Spectral partitions on infinite graphs

Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well defined spectral dimensions and spectral weights. These subgraphs are shown to be thermodynamically homogeneous and effectively decoupled.Comment: 8 pages, to appear on Journal of Physics

Graph-based Features for Automatic Online Abuse Detection

While online communities have become increasingly important over the years, the moderation of user-generated content is still performed mostly manually. Automating this task is an important step in reducing the financial cost associated with moderation, but the majority of automated approaches strictly based on message content are highly vulnerable to intentional obfuscation. In this paper, we discuss methods for extracting conversational networks based on raw multi-participant chat logs, and we study the contribution of graph features to a classification system that aims to determine if a given message is abusive. The conversational graph-based system yields unexpectedly high performance , with results comparable to those previously obtained with a content-based approach

Exact Ground States of Large Two-Dimensional Planar Ising Spin Glasses

Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to 3000x3000 spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the Bieche et al. approach.Comment: 11 pages, 5 figures; shortened introduction, extended results; to appear in Physical Review E 7

Meeting the Expectations of Your Heritage Culture: Links between Attachment Style, Intragroup Marginalisation, and Psychological Adjustment

This article has been made available through the Brunel Open Access Publishing Fund.This article has been made available through the Brunel Open Access Publishing Fund.Do insecurely-attached individuals perceive greater rejection from their heritage culture? Few studies have examined the antecedents and outcomes of this perceived rejection – termed intragroup marginalisation – in spite of its implications for the adjustment of cultural migrants to the mainstream culture. The present study investigated whether anxious and avoidant attachment orientations among cultural migrants were associated with greater intragroup marginalisation and, in turn, with lower subjective well-being and flourishing, and higher acculturative stress. Anxious attachment was associated with heightened intragroup marginalisation from friends and, in turn, with increased acculturative stress; anxious attachment was also associated with increased intragroup marginalisation from family. Avoidant attachment was linked with increased intragroup marginalisation from family and, in turn, with decreased subjective well-being

"Almost stable" matchings in the Roommates problem

An instance of the classical Stable Roommates problem (SR) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an SR instance with n agents, in which all preference lists are complete, the problem of finding a matching with the fewest number of blocking pairs is NP-hard and not approximable within n^{\frac{1}{2}-\varepsilon}, for any \varepsilon>0, unless P=NP. If the preference lists contain ties, we improve this result to n^{1-\varepsilon}. Also, we show that, given an integer K and an SR instance I in which all preference lists are complete, the problem of deciding whether I admits a matching with exactly K blocking pairs is NP-complete. By contrast, if K is constant, we give a polynomial-time algorithm that finds a matching with at most (or exactly) K blocking pairs, or reports that no such matching exists. Finally, we give upper and lower bounds for the minimum number of blocking pairs over all matchings in terms of some properties of a stable partition, given an SR instance I

A transition from river networks to scale-free networks

A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$ such points the network is grown by including them one by one according to the serial number into the growing network. The $t$-th point is attached to the $i$-th node of the network using the probability: $\pi_i(t) \sim k_i(t)\ell_{ti}^{\alpha}$ where $k_i(t)$ is the degree of the $i$-th node and $\ell_{ti}$ is the Euclidean distance between the points $t$ and $i$. Here $\alpha$ is a continuously tunable parameter and while for $\alpha=0$ one gets the simple Barab\'asi-Albert network, the case for $\alpha \to -\infty$ corresponds to the spatially continuous version of the well known Scheidegger's river network problem. The modulating parameter $\alpha$ is tuned to study the transition between the two different critical behaviors at a specific value $\alpha_c$ which we numerically estimate to be -2.Comment: 5 pages, 5 figur

Smallest Cubic and Quartic Graphs With a Given Number of Cutpoints and Bridges

For positive integers b and c, with c even, satisfying the inequalities b+1≤c≤2b, the minimum order of a connected cubic graph with b bridges and c cutpoints is computed. Furthermore, the structure of all such smallest cubic graphs is determined. For each positive integer c, the minimum order of a quartic graph with c cutpoints is calculated. Moreover, the structure and number of all such smallest quartic graphs are determined

Scanning Tunneling Microscopy and Fabrication of Nanometer Scale Structures at the Liquid-Gold Interface

The Scanning Tunneling Microscope (STM) can image gold surfaces covered with a variety of liquids. This paper reviews the results obtained using the STM to image gold surfaces covered with liquid. These results include the creation of 10 nm structures, images of the electrochemical process of electroplating, and the production of atomically flat Au (111) surfaces. We conclude that in the future STM will find further application in the area of nanostructure fabrication and electrochemistry. The trend in the field is toward greater control of the electrochemical environment

The Local Time Distribution of a Particle Diffusing on a Graph

We study the local time distribution of a Brownian particle diffusing along the links on a graph. In particular, we derive an analytic expression of its Laplace transform in terms of the Green's function on the graph. We show that the asymptotic behavior of this distribution has non-Gaussian tails characterized by a nontrivial large deviation function.Comment: 8 pages, two figures (included

Dynamics of Social Balance on Networks

We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad--a triangular loop with 1 or 3 unfriendly links--is reversed to make the triad balanced. With this dynamics, an infinite network undergoes a dynamic phase transition from a steady state to "paradise"--all links are friendly--as the propensity p for friendly links in an update event passes through 1/2. A finite network always falls into a socially-balanced absorbing state where no imbalanced triads remain. If the additional constraint that the number of imbalanced triads in the network does not increase in an update is imposed, then the network quickly reaches a balanced final state.Comment: 10 pages, 7 figures, 2-column revtex4 forma