Ultrastructural analysis of neuronal plasticity in the adult mouse

ABSTRACT Adult neuronal plasticity is a term that corresponds to a set of biological mechanisms allowing a neuronal circuit to respond and adapt to modifications of the received inputs. Mystacial whiskers of the mouse are the starting point of a major sensory pathway that provides the animal with information from its immediate environment. Through whisking, information is gathered that allows the animal to orientate itself and to recognize objects. This sensory system is crucial for nocturnal behaviour during which vision is not of much use. Sensory information of the whiskers are sent via brainstem and thalamus to the primary somatosensory area (S1) of the cerebral cortex in a strictly topological manner. Cell bodies in the layer N of S 1 are arranged in ring forming structures called barrels. As such, each barrel corresponds to the cortical representation in layer IV of a single whisker follicle. This histological feature allows to identify with uttermost precision the part of the cortex devoted to a given whisker and to study modifications induced by different experimental conditions. The condition used in the studies of my thesis is the passive stimulation of one whisker in the adult mouse for a period of 24 hours. It is performed by glueing a piece of metal on one whisker and placing the awake animal in a cage surrounded by an electromagnetic coil that generates magnetic field burst inducing whisker movement at a given frequency during 24 hours. I analysed the ultrastructure of the barrel corresponding the stimulated whisker using serial sections electron microscopy and computer-based three-dimensional reconstructions; analysis of neighbouring, unstimulated barrels as well as those from unstimulated mice served as control. The following elements were structurally analyzed: the spiny dendrites, the axons of excitatory as well as inhibitory cells, their connections via synapses and the astrocytic processes. The density of synapses and spines is upregulated in a barrel corresponding to a stimulated whisker. This upregulation is absent in the BDNF heterozygote mice, indicating that a certain level of activity-dependent released BDNF is required for synaptogenesis in the adult cerebral cortex. Synpaptogenesis is correlated with a modification of the astrocytes that place themselves in closer vicinity of the excitatory synapses on spines. Biochemical analysis revealed that the astrocytes upregulate the expression of transporters by which they internalise glutamate, the neurotransmitter responsible for the excitatory response of cortical neurons. In the final part of my thesis, I show that synaptogenesis in the stimulated barrel is due to the increase in the size of excitatory axonal boutons that become more frequently multisynaptic, whereas the inhibitory axons do not change their morphology but form more synapses with spines apposed to them. Taken together, my thesis demonstrates that all the cellular elements present in the neuronal tissue of the adult brain contribute to activity-dependent cortical plasticity and form part of a mechanism by which the animal responds to a modified sensory experience. Throughout life, the neuronal circuit keeps the faculty to adapt its function. These adaptations are partially transitory but some aspects remain and could be the structural basis of a memory trace in the cortical circuit. RESUME La plasticité neuronale chez l'adulte désigne un ensemble de mécanismes biologiques qui permettent aux circuits neuronaux de répondre et de s'adapter aux modifications des stimulations reçues. Les vibrisses des souris sont un système crucial fournissant des informations sensorielles au sujet de l'environnement de l'animal. L'information sensorielle collectée par les vibrisses est envoyée via le tronc cérébral et le thalamus à l'aire sensorielle primaire (S 1) du cortex cérébral en respectant strictement la somatotopie. Les corps cellulaires dans la couche IV de S 1 sont organisés en anneaux délimitant des structures nommées tonneaux. Chaque tonneau reçoit l'information d'une seule vibrisse et l'arrangement des tonneaux dans le cortex correspond à l'arrangement des vibrisses sur le museau de la souris. Cette particularité histologique permet de sélectionner avec certitude la partie du cortex dévolue à une vibrisse et de l'étudier dans diverses conditions. Le paradigme expérimental utilisé dans cette thèse est la stimulation passive d'une seule vibrisse durant 24 heures. Pour ce faire, un petit morceau de métal est collé sur une vibrisse et la souris est placée dans une cage entourée d'une bobine électromagnétique générant un champ qui fait vibrer le morceau de métal durant 24 heures. Nous analysons l'ultrastructure du cortex cérébral à l'aide de la microscopie électronique et des coupes sériées permettant la reconstruction tridimensionnelle à l'aide de logiciels informatiques. Nous observons les modifications des structures présentes : les dendrites épineuses, les axones des cellules excitatrices et inhibitrices, leurs connections par des synapses et les astrocytes. Le nombre de synapses et d'épines est augmenté dans un tonneau correspondant à une vibrisse stimulée 24 heures. Basé sur cela, nous montrons dans ces travaux que cette réponse n'est pas observée dans des souris hétérozygotes BDNF+/-. Cette neurotrophine sécrétée en fonction de l'activité neuronale est donc nécessaire pour la synaptogenèse. La synaptogenèse est accompagnée d'une modification des astrocytes qui se rapprochent des synapses excitatrices au niveau des épines dendritiques. Ils expriment également plus de transporteurs chargés d'internaliser le glutamate, le neurotransmetteur responsable de la réponse excitatrice des neurones. Nous montrons aussi que les axones excitateurs deviennent plus larges et forment plus de boutons multi-synaptiques à la suite de la stimulation tandis que les axones inhibiteurs ne changent pas de morphologie mais forment plus de synapses avec des épines apposées à leur membrane. Tous les éléments analysés dans le cerveau adulte ont maintenu la capacité de réagir aux modifications de l'activité neuronale et répondent aux modifications de l'activité permettant une constante adaptation à de nouveaux environnements durant la vie. Les circuits neuronaux gardent la capacité de créer de nouvelles synapses. Ces adaptations peuvent être des réponses transitoires aux stimuli mais peuvent aussi laisser une trace mnésique dans les circuits.

