Statistical mechanics of scale-free networks at a critical point: Complexity without irreversibility?

Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their utility by linking to nodes with a higher/lower degree than their own. We interpret utility as an equivalent to energy in physical systems and discuss the temperature dependence of the emerging networks. We observe the existence of a critical temperature $T_c$ where total energy (utility) and network-architecture undergo radical changes. Along this topological transition we obtain scale-free networks with complex hierarchical topology. In contrast to models for scale-free networks introduced so far, the scale-free nature emerges within equilibrium, with a clearly defined microcanonical ensemble and the principle of detailed balance strictly fulfilled. This provides clear evidence that 'complex' networks may arise without irreversibility. The results presented here should find a wide variety of applications in socio-economic statistical systems.Comment: 4 pages, 5 figure

Selection of noise level in strategy adoption for spatial social dilemmas

We studied spatial Prisoner's Dilemma and Stag Hunt games where both the strategy distribution and the players' individual noise level could evolve to reach higher individual payoff. Players are located on the sites of different two-dimensional lattices and gain their payoff from games with their neighbors by choosing unconditional cooperation or defection. The way of strategy adoption can be characterized by a single $K$ (temperature-like) parameter describing how strongly adoptions depend on the payoff-difference. If we start the system from a random strategy distribution with many different player specific $K$ parameters, the simultaneous evolution of strategies and $K$ parameters drives the system to a final stationary state where only one $K$ value remains. In the coexistence phase of cooperator and defector strategies the surviving $K$ parameter is in good agreement with the noise level that ensures the highest cooperation level if uniform $K$ is supposed for all players. In this paper we give a thorough overview about the properties of this evolutionary process.Comment: 10 two-column pages, 10 figures; accepted for publication in Physical Review

Opinion Formation in Laggard Societies

We introduce a statistical physics model for opinion dynamics on random networks where agents adopt the opinion held by the majority of their direct neighbors only if the fraction of these neighbors exceeds a certain threshold, p_u. We find a transition from total final consensus to a mixed phase where opinions coexist amongst the agents. The relevant parameters are the relative sizes in the initial opinion distribution within the population and the connectivity of the underlying network. As the order parameter we define the asymptotic state of opinions. In the phase diagram we find regions of total consensus and a mixed phase. As the 'laggard parameter' p_u increases the regions of consensus shrink. In addition we introduce rewiring of the underlying network during the opinion formation process and discuss the resulting consequences in the phase diagram.Comment: 5 pages, eps fig

Purification and mechanistic characterisation of two polygalacturonases from Sclerotium rolfsii

Sclerotium rolfsii (strain CBS 350.80) was found to produce extraordinary high amounts of polygalacturonases (PGs). Two of these extracellular enzymes were purified by a recently introduced preparative electrophoretic device (isoelectric focusing mode of free flow electrophoresis). PG 1 (39.5 kDa, pI 6.5) and PG 2 (38 kDa, pI 5.4) exhibited quite similar properties, they were found to be both endo-acting enzymes. Both PGs cleaved penta- and trigalacturonic acid while tetragalacturonic acid was only cleaved when trigalacturonic acid was present. The latter substrate was hydrolysed much faster by PG 2. Both enzymes were active on pectins with different degrees of esterification, they were sensitive towards Ca-cations and not glycosylated. The kinetic properties were measured by viscosimetry with polygalacturonic acid as a substrate. NMR experiments on a model substrate revealed an inverting mechanism of carbohydrate hydrolysis for both enzymes

Gathering in Dynamic Rings

The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares the same fundamental assumption: the topological structure does not change during the rendezvous or the gathering; this is true also for those investigations that consider faulty nodes. In other words, they only consider static graphs. In this paper we start the investigation of gathering in dynamic graphs, that is networks where the topology changes continuously and at unpredictable locations. We study the feasibility of gathering mobile agents, identical and without explicit communication capabilities, in a dynamic ring of anonymous nodes; the class of dynamics we consider is the classic 1-interval-connectivity. We focus on the impact that factors such as chirality (i.e., a common sense of orientation) and cross detection (i.e., the ability to detect, when traversing an edge, whether some agent is traversing it in the other direction), have on the solvability of the problem. We provide a complete characterization of the classes of initial configurations from which the gathering problem is solvable in presence and in absence of cross detection and of chirality. The feasibility results of the characterization are all constructive: we provide distributed algorithms that allow the agents to gather. In particular, the protocols for gathering with cross detection are time optimal. We also show that cross detection is a powerful computational element. We prove that, without chirality, knowledge of the ring size is strictly more powerful than knowledge of the number of agents; on the other hand, with chirality, knowledge of n can be substituted by knowledge of k, yielding the same classes of feasible initial configurations

Phylogeny, classification and metagenomic bioprospecting of microbial acetyl xylan esterases

