Ordering a sparse graph to minimize the sum of right ends of edges

Motivated by a warehouse logistics problem we study mappings of the vertices of a graph onto prescribed points on the real line that minimize the sum (or equivalently, the average) of the coordinates of the right ends of all edges. We focus on graphs whose edge numbers do not exceed the vertex numbers too much, that is, graphs with few cycles. Intuitively, dense subgraphs should be placed early in the ordering, in order to finish many edges soon. However, our main “calculation trick” is to compare the objective function with the case when (almost) every vertex is the right end of exactly one edge. The deviations from this case are described by “charges” that can form “dipoles”. This reformulation enables us to derive polynomial algorithms and NP-completeness results for relevant special cases, and FPT results

Helium-oxygen reduces the production of carbon dioxide during weaning from mechanical ventilation

<p>Abstract</p> <p>Background</p> <p>Prolonged weaning from mechanical ventilation has a major impact on ICU bed occupancy and patient outcome, and has significant cost implications.</p> <p>There is evidence in patients around the period of extubation that helium-oxygen leads to a reduction in the work of breathing. Therefore breathing helium-oxygen during weaning may be a useful adjunct to facilitate weaning. We hypothesised that breathing helium-oxygen would reduce carbon dioxide production during the weaning phase of mechanical ventilation.</p> <p>Materials/patients and methods</p> <p>We performed a prospective randomised controlled single blinded cross-over trial on 19 adult intensive care patients without significant airways disease who fulfilled criteria for weaning with CPAP. Patients were randomised to helium-oxygen and air-oxygen delivered during a 2 hour period of CPAP ventilation. Carbon dioxide production (VCO₂) was measured using a near patient main stream infrared carbon dioxide sensor and fixed orifice pneumotachograph.</p> <p>Results</p> <p>Compared to air-oxygen, helium-oxygen significantly decreased VCO₂production at the end of the 2 hour period of CPAP ventilation; there was a mean difference in CO₂production of 48.9 ml/min (95% CI 18.7-79.2 p = 0.003) between the groups. There were no significant differences in other respiratory and haemodynamic parameters.</p> <p>Conclusion</p> <p>This study shows that breathing a helium-oxygen mixture during weaning reduces carbon dioxide production. This physiological study supports the need for a clinical trial of helium-oxygen mixture during the weaning phase of mechanical ventilation with duration of weaning as the primary outcome.</p> <p>Trial registration</p> <p>ISRCTN56470948</p

A supercritical elliptic problem in a cylindrical shell

We consider the problem $$-\Delta u=|u|^{p-2}u in \Omega, u=0 on \partial\Omega,$$ where $\Omega:=\{(y,z)\in\mathbb{R}^{m+1}\times\mathbb{R}^{N-m-1}: 0<a<|y|<b<\infty\}$, $0\leq m\leq N-1$ and $N\geq2$. Let $2_{N,m}^{\ast}:=2(N-m)/(N-m-2)$ if $m<N-2$ and $2_{N,m}^{\ast}:=\infty$ if $m=N-2$ or $N-1$. We show that $2_{N,m}^{\ast}$ is the true critical exponent for this problem, and that there exist nontrivial solutions if $2<p<2_{N,m}^{\ast}$ but there are no such solutions if $p\geq2_{N,m}^{\ast}$

Influence of climatic variables on crown condition in pine forests of Northern Spain

Producción CientíficaThe aim of this study was to find relationships between crown condition and some climatic parameters to identify which are those having a main influence on crown condition, and how this influence is shown in the tree (crown transparency), and to contribute to the understanding of how these parameters will affect under future climate change scenarios

Crítica de Libros.

Libro del Año, Psiquiatría 1992., R. Gómez Esteban El sistema humano y su mente. F. García Rodríguez Ediciones Díaz de Santos, S.A. 1992. Rústica, 391 págs.A. García-Ordás Alvarez No veo, no oigo, no hablo. El autismo infantil. M. Zappella Editorial Paidós Terapia Familiar. 1ª Edición, 1992. J.L. Fernández Sastre Autismo: cuidados y tratamiento PH.J. Parquet, C. Bursztejn, B. Golse Masson. Barcelona, 1992. Rústica, 222 págs. J.L. Pedreira Massa Abordaje terapéutico de la familia. G. Salem. Masson. Barcelona, 1990. Rústica, 169 págs. J.L. Pedreira Massa Adolescencia y depresión O. Mareelli Masson. Barcelona, 1992. Rústica, 167. J.L. Pedreira Massa Semiología Clínica Psiquiátrica D. Barcia, L. Gayral. Editorial Arán, S.A. ELA. Madrid, 1991. Rústica, 245 pág. J.L. Pedreira Massa. Manual de diagnóstico diferencial y tratamiento en psiquiatría c. Gasto Ferrer, J. Vallejo Ruiloba Masson. Barcelona, 19992. Rústica, 228 págs. J.L. Pedreira Massa

Crítica de Libros.

Libro del Año, Psiquiatría 1992., R. Gómez Esteban El sistema humano y su mente. F. García Rodríguez Ediciones Díaz de Santos, S.A. 1992. Rústica, 391 págs.A. García-Ordás Alvarez No veo, no oigo, no hablo. El autismo infantil. M. Zappella Editorial Paidós Terapia Familiar. 1ª Edición, 1992. J.L. Fernández Sastre Autismo: cuidados y tratamiento PH.J. Parquet, C. Bursztejn, B. Golse Masson. Barcelona, 1992. Rústica, 222 págs. J.L. Pedreira Massa Abordaje terapéutico de la familia. G. Salem. Masson. Barcelona, 1990. Rústica, 169 págs. J.L. Pedreira Massa Adolescencia y depresión O. Mareelli Masson. Barcelona, 1992. Rústica, 167. J.L. Pedreira Massa Semiología Clínica Psiquiátrica D. Barcia, L. Gayral. Editorial Arán, S.A. ELA. Madrid, 1991. Rústica, 245 pág. J.L. Pedreira Massa. Manual de diagnóstico diferencial y tratamiento en psiquiatría c. Gasto Ferrer, J. Vallejo Ruiloba Masson. Barcelona, 19992. Rústica, 228 págs. J.L. Pedreira Massa