Magnetic exponents of two-dimensional Ising spin glasses

The magnetic critical properties of two-dimensional Ising spin glasses are controversial. Using exact ground state determination, we extract the properties of clusters flipped when increasing continuously a uniform field. We show that these clusters have many holes but otherwise have statistical properties similar to those of zero-field droplets. A detailed analysis gives for the magnetization exponent delta = 1.30 +/- 0.02 using lattice sizes up to 80x80; this is compatible with the droplet model prediction delta = 1.282. The reason for previous disagreements stems from the need to analyze both singular and analytic contributions in the low-field regime.Comment: 4 pages, 4 figures, title now includes "Ising

Universality-class dependence of energy distributions in spin glasses

We study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering Monte Carlo and branch, cut, and price algorithms. By tuning the exponent of the power-law interactions we are able to scan several universality classes. Our results suggest that mean-field models have a non-Gaussian limiting distribution of the ground-state energies, whereas non-mean-field models have a Gaussian limiting distribution. We compare the results of the disordered one-dimensional Ising chain to results for a disordered two-leg ladder, for which large system sizes can be studied, and find a qualitative agreement between the disordered one-dimensional Ising chain in the short-range universality class and the disordered two-leg ladder. We show that the mean and the standard deviation of the ground-state energy distributions scale with a power of the system size. In the mean-field universality class the skewness does not follow a power-law behavior and converges to a nonzero constant value. The data for the Sherrington-Kirkpatrick model seem to be acceptably well fitted by a modified Gumbel distribution. Finally, we discuss the distribution of the internal energy of the Sherrington-Kirkpatrick model at finite temperatures and show that it behaves similar to the ground-state energy of the system if the temperature is smaller than the critical temperature.Comment: 15 pages, 20 figures, 1 tabl

Low Energy Excitations in Spin Glasses from Exact Ground States

We investigate the nature of the low-energy, large-scale excitations in the three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and free boundary conditions, by studying the response of the ground state to a coupling-dependent perturbation introduced previously. The ground states are determined exactly for system sizes up to 12^3 spins using a branch and cut algorithm. The data are consistent with a picture where the surface of the excitations is not space-filling, such as the droplet or the ``TNT'' picture, with only minimal corrections to scaling. When allowing for very large corrections to scaling, the data are also consistent with a picture with space-filling surfaces, such as replica symmetry breaking. The energy of the excitations scales with their size with a small exponent \theta', which is compatible with zero if we allow moderate corrections to scaling. We compare the results with data for periodic boundary conditions obtained with a genetic algorithm, and discuss the effects of different boundary conditions on corrections to scaling. Finally, we analyze the performance of our branch and cut algorithm, finding that it is correlated with the existence of large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with more discussion of the numerical data. Fig.11 adde

Oxidoreductases on their way to industrial biotransformations

Fungi produce heme-containing peroxidases and peroxygenases, flavin-containing oxidases and dehydrogenases, and different copper-containing oxidoreductases involved in the biodegradation of lignin and other recalcitrant compounds. Heme peroxidases comprise the classical ligninolytic peroxidases and the new dye-decolorizing peroxidases, while heme peroxygenases belong to a still largely unexplored superfamily of heme-thiolate proteins. Nevertheless, basidiomycete unspecific peroxygenases have the highest biotechnological interest due to their ability to catalyze a variety of regio- and stereo-selective monooxygenation reactions with H2O2 as the source of oxygen and final electron acceptor. Flavo-oxidases are involved in both lignin and cellulose decay generating H2O2 that activates peroxidases and generates hydroxyl radical. The group of copper oxidoreductases also includes other H2O2 generating enzymes - copper-radical oxidases - together with classical laccases that are the oxidoreductases with the largest number of reported applications to date. However, the recently described lytic polysaccharide monooxygenases have attracted the highest attention among copper oxidoreductases, since they are capable of oxidatively breaking down crystalline cellulose, the disintegration of which is still a major bottleneck in lignocellulose biorefineries, along with lignin degradation. Interestingly, some flavin-containing dehydrogenases also play a key role in cellulose breakdown by directly/indirectly "fueling" electrons for polysaccharide monooxygenase activation. Many of the above oxidoreductases have been engineered, combining rational and computational design with directed evolution, to attain the selectivity, catalytic efficiency and stability properties required for their industrial utilization. Indeed, using ad hoc software and current computational capabilities, it is now possible to predict substrate access to the active site in biophysical simulations, and electron transfer efficiency in biochemical simulations, reducing in orders of magnitude the time of experimental work in oxidoreductase screening and engineering. What has been set out above is illustrated by a series of remarkable oxyfunctionalization and oxidation reactions developed in the frame of an intersectorial and multidisciplinary European RTD project. The optimized reactions include enzymatic synthesis of 1-naphthol, 25-hydroxyvitamin D3, drug metabolites, furandicarboxylic acid, indigo and other dyes, and conductive polyaniline, terminal oxygenation of alkanes, biomass delignification and lignin oxidation, among others. These successful case stories demonstrate the unexploited potential of oxidoreductases in medium and large-scale biotransformations

A Fixed-Parameter Algorithm for the Max-Cut Problem on Embedded 1-Planar Graphs

We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with at most one crossing per edge. Our algorithm recursively reduces a 1-planar graph to at most $3^k$ planar graphs, using edge removal and node contraction. The \textsc{Max-Cut} problem is then solved on the planar graphs using established polynomial-time algorithms. We show that a maximum cut in the given 1-planar graph can be derived from the solutions for the planar graphs. Our algorithm computes a maximum cut in an embedded 1-planar graph with $n$ nodes and $k$ edge crossings in time $\mathcal{O}(3^k \cdot n^{3/2} \log n)$.Comment: conference version from IWOCA 201

Progress and Research Needs of Plant Biomass Degradation by Basidiomycete Fungi

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