Equivalence between Hypergraph Convexities

Let G be a connected graph on V. A subset X of V is all-paths convex (or ap -convex) if X contains each vertex on every path joining two vertices in X and is monophonically convex (or m-convex) if X contains each vertex on every chordless path joining two vertices in X. First of all, we prove that ap -convexity and m-convexity coincide in G if and only if G is a tree. Next, in order to generalize this result to a connected hypergraph H, in addition to the hypergraph versions of ap -convexity and m-convexity, we consider canonical convexity (or c-convexity) and simple-path convexity (or sp -convexity) for which it is well known that m-convexity is finer than both c-convexity and sp -convexity and sp -convexity is finer than ap -convexity. After proving sp -convexity is coarser than c-convexity, we characterize the hypergraphs in which each pair of the four convexities above is equivalent. As a result, we obtain a convexity-theoretic characterization of Berge-acyclic hypergraphs and of γ-acyclic hypergraphs

Towards Empathetic Social Robots: Investigating the Interplay between Facial Expressions and Brain Activity

The pursuit of creating empathetic social robots that can understand and respond to human emotions is a critical challenge in Robotics and Artificial Intelligence. Social robots, designed to interact with humans in various settings, from healthcare to customer service, require a sophisticated understanding of human emotional states to resonate and effectively assist truly. Our research contributes to this ambitious goal by exploring the relationship between natural facial expressions and brain activity in these human-robot interactions, as captured by electroencephalogram (EEG) signals. This paper presents our initial steps towards this attempt. We want to find which areas in the participant user’s brain are most activated and how these activations correlate with facial expressions. Understanding these correlations is essential for developing social robots that recognize and empathize with various human emotions. Our approach combines neuroscience and computer science, offering a novel perspective in the quest to enhance the emotional intelligence of social robots. We share some preliminary results on a new multimodal dataset that we are developing, providing valuable insights into the potential of our work to improve the personalization and emotional depth of social robot interactions

Trauma coagulopathy and its outcomes

Background and Objectives: Trauma coagulopathy begins at the moment of trauma. This study investigated whether coagulopathy upon arrival in the emergency room (ER) is correlated with increased hemotransfusion requirement, more hemodynamic instability, more severe anatomical damage, a greater need for hospitalization, and hospitalization in the intensive care unit (ICU). We also analyzed whether trauma coagulopathy is correlated with unfavorable indices, such as acidemia, lactate increase, and base excess (BE) increase. Material and Methods: We conducted a prospective, monocentric, observational study of all patients (n = 503) referred to the Department of Emergency and Acceptance, IRCCS Fondazione Policlinico San Matteo, Pavia, for major trauma from 1 January 2018 to 30 January 2019. Results: Of the 503 patients, 204 had trauma coagulopathy (group 1), whereas 299 patients (group 2) did not. Group 1 had a higher hemotransfusion rate than group 2. In group 1, 15% of patients showed hemodynamic instability compared with only 8% of group 2. The shock index (SI) distribution was worse in group 1 than in group 2. Group 1 was more often hypotensive, tachycardic, and with low oxygen saturation, and had a more severe injury severity score than group 2. In addition, 47% of group 1 had three or more body districts involved compared with 23% of group 2. The hospitalization rate was higher in group 1 than in group 2 (76% vs. 58%). The length of hospitalization was >10 days for 45% of group 1 compared with 28% of group 2. The hospitalization rate in the ICU was higher in group 1 than in group 2 (22% vs. 14.8%). The average duration of ICU hospitalization was longer in group 1 than in group 2 (12.5 vs. 9.78 days). Mortality was higher in group 1 than in group 2 (3.92% vs. 0.98%). Group 1 more often had acidemia and high lactates than group 2. Group 1 also more often had BE <−6. Conclusions: Trauma coagulopathy patients, upon arrival in the ER, have greater hemotransfusion (p = 0.016) requirements and need hospitalization (p = 0.032) more frequently than patients without trauma coagulopathy. Trauma coagulopathy seems to be more present in patients with a higher injury severity score (ISS) (p = 0.000) and a greater number of anatomical districts involved (p = 0.000). Head trauma (p = 0.000) and abdominal trauma (p = 0.057) seem related to the development of trauma coagulopathy. Males seem more exposed than females in developing trauma coagulopathy (p = 0.018). Upon arrival in the ER, the presence of tachycardia or alteration of SI and its derivatives can allow early detection of patients with trauma coagulopathy