Reconstruction of networks from their betweenness centrality

In this paper we study the reconstruction of a network topology from the values of its betweenness centrality, a measure of the influence of each of its nodes in the dissemination of information over the network. We consider a simple metaheuristic, simulated annealing, as the combinatorial optimization method to generate the network from the values of the betweenness centrality. We compare the performance of this technique when reconstructing different categories of networks –random, regular, small-world, scale-free and clustered–. We show that the method allows an exact reconstruction of small networks and leads to good topological approximations in the case of networks with larger orders. The method can be used to generate a quasi-optimal topology fora communication network from a list with the values of the maximum allowable traffic for each node.

Asymptotic equivalence between the unconditional maximum likelihood and the square-law nonlinearity symbol timing estimation

This paper provides a systematic approach to theproblem of nondata aided symbol-timing estimation for linearmodulations. The study is performed under the unconditionalmaximum likelihood framework where the carrier-frequencyerror is included as a nuisance parameter in the mathematicalderivation. The second-order moments of the received signal arefound to be the sufficient statistics for the problem at hand and theyallow the provision of a robust performance in the presence of acarrier-frequency error uncertainty. We particularly focus on theexploitation of the cyclostationary property of linear modulations.This enables us to derive simple and closed-form symbol-timingestimators which are found to be based on the well-known squaretiming recovery method by Oerder and Meyr. Finally, we generalizethe OM method to the case of linear modulations withoffset formats. In this case, the square-law nonlinearity is foundto provide not only the symbol-timing but also the carrier-phaseerror.

Unification of multi-species vertebrate anatomy ontologies for comparative biology in Uberon.

BACKGROUND: Elucidating disease and developmental dysfunction requires understanding variation in phenotype. Single-species model organism anatomy ontologies (ssAOs) have been established to represent this variation. Multi-species anatomy ontologies (msAOs; vertebrate skeletal, vertebrate homologous, teleost, amphibian AOs) have been developed to represent 'natural' phenotypic variation across species. Our aim has been to integrate ssAOs and msAOs for various purposes, including establishing links between phenotypic variation and candidate genes. RESULTS: Previously, msAOs contained a mixture of unique and overlapping content. This hampered integration and coordination due to the need to maintain cross-references or inter-ontology equivalence axioms to the ssAOs, or to perform large-scale obsolescence and modular import. Here we present the unification of anatomy ontologies into Uberon, a single ontology resource that enables interoperability among disparate data and research groups. As a consequence, independent development of TAO, VSAO, AAO, and vHOG has been discontinued. CONCLUSIONS: The newly broadened Uberon ontology is a unified cross-taxon resource for metazoans (animals) that has been substantially expanded to include a broad diversity of vertebrate anatomical structures, permitting reasoning across anatomical variation in extinct and extant taxa. Uberon is a core resource that supports single- and cross-species queries for candidate genes using annotations for phenotypes from the systematics, biodiversity, medical, and model organism communities, while also providing entities for logical definitions in the Cell and Gene Ontologies. THE ONTOLOGY RELEASE FILES ASSOCIATED WITH THE ONTOLOGY MERGE DESCRIBED IN THIS MANUSCRIPT ARE AVAILABLE AT: http://purl.obolibrary.org/obo/uberon/releases/2013-02-21/ CURRENT ONTOLOGY RELEASE FILES ARE AVAILABLE ALWAYS AVAILABLE AT: http://purl.obolibrary.org/obo/uberon/releases/

