Normalized ground states for Schr\"odinger equations on