Using multilayer network analysis to explore the temporal dynamics of collective behavior

This work was supported by the National Science Foundation IOS grant 1456010 and the National Institute of Health grant GM115509 to N.P.-W.Peer reviewedPublisher PD

Can multilayer networks advance animal behavior research?

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Interactions among individual animals — and between these individuals and their environment — yield complex, multifaceted systems. The development of multilayer network analysis offers a promising new approach for studying animal social behavior and relating it to eco-evolutionary dynamics

The use of multilayer network analysis in animal behaviour

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.We gratefully acknowledge the 806 supporters of MX16: the UC Davis Institute for Social Sciences, the U.S. Army Research Office 807 under Multidisciplinary University Research Initiative Award No. W911NF-13-1-0340, the UC 808 Davis Complexity Sciences Center, the UC Davis Anthropology Department, the UC Davis 809 Graduate Student Association, the UC Davis Department of Engineering, and the UC Davis 810 Office of Research.Network analysis has driven key developments in research on animal behaviour by providing quantitative methods to study the social structures of animal groups and populations. A recent formalism, known as multilayer network analysis, has advanced the study of multifaceted networked systems in many disciplines. It offers novel ways to study and quantify animal behaviour through connected ‘layers’ of interactions. In this article, we review common questions in animal behaviour that can be studied using a multilayer approach, and we link these questions to specific analyses. We outline the types of behavioural data and questions that may be suitable to study using multilayer network analysis. We detail several multilayer methods, which can provide new insights into questions about animal sociality at individual, group, population and evolutionary levels of organization. We give examples for how to implement multilayer methods to demonstrate how taking a multilayer approach can alter inferences about social structure and the positions of individuals within such a structure. Finally, we discuss caveats to undertaking multilayer network analysis in the study of animal social networks, and we call attention to methodological challenges for the application of these approaches. Our aim is to instigate the study of new questions about animal sociality using the new toolbox of multilayer network analysis.Natural Environment Research Council (NERC)National Science Foundation (NSF) Graduate Research FellowshipNFS IOS grantNIH R01NERC standard gran

Critical currents in Josephson junctions, with unconventional pairing symmetry: dx2−y2+isd_{x^2-y^2}+is versus dx2−y2+idxyd_{x^2-y^2}+id_{xy}

Phenomenological Ginzburg-Landau theory is used to calculate the possible spontaneous vortex states that may exist at corner junctions of $d_{x^2-y^2}+ix$-wave, (where $x=s$ or $x=d_{xy}$) and s-wave superconductors. We study the magnetic flux and the critical current modulation with the junction orientation angle $\theta$, the magnitude of the order parameter, and the magnetic field $H$. It is seen that the critical current $I_c$ versus the magnetic flux $\Phi$ relation is symmetric / asymmetric for $x=d_{xy}/s$ when the orientation is exactly such that the lobes of the dominant $d_{x^2-y^2}$-wave order parameter points towards the two junctions, which are at right angles for the corner junction. The conclusion is that a measurement of the $I_c(\Phi)$ relation may distinguish which symmetry ($d_{x^2-y^2}+is$ or $d_{x^2-y^2}+id_{xy}$) the order parameter has.Comment: 11 pages with 11 figures, Changed conten

Superconducting Order Parameter in Bi-Layer Cuprates: Occurrence of π\pi Phase Shifts in Corner Junctions

We study the order parameter symmetry in bi-layer cuprates such as YBaCuO, where interesting $\pi$ phase shifts have been observed in Josephson junctions. Taking models which represent the measured spin fluctuation spectra of this cuprate, as well as more general models of Coulomb correlation effects, we classify the allowed symmetries and determine their associated physical properties. $\pi$ phase shifts are shown to be a general consequence of repulsive interactions, independent of whether a magnetic mechanism is operative. While it is known to occur in d-states, this behavior can also be associated with (orthorhombic) s-symmetry when the two sub-band gaps have opposite phase. Implications for the magnitude of $T_c$ are discussed.Comment: 5 pages, RevTeX 3.0, 9 figures (available upon request

Infrared conductivity of a d_{x^2-y^2}-wave superconductor with impurity and spin-fluctuation scattering

Calculations are presented of the in-plane far-infrared conductivity of a d_{x^2-y^2}-wave superconductor, incorporating elastic scattering due to impurities and inelastic scattering due to spin fluctuations. The impurity scattering is modeled by short-range potential scattering with arbitrary phase shift, while scattering due to spin fluctuations is calculated within a weak-coupling Hubbard model picture. The conductivity is characterized by a low-temperature residual Drude feature whose height and weight are controlled by impurity scattering, as well as a broad peak centered at 4 Delta_0 arising from clean-limit inelastic processes. Results are in qualitative agreement with experiment despite missing spectral weight at high energies.Comment: 29 pages (11 tar-compressed-uuencoded Postscript figures), REVTeX 3.0 with epsf macro

Local density of states for the corner geometry interface of d-wave superconductors, within the extended Hubbard model

The spatial variations of the order parameter, and the local density of states (LDOS) on the corner of s-wave or $d_{x^2-y^2}$-wave superconductors, as well as in superconductor-insulator-normal metal interfaces, are calculated self consistently using the Bogoliubov-deGennes formalism within the two dimensional extended Hubbard model. The exact diagonalization method is used. Due to the suppression of the dominant d-wave order parameter, the extended s-wave order parameter is induced near the surface, that alternates its sign for the topmost sites at adjacent edges of the lattice and decays to zero in the bulk. The presence of surface roughness results into the appearance of the zero band conduction peak (ZBCP) near the corner surface which lacks from the predictions of the quasiclassical theory.Comment: 13 pages with 17 figure

Magnetic-interference patterns in Josephson junctions with d+is symmetry

The magnetic interference pattern and the spontaneous flux in unconventional Josephson junctions of superconductors with d+is symmetry are calculated for different reduced junction lengths and the relative factor of the d and s wave components. This is a time reversal broken symmetry state. We study the stability of the fractional vortex and antivortex which are spontaneously formed and examine their evolution as we change the length and the relative factor of d and s wave components. The asymmetry in the field modulated diffraction pattern exists for lengths as long as L=10\lambda_J.Comment: 8 pages, 6 eps files, submitted to PR