Knotted domain strings

We construct meta-stable knotted domain strings on the surface of a soliton of the shape of a torus in 3+1 dimensions. We consider the simplest case of Z2 Wess-Zumino-type domain walls for which we can cover the torus with a domain string accompanied with an anti-domain string. In this theory, all (p,q)-torus knots can be realized as a linked pair of a(n) (un)knotted domain string and an anti-domain string.Comment: 6 pages, 8 figures; V2: extended version with more details about the host model, the numerics and the stability of the solution

Exploiting the Synergy Between Gossiping and Structured Overlays

In this position paper we argue for exploiting the synergy between gossip-based algorithms and structured overlay networks (SON). These two strands of research have both aimed at building fault-tolerant, dynamic, self-managing, and large-scale distributed systems. Despite the common goals, the two areas have, however, been relatively isolated. We focus on three problem domains where there is an untapped potential of using gossiping combined with SONs. We argue for applying gossip-based membership for ring-based SONs---such as Chord and Bamboo---to make them handle partition mergers and loopy networks. We argue that small world SONs---such as Accordion and Mercury---are specifically well-suited for gossip-based membership management. The benefits would be better graph-theoretic properties. Finally, we argue that gossip-based algorithms could use the overlay constructed by SONs. For example, many unreliable broadcast algorithms for SONs could be augmented with anti-entropy protocols. Similarly, gossip-based aggregation could be used in SONs for network size estimation and load-balancing purposes

Scalable Peer-to-Peer Indexing with Constant State

We present a distributed indexing scheme for peer to peer networks. Past work on distributed indexing traded off fast search times with non-constant degree topologies or network-unfriendly behavior such as flooding. In contrast, the scheme we present optimizes all three of these performance measures. That is, we provide logarithmic round searches while maintaining connections to a fixed number of peers and avoiding network flooding. In comparison to the well known scheme Chord, we provide competitive constant factors. Finally, we observe that arbitrary linear speedups are possible and discuss both a general brute force approach and specific economical optimizations

Self-Organizing Flows in Social Networks

Social networks offer users new means of accessing information, essentially relying on "social filtering", i.e. propagation and filtering of information by social contacts. The sheer amount of data flowing in these networks, combined with the limited budget of attention of each user, makes it difficult to ensure that social filtering brings relevant content to the interested users. Our motivation in this paper is to measure to what extent self-organization of the social network results in efficient social filtering. To this end we introduce flow games, a simple abstraction that models network formation under selfish user dynamics, featuring user-specific interests and budget of attention. In the context of homogeneous user interests, we show that selfish dynamics converge to a stable network structure (namely a pure Nash equilibrium) with close-to-optimal information dissemination. We show in contrast, for the more realistic case of heterogeneous interests, that convergence, if it occurs, may lead to information dissemination that can be arbitrarily inefficient, as captured by an unbounded "price of anarchy". Nevertheless the situation differs when users' interests exhibit a particular structure, captured by a metric space with low doubling dimension. In that case, natural autonomous dynamics converge to a stable configuration. Moreover, users obtain all the information of interest to them in the corresponding dissemination, provided their budget of attention is logarithmic in the size of their interest set

Multiple firing coherence resonances in excitatory and inhibitory coupled neurons

The impact of inhibitory and excitatory synapses in delay-coupled Hodgkin--Huxley neurons that are driven by noise is studied. If both synaptic types are used for coupling, appropriately tuned delays in the inhibition feedback induce multiple firing coherence resonances at sufficiently strong coupling strengths, thus giving rise to tongues of coherency in the corresponding delay-strength parameter plane. If only inhibitory synapses are used, however, appropriately tuned delays also give rise to multiresonant responses, yet the successive delays warranting an optimal coherence of excitations obey different relations with regards to the inherent time scales of neuronal dynamics. This leads to denser coherence resonance patterns in the delay-strength parameter plane. The robustness of these findings to the introduction of delay in the excitatory feedback, to noise, and to the number of coupled neurons is determined. Mechanisms underlying our observations are revealed, and it is suggested that the regularity of spiking across neuronal networks can be optimized in an unexpectedly rich variety of ways, depending on the type of coupling and the duration of delays.Comment: 7 two-column pages, 6 figures; accepted for publication in Communications in Nonlinear Science and Numerical Simulatio

Computing Multidimensional Persistence

The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a polynomial time algorithm for computing multidimensional persistence. We recast this computation as a problem within computational algebraic geometry and utilize algorithms from this area to solve it. While the resulting problem is Expspace-complete and the standard algorithms take doubly-exponential time, we exploit the structure inherent withing multifiltrations to yield practical algorithms. We implement all algorithms in the paper and provide statistical experiments to demonstrate their feasibility.Comment: This paper has been withdrawn by the authors. Journal of Computational Geometry, 1(1) 2010, pages 72-100. http://jocg.org/index.php/jocg/article/view/1

Discovering universal statistical laws of complex networks

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their generalisation power, which we identify with large structural variability and absence of constraints imposed by the construction scheme. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This allows, for instance, to infer global features from local ones using regression models trained on networks with high generalisation power. Our results confirm and extend previous findings regarding the synchronisation properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks with good approximation. Finally, we demonstrate on three different data sets (C. elegans' neuronal network, R. prowazekii's metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models

The role of acid in the formation of hydrogen-bonded networks featuring 4,4'-dicarboxy-2,2'-bipyridine (H2dcbp): Synthesis, structural and magnetic characterisation of {[Cu(H2dcbp)Cl2].H2O}2 and [Cu(H2dcbp)(NO3)2(H2O)]

Reported herein are the synthesis, structural and magnetic characterisation of two hydrogen-bonded networks featuring the 4,4?-dicarboxy-2,2?-bipyridine (H2dcbp) ligand: {[Cu(H2dcbp)(Cl)2]·H2O}2 1 and [Cu(H2dcbp)(NO3)2(H2O)] 2. Compounds 1 and 2 result from the reaction of CuCl2 and Cu(NO3)2, respectively, with H2dcbp under hydrothermal conditions in the presence of either HCl or HNO3. The acid ensures that H2dcbp remains protonated and provides the anions required for charge balance irrespective of Cu(II) precursor. Within 1 and 2 the H2dcbp ligand performs a dual role of Cu(II) coordination, via the 2,2?-bipyridine moiety, and propagates the formation of chains through hydrogen-bonding involving the peripheral 4,4?-dicarboxylic acid functionalities. Additional hydrogen bonding between the 4,4?-dicarboxylic acid groups, metal bound chloride and nitrate anions, in 1 and 2 respectively, and water molecules generate 3D networks. Variable temperature magnetic susceptibility measurements reveal very weak antiferromagnetic coupling between the Cu(II) centres across the chloride bridges in 1 (J = ?3.02 cm?1)