Spectral Graph Forge: Graph Generation Targeting Modularity

Community structure is an important property that captures inhomogeneities common in large networks, and modularity is one of the most widely used metrics for such community structure. In this paper, we introduce a principled methodology, the Spectral Graph Forge, for generating random graphs that preserves community structure from a real network of interest, in terms of modularity. Our approach leverages the fact that the spectral structure of matrix representations of a graph encodes global information about community structure. The Spectral Graph Forge uses a low-rank approximation of the modularity matrix to generate synthetic graphs that match a target modularity within user-selectable degree of accuracy, while allowing other aspects of structure to vary. We show that the Spectral Graph Forge outperforms state-of-the-art techniques in terms of accuracy in targeting the modularity and randomness of the realizations, while also preserving other local structural properties and node attributes. We discuss extensions of the Spectral Graph Forge to target other properties beyond modularity, and its applications to anonymization

Direct Calculation of the Boundary SS Matrix for the Open Heisenberg Chain

We calculate the boundary $S$ matrix for the open antiferromagnetic spin $1/2$ isotropic Heisenberg chain with boundary magnetic fields. Our approach, which starts from the model's Bethe Ansatz solution, is an extension of the Korepin-Andrei-Destri method. Our result agrees with the boundary $S$ matrix for the boundary sine-Gordon model with $\beta^2 \rightarrow 8\pi$ and with ``fixed'' boundary conditions.Comment: 29 pages, plain TEX, UMTG-17

Solution of a minimal model for many-body quantum chaos

We solve a minimal model for quantum chaos in a spatially extended many-body system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time evolution. Quantum states at each site span a $q$-dimensional Hilbert space and time evolution for a pair of sites is generated by a $q^2\times q^2$ random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbour on one side during the first half of the evolution period, and to its neighbour on the other side during the second half of the period. We show how dynamical behaviour averaged over realisations of the random matrices can be evaluated using diagrammatic techniques, and how this approach leads to exact expressions in the large-$q$ limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth and operator spreading.Comment: Accepted in PR

Scale hierarchy in Horava-Lifshitz gravity: a strong constraint from synchrotron radiation in the Crab nebula

Horava-Lifshitz gravity models contain higher order operators suppressed by a characteristic scale, which is required to be parametrically smaller than the Planck scale. We show that recomputed synchrotron radiation constraints from the Crab nebula suffice to exclude the possibility that this scale is of the same order of magnitude as the Lorentz breaking scale in the matter sector. This highlights the need for a mechanism that suppresses the percolation of Lorentz violation in the matter sector and is effective for higher order operators as well.Comment: 4 page, 2 figures; v2: minor changes to match published versio

A Finite Element Model for Describing the Effect of Muscle Shortening on Surface EMG

A finite-element model for the generation of single fiber action potentials in a muscle undergoing various degrees of fiber shortening is developed. The muscle is assumed fusiform with muscle fibers following a curvilinear path described by a Gaussian function. Different degrees of fiber shortening are simulated by changing the parameters of the fiber path and maintaining the volume of the muscle constant. The conductivity tensor is adapted to the muscle fiber orientation. In each point of the volume conductor, the conductivity of the muscle tissue in the direction of the fiber is larger than that in the transversal direction. Thus, the conductivity tensor changes point-by-point with fiber shortening, adapting to the fiber paths. An analytical derivation of the conductivity tensor is provided. The volume conductor is then studied with a finite-element approach using the analytically derived conductivity tensor. Representative simulations of single fiber action potentials with the muscle at different degrees of shortening are presented. It is shown that the geometrical changes in the muscle, which imply changes in the conductivity tensor, determine important variations in action potential shape, thus affecting its amplitude and frequency content. The model provides a new tool for interpreting surface EMG signal features with changes in muscle geometry, as it happens during dynamic contractions

Challenging the paradigm of singularity excision in gravitational collapse

A paradigm deeply rooted in modern numerical relativity calculations prescribes the removal of those regions of the computational domain where a physical singularity may develop. We here challenge this paradigm by performing three-dimensional simulations of the collapse of uniformly rotating stars to black holes without excision. We show that this choice, combined with suitable gauge conditions and the use of minute numerical dissipation, improves dramatically the long-term stability of the evolutions. In turn, this allows for the calculation of the waveforms well beyond what previously possible, providing information on the black-hole ringing and setting a new mark on the present knowledge of the gravitational-wave emission from the stellar collapse to a rotating black hole.Comment: 4 pages, 4 figures, accepted for publication on Phys. Rev. Let