Real space Renormalization Group analysis of a non-mean field spin-glass

A real space Renormalization Group approach is presented for a non-mean field spin-glass. This approach has been conceived in the effort to develop an alternative method to the Renormalization Group approaches based on the replica method. Indeed, non-perturbative effects in the latter are quite generally out of control, in such a way that these approaches are non-predictive. On the contrary, we show that the real space method developed in this work yields precise predictions for the critical behavior and exponents of the model

Finite-size scaling analysis of the distributions of pseudo-critical temperatures in spin glasses

Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three-dimensional Edwards-Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick model. We find that the behavior of our data is nicely described by straightforward finite-size scaling relations.Comment: 23 pages, 9 figures. Version accepted for publication in J. Stat. Mec

Spatial correlations in attribute communities

Community detection is an important tool for exploring and classifying the properties of large complex networks and should be of great help for spatial networks. Indeed, in addition to their location, nodes in spatial networks can have attributes such as the language for individuals, or any other socio-economical feature that we would like to identify in communities. We discuss in this paper a crucial aspect which was not considered in previous studies which is the possible existence of correlations between space and attributes. Introducing a simple toy model in which both space and node attributes are considered, we discuss the effect of space-attribute correlations on the results of various community detection methods proposed for spatial networks in this paper and in previous studies. When space is irrelevant, our model is equivalent to the stochastic block model which has been shown to display a detectability-non detectability transition. In the regime where space dominates the link formation process, most methods can fail to recover the communities, an effect which is particularly marked when space-attributes correlations are strong. In this latter case, community detection methods which remove the spatial component of the network can miss a large part of the community structure and can lead to incorrect results.Comment: 10 pages and 7 figure

Router-level community structure of the Internet Autonomous Systems

The Internet is composed of routing devices connected between them and organized into independent administrative entities: the Autonomous Systems. The existence of different types of Autonomous Systems (like large connectivity providers, Internet Service Providers or universities) together with geographical and economical constraints, turns the Internet into a complex modular and hierarchical network. This organization is reflected in many properties of the Internet topology, like its high degree of clustering and its robustness. In this work, we study the modular structure of the Internet router-level graph in order to assess to what extent the Autonomous Systems satisfy some of the known notions of community structure. We show that the modular structure of the Internet is much richer than what can be captured by the current community detection methods, which are severely affected by resolution limits and by the heterogeneity of the Autonomous Systems. Here we overcome this issue by using a multiresolution detection algorithm combined with a small sample of nodes. We also discuss recent work on community structure in the light of our results

Message Passing for Optimization and Control of Power Grid: Model of Distribution System with Redundancy

We use a power grid model with $M$ generators and $N$ consumption units to optimize the grid and its control. Each consumer demand is drawn from a predefined finite-size-support distribution, thus simulating the instantaneous load fluctuations. Each generator has a maximum power capability. A generator is not overloaded if the sum of the loads of consumers connected to a generator does not exceed its maximum production. In the standard grid each consumer is connected only to its designated generator, while we consider a more general organization of the grid allowing each consumer to select one generator depending on the load from a pre-defined consumer-dependent and sufficiently small set of generators which can all serve the load. The model grid is interconnected in a graph with loops, drawn from an ensemble of random bipartite graphs, while each allowed configuration of loaded links represent a set of graph covering trees. Losses, the reactive character of the grid and the transmission-level connections between generators (and many other details relevant to realistic power grid) are ignored in this proof-of-principles study. We focus on the asymptotic limit and we show that the interconnects allow significant expansion of the parameter domains for which the probability of a generator overload is asymptotically zero. Our construction explores the formal relation between the problem of grid optimization and the modern theory of sparse graphical models. We also design heuristic algorithms that achieve the asymptotically optimal selection of loaded links. We conclude discussing the ability of this approach to include other effects, such as a more realistic modeling of the power grid and related optimization and control algorithms.Comment: 10 page

Metrics matter in community detection

We present a critical evaluation of normalized mutual information (NMI) as an evaluation metric for community detection. NMI exaggerates the leximin method's performance on weak communities: Does leximin, in finding the trivial singletons clustering, truly outperform eight other community detection methods? Three NMI improvements from the literature are AMI, rrNMI, and cNMI. We show equivalences under relevant random models, and for evaluating community detection, we advise one-sided AMI under the $\mathbb{M}_{\mathrm{all}}$ model (all partitions of $n$ nodes). This work seeks (1) to start a conversation on robust measurements, and (2) to advocate evaluations which do not give "free lunch"

