Control of Multilayer Networks

The controllability of a network is a theoretical problem of relevance in a variety of contexts ranging from financial markets to the brain. Until now, network controllability has been characterized only on isolated networks, while the vast majority of complex systems are formed by multilayer networks. Here we build a theoretical framework for the linear controllability of multilayer networks by mapping the problem into a combinatorial matching problem. We found that correlating the external signals in the different layers can significantly reduce the multiplex network robustness to node removal, as it can be seen in conjunction with a hybrid phase transition occurring in interacting Poisson networks. Moreover we observe that multilayer networks can stabilize the fully controllable multiplex network configuration that can be stable also when the full controllability of the single network is not stable

Electronic structure and magnetic properties of few-layer Cr2_2Ge2_2Te6_6: the key role of nonlocal electron-electron interaction effects

Atomically-thin magnetic crystals have been recently isolated experimentally, greatly expanding the family of two-dimensional materials. In this Article we present an extensive comparative analysis of the electronic and magnetic properties of ${\rm Cr}_2{\rm Ge}_2{\rm Te}_6$, based on density functional theory (DFT). We first show that the often-used ${\rm DFT}+U$ approaches fail in predicting the ground-state properties of this material in both its monolayer and bilayer forms, and even more spectacularly in its bulk form. In the latter case, the fundamental gap {\it decreases} by increasing the Hubbard-$U$ parameter, eventually leading to a metallic ground state for physically relevant values of $U$, in stark contrast with experimental data. On the contrary, the use of hybrid functionals, which naturally take into account nonlocal exchange interactions between all orbitals, yields good account of the available ARPES experimental data. We then calculate all the relevant exchange couplings (and the magneto-crystalline anisotropy energy) for monolayer, bilayer, and bulk ${\rm Cr}_2{\rm Ge}_2{\rm Te}_6$ with a hybrid functional, with super-cells containing up to $270$ atoms, commenting on existing calculations with much smaller super-cell sizes. In the case of bilayer ${\rm Cr}_2{\rm Ge}_2{\rm Te}_6$, we show that two distinct intra-layer second-neighbor exchange couplings emerge, a result which, to the best of our knowledge, has not been noticed in the literature.Comment: 13 pages, 6 figures, 3 table

Efficient potential of mean force calculation from multiscale simulations: solute insertion in a lipid membrane

The determination of potentials of mean force for solute insertion in a membrane by means of all-atom molecular dynamics simulations is often hampered by sampling issues. A multiscale approach to conformational sampling was recently proposed by Bereau and Kremer (2016). It aims at accelerating the sampling of the atomistic conformational space by means of a systematic backmapping of coarse-grained snapshots. In this work, we first analyze the efficiency of this method by comparing its predictions for propanol insertion into a 1,2-Dimyristoyl-sn-glycero-3-phosphocholine membrane (DMPC) against reference atomistic simulations. The method is found to provide accurate results with a gain of one order of magnitude in computational time. We then investigate the role of the coarse-grained representation in affecting the reliability of the method in the case of a 1,2-Dioleoyl-sn-glycero-3-phosphocholine membrane (DOPC). We find that the accuracy of the results is tightly connected to the presence a good configurational overlap between the coarse-grained and atomistic models---a general requirement when developing multiscale simulation methods.Comment: 6 pages, 5 figure

Network measures for protein folding state discrimination

Proteins fold using a two-state or multi-state kinetic mechanisms, but up to now there is not a first-principle model to explain this different behavior. We exploit the network properties of protein structures by introducing novel observables to address the problem of classifying the different types of folding kinetics. These observables display a plain physical meaning, in terms of vibrational modes, possible configurations compatible with the native protein structure, and folding cooperativity. The relevance of these observables is supported by a classification performance up to 90%, even with simple classifiers such as discriminant analysis

Comparing different coarse-grained potentials for star polymers

We compare different coarse-grained models for star polymers. We find that phenomenological models inspired by the Daoud-Cotton model reproduce quite poorly the thermodynamics of these systems, even if the potential is assumed to be density dependent, as done in the analysis of experimental results. We also determine the minumum value fc of the functionality of the star polymer for which a fluid-solid transition occurs. By applying the Hansen-Verlet criterion we find 35 < fc < 40. This result is confirmed by an analysis based on the modified (reference) hypernetted chain method and is qualitatively consistent with previous work.Comment: 9 pages. In the new version, comments added and a few typos corrected. To appear in J. Chem. Phy

Integral-equation analysis of single-site coarse-grained models for polymer-colloid mixtures

We discuss the reliability of integral-equation methods based on several commonly used closure relations in determining the phase diagram of coarse-grained models of soft-matter systems characterized by mutually interacting soft and hard-core particles. Specifically, we consider a set of potentials appropriate to describe a system of hard-sphere colloids and linear homopolymers in good solvent, and investigate the behavior when the soft particles are smaller than the colloids, which is the regime of validity of the coarse-grained models. Using computer-simulation results as a benchmark, we find that the hypernetted-chain approximation provides accurate estimates of thermodynamics and structure in the colloid-gas phase in which the density of colloids is small. On the other hand, all closures considered appear to be unable to describe the behavior of the mixture in the colloid-liquid phase, as they cease to converge at polymer densities significantly smaller than those at the binodal. As a consequence, integral equations appear to be unable to predict a quantitatively correct phase diagram.Comment: 16 pages, 11 figures, 3 table

Coarse-graining polymer solutions: a critical appraisal of single- and multi-site models

We critically discuss and review the general ideas behind single- and multi-site coarse-grained (CG) models as applied to macromolecular solutions in the dilute and semi-dilute regime. We first consider single-site models with zero-density and density-dependent pair potentials. We highlight advantages and limitations of each option in reproducing the thermodynamic behavior and the large-scale structure of the underlying reference model. As a case study we consider solutions of linear homopolymers in a solvent of variable quality. Secondly, we extend the discussion to multi-component systems presenting, as a test case, results for mixtures of colloids and polymers. Specifically, we found the CG model with zero-density potentials to be unable to predict fluid-fluid demixing in a reasonable range of densities for mixtures of colloids and polymers of equal size. For larger colloids, the polymer volume fractions at which phase separation occurs are largely overestimated. CG models with density-dependent potentials are somewhat less accurate than models with zero-density potentials in reproducing the thermodynamics of the system and, although they presents a phase separation, they significantly underestimate the polymer volume fractions along the binodal. Finally, we discuss a general multi-site strategy, which is thermodynamically consistent and fully transferable with the number of sites, and that allows us to overcome most of the limitations discussed for single-site models.Comment: 23 pages, 9 figures, 4 table

In silico screening of drug-membrane thermodynamics reveals linear relations between bulk partitioning and the potential of mean force

The partitioning of small molecules in cell membranes---a key parameter for pharmaceutical applications---typically relies on experimentally-available bulk partitioning coefficients. Computer simulations provide a structural resolution of the insertion thermodynamics via the potential of mean force, but require significant sampling at the atomistic level. Here, we introduce high-throughput coarse-grained molecular dynamics simulations to screen thermodynamic properties. This application of physics based models in a large-scale study of small molecules establishes linear relationships between partitioning coefficients and key features of the potential of mean force. This allows us to predict the structure of the insertion from bulk experimental measurements for more than 400,000 compounds. The potential of mean force hereby becomes an easily accessible quantity---already recognized for its high predictability of certain properties, e.g., passive permeation. Further, we demonstrate how coarse graining helps reduce the size of chemical space, enabling a hierarchical approach to screening small molecules.Comment: 8 pages, 6 figures. Typos fixed, minor correction