Applications of Structural Balance in Signed Social Networks

We present measures, models and link prediction algorithms based on the structural balance in signed social networks. Certain social networks contain, in addition to the usual 'friend' links, 'enemy' links. These networks are called signed social networks. A classical and major concept for signed social networks is that of structural balance, i.e., the tendency of triangles to be 'balanced' towards including an even number of negative edges, such as friend-friend-friend and friend-enemy-enemy triangles. In this article, we introduce several new signed network analysis methods that exploit structural balance for measuring partial balance, for finding communities of people based on balance, for drawing signed social networks, and for solving the problem of link prediction. Notably, the introduced methods are based on the signed graph Laplacian and on the concept of signed resistance distances. We evaluate our methods on a collection of four signed social network datasets.Comment: 37 page

Cluster Model of Decagonal Tilings

A relaxed version of Gummelt's covering rules for the aperiodic decagon is considered, which produces certain random-tiling-type structures. These structures are precisely characterized, along with their relationships to various other random tiling ensembles. The relaxed covering rule has a natural realization in terms of a vertex cluster in the Penrose pentagon tiling. Using Monte Carlo simulations, it is shown that the structures obtained by maximizing the density of this cluster are the same as those produced by the corresponding covering rules. The entropy density of the covering ensemble is determined using the entropic sampling algorithm. If the model is extended by an additional coupling between neighboring clusters, perfectly ordered structures are obtained, like those produced by Gummelt's perfect covering rules.Comment: 10 pages, 20 figures, RevTeX; minor changes; to be published in Phys. Rev.

A Hybrid Genetic Algorithm for the Traveling Salesman Problem with Drone

This paper addresses the Traveling Salesman Problem with Drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or minimize the completion time for the truck and drone (min-time TSP-D). This problem has gained a lot of attention in the last few years since it is matched with the recent trends in a new delivery method among logistics companies. To solve the TSP-D, we propose a hybrid genetic search with dynamic population management and adaptive diversity control based on a split algorithm, problem-tailored crossover and local search operators, a new restore method to advance the convergence and an adaptive penalization mechanism to dynamically balance the search between feasible/infeasible solutions. The computational results show that the proposed algorithm outperforms existing methods in terms of solution quality and improves best known solutions found in the literature. Moreover, various analyses on the impacts of crossover choice and heuristic components have been conducted to analysis further their sensitivity to the performance of our method.Comment: Technical Report. 34 pages, 5 figure

A gradient system with a wiggly energy and relaxed EDP-convergence

If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic effects. We introduce a notion of evolutionary Gamma-convergence that relates the microscopic energy and the microscopic dissipation potential with their macroscopic limits via Gamma-convergence. This new notion generalizes the concept of EDP-convergence, which was introduced in arXiv:1507.06322, and is called "relaxed EDP-convergence". Both notions are based on De Giorgi's energy-dissipation principle, however the special structure of the dissipation functional in terms of the primal and dual dissipation potential is, in general, not preserved under Gamma-convergence. By investigating the kinetic relation directly and using general forcings we still derive a unique macroscopic dissipation potential. The wiggly-energy model of James et al serves as a prototypical example where this nontrivial limit passage can be fully analyzed.Comment: 43 pages, 8 figure

Size-effects of metamaterial beams subjected to pure bending: on boundary conditions and parameter identification in the relaxed micromorphic model

In this paper we model the size-effects of metamaterial beams under bending with the aid of the relaxed micromorphic continuum. We analyze first the size-dependent bending stiffness of heterogeneous fully discretized metamaterial beams subjected to pure bending loads. Two equivalent loading schemes are introduced which lead to a constant moment along the beam length with no shear force. The relaxed micromorphic model is employed then to retrieve the size-effects. We present a procedure for the determination of the material parameters of the relaxed micromorphic model based on the fact that the model operates between two well-defined scales. These scales are given by linear elasticity with micro and macro elasticity tensors which bound the relaxed micromorphic continuum from above and below, respectively. The micro elasticity tensor is specified as the maximum possible stiffness that is exhibited by the assumed metamaterial while the macro elasticity tensor is given by standard periodic first-order homogenization. For the identification of the micro elasticity tensor, two different approaches are shown which rely on affine and non-affine Dirichlet boundary conditions of candidate unit cell variants with the possible stiffest response. The consistent coupling condition is shown to allow the model to act on the whole intended range between macro and micro elasticity tensors for both loading cases. We fit the relaxed micromorphic model against the fully resolved metamaterial solution by controlling the curvature magnitude after linking it with the specimen's size. The obtained parameters of the relaxed micromorphic model are tested for two additional loading scenarios

Partial Strategyproofness: Relaxing Strategyproofness for the Random Assignment Problem

We present partial strategyproofness, a new, relaxed notion of strategyproofness for studying the incentive properties of non-strategyproof assignment mechanisms. Informally, a mechanism is partially strategyproof if it makes truthful reporting a dominant strategy for those agents whose preference intensities differ sufficiently between any two objects. We demonstrate that partial strategyproofness is axiomatically motivated and yields a parametric measure for "how strategyproof" an assignment mechanism is. We apply this new concept to derive novel insights about the incentive properties of the probabilistic serial mechanism and different variants of the Boston mechanism.Comment: Working Pape

Wellposedness of the discontinuous ODE associated with two-phase flows

We consider the initial value problem \dot x (t) = v(t,x(t)) \;\mbox{ for } t\in (a,b), \;\; x(t_0)=x_0 which determines the pathlines of a two-phase flow, i.e.\ $v=v(t,x)$ is a given velocity field of the type $$v(t,x)= \begin{cases} v^+(t,x) &\text{ if } x \in \Omega^+(t)\\ v^-(t,x) &\text{ if } x \in \Omega^-(t) \end{cases}$$ with $\Omega^\pm (t)$ denoting the bulk phases of the two-phase fluid system under consideration. The bulk phases are separated by a moving and deforming interface $\Sigma (t)$. Since we allow for flows with phase change, these pathlines are allowed to cross or touch the interface. Imposing a kind of transversality condition at $\Sigma (t)$, which is intimately related to the mass balance in such systems, we show existence and uniqueness of absolutely continuous solutions of the above ODE in case the one-sided velocity fields $v^\pm:\overline{{\rm gr}(\Omega^\pm)}\to \mathbb{R}^n$ are continuous in $(t,x)$ and locally Lipschitz continuous in $x$. Note that this is a necessary prerequisite for the existence of well-defined co-moving control volumes for two-phase flows, a basic concept for mathematical modeling of two-phase continua