A shadowing problem in the detection of overlapping communities: lifting the resolution limit through a cascading procedure

Community detection is the process of assigning nodes and links in significant communities (e.g. clusters, function modules) and its development has led to a better understanding of complex networks. When applied to sizable networks, we argue that most detection algorithms correctly identify prominent communities, but fail to do so across multiple scales. As a result, a significant fraction of the network is left uncharted. We show that this problem stems from larger or denser communities overshadowing smaller or sparser ones, and that this effect accounts for most of the undetected communities and unassigned links. We propose a generic cascading approach to community detection that circumvents the problem. Using real and artificial network datasets with three widely used community detection algorithms, we show how a simple cascading procedure allows for the detection of the missing communities. This work highlights a new detection limit of community structure, and we hope that our approach can inspire better community detection algorithms.Comment: 14 pages, 12 figures + supporting information (5 pages, 6 tables, 3 figures

Propagation dynamics on networks featuring complex topologies

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (nodes, vertices, individuals...) on the one hand and their recurrent topological patterns (subgraphs, groups...) on the other hand. In a SIS model of epidemic spread on social networks with community structure, this approach yields a set of ODEs for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce random networks behavior in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.Comment: 10 pages, 5 figures, 1 Appendix. Published in Phys. Rev. E (mistakes in the PRE version are corrected here

Field-Induced Magnetization Steps in Intermetallic Compounds and Manganese Oxides: The Martensitic Scenario

Field-induced magnetization jumps with similar characteristics are observed at low temperature for the intermetallic germanide Gd5Ge4and the mixed-valent manganite Pr0.6Ca0.4Mn0.96Ga0.04O3. We report that the field location -and even the existence- of these jumps depends critically on the magnetic field sweep rate used to record the data. It is proposed that, for both compounds, the martensitic character of their antiferromagnetic-to-ferromagnetic transitions is at the origin of the magnetization steps.Comment: 4 pages,4 figure

Localization, epidemic transitions, and unpredictability of multistrain epidemics with an underlying genotype network

Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. Here, we introduce a disease model with an underlying genotype network to account for two important mechanisms. One, the disease can mutate along network pathways as it spreads in a host population. Two, the genotype network allows us to define a genetic distance across strains and therefore to model the transcendence of immunity often observed in real world pathogens. We study the emergence of epidemics in this model, through its epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases, large scale fluctuations, sequential epidemic transitions, as well as localization around specific strains of the associated pathogen. More generally, our model illustrates the richness of behaviours that are possible even in well-mixed host populations once we consider strain diversity and go beyond the "one disease equals one pathogen" paradigm

Correspondence Between Continuous and Discrete 2 Flux Models for Reflectance and Transmittance of Diffusing Layers

This paper provides a theoretical connection between two different mathematical models dedicated to the reflectance and the transmittance of diffusing layers. The Kubelka–Munk model proposes a continuous description of scattering and absorption for two opposite diffuse fluxes in a homogeneous layer (continuous two-flux model). On the other hand, Kubelka's layering model describes the multiple reflections and transmissions of light taking place between various superposed diffusing layers (discrete two-flux model). The compatibility of these two models is shown. In particular, the Kubelka–Munk reflectance and transmittance expressions are retrieved, using Kubelka's layering model, with mathematical arguments using infinitely thin sublayers. A new approach to the Kubelka–Munk expressions is thus obtained, giving, moreover, new details for physical interpretation of the Kubelka–Munk theory

Pair formation and collapse in imbalanced Fermion populations with unequal masses

We present an exact Quantum Monte Carlo study of the effect of unequal masses on pair formation in Fermionic systems with population imbalance loaded into optical lattices. We have considered three forms of the attractive interaction and find in all cases that the system is unstable and collapses as the mass difference increases and that the ground state becomes an inhomogeneous collapsed state. We also address the question of canonical vs grand canonical ensemble and its role, if any, in stabilizing certain phases

The eSMAF: a software for the assessment and follow-up of functional autonomy in geriatrics