Hardness and approximation for the geodetic set problem in some graph classes

In this paper, we study the computational complexity of finding the \emph{geodetic number} of graphs. A set of vertices $S$ of a graph $G$ is a \emph{geodetic set} if any vertex of $G$ lies in some shortest path between some pair of vertices from $S$. The \textsc{Minimum Geodetic Set (MGS)} problem is to find a geodetic set with minimum cardinality. In this paper, we prove that solving the \textsc{MGS} problem is NP-hard on planar graphs with a maximum degree six and line graphs. We also show that unless $P=NP$, there is no polynomial time algorithm to solve the \textsc{MGS} problem with sublogarithmic approximation factor (in terms of the number of vertices) even on graphs with diameter $2$. On the positive side, we give an $O\left(\sqrt[3]{n}\log n\right)$-approximation algorithm for the \textsc{MGS} problem on general graphs of order $n$. We also give a $3$-approximation algorithm for the \textsc{MGS} problem on the family of solid grid graphs which is a subclass of planar graphs

On the complexity of finding chordless paths in bipartite graphs and some interval operators in graphs and hypergraphs

In this paper we show that the problem of finding a chordless path between a vertex s and a vertex t containing a vertex v remains NP-complete in bipartite graphs, thereby strengthening the previous results on the same problem. We show a relation between this problem and two interval operators: the simple path interval operator in hypergraphs and the even-chorded path interval operator in graphs. We show that the problem of computing the two mentioned intervals is NP-complete

Simple algorithms for minimal triangulation of a graph and backward selection of a decomposable Markov network

In this paper we propose a simple algorithm called CliqueMinTriang for computing a minimal triangulation of a graph. If F is the set of edges that is added to G to make it a complete graph Kn then the asymptotic complexity of CliqueMinTriang is O(|F|(δ2+|F|)) where δ is the degree of the subgraph of Kn induced by F. Therefore our algorithm performs well when G is a dense graph. We also show how to exploit the existing minimal triangulation techniques in conjunction with CliqueMinTriang to efficiently find a minimal triangulation of nondense graphs. Finally we show how the algorithm can be adapted to perform a backward stepwise selection of decomposable Markov networks; the resulting procedure has the same time complexity as that of existing similar algorithms

On the geodeticity of the contour of a graph

The eccentricity of a vertex vv in a graph GG is the maximum distance of vv from any other vertex of GG and vv is a contour vertex of GG if each vertex adjacent to vv has eccentricity not greater than the eccentricity of vv. The set of contour vertices of GG is geodetic if every vertex of GG lies on a shortest path between a pair of contour vertices. In this paper, we firstly investigate the existence of operations on graphs that allow to construct graphs in which the contour is geodetic. Then, after providing an alternative proof of the fact that the contour is geodetic in every HHD-free graph, we show that the contour is geodetic in every cactus and in every graph whose blocks are HHD-free or cycles or cographs. Finally, we generalize the above result by introducing the concept of geodetic-contour-preserving class of graphs and by proving that, if each block BB in a graph GG belongs to a class GBGB of graphs which is geodetic-contour-preserving, then the contour of GG is geodetic

Auditing Sum Queries

Lecture Notes in Computer Science 2572 (G. Goos, J. Hartmanis, J. Van Leeuwen, eds.

Privacy Preserving and Data Mining in an On-Line Statistical Database of Additive Type

It is shown how to protect sensitive data and mine summary data when data is additiv

The contour of a bridged graph is geodetic

The eccentricity of a vertex vv in a graph GG is the maximum distance of vv from any other vertex of GG and vv is a contour vertex of GG if each vertex adjacent to vv has eccentricity not greater than the eccentricity of vv. The set of contour vertices of GG is geodetic if every vertex of GG lies on a shortest path between a pair of contour vertices. An induced connected subgraph HH of GG is isometric if, every two vertices of HH, have in HH the same distance as in GG. A graph is bridged if it does not contains an isometric cycle with length greater than 3. In this note, we show that the contour of a bridged graph is geodetic