Language variation in source texts and their translations: the case of L3 in film translation

In addition to the two languages essentially involved in translation, that of the source text (L1) and that of the target text (L2), we propose a third language (L3) to refer to any other language(s) found in the text. L3 may appear in the source text (ST) or the target text (TT), actually appearing more frequently inSTs in our case studies. We present a range of combinations for the convergence and divergence of L1, L2 and L3, for the case of feature films and their translations using examples from dubbed and subtitled versions of films, but we are hopeful that our tentative conclusions may be relevant to other modalities of translation, audiovisual and otherwise. When L3 appears in an audiovisual ST,we find a variety of solutions whereby L3 is deleted from or adapted to the TT.In the latter case, L3 might be rendered in a number of ways, depending on factors such as the audience’s familiarity with L3, and the possibility that L3 inthe ST is an invented language.

Validation of an Adapted French Form of the Career Adapt-Abilities Scale in four Francophone Countries

This study presents the validation of a French version of the Career Adapt-Abilities Scale in four Francophone countries. The aim was to re-analyze the item selection and then compare this newly developed French-language form with the international form 2.0. Exploratory factor analysis was used as a tool for item selection, and confirmatory factor analysis (CFA) verified the structure of the CAAS French-language form. Measurement equivalence across the four countries was tested using multi-group CFA. Adults and adolescents (N=1,707) participated from Switzerland, Belgium, Luxembourg, and France. Items chosen for the final version of the CAAS French-language form are different to those in the CAAS international form 2.0 and provide an improvement in terms of reliability. The factor structure is replicable across country, age, and gender. Strong evidence for metric invariance and partial evidence for scalar invariance of the CAAS French-language form across countries is given. The CAAS French-language and CAAS international form 2.0 can be used in a combined form of 31 items. The CAAS French-language form will certainly be interesting for practitioners using interventions based on the life design paradigm or aiming at increasing career adapt-ability.