BACKGROUND: Functional status or disability forms the core of most assessment instruments used to identify mix and level of resources and services needed by older adults who possess common characteristics. The Functional Autonomy Measurement System (SMAF) is a 29-item scale measuring functional ability in five different areas. It has been recommended for use for home care, for allocation of chronic beds, for developing care plans in institutional settings and for epidemiological and evaluative studies. The SMAF can also be used with a case-mix classification system (Iso-SMAF) to allocate resources based on patients' functional autonomy characteristics. The objective of this project was to develop a software version of the SMAF to facilitate the evaluation of the functional status of older adults in health services research and to optimize the clinical decision-making process. RESULTS: The eSMAF was developed over an 24-month period using a modified waterfall software engineering process. Requirements and functional specifications were determined using focus groups of stakeholders. Different versions of the software were iteratively field-tested in clinical and research environments and software adaptations made accordingly. User documentation and online help were created to assist the deployment of the software. The software is available in French or English versions under a 30-day unregistered demonstration license or a free restricted registered academic license. It can be used locally on a Windows-based PC or over a network to input SMAF data into a database, search and aggregate client data according to clinical and/or administrative criteria, and generate summary or detailed reports of selected data sets for print or export to another database. CONCLUSION: In the last year, the software has been successfully deployed in the clinical workflow of different institutions in research and clinical applications. The software performed relatively well in terms of stability and performance. Barriers to implementation included antiquated computer hardware, low computer literacy and access to IT support. Key factors for the deployment of the software included standardization of the workflow, user training and support

Compositional reflectance and transmittance model for multilayer specimens

We propose a compositional model for predicting the reflectance and the transmittance of multilayer specimens composed of layers having possibly distinct refractive indices. The model relies on the laws of geometrical optics and on a description of the multiple reflection-transmission of light between the different layers and interfaces. The highly complex multiple reflection-transmission process occurring between several superposed layers is described by Markov chains. An optical element such as a layer or an interface forms a biface. The multiple reflection-transmission process is developed for a superposition of two bifaces. We obtain general composition formulas for the reflectance and the transmittance of a pair of layers and/or interfaces. Thanks to these compositional expressions, we can calculate the reflectance and the transmittance of three or more superposed bifaces. The model is applicable to regular compositions of bifaces, i.e., multifaces having on each face an angular light distribution that remains constant along successive reflection and transmission events. Kubelka's layering model, Saunderson's correction of the Kubelka-Munk model, and the Williams-Clapper model of a color layer superposed on a diffusing substrate are special cases of the proposed compositional model

Properties of helium bubbles in covalent systems at the nanoscale: A combined numerical and experimental study

International audienceThe properties of nanometric-sized helium bubbles in silicon have been investigated using both spatially resolved electron-energy-loss spectroscopy combined with a recently developed method, and molecular-dynamics simulations. The experiments allowed for an accurate determination of size, aspect ratio, and helium density for a large number of single bubbles, whose diameters ranged from 6 to 20 nm. Very high helium densities, from 60 to 180 He nm −3 , have been measured depending on the conditions, in stark contrast with previous investigations of helium bubbles in metal with similar sizes. To supplement experiments on a smaller scale, and to obtain insights into the silicon matrix state, atomistic calculations have been performed for helium bubbles in the diameter range 1-13 nm. Molecular-dynamics simulations revealed that the maximum attainable helium density is critically related to the strength of the silicon matrix, which tends to yield by amorphization at the highest density levels. Calculations give helium density values for isolated single bubbles that are typically lower than measurements. However, excellent agreement is recovered when the interactions between bubbles and the presence of helium interstitials in the matrix are taken into account. Both experiments and numerical simulations suggest that the Laplace-Young law cannot be used to predict helium density in nanometric-sized bubbles in a covalent material such as silicon

Mott transition, Widom line and pseudogap in the half-filled triangular lattice Hubbard model

The Mott transition is observed experimentally in materials that are magnetically frustrated so that long-range order does not hide the Mott transition at finite temperature. The Hubbard model on the triangular lattice at half-filling is a paradigmatic model to study the interplay of interactions and frustration on the normal-state phase diagram. We use the dynamical cluster approximation with continuous time auxiliary field quantum Monte Carlo to solve this model for 1, 4, 6, 12, and 16 site clusters with detailed analysis performed for the 6 site cluster. We show that a) for every cluster there is an inflection point in the double occupancy as a function of interaction, defining a Widom line that extends above the critical point of the first-order Mott transition; b) the presence of this line and the cluster size dependence argue for the observability of the Mott transition at finite temperature in the thermodynamic limit; c) the loss of spectral weight in the metal to Mott insulator transition as a function of temperature and for strong interactions is momentum dependent, the hallmark of a pseudogap. That pseudogap spans a large region of the phase diagram near the Mott transition.Comment: Open source version of the published paper. 16 pages, 8 figures, LaTe