69,722 research outputs found
Encoding Robust Representation for Graph Generation
Generative networks have made it possible to generate meaningful signals such
as images and texts from simple noise. Recently, generative methods based on
GAN and VAE were developed for graphs and graph signals. However, the
mathematical properties of these methods are unclear, and training good
generative models is difficult. This work proposes a graph generation model
that uses a recent adaptation of Mallat's scattering transform to graphs. The
proposed model is naturally composed of an encoder and a decoder. The encoder
is a Gaussianized graph scattering transform, which is robust to signal and
graph manipulation. The decoder is a simple fully connected network that is
adapted to specific tasks, such as link prediction, signal generation on graphs
and full graph and signal generation. The training of our proposed system is
efficient since it is only applied to the decoder and the hardware requirements
are moderate. Numerical results demonstrate state-of-the-art performance of the
proposed system for both link prediction and graph and signal generation.Comment: 9 pages, 7 figures, 6 table
Hydrogenic states of monopoles in diluted quantum spin ice
We consider the effect of adding quantum dynamics to a classical topological
spin liquid, with particular view to how best to detect its presence in
experiment. For the Coulomb phase of spin ice, we find quantum effects to be
most visible in the gauge-charged monopole excitations. In the presence of weak
dilution with nonmagnetic ions we find a particularly crisp phenomenon, namely
the emergence of hydrogenic excited states in which a magnetic monopole is
bound to a vacancy at various distances. Via a mapping to an analytically
tractable single particle problem on the Bethe lattice, we obtain an
approximate expression for the dynamic neutron scattering structure factor.Comment: 4 pages, 4 figures; supplemental material: 3 pages, 2 figure
Local and average behavior in inhomogeneous superdiffusive media
We consider a random walk on one-dimensional inhomogeneous graphs built from
Cantor fractals. Our study is motivated by recent experiments that demonstrated
superdiffusion of light in complex disordered materials, thereby termed L\'evy
glasses. We introduce a geometric parameter which plays a role
analogous to the exponent characterizing the step length distribution in random
systems. We study the large-time behavior of both local and average
observables; for the latter case, we distinguish two different types of
averages, respectively over the set of all initial sites and over the
scattering sites only. The "single long jump approximation" is applied to
analytically determine the different asymptotic behaviours as a function of
and to understand their origin. We also discuss the possibility that
the root of the mean square displacement and the characteristic length of the
walker distribution may grow according to different power laws; this anomalous
behaviour is typical of processes characterized by L\'evy statistics and here,
in particular, it is shown to influence average quantities
Propagation of Discrete Solitons in Inhomogeneous Networks
In many physical applications solitons propagate on supports whose
topological properties may induce new and interesting effects. In this paper,
we investigate the propagation of solitons on chains with a topological
inhomogeneity generated by the insertion of a finite discrete network on the
chain. For networks connected by a link to a single site of the chain, we
derive a general criterion yielding the momenta for perfect reflection and
transmission of traveling solitons and we discuss solitonic motion on chains
with topological inhomogeneities
Spin-polarized Quantum Transport in Mesoscopic Conductors: Computational Concepts and Physical Phenomena
Mesoscopic conductors are electronic systems of sizes in between nano- and
micrometers, and often of reduced dimensionality. In the phase-coherent regime
at low temperatures, the conductance of these devices is governed by quantum
interference effects, such as the Aharonov-Bohm effect and conductance
fluctuations as prominent examples. While first measurements of quantum charge
transport date back to the 1980s, spin phenomena in mesoscopic transport have
moved only recently into the focus of attention, as one branch of the field of
spintronics. The interplay between quantum coherence with confinement-,
disorder- or interaction-effects gives rise to a variety of unexpected spin
phenomena in mesoscopic conductors and allows moreover to control and engineer
the spin of the charge carriers: spin interference is often the basis for
spin-valves, -filters, -switches or -pumps. Their underlying mechanisms may
gain relevance on the way to possible future semiconductor-based spin devices.
A quantitative theoretical understanding of spin-dependent mesoscopic
transport calls for developing efficient and flexible numerical algorithms,
including matrix-reordering techniques within Green function approaches, which
we will explain, review and employ.Comment: To appear in the Encyclopedia of Complexity and System Scienc
Quantum channels in nonlinear optical processes
Quantum electrodynamics furnishes a new type of representation for the characterisation of nonlinear optical processes. The treatment elicits the detailed role and interplay of specific quantum channels, information that is not afforded by other methods. Following an illustrative application to the case of Rayleigh scattering, the method is applied to second and third harmonic generation. Derivations are given of parameters that quantify the various quantum channels and their interferences; the results are illustrated graphically. With given examples, it is shown in some systems that optical nonlinearity owes its origin to an isolated channel, or a small group of channels. © 2009 World Scientific Publishing Company
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