Complex networks as an emerging property of hierarchical preferential attachment

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.Comment: 12 pages, 7 figure

Deep learning of contagion dynamics on complex networks

Forecasting the evolution of contagion dynamics is still an open problem to which mechanistic models only offer a partial answer. To remain mathematically or computationally tractable, these models must rely on simplifying assumptions, thereby limiting the quantitative accuracy of their predictions and the complexity of the dynamics they can model. Here, we propose a complementary approach based on deep learning where the effective local mechanisms governing a dynamic on a network are learned from time series data. Our graph neural network architecture makes very few assumptions about the dynamics, and we demonstrate its accuracy using different contagion dynamics of increasing complexity. By allowing simulations on arbitrary network structures, our approach makes it possible to explore the properties of the learned dynamics beyond the training data. Finally, we illustrate the applicability of our approach using real data of the COVID-19 outbreak in Spain. Our results demonstrate how deep learning offers a new and complementary perspective to build effective models of contagion dynamics on networks

Deep learning of contagion dynamics on complex networks

Forecasting the evolution of contagion dynamics is still an open problem to which mechanistic models only offer a partial answer. To remain mathematically or computationally tractable, these models must rely on simplifying assumptions, thereby limiting the quantitative accuracy of their predictions and the complexity of the dynamics they can model. Here, we propose a complementary approach based on deep learning where effective local mechanisms governing a dynamic on a network are learned from time series data. Our graph neural network architecture makes very few assumptions about the dynamics, and we demonstrate its accuracy using different contagion dynamics of increasing complexity. By allowing simulations on arbitrary network structures, our approach makes it possible to explore the properties of the learned dynamics beyond the training data. Finally, we illustrate the applicability of our approach using real data of the COVID-19 outbreak in Spain. Our results demonstrate how deep learning offers a new and complementary perspective to build effective models of contagion dynamics on networks

Geometric evolution of complex networks with degree correlations

We present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time t are distributed homogeneously between a new node and the existing nodes selected uniformly. This is achieved by creating links between nodes uniformly distributed in a homogeneous metric space according to a Fermi-Dirac connection probability with inverse temperature β and general time-dependent chemical potential μ(t). The chemical potential limits the spatial extent of newly created links. Using a hidden variable framework, we obtain an analytical expression for the degree sequence and show that μ(t) can be fixed to yield any given degree distributions, including a scale-free degree distribution. Additionally, we find that depending on the order in which nodes appear in the network—its history—the degree-degree correlations can be tuned to be assortative or disassortative. The effect of the geometry on the structure is investigated through the average clustering coefficient ⟨c⟩. In the thermodynamic limit, we identify a phase transition between a random regime where ⟨c⟩→ 0 when β 0 when β>βc

Everything in Moderation: Investigating the U-Shaped Link Between HDL Cholesterol and Adverse Outcomes

Despite historical evidence suggesting an inverse association between HDL cholesterol (HDL-C) and adverse cardiovascular events, pharmacological efforts to increase HDL-C and improve outcomes have not been successful. Recently, a U-shaped association between HDL-C and adverse events has been demonstrated in several population cohorts, further complicating our understanding of the clinical significance of HDL. Potential explanations for this finding include genetic mutations linked to very high HDL-C, impaired HDL function at high HDL-C levels, and residual confounding. However, our understanding of this association remains premature and needs further investigation

Bacillus subtilis Early Colonization of Arabidopsis thaliana Roots Involves Multiple Chemotaxis Receptors

ABSTRACT Colonization of plant roots by Bacillus subtilis is mutually beneficial to plants and bacteria. Plants can secrete up to 30% of their fixed carbon via root exudates, thereby feeding the bacteria, and in return the associated B. subtilis bacteria provide the plant with many growth-promoting traits. Formation of a biofilm on the root by matrix-producing B. subtilis is a well-established requirement for long-term colonization. However, we observed that cells start forming a biofilm only several hours after motile cells first settle on the plant. We also found that intact chemotaxis machinery is required for early root colonization by B. subtilis and for plant protection. Arabidopsis thaliana root exudates attract B. subtilis in vitro, an activity mediated by the two characterized chemoreceptors, McpB and McpC, as well as by the orphan receptor TlpC. Nonetheless, bacteria lacking these chemoreceptors are still able to colonize the root, suggesting that other chemoreceptors might also play a role in this process. These observations suggest that A. thaliana actively recruits B. subtilis through root-secreted molecules, and our results stress the important roles of B. subtilis chemoreceptors for efficient colonization of plants in natural environments. These results demonstrate a remarkable strategy adapted by beneficial rhizobacteria to utilize carbon-rich root exudates, which may facilitate rhizobacterial colonization and a mutualistic association with the host

