Endemic infections are always possible on regular networks

We study the dependence of the largest component in regular networks on the clustering coefficient, showing that its size changes smoothly without undergoing a phase transition. We explain this behavior via an analytical approach based on the network structure, and provide an exact equation describing the numerical results. Our work indicates that intrinsic structural properties always allow the spread of epidemics on regular networks

Finding network communities using modularity density

Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network partition that maximizes a quality function. Here, we present a detailed analysis of a recently proposed function, namely modularity density. We show that it does not incur in the drawbacks suffered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic random graphs. In addition, we show that modularity density allows an easy comparison between networks of different sizes, and we also present some limitations that methods based on modularity density may suffer from. Finally, we introduce an efficient, quadratic community detection algorithm based on modularity density maximization, validating its accuracy against theoretical predictions and on a set of benchmark networks

Data Mining a Medieval Medical Text Reveals Patterns in Ingredient Choice That Reflect Biological Activity against Infectious Agents

We used established methodologies from network science to identify patterns in medicinal ingredient combinations in a key medieval text, the 15th-century Lylye of Medicynes, focusing on recipes for topical treatments for symptoms of microbial infection. We conducted experiments screening the antimicrobial activity of selected ingredients. These experiments revealed interesting examples of ingredients that potentiated or interfered with each other’s activity and that would be useful bases for future, more detailed experiments. Our results highlight (i) the potential to use methodologies from network science to analyze medieval data sets and detect patterns of ingredient combination, (ii) the potential of interdisciplinary collaboration to reveal different aspects of the ethnopharmacology of historical medical texts, and (iii) the potential development of novel therapeutics inspired by premodern remedies in a time of increased need for new antibiotics.The pharmacopeia used by physicians and laypeople in medieval Europe has largely been dismissed as placebo or superstition. While we now recognize that some of the materia medica used by medieval physicians could have had useful biological properties, research in this area is limited by the labor-intensive process of searching and interpreting historical medical texts. Here, we demonstrate the potential power of turning medieval medical texts into contextualized electronic databases amenable to exploration by the use of an algorithm. We used established methodologies from network science to reveal patterns in ingredient selection and usage in a key text, the 15th-century Lylye of Medicynes, focusing on remedies to treat symptoms of microbial infection. In providing a worked example of data-driven textual analysis, we demonstrate the potential of this approach to encourage interdisciplinary collaboration and to shine a new light on the ethnopharmacology of historical medical texts

Tomographic docking suggests the mechanism of auxin receptor TIR1 selectivity

We study the binding of plant hormone IAA on its receptor TIR1 introducing a novel computational method that we call tomographic docking and that accounts for interactions occurring along the depth of the binding pocket. Our results suggest that selectivity is related to constraints that potential ligands encounter on their way from the surface of the protein to their final position at the pocket bottom. Tomographic docking helps develop specific hypotheses about ligand binding, distinguishing binders from non-binders, and suggests that binding is a three-step mechanism, consisting of engagement with a niche in the back wall of the pocket, interaction with a molecular filter which allows or precludes further descent of ligands, and binding on the pocket base. Only molecules that are able to descend the pocket and bind at its base allow the co-receptor IAA7 to bind on the complex, thus behaving as active auxins. Analyzing the interactions at different depths, our new method helps in identifying critical residues that constitute preferred future study targets and in the quest for safe and effective herbicides. Also, it has the potential to extend the utility of docking from ligand searches to the study of processes contributing to selectivity.Comment: 11 pages, 7 figure

Phase Diagram for a 2-D Two-Temperature Diffusive XY Model

Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow through the system from the higher temperature heat-bath to the lower temperature one and reaches a far-from-equilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin-wave order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium the KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent of phi = 2.52 \pm 0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point.Comment: 5 pages, 4 figure

Mean-field nature of synchronization stability in networks with multiple interaction layers

The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of synchronization in dynamical systems. However, the resulting equations are computationally expensive, and therefore difficult, if not impossible, to solve for large systems. To bridge this gap, we develop a mean-field theory of synchronization for networks with multiple interaction layers. By assuming quasi-identical layers, we obtain accurate assessments of synchronization stability that are comparable with the exact results. In fact, the accuracy of our theory remains high even for networks with very dissimilar layers, thus posing a general question about the mean-field nature of synchronization stability in multilayer networks. Moreover, the computational complexity of our approach is only quadratic in the number of nodes, thereby allowing the study of systems whose investigation was thus far precluded. Multilayer networks can achieve synchronization, both for homogeneous and heterogeneous layers, whose dynamics is described by a system of equations often computationally complex and expensive. Here, the authors propose a mean-field approach for estimating the stability of the synchronized state of multilayer networks and show this applies to both homogeneous and heterogeneous layers, lowering computational complexity

Synchronization in networks with multiple interaction layers

The structure of many real-world systems is best captured by networks consisting of several interaction layers. Understanding how a multilayered structure of connections affects the synchronization properties of dynamical systems evolving on top of it is a highly relevant endeavor in mathematics and physics and has potential applications in several socially relevant topics, such as power grid engineering and neural dynamics. We propose a general framework to assess the stability of the synchronized state in networks with multiple interaction layers, deriving a necessary condition that generalizes the master stability function approach. We validate our method by applying it to a network of Rössler oscillators with a double layer of interactions and show that highly rich phenomenology emerges from this. This includes cases where the stability of synchronization can be induced even if both layers would have individually induced unstable synchrony, an effect genuinely arising from the true multilayer structure of the interactions among the units in the network

Anomalous ordering in inhomogeneously strained materials

We study a continuous quasi-two-dimensional order-disorder phase transition that occurs in a simple model of a material that is inhomogeneously strained due to the presence of dislocation lines. Performing Monte Carlo simulations of different system sizes and using finite size scaling, we measure critical exponents describing the transition of beta=0.18\pm0.02, gamma=1.0\pm0.1, and alpha=0.10\pm0.02. Comparable exponents have been reported in a variety of physical systems. These systems undergo a range of different types of phase transitions, including structural transitions, exciton percolation, and magnetic ordering. In particular, similar exponents have been found to describe the development of magnetic order at the onset of the pseudogap transition in high-temperature superconductors. Their common universal critical exponents suggest that the essential physics of the transition in all of these physical systems is the same as in our model. We argue that the nature of the transition in our model is related to surface transitions, although our model has no free surface.Comment: 5 pages, 3 figure

A case study of the Ancientbiotics collaboration

Collaborations that cross traditional boundaries between disciplines in STEM and the arts and humanities open up exciting research possibilities. In our team’s case, we combined expertise in historical manuscripts, data science, and microbiology to explore the structure and potential efficacy of historical medical recipes. Such an approach can highlight patterns or questions that a single-disciplinary approach is likely to miss. But learning to speak each other’s disciplinary languages is not always easy, and misunderstandings can impede work. Here, we present our own experiences as a case study of how we have learned from each other to ask new questions of our source material and the problems we have had to solve along the way

All scale-free networks are sparse

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.Comment: 4 pages, 2 figure