Limited resolution and multiresolution methods in complex network community detection

Detecting community structure in real-world networks is a challenging problem. Recently, it has been shown that the resolution of methods based on optimizing a modularity measure or a corresponding energy is limited; communities with sizes below some threshold remain unresolved. One possibility to go around this problem is to vary the threshold by using a tuning parameter, and investigate the community structure at variable resolutions. Here, we analyze the resolution limit and multiresolution behavior for two different methods: a q-state Potts method proposed by Reichard and Bornholdt, and a recent multiresolution method by Arenas, Fernandez, and Gomez. These methods are studied analytically, and applied to three test networks using simulated annealing.Comment: 6 pages, 2 figures.Minor changes from previous version, shortened a couple of page

A powder metallurgy austenitic stainless steel for application at very low temperatures

The Large Hadron Collider to be built at CERN will require 1232 superconducting dipole magnets operating at 1.9 K. By virtue of their mechanical properties, weldability and improved austenite stability, nitrogen enriched austenitic stainless steels have been chosen as the material for several of the structural components of these magnets. Powder Metallurgy (PM) could represent an attractive production technique for components of complex shape for which dimension tolerances, dimensional stability, weldability are key issues during fabrication, and mechanical properties, ductility and leak tightness have to be guaranteed during operation. PM Hot Isostatic Pressed test plates and prototype components of 316LN-type grade have been produced by Santasalo Powdermet Oy. They have been fully characterized and mechanically tested down to 4.2 K at CERN. The fine grained structure, the absence of residual stresses, the full isotropy of mechanical properties associated to the low level of Prior Particle Boundaries oxides resulted in superior mechanical properties and high ductility down to liquid helium temperature. The ready weldability and the leak tightness of the alloy have been demonstrated. The properties measured on test plates are comparable to those found in real components, such as prototype end covers fabricated by the same PM technique

Emergence of communities in weighted networks

Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By tuning a model parameter governing the importance of weights, the resulting networks undergo a gradual structural transition from a module free topology to one with communities. The model also reproduces many features of large social networks, including the "weak links" property.Comment: 4 pages, 5 figure

Large-scale structure of a nation-wide production network

Production in an economy is a set of firms' activities as suppliers and customers; a firm buys goods from other firms, puts value added and sells products to others in a giant network of production. Empirical study is lacking despite the fact that the structure of the production network is important to understand and make models for many aspects of dynamics in economy. We study a nation-wide production network comprising a million firms and millions of supplier-customer links by using recent statistical methods developed in physics. We show in the empirical analysis scale-free degree distribution, disassortativity, correlation of degree to firm-size, and community structure having sectoral and regional modules. Since suppliers usually provide credit to their customers, who supply it to theirs in turn, each link is actually a creditor-debtor relationship. We also study chains of failures or bankruptcies that take place along those links in the network, and corresponding avalanche-size distribution.Comment: 17 pages with 8 figures; revised section VI and references adde

Comparison of remote sensing based approaches for mapping bathymetry of shallow, clear water rivers

Shallow rivers provide important habitat for various aquatic and terrestrial species. The bathymetry of such environments is, however, difficult to measure as devices and approaches have been traditionally developedmainly for deeper waters. This study addresses the mapping of shallow water bathymetry with high spatial resolution and accuracy by comparing three remote sensing (RS) approaches: one based on echo sounding (active RS) and two on photogrammetry (passive RS): bathymetric Structure from Motion (SfM) and optical modelling. The tests were conducted on a 500 m long and ~30 m wide reach of sand bedded meandering river: (1) during a rising spring flood (Q=10–15m3/s)withmediumturbidity and highwater color and; (2) during autumn low discharge (Q =4 m3/s) with low turbidity and color. Each method was used to create bathymetric models. The models were compared with high precision field measurements with a mean point spacing of 0.86 m. Echo sounding provided themost accurate (ME~−0.02 m) and precise (SDE=±0.08 m) bathymetricmodels despite the high degree of interpolation needed. However, the echo sounding-based models were spatially restricted to areas deeper than 0.2 m and no small scale bathymetric variability was captured. The quality of the bathymetric SfM was highly sensitive to flow turbidity and color and therefore depth. However, bathymetric SfM suffers less from substrate variability, turbulent flow or large stones and cobbles on the river bed than optical modelling. Color and depth did affect optical model performance, but clearly less than the bathymetric SfM. The optical model accuracy improved in autumn with lower water color and turbidity (ME = −0.05) compared to spring (ME=−0.12). Correlations between the measured and modelled depth values (r=0.96) and the models precision (SDE=0.09–0.11) were close to those achieved with echo sounding. Shadows caused by riparian vegetation restricted the spatial extent of the optical models.</p

Detecting modules in dense weighted networks with the Potts method

We address the problem of multiresolution module detection in dense weighted networks, where the modular structure is encoded in the weights rather than topology. We discuss a weighted version of the q-state Potts method, which was originally introduced by Reichardt and Bornholdt. This weighted method can be directly applied to dense networks. We discuss the dependence of the resolution of the method on its tuning parameter and network properties, using sparse and dense weighted networks with built-in modules as example cases. Finally, we apply the method to data on stock price correlations, and show that the resulting modules correspond well to known structural properties of this correlation network.Comment: 14 pages, 6 figures. v2: 1 figure added, 1 reference added, minor changes. v3: 3 references added, minor change