Multiple Invaded Consolidating Materials

We study a multiple invasion model to simulate corrosion or intrusion processes. Estimated values for the fractal dimension of the invaded region reveal that the critical exponents vary as function of the generation number $G$, i.e., with the number of times the invasion process takes place. The averaged mass $M$ of the invaded region decreases with a power-law as a function of $G$, $M\sim G^{\beta}$, where the exponent $\beta\approx 0.6$. We also find that the fractal dimension of the invaded cluster changes from $d_{1}=1.887\pm0.002$ to $d_{s}=1.217\pm0.005$. This result confirms that the multiple invasion process follows a continuous transition from one universality class (NTIP) to another (optimal path). In addition, we report extensive numerical simulations that indicate that the mass distribution of avalanches $P(S,L)$ has a power-law behavior and we find that the exponent $\tau$ governing the power-law $P(S,L)\sim S^{-\tau}$ changes continuously as a function of the parameter $G$. We propose a scaling law for the mass distribution of avalanches for different number of generations $G$.Comment: 8 pages and 16 figure

Underuse of coronary revascularization procedures in patients considered appropriate candidates for revascularization.

Background: Ratings by an expert panel of the appropriateness of treatments may offer better guidance for clinical practice than the variable decisions of individual clinicians, yet there have been no prospective studies of clinical outcomes. We compared the clinical outcomes of patients treated medically after angiography with those of patients who underwent revascularization, within groups defined by ratings of the degree of appropriateness of revascularization in varying clinical circumstances.Methods: This was a prospective study of consecutive patients undergoing coronary angiography at three London hospitals. Before patients were recruited, a nine-member expert panel rated the appropriateness of percutaneous transluminal coronary angioplasty (PTCA) and coronary-artery bypass grafting (CABG) on a nine-point scale (with 1 denoting highly inappropriate and 9 denoting highly appropriate) for specific clinical indications. These ratings were then applied to a population of patients with coronary artery disease. However, the patients were treated without regard to the ratings. A total of 2552 patients were followed for a median of 30 months after angiography.Results: Of 908 patients with indications for which PTCA was rated appropriate (score, 7 to 9), 34 percent were treated medically; these patients were more likely to have angina at follow-up than those who underwent PTCA (odds ratio, 1.97; 95 percent confidence interval, 1.29 to 3.00). Of 1353 patients with indications for which CABG was considered appropriate, 26 percent were treated medically; they were more likely than those who underwent CABG to die or have a nonfatal myocardial infarction - the composite primary outcome (hazard ratio, 4.08; 95 percent confidence interval, 2.82 to 5.93) - and to have angina (odds ratio, 3.03; 95 percent confidence interval, 2.08 to 4.42). Furthermore, there was a graded relation between rating and outcome over the entire scale of appropriateness (P for linear trend = 0.002).Conclusions: On the basis of the ratings of the expert panel, we identified substantial underuse of coronary revascularization among patients who were considered appropriate candidates for these procedures. Underuse was associated with adverse clinical outcomes. (N Engl J Med 2001;344:645-54.) Copyright (C) 2001 Massachusetts Medical Society

Optimal box-covering algorithm for fractal dimension of complex networks

The self-similarity of complex networks is typically investigated through computational algorithms the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce a box-covering algorithm that not only outperforms previous ones, but also finds optimal solutions. For the two benchmark cases tested, namely, the E. Coli and the WWW networks, our results show that the improvement can be rather substantial, reaching up to 15% in the case of the WWW network.Comment: 5 pages, 6 figure

Universal quantum computation by discontinuous quantum walk

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This `discontinuous' quantum walk employs perfect quantum state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one timestep apart.Comment: 7 pages, revte

Cellular automaton rules conserving the number of active sites

This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interacting particles whose total number is conserved. Some of these rules, which allow motion in both directions, mimic ensembles of one-dimensional pseudo-random walkers. Numerical evidence indicates that the corresponding stochastic processes might be non-Gaussian.Comment: 14 pages, 5 figure

Structure of plastically compacting granular packings

The developing structure in systems of compacting ductile grains were studied experimentally in two and three dimensions. In both dimensions, the peaks of the radial distribution function were reduced, broadened, and shifted compared with those observed in hard disk- and sphere systems. The geometrical three--grain configurations contributing to the second peak in the radial distribution function showed few but interesting differences between the initial and final stages of the two dimensional compaction. The evolution of the average coordination number as function of packing fraction is compared with other experimental and numerical results from the literature. We conclude that compaction history is important for the evolution of the structure of compacting granular systems.Comment: 12 pages, 12 figure

1/fα1/f^\alpha spectra in elementary cellular automata and fractal signals

We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays $1/f$ spectra though considered as trivial, and on the other hand that various automata classified as chaotic/complex display no $1/f$ spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce $1/f^{\alpha}$ spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics and computer sciences, there are various candidates to show spectra similar to our results.Comment: 4 pages (3 figs included

A Complexity View of Rainfall

We show that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches. Analysis of high-resolution rain data reveals that power laws describe the number of rain events versus size and number of droughts versus duration. In addition, the accumulated water column displays scale-less fluctuations. These statistical properties are the fingerprints of a self-organized critical process and may serve as a benchmark for models of precipitation and atmospheric processes.Comment: 4 pages, 5 figure

Universality classes for rice-pile models

We investigate sandpile models where the updating of unstable columns is done according to a stochastic rule. We examine the effect of introducing nonlocal relaxation mechanisms. We find that the models self-organize into critical states that belong to three different universality classes. The models with local relaxation rules belong to a known universality class that is characterized by an avalanche exponent $\tau \approx 1.55$, whereas the models with nonlocal relaxation rules belong to new universality classes characterized by exponents $\tau \approx 1.35$ and $\tau \approx 1.63$. We discuss the values of the exponents in terms of scaling relations and a mapping of the sandpile models to interface models.Comment: 4 pages, including 3 figure

Domain size effects in Barkhausen noise

The possible existence of self-organized criticality in Barkhausen noise is investigated theoretically through a single interface model, and experimentally from measurements in amorphous magnetostrictive ribbon Metglas 2605TCA under stress. Contrary to previous interpretations in the literature, both simulation and experiment indicate that the presence of a cutoff in the avalanche size distribution may be attributed to finite size effects.Comment: 5 pages, 3 figures, submitted so Physical Review