Acetyl xylan esterases (AcXEs), also termed xylan deacetylases, are broad specificity Carbohydrate-Active Enzymes (CAZymes) that hydrolyse ester bonds to liberate acetic acid from acetylated hemicellulose (typically polymeric xylan and xylooligosaccharides). They belong to eight families within the Carbohydrate Esterase (CE) class of the CAZy database. AcXE classification is largely based on sequence-dependent phylogenetic relationships, supported in some instances with substrate specificity data. However, some sequence-based predictions of AcXE-encoding gene identity have proved to be functionally incorrect. Such ambiguities can lead to mis-assignment of genes and enzymes during sequence data-mining, reinforcing the necessity for the experimental confirmation of the functional properties of putative AcXE-encoding gene products. Although one-third of all characterized CEs within CAZy families 1–7 and 16 are AcXEs, there is a need to expand the sequence database in order to strengthen the link between AcXE gene sequence and specificity. Currently, most AcXEs are derived from a limited range of (mostly microbial) sources and have been identified via culture-based bioprospecting methods, restricting current knowledge of AcXEs to data from relatively few microbial species. More recently, the successful identification of AcXEs via genome and metagenome mining has emphasised the huge potential of culture-independent bioprospecting strategies. We note, however, that the functional metagenomics approach is still hampered by screening bottlenecks. The most relevant recent reviews of AcXEs have focused primarily on the biochemical and functional properties of these enzymes. In this review, we focus on AcXE phylogeny, classification and the future of metagenomic bioprospecting for novel AcXEs.The South African Department of Science and Technology Biocatalysis Initiative, National Research Foundation (DAC, TPM), the University of Pretoria’s Genomics Research Institute (DAC) and Research Development Program (TPM). FAA was supported by funds from the Organisation for Women in Science in the Developing World (OWSD).http://www.elsevier.com/locate/emt2017-11-30hb2016Genetic

Universal correlations and power-law tails in financial covariance matrices

Signatures of universality are detected by comparing individual eigenvalue distributions and level spacings from financial covariance matrices to random matrix predictions. A chopping procedure is devised in order to produce a statistical ensemble of asset-price covariances from a single instance of financial data sets. Local results for the smallest eigenvalue and individual spacings are very stable upon reshuffling the time windows and assets. They are in good agreement with the universal Tracy-Widom distribution and Wigner surmise, respectively. This suggests a strong degree of robustness especially in the low-lying sector of the spectra, most relevant for portfolio selections. Conversely, the global spectral density of a single covariance matrix as well as the average over all unfolded nearest-neighbour spacing distributions deviate from standard Gaussian random matrix predictions. The data are in fair agreement with a recently introduced generalised random matrix model, with correlations showing a power-law decay

Yeast diversity in relation to the production of fuels and chemicals

In addition to ethanol, yeasts have the potential to produce many other industrially-relevant chemicals from numerous different carbon sources. However there remains a paucity of information about overall capability across the yeast family tree. Here, 11 diverse species of yeasts with genetic backgrounds representative of different branches of the family tree were investigated. They were compared for their abilities to grow on a range of sugar carbon sources, to produce potential platform chemicals from such substrates and to ferment hydrothermally pretreated rice straw under simultaneous saccharification and fermentation conditions. The yeasts differed considerably in their metabolic capabilities and production of ethanol. A number could produce significant amounts of ethyl acetate, arabinitol, glycerol and acetate in addition to ethanol, including from hitherto unreported carbon sources. They also demonstrated widely differing efficiencies in the fermentation of sugars derived from pre-treated rice straw biomass and differential sensitivities to fermentation inhibitors. A new catabolic property of Rhodotorula mucilaginosa (NCYC 65) was discovered in which sugar substrate is cleaved but the products are not metabolised. We propose that engineering this and some of the other properties discovered in this study and transferring such properties to conventional industrial yeast strains could greatly expand their biotechnological utility

A novel xylan degrading β-D-xylosidase: purification and biochemical characterization

Aspergillus ochraceus, a thermotolerant fungus isolated in Brazil from decomposing materials, produced an extracellular b-xylosidase that was purified using DEAE-cellulose ion exchange chromatography, Sephadex G-100 and Biogel P-60 gel filtration. b-xylosidase is a glycoprotein (39 % carbohydrate content) and has a molecular mass of 137 kDa by SDS-PAGE, with optimal temperature and pH at 70 C and 3.0–5.5, respectively.b-xylosidase was stable in acidic pH (3.0–6.0) and 70 C for 1 h. The enzyme was activated by 5 mM MnCl2 (28 %)and MgCl2 (20 %) salts. The b-xylosidase produced by A. ochraceus preferentially hydrolyzed p-nitrophenyl-b- D-xylopyranoside, exhibiting apparent Km and Vmax values of 0.66 mM and 39 U (mg protein)-1 respectively, and to a lesser extent p-nitrophenyl-b-D-glucopyranoside. The enzyme was able to hydrolyze xylan from different sources,suggesting a novel b-D-xylosidase that degrades xylan. HPLC analysis revealed xylans of different compositions which allowed explaining the differences in specificity observed by b-xylosidase. TLC confirmed the capacity.This work was supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), and the Conselho de Desenvolvimento Científico e Tecnológico (CNPq). J. A. J. and M. L. T. M. P are Research Fellows of CNPq. M. M. was a recipient of a FAPESP fellowship and this work is part of her Doctoral Thesis. It is also part of the project SISBIOTA CNPq: 563260/2010-6 and FAPESP: 2010/52322-3