Thermodynamic Analysis of Interacting Nucleic Acid Strands

Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality

Generators of simple Lie algebras in arbitrary characteristics

In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.Comment: 26 pages, final version, to appear in Math. Z. Main improvements and corrections in Section 4.

The ATLAS3D project - XXV: Two-dimensional kinematic analysis of simulated galaxies and the cosmological origin of fast and slow rotators

We present a detailed two-dimensional stellar dynamical analysis of as ample of 44 cosmological hydrodynamical simulations of individual central galaxies with stellar masses of 2 x 1010Msun ∼≤ Mstar ∼≤ 6x 1011Msun. Kinematic maps of the stellar line-of-sight velocity, velocity dispersion, and higher-order Gauss-Hermite moments h3 and h4 are constructed for each central galaxy and for the most massive satellites. The amount of rotation is quantified using the λR-parameter. The velocity, velocity dispersion, h3, and h4 fields of the simulated galaxies show a diversity similar to observed kinematic maps of early-type galaxies in the ATLAS3D survey. This includes fast (regular), slow, and misaligned rotation, hot spheroids with embedded cold disk components as well as galaxies with counter-rotating cores or central depressions in the velocity dispersion. We link the present-day kinematic properties to the individual cosmological formation histories of the galaxies. In general, major galaxy mergers have a significant influence on the rotation properties resulting in both a spin-down as well as a spin-up of the merger remnant. Lower mass galaxies with significant in-situ formation of stars, or with additional gas-rich major mergers - resulting in a spin-up - in their formation history, form elongated fast rotators with a clear anti-correlation of h3 and v/σ. An additional formation path for fast rotators includes gas-poor major mergers leading to a spin-up of the remnants. This formation path does not result in anti-correlated h3 and v/σ. The galaxies most consistent with the rare class of non-rotating round early-type galaxies grow by gas-poor minor mergers alone. In general, more massive galaxies have less in-situ star formation since z ∼ 2, rotate slower and have older stellar populations. (shortened)PostprintPeer reviewe

Gravitational decoherence of planetary motions

We study the effect of the scattering of gravitational waves on planetary motions, say the motion of the Moon around the Earth. Though this effect has a negligible influence on dissipation, it dominates fluctuations and the associated decoherence mechanism, due to the very high effective temperature of the background of gravitational waves in our galactic environment.Comment: 6 pages, no figure, to appear in EuroPhysics Letters; needs `epl.cls

Enhanced Raman Scattering of amorphous matrices for Fiber Optics Sensor

International audienc

The importance of the commons in the context of intellectual property

CITATION: Van Der Walt, A.J. & Du Bois, M. 2013. The importance of the commons in the context of intellectual property. Stellenbosch Law Review = Stellenbosch Regstydskrif 24(1):31-54.The original publication is available at https://journals.co.za/content/journal/ju_slrThe intellectual commons or public domain is an important part of intellectual property law scholarship. In this regard it is necessary to examine the origins of the commons, what exactly the intellectual commons is and how the notion of the intellectual commons may be further developed. Especially in the United States of America there are concerns that the intellectual commons is currently being enclosed by extending intellectual property protection to areas of intellectual activity that were previously excluded from propertisation; and by extending intellectual property protection of existing rights. It may be argued that some intellectual products should remain in the commons or revert back to the commons in order to ensure that enough remains so that new intellectual products may be developed based on these existing products. However, there must also be enough of a property-right based incentive in order to ensure continued investment in the creation of new intellectual products. The important question is then, how may these two interests be balanced? This article examines the issues related to the commons in order to provide a framework which future revisions to intellectual property legislation may use as a point of departure to ensure that South African legislation does not encroach on the intellectual commons unduly. Examples from copyright law, patent law and traditional knowledge are used to demonstrate how the intellectual commons and intellectual property statutes interact.Publishers versio

Topological constraints in nucleic acid hybridization kinetics

A theoretical examination of kinetic mechanisms for forming knots and links in nucleic acid structures suggests that molecules involving base pairs between loops are likely to become topologically trapped in persistent frustrated states through the mechanism of ‘helix-driven wrapping’. Augmentation of the state space to include both secondary structure and topology in describing the free energy landscape illustrates the potential for topological effects to influence the kinetics and function of nucleic acid strands. An experimental study of metastable complementary ‘kissing hairpins’ demonstrates that the topological constraint of zero linking number between the loops effectively prevents conversion to the minimum free energy helical state. Introduction of short catalyst strands that break the topological constraint causes rapid conversion to full duplex

Differential Forms on Log Canonical Spaces

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared in Publications math\'ematiques de l'IH\'ES. The final publication is available at http://www.springerlink.co