123,484 research outputs found
Accelerated Gossip in Networks of Given Dimension using Jacobi Polynomial Iterations
Consider a network of agents connected by communication links, where each
agent holds a real value. The gossip problem consists in estimating the average
of the values diffused in the network in a distributed manner. We develop a
method solving the gossip problem that depends only on the spectral dimension
of the network, that is, in the communication network set-up, the dimension of
the space in which the agents live. This contrasts with previous work that
required the spectral gap of the network as a parameter, or suffered from slow
mixing. Our method shows an important improvement over existing algorithms in
the non-asymptotic regime, i.e., when the values are far from being fully mixed
in the network. Our approach stems from a polynomial-based point of view on
gossip algorithms, as well as an approximation of the spectral measure of the
graphs with a Jacobi measure. We show the power of the approach with
simulations on various graphs, and with performance guarantees on graphs of
known spectral dimension, such as grids and random percolation bonds. An
extension of this work to distributed Laplacian solvers is discussed. As a side
result, we also use the polynomial-based point of view to show the convergence
of the message passing algorithm for gossip of Moallemi \& Van Roy on regular
graphs. The explicit computation of the rate of the convergence shows that
message passing has a slow rate of convergence on graphs with small spectral
gap
Cluster-scaling, chaotic order and coherence in DNA
Different numerical mappings of the DNA sequences have been studied using a
new cluster-scaling method and the well known spectral methods. It is shown, in
particular, that the nucleotide sequences in DNA molecules have robust
cluster-scaling properties. These properties are relevant to both types of
nucleotide pair-bases interactions: hydrogen bonds and stacking interactions.
It is shown that taking into account the cluster-scaling properties can help to
improve heterogeneous models of the DNA dynamics. It is also shown that a
chaotic (deterministic) order, rather than a stochastic randomness, controls
the energy minima positions of the stacking interactions in the DNA sequences
on large scales. The chaotic order results in a large-scale chaotic coherence
between the two complimentary DNA-duplex's sequences. A competition between
this broad-band chaotic coherence and the resonance coherence produced by
genetic code has been briefly discussed. The Arabidopsis plant genome (which is
a model plant for genome analysis) and two human genes: BRCA2 and NRXN1, have
been considered as examples.Comment: extended. arXiv admin note: substantial text overlap with
arXiv:1008.135
Dielectric resonances in disordered media
Binary disordered systems are usually obtained by mixing two ingredients in
variable proportions: conductor and insulator, or conductor and
super-conductor. and are naturally modeled by regular bi-dimensional or
tri-dimensional lattices, on which sites or bonds are chosen randomly with
given probabilities. In this article, we calculate the impedance of the
composite by two independent methods: the so-called spectral method, which
diagonalises Kirchhoff's Laws via a Green function formalism, and the Exact
Numerical Renormalization method (ENR). These methods are applied to mixtures
of resistors and capacitors (R-C systems), simulating e.g. ionic
conductor-insulator systems, and to composites consituted of resistive
inductances and capacitors (LR-C systems), representing metal inclusions in a
dielectric bulk. The frequency dependent impedances of the latter composites
present very intricate structures in the vicinity of the percolation threshold.
We analyse the LR-C behavior of compounds formed by the inclusion of small
conducting clusters (``-legged animals'') in a dielectric medium. We
investigate in particular their absorption spectra who present a pattern of
sharp lines at very specific frequencies of the incident electromagnetic field,
the goal being to identify the signature of each animal. This enables us to
make suggestions of how to build compounds with specific absorption or
transmission properties in a given frequency domain.Comment: 10 pages, 6 figures, LaTeX document class EP
Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs
We present exact, explicit, convergent periodic-orbit expansions for
individual energy levels of regular quantum graphs. One simple application is
the energy levels of a particle in a piecewise constant potential. Since the
classical ray trajectories (including ray splitting) in such systems are
strongly chaotic, this result provides the first explicit quantization of a
classically chaotic system.Comment: 25 pages, 5 figure
Spectral determinant on quantum graphs
We study the spectral determinant of the Laplacian on finite graphs
characterized by their number of vertices V and of bonds B. We present a path
integral derivation which leads to two equivalent expressions of the spectral
determinant of the Laplacian either in terms of a V x V vertex matrix or a 2B x
2B link matrix that couples the arcs (oriented bonds) together. This latter
expression allows us to rewrite the spectral determinant as an infinite product
of contributions of periodic orbits on the graph. We also present a
diagrammatic method that permits us to write the spectral determinant in terms
of a finite number of periodic orbit contributions. These results are
generalized to the case of graphs in a magnetic field. Several examples
illustrating this formalism are presented and its application to the
thermodynamic and transport properties of weakly disordered and coherent
mesoscopic networks is discussed.Comment: 33 pages, submitted to Ann. Phy
Prediction of naturally-occurring, industrially-induced and total trans fatty acids in butter, dairy spreads and Cheddar cheese using vibrational spectroscopy and multivariate data analysis
peer-reviewedThis study investigated the use of vibrational spectroscopy [near infrared (NIR), Fourier-transform mid-infrared (FT-MIR), Raman] and multivariate data analysis for (1) quantifying total trans fatty acids (TT), and (2) separately predicting naturally-occurring (NT; i.e., C16:1 t9; C18:1 trans-n, n = 6 … 9, 10, 11; C18:2 trans) and industrially-induced trans fatty acids (IT = TT – NT) in Irish dairy products, i.e., butter (n = 60), Cheddar cheese (n = 44), and dairy spreads (n = 54). Partial least squares regression models for predicting NT, IT and TT in each type of dairy product were developed using FT-MIR, NIR and Raman spectral data. Models based on NIR, FT-MIR and Raman spectra were used for the prediction of NT and TT content in butter; best prediction performance achieved a coefficient of determination in validation (R2V) ∼ 0.91–0.95, root mean square error of prediction (RMSEP) ∼ 0.07–0.30 for NT; R2V ∼ 0.92–0.95, RMSEP ∼ 0.23–0.29 for TT.This project was funded by the Irish Department of Agriculture, Food and the Marine as part of CheeseBoard 2015. Ming Zhao is a Teagasc Walsh Fellow
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