515 research outputs found
Centrality measures for graphons: Accounting for uncertainty in networks
As relational datasets modeled as graphs keep increasing in size and their
data-acquisition is permeated by uncertainty, graph-based analysis techniques
can become computationally and conceptually challenging. In particular, node
centrality measures rely on the assumption that the graph is perfectly known --
a premise not necessarily fulfilled for large, uncertain networks. Accordingly,
centrality measures may fail to faithfully extract the importance of nodes in
the presence of uncertainty. To mitigate these problems, we suggest a
statistical approach based on graphon theory: we introduce formal definitions
of centrality measures for graphons and establish their connections to
classical graph centrality measures. A key advantage of this approach is that
centrality measures defined at the modeling level of graphons are inherently
robust to stochastic variations of specific graph realizations. Using the
theory of linear integral operators, we define degree, eigenvector, Katz and
PageRank centrality functions for graphons and establish concentration
inequalities demonstrating that graphon centrality functions arise naturally as
limits of their counterparts defined on sequences of graphs of increasing size.
The same concentration inequalities also provide high-probability bounds
between the graphon centrality functions and the centrality measures on any
sampled graph, thereby establishing a measure of uncertainty of the measured
centrality score. The same concentration inequalities also provide
high-probability bounds between the graphon centrality functions and the
centrality measures on any sampled graph, thereby establishing a measure of
uncertainty of the measured centrality score.Comment: Authors ordered alphabetically, all authors contributed equally. 21
pages, 7 figure
A Study of the Antiferromagnetic Phase in the Hubbard Model by means of the Composite Operator Method
We have investigated the antiferromagnetic phase of the 2D, the 3D and the
extended Hubbard models on a bipartite cubic lattice by means of the Composite
Operator Method within a two-pole approximation. This approach yields a fully
self-consistent treatment of the antiferromagnetic state that respects the
symmetry properties of both the model and the algebra. The complete phase
diagram, as regards the antiferromagnetic and the paramagnetic phases, has been
drawn. We firstly reported, within a pole approximation, three kinds of
transitions at half-filling: Mott-Hubbard, Mott-Heisenberg and Heisenberg. We
have also found a metal-insulator transition, driven by doping, within the
antiferromagnetic phase. This latter is restricted to a very small region near
half filling and has, in contrast to what has been found by similar approaches,
a finite critical Coulomb interaction as lower bound at half filling. Finally,
it is worth noting that our antiferromagnetic gap has two independent
components: one due to the antiferromagnetic correlations and another coming
from the Mott-Hubbard mechanism.Comment: 20 pages, 37 figures, RevTeX, submitted to Phys. Rev.
Co-evolutionnary network approach to cultural dynamics controlled by intolerance
Starting from Axelrod's model of cultural dissemination, we introduce a
rewiring probability, enabling agents to cut the links with their unfriendly
neighbors if their cultural similarity is below a tolerance parameter. For low
values of tolerance, rewiring promotes the convergence to a frozen monocultural
state. However, intermediate tolerance values prevent rewiring once the network
is fragmented, resulting in a multicultural society even for values of initial
cultural diversity in which the original Axelrod model reaches globalization
Tracking spin and charge with spectroscopy in spin-polarised 1D systems
We calculate the spectral function of a one-dimensional strongly interacting
chain of fermions, where the response can be well understood in terms of spinon
and holon excitations. Upon increasing the spin imbalance between the spin
species, we observe the single-electron response of the fully polarised system
to emanate from the holon peak while the spinon response vanishes. For
experimental setups that probe one-dimensional properties, we propose this
method as an additional generic tool to aid the identification of spectral
structures, e.g. in ARPES measurements. We show that this applies even to
trapped systems having cold atomic gas experiments in mind.Comment: 5 pages, 4 figure
Influence of the crystallization process on the luminescence of multilayers of SiGe nanocrystals embedded in SiO2
Multilayers of SiGe nanocrystals embedded in an oxide matrix have been fabricated by low-pressure chemical vapor deposition SiO2 onto Si wafers (in a single run at 390 ◦C and 50mTorr, using GeH4, Si2 H6 and O2) followed by a rapid thermal annealing crystallize the SiGe nanoparticles. The main emission band is located at 400 nm in both cathodoluminescence and photoluminescence at 80K and also at room temperature. The annealing conditions (temperatures ranging from 700 to 1000 ◦C and for times of 30 investigated in samples with different diameter of the nanoparticles (from ≈3 to ≥5 nm) and oxide interlayer thickness (15 and establish a correlation between the crystallization of the nanoparticles, the degradation of their composition by Ge diffusion the luminescence emission band. Structures with small nanoparticles (3–4.5 nm) separated by thick oxide barriers (≈35 nm) annealed 60 s yield the maximum intensity of the luminescence. An additional treatment at 450 ◦C in forming gas for dangling-bond the intensity of the luminescence band by 25–30%
