The Partial Visibility Representation Extension Problem

For a graph $G$, a function $\psi$ is called a \emph{bar visibility representation} of $G$ when for each vertex $v \in V(G)$, $\psi(v)$ is a horizontal line segment (\emph{bar}) and $uv \in E(G)$ iff there is an unobstructed, vertical, $\varepsilon$-wide line of sight between $\psi(u)$ and $\psi(v)$. Graphs admitting such representations are well understood (via simple characterizations) and recognizable in linear time. For a directed graph $G$, a bar visibility representation $\psi$ of $G$, additionally, puts the bar $\psi(u)$ strictly below the bar $\psi(v)$ for each directed edge $(u,v)$ of $G$. We study a generalization of the recognition problem where a function $\psi'$ defined on a subset $V'$ of $V(G)$ is given and the question is whether there is a bar visibility representation $\psi$ of $G$ with $\psi(v) = \psi'(v)$ for every $v \in V'$. We show that for undirected graphs this problem together with closely related problems are \NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Planar L-Drawings of Directed Graphs

We study planar drawings of directed graphs in the L-drawing standard. We provide necessary conditions for the existence of these drawings and show that testing for the existence of a planar L-drawing is an NP-complete problem. Motivated by this result, we focus on upward-planar L-drawings. We show that directed st-graphs admitting an upward- (resp. upward-rightward-) planar L-drawing are exactly those admitting a bitonic (resp. monotonically increasing) st-ordering. We give a linear-time algorithm that computes a bitonic (resp. monotonically increasing) st-ordering of a planar st-graph or reports that there exists none.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Planar Embeddings with Small and Uniform Faces

Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MINMAXFACE and UNIFORMFACES of embedding a given biconnected multi-graph such that the largest face is as small as possible and such that all faces have the same size, respectively. We prove a complexity dichotomy for MINMAXFACE and show that deciding whether the maximum is at most $k$ is polynomial-time solvable for $k \leq 4$ and NP-complete for $k \geq 5$. Further, we give a 6-approximation for minimizing the maximum face in a planar embedding. For UNIFORMFACES, we show that the problem is NP-complete for odd $k \geq 7$ and even $k \geq 10$. Moreover, we characterize the biconnected planar multi-graphs admitting 3- and 4-uniform embeddings (in a $k$-uniform embedding all faces have size $k$) and give an efficient algorithm for testing the existence of a 6-uniform embedding.Comment: 23 pages, 5 figures, extended version of 'Planar Embeddings with Small and Uniform Faces' (The 25th International Symposium on Algorithms and Computation, 2014

Density modelling with functional data analysis

[EN] Recent technological advances have eased the collection of big amounts of data in many research fields. In this scenario density estimation may represent an important source of information. One dimensional density functions represent a special case of functional data subject to the constraints to be non-negative and with a constant integral equal to one. Because of these constraints, a naive application of functional data analysis (FDA) methods may lead to non-valid results. To solve this problem, by means of an appropriate transformation, densities are embedded in the Hilbert space of square integrable functions where standard FDA methodologies can be applied.Gattone, SA.; Di Battista, T. (2023). Density modelling with functional data analysis. Editorial Universitat Politècnica de València. 87-91. https://doi.org/10.4995/CARMA2023.2023.16467879

Knuthian Drawings of Series-Parallel Flowcharts

Inspired by a classic paper by Knuth, we revisit the problem of drawing flowcharts of loop-free algorithms, that is, degree-three series-parallel digraphs. Our drawing algorithms show that it is possible to produce Knuthian drawings of degree-three series-parallel digraphs with good aspect ratios and small numbers of edge bends.Comment: Full versio

3D Visibility Representations of 1-planar Graphs

We prove that every 1-planar graph G has a z-parallel visibility representation, i.e., a 3D visibility representation in which the vertices are isothetic disjoint rectangles parallel to the xy-plane, and the edges are unobstructed z-parallel visibilities between pairs of rectangles. In addition, the constructed representation is such that there is a plane that intersects all the rectangles, and this intersection defines a bar 1-visibility representation of G.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Non-pharmacological treatments for pediatric refractory epilepsies

Introduction: Antiseizure medications (ASMs) are the primary treatment option for epilepsies of wide etiologies, however, about 10–20% of children do not gain sustained seizure control and in this case, it is worth investigating ‘alternative’ therapeutic approaches aside from ASMs. Nowadays, non-pharmacological strategies for epilepsy treatment encompass dietary interventions, neurostimulation-based techniques, and biobehavioral approaches. Areas covered: A search on PubMed database was conducted. Experimental and clinical studies, as well as meta-analysis and structured reviews on the latest non-pharmacological treatments for drug-resistant epilepsy (DRE) in children, were included. Special attention is given to the efficacy and tolerability outcomes, trying to infer the role novel approaches may have in the future. Expert opinion: The large heterogeneity of primary clinical outcomes and the unavoidable subjective response of each patient to treatments prevents Researchers from the identification of a single, reliable, approach to treat DRE. The understanding of fine pathophysiologic processes is giving the way to the use of alternative therapies, such as the well-known ketogenic diet, in a ‘personalized’ view of treatment. The goal is to apply the non-pharmacological treatment most suitable for the patients sake