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Graph Isomorphism is such an important problem in computer science, that it has been widely studied over the last decades. It is well known that it belongs to NP class, but is not NP-complete. It is thought to be of comparable difficulty to integer factorisation. The best known proved algorithm to solve this problem in general, was proposed by László Babai and Eugene Luks in 1983. Recently, there has been some research in the topic by using quantum computing, that also leads the present piece of research. In fact, we present a quantum computing algorithm that defines an invariant over Graph Isomorphism characterisation. This quantum algorithm is able to distinguish more non-isomorphic graphs than most of the known invariants so far. The proof of correctness and some hints illustrating the extent and reason of the improvement are also included in this paper.

Based on current trends in graduation rates, 39% of todays young adults on average across OECD countries are expected to complete tertiary-type A (university level) education during their lifetime. In 2017, an average of 10.6% of young people in the EU-28 were early leavers from education and training. Therefore the level of dropout in the scenery of European education is one of the major issue to be faced in a near future. The main aim of the research is to predict, as early as possible, which student will dropout in the Higher Education context. The accurate knowledge of this information would allow one to effectively carry out targeted actions in order to limit the incidence of the phenomenon. The recent breakthrough on Neural Networks with the use of Convolutional Neural Networks architectures has become disruptive in AI. By stacking together tens or hundreds of convolutional neural layers, a “deep” network structure is obtained, which has been proved very effective in producing high accuracy models. In this research the administrative data of about 6000 students enrolled from 2009 in the Department of Education at Roma Tre University had been used to train a Convolutional Neural Network based. Then, the trained network provides a predictive model that predicts whether the student will dropout. Furthermore, we compared the results obtained using deep learning models to the ones using Bayesian networks. The accuracy of the obtained deep learning models ranged from 67.1% for the first-year students up to 94.3% for the third-year students., Journal of e-Learning and Knowledge Society, Vol 16 No 1 (2020): Je-LKS - Special Issue on "Smart Learning in Smart Cities"

Bayesian networks are multivariate statistical models using a di- rected acyclic graph to represent statistical dependencies among vari- ables. When dealing with Bayesian Networks it is common to assume that all the variables are discrete. This is not often the case in many real contexts where also continuous variables are observed. A common solution consists in discretizing the continuous variables. In this paper we propose a discretization algorithm based on the Kullback-Leibler divergence measure. Formally, we deal with the problem of discretiz- ing a continuous variable Y conditionally on its parents. We show that such a problem is polynomially solvable. A simulation study is finally performed.

Measurement error is the difference between a feature value provided by the respondent and the corresponding true but unknown value. Measurement error is one of the main nonsampling error sources. Object-oriented Bayesian networks (OOBNs) have been recently proposed to model and correct measurement errors. In particular, the measurement error in a categorical variable is described by a mixed measurement model implemented in a BN. We apply this model to 2008 Survey on Household Income and Wealth (SHIW), conducted by Banca d’Italia. In particular, financial assets in SHIW are affected by misreporting of financial amounts with a prevalence of underreporting. The measurement error model is estimated using a validation sample. Specifically, the probability of an error is estimated from the validation sample using a BN model. The variables are mixed continuous and discrete. Hence, we need to discretize before learning the BN. This is a challenging problem since discretization should be performed accounting for the association structure; otherwise, if the continuous variables are independently discretized, their relation structure could be dramatically altered. Here we propose a methodology to learn the network while discretizing. Once the error probability is estimated, the overall measurement error model is implemented and microdata are imputed.

Marina Moscarini, Fancesco Malvestuto, Tiziana Calamoneri

We propose dynamic algorithms and data structures for chordal graphs supporting the following operation: determine if an edge can be added or removed from the graph while preserving the chordality in O(1) time. We show that the complexity of the algorithms for updating the data structures when an edge is actually inserted or deleted is O(n2) where n is the number of vertices of the graph.

The awareness of the visitor’s role centrality in museums has led to the constant development of techniques and methodologies aimed at improving the visitor’s experience. In this context, Augello et al. suggest the four pillars to enhance the user experience: User Localization, User Understanding, Multimodal Interaction, and Gamification. As part of our research activities, we have focused on the latter two pillars. More specifically, User Localization allows museum curators and staff to understand the user movements in the museum and how much time she spends in front of the artworks. This information can help personalize the user experience to make it more and more satisfying. To collect this information, we believe that rather than using traditional techniques, such as beacons or IR, it is better to leverage deep learning techniques using cameras, thus supporting subsequent analyzes such as an automatic analysis of the user’s face. In particular, analyzing the user’s face allows us to grasp her reactions in front of the artworks and establish whether she may have liked that artwork or not, and if she may want to see similar artworks. The aim of this research is to understand how to use localization systems and automatic face analysis to build a user model that could allow museum staff to customize her experience. The first results obtained regarding an innovative localization system, based on deep learning, show the potential of this technique, which permits the extraction of information from faces through the same cameras. As regards this second part, techniques based on deep neural networks, such as Convolutional and Recurrent Neural Networks, are being tested to identify the best approach to extract implicit feedback from users’ faces without making them fill out long questionnaires that require active participation and steal time from the visit.