• A novel architecture is proposed to solve traffic flow reconstruction problems • The architecture leverages graph neural networks and learned feature embeddings • A continuous estimation strategy is proposed to use the solution on real scenarios • The proposed approach is highly generalizable to previously unseen scenarios Traffic control and management play a crucial role within intelligent transportation systems. However, comprehensive traffic monitoring is often constrained by the limited availability of traffic sensors across urban road networks. This paper addresses the problem of Traffic Flow Reconstruction (TFR), which aims to estimate traffic conditions over an entire road network starting from a few sparse traffic sensor measurements. This approach does not require full road coverage by sensors, thereby reducing deployment costs and supporting sustainable urban mobility. In the present research, we propose a lightweight Graph Neural Network (GNN) architecture for real-time TFR using data from a few number of fixed sensors. The model exploits a carefully designed road graph, explicitly augmented to capture traffic propagation and backpropagation effects at junctions, and well-studied node features augmented though a learned encoder. Compared to classical Partial Differential Equations-based TFR solutions, the proposed method achieves satisfactory estimation accuracy while significantly reducing setup times by avoiding scenario-dependent optimizations and precomputation of traffic flow distributions at junctions. Moreover, it overcomes the limitations of existing GNN-based approaches, which often rely on complex architectures that are difficult to adapt to different urban contexts without reprocessing them. Extensive experiments have been conducted and presented in this paper taking into account different moments of the year, various road graph representations and sensors’ positioning, and multiple city environments. Results demonstrate the robustness, generalization capability, and computational efficiency of the proposed approach, making it suitable for large-scale and real-world mobility and transport applications.

Climate change is a challenge of global relevance that requires in-depth understanding and immediate response. Urban CO 2 emissions are one of the main causes of climate change, and their estimation is crucial for planning actions aimed at creating more sustainable cities. Currently, models for estimating CO 2 emissions mainly focus on traffic patterns, energy consumption, or a limited set of socio-economic factors, often overlooking the increasing role of urban services in today’s cities. Moreover, these data are rarely accessible, which limits their usefulness for policy design. In the present paper, a general CO 2 emission estimation approach, based on a large range of often accessible open data as predictors, is presented. Such open data are related to human activity regarding services and (socio-economic) conditions arising in a given (urban) area. The proposed model focuses on fine-scale prediction to better understand the dynamics of emissions via machine learning approaches, while taking into account an innovative study based on open data sources including city services. The resulting best models have been based on XgBoost and GCN (graph convolutional network). The outcomes provided better precision (MAPE in the order of 8%) with respect to the state-of-the-art solutions. The goal has been to understand how specific predictors can contribute to or mitigate CO 2 emissions in the observed area. To this end, the impact of several features has been analyzed in order to identify the related key factors influencing emissions. A formal study has been conducted to perform feature relevance analysis by using eXplainable AI (XAI) approach. The proposed model is useful to define targeted policies reducing the pollutant impact of cities, promote a more ecologically sustainable urban lifestyle and improve sustainable urban planning. Both solutions and models have been assessed and improved, so as to be more flexible by using some transfer learning techniques. This research and its related results have been produced and validated by exploiting the Snap4City framework for smart city, mobility and transport and data analytics on CN MOST, national center on sustainable mobility. In particular, such results deal with the metropolitan cities of Florence and Bologna. © 2017 Elsevier Inc. All rights reserved.

Traffic management and sustainable mobility are the central topics for intelligent transportation systems (ITS). By means of modern technologies, it is possible to collect real-time traffic flow data to extract useful information to monitor and control vehicular traffic. On the other hand, costs to obtain this piece of information are high. It requires either direct measures in the network road by installing large number of sensors (more precise data) or acquiring data from international providers supplying data coming from onboard units, mobile app, navigators, etc. In current paper, this problem has been addressed providing a solution granting traffic flow data in each road segment of the whole network by reconstructing the computation by means of data from few scattered traffic sensors in fixed positions of the road network. The proposed approach combines the solution of nonlinear Partial Differential Equations (PDEs) with machine learning for improving the state-of-the-art solutions of PDE. The result has been a higher precision with respect to PDE-based solutions, and a strongly reduced execution time. Several different machine learning models have been compared for such a purpose, demonstrating the general viability of the hybrid architecture proposed. The research result has been obtained in the framework of both the Sii-Mobility national project on transport systems, and MOST, the National Center on Sustainable mobility (both funded by the Italian Ministry of Research), by exploiting the Snap4City platform.

