309,101 research outputs found
Non-Universality in Semi-Directed Barabasi-Albert Networks
In usual scale-free networks of Barabasi-Albert type, a newly added node
selects randomly m neighbors from the already existing network nodes,
proportionally to the number of links these had before. Then the number N(k) of
nodes with k links each decays as 1/k^gamma where gamma=3 is universal, i.e.
independent of m. Now we use a limited directedness in the construction of the
network, as a result of which the exponent gamma decreases from 3 to 2 for
increasing m.Comment: 5 pages including 2 figures and computer progra
On the Constant that Fixes the Area Spectrum in Canonical Quantum Gravity
The formula for the area eigenvalues that was obtained by many authors within
the approach known as loop quantum gravity states that each edge of a spin
network contributes an area proportional to sqrt{j(j+1)} times Planck length
squared to any surface it transversely intersects. However, some confusion
exists in the literature as to a value of the proportionality coefficient. The
purpose of this rather technical note is to fix this coefficient. We present a
calculation which shows that in a sector of quantum theory based on the
connection A=Gamma-gamma*K, where Gamma is the spin connection compatible with
the triad field, K is the extrinsic curvature and gamma is Immirzi parameter,
the value of the multiplicative factor is 8*pi*gamma. In other words, each edge
of a spin network contributes an area 8*pi*gamma*l_p^2*sqrt{j(j+1)} to any
surface it transversely intersects.Comment: Revtex, 7 pages, no figure
Gating of memory encoding of time-delayed cross-frequency MEG networks revealed by graph filtration based on persistent homology
To explain gating of memory encoding, magnetoencephalography (MEG) was analyzed over multi-regional network of negative correlations between alpha band power during cue (cue-alpha) and gamma band power during item presentation (item-gamma) in Remember (R) and No-remember (NR) condition. Persistent homology with graph filtration on alpha-gamma correlation disclosed topological invariants to explain memory gating. Instruction compliance (R-hits minus NR-hits) was significantly related to negative coupling between the left superior occipital (cue-alpha) and the left dorsolateral superior frontal gyri (item-gamma) on permutation test, where the coupling was stronger in R than NR. In good memory performers (R-hits minus false alarm), the coupling was stronger in R than NR between the right posterior cingulate (cue-alpha) and the left fusiform gyri (item-gamma). Gating of memory encoding was dictated by inter-regional negative alpha-gamma coupling. Our graph filtration over MEG network revealed these inter-regional time-delayed cross-frequency connectivity serve gating of memory encoding
Evolution of reference networks with aging
We study the growth of a reference network with aging of sites defined in the
following way. Each new site of the network is connected to some old site with
probability proportional (i) to the connectivity of the old site as in the
Barab\'{a}si-Albert's model and (ii) to , where is the
age of the old site. We consider of any sign although reasonable
values are . We find both from simulation and
analytically that the network shows scaling behavior only in the region . When increases from to 0, the exponent of the
distribution of connectivities ( for large ) grows
from 2 to the value for the network without aging, i.e. to 3 for the
Barab\'{a}si-Albert's model. The following increase of to 1 makes
to grow to . For the distribution is
exponentional, and the network has a chain structure.Comment: 4 pages revtex (twocolumn, psfig), 5 figure
Connectivity of Growing Random Networks
A solution for the time- and age-dependent connectivity distribution of a
growing random network is presented. The network is built by adding sites which
link to earlier sites with a probability A_k which depends on the number of
pre-existing links k to that site. For homogeneous connection kernels, A_k ~
k^gamma, different behaviors arise for gamma1, and gamma=1. For
gamma<1, the number of sites with k links, N_k, varies as stretched
exponential. For gamma>1, a single site connects to nearly all other sites. In
the borderline case A_k ~ k, the power law N_k ~k^{-nu} is found, where the
exponent nu can be tuned to any value in the range 2<nu<infinity.Comment: 4 pages, 2 figures, 2 column revtex format final version to appear in
PRL; contains additional result
A role for fast rhythmic bursting neurons in cortical gamma oscillations in vitro
Basic cellular and network mechanisms underlying gamma frequency oscillations (30–80 Hz) have been well characterized in the hippocampus and associated structures. In these regions, gamma rhythms are seen as an emergent property of networks of principal cells and fast-spiking interneurons. In contrast, in the neocortex a number of elegant studies have shown that specific types of principal neuron exist that are capable of generating powerful gamma frequency outputs on the basis of their intrinsic conductances alone. These fast rhythmic bursting (FRB) neurons (sometimes referred to as "chattering" cells) are activated by sensory stimuli and generate multiple action potentials per gamma period. Here, we demonstrate that FRB neurons may function by providing a large-scale input to an axon plexus consisting of gap-junctionally connected axons from both FRB neurons and their anatomically similar counterparts regular spiking neurons. The resulting network gamma oscillation shares all of the properties of gamma oscillations generated in the hippocampus but with the additional critical dependence on multiple spiking in FRB cells
- …