Integral cohomology of finite postnikov towers

Depuis le séminaire H. Cartan de 1954-55, il est bien connu que l'on peut trouver des éléments de torsion arbitrairement grande dans l'homologie entière des espaces d'Eilenberg-MacLane K(G,n) où G est un groupe abélien non trivial et n>1. L'objectif majeur de ce travail est d'étendre ce résultat à des H-espaces possédant plus d'un groupe d'homotopie non trivial. Dans le but de contrôler précisément le résultat de H. Cartan, on commence par étudier la dualité entre l'homologie et la cohomologie des espaces d'Eilenberg-MacLane 2-locaux de type fini. On parvient ainsi à raffiner quelques résultats qui découlent des calculs de H. Cartan. Le résultat principal de ce travail peut être formulé comme suit. Soit X un H-espace ne possédant que deux groupes d'homotopie non triviaux, tous deux finis et de 2-torsion. Alors X n'admet pas d'exposant pour son groupe gradué d'homologie entière réduite. On construit une large classe d'espaces pour laquelle ce résultat n'est qu'une conséquence d'une caractéristique topologique, à savoir l'existence d'un rétract faible X K(G,n) pour un certain groupe abélien G et n>1. On généralise également notre résultat principal à des espaces plus compliqués en utilisant la suite spectrale d'Eilenberg-Moore ainsi que des méthodes analytiques faisant apparaître les nombres de Betti et leur comportement asymptotique. Finalement, on conjecture que les espaces qui ne possédent qu'un nombre fini de groupes d'homotopie non triviaux n'admettent pas d'exposant homologique. Ce travail contient par ailleurs la présentation de la « machine d'Eilenberg-MacLane », un programme C++ conçu pour calculer explicitement les groupes d'homologie entière des espaces d'Eilenberg-MacLane. <br/><br/>By the work of H. Cartan, it is well known that one can find elements of arbitrarilly high torsion in the integral (co)homology groups of an Eilenberg-MacLane space K(G,n), where G is a non-trivial abelian group and n>1. The main goal of this work is to extend this result to H-spaces having more than one non-trivial homotopy groups. In order to have an accurate hold on H. Cartan's result, we start by studying the duality between homology and cohomology of 2-local Eilenberg-MacLane spaces of finite type. This leads us to some improvements of H. Cartan's methods in this particular case. Our main result can be stated as follows. Let X be an H-space with two non-vanishing finite 2-torsion homotopy groups. Then X does not admit any exponent for its reduced integral graded (co)homology group. We construct a wide class of examples for which this result is a simple consequence of a topological feature, namely the existence of a weak retract X K(G,n) for some abelian group G and n>1. We also generalize our main result to more complicated stable two stage Postnikov systems, using the Eilenberg-Moore spectral sequence and analytic methods involving Betti numbers and their asymptotic behaviour. Finally, we investigate some guesses on the non-existence of homology exponents for finite Postnikov towers. We conjecture that Postnikov pieces do not admit any (co)homology exponent. This work also includes the presentation of the "Eilenberg-MacLane machine", a C++ program designed to compute explicitely all integral homology groups of Eilenberg-MacLane spaces. <br/><br/>Il est toujours difficile pour un mathématicien de parler de son travail. La difficulté réside dans le fait que les objets qu'il étudie sont abstraits. On rencontre assez rarement un espace vectoriel, une catégorie abélienne ou une transformée de Laplace au coin de la rue ! Cependant, même si les objets mathématiques sont difficiles à cerner pour un non-mathématicien, les méthodes pour les étudier sont essentiellement les mêmes que celles utilisées dans les autres disciplines scientifiques. On décortique les objets complexes en composantes plus simples à étudier. On dresse la liste des propriétés des objets mathématiques, puis on les classe en formant des familles d'objets partageant un caractère commun. On cherche des façons différentes, mais équivalentes, de formuler un problème. Etc. Mon travail concerne le domaine mathématique de la topologie algébrique. Le but ultime de cette discipline est de parvenir à classifier tous les espaces topologiques en faisant usage de l'algèbre. Cette activité est comparable à celle d'un ornithologue (topologue) qui étudierait les oiseaux (les espaces topologiques) par exemple à l'aide de jumelles (l'algèbre). S'il voit un oiseau de petite taille, arboricole, chanteur et bâtisseur de nids, pourvu de pattes à quatre doigts, dont trois en avant et un, muni d'une forte griffe, en arrière, alors il en déduira à coup sûr que c'est un passereau. Il lui restera encore à déterminer si c'est un moineau, un merle ou un rossignol. Considérons ci-dessous quelques exemples d'espaces topologiques: a) un cube creux, b) une sphère et c) un tore creux (c.-à-d. une chambre à air). a) b) c) Si toute personne normalement constituée perçoit ici trois figures différentes, le topologue, lui, n'en voit que deux ! De son point de vue, le cube et la sphère ne sont pas différents puisque ils sont homéomorphes: on peut transformer l'un en l'autre de façon continue (il suffirait de souffler dans le cube pour obtenir la sphère). Par contre, la sphère et le tore ne sont pas homéomorphes: triturez la sphère de toutes les façons (sans la déchirer), jamais vous n'obtiendrez le tore. Il existe un infinité d'espaces topologiques et, contrairement à ce que l'on serait naïvement tenté de croire, déterminer si deux d'entre eux sont homéomorphes est très difficile en général. Pour essayer de résoudre ce problème, les topologues ont eu l'idée de faire intervenir l'algèbre dans leurs raisonnements. Ce fut la naissance de la théorie de l'homotopie. Il s'agit, suivant une recette bien particulière, d'associer à tout espace topologique une infinité de ce que les algébristes appellent des groupes. Les groupes ainsi obtenus sont appelés groupes d'homotopie de l'espace topologique. Les mathématiciens ont commencé par montrer que deux espaces topologiques qui sont homéomorphes (par exemple le cube et la sphère) ont les même groupes d'homotopie. On parle alors d'invariants (les groupes d'homotopie sont bien invariants relativement à des espaces topologiques qui sont homéomorphes). Par conséquent, deux espaces topologiques qui n'ont pas les mêmes groupes d'homotopie ne peuvent en aucun cas être homéomorphes. C'est là un excellent moyen de classer les espaces topologiques (pensez à l'ornithologue qui observe les pattes des oiseaux pour déterminer s'il a affaire à un passereau ou non). Mon travail porte sur les espaces topologiques qui n'ont qu'un nombre fini de groupes d'homotopie non nuls. De tels espaces sont appelés des tours de Postnikov finies. On y étudie leurs groupes de cohomologie entière, une autre famille d'invariants, à l'instar des groupes d'homotopie. On mesure d'une certaine manière la taille d'un groupe de cohomologie à l'aide de la notion d'exposant; ainsi, un groupe de cohomologie possédant un exposant est relativement petit. L'un des résultats principaux de ce travail porte sur une étude de la taille des groupes de cohomologie des tours de Postnikov finies. Il s'agit du théorème suivant: un H-espace topologique 1-connexe 2-local et de type fini qui ne possède qu'un ou deux groupes d'homotopie non nuls n'a pas d'exposant pour son groupe gradué de cohomologie entière réduite. S'il fallait interpréter qualitativement ce résultat, on pourrait dire que plus un espace est petit du point de vue de la cohomologie (c.-à-d. s'il possède un exposant cohomologique), plus il est intéressant du point de vue de l'homotopie (c.-à-d. il aura plus de deux groupes d'homotopie non nuls). Il ressort de mon travail que de tels espaces sont très intéressants dans le sens où ils peuvent avoir une infinité de groupes d'homotopie non nuls. Jean-Pierre Serre, médaillé Fields en 1954, a montré que toutes les sphères de dimension >1 ont une infinité de groupes d'homotopie non nuls. Des espaces avec un exposant cohomologique aux sphères, il n'y a qu'un pas à franchir...

