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 $64,100,200,300$ 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 $T\to 0$ 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 $^3He$, $UBe_3$, and $CeCu_{6-x}Al_x$. 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