Universality classes in directed sandpile models

We perform large scale numerical simulations of a directed version of the two-state stochastic sandpile model. Numerical results show that this stochastic model defines a new universality class with respect to the Abelian directed sandpile. The physical origin of the different critical behavior has to be ascribed to the presence of multiple topplings in the stochastic model. These results provide new insights onto the long debated question of universality in abelian and stochastic sandpiles.Comment: 5 pages, RevTex, includes 9 EPS figures. Minor english corrections. One reference adde

Crack roughness and avalanche precursors in the random fuse model

We analyze the scaling of the crack roughness and of avalanche precursors in the two dimensional random fuse model by numerical simulations, employing large system sizes and extensive sample averaging. We find that the crack roughness exhibits anomalous scaling, as recently observed in experiments. The roughness exponents ($\zeta$, $\zeta_{loc}$) and the global width distributions are found to be universal with respect to the lattice geometry. Failure is preceded by avalanche precursors whose distribution follows a power law up to a cutoff size. While the characteristic avalanche size scales as $s_0 \sim L^D$, with a universal fractal dimension $D$, the distribution exponent $\tau$ differs slightly for triangular and diamond lattices and, in both cases, it is larger than the mean-field (fiber bundle) value $\tau=5/2$

Hyperbolicity Measures "Democracy" in Real-World Networks

We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of vertices involved in many shortest paths, so that few elements "connect" the systems, while a network with large hyperbolicity has a more "democratic" structure with a larger number of crucial elements. We prove mathematically the soundness of this interpretation, and we derive its consequences by analyzing a large dataset of real-world networks. We confirm and improve previous results on hyperbolicity, and we analyze them in the light of our interpretation. Moreover, we study (for the first time in our knowledge) the hyperbolicity of the neighborhood of a given vertex. This allows to define an "influence area" for the vertices in the graph. We show that the influence area of the highest degree vertex is small in what we define "local" networks, like most social or peer-to-peer networks. On the other hand, if the network is built in order to reach a "global" goal, as in metabolic networks or autonomous system networks, the influence area is much larger, and it can contain up to half the vertices in the graph. In conclusion, our newly introduced approach allows to distinguish the topology and the structure of various complex networks

Corrections to scaling in the forest-fire model

We present a systematic study of corrections to scaling in the self-organized critical forest-fire model. The analysis of the steady-state condition for the density of trees allows us to pinpoint the presence of these corrections, which take the form of subdominant exponents modifying the standard finite-size scaling form. Applying an extended version of the moment analysis technique, we find the scaling region of the model and compute the first non-trivial corrections to scaling.Comment: RevTeX, 7 pages, 7 eps figure

Crossover phenomenon in self-organized critical sandpile models

We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a crossover to the scaling behavior of a different sandpile model takes place where the sand-grains are equally transferred to the nearest neighbors. The crossover behavior is numerically analyzed in detail, especially we consider the exponents which determine the scaling behavior.Comment: 6 pages, 9 figures, accepted for publication in Physical Review

Universal 1/f Noise from Dissipative SOC Models

We introduce a model able to reproduce the main features of 1/f noise: hyper-universality (the power-law exponents are independent on the dimension of the system; we show here results in d=1,2) and apparent lack of a low-frequency cutoff in the power spectrum. Essential ingredients of this model are an activation-deactivation process and dissipation.Comment: 3 Latex pages, 2 eps Figure

Short communication: Carora cattle shows high variability at αsl-casein

The objective of this study was to analyze the genetic variability of milk proteins of the Carora, a shorthorned Bos taurus cattle breed in Venezuela and in other Southern American countries that is primarily used for milk production. A total of 184 individual milk samples were collected from Carora cattle in 5 herds in Venezuela. The milk protein genes alphas1-casein (CN) (CSN1S1), alphas2-CN (CSN2), beta-CN (CSN3), and beta-lactoglobulin (LGB) were typed at the protein level by isoelectrofocusing. It was necessary to further analyze CSN1S1 at the DNA level by a PCR-based method to distinguish CSN1S1*G from B. Increased variation was found in particular at the CSN1S1 gene, where 4 variants were identified. The predominant variant was CSN1S1*B (frequency = 0.8). The second most common CSN1S1 variant was CSN1S1*G (0.101), followed by CSN1S1*C (0.082). Moreover, a new isoelectrofocusing pattern was identified, which may result from a novel CSN1S1 variant, named CSN1S1*I, migrating at an intermediate position between CSN1S1*B and CSN1S1*C. Six cows carried the variant at the heterozygous condition. For the other loci, predominance of CSN2*A2 (0.764), CSN3*B (0.609), and LGB*B (0.592) was observed. Haplotype frequencies (AF) at the CSN1S1-CSN2-CSN3 complex were also estimated by taking association into account. Only 7 haplotypes showed AF values >0.05, accounting for a cumulative frequency of 0.944. The predominant haplotype was B-A2-B (frequency = 0.418), followed by B-A2-A (0.213). The occurrence of the G variant is at a rather high frequency, which is of interest for selection within the Carora breed because of the negative association of this variant with the synthesis of the specific protein. From a cheese-making point of view, this variant is associated with improved milk-clotting parameters but is negatively associated with cheese ripening. Thus, milk protein typing should be routinely carried out in the breed, with particular emphasis on using a DNA test to detect the CSN1S*G variant. The CSN1S*G allele is likely to have descended from the Brown Swiss, which contributed to the Carora breed and also carries this allele

Gravity model in the Korean highway

We investigate the traffic flows of the Korean highway system, which contains both public and private transportation information. We find that the traffic flow T(ij) between city i and j forms a gravity model, the metaphor of physical gravity as described in Newton's law of gravity, P(i)P(j)/r(ij)^2, where P(i) represents the population of city i and r(ij) the distance between cities i and j. It is also shown that the highway network has a heavy tail even though the road network is a rather uniform and homogeneous one. Compared to the highway network, air and public ground transportation establish inhomogeneous systems and have power-law behaviors.Comment: 13 page

Fluctuations and correlations in sandpile models

We perform numerical simulations of the sandpile model for non-vanishing driving fields $h$ and dissipation rates $\epsilon$. Unlike simulations performed in the slow driving limit, the unique time scale present in our system allows us to measure unambiguously response and correlation functions. We discuss the dynamic scaling of the model and show that fluctuation-dissipation relations are not obeyed in this system.Comment: 5 pages, latex, 4 postscript figure

From waves to avalanches: two different mechanisms of sandpile dynamics

Time series resulting from wave decomposition show the existence of different correlation patterns for avalanche dynamics. For the d=2 Bak-Tang-Wiesenfeld model, long range correlations determine a modification of the wave size distribution under coarse graining in time, and multifractal scaling for avalanches. In the Manna model, the distribution of avalanches coincides with that of waves, which are uncorrelated and obey finite size scaling, a result expected also for the d=3 Bak et al. model.Comment: 5 pages, 4 figure