Crossover from Endogenous to Exogenous Activity in Open-Source Software Development

We have investigated the origin of fluctuations in the aggregated behaviour of an open-source software community. In a recent series of papers, de Menezes and co-workers have shown how to separate internal dynamics from external fluctuations by capturing the simultaneous activity of many system's components. In spite of software development being a planned activity, the analysis of fluctuations reveals how external driving forces can be only observed at weekly and higher time scales. Hourly and higher change frequencies mostly relate to internal maintenance activities. There is a crossover from endogenous to exogenous activity depending on the average number of file changes. This new evidence suggests that software development is a non-homogeneous design activity where stronger efforts focus in a few project files. The crossover can be explained with a Langevin equation associated to the cascading process, where changes to any file trigger additional changes to its neighbours in the software network. In addition, analysis of fluctuations enables us to detect whether a software system can be decomposed in several subsystems with different development dynamics.Comment: 7 pages, 4 figures, submitted to Europhysics Letter

Clustering properties of a generalised critical Euclidean network

Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its $i$th predecessor of degree $k_i$ with a link of length $\ell$ using a probability proportional to $k^\beta_i \ell^{\alpha}$. For $\alpha > -0.5$, the network is scale free at $\beta = 1$ with the degree distribution $P(k) \propto k^{-\gamma}$ and $\gamma = 3.0$ as in the Barab\'asi-Albert model ($\alpha =0, \beta =1$). We find a phase boundary in the $\alpha-\beta$ plane along which the network is scale-free. Interestingly, we find scale-free behaviour even for $\beta > 1$ for $\alpha < -0.5$ where the existence of a new universality class is indicated from the behaviour of the degree distribution and the clustering coefficients. The network has a small diameter in the entire scale-free region. The clustering coefficients emulate the behaviour of most real networks for increasing negative values of $\alpha$ on the phase boundary.Comment: 4 pages REVTEX, 4 figure

Modeling the Internet's Large-Scale Topology

Network generators that capture the Internet's large-scale topology are crucial for the development of efficient routing protocols and modeling Internet traffic. Our ability to design realistic generators is limited by the incomplete understanding of the fundamental driving forces that affect the Internet's evolution. By combining the most extensive data on the time evolution, topology and physical layout of the Internet, we identify the universal mechanisms that shape the Internet's router and autonomous system level topology. We find that the physical layout of nodes form a fractal set, determined by population density patterns around the globe. The placement of links is driven by competition between preferential attachment and linear distance dependence, a marked departure from the currently employed exponential laws. The universal parameters that we extract significantly restrict the class of potentially correct Internet models, and indicate that the networks created by all available topology generators are significantly different from the Internet

Self Consistent Expansion for the Molecular Beam Epitaxy Equation

Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the non linear molecular beam epitaxy (MBE) equation, a self-consistent expansion (SCE) for the non linear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form $D({\vec r - \vec r',t - t'}) = 2D_0 | {\vec r - \vec r'} |^{2\rho - d} \delta ({t - t'})$. I find a lower critical dimension $d_c (\rho) = 4 + 2\rho$, above, which the linear MBE solution appears. Below the lower critical dimension a r-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe non linear MBE, using a reliable method that proved itself in the past by predicting reasonable results for the Kardar-Parisi-Zhang (KPZ) system, where DRG failed to do so.Comment: 16 page

Diffusive Capture Process on Complex Networks

We study the dynamical properties of a diffusing lamb captured by a diffusing lion on the complex networks with various sizes of $N$. We find that the life time $of a lamb scales as \sim N$ and the survival probability $S(N\to \infty,t)$ becomes finite on scale-free networks with degree exponent $\gamma>3$. However, $S(N,t)$ for $\gamma<3$ has a long-living tail on tree-structured scale-free networks and decays exponentially on looped scale-free networks. It suggests that the second moment of degree distribution $is the relevant factor for the dynamical properties in diffusive capture process. We numerically find that the normalized number of capture events at a node with degree$k$,$n(k)$, decreases as$n(k)\sim k^{-\sigma}$. When$\gamma<3$,$n(k)$still increases anomalously for$k\approx k_{max}$. We analytically show that$n(k)$satisfies the relation$n(k)\sim k^2P(k)$and the total number of capture events$N_{tot}$is proportional to$, which causes the $\gamma$ dependent behavior of $S(N,t)$ and $.Comment: 9 pages, 6 figure

A Study on the Tritium Behavior in the Rice Plant after a Short-Term Exposure of HTO

In many Asian countries including Korea, rice is a very important food crop. Its grain is consumed by humans and its straw is used to feed animals. In Korea, there are four CANDU type reactors that release relatively large amounts of tritium into the environment. Since 1997, KAERI (Korea Atomic Energy Research Institute) has carried out the experimental studies to obtain domestic data on various parameters concerning the direct contamination of plant. In this study, the behavior of tritium in the rice plant is predicted and compared with the measurement performed at KAERI. Using the conceptual model of the soil-plant-atmosphere tritiated water transport system which was suggested by Charles E. Murphy, tritium concentrations in the soil and in leaves to time were derived. If the effect of tritium concentration in the soil is considered, the tritium concentration in leaves is described as a double exponential model. On the other hand if the tritium concentration in the soil is disregarded, the tritium concentration in leaves is described by a single exponential term as other models (e.g. Belot's or STAR-H3 model). Also concentration of organically bound tritium in the seed is predicted and compared with measurements. The results can be used to predict the tritium concentration in the rice plant at a field around the site and the ingestion dose following the release of tritium to the environment

Dynamical surface structures in multi-particle-correlated surface growths

We investigate the scaling properties of the interface fluctuation width for the $Q$-mer and $Q$-particle-correlated deposition-evaporation models. These models are constrained with a global conservation law that the particle number at each height is conserved modulo $Q$. In equilibrium, the stationary roughness is anomalous but universal with roughness exponent $\alpha=1/3$, while the early time evolution shows nonuniversal behavior with growth exponent $\beta$ varying with models and $Q$. Nonequilibrium surfaces display diverse growing/stationary behavior. The $Q$-mer model shows a faceted structure, while the $Q$-particle-correlated model a macroscopically grooved structure.Comment: 16 pages, 10 figures, revte

Weighted Evolving Networks

Many biological, ecological and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most network models studied so far are binary, the link strength being either 0 or 1. In this paper we introduce and investigate the scaling properties of a class of models which assign weights to the links as the network evolves. The combined numerical and analytical approach indicates that asymptotically the total weight distribution converges to the scaling behavior of the connectivity distribution, but this convergence is hampered by strong logarithmic corrections.Comment: 5 pages, 3 figure

Self-similar disk packings as model spatial scale-free networks

The network of contacts in space-filling disk packings, such as the Apollonian packing, are examined. These networks provide an interesting example of spatial scale-free networks, where the topology reflects the broad distribution of disk areas. A wide variety of topological and spatial properties of these systems are characterized. Their potential as models for networks of connected minima on energy landscapes is discussed.Comment: 13 pages, 12 figures; some bugs fixed and further discussion of higher-dimensional packing