Renormalization group for critical phenomena in complex networks

We discuss the behavior of statistical models on a novel class of complex “Hanoi” networks. Such modeling is often the cornerstone for the understanding of many dynamical processes in complex networks. Hanoi networks are special because they integrate small-world hierarchies common to many social and economical structures with the inevitable geometry of the real world these structures exist in. In addition, their design allows exact results to be obtained with the venerable renormalization group (RG). Our treatment will provide a detailed, pedagogical introduction to RG. In particular, we will study the Ising model with RG, for which the fixed points are determined and the RG flow is analyzed. We show that the small-world bonds result in non-universal behavior. It is shown that a diversity of different behaviors can be observed with seemingly small changes in the structure of hierarchical networks generally, and we provide a general theory to describe our findings.

Quantum transport through hierarchical structures

The transport of quantum electrons through hierarchical lattices is of interest because such lattices have some properties of both regular lattices and random systems. We calculate the electron transmission as a function of energy in the tight-binding approximation for two related Hanoi networks. HN3 is a Hanoi network with every site having three bonds. HN5 has additional bonds added to HN3 to make the average number of bonds per site equal to five. We present a renormalization group approach to solve the matrix equation involved in this quantum transport calculation. We observe band gaps in HN3, while no such band gaps are observed in linear networks or in HN5. We provide a detailed scaling analysis near the edges of these band gaps.

Fixed-point properties of the Ising ferromagnet on the Hanoi networks

The Ising model with ferromagnetic couplings on the Hanoi networks is analyzed with an exact renormalization group. In particular, the fixed points are determined and the renormalization- flow for certain initial conditions is analyzed. Hanoi networks combine a one-dimensional lattice structure with a hierarchy of long-range bonds to create a mix of geometric and small-world properties. Generically, those small-world bonds result in nonuniversal behavior, i.e., fixed points and scaling exponents that depend on temperature and the initial choice of coupling strengths. It is shown that a diversity of different behaviors can be observed with seemingly small changes in the structure of the networks. Defining interpolating families of such networks, we find tunable transitions between regimes with power-law and certain essential singularities in the critical scaling of the correlation length. These are similar to the so-called inverted Berezinskii-Kosterlitz-Thouless transition previously observed only in scale-free or dense networks.

Decomposition of the telomere-targeting agent BRACO19 in physiological media results in products with decreased inhibitory potential

The stability of the acridine-based telomere-targeting agent BRACO19, a G-quadruplex stabilizing substance, was tested at different pH, temperature and in different dissolution media. Analysis was performed by HPLC. Decomposition products were examined by LC/MS and NMR. The TRAP assay was used to determine the inhibitory potential of the decomposition products on telomerase activity. The results show that the stability of BRACO19 strongly depends on pH and temperature. Decomposition was fastest at physiological pH and temperature while the type of dissolution medium had no major influence on stability. The most probable mechanism for this decomposition seems to be a hydrolysis of the amide bonds in position 3 and 6 of the acridine ring and/or a deamination of the phenyl ring. The decomposition products showed a reduced inhibitory potential compared to the parent compound BRACO19. The results demonstrate that the preparation of dosage forms and their storage conditions will have an important influence on the stability--and hence biological efficacy--of BRACO19 and related substances.

Thermal inactivation of foot-and-mouth disease virus in milk using high-temperature, short-time pasteurization

Previous studies of laboratory simulation of high temperature, short time pasteurization (HTST) to eliminate foot-and-mouth disease virus (FMDV) in milk have shown that the virus is not completely inactivated at the legal pasteurization minimum (71.7 degrees C/15 s) but is inactivated in a flow apparatus at 148 degrees C with holding times of 2 to 3 s. It was the intent of this study to determine whether HTST pasteurization conducted in a continuous-flow pasteurizer that simulates commercial operation would enhance FMDV inactivation in milk. Cows were inoculated in the mammary gland with the field strain of FMDV (01/UK). Infected raw whole milk and 2% milk were then pasteurized using an Arm-field pilot-scale, continuous-flow HTST pasteurizer equipped with a plate-and-frame heat exchanger and a holding tube. The milk samples, containing FMDV at levels of up to 10(4) plaque-forming units/mL, were pasteurized at temperatures ranging from 72 to 95 degrees C at holding times of either 18.6 or 36 s. Pasteurization decreased virus infectivity by 4 log10 to undetectable levels in tissue culture. However, residual infectivity was still detectable for selected pasteurized milk samples, as shown by intramuscular and intradermal inoculation of milk into naïve steers. Although HTST pasteurization did not completely inactivate viral infectivity in whole and 2% milk, possibly because a fraction of the virus was protected by the milk fat and the casein proteins, it greatly reduced the risk of natural transmission of FMDV by milk.

