1,351 research outputs found
Approximating the largest eigenvalue of network adjacency matrices
The largest eigenvalue of the adjacency matrix of a network plays an
important role in several network processes (e.g., synchronization of
oscillators, percolation on directed networks, linear stability of equilibria
of network coupled systems, etc.). In this paper we develop approximations to
the largest eigenvalue of adjacency matrices and discuss the relationships
between these approximations. Numerical experiments on simulated networks are
used to test our results.Comment: 7 pages, 4 figure
FPTAS for Weighted Fibonacci Gates and Its Applications
Fibonacci gate problems have severed as computation primitives to solve other
problems by holographic algorithm and play an important role in the dichotomy
of exact counting for Holant and CSP frameworks. We generalize them to weighted
cases and allow each vertex function to have different parameters, which is a
much boarder family and #P-hard for exactly counting. We design a fully
polynomial-time approximation scheme (FPTAS) for this generalization by
correlation decay technique. This is the first deterministic FPTAS for
approximate counting in the general Holant framework without a degree bound. We
also formally introduce holographic reduction in the study of approximate
counting and these weighted Fibonacci gate problems serve as computation
primitives for approximate counting. Under holographic reduction, we obtain
FPTAS for other Holant problems and spin problems. One important application is
developing an FPTAS for a large range of ferromagnetic two-state spin systems.
This is the first deterministic FPTAS in the ferromagnetic range for two-state
spin systems without a degree bound. Besides these algorithms, we also develop
several new tools and techniques to establish the correlation decay property,
which are applicable in other problems
The onset of synchronization in large networks of coupled oscillators
We study the transition from incoherence to coherence in large networks of
coupled phase oscillators. We present various approximations that describe the
behavior of an appropriately defined order parameter past the transition, and
generalize recent results for the critical coupling strength. We find that,
under appropriate conditions, the coupling strength at which the transition
occurs is determined by the largest eigenvalue of the adjacency matrix. We show
how, with an additional assumption, a mean field approximation recently
proposed is recovered from our results. We test our theory with numerical
simulations, and find that it describes the transition when our assumptions are
satisfied. We find that our theory describes the transition well in situations
in which the mean field approximation fails. We study the finite size effects
caused by nodes with small degree and find that they cause the critical
coupling strength to increase.Comment: To appear in PRE; Added an Appendix, a reference, modified two
figures and improved the discussion of the range of validity of perturbative
approache
Statistical Properties of Avalanches in Networks
We characterize the distributions of size and duration of avalanches
propagating in complex networks. By an avalanche we mean the sequence of events
initiated by the externally stimulated `excitation' of a network node, which
may, with some probability, then stimulate subsequent firings of the nodes to
which it is connected, resulting in a cascade of firings. This type of process
is relevant to a wide variety of situations, including neuroscience, cascading
failures on electrical power grids, and epidemology. We find that the
statistics of avalanches can be characterized in terms of the largest
eigenvalue and corresponding eigenvector of an appropriate adjacency matrix
which encodes the structure of the network. By using mean-field analyses,
previous studies of avalanches in networks have not considered the effect of
network structure on the distribution of size and duration of avalanches. Our
results apply to individual networks (rather than network ensembles) and
provide expressions for the distributions of size and duration of avalanches
starting at particular nodes in the network. These findings might find
application in the analysis of branching processes in networks, such as
cascading power grid failures and critical brain dynamics. In particular, our
results show that some experimental signatures of critical brain dynamics
(i.e., power-law distributions of size and duration of neuronal avalanches),
are robust to complex underlying network topologies.Comment: 11 pages, 7 figure
Dynamics and Pattern Formation in Large Systems of Spatially-Coupled Oscillators with Finite Response Times
We consider systems of many spatially distributed phase oscillators that
interact with their neighbors. Each oscillator is allowed to have a different
natural frequency, as well as a different response time to the signals it
receives from other oscillators in its neighborhood. Using the ansatz of Ott
and Antonsen (Ref. \cite{OA1}) and adopting a strategy similar to that employed
in the recent work of Laing (Ref. \cite{Laing2}), we reduce the microscopic
dynamics of these systems to a macroscopic partial-differential-equation
