67,982 research outputs found
A framework for evaluating complex networks measurements
A good deal of current research in complex networks involves the
characterization and/or classification of the topological properties of given
structures, which has motivated several respective measurements. This letter
proposes a framework for evaluating the quality of complex network measurements
in terms of their effective resolution, degree of degeneracy and
discriminability. The potential of the suggested approach is illustrated with
respect to comparing the characterization of several model and real-world
networks by using concentric and symmetry measurements. The results indicate a
markedly superior performance for the latter type of mapping
Structure and dynamics of core-periphery networks
Recent studies uncovered important core/periphery network structures
characterizing complex sets of cooperative and competitive interactions between
network nodes, be they proteins, cells, species or humans. Better
characterization of the structure, dynamics and function of core/periphery
networks is a key step of our understanding cellular functions, species
adaptation, social and market changes. Here we summarize the current knowledge
of the structure and dynamics of "traditional" core/periphery networks,
rich-clubs, nested, bow-tie and onion networks. Comparing core/periphery
structures with network modules, we discriminate between global and local
cores. The core/periphery network organization lies in the middle of several
extreme properties, such as random/condensed structures, clique/star
configurations, network symmetry/asymmetry, network
assortativity/disassortativity, as well as network hierarchy/anti-hierarchy.
These properties of high complexity together with the large degeneracy of core
pathways ensuring cooperation and providing multiple options of network flow
re-channelling greatly contribute to the high robustness of complex systems.
Core processes enable a coordinated response to various stimuli, decrease
noise, and evolve slowly. The integrative function of network cores is an
important step in the development of a large variety of complex organisms and
organizations. In addition to these important features and several decades of
research interest, studies on core/periphery networks still have a number of
unexplored areas.Comment: a comprehensive review of 41 pages, 2 figures, 1 table and 182
reference
Complexity, BioComplexity, the Connectionist Conjecture and Ontology of Complexity\ud
This paper develops and integrates major ideas and concepts on complexity and biocomplexity - the connectionist conjecture, universal ontology of complexity, irreducible complexity of totality & inherent randomness, perpetual evolution of information, emergence of criticality and equivalence of symmetry & complexity. This paper introduces the Connectionist Conjecture which states that the one and only representation of Totality is the connectionist one i.e. in terms of nodes and edges. This paper also introduces an idea of Universal Ontology of Complexity and develops concepts in that direction. The paper also develops ideas and concepts on the perpetual evolution of information, irreducibility and computability of totality, all in the context of the Connectionist Conjecture. The paper indicates that the control and communication are the prime functionals that are responsible for the symmetry and complexity of complex phenomenon. The paper takes the stand that the phenomenon of life (including its evolution) is probably the nearest to what we can describe with the term “complexity”. The paper also assumes that signaling and communication within the living world and of the living world with the environment creates the connectionist structure of the biocomplexity. With life and its evolution as the substrate, the paper develops ideas towards the ontology of complexity. The paper introduces new complexity theoretic interpretations of fundamental biomolecular parameters. The paper also develops ideas on the methodology to determine the complexity of “true” complex phenomena.\u
Symmetry & Controllability for Spin Networks with a Single-Node Control
We consider the relation of symmetries and subspace controllability for spin
networks with XXZ coupling subject to control of a single node by a local
potential (Z-control). Such networks decompose into excitation subspaces.
Focusing on the single excitation subspace it is shown that for single-node
Z-controls external symmetries are characterized by eigenstates of the system
Hamiltonian that have zero overlap with the control node, and there are no
internal symmetries. It is further shown that there are symmetries that persist
even in the presence of random perturbations. For uniformly coupled XXZ chains
a characterization of all possible symmetries is given, which shows a strong
dependence on the position of the node we control. Finally, it is shown
rigorously for uniform Heisenberg and XX chains subject to single-node
Z-control that the lack of symmetry is not only necessary but sufficient for
subspace controllability. The latter approach is then generalized to establish
controllability results for simple branched networks.Comment: 11 pages, some figures. 3 tables, minor revisio
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