354 research outputs found
Spectral properties of Google matrix of Wikipedia and other networks
We study the properties of eigenvalues and eigenvectors of the Google matrix
of the Wikipedia articles hyperlink network and other real networks. With the
help of the Arnoldi method we analyze the distribution of eigenvalues in the
complex plane and show that eigenstates with significant eigenvalue modulus are
located on well defined network communities. We also show that the correlator
between PageRank and CheiRank vectors distinguishes different organizations of
information flow on BBC and Le Monde web sites.Comment: 10 pages, 9 figure
Google matrix analysis of directed networks
In past ten years, modern societies developed enormous communication and
social networks. Their classification and information retrieval processing
become a formidable task for the society. Due to the rapid growth of World Wide
Web, social and communication networks, new mathematical methods have been
invented to characterize the properties of these networks on a more detailed
and precise level. Various search engines are essentially using such methods.
It is highly important to develop new tools to classify and rank enormous
amount of network information in a way adapted to internal network structures
and characteristics. This review describes the Google matrix analysis of
directed complex networks demonstrating its efficiency on various examples
including World Wide Web, Wikipedia, software architecture, world trade, social
and citation networks, brain neural networks, DNA sequences and Ulam networks.
The analytical and numerical matrix methods used in this analysis originate
from the fields of Markov chains, quantum chaos and Random Matrix theory.Comment: 56 pages, 58 figures. Missed link added in network example of Fig3
Transient features of quantum open maps
We study families of open chaotic maps that classically share the same
asymptotic properties -- forward and backwards trapped sets, repeller
dimensions, escape rate -- but differ in their short time behavior. When these
maps are quantized we find that the fine details of the distribution of
resonances and the corresponding eigenfunctions are sensitive to the initial
shape and size of the openings. We study phase space localization of the
resonances with respect to the repeller and find strong delocalization effects
when the area of the openings is smaller than .Comment: 7 pages, 7 figure
Breaking Free with AI: The Deconfinement Transition
Employing supervised machine learning techniques, we investigate the
deconfinement phase transition within -dimensional Yang-Mills (YM)
theory, compactified on a small circle and endowed with center-stabilizing
potential. This exploration encompasses scenarios both without and with matter
in either the fundamental or adjoint representations. Central to our study is a
profound duality relationship, intricately mapping the YM theory onto an
XY-spin model with -preserving perturbations. The parameter
embodies the essence of the matter representation, with values of and
for fundamental and adjoint representations, respectively, while
corresponds to pure YM theory. The logistic regression method struggles to
produce satisfactory results, particularly in predicting the transition
temperature. Contrarily, convolutional neural networks (CNNs) exhibit
remarkable prowess, effectively foreseeing critical temperatures in cases where
and . Furthermore, by harnessing CNNs, we compute critical exponents
at the transition, aligning favorably with computations grounded in
conventional order parameters. Taking our investigation a step further, we use
CNNs to lend meaning to phases within YM theory with fundamental matter.
Notably, this theory lacks conventional order parameters. Interestingly, CNNs
manage to predict a transition temperature in this context. However, the
fragility of this prediction under variations in the boundaries of the training
window undermines its utility as a robust order parameter. This outcome
underscores the constraints inherent in employing supervised machine learning
techniques as innovative substitutes for traditional order parameters.Comment: 12 pages, 8 figure
Fractal Weyl law for Linux Kernel Architecture
We study the properties of spectrum and eigenstates of the Google matrix of a
directed network formed by the procedure calls in the Linux Kernel. Our results
obtained for various versions of the Linux Kernel show that the spectrum is
characterized by the fractal Weyl law established recently for systems of
quantum chaotic scattering and the Perron-Frobenius operators of dynamical
maps. The fractal Weyl exponent is found to be that
corresponds to the fractal dimension of the network . The
eigenmodes of the Google matrix of Linux Kernel are localized on certain
principal nodes. We argue that the fractal Weyl law should be generic for
directed networks with the fractal dimension .Comment: RevTex 6 pages, 7 figs, linked to arXiv:1003.5455[cs.SE]. Research at
http://www.quantware.ups-tlse.fr/, Improved version, changed forma
Dynamical thermalization of interacting fermionic atoms in a sinai oscillator trap
We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that, for a many-body system of cold atoms, the interactions, with a strength above a certain quantum chaos border given by the Åberg criterion, lead to the Fermi–Dirac distribution and relaxation of many-body initial states to the thermalized state in the absence of any contact with a thermostate. We discuss the properties of this dynamical thermalization and its links with the Loschmidt–Boltzmann dispute.Fil: Frahm, Klaus M.. Université Paul Sabatier; Francia. Centre National de la Recherche Scientifique; FranciaFil: Ermann, Leonardo. Comisión Nacional de Energía Atómica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Shepelyansky, Dima L.. Université Paul Sabatier; Franci
On the environmental stability of quantum chaotic ratchets
The transitory and stationary behavior of a quantum chaotic ratchet
consisting of a biharmonic potential under the effect of different drivings in
contact with a thermal environment is studied. For weak forcing and finite
, we identify a strong dependence of the current on the structure of the
chaotic region. Moreover, we have determined the robustness of the current
against thermal fluctuations in the very weak coupling regime. In the case of
strong forcing, the current is determined by the shape of a chaotic attractor.
In both cases the temperature quickly stabilizes the ratchet, but in the latter
it also destroys the asymmetry responsible for the current generation. Finally,
applications to isomerization reactions are discussed.Comment: 6 pages, 5 figure
Google matrix of business process management
Development of efficient business process models and determination of their
characteristic properties are subject of intense interdisciplinary research.
Here, we consider a business process model as a directed graph. Its nodes
correspond to the units identified by the modeler and the link direction
indicates the causal dependencies between units. It is of primary interest to
obtain the stationary flow on such a directed graph, which corresponds to the
steady-state of a firm during the business process. Following the ideas
developed recently for the World Wide Web, we construct the Google matrix for
our business process model and analyze its spectral properties. The importance
of nodes is characterized by Page-Rank and recently proposed CheiRank and
2DRank, respectively. The results show that this two-dimensional ranking gives
a significant information about the influence and communication properties of
business model units. We argue that the Google matrix method, described here,
provides a new efficient tool helping companies to make their decisions on how
to evolve in the exceedingly dynamic global market.Comment: submitted to European Journal of Physics
Towards an arthritis flare-responsive drug delivery system
Local delivery of therapeutics for the treatment of inflammatory arthritis (IA) is limited by short intra-articular half-lives. Since IA severity often fluctuates over time, a local drug delivery method that titrates drug release to arthritis activity would represent an attractive paradigm in IA therapy. Here we report the development of a hydrogel platform that exhibits disassembly and drug release controlled by the concentration of enzymes expressed during arthritis flares. In vitro, hydrogel loaded with triamcinolone acetonide (TA) releases drug on-demand upon exposure to enzymes or synovial fluid from patients with rheumatoid arthritis. In arthritic mice, hydrogel loaded with a fluorescent dye demonstrates flare-dependent disassembly measured as loss of fluorescence. Moreover, a single dose of TA-loaded hydrogel but not the equivalent dose of locally injected free TA reduces arthritis activity in the injected paw. Together, our data suggest flare-responsive hydrogel as a promising next-generation drug delivery approach for the treatment of IA
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