description. Using this macroscopic formulation, we numerically find that
finite oscillator response time leads to interesting spatio-temporal dynamical
behaviors including propagating fronts, spots, target patterns, chimerae,
spiral waves, etc., and we study interactions and evolutionary behaviors of
these spatio-temporal patterns
A model for microinstability destabilization and enhanced transport in the presence of shielded 3-D magnetic perturbations
A mechanism is presented that suggests shielded 3-D magnetic perturbations
can destabilize microinstabilities and enhance the associated anomalous
transport. Using local 3-D equilibrium theory, shaped tokamak equilibria with
small 3-D deformations are constructed. In the vicinity of rational magnetic
surfaces, the infinite-n ideal MHD ballooning stability boundary is strongly
perturbed by the 3-D modulations of the local magnetic shear associated with
the presence of nearresonant Pfirsch-Schluter currents. These currents are
driven by 3-D components of the magnetic field spectrum even when there is no
resonant radial component. The infinite-n ideal ballooning stability boundary
is often used as a proxy for the onset of virulent kinetic ballooning modes
(KBM) and associated stiff transport. These results suggest that the achievable
pressure gradient may be lowered in the vicinity of low order rational surfaces
when 3-D magnetic perturbations are applied. This mechanism may provide an
explanation for the observed reduction in the peak pressure gradient at the top
of the edge pedestal during experiments where edge localized modes have been
completely suppressed by applied 3-D magnetic fields
Non anomalous U(1)_H gauge model of flavor
A non anomalous horizontal gauge symmetry can be responsible for the
fermion mass hierarchies of the minimal supersymmetric standard model. Imposing
the consistency conditions for the absence of gauge anomalies yields the
following results: i) unification of leptons and down-type quarks Yukawa
couplings is allowed at most for two generations. ii) The term is
necessarily somewhat below the supersymmetry breaking scale. iii) The
determinant of the quark mass matrix vanishes, and there is no strong
problem. iv) The superpotential has accidental and symmetries. The
prediction allows for an unambiguous test of the model at low
energy.Comment: 5 pages, RevTex. Title changed, minor modifications. Final version to
appear in Phys. Rev.
From Multiview Image Curves to 3D Drawings
Reconstructing 3D scenes from multiple views has made impressive strides in
recent years, chiefly by correlating isolated feature points, intensity
patterns, or curvilinear structures. In the general setting - without
controlled acquisition, abundant texture, curves and surfaces following
specific models or limiting scene complexity - most methods produce unorganized
point clouds, meshes, or voxel representations, with some exceptions producing
unorganized clouds of 3D curve fragments. Ideally, many applications require
structured representations of curves, surfaces and their spatial relationships.
This paper presents a step in this direction by formulating an approach that
combines 2D image curves into a collection of 3D curves, with topological
connectivity between them represented as a 3D graph. This results in a 3D
drawing, which is complementary to surface representations in the same sense as
a 3D scaffold complements a tent taut over it. We evaluate our results against
truth on synthetic and real datasets.Comment: Expanded ECCV 2016 version with tweaked figures and including an
overview of the supplementary material available at
multiview-3d-drawing.sourceforge.ne
Potential use of antibodies to provide an earlier indication of lymphatic filariasis resurgence in post–mass drug ad ministration surveillance in American Samoa
Background: Under the Global Programme to Eliminate Lymphatic Filariasis (LF), American Samoa conducted 7 rounds of mass drug administration (MDA) between 2000 and 2006. The territory passed transmission assessment surveys (TASs) in 2011 (TAS-1) and 2015 (TAS-2). In 2016, the territory failed TAS-3, indicating resurgence. This study aims to determine if antibodies (Abs) may have provided a timelier indication of LF resurgence in American Samoa.
Methods: We examined school-level antigen (Ag) and Ab status (presence/absence of Ag- and Ab-positive children) and prevalence of single and combined Ab responses to Wb123, Bm14, and Bm33 Ags at each TAS. Pearson chi-square test and logistic regression were used to examine associations between school-level Ab prevalence in TAS-1 and TAS-2 and school-level Ag status in TAS-3.
Results: Schools with higher prevalence of Wb123 Ab in TAS-2 had higher odds of being Ag-positive in TAS-3 (odds ratio [OR] 24.5, 95% confidence interval [CI] 1.2–512.7). Schools that were Ab-positive for WB123 plus Bm14, Bm33, or both Bm14 and Bm33 in TAS-2 had higher odds of being Ag-positive in TAS-3 (OR 16.0–24.5).
Conclusion: Abs could provide earlier signals of resurgence and enable a timelier response. The promising role of Abs in surveillance after MDA and decision making should be further investigated in other settings
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