Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Fractal dimension and size scaling of domains in thin films of multiferroic BiFeO3

We have analyzed the morphology of ferroelectric domains in very thin films of multiferroic BiFeO3. Unlike the more common stripe domains observed in thicker films BiFeO3 or in other ferroics, the domains tend not to be straight, but irregular in shape, with significant domain wall roughening leading to a fractal dimensionality. Also contrary to what is usually observed in other ferroics, the domain size appears not to scale as the square root of the film thickness. A model is proposed in which the observed domain size as a function of film thickness can be directly linked to the fractal dimension of the domains.Comment: 4 pages, 3 figure

Application of multidisciplinary optimization methods to the design of a supersonic transport

An optimization design method is discussed. This method is based on integrating existing disciplinary analysis and sensitivity analysis techniques by means of generalized sensitivity equations. A generic design system implementing this method is described. The system is being used to design the configuration and internal structure of a supersonic transport wing for optimum performance. This problem combines the disciplines of linear aerodynamics, structures, and performance. Initial results which include the disciplines of aerodynamics and structures in a conventional minimum weight design under static aeroelastic constraints are presented

Nearly total spin polarization in La2/3Sr1/3MnO3 from tunneling experiments

We have performed magnetotransport measurements on La2/3Sr1/3MnO3 / SrTiO3 / La2/3Sr1/3MnO3 magnetic tunnel junctions. A magnetoresistance ratio of more than 1800 % is obtained at 4K, from which we infer an electrode spin polarization of at least 95 %. This result strongly underscores the half-metallic nature of mixed-valence manganites and demonstrates its capability as a spin analyzer. The magnetoresistance extends up to temperatures of more than 270K. We argue that these improvements over most previous works may result from optimizing the patterning process for oxide heterostructures.Comment: to appear in Applied Physics Letter

Co-doped (La,Sr)TiO3-d: a high-Curie temperature diluted magnetic system with large spin-polarization

We report on tunneling magnetoresistance (TMR) experiments that demonstrate the existence of a significant spin polarization in Co-doped (La,Sr)TiO3-d (Co-LSTO), a ferromagnetic diluted magnetic oxide system (DMOS) with high Curie temperature. These TMR experiments have been performed on magnetic tunnel junctions associating Co-LSTO and Co electrodes. Extensive structural analysis of Co-LSTO combining high-resolution transmission electron microscopy and Auger electron spectroscopy excluded the presence of Co clusters in the Co-LSTO layer and thus, the measured ferromagnetism and high spin polarization are intrinsic properties of this DMOS. Our results argue for the DMOS approach with complex oxide materials in spintronics

Spatial correlations in attribute communities

Community detection is an important tool for exploring and classifying the properties of large complex networks and should be of great help for spatial networks. Indeed, in addition to their location, nodes in spatial networks can have attributes such as the language for individuals, or any other socio-economical feature that we would like to identify in communities. We discuss in this paper a crucial aspect which was not considered in previous studies which is the possible existence of correlations between space and attributes. Introducing a simple toy model in which both space and node attributes are considered, we discuss the effect of space-attribute correlations on the results of various community detection methods proposed for spatial networks in this paper and in previous studies. When space is irrelevant, our model is equivalent to the stochastic block model which has been shown to display a detectability-non detectability transition. In the regime where space dominates the link formation process, most methods can fail to recover the communities, an effect which is particularly marked when space-attributes correlations are strong. In this latter case, community detection methods which remove the spatial component of the network can miss a large part of the community structure and can lead to incorrect results.Comment: 10 pages and 7 figure

Surface effects on nanowire transport: numerical investigation using the Boltzmann equation

A direct numerical solution of the steady-state Boltzmann equation in a cylindrical geometry is reported. Finite-size effects are investigated in large semiconducting nanowires using the relaxation-time approximation. A nanowire is modelled as a combination of an interior with local transport parameters identical to those in the bulk, and a finite surface region across whose width the carrier density decays radially to zero. The roughness of the surface is incorporated by using lower relaxation-times there than in the interior. An argument supported by our numerical results challenges a commonly used zero-width parametrization of the surface layer. In the non-degenerate limit, appropriate for moderately doped semiconductors, a finite surface width model does produce a positive longitudinal magneto-conductance, in agreement with existing theory. However, the effect is seen to be quite small (a few per cent) for realistic values of the wire parameters even at the highest practical magnetic fields. Physical insights emerging from the results are discussed.Comment: 15 pages, 7 figure

Quantification of valvular regurgitation by cardiac blood pool scintigraphy: correlation with catheterization

The diagnosis of valvular regurgitation (R) is usually based on clinical signs. Quantification conventionally requires catheterization (C). We have quantified R with cardiac blood pool scintigraphy (CBPS) and compared the results with those obtained by C. Regurgitant fraction (RF) determined by C was calculated with the technique of Dodge. Forward output was measured by thermodilution or cardiogreen dilution. The RF at CBPS was obtained by the stroke index ratio (SIR) minus 1.2 divided by SIR, where SIR is the ratio of the stroke counts of left venticle over those of the right ventricle. Stroke counts are calculated directly from the time-activity curves. Each time-activity curve was obtained by drawing one region of interest around each diastolic image. The correction factor (1.2) was calculated from a large normal population. 22 patients had aortic R, 7 mitral R, 12 both, 8 patients had no evidence of regurgitation. RF of the patients with R varied from 27 to 71% (x = 42%) at C and from 26 to 74% (Y = 41%) at CBPS. Linear regression shows a good correlation coefficient (r = 0.82). The regression equation is y = 0.93x + 1.8. No correlation was found between RF (CBPS or C) and the severity of R assessed visually from angiography. In conclusion: CBPS, a non-invasive method, allows easy and repeatable determination of RF and correlates well with data obtained at catheterizatio