High precision simulations of the longest common subsequence problem

The longest common subsequence problem is a long studied prototype of pattern matching problems. In spite of the effort dedicated to it, the numerical value of its central quantity, the Chvatal-Sankoff constant, is not yet known. Numerical estimations of this constant are very difficult due to finite size effects. We propose a numerical method to estimate the Chvatal-Sankoff constant which combines the advantages of an analytically known functional form of the finite size effects with an efficient multi-spin coding scheme. This method yields very high precision estimates of the Chvatal-Sankoff constant. Our results correct earlier estimates for small alphabet size while they are consistent with (albeit more precise than) earlier results for larger alphabet size.Comment: 8 pages, 4 figure

A Statistical Analysis of RNA Folding Algorithms Through Thermodynamic Parameter Perturbation

Computational RNA secondary structure prediction is rather well established. However, such prediction algorithms always depend on a large number of experimentally measured parameters. Here, we study how sensitive structure prediction algorithms are to changes in these parameters. We find that already for changes corresponding to the actual experimental error to which these parameters have been determined 30% of the structure are falsly predicted and the ground state structure is preserved under parameter perturbation in only 5% of all cases. We establish that base pairing probabilities calculated in a thermal ensemble are a viable though not perfect measure for the reliability of the prediction of individual structure elements. A new measure of stability using parameter perturbation is proposed, and its limitations discussed.Comment: 6 pages, 3 figures, 1 table submitted to Nucleic Acids Researc

Nature of the glassy phase of RNA secondary structure

We characterize the low temperature phase of a simple model for RNA secondary structures by determining the typical energy scale E(l) of excitations involving l bases. At zero temperature, we find a scaling law E(l) \sim l^\theta with \theta \approx 0.23, and this same scaling holds at low enough temperatures. Above a critical temperature, there is a different phase characterized by a relatively flat free energy landscape resembling that of a homopolymer with a scaling exponent \theta=1. These results strengthen the evidence in favour of the existence of a glass phase at low temperatures.Comment: 7 pages, 1 figur

A rural agricultural-sustainable energy community model and its application to Felton Valley, Australia

Energy and food security require a delicate balance which should not threaten or undermine community prosperity. Where it is proposed to derive energy from conventional fossil fuel resources (such as coal, shale oil, natural gas, coal seam gas) located in established rural areas, and particularly where these areas are used for productive agricultural purposes, there are often both intense community concern as well as broader questions regarding the relative social, economic and environmental costs and benefits of different land uses and, increasingly, different energy sources. The advent of mainstream renewable energy technologies means that alternative energy options may provide a viable alternative, allowing energy demand to be met without compromising existing land uses. We demonstrate how such a Sustainable Energy Rural Model can be designed to achieve a balance between the competing social goals of energy supply, agricultural production, environmental integrity and social well-being, and apply it to the Felton Valley, a highly productive and resilient farming community in eastern Australia. Research into available wind and solar resources found that Felton Valley has a number of attributes that indicate its suitability for the development of an integrated renewable energy precinct which would complement, rather than displace, existing agricultural enterprises. Modelling results suggest a potential combined annual renewable energy output from integrated wind and solar resources of 1,287 GWh/yr from peak installed capacity of 713 MW, sufficient to supply the electrical energy needs of about 160,000 homes, in combination with total biomass food production of 31,000 tonnes per annum or 146 GWh/yr of human food energy. The portfolio of renewable energy options will not only provide energy source diversity but also ensures long-term food security and regional stability. The Felton Valley model provides an example of community-led energy transformation and has potential as a pilot project for the development of smart distributed grids that would negate the need for further expansion of coal mining and coal fired power stations

Statistical mechanics of RNA folding: a lattice approach

We propose a lattice model for RNA based on a self-interacting two-tolerant trail. Self-avoidance and elements of tertiary structure are taken into account. We investigate a simple version of the model in which the native state of RNA consists of just one hairpin. Using exact arguments and Monte Carlo simulations we determine the phase diagram for this case. We show that the denaturation transition is first order and can either occur directly or through an intermediate molten phase.Comment: 8 pages, 9 figure

Quasiparticle density of states in dirty high-T_c superconductors

We study the density of quasiparticle states of dirty d-wave superconductors. We show the existence of singular corrections to the density of states due to quantum interference effects. We then argue that the density of states actually vanishes in the localized phase as $|E|$ or $E^2$ depending on whether time reversal is a good symmetry or not. We verify this result for systems without time reversal symmetry in one dimension using supersymmetry techniques. This simple, instructive calculation also provides the exact universal scaling function for the density of states for the crossover from ballistic to localized behaviour in one dimension. Above two dimensions, we argue that in contrast to the conventional Anderson localization transition, the density of states has critical singularities which we calculate in a $2+\epsilon$ expansion. We discuss consequences of our results for various experiments on dirty high-$T_c$ materials

Superconducting ``metals'' and ``insulators''

We propose a characterization of zero temperature phases in disordered superconductors on the basis of the nature of quasiparticle transport. In three dimensional systems, there are two distinct phases in close analogy to the distinction between normal metals and insulators: the superconducting "metal" with delocalized quasiparticle excitations and the superconducting "insulator" with localized quasiparticles. We describe experimental realizations of either phase, and study their general properties theoretically. We suggest experiments where it should be possible to tune from one superconducting phase to the other, thereby probing a novel "metal-insulator" transition inside a superconductor. We point out various implications of our results for the phase transitions where the superconductor is destroyed at zero temperature to form either a normal metal or a normal insulator.Comment: 18 page

Statistical mechanics of RNA folding: importance of alphabet size

We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two kinds of bases, there are many alternate folding configurations, yielding thermodynamically stable ground-states only for a small set of structures of high designability, i.e., total number of associated sequences. In contrast, sequences made from four bases, as found in nature, or six bases have far fewer competing folding configurations, resulting in a much greater average stability of the ground state.Comment: 7 figures; uses revtex