Pedestrian behaviour in urban area

The pedestrian behavior is influenced by several factors, including: characteristics of the user, numerousness of group, road infrastructures and environmental factors. These factors were studied by means the collection of data carried out in the city of Oristano (Sardinia-Italy) on eleven sidewalks and five crosswalks. The objective was to study the pedestrians behavior, researching the link between independent variables and the dependent variables that, for sidewalks was only the pedestrian speed while for crosswalks were the speed of crossing, the crossing time, the waiting time and the total time. The regression models were constructed by using ten sidewalks and four crosswalks so ignoring one for each. In the construction, were considered more variables that gradually were excluded on the basis of the p-value. The models thus detected were deemed significant according to their coefficient of determination and were validated with data from the sidewalk or crosswalk excluded from the construction of the same. Both for sidewalks that crosswalks were found some reliable models. The models construction is useful to improve the understanding of the pedestrians behavior and then obtain useful indications to design pedestrian infrastructures with characteristics closer to the real pedestrians behavior. The present study aims to give greater importance to pedestrians, analyzing how they relate with the urban context in which they live and how it conditions their behavior, so as to design infrastructure in which they feel an integral part and main actors of the urban scene, giving them the respect they deserve and a new sense of belonging to the city in which they live

Packing Topological Minors Half-Integrally

The packing problem and the covering problem are two of the most general questions in graph theory. The Erd\H{o}s-P\'{o}sa property characterizes the cases when the optimal solutions of these two problems are bounded by functions of each other. Robertson and Seymour proved that when packing and covering $H$-minors for any fixed graph $H$, the planarity of $H$ is equivalent with the Erd\H{o}s-P\'{o}sa property. Thomas conjectured that the planarity is no longer required if the solution of the packing problem is allowed to be half-integral. In this paper, we prove that this half-integral version of Erd\H{o}s-P\'{o}sa property holds with respect to the topological minor containment, which easily implies Thomas' conjecture. Indeed, we prove an even stronger statement in which those subdivisions are rooted at any choice of prescribed subsets of vertices. Precisely, we prove that for every graph $H$, there exists a function $f$ such that for every graph $G$, every sequence $(R_v: v \in V(H))$ of subsets of $V(G)$ and every integer $k$, either there exist $k$ subgraphs $G_1,G_2,...,G_k$ of $G$ such that every vertex of $G$ belongs to at most two of $G_1,...,G_k$ and each $G_i$ is isomorphic to a subdivision of $H$ whose branch vertex corresponding to $v$ belongs to $R_v$ for each $v \in V(H)$, or there exists a set $Z \subseteq V(G)$ with size at most $f(k)$ intersecting all subgraphs of $G$ isomorphic to a subdivision of $H$ whose branch vertex corresponding to $v$ belongs to $R_v$ for each $v \in V(H)$. Applications of this theorem include generalizations of algorithmic meta-theorems and structure theorems for $H$-topological minor free (or $H$-minor free) graphs to graphs that do not half-integrally pack many $H$-topological minors (or $H$-minors)

Genus Ranges of 4-Regular Rigid Vertex Graphs

We introduce a notion of genus range as a set of values of genera over all surfaces into which a graph is embedded cellularly, and we study the genus ranges of a special family of four-regular graphs with rigid vertices that has been used in modeling homologous DNA recombination. We show that the genus ranges are sets of consecutive integers. For any positive integer $n$, there are graphs with $2n$ vertices that have genus range ${m,m+1,...,m'}$ for all $0\le m<m'\le n$, and there are graphs with $2n-1$ vertices with genus range ${m,m+1,...,m'}$ for all $0\le m<m' <n$ or $0<m<m'\le n$. Further, we show that for every $n$ there is $k<n$ such that ${h}$ is a genus range for graphs with $2n-1$ and $2n$ vertices for all $h\le k$. It is also shown that for every $n$, there is a graph with $2n$ vertices with genus range ${0,1,...,n}$, but there is no such a graph with $2n-1$ vertices