A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

Visibility, perception and roundabout safety

In Italy, over the past fifteen years, modern, or second generation roundabouts have become very popular. In these roundabouts, entering vehicles must yield to vehicles already within the circle. This modern design provides for much higher capacity of operation. Although first implemented in the UK in the 1960s, it took twenty years for the second generation to begin to spread to other European countries. Between 1987 and 2002, in particular, Germany, France and Switzerland conducted research that led to standards techniques that, along with English ones, now comprise the major technical references. The causes of the delay in implementation are uncertain and the subject of much speculation. The United States has only recently begun implementation, as it was not until the 1998 version did a chapter on roundabouts appear in the Highway Capacity Manual (developed further in the 2000 edition). In Italy, the first standards were proposed for the 1993 New Road Code, but it was not until 2004 that the standards were passed through national legislation. However, these codes are approximate and inadequate, and lack elementary technical foundations (see for instance Art. 4.5 of D.M. 19/04/2006, no.1699). A quick calculation for 4 legs and 60 meters diameter is sufficient to demonstrate its failure and infeasibility. The design of a roundabout, like that of any other road element, should be based on principles of safety, and should be deployed in a systemic context that combines geometric characteristics to meet capacity requirements – the perception of road space is also important. When designing a roundabout, the engineer should consider simultaneously both safety factors and capacity. But in addition to using geometric standards, formulas and models, aspects of perception and visual appeal should be considered

Regularity of isoperimetric sets in ℝ² with density

We consider the isoperimetric problem in R2with density. We show that, if the density is C0,α, then the boundary of any isoperimetric set is of class C1,α3-2α. This improves the previously known regularity

Testing for a large roundabout capacity model: experimental comparisons between Italy and Bahrain

It is well-known that the maximum traffic flow that a roundabout entry is able to accommodate depends on the amount of flow circulating in the roundabout carriageway that conflicts with the entry flow, that exiting from it and strictly related to the geometric characteristics of the roundabout. International guidelines deal with various capacity models requiring different input data and often leading to different results for the same roundabout entry. Recently, an exponential model has been developed for capacity estimates of multi-lane roundabout entries under different conditions of circulating flow and geometrical factors. Such a model was validated by Al-Madani and Saad [1] on data gathered from a sample of existing large roundabouts in Bahrain. Calculations made applying the developed model, or BAHR model, showed a reasonable fitting to computational data obtained from different international models, as German, French SETRA, American HCM, and so on. In this paper, we have collected traffic data during peaks or congested periods and measured geometry parameters on twelve large roundabouts located in Tuscany, Italy. The main goal was in view of testing if the BAHR model could be well suited or not to Italian context. The same previous methodology applied for the BAHR model was followed and found a new exponential entry capacity model, called TUSC. Statistical tests are performed and the paper ends with some comments about the obtained results

Car-sharing relocation strategies: a state of the art

Traditional car sharing systems are round-trip and require advance reservations. The advances of ICT and vehicle automation allow to improve car sharing sys-tems and to provide users with greater flexibility. As it concerns reservation, new car sharing systems offer users open-ended reservation and/or instant access. As it concerns the trip typology, new car sharing systems are multiple station shared vehicle systems (MSSVS). Roundtrips still occur in this type of system, however there is a large number of one-way trips made between the multiple stations. Operating an MSSVS is much more difficult than operating a round-trip shared vehicle systems. The problem is that the system can quickly become imbalanced with respect to the number of vehicles at the multiple stations. These systems are called new (or second) generation car sharing systems. Third generation systems are the last being developed; in these systems vehicles can be accessed at any point of the area. An overview of all these car sharing systems is provided in this paper

