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

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

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

Iterative Approximate Consensus in the presence of Byzantine Link Failures

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each directed link of the underlying communication graph represents a communication channel between a pair of nodes. We adopt the transient Byzantine link failure model [15, 16], where an omniscient adversary controls a subset of the directed communication links, but the nodes are assumed to be fault-free. Recent work has addressed the problem of reaching approximate consen- sus in incomplete graphs with Byzantine nodes using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations [22, 21, 23, 12]. However, to the best of our knowledge, we are the first to consider approximate consensus in the presence of Byzan- tine links. We extend our past work that provided exact characterization of graphs in which the iterative approximate consensus problem in the presence of Byzantine node failures is solvable [22, 21]. In particular, we prove a tight necessary and sufficient condition on the underlying com- munication graph for the existence of iterative approximate consensus algorithms under transient Byzantine link model. The condition answers (part of) the open problem stated in [16].Comment: arXiv admin note: text overlap with arXiv:1202.609

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

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

Site-directed mutagenesis of conserved inverted repeat sequences in the xylanase C promoter region from Streptomyces sp EC3

Streptomyces sp. EC3, a strain which was originally isolated from cattle manure compost, was shown to possess a strong xylanolytic activity. One of the genes responsible for this activity, xlnC, encodes a secreted xylanase. In the native strain, as in the heterologous host S. lividans, expression of xlnC was detectable in the presence of xylan but not in the presence of glucose. Induction by xylan was shown to take place at the transcriptional level. The transcriptional start site of xlnC was mapped and likely -35 (5'-TTGACA-3') and -10 (5'-GAGAAC-3') motifs were identified. In order to localise putative conserved regulatory sequences, the promoter regions of xylanase-encoding genes from various Streptomyces species were aligned. This alignment revealed the existence of three sets of quite well conserved palindromic AT rich sequences called boxes 1, 2 and 3. Box 3 (5'-CGAAA N TTTCG-3') is the farthest away from the promoter region (150-200 bp). A shorter version of this palindrome (5'-GAAA NN TTTC-3') or (5'-CGAAA-3') constitutes box 1, which is located just upstream of the putative -35 promoter sequence. Box 2, located 5-7 bp upstream of box 1, comprises a shorter palindrome than box 3, with inverted polarity [5'-(G/C)TTTC (N) GAAA(G/C)-3']. The putative regulatory role of the conserved inverted repeats in boxes 2 and 3 in the promoter region of the xlnC gene from Streptomyces sp. EC3, was assessed. These boxes were modified by site-directed mutagenesis, and the mutant promoter regions, as well as the wild-type promoter region, were separately fused to a beta-lactamase reporter gene. Analysis of the expression patterns of these fusions in cultures grown in the presence of glucose, xylan or both carbon sources demonstrated that these motifs were cis -acting negative regulatory elements, each playing a specific role in the regulation of xlnC expression. Box 3 was shown to be critical for the establishment of repression of xlnC expression by glucose, whereas box 2 was shown to play an important role in the induction of xlnC expression by xylan.Peer reviewe

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

Eo-Alpine metamorphism and the ‘mid-Miocene thermal event’ in the Western Carpathians (Slovakia): New evidence from multiple thermochronology

A combination of zircon (U–Th)/He (ZHe), apatite fission track (AFT) and apatite (U–Th)/He (AHe) dating methods is applied to constrain the metamorphic and exhumation history of the Tatric part of the Branisko Mountains in the Western Carpathians. ZHe ages from the basement samples prove the basement experienced a very low-grade to low-grade Eo-Alpine metamorphic overprint in mid-Cretaceous times. Miocene AFT and AHe ages found in the basement and in the Palaeogene sediments conclusively demonstrate that the Branisko Mts experienced a ‘mid-Miocene thermal event’. This thermal event had a regional character and was related to magmatic and/or burial heating that exposed the sediment and basement samples to ~ 120–130°C and ~ 100–190°C, respectively