We study the superconductivity pairing symmetry in Sr2RuO4 in the limit of small interaction by extending a renormalization group calculation developed by Raghu et al. [Phys. Rev. B 81, 224505 (2010)] to include spin-orbit coupling and multiband effects. We show these effects to be crucial to discriminate between the possible order parameters. In contrast to previous results and without the necessity of fine-tuning, we obtain pseudospin-triplet gaps of the same order of magnitude on the two-dimensional γ band and the quasi-one-dimensional α and β bands. The ratio of the gap amplitude on the different bands varies continuously with the interaction parameter. The favored pairing symmetry is shown to be chiral when γ is slightly dominant and helical when α and β are slightly dominant.

We reformulate the topological symmetry breaking scheme for phase transitions in systems with anyons in a grahical manner. A new set of quantities called vertex lifiting coefficients (VLCs) is introduced and used to specify the the full operator content of the broken phase. First, it is shown how the assumption that a set of charges behaves like the vacuum of a new theory naturally leads to diagrammatic consistency conditions for a condensate. This recovers the notion of a condensate used in earlier aproaches and uncovers the connection to pure mathematics. The VLCs are needed to solve the consistency conditions and establish the mapping of the fusion and splitting spaces of the broken theory into the parent phase. This enables one to calculate the full set of topological data (S-, T -, R-and F -matrices) for the condensed phase and closed form expressions in terms of the VLCs are provided. We furthermore furnish a cocrete recipe to lift arbitrary diagrams directly from the condensed phase to the original phase using only a limited number of VLCs and we describe a method for the explicit calculation of VLCs for a large class of bosonic condensates. This allows for the explicit calculation of condensed-phase diagrams in many physically relevant cases and representative examples are worked out in detail.

We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling constant for each conjugacy class of the gauge group. To probe the phase structure we use a complete set of open and closed anyonic string operators. The open strings allow one to determine the particle content of the condensate, whereas the closed strings enable us to determine the matrix elements of the modular S-matrix, in both the unbroken and broken phases. From the measured broken S-matrix we may read off the sectors that split or get identified in the broken phase, as well as the sectors that are confined. In this sense the modular S-matrix can be employed as a matrix valued nonlocal order parameter from which the low-energy effective theories that occur in different regions of parameter space can be fully determined. To verify our predictions, we studied a non-abelian anyon model based on the quaternion group H =D 2 of the order of eight by Monte Carlo simulation. We probe part of the phase diagram for the pure gauge theory and find a variety of phases with magnetic condensates leading to various forms of (partial) confinement in complete agreement with the algebraic breaking analysis. Also the order of various transitions is established.

The metabolic modelling community has established the gold standard for bottom-up systems biology with reconstruction, validation and simulation of mechanistic genome-scale models. Similar methods have not been established for signal transduction networks, where the representation of complexes and internal states leads to scalability issues in both model formulation and execution. While rule-and agent-based methods allow efficient model definition and execution, respectively, model parametrisation introduces an additional layer of uncertainty due to the sparsity of reliably measured parameters. Here, we present a scalable method for parameter-free simulation of mechanistic signal transduction networks. It is based on rxncon and uses a bipartite Boolean logic with separate update rules for reactions and states. Using two generic update rules, we enable translation of any rxncon model into a unique Boolean model, which can be used for network validation and simulation-allowing the prediction of system-level function directly from molecular mechanistic data. Through scalable model definition and simulation, and the independence of quantitative parameters, it opens up for simulation and validation of mechanistic genome-scale models of signal transduction networks.

We present a new family of gauge invariant non-local order parameters ∆ A α for (non-abelian) discrete gauge theories on a Euclidean lattice, which are in one-to-one correspondence with the excitation spectrum that follows from the representation theory of the quantum double D(H) of the finite group H. These combine magnetic flux-sector labeled by a conjugacy class with an electric representation of the centralizer subgroup that commutes with the flux. In particular cases like the trivial class for magnetic flux, or the trivial irrep for electric charge, these order parameters reduce to the familiar Wilson and the 't Hooft operators respectively. It is pointed out that these novel operators are crucial for probing the phase structure of a class of discrete lattice models we define, using Monte Carlo simulations.

We present a protocol for building, validating and simulating models of signal transduction networks.These networks are challenging modelling targets due to the combinatorial complexity and sparse data, which have made it a major challenge even to formalise the current knowledge. To address this, the community has developed methods to model biomolecular reaction networks based on site dynamics. The strength of this approach is that reactions and states can be defined at variable resolution, which makes it possible to adapt the model resolution to the empirical data. This improves both scalability and accuracy, making it possible to formalise large models of signal transduction networks. Here, we present a method to build and validate large models of signal transduction networks. The workflow is based on rxncon, the reaction-contingency language. In a five-step process, we create a mechanistic network model, convert it into an executable Boolean model, use the Boolean model to evaluate and improve the network, and finally export the rxncon model into a rule based format. We provide an introduction to the rxncon language and an annotated, step-by-step protocol for the workflow. Finally, we create a small model of the insulin signalling pathway to illustrate the protocol, together with some of the challenges -and some of their solutions -in modelling signal transduction.

We study charged spin textures (CST) over the Moore-Read quantum Hall state at filling factor 5/2. We develop an algebraic framework and show that the pairing condition that is inherent in the Moore-Read state naturally leads to a class of charged spin textures, labeled by winding numbers [w I , w II ]. The fundamental CST, with labels [1, 0] and electric charge e/4, is identified with the polar core vortex known in the spin-1 BEC literature. The spin texture carried by the fusion product of fundamental CSTs is correlated with the fusion channel of the underlying non-Abelian quasiholes.

The metabolic modelling community has established the gold standard for bottom-up systems biology with reconstruction, validation and simulation of mechanistic genome-scale models. In contrast, current established methods do not support genome-scale mechanistic models of signal transduction networks. These networks encode information through internal states, and dealing with these states leads to scalability issues both in model formulation and execution. While rule based modelling can be used for efficient model definition (through rules) and simulation (through agent based execution), these quantitative models require parametrisation. This introduces yet another layer of uncertainty, due to the sparsity of reliably measured parameters. Hence, parameter-free simulation and validation will be important to support large-scale reconstruction and analysis of signal transduction network models. Here, we present a scalable method for parameterfree simulation of mechanistic signal transduction network models. It is based on rxncon, the reaction-contingency language, which describes the signalling network in terms of elemental reactions and states. We develop two generic update rules for states and reactions, based on detail analysis of two minimal reaction motifs, that can be used to map an arbitrary rxncon network on fully defined bipartite Boolean model. Locally defined update rules are assembled into a functional model without system level optimisation, making the methods suitable for network validation. Furthermore, an underlying model defined solely in terms of molecular reactions and causalities can be used to explain and predict system level behaviour. Taken together, we present a method for parameter-free simulation of mechanistic signal transduction models. Through scalable model definition and simulation, and the independence of quantitative parameters, it opens up for simulation and validation of mechanistic genome-scale models of signal transduction networks.