7,827 research outputs found
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
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