defined by eBURST analysis. The capacity of binary markers to improve resolution was tested using 107 diverse MRSA isolates of Australian origin that encompass nine SNP-based genotypes. The addition of the virulence-associated genes cna, pvl and bbplsdrE, and the integrated plasmids pT181, p1258 and pUB110, resolved the nine SNP-based genotypes into 21 combinatorial genotypes. Subtyping of the SCCmec locus revealed new SCCmec types and increased the number of combinatorial genotypes to 24. It was concluded that these polymorphisms provide a facile means of assigning MRSA isolates into well-recognized lineages.

Heuristic algorithm for computing reversal distance with multigene families via binary integer programming

Hannenhalli and Pevzner developed the first polynomial-time algorithm for the combinatorial problem of sorting of signed genomic data. Their algorithm solves the minimum number of reversals required for rearranging a genome to another when gene duplication is nonexisting. In this paper, we show how to extend the Hannenhalli-Pevzner approach to genomes with multigene families. We propose a new heuristic algorithm to compute the reversal distance between two genomes with multigene families via the concept of binary integer programming without removing gene duplicates. The experimental results on simulated and real biological data demonstrate that the proposed algorithm is able to find the reversal distance accurately. ©2005 IEEE

Dartboard arrangements with a concave penalty function

This paper investigates combinatorial arrangements of the dartboard to maximize a penalty function derived from the differences of adjacent sectors. The particular penalty function is constructed by summing the absolute differences of neighbouring sectors raised to a power between zero and one. The arrangement to give the maximum penalty is found