Multiparty multilevel Greenberger-Horne-Zeilinger states

The proof of Bell's theorem without inequalities by Greenberger, Horne, and Zeilinger (GHZ) is extended to multiparticle multilevel systems. The proposed procedure generalizes previous partial results and provides an operational characterization of the so-called GHZ states for multiparticle multilevel systems.Comment: REVTeX, 5 pages, 1 figur

Multilevel comparison of large urban systems

For the first time the systems of cities in seven countries or regions among the largest in the world (China, India, Brazil, Europe, the Former Soviet Union (FSU), the United States and South Africa) are made comparable through the building of spatio-temporal standardised statistical databases. We first explain the concept of a generic evolutionary urban unit ("city") and its necessary adaptations to the information provided by each national statistical system. Second, the hierarchical structure and the urban growth process are compared at macro-scale for the seven countries with reference to Zipf's and Gibrat's model: in agreement with an evolutionary theory of urban systems, large similarities shape the hierarchical structure and growth processes in BRICS countries as well as in Europe and United States, despite their positions at different stages in the urban transition that explain some structural peculiarities. Third, the individual trajectories of some 10,000 cities are mapped at micro-scale following a cluster analysis of their evolution over the last fifty years. A few common principles extracted from the evolutionary theory of urban systems can explain the diversity of these trajectories, including a specific pattern in their geographical repartition in the Chinese case. We conclude that the observations at macro-level when summarized as stylised facts can help in designing simulation models of urban systems whereas the urban trajectories identified at micro-level are consistent enough for constituting the basis of plausible future population projections.Comment: 14 pages, 9 figures; Pumain, Denise, et al. "Multilevel comparison of large urban systems." Cybergeo: European Journal of Geography (2015

Molecular Networks in Dynamic Multilevel Systems

Dynamic multilevel systems can be assembled from molecular building blocks through two or more reversible reactions that form covalent bonds. Molecular networks of dynamic multilevel systems can exhibit different connectivities between nodes. The design and creation of molecular networks in multilevel systems require control of the crossed reactivity of the functional groups (how to connect nodes) and the conditions of the reactions (when to connect nodes). In recent years, the combination of orthogonal and communicating reactions, which can be simultaneous or individually activated, has produced a variety of systems that have given rise to macrocycles and cages, as well as molecular motors and multicomponent architectures on surfaces. A given set of reactions can lead to systems with unique responsiveness, compositions, and functions as a result of the relative reactivities. In this Concept article, different molecular networks from synthetic systems that can be produced by combinations of different reaction types are discussed. Moreover, applications of this chemistry are highlighted, and future perspectives are envisioned.Fil: Orrillo, Alfredo Gastón. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas; ArgentinaFil: Escalante, Andrea Marta. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas; ArgentinaFil: Martinez Amezaga, Maitena. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas; ArgentinaFil: Cabezudo, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas; ArgentinaFil: Furlan, Ricardo Luis Eugenio. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Hypernetworks for reconstructing the dynamics of multilevel systems

Networks are fundamental for reconstructing the dynamics of many systems, but have the drawback that they are restricted to binary relations. Hypergraphs extend relational structure to multi-vertex edges, but are essentially set-theoretic and unable to represent essential structural properties. Hypernetworks are a natural multidimensional generalisation of networks, representing n-ary relations by simplices with n vertices. The assembly of vertices to make simplices is key for moving between levels in multilevel systems, and integrating dynamics between levels. It is argued that hypernetworks are necessary, if not sufficient, for reconstructing the dynamics of multilevel complex systems

Multilevel compression of random walks on networks reveals hierarchical organization in large integrated systems

To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between compression and pattern detection; by compressing a description of a random walker as a proxy for real flow on a network, we find regularities in the network that induce this system-wide flow. Finding the shortest multilevel description of the random walker therefore gives us the best hierarchical clustering of the network, the optimal number of levels and modular partition at each level, with respect to the dynamics on the network. With a novel search algorithm, we extract and illustrate the rich multilevel organization of several large social and biological networks. For example, from the global air traffic network we uncover countries and continents, and from the pattern of scientific communication we reveal more than 100 scientific fields organized in four major disciplines: life sciences, physical sciences, ecology and earth sciences, and social sciences. In general, we find shallow hierarchical structures in globally interconnected systems, such as neural networks, and rich multilevel organizations in systems with highly separated regions, such as road networks.Comment: 11 pages, 5 figures. For associated code, see http://www.tp.umu.se/~rosvall/code.htm