Online Maintenance of Minimal Directed Hypergraphs

In this paper we deal with directed hypergraphs, a generalization of directed graphs previously introduced in the literature. In particular, we investigate the problem of maintaining efficiently information about minimal hyperpaths while new hyperarcs are inserted. We consider several definitions of minimal hyperpath and we prove that accordingly to some of such definitions the problem of finding the minimal hyperpath is NP-complete, while hyperpaths with minimal GAP and minimal RANK can be found in polynomial time. We deal with this problem in an online fashion, by allowing insertions of hyperarcs in the hypergraphs. We present data structures and algorithms which allow to return a hyperpath with minimal GAP or RANK between an arbitrarily given pair of nodes in a time which is linear in its size. The total time required to maintain the data structure during the insertion of new hyperarcs is (9(m n2) for min-GAP and (9(m n2 log n) for min-RANK (where m is the total size of the description of the hyperarcs and n is the number of nodes). These results are useful in applications where directed hypergraphs are known to be a suitable model (e.g. transition networks, rewriting systems, database schemes, logic programming and problem solving)

Dynamic Data Structures for Series Parallel Digraphs

We consider the problem of dynamically maintaining general series parallel directed acyclic graphs (GSP dags), two-terminal series parallel directed acyclic graphs (TTSP dags) and looped series parallel directed graphs (looped SP digraphs). We present data structures for updating (by both inserting and deleting either a group of edges or vertices) GSP dags, TTSP clags and looped SP digraphs of m edges and n vertices in O( log n) worst-case time. The time required to check whether there is a path between two given vertices is O(log n), while a path of length k can be traced out in O(k + log n) time. For GSP and TTSP dags, our data structures are able to report a regular expression describing all the paths between two vertices x and y in O(h + log n), where h ≤ n is the total number of vertices which are contained in paths from x to y. Although GSP dags can have as many as O(n2) edges, we use an implicit representation which requires only O(n) space. Motivations for studying dynamic graphs arise in several areas, such as communication networks, Incremental compilation environments and the design of very high level languages, while the dynamic maintenance of series parallel graphs is also relevant in reducible flow diagrams

The Italian air force sea level pressure data set (1951-2000)

A set of 39 homogenised sea level pressure records, extracted from the Italian Air Force dataset (1951-2000), is introduced and analysed for trends. The data consist of 3-hourly observations. Daily mean pressures are obtained using a method that allows biases to be avoided due to the presence of a high fraction of days that do not have all 8 observations. Trend analysis is performed on seasonal and yearly basis and concerns both the individual station records and the series of their averages. The results show a highly significant positive trend in winter and yearly air pressure all over Italy. It is mainly due to a change-point around 1980. The Italian air pressure records are also compared with the NCAR/NCEP and UKMO gridded data sets. The results give evidence that gridded data capture most of the trend and variability of air pressure over Italy, even if NCAR/NCEP data display some significant inhomogeneities with respect to the station records

Ranking places in attributed temporal urban mobility networks

Drawing on the recent advances in complex network theory, urban mobility flow patterns, typically encoded as origin-destination (OD) matrices, can be represented as weighted directed graphs, with nodes denoting city locations and weighted edges the number of trips between them. Such a graph can further be augmented by node attributes denoting the various socio-economic characteristics at a particular location in the city. In this paper, we study the spatio-temporal characteristics of “hotspots” of different types of socio-economic activities as characterized by recently developed attribute-augmented network centrality measures within the urban OD network. The workflow of the proposed paper comprises the construction of temporal OD networks using two custom data sets on urban mobility in Rome and London, the addition of socio-economic activity attributes to the OD network nodes, the computation of network centrality measures, the identification of “hotspots” and, finally, the visualization and analysis of measures of their spatio-temporal heterogeneity. Our results show structural similarities and distinctions between the spatial patterns of different types of human activity in the two cities. Our approach produces simple indicators thus opening up opportunities for practitioners to develop tools for real-time monitoring and visualization of interactions between mobility and economic activity in cities.This work is supported by the Spanish Government, Ministerio de Economía y Competividad, grant number TIN2017-84821-P. It is also funded by the EU H2020 programme under Grant Agreement No. 780754, “Track & Know”

Polylactic acid as biobased binder for the production of 3D printing filaments for Ti6Al4V alloy manufacturing via bound metal deposition

In this paper, a biobased binder mainly composed of polylactic acid (PLA) was developed for the production of Ti6Al4V feedstock suitable for 3D printing via material extrusion. 3D printed samples were debound via solvent and thermal treatments and successfully sintered in reducing atmosphere obtaining dense metallic components. The designed and produced bio-binder is completely eliminated during the debinding processes leading to sintered samples showing a high densification (93–94%), with a microstructure composed of primary alpha phase with segregated beta phase at grain boundaries and having average grain size of 70 μm. 3D printed sintered samples show good mechanical properties (yield strength (σy) = 662 MPa, ultimate tensilte strength (UTS) = 743 MPa, elongation at break (εmax) = 12%, hardness = 5.15 GPa) influenced by the sintering parameters and the presence of some degree of micro-porosity in the final structure