983 research outputs found
Spectral Theory for Networks with Attractive and Repulsive Interactions
There is a wealth of applied problems that can be posed as a dynamical system
defined on a network with both attractive and repulsive interactions. Some
examples include: understanding synchronization properties of nonlinear
oscillator;, the behavior of groups, or cliques, in social networks; the study
of optimal convergence for consensus algorithm; and many other examples.
Frequently the problems involve computing the index of a matrix, i.e. the
number of positive and negative eigenvalues, and the dimension of the kernel.
In this paper we consider one of the most common examples, where the matrix
takes the form of a signed graph Laplacian. We show that the there are
topological constraints on the index of the Laplacian matrix related to the
dimension of a certain homology group. In certain situations, when the homology
group is trivial, the index of the operator is rigid and is determined only by
the topology of the network and is independent of the strengths of the
interactions. In general these constraints give upper and lower bounds on the
number of positive and negative eigenvalues, with the dimension of the homology
group counting the number of eigenvalue crossings. The homology group also
gives a natural decomposition of the dynamics into "fixed" degrees of freedom,
whose index does not depend on the edge-weights, and an orthogonal set of
"free" degrees of freedom, whose index changes as the edge weights change. We
also present some numerical studies of this problem for large random matrices.Comment: 27 pages; 9 Figure
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Integrative machine learning approach for multi-class SCOP protein fold classification
Classification and prediction of protein structure has been a central research theme in structural bioinformatics. Due to the imbalanced distribution of proteins over multi SCOP classification, most discriminative machine learning suffers the well-known ‘False Positives ’ problem when learning over these types of problems. We have devised eKISS, an ensemble machine learning specifically designed to increase the coverage of positive examples when learning under multiclass imbalanced data sets. We have applied eKISS to classify 25 SCOP folds and show that our learning system improved over classical learning methods
Extended Red Emission and the evolution of carbonaceaous nanograins in NGC 7023
Extended Red Emission (ERE) was recently attributed to the photo-luminescence
of either doubly ionized Polycyclic Aromatic Hydrocarbons (PAH), or
charged PAH dimers. We analysed the visible and mid-infrared (mid-IR) dust
emission in the North-West and South photo-dissociation regions of the
reflection nebula NGC 7023.Using a blind signal separation method, we extracted
the map of ERE from images obtained with the Hubble Space Telescope, and at the
Canada France Hawaii Telescope. We compared the extracted ERE image to the
distribution maps of the mid-IR emission of Very Small Grains (VSGs), neutral
and ionized PAHs (PAH and PAH) obtained with the Spitzer Space
Telescope and the Infrared Space Observatory. ERE is dominant in transition
regions where VSGs are being photo-evaporated to form free PAH molecules, and
is not observed in regions dominated by PAH. Its carrier makes a minor
contribution to the mid-IR emission spectrum. These results suggest that the
ERE carrier is a transition species formed during the destruction of VSGs.
Singly ionized PAH dimers appear as good candidates but PAH molecules
seem to be excluded.Comment: Accepted for publication in A&
Three-dimensional flow instability in a lid-driven isosceles triangular cavity
Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed
Resistance noise scaling in a 2D system in GaAs
The 1/f resistance noise of a two-dimensional (2D) hole system in a high
mobility GaAs quantum well has been measured on both sides of the 2D
metal-insulator transition (MIT) at zero magnetic field (B=0), and deep in the
insulating regime. The two measurement methods used are described: I or V
fixed, and measurement of resp. V or I fluctuations. The normalized noise
magnitude SR/R^2 increases strongly when the hole density is decreased, and its
temperature (T) dependence goes from a slight increase with T at the largest
densities, to a strong decrease at low density. We find that the noise
magnitude scales with the resistance, SR /R^2 ~ R^2.4. Such a scaling is
expected for a second order phase transition or a percolation transition. The
possible presence of such a transition is investigated by studying the
dependence of the conductivity as a function of the density. This dependence is
consistent with a critical behavior close to a critical density p* lower than
the usual MIT critical density pc.Comment: 13 pages, 8 figures, Proceedings of SPIE: Fluctuations and noise in
materials, D. Popovic, M.B. Weissman, Z.A. Racz Eds., Vol. 5469, pp. 101-113,
Mspalomas, Spain, 200
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