Raised crosswalks efficacy on the lowering of vehicle speeds

A road hump, or speed hump, is a traffic calming device used to reduce vehicle speed and volume on residential streets. Road humps are placed across the road to slow traffic and are often installed in a series of several humps in order to prevent cars from speeding before and after the hump. Speed humps are used in locations where very low speeds are desired and reasonable. Speed humps are typically placed on residential roads and are not used on major roads, bus routes, or primary emergency response routes. In Italy, the road humps are often built in shape of raised crosswalks, or RCWs, and they are generally placed both close and between intersections. This paper deals with the analysis of observed data on a large sample of RCWs located in Tuscany, central Italy. Such data were referred both to geometry characteristics of the single raised crosswalk and recorded differences in vehicle speeds before and after it. Speed data were gathered using two automatic radar-recorders for each one of the sampled raised crosswalks. All the collected data were analyzed trough statistical tests in order to assess their homogeneity or not between different locations and various types of roads. Finally, we were able of making some conclusions and highlighting design aspects. On one side, RCWs with similar geometries and higher heights (about 15 cm) have similar effects on vehicle speeds lowering, regardless of local conditions (location, road geometry, driver behaviour, etc.). Moreover, raised crosswalks installed in a series have strong efficacy than the isolated ones. On the opposite side, the effects of raised crosswalks with smaller heights (less than 6 cm) show clearly a very low influence on vehicle speed variations

Canine respiratory coronavirus employs caveolin-1-mediated pathway for internalization to HRT-18G cells

Canine respiratory coronavirus (CRCoV), identified in 2003, is a member of the Coronaviridae family. The virus is a betacoronavirus and a close relative of human coronavirus OC43 and bovine coronavirus. Here, we examined entry of CRCoV into human rectal tumor cells (HRT-18G cell line) by analyzing co-localization of single virus particles with cellular markers in the presence or absence of chemical inhibitors of pathways potentially involved in virus entry. We also targeted these pathways using siRNA. The results show that the virus hijacks caveolin-dependent endocytosis to enter cells via endocytic internalization

The Development of Deep and Short Sea Shipping Container Routes Departing from Italian Ports

In this paper, an analysis of the development of Deep Sea Shipping (DSS) and Short Sea Shipping (SSS) container routes calling at Italian ports, is carried out. Data about DSS routes have been collected in the years: 2011, 2014, 2018 and 2019, while data about SSS services have been collected in 2010 and 2018. Italian ports have been classified as follows: Ligurian multi-port gateway cluster, which is formed by Leghorn, La Spezia, Genoa, Savona/Vado Ligure; Northern Adriatic multi-port gateway cluster, made up of Ancona, Ravenna, Venice and Trieste; Campanian multi-port gateway cluster, composed of Naples and Salerno; hub ports, i.e. Gioia Tauro, Cagliari (only until 2018) and Taranto (only until 2014). The most important gateway cluster, for both DSS and SSS services, is the Ligurian one which includes Genoa which is by far the major Italian container gateway port. Genoa has shown an almost constant increase in container traffic in the time period analyzed. Italian hub ports are also an important group, but they have registered a negative trend in the years under analysis. DSS routes, to Far East and the American Continent, usually call at the Ligurian ports and the hub port of Gioia Tauro. Northern Adriatic ports are crossed by only a few DSS routes, but they are crossed by a large number of SSS routes, especially feeder ones, with transshipment mainly in the hub ports of Gioia Tauro, Marsaxlokk, Piraeus and Port Said. The evolution of DSS services shows clearly the effects of naval gigantism phenomenon: the number of DSS services has decreased, but the total and, especially, the average DWT have increased. As regards SSS routes, also their frequencies have decreased, but their length and, in particular, the number of ports called, have increased: this choice is performed by container operators in order to increase the ships ’load factor’

Railway lines across the alps: Analysis of their usage through a new railway link cost function

In this paper, the usage of railway lines across the Alps is evaluated, both at present and after the new lines and base tunnels will be in operation. The railway network of a large part of Europe has been modelled through a graph, and the best routes between some of the most important origin/destination pairs in Italy and Europe have been determined. A new cost function has been developed for the links of the network. The proposed cost function is an improvement of those existing in the literature, because all cost components are taken into account in detail, while the traction cost and the number of locomotives utilized explicitly depend on the geometrical characteristics of rail lines. This last aspect is crucial in analyzing the rail lines across the Alps, as they are often operated in double or triple traction. The results of the study show the importance of new Alpine rail lines and base tunnels: the Ceneri base tunnel will remove a bottleneck on the Gotthard line, while the Brenner and Frejus base tunnels will take up a quota of demand currently served by other lines. Moreover, the new Alpine lines will create an east-west rail connection, through the Italian Padan Plain, alternative to the rail route which currently bypasses the Alps to the north

Integral estimates for transport densities

The integration-by-parts methods introduced in this paper improve upon the Lp estimates on transport densities given in the recent paper by L. De Pascale and A. Pratelli (Calc. Var. Partial Differential Equations 14 (2002) 249–274)