Morphological and functional variability in the root system of Quercus ilex L. subject to confinement: consequences for afforestation

We examined root morphological and functional differences caused by restrictions imposed to vertical growth in the root system of holm oak (Quercus ilex L.) seedlings to assess the consequences of using nursery containers in the development of a confined root system for this species. Thus, root morphological, topological and functional parameters, including hydraulic conductance per leaf unit surface area (K $_{\rm RL})$, were investigated in one-year seedlings cultivated in three PVC tubes differing in length (20, 60 and 100 cm). Longer tubes showed greater projected root area, root volume, total and fine root lengths, specific root length (SRL) and K$_{\rm RL}$ values than did shorter tubes. On the other hand, the length of coarse roots (diameter > 4.5 mm) and the average root diameter were greater in shorter tubes. The strong positive correlation found between K$_{\rm RL}$ and SRL (r=+0.69; P<0.001) indicated that root thickness was inversely related to water flow through the root system. We concluded that root systems developed in longer tubes are more efficient for plant water uptake and, therefore, changes in root pattern produced in standard forest containers (i.e. about 20 cm length) may in fact prevent a proper establishment of the holm oak in the field, particularly in xeric environments.

The Smc5/6 complex is required for dissolution of DNA-mediated sister chromatid linkages

Mitotic chromosome segregation requires the removal of physical connections between sister chromatids. In addition to cohesin and topological entrapments, sister chromatid separation can be prevented by the presence of chromosome junctions or ongoing DNA replication. We will collectively refer to them as DNA-mediated linkages. Although this type of structures has been documented in different DNA replication and repair mutants, there is no known essential mechanism ensuring their timely removal before mitosis. Here, we show that the dissolution of these connections is an active process that requires the Smc5/6 complex, together with Mms21, its associated SUMO-ligase. Failure to remove DNA-mediated linkages causes gross chromosome missegregation in anaphase. Moreover, we show that Smc5/6 is capable to dissolve them in metaphase-arrested cells, thus restoring chromosome resolution and segregation. We propose that Smc5/6 has an essential role in the removal of DNA-mediated linkages to prevent chromosome missegregation and aneuploidy.