The knowledge of the real time traffic flow status in each segment of a whole road network in a city or area is becoming fundamental for a large number of smart services such as: routing, planning, dynamic tuning services, healthy walk, etc. Rescue teams, police department, and ambulances need to know with high precision the status of the network in real time. On the other hand, the costs to obtain this information either with direct measures meant to add instruments on the whole network or acquiring data from international providers such as Google, TomTom, etc. is very high. The traditional modeling and computing approaches are not satisfactory since they are based on many assumptions that typically are doomed to change over time, as it occurs with traffic distribution at junctions; in short they cannot cover the whole network with the needed precision. In this paper, the above problem has been addressed providing a solution granting any traffic flow reconstruction with high precision and solving the indeterminacy of traffic distribution at junctions for large networks. The identified solution can be classified as a stochastic relaxation technique and resulted affordable on a parallel architecture based on GPU. The result has been obtained in the framework of the Sii-Mobility national project on smart city transport systems in Italy, a very large research project, and it is at present exploited in a number of cities/regions across Europe and by a number of research projects (Snap4City, TRAFAIR) of the European Commission.

In recent years, there is an increasing attention on Air Quality and derived services. In most cases, the main objective consists in providing services independently on the number of sensors, and on any position of the users. On the other hand, sensors are collected in limited positions, then a dense grid is computed to satisfy the needs of services such as: conditional routing, alerting on data values for personal usage, general heatmap production for Dashboards in control room of the operators, and for web and mobile applications for the city users. The paper formalizes the development process and describes how it is possible to automatically integrate Data Analytics in data flow real time processes, called in the paper IoT Applications. Two interpolation methods have been compared and validated in order to assess the accuracy. Interpolation errors trends have been used to detected devices' dysfunctions on sensors. The specific case presented in this paper refers to the data and the solution of Snap4City for Helsinki. Snap4City (https://www.snap4city.org) has been developed as a part Select4Cities PCP of the European Commission, and it is presently used in a number of cities and areas in Europe.

Real time traffic flow data in terms of road-segments traffic densities are relevant information at the basis of several smart services, such as smart routing, smart planning for evacuations, planning of civil works on the city, etc. The traditional methods for traffic flow measured via sensors using data from navigator Apps (e.g., TomTom, Google map, Waze) could be very expensive to be acquired. For this reason, there is the space for low cost and fast solutions for dense traffic flow reconstruction from scattered data coming from a limited number of street sensors spread on the city. The proposed method is based on differential equations and physical constraints applied to a detailed street graph which is enriched of several features. A stochastic learning approach has been adopted to estimate the weights representing in certain sense the road-segments capacity at each time slot of the day. The proposed solution allows computing in real-time the traffic density reconstruction in unmeasured road-segments. The solution has been validated estimating the error in the places where the sensors are positioned, excluding each of them iteratively and reconstructing the flow without it. Then, it has been possible to estimate the error between the reconstructed traffic density and the measured values. This approach allowed setting up a converging algorithm for estimating the traffic density in the whole city graph from detailed parameters. The proposed reconstruction model has been created by exploiting open and real-time data in the context of Sii-Mobility research project by using Km4City infrastructure in the area of Florence, Italy, for its corresponding Smart City solution.

In this paper we give a combinatorial interpretation of linear recurrences having constant coefficients. In particular, we describe a recursive construction for a language ℒ such that the words in ℒ having length n satisfy the given recurrence and avoid a cross-bifix-free set of patterns.

A cross-bifix-free set of words is a set in which no prefix of any length of any word is the suffix of any other word in the set. A construction of cross-bifix-free sets has recently been proposed in Cheeet al.(2013) within a constant factor of optimality. We propose a Gray code for these cross-bifix-free sets and a CAT algorithm generating it. Our Gray code list is trace partitioned, that is, words with zero in the same positions are consecutive in the list.

We define a variable-length code having the property that no (non-empty) prefix of each its codeword is a suffix of any other one, and vice versa. This kind of code can be seen as an extension of two well-known codes in the literature, called, respectively, fix-free code and non-overlapping code. In this paper we present constructive algorithms for such codes and some numerical results about their cardinality.

In this paper we consider the class of column-convex permutominoes, i.e. column-convex polyominoes defined by a pair of permutations (π 1 , π 2 ). First, using a geometric construction, we prove that for every permutation π there is at least one column-convex permutomino P such that π 1 (P) = π or π 2 (P) = π. In the second part of the paper, we show how, for any given permutation π, it is possible to define a set of logical implications on the points of π, and prove that there exists a column-convex permutomino P such that π 1 (P) = π if and only if is satisfiable. This property can be then used to give a characterization of the set of column-convex permutominoes P such that π 1 (P) = π.

In this paper we study the enumeration and the construction of particular binary words avoiding the pattern 1j+1 0j . By means of the theory of Riordan arrays, we solve the enumeration problem and we give a particular succession rule, called jumping

Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to determine a cross-bifix-free words subset which has the property to be non-expandable.