Modelling home care organisations from an operations management perspective

Home Care (HC) service consists of providing care to patients in their homes. During the last decade, the HC service industry experienced significant growth in many European countries. This growth stems from several factors, such as governmental pressure to reduce healthcare costs, demographic changes related to population ageing, social changes, an increase in the number of patients that suffer from chronic illnesses, and the development of new home-based services and technologies. This study proposes a framework that will enable HC service providers to better understand HC operations and their management. The study identifies the main processes and decisions that relate to the field of HC operations management. Hence, an IDEF0 (Integrated Definition for Function Modelling) activity-based model describes the most relevant clinical, logistical and organisational processes associated with HC operations. A hierarchical framework for operations management decisions is also proposed. This analysis is derived from data that was collected by nine HC service providers, which are located in France and Italy, and focuses on the manner in which operations are run, as well as associated constraints, inputs and outputs. The most challenging research areas in the field of HC operations management are also discussed

High modularity creates scaling laws

Scaling laws have been observed in many natural and engineered systems. Their existence can give useful information about the growth or decay of one quantitative feature in terms of another. For example, in the field of city analytics, it is has been fruitful to compare some urban attribute, such as energy usage or wealth creation, with population size. In this work, we use network science and dynamical systems perspectives to explain that the observed scaling laws, and power laws in particular, arise naturally when some feature of a complex system is measured in terms of the system size. Our analysis is based on two key assumptions that may be posed in graph theoretical terms. We assume (a) that the large interconnection network has a well-defined set of communities and (b) that the attribute under study satisfies a natural continuity-type property. We conclude that precise mechanistic laws are not required in order to explain power law effects in complex systems—very generic network-based rules can reproduce the behaviors observed in practice. We illustrate our results using Twitter interaction between accounts geolocated to the city of Bristol, UK

Cytoklepty in the plankton: A host strategy to optimize the bioenergetic machinery of endosymbiotic algae

Endosymbioses have shaped the evolutionary trajectory of life and remain ecologically important. Investigating oceanic photosymbioses can illuminate how algal endosymbionts are energetically exploited by their heterotrophic hosts and inform on putative initial steps of plastid acquisition in eukaryotes. By combining three-dimensional subcellular imaging with photophysiology, carbon flux imaging, and transcriptomics, we show that cell division of endosymbionts (Phaeocystis) is blocked within hosts (Acantharia) and that their cellular architecture and bioenergetic machinery are radically altered. Transcriptional evidence indicates that a nutrient-independent mechanism prevents symbiont cell division and decouples nuclear and plastid division. As endosymbiont plastids proliferate, the volume of the photosynthetic machinery volume increases 100-fold in correlation with the expansion of a reticular mitochondrial network in close proximity to plastids. Photosynthetic efficiency tends to increase with cell size, and photon propagation modeling indicates that the networked mitochondrial architecture enhances light capture. This is accompanied by 150-fold higher carbon uptake and up-regulation of genes involved in photosynthesis and carbon fixation, which, in conjunction with a ca.15-fold size increase of pyrenoids demonstrates enhanced primary production in symbiosis. Mass spectrometry imaging revealed major carbon allocation to plastids and transfer to the host cell. As in most photosymbioses, microalgae are contained within a host phagosome (symbiosome), but here, the phagosome invaginates into enlarged microalgal cells, perhaps to optimize metabolic exchange. This observation adds evidence that the algal metamorphosis is irreversible. Hosts, therefore, trigger and benefit from major bioenergetic remodeling of symbiotic microalgae with potential consequences for the oceanic carbon cycle. Unlike other photosymbioses, this interaction represents a so-called cytoklepty, which is a putative initial step toward plastid acquisition

The coral core microbiome identifies rare bacterial taxa as ubiquitous endosymbionts

© 2015 International Society for Microbial Ecology All rights reserved. Despite being one of the simplest metazoans, corals harbor some of the most highly diverse and abundant microbial communities. Differentiating core, symbiotic bacteria from this diverse hostassociated consortium is essential for characterizing the functional contributions of bacteria but has not been possible yet. Here we characterize the coral core microbiome and demonstrate clear phylogenetic and functional divisions between the micro-scale, niche habitats within the coral host. In doing so, we discover seven distinct bacterial phylotypes that are universal to the core microbiome of coral species, separated by thousands of kilometres of oceans. The two most abundant phylotypes are co-localized specifically with the corals' endosymbiotic algae and symbiont-containing host cells. These bacterial symbioses likely facilitate the success of the dinoflagellate endosymbiosis with corals in diverse environmental regimes