Colouring exact distance graphs of chordal graphs

For a graph $G=(V,E)$ and positive integer $p$, the exact distance-$p$ graph $G^{[\natural p]}$ is the graph with vertex set $V$ and with an edge between vertices $x$ and $y$ if and only if $x$ and $y$ have distance $p$. Recently, there has been an effort to obtain bounds on the chromatic number $\chi(G^{[\natural p]})$ of exact distance-$p$ graphs for $G$ from certain classes of graphs. In particular, if a graph $G$ has tree-width $t$, it has been shown that $\chi(G^{[\natural p]}) \in \mathcal{O}(p^{t-1})$ for odd $p$, and $\chi(G^{[\natural p]}) \in \mathcal{O}(p^{t}\Delta(G))$ for even $p$. We show that if $G$ is chordal and has tree-width $t$, then $\chi(G^{[\natural p]}) \in \mathcal{O}(p\, t^2)$ for odd $p$, and $\chi(G^{[\natural p]}) \in \mathcal{O}(p\, t^2 \Delta(G))$ for even $p$. If we could show that for every graph $H$ of tree-width $t$ there is a chordal graph $G$ of tree-width $t$ which contains $H$ as an isometric subgraph (i.e., a distance preserving subgraph), then our results would extend to all graphs of tree-width $t$. While we cannot do this, we show that for every graph $H$ of genus $g$ there is a graph $G$ which is a triangulation of genus $g$ and contains $H$ as an isometric subgraph.Comment: 11 pages, 2 figures. Versions 2 and 3 include minor changes, which arise from reviewers' comment

Etnografía de la Planta Ballenera de Quintay: Reportajes, Informes, Historias

The processing of a whale in a shore whaling station began with their arrival. The whale was moored with a line to the winch and hoisted to the slipwayand on the platform flensing. At the platform,bubbler, meat and bones were separated and send to their own cooking units or “cocinerías”. From cookeries, oil and a mixture of liquids and solids were sent to be purified. Solid wastes were sent to the whale-meal or guanoplant. Eight shore whaling station was built in Chile, located between Punta Arenas in the south and Iquique in the north. In this paper, we construct a retrospective ethnography of Quintayshore whaling station,using the reports and written reports by people who observed the plant in full operation. In the reportages, the issues about whale processing, has been selectively represented by those who knew the practices in a “ethnographic present.”El procesamiento de una ballena en una planta costera terrestre comienza con la llegada de la ballena. La ballena era amarrada con una línea al huinche e izada a la rampa y luego a la plataforma de descuartizamiento. Allí se separaba el tocino, la carne y los huesos que iban a sus propias unidades de cocción o “cocinerías”. Se obtenía aceite y una mezcla de líquidos y sólidos que eran enviados a plantas de purificación. Los residuos sólidos eran enviados a la planta de harina o de guano. En Chile se construyeron ocho plantas industriales costeras localizadas entre Punta Arenas por el sur e Iquique por el norte. En este trabajo se intentará construir una etnografía retrospectiva de la planta ballenera de Quintay, utilizando los relatos en forma de reportajes, escritos por personas que observaron la planta en pleno funcionamiento. Nos interesa dar cuenta como han sido selectivamente representados determinados aspectos del procesamiento de las ballenas en una planta costera por aquellos que pudieron conocer las prácticas en un “presente etnográfico”

New automatic control system to improve the operation of PMD devices

In this thesis project, a functional PMD device was designed for the implementation of a control system and thus achieve a more efficient and controlled way of the propellant extraction process. For this design process, an analysis was carried out on the different types of PMD devices and which ones could be used in a control system, as well as the selection of certain conditions of the meteosat second generation (MSG) satellite, to focus the design to something more attached to in practice.Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i InfraestructuraObjectius de Desenvolupament Sostenible::12 - Producció i Consum Responsable

Clique immersions in graphs of independence number two with certain forbidden subgraphs

The Lescure-Meyniel conjecture is the analogue of Hadwiger's conjecture for the immersion order. It states that every graph $G$ contains the complete graph $K_{\chi(G)}$ as an immersion, and like its minor-order counterpart it is open even for graphs with independence number 2. We show that every graph $G$ with independence number $\alpha(G)\ge 2$ and no hole of length between $4$ and $2\alpha(G)$ satisfies this conjecture. In particular, every $C_4$-free graph $G$ with $\alpha(G)= 2$ satisfies the Lescure-Meyniel conjecture. We give another generalisation of this corollary, as follows. Let $G$ and $H$ be graphs with independence number at most 2, such that $|V(H)|\le 4$. If $G$ is $H$-free, then $G$ satisfies the Lescure-Meyniel conjecture.Comment: 14 pages, 3 figures. The statements of lemmas 3.1, 4.1, and 4.2 are slightly changed from the previous version in order to fix some minor errors in the proofs of theorems 3.2 and 4.3. Shorter proof of Proposition 5.2 give

Birth and death chains on finite trees: computing their stationary distribution and hitting times

Every birth and death chain on a finite tree can be represented as a random walk on the underlying tree endowed with appropriate conductances. We provide an algorithm that finds these conductances in linear time. Then, using the electric network approach, we find the values for the stationary distribution and for the expected hitting times between any two vertices in the tree. We show that our algorithms improve classical procedures: they do not exhibit ill-posedness and the orders of their complexities are smaller than those of traditional algorithms found in the literature

Quadratic Dynamical Decoupling with Non-Uniform Error Suppression

We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N1 and N2 pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N1 and N2, and near-optimal performance is achieved for general single-qubit interactions when N1=N2.Comment: 17 pages, 22 figure