Adjustable reach in a network centrality based on current flows

Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. Most prominent centrality measures can be expressed as an aggregation of influence flows between pairs of nodes. As there are many ways in which influence can be defined, many different centrality measures are in use. Parametrized centralities allow further flexibility and utility by tuning the centrality calculation to the regime most appropriate for a given network. Here, we identify two categories of centrality parameters. Reach parameters control the attenuation of influence flows between distant nodes. Grasp parameters control the centrality's potential to send influence flows along multiple, often nongeodesic paths. Combining these categories with Borgatti's centrality types [S. P. Borgatti, Social Networks 27, 55-71 (2005)], we arrive at a novel classification system for parametrized centralities. Using this classification, we identify the notable absence of any centrality measures that are radial, reach parametrized, and based on acyclic, conservative flows of influence. We therefore introduce the ground-current centrality, which is a measure of precisely this type. Because of its unique position in the taxonomy, the ground-current centrality has significant advantages over similar centralities. We demonstrate that, compared to other conserved-flow centralities, it has a simpler mathematical description. Compared to other reach centralities, it robustly preserves an intuitive rank ordering across a wide range of network architectures. We also show that it produces a consistent distribution of centrality values among the nodes, neither trivially equally spread (delocalization), nor overly focused on a few nodes (localization). Other reach centralities exhibit both of these behaviors on regular networks and hub networks, respectively

Absorbing Random Walks Interpolating Between Centrality Measures on Complex Networks

Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and it closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs of nodes. Here we develop a method, based on absorbing Markov chains, that enables us to continuously interpolate both of these centrality measures away from the geodesic limit and toward a limit where no restriction is placed on the length of the paths the walkers can explore. At this second limit, the interpolated betweenness and closeness centralities reduce, respectively, to the well-known it current betweenness and resistance closeness (information) centralities. The method is tested numerically on four real networks, revealing complex changes in node centrality rankings with respect to the value of the interpolation parameter. Non-monotonic betweenness behaviors are found to characterize nodes that lie close to inter-community boundaries in the studied networks

The spectro-contextual encoding and retrieval theory of episodic memory.

The spectral fingerprint hypothesis, which posits that different frequencies of oscillations underlie different cognitive operations, provides one account for how interactions between brain regions support perceptual and attentive processes (Siegel etal., 2012). Here, we explore and extend this idea to the domain of human episodic memory encoding and retrieval. Incorporating findings from the synaptic to cognitive levels of organization, we argue that spectrally precise cross-frequency coupling and phase-synchronization promote the formation of hippocampal-neocortical cell assemblies that form the basis for episodic memory. We suggest that both cell assembly firing patterns as well as the global pattern of brain oscillatory activity within hippocampal-neocortical networks represents the contents of a particular memory. Drawing upon the ideas of context reinstatement and multiple trace theory, we argue that memory retrieval is driven by internal and/or external factors which recreate these frequency-specific oscillatory patterns which occur during episodic encoding. These ideas are synthesized into a novel model of episodic memory (the spectro-contextual encoding and retrieval theory, or "SCERT") that provides several testable predictions for future research

Spin transport in proximity induced ferromagnetic graphene

Magnetic gates in close proximity to graphene can induce ferromagnetic correlations. We study the effect of such induced magnetization dependent Zeeman splittings on the graphene transport properties. We estimate that induced spin splittings of the order of \Delta ~ 5 meV could be achieved with the use of magnetic insulator gates, e.g. EuO-gates, deposited on top of graphene. We demonstrate that such splittings in proximity induced ferromagnetic graphene could be determined directly from the tunneling resonances in the linear response conductance, as the top gate creates also a tunable barrier in the graphene layer. We show how such splittings could also be determined independently by magnetoresistance measurements in a spin-valve geometry. Because the spin polarization of the current near the Dirac point increases with the length of the barrier, long magnetic gates are desirable for determining \Delta experimentally.Comment: 9 pages, 11 figure

Non-collinear Magnetoelectronics

The electron transport properties of hybrid ferromagnetic|normal metal structures such as multilayers and spin valves depend on the relative orientation of the magnetization direction of the ferromagnetic elements. Whereas the contrast in the resistance for parallel and antiparallel magnetizations, the so-called Giant Magnetoresistance, is relatively well understood for quite some time, a coherent picture for non-collinear magnetoelectronic circuits and devices has evolved only recently. We review here such a theory for electron charge and spin transport with general magnetization directions that is based on the semiclassical concept of a vector spin accumulation. In conjunction with first-principles calculations of scattering matrices many phenomena, e.g. the current-induced spin-transfer torque, can be understood and predicted quantitatively for different material combinations.Comment: 163 pages, to be published in Physics Report

Intrinsic Domain Wall Resistance in Ferromagnetic Semiconductors

Transport through zincblende magnetic semiconductors with magnetic domain walls is studied theoretically. We show that these magnetic domain walls have an intrinsic resistance due to the spin-orbit interaction. The intrinsic resistance is independent of the domain wall shape and width when the latter is larger than the Fermi wavelength. For typical parameters, the intrinsic domain wall resistance is comparable to the Sharvin resistance and should be experimentally measurable.Comment: Final versio

Spontaneous-Symmetry-Breaking Mechanism of Adiabatic Pumping

We consider heterostructures consisting of regions with a continuous symmetry in contact with regions wherein the symmetry is spontaneously broken. The low-frequency dynamics of the corresponding order parameter are shown to induce nonequilibrium transport, a ``pumping,'' out of the symmetry-broken regions, which is governed by the generator of the broken-symmetry operator. This pumping damps Goldstone-mode excitations and transfers them beyond traditional (static) proximity length scales. Our general conclusions are discussed for specific examples of order parameters in helimagnets, charge/spin-density waves, superconductors, and ferromagnets. We carry out a detailed calculation of such pumping for spiral magnetic orders in helimagnets possessing a duality in the representation of its symmetry-broken states.Comment: 5 pages, 2 figure

Dynamics of Multidimensional Secession

We explore a generalized Seceder Model with variable size selection groups and higher dimensional genotypes, uncovering its well-defined mean-field limiting behavior. Mapping to a discrete, deterministic version, we pin down the upper critical size of the multiplet selection group, characterize all relevant dynamically stable fixed points, and provide a complete analytical description of its self-similar hierarchy of multiple branch solutions.Comment: 4 pages, 4 figures, PR