The universality theorem for neighborly polytopes

In this note, we prove that every open primary basic semialgebraic set is stably equivalent to the realization space of an even-dimensional neighborly polytope. This in particular provides the final step for Mn\"ev's proof of the universality theorem for simplicial polytopes.Comment: 5 pages, 1 figure. Small change

Universality theorems for inscribed polytopes and Delaunay triangulations

We prove that every primary basic semialgebraic set is homotopy equivalent to the set of inscribed realizations (up to M\"obius transformation) of a polytope. If the semialgebraic set is moreover open, then, in addition, we prove that (up to homotopy) it is a retract of the realization space of some inscribed neighborly (and simplicial) polytope. We also show that all algebraic extensions of $\mathbb{Q}$ are needed to coordinatize inscribed polytopes. These statements show that inscribed polytopes exhibit the Mn\"ev universality phenomenon. Via stereographic projections, these theorems have a direct translation to universality theorems for Delaunay subdivisions. In particular, our results imply that the realizability problem for Delaunay triangulations is polynomially equivalent to the existential theory of the reals.Comment: 15 pages, 2 figure

Six topics on inscribable polytopes

Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along the way we collect a list of (new and old) open questions.Comment: 11 page

Overlapping Community Detection in Networks: the State of the Art and Comparative Study

This paper reviews the state of the art in overlapping community detection algorithms, quality measures, and benchmarks. A thorough comparison of different algorithms (a total of fourteen) is provided. In addition to community level evaluation, we propose a framework for evaluating algorithms' ability to detect overlapping nodes, which helps to assess over-detection and under-detection. After considering community level detection performance measured by Normalized Mutual Information, the Omega index, and node level detection performance measured by F-score, we reached the following conclusions. For low overlapping density networks, SLPA, OSLOM, Game and COPRA offer better performance than the other tested algorithms. For networks with high overlapping density and high overlapping diversity, both SLPA and Game provide relatively stable performance. However, test results also suggest that the detection in such networks is still not yet fully resolved. A common feature observed by various algorithms in real-world networks is the relatively small fraction of overlapping nodes (typically less than 30%), each of which belongs to only 2 or 3 communities.Comment: This paper (final version) is accepted in 2012. ACM Computing Surveys, vol. 45, no. 4, 2013 (In press) Contact: [email protected]

Colitis eosinofílica. A propósito de un caso clínico

La gastro-enteritis eosinofílica és una malaltia poc freqüent, de la qual s'han escrit uns 150 casos en la bibliografia mundial i 8 a l'Estat espanyol. Es caracteritza per la infiltració d'eosinòfils a la paret del tracte digestiu, encara que es pot acompanyar de l'afectació d'altres sistemes. Hi ha una forma d'infiltració difusa que acostuma a cursar amb síndrome de malabsorció i una forma circumscrita que produeix síndromes oclusives o suboclusives. L'etiologia és desconeguda, encara que molts dels casos descrits tenen una base al·lèrgica. En aquest treball es presenta un cas de gastro-enteritis eosinofílica de localització sigmoïdal. Creiem que es justifica la seva comunicació per les característiques pròpies del cas i per la raresa d'aquesta localització, ja que fins ara dels 27 casos d'afectació del còlon tan sols un ho era exclusivament al sigma

Colitis eosinofílica. A propósito de un caso clínico

La gastro-enteritis eosinofílica és una malaltia poc freqüent, de la qual s'han escrit uns 150 casos en la bibliografia mundial i 8 a l'Estat espanyol. Es caracteritza per la infiltració d'eosinòfils a la paret del tracte digestiu, encara que es pot acompanyar de l'afectació d'altres sistemes. Hi ha una forma d'infiltració difusa que acostuma a cursar amb síndrome de malabsorció i una forma circumscrita que produeix síndromes oclusives o suboclusives. L'etiologia és desconeguda, encara que molts dels casos descrits tenen una base al·lèrgica. En aquest treball es presenta un cas de gastro-enteritis eosinofílica de localització sigmoïdal. Creiem que es justifica la seva comunicació per les característiques pròpies del cas i per la raresa d'aquesta localització, ja que fins ara dels 27 casos d'afectació del còlon tan sols un ho era exclusivament al sigma