Hunting for brown dwarf binaries with X-Shooter

The refinement of the brown dwarf binary fraction may contribute to the understanding of the substellar formation mechanisms. Peculiar brown dwarf spectra or discrepancy between optical and near-infrared spectral type classification of brown dwarfs may indicate unresolved brown dwarf binary systems. We obtained medium-resolution spectra of 22 brown dwarfs of potential binary candidates using X-Shooter at the VLT. We aimed to select brown dwarf binary candidates. We also tested whether BT-Settl 2014 atmospheric models reproduce the physics in the atmospheres of these objects. To find different spectral type spectral binaries, we used spectral indices and we compared the selected candidates to single spectra and composition of two single spectra from libraries, to try to reproduce our X-Shooter spectra. We also created artificial binaries within the same spectral class, and we tried to find them using the same method as for brown dwarf binaries with different spectral types. We compared our spectra to the BT-Settl models 2014. We selected six possible candidates to be combination of L plus T brown dwarfs. All candidates, except one, are better reproduced by a combination of two single brown dwarf spectra than by a single spectrum. The one-sided F-test discarded this object as a binary candidate. We found that we are not able to find the artificial binaries with components of the same spectral type using the same method used for L plus T brown dwarfs. Best matches to models gave a range of effective temperatures between 950 K and 1900 K, a range of gravities between 4.0 and 5.5. Some best matches corresponded to supersolar metallicity

X-Shooter Medium Resolution Brown Dwarfs Library

} We obtain medium-resolution spectra in the optical (550-1000 nm, R̃5400) and the near-infrared (1000-2500 nm, R̃3300) using the Wideband ultraviolet-infrared single target spectrograph (X-Shooter) at the Very Large Telescope (VLT). Our sample is compound of 22 brown dwarfs binary candidates with spectral types between L1 and T7. We aim to empirically confirm or refute the binarity of our candidates, comparing them to spectral templates and to other brown dwarfs in a color-magnitude diagram, for targets that have published parallaxes. } We use X-shooter at the VLT to obtain medium resolution spectra of the targets. We develop a slightly different analysis depending of the type of binaries we search for. To find L plus T brown dwarf binaries candidates, we comput spectral indices to select L-brown dwarfs plus T-brown dwarf binaries, and then we compare them to single and composite template spectra. To find potential L plus L or T plus T brown dwarf binaries, we first simulate their spectra creating synthetic binaries using combination of single template spectra. Then we compare them to our set of spectral libraries and composite of them to test if our method is able to find these binaries. } Using spectral indices, we select four possible candidates to be combination of L plus T brown dwarfs: SIMP 0136 662+0933473, 2MASSI J0423485-041403 (T0, known binary), DENIS-P J0255.0-4700 and 2MASS J13411160-3052505 We compare these candidates to single brown dwarf template spectra and combinations of them, and we select the best matches. All candidates beside SIMP 0136 662+0933473 have decent matches to composite of two single template spectra. DENIS-P J0255.0-4700 have also good agreements to several late L and early T single template spectra. To find L plus L or T plus T brown dwarfs candidates, test the comparison to templates method use before to find L plus T brown dwarf binaries. The test consist on finding synthetic L plus L and T plus T binaries by comparing with spectral templates. We conclude that we cannot find L plus L and T plus T binaries using comparing to single and composite spectral templates, because the main difference between different L or T spectral types is just the spectral energy distribution.} Optical and near infrared spectra report in this paper will serve as templates for future studies in any of these wavelengths. In the near future, Gaia satellite will release high precision parallaxes of more than one billion of objects in the Milky Way, including hundred of brown dwarfs. These parallaxes will allow us to detect the overluminosity of brown dwarf binaries.} <P /