Argonaute2, a link between genetic and biochemical analyses of RNAi

Double-stranded RNA induces potent and specific gene silencing through a process referred to as RNA interference (RNAi) or posttranscriptional gene silencing (PTGS). RNAi is mediated by RNA-induced silencing complex (RISC), a sequence-specific, multicomponent nuclease that destroys messenger RNAs homologous to the silencing trigger. RISC is known to contain short RNAs ( approximately 22 nucleotides) derived from the double-stranded RNA trigger, but the protein components of this activity are unknown. Here, we report the biochemical purification of the RNAi effector nuclease from cultured Drosophila cells. The active fraction contains a ribonucleoprotein complex of approximately 500 kilodaltons. Protein microsequencing reveals that one constituent of this complex is a member of the Argonaute family of proteins, which are essential for gene silencing in Caenorhabditis elegans, Neurospora, and Arabidopsis. This observation begins the process of forging links between genetic analysis of RNAi from diverse organisms and the biochemical model of RNAi that is emerging from Drosophila in vitro systems.

Extremal optimization for graph partitioning

Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the computationally hard (NP-hard) graph partitioning problem. We discuss the scaling behavior of extremal optimization, focusing on the convergence of the average run as a function of run time and system size. The method has a single free parameter, which we determine numerically and justify using a simple argument. On random graphs, our numerical results demonstrate that extremal optimization maintains consistent accuracy for increasing system sizes, with an approximation error decreasing over run time roughly as a power law t(-0.4). On geometrically structured graphs, the scaling of results from the average run suggests that these are far from optimal with large fluctuations between individual trials. But when only the best runs are considered, results consistent with theoretical arguments are recovered.

Optimization with extremal dynamics

We explore a new general-purpose heuristic for finding high-quality solutions to hard discrete optimization problems. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent complexity in physical systems. Extremal optimization successively updates extremely undesirable variables of a single suboptimal solution, assigning them new, random values. Large fluctuations ensue, efficiently exploring many local optima. We use extremal optimization to elucidate the phase transition in the 3-coloring problem, and we provide independent confirmation of previously reported extrapolations for the ground-state energy of +/-J spin glasses in d = 3 and 4.

Ventilation-induced chemokine and cytokine release is associated with activation of nuclear factor-kappaB and is blocked by steroids

Recent clinical trials have shown that the survival of patients with acute respiratory distress syndrome (ARDS) is improved by ventilation with reduced volumes. These studies suggested that overinflation of the lungs causes overactivation of the immune system. The present study investigated the hypothesis that ventilation with increased tidal volumes results in early responses similar to those caused by stimulation with one of the major risk factors for ARDS: bacterial lipopolysaccharide (LPS). We therefore compared the effects of ventilation (-10 cm H2O or -25 cm H2O end-inspiratory pressure) and LPS (50 microg/ml) on nuclear factor (NF)-kappaB activation, chemokine release, and cytokine release in isolated perfused lungs obtained from BALB/C mice. We found that both LPS and ventilation with -25 cm H2O (overventilation; OV) caused translocation of NF-kappaB, which was abolished by pretreatment with the steroid dexamethasone. Furthermore, both treatments resulted in similar increases in perfusate levels of alpha-chemokines (macrophage inflammatory protein; [MIP]-2; KC), beta-chemokines (macrophage chemotactic protein-1; MIP-1alpha), and cytokines (tumor necrosis factor-alpha, interleukin-6), which were largely prevented by dexamethasone pretreatment. In LPS-resistant C3H/HeJ mice, only OV, and not LPS, caused translocation of NF-kappaB and release of MIP-2. We conclude that OV evokes early inflammatory responses similar to those evoked by LPS (i.e., NF-kappaB translocation and release of proinflammatory mediators). The NF-kappaB translocation elicited by OV appears to be independent of Toll-like receptor 4 and not due to LPS contamination introduced by the ventilator. Our data further suggest that steroids might be considered as a subsidiary treatment during artificial mechanical ventilation.

dc = 4 is the upper critical dimension for the Bak-Sneppen model

Numerical results are presented indicating d(c) = 4 as the upper critical dimension for the Bak-Sneppen evolution model. This finding agrees with previous theoretical arguments, but contradicts a recent Letter [Phys. Rev. Lett. 80, 5746 (1998)] that placed d(c) as high as d = 8. In particular, we find that avalanches are compact for all dimensions d< or =4 and are fractal for d>4. Under those conditions, scaling arguments predict a d(c) = 4, where hyperscaling relations hold for d< or =4. Other properties of avalanches, studied for 1< or =d< or =6, corroborate this result. To this end, an improved numerical algorithm is presented that is based on the equivalent branching process.