On characters of Chevalley groups vanishing at the non-semisimple elements

Let G be a finite simple group of Lie type. In this paper we study characters of G that vanish at the non-semisimple elements and whose degree is equal to the order of a maximal unipotent subgroup of G. Such characters can be viewed as a natural generalization of the Steinberg character. For groups G of small rank we also determine the characters of this degree vanishing only at the non-identity unipotent elements.Comment: Dedicated to Lino Di Martino on the occasion of his 65th birthda

Dynamics of a particle confined in a two-dimensional dilating and deforming domain

Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving, by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the "pantographic", case (same shape of the box through all the process) and the case with deformation.Comment: 13 pages, 2 figure

Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain Networks

Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance or similarity metric is, however, not trivial and can be highly dependent on the application at hand. In this work, we propose a novel metric learning method to evaluate distance between graphs that leverages the power of convolutional neural networks, while exploiting concepts from spectral graph theory to allow these operations on irregular graphs. We demonstrate the potential of our method in the field of connectomics, where neuronal pathways or functional connections between brain regions are commonly modelled as graphs. In this problem, the definition of an appropriate graph similarity function is critical to unveil patterns of disruptions associated with certain brain disorders. Experimental results on the ABIDE dataset show that our method can learn a graph similarity metric tailored for a clinical application, improving the performance of a simple k-nn classifier by 11.9% compared to a traditional distance metric.Comment: International Conference on Medical Image Computing and Computer-Assisted Interventions (MICCAI) 201

Assessing Metacomprehension and Metacognitive Reading Strategies

The aim of the study was to establish the similarities and differences among existing instruments for measuring metacognition, in particular the awareness of reading comprehension and further to construct an original instrument for measuring features of metacognition, henceforth referred to as the Metacomprehension and Metacognitive Reading Strategies (M&MRS) Inventory. The M&MRS Inventory was distributed to 115 students at University of Palermo. The results revealed a good reliabilit

Feynman graphs and the large dimensional limit of multipartite entanglement

We are interested in the properties of multipartite entanglement of a system composed by $n$ $d$-level parties (qudits). Focussing our attention on pure states we want to tackle the problem of the maximization of the entanglement for such systems. In particular we effort the problem trying to minimize the purity of the system. It has been shown that not for all systems this function can reach its lower bound, however it can be proved that for all values of $n$ a $d$ can always be found such that the lower bound can be reached. In this paper we examine the high-temperature expansion of the distribution function of the bipartite purity over all balanced bipartition considering its optimization problem as a problem of statistical mechanics. In particular we prove that the series characterizing the expansion converges and we analyze the behavior of each term of the series as $d\to \infty$.Comment: 29 pages, 11 figure

第1章 A Review of Theoretical Approches to Governance and Cross-border Governance in the European Union

平成14年度～平成17年度科学研究費補助金(基盤研究 (A))　「国境を越える地域経済ガバナンス・EU諸地域の先行例を中心とした比較研究」 (課題番号 14252007) 研究成果報告書

International financial flows, domestic banks, and the economic development of the periphery: Italy 1861-1913

This paper analyses the impact of different sources of financing (foreign capital, migrants’ remittances, and domestic banks intermediation) on economic development in Italy between 1861 and WWI. Existing literature has analysed the role of these channels of financial intermediation separately, while this paper for the first time considers them in conjunction. Using IRF from a Cholesky identification structure of a VAR model and relying on an original dataset that combines the most recent series of several financial and economic aggregates, this paper shows that both international capital and domestic saving had a significant impact on investment, while remittances did not. Foreign capital was invested directly, but also via domestic banks, in particular the “German-style” universal banks. Finally, foreign and d omestic capital had different attitudes towards the types of investment (construction vs. plant, machinery and transport equipment) and industries they financed. Combined together, these results shed a new light on the process of economic development of Italy and, more generally, of peripheral economies in the age of the international gold standard

第14章 イタリアの北東部における産業地区の国際的ガバナンス

平成14年度～平成17年度科学研究費補助金(基盤研究 (A))　「国境を越える地域経済ガバナンス・EU諸地域の先行例を中心とした比較研究」 (課題番号 14252007) 研究成果報告書

Spectral Graph Convolutions for Population-based Disease Prediction

Exploiting the wealth of imaging and non-imaging information for disease prediction tasks requires models capable of representing, at the same time, individual features as well as data associations between subjects from potentially large populations. Graphs provide a natural framework for such tasks, yet previous graph-based approaches focus on pairwise similarities without modelling the subjects' individual characteristics and features. On the other hand, relying solely on subject-specific imaging feature vectors fails to model the interaction and similarity between subjects, which can reduce performance. In this paper, we introduce the novel concept of Graph Convolutional Networks (GCN) for brain analysis in populations, combining imaging and non-imaging data. We represent populations as a sparse graph where its vertices are associated with image-based feature vectors and the edges encode phenotypic information. This structure was used to train a GCN model on partially labelled graphs, aiming to infer the classes of unlabelled nodes from the node features and pairwise associations between subjects. We demonstrate the potential of the method on the challenging ADNI and ABIDE databases, as a proof of concept of the benefit from integrating contextual information in classification tasks. This has a clear impact on the quality of the predictions, leading to 69.5% accuracy for ABIDE (outperforming the current state of the art of 66.8%) and 77% for ADNI for prediction of MCI conversion, significantly outperforming standard linear classifiers where only individual features are considered.Comment: International Conference on Medical Image Computing and Computer-Assisted Interventions (MICCAI) 201