Sophia N. Yaliraki

Stability of graph communities across time scales

The complexity of biological, social, and engineering networks makes it desirable to find natural partitions into clusters (or communities) that can provide insight into the structure of the overall system and even act as simplified functional descriptions. Although methods for community detection abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We introduce here the stability of a partition, a measure of its quality as a community structure based on the clustered autocovariance of a dynamic Markov process taking place on the network. Because the stability has an intrinsic dependence on time scales of the graph, it allows us to compare and rank partitions at each time and also to establish the time spans over which partitions are optimal. Hence the Markov time acts effectively as an intrinsic resolution parameter that establishes a hierarchy of increasingly coarser communities. Our dynamical definition provides a unifying framework for several standard partitioning measures: modularity and normalized cut size can be interpreted as one-step time measures, whereas Fiedler’s spectral clustering emerges at long times. We apply our method to characterize the relevance of partitions over time for constructive and real networks, including hierarchical graphs and social networks, and use it to obtain reduced descriptions for atomic-level protein structures over different time scales.

The injecting energy at molecule/metal interfaces: Implications for conductance of molecular junctions from an ab initio molecular description

To study the electronic transport of molecular wire circuits, we present a time-independent scattering formalism which includes an ab initio description of the molecular electronic structure. This allows us to obtain the molecule–metal coupling description at the same level of theory. The conductance of junction α, α′ xylyl dithiol and benzene-1,4-dithiol between gold electrodes is obtained and compared with available experimental data. The conductance depends dramatically on the relative position of the Fermi energy of the metal with respect to the molecular levels. We obtain an estimate for the injecting energy of the electron onto the molecule by varying the distance between the molecule and the attached gold clusters. Contrary to the standard assumption, we find that the injecting energy lies close to the molecular highest occupied molecular orbital, rather than in the middle of the gap; it is just the work function of the bulk metal. Finally, the adequacy of the widely used extended Huckel method for...

Molecule-interface coupling effects on electronic transport in molecular wires

Transport studies of molecular wire circuits require a description of the molecule and the leads. Here we focus on the molecule–lead interaction. We extend a time-independent scattering formalism to include a more realistic description of the interface. This allows us to obtain the conductance as a function of dimensionality of contact and of electrode, number of contacts, and geometry between molecule and interface. We study conductance in adlayers of molecules by considering transport through two identical wires. Implications for experiments are discussed.

Markov Dynamics as a Zooming Lens for Multiscale Community Detection: Non Clique-Like Communities and the Field-of-View Limit

In recent years, there has been a surge of interest in community detection algorithms for complex networks. A variety of computational heuristics, some with a long history, have been proposed for the identification of communities or, alternatively, of good graph partitions. In most cases, the algorithms maximize a particular objective function, thereby finding the ‘right’ split into communities. Although a thorough comparison of algorithms is still lacking, there has been an effort to design benchmarks, i.e., random graph models with known community structure against which algorithms can be evaluated. However, popular community detection methods and benchmarks normally assume an implicit notion of community based on clique-like subgraphs, a form of community structure that is not always characteristic of real networks. Specifically, networks that emerge from geometric constraints can have natural non clique-like substructures with large effective diameters, which can be interpreted as long-range communities. In this work, we show that long-range communities escape detection by popular methods, which are blinded by a restricted ‘field-of-view’ limit, an intrinsic upper scale on the communities they can detect. The field-of-view limit means that long-range communities tend to be overpartitioned. We show how by adopting a dynamical perspective towards community detection [1], [2], in which the evolution of a Markov process on the graph is used as a zooming lens over the structure of the network at all scales, one can detect both clique- or non clique-like communities without imposing an upper scale to the detection. Consequently, the performance of algorithms on inherently low-diameter, clique-like benchmarks may not always be indicative of equally good results in real networks with local, sparser connectivity. We illustrate our ideas with constructive examples and through the analysis of real-world networks from imaging, protein structures and the power grid, where a multiscale structure of non clique-like communities is revealed.

