Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra osp(5|2) and differing only in details of the symmetry breaking pattern during the last step.Comment: 34 pages, 9 tables, LaTe

Equality: A tool for free-form equation editing

We describe a new tool, Equality, for equation entry using free-form layout of components drawn from a palette of symbols. Our approach is designed to enable learners to easily manipulate the structure of their equations, to be functional in both desktop and mobile environments, and to minimize the amount of learning required to use the tool.We present the results of a study comparing a prototype of our approach with Microsoft Equation Editor using a desktop machine. The initial results are promising with participants reporting that the mechanism is easy to learn and an easy way to manipulate their equations. We report the results of the study and the views of the participants and identify how these will inform the future development of Equality.We thank the Department for Education (United Kingdom) for their support in funding this work through the Isaac Physics project.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ICALT.2015.3

General criteria for the stability of uniaxially ordered states of Incommensurate-Commensurate Systems

Reconsidering the variational procedure for uniaxial systems modeled by continuous free energy functionals, we derive new general conditions for thermodynamic extrema. The utility of these conditions is briefly illustrated on the models for the classes I and II of incommensurate-commensurate systems.Comment: 5 pages, to be published in Phys. Rev. Let

Brillouin scattering studies in Fe3_3O4_4 across the Verwey transition

Brillouin scattering studies have been carried out on high quality single crystals of Fe$_3$O$_4$ with [100] and [110] faces in the temperature range of 300 to 30 K. The room temperature spectrum shows a surface Rayleigh wave (SRW) mode at 8 GHz and a longitudinal acoustic (LA) mode at 60 GHz. The SRW mode frequency shows a minimum at the Verwey transition temperature $T_V$ of 123 K. The softening of the SRW mode frequency from about 250 K to $T_V$ can be quantitatively understood as a result of a decrease in the shear elastic constant C$_{44}$, arising from the coupling of shear strain to charge fluctuations. On the other hand, the LA mode frequency does not show any significant change around $T_V$, but shows a large change in its intensity. The latter shows a maximum at around 120 K in the cooling run and at 165 K in the heating run, exhibiting a large hysteresis of 45 K. This significant change in intensity may be related to the presence of stress-induced ordering of Fe$^{3+}$ and Fe$^{2+}$ at the octahedral sites, as well as to stress-induced domain wall motion.Comment: 14 pages, 3 figures, accepted in Physical Review B 200

Two-Stage Rotational Disordering of a Molecular Crystal Surface: C60

We propose a two-stage mechanism for the rotational surface disordering phase transition of a molecular crystal, as realized in C$_{60}$ fullerite. Our study, based on Monte Carlo simulations, uncovers the existence of a new intermediate regime, between a low temperature ordered $(2 \times 2)$ state, and a high temperature $(1 \times 1)$ disordered phase. In the intermediate regime there is partial disorder, strongest for a subset of particularly frustrated surface molecules. These concepts and calculations provide a coherent understanding of experimental observations, with possible extension to other molecular crystal surfaces.Comment: 4 pages, 2 figure

ROM-based quantum computation: Experimental explorations using Nuclear Magnetic Resonance, and future prospects

ROM-based quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less ``magical'', and being more suited to implementing space-efficient computation (i.e. computation using the minimum number of writable qubits). Here we consider a number of small (one and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using NMR ensemble QC. The average fidelities for the implementation were in the ranges 0.9 - 0.97 for the one-qubit algorithms, and 0.84 - 0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature ``real-world'' problem relating to the lengths of paths in a network.Comment: 11 pages, 5 figure

NMR Techniques for Quantum Control and Computation

Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to a new level, motivated by the interest in quantum information processing. NMR has been the workhorse for the experimental implementation of quantum protocols, allowing exquisite control of systems up to seven qubits in size. Here, we survey and summarize a broad variety of pulse control and tomographic techniques which have been developed for and used in NMR quantum computation. Many of these will be useful in other quantum systems now being considered for implementation of quantum information processing tasks.Comment: 33 pages, accepted for publication in Rev. Mod. Phys., added subsection on T_{1,\rho} (V.A.6) and on time-optimal pulse sequences (III.A.6), redid some figures, made many small changes, expanded reference

Scheme for the implementation of a universal quantum cloning machine via cavity-assisted atomic collisions in cavity QED

We propose a scheme to implement the $1\to2$ universal quantum cloning machine of Buzek et.al [Phys. Rev.A 54, 1844(1996)] in the context of cavity QED. The scheme requires cavity-assisted collision processes between atoms, which cross through nonresonant cavity fields in the vacuum states. The cavity fields are only virtually excited to face the decoherence problem. That's why the requirements on the cavity quality factor can be loosened.Comment: to appear in PR

Basal-plane Incommensurate Phases in HCP Structures

An Ising model with competing interaction is used to study the appearance of incommensurate phases in the basal plane of an hexagonal closed-packed structure. The calculated mean-field phase diagram reveals various 1q-incommensurate and lock-in phases. The results are applied to explain the basal-plane incommensurate phase in some compounds of the A'A"BX_4 family, like K_2MoO_4, K_2WO_4, Rb_2WO4 and to describe the sequence of high-temperature phase transitions in other compounds of this family.Comment: 8 pages, RevTeX + 4 ps figure

Biological and technical variables affecting immunoassay recovery of cytokines from human serum and simulated vaginal fluid: A multicenter study

The increase of proinflammatory cytokines in vaginal secretions may serve as a surrogate marker of unwanted inflammatory reaction to microbicide products topically applied for the prevention of sexually transmitted diseases, including HIV-1. Interleukin (IL)-1β and IL-6 have been proposed as indicators of inflammation and increased risk of HIV-1 transmission; however, the lack of information regarding detection platforms optimal for vaginal fluids and interlaboratory variation limit their use for microbicide evaluation and other clinical applications. This study examines fluid matrix variants relevant to vaginal sampling techniques and proposes a model for interlaboratory comparisons across current cytokine detection technologies. IL-1β and IL-6 standards were measured by 12 laboratories in four countries, using 14 immunoassays and four detection platforms based on absorbance, chemiluminescence, electrochemiluminescence, and fluorescence. International reference preparations of cytokines with defined biological activity were spiked into (1) a defined medium simulating the composition of human vaginal fluid at pH 4.5 and 7.2, (2) physiologic salt solutions (phosphate-buffered saline and saline) commonly used for vaginal lavage sampling in clinical studies of cytokines, and (3) human blood serum. Assays were assessed for reproducibility, linearity, accuracy, and significantly detectable fold difference in cytokine level. Factors with significant impact on cytokine recovery were determined by Kruskal−Wallis analysis of variance with Dunn’s multiple comparison test and multiple regression models. All assays showed acceptable intra-assay reproducibility; however, most were associated with significant interlaboratory variation. The smallest reliably detectable cytokine differences (P < 0.05) derived from pooled interlaboratory data varied from 1.5- to 26-fold depending on assay, cytokine, and matrix type. IL-6 but not IL-1β determinations were lower in both saline and phosphate-buffered saline as compared to vaginal fluid matrix, with no significant effect of pH. The (electro)chemiluminescence-based assays were most discriminative and consistently detected <2-fold differences within each matrix type. The Luminex-based assays were less discriminative with lower reproducibility between laboratories. These results suggest the need for uniform vaginal sampling techniques and a better understanding of immunoassay platform differences and cross-validation before the biological significance of cytokine variations can be validated in clinical trials. This investigation provides the first standardized analytic approach for assessing differences in mucosal cytokine levels and may improve strategies for monitoring immune responses at the vaginal mucosal interface