Hydrogen-free SiCN films obtained by electron cyclotron resonance plasma: a study of composition, optical and luminescent properties
The Electrochemical Society, Inc. 2007. All rights reserved. Except as provided under U.S. copyright law, this work may not be reproduced, resold, distributed, or modified without the express permission of The Electrochemical Society (ECS). The archival version of this work was published in Journal of the Electrochemical Society Vol. 154 Issue 4 (2007): H325-H33
The Hubbard model within the equations of motion approach
The Hubbard model has a special role in Condensed Matter Theory as it is
considered as the simplest Hamiltonian model one can write in order to describe
anomalous physical properties of some class of real materials. Unfortunately,
this model is not exactly solved except for some limits and therefore one
should resort to analytical methods, like the Equations of Motion Approach, or
to numerical techniques in order to attain a description of its relevant
features in the whole range of physical parameters (interaction, filling and
temperature). In this manuscript, the Composite Operator Method, which exploits
the above mentioned analytical technique, is presented and systematically
applied in order to get information about the behavior of all relevant
properties of the model (local, thermodynamic, single- and two- particle ones)
in comparison with many other analytical techniques, the above cited known
limits and numerical simulations. Within this approach, the Hubbard model is
shown to be also capable to describe some anomalous behaviors of the cuprate
superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference
Is There a Major Role for Undetected Autism Spectrum Disorder with Childhood Trauma in a Patient with a Diagnosis of Bipolar Disorder, Self-Injuring, and Multiple Comorbidities?
This case report highlights the relevance of the consequences of trauma in a female patient with an undetected autism spectrum disorder (ASD) affected by bipolar disorder (BD) with multiple comorbidities. A 35-year-old woman with BD type II, binge eating disorder and panic disorder was admitted in the Inpatient Unit of the Psychiatric Clinic of the University of Pisa because of a recrudescence of depressive symptomatology, associated with increase of anxiety, noticeable ruminations, significant alteration in neurovegetative pattern, and serious suicide ideation. During the hospitalization, a diagnosis of ASD emerged besides a history of childhood trauma and affective dysregulation, marked impulsivity, feeling of emptiness, and self-harm behavior. The patient was assessed by the Autism-Spectrum Quotient (AQ), Ritvo Autism and Asperger Diagnostic Scale (RAADS-R), the Adult Autism Subthreshold Spectrum (AdAS Spectrum), Trauma and Loss Spectrum (TALS-SR), and Ruminative Response Scale (RRS). Total scores of 38/50 in the AQ, 146/240 in the RAADS-R, 99/160 in the AdAS Spectrum emerged, compatible with ASD, 47/116 in the TALS-SR, and 64/88 in the RRS. We discuss the implications of the trauma she underwent during her childhood, in the sense that caused a complex posttraumatic disorder, a lifelong disease favored and boosted by the rumination tendency of high functioning ASD
The phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain
By using Density Matrix Renormalization Group (DMRG) technique we study the
phase diagram of 1D extended anisotropic Heisenberg model with ferromagnetic
nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We
analyze the static correlation functions for the spin operators both in- and
out-of-plane and classify the zero-temperature phases by the range of their
correlations. On clusters of sites with open boundary
conditions we isolate the boundary effects and make finite-size scaling of our
results. Apart from the ferromagnetic phase, we identify two gapless spin-fluid
phases and two ones with massive excitations. Based on our phase diagram and on
estimates for the coupling constants known from literature, we classify the
ground states of several edge-sharing materials.Comment: 12 pages, 13 figure
Local Dynamics and Strong Correlation Physics I: 1D and 2D Half-filled Hubbard Models
We report on a non-perturbative approach to the 1D and 2D Hubbard models that
is capable of recovering both strong and weak-coupling limits. We first show
that even when the on-site Coulomb repulsion, U, is much smaller than the
bandwith, the Mott-Hubbard gap never closes at half-filling in both 1D and 2D.
Consequently, the Hubbard model at half-filling is always in the
strong-coupling non-perturbative regime. For both large and small U, we find
that the population of nearest-neighbour singlet states approaches a value of
order unity as as would be expected for antiferromagnetic order. We
also find that the double occupancy is a smooth monotonic function of U and
approaches the anticipated non-interacting limit and large U limits. Finally,
in our results for the heat capacity in 1D differ by no more than 1% from the
Bethe ansatz predictions. In addition, we find that in 2D, the heat capacity vs
T for different values of U exhibits a universal crossing point at two
characteristic temperatures as is seen experimentally in a wide range of
strongly-correlated systems such as , , and . The
success of this method in recovering well-established results that stem
fundamentally from the Coulomb interaction suggests that local dynamics are at
the heart of the physics of strongly correlated systems.Comment: 10 pages, 16 figures included in text, Final version for publication
with a reference added and minor corrections. Phys. Rev. B, in pres
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