Conformational disorder of conjugated polymers: Implications for optical properties

A physical picture of a conjugated chain as a collection of almost planar segments, separated by large angular breaks arises from a microscopic model which includes conjugation and steric interactions. The conjugation part of the standard phenomenological Hamiltonian for torsional motion is also derived from the model. We obtain a probability distribution of the length of segments between those breaks as the relevant factor for the behavior of the chain. We also perform numerical simulations of the structure and properties of these chains; the results of this are in agreement with our analytic predictions. In explaining experimental data for optical properties, such as the second hyperpolarizability, γ, our theory provides improved agreement over previous models.

Molecular Wires: Charge Transport, Mechanisms, and Control

ABSTRACT: By molecular wires, one generally means molecular structures that transmit a signal between two termini. We discuss some theoretical models and analysis for electronically conductive molecular wires in which a single molecule conducts charge between two electrodes. This situation resembles both intramolecular non‐adiabatic electron transfer, in which electronic tunneling between donor and acceptor is seen, and mesoscopic quantum transport.

Third-order microscopic nonlinearities of very long chain polyenes: saturation phenomena and conformational effects

Abstract Using the living cyclopolymerization of diethyldipropargylmalonate, very long polyenes (up to 1100 carbon–carbon double bonds) are now available. Molecular masses of these polyenes are determined using the MALDI-TOF technique. Third-order polarizabilities γ of polyene-like molecules with very long conjugation length (N up to 1100 carbon–carbon double bonds) are measured using third-harmonic generation at 1.9 μm in THF solutions. γ values saturate around N=60 double bonds. Modelization of the dependence of γ with respect to N is based on a representation of a conjugated chain as a collection of planar segments separated by large angular breaks. A very good quantitive agreement between calculated and experimental data, both in terms of saturation length and γ/N values is clearly demonstrated.

The directional contact distance of two ellipsoids: Coarse-grained potentials for anisotropic interactions

We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation measured along their intercenter vector. This directional distance is derived from the elliptic contact function. The geometric meaning behind this approach is clarified. An elliptic pair potential for modeling arbitrary mixtures of elliptic particles, whether hard or soft, is proposed based on this distance. Comparisons with Gay-Berne potentials are discussed. Analytic expressions for the forces and torques acting on the elliptic particles are given.

Stochastic Kinetics of Viral Capsid Assembly Based on Detailed Protein Structures

We present a generic computational framework for the simulation of viral capsid assembly which is quantitative and specific. Starting from PDB files containing atomic coordinates, the algorithm builds a coarse-grained description of protein oligomers based on graph rigidity. These reduced protein descriptions are used in an extended Gillespie algorithm to investigate the stochastic kinetics of the assembly process. The association rates are obtained from a diffusive Smoluchowski equation for rapid coagulation, modified to account for water shielding and protein structure. The dissociation rates are derived by interpreting the splitting of oligomers as a process of graph partitioning akin to the escape from a multidimensional well. This modular framework is quantitative yet computationally tractable, with a small number of physically motivated parameters. The methodology is illustrated using two different viruses which are shown to follow quantitatively different assembly pathways. We also show how in this model the quasi-stationary kinetics of assembly can be described as a Markovian cascading process, in which only a few intermediates and a small proportion of pathways are present. The observed pathways and intermediates can be related a posteriori to structural and energetic properties of the capsid oligomers.

Protein multi-scale organization through graph partitioning and robustness analysis: application to the myosin-myosin light chain interaction.

Despite the recognized importance of the multi-scale spatio-temporal organization of proteins, most computational tools can only access a limited spectrum of time and spatial scales, thereby ignoring the effects on protein behavior of the intricate coupling between the different scales. Starting from a physico-chemical atomistic network of interactions that encodes the structure of the protein, we introduce a methodology based on multi-scale graph partitioning that can uncover partitions and levels of organization of proteins that span the whole range of scales, revealing biological features occurring at different levels of organization and tracking their effect across scales. Additionally, we introduce a measure of robustness to quantify the relevance of the partitions through the generation of biochemically-motivated surrogate random graph models. We apply the method to four distinct conformations of myosin tail interacting protein, a protein from the molecular motor of the malaria parasite, and study properties that have been experimentally addressed such as the closing mechanism, the presence of conserved clusters, and the identification through computational mutational analysis of key residues for binding.