Using Pareto optimality to explore the topology and dynamics of the human connectome.

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

Quest for Orthologs Entails Quest for Tree of Life: In Search of the Gene Stream.

Quest for Orthologs (QfO) is a community effort with the goal to improve and benchmark orthology predictions. As quality assessment assumes prior knowledge on species phylogenies, we investigated the congruency between existing species trees by comparing the relationships of 147 QfO reference organisms from six Tree of Life (ToL)/species tree projects: The National Center for Biotechnology Information (NCBI) taxonomy, Opentree of Life, the sequenced species/species ToL, the 16S ribosomal RNA (rRNA) database, and trees published by Ciccarelli et al. (Ciccarelli FD, et al. 2006. Toward automatic reconstruction of a highly resolved tree of life. Science 311:1283-1287) and by Huerta-Cepas et al. (Huerta-Cepas J, Marcet-Houben M, Gabaldon T. 2014. A nested phylogenetic reconstruction approach provides scalable resolution in the eukaryotic Tree Of Life. PeerJ PrePrints 2:223) Our study reveals that each species tree suggests a different phylogeny: 87 of the 146 (60%) possible splits of a dichotomous and rooted tree are congruent, while all other splits are incongruent in at least one of the species trees. Topological differences are observed not only at deep speciation events, but also within younger clades, such as Hominidae, Rodentia, Laurasiatheria, or rosids. The evolutionary relationships of 27 archaea and bacteria are highly inconsistent. By assessing 458,108 gene trees from 65 genomes, we show that consistent species topologies are more often supported by gene phylogenies than contradicting ones. The largest concordant species tree includes 77 of the QfO reference organisms at the most. Results are summarized in the form of a consensus ToL (http://swisstree.vital-it.ch/species_tree) that can serve different benchmarking purposes.

Reliable computation of robust response tori on the verge of breakdown

We prove the existence and local uniqueness of invariant tori on the verge of breakdown for two systems: the quasi-periodically driven logistic map and the quasi-periodically forced standard map. These systems exemplify two scenarios: the Heagy-Hammel route for the creation of strange non- chaotic attractors and the nonsmooth bifurcation of saddle invariant tori. Our proofs are computer- assisted and are based on a tailored version of the Newton-Kantorovich theorem. The proofs cannot be performed using classical perturbation theory because the two scenarios are very far from the perturbative regime, and fundamental hypotheses such as reducibility or hyperbolicity either do not hold or are very close to failing. Our proofs are based on a reliable computation of the invariant tori and a careful study of their dynamical properties, leading to the rigorous validation of the numerical results with our novel computational techniques.

Quantum Hall Phases of two-component bosons

The recent production of synthetic magnetic fields acting on electroneutral particles, such as atoms or photons, has boosted interest in the quantum Hall physics of bosons. Adding pseudospin 1/2 to the bosons greatly enriches the scenario, as it allows them to form an interacting integer quantum Hall (IQH) phase with no fermionic counterpart. Here we show that, for a small two-component Bose gas on a disk, the complete strongly correlated regime, extending from the integer phase at filling factor ν = 2 to the Halperin phase at filling factor ν = 2 / 3, is well described by composite fermionization of the bosons. Moreover we study the edge excitations of the IQH state, which, in agreement with expectations from topological field theory, are found to consist of forward-moving charge excitations and backward-moving spin excitations. Finally, we demonstrate how pair-correlation functions allow one to experimentally distinguish the IQH state from competing states, such as non-Abelian spin singlet (NASS) states.

Nature of the Epidemic Threshold for the Susceptible-Infected-Susceptible Dynamics in Networks

We develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.

Effect of the surface charge discretization on electric double layers. A Monte Carlo simulation study

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups,a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.