Backbone colorings along perfect matchings

Given a graph $G=(V,E)$ and a spanning subgraph $H$ of $G$ (the backbone of $G$), a backbone coloring for $G$ and $H$ is a proper vertex coloring $V\rightarrow \{1,2,\ldots\}$ of $G$ in which the colors assigned to adjacent vertices in $H$ differ by at least two. In a recent paper, backbone colorings were introduced and studied in cases were the backbone is either a spanning tree or a spanning path. Here we study the case where the backbone is a perfect matching. We show that for perfect matching backbones of $G$ the number of colors needed for a backbone coloring of $G$ can roughly differ by a multiplicative factor of at most $\frac{4}{3}$ from the chromatic number $\chi(G)$. We show that the computational complexity of the problem ``Given a graph $G$ with a perfect matching $M$, and an integer $\ell$, is there a backbone coloring for $G$ and $M$ with at most $\ell$ colors?'' jumps from polynomial to NP-complete between $\ell=3$ and $\ell=4$. Finally, we consider the case where $G$ is a planar graph

Toughness and hamiltonicity in kk-trees

We consider toughness conditions that guarantee the existence of a hamiltonian cycle in $k$-trees, a subclass of the class of chordal graphs. By a result of Chen et al.\ 18-tough chordal graphs are hamiltonian, and by a result of Bauer et al.\ there exist nontraceable chordal graphs with toughness arbitrarily close to $\frac{7}{4}$. It is believed that the best possible value of the toughness guaranteeing hamiltonicity of chordal graphs is less than 18, but the proof of Chen et al.\ indicates that proving a better result could be very complicated. We show that every 1-tough 2-tree on at least three vertices is hamiltonian, a best possible result since 1-toughness is a necessary condition for hamiltonicity. We generalize the result to $k$-trees for $k\ge 2$: Let $G$ be a $k$-tree. If $G$ has toughness at least $\frac{k+1}{3},$ then $G$ is hamiltonian. Moreover, we present infinite classes of nonhamiltonian 1-tough $k$-trees for each $k\ge 3

Closing the gap? Twitter as an instrument for connected representation

In this chapter, we present a typology of the tweeting behaviour of candidates as a means of analysing the extent to which politicians are harnessing the potential of social media to actively interact with their constituents. Our research, which included content analysis of tweets (n = 13,637) from all the Conservative and Labour tweeting candidates during the 2010 U.K. General Election, focused on four aspects of tweets: type (normal post, interaction, retweet, retweet with comment); interaction (with, e.g. a politician, journalist, citizen); function (e.g. updating, promoting, advice giving, debating); and topic. Additionally, a qualitative reading on the use of personal tweets was carried out. By examining candidates’ tweeting behaviour, we show that British politicians still mainly use Twitter as a unidirectional form of communication. They are neglecting the possibility this social network offers for, what we call, connected representation

Imitating speech in an unfamiliar language and an unfamiliar non-native accent in the native language

This study concerns individual differences in speech imitation ability and the role that lexical representations play in imitation. We examined 1) whether imitation of sounds in an unfamiliar language (L0) is related to imitation of sounds in an unfamiliar non-native accent in the speaker’s native language (L1) and 2) whether it is easier or harder to imitate speech when you know the words to be imitated. Fifty-nine native Dutch speakers imitated words with target vowels in Basque (/a/ and /e/) and Greekaccented Dutch (/i/ and /u/). Spectral and durational analyses of the target vowels revealed no relationship between the success of L0 and L1 imitation and no difference in performance between tasks (i.e., L1 imitation was neither aided nor blocked by lexical knowledge about the correct pronunciation). The results suggest instead that the relationship of the vowels to native phonological categories plays a bigger role in imitatio

List coloring in the absence of a linear forest.

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,…,k}. Let Pn denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that Listk-Coloring can be solved in polynomial time for graphs with no induced rP1+P5, hereby extending the result of Hoàng, Kamiński, Lozin, Sawada and Shu for graphs with no induced P5. Our result is tight; we prove that for any graph H that is a supergraph of P1+P5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H

λ-backbone colorings along pairwise disjoint stars and matchings

Given an integer λ≥2, a graph G=(V,E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring of (G,H) is a proper vertex coloring V→{1,2,…} of G, in which the colors assigned to adjacent vertices in H differ by at least λ. We study the case where the backbone is either a collection of pairwise disjoint stars or a matching. We show that for a star backbone S of G the minimum number ℓ for which a λ-backbone coloring of (G,S) with colors in {1,…,ℓ} exists can roughly differ by a multiplicative factor of at most View the MathML source from the chromatic number χ(G). For the special case of matching backbones this factor is roughly View the MathML source. We also show that the computational complexity of the problem “Given a graph G with a star backbone S, and an integer ℓ, is there a λ-backbone coloring of (G,S) with colors in {1,…,ℓ}?” jumps from polynomially solvable to NP-complete between ℓ=λ+1 and ℓ=λ+2 (the case ℓ=λ+2 is even NP-complete for matchings). We finish the paper by discussing some open problems regarding planar graphs

Fusion cuisine:A functional approach to interdisciplinary cooking in journalism studies

Journalism studies as an academic field is characterized by multidisciplinarity. Focusing on one object of study, journalism and the news, it established itself by integrating and synthesizing approaches from established disciplines – a tendency that lives on today. This constant gaze to the outside for conceptual inspiration and methodological tools lends itself to a journalism studies that is a fusion cuisine of media, communication, and related scholarship. However, what happens when this object becomes as fragmented and multifaceted as the ways we study it? This essay addresses the challenge of multiplicity in journalism studies by introducing an audience-centred, functional approach to scholarship. We argue this approach encourages the creative intellectual advancements afforded by interdisciplinary experimental cooking while respecting the classical intellectual questions that helped define the culinary tradition of journalism studies in the first place. In so doing, we offer a recipe for journalism studies fusion cooking that: (1) considers technological change (audiences’ diets), (2) analyses institutional change (audiences’ supermarket of information), and (3) evaluates journalism’s societal and democratic impact (audiences’ cuisines and health)

Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale

The detection of sound begins when energy derived from acoustic stimuli deflects the hair bundles atop hair cells. As hair bundles move, the viscous friction between stereocilia and the surrounding liquid poses a fundamental challenge to the ear's high sensitivity and sharp frequency selectivity. Part of the solution to this problem lies in the active process that uses energy for frequency-selective sound amplification. Here we demonstrate that a complementary part involves the fluid-structure interaction between the liquid within the hair bundle and the stereocilia. Using force measurement on a dynamically scaled model, finite-element analysis, analytical estimation of hydrodynamic forces, stochastic simulation and high-resolution interferometric measurement of hair bundles, we characterize the origin and magnitude of the forces between individual stereocilia during small hair-bundle deflections. We find that the close apposition of stereocilia effectively immobilizes the liquid between them, which reduces the drag and suppresses the relative squeezing but not the sliding mode of stereociliary motion. The obliquely oriented tip links couple the mechanotransduction channels to this least dissipative coherent mode, whereas the elastic horizontal top connectors stabilize the structure, further reducing the drag. As measured from the distortion products associated with channel gating at physiological stimulation amplitudes of tens of nanometres, the balance of forces in a hair bundle permits a relative mode of motion between adjacent stereocilia that encompasses only a fraction of a nanometre. A combination of high-resolution experiments and detailed numerical modelling of fluid-structure interactions reveals the physical principles behind the basic structural features of hair bundles and shows quantitatively how these organelles are adapted to the needs of sensitive mechanotransduction.Comment: 21 pages, including 3 figures. For supplementary information, please see the online version of the article at http://www.nature.com/natur

Computing with carbon nanotubes: optimization of threshold logic gates using disordered nanotube/polymer composites

This paper explores the use of single-walled carbon nanotube (SWCNT)/poly(butyl methacrylate) composites as a material for use in unconventional computing. The mechanical and electrical properties of the materials are investigated. The resulting data reveal a correlation between the SWCNT concentration/viscosity/conductivity and the computational capability of the composite. The viscosity increases significantly with the addition of SWCNTs to the polymer, mechanically reinforcing the host material and changing the electrical properties of the composite. The electrical conduction is found to depend strongly on the nanotube concentration; Poole-Frenkel conduction appears to dominate the conductivity at very low concentrations (0.11% by weight). The viscosity and conductivity both show a threshold point around 1% SWCNT concentration; this value is shown to be related to the computational performance of the material. A simple optimization of threshold logic gates shows that satisfactory computation is only achieved above a SWCNT concentration of 1%. In addition, there is some evidence that further above this threshold the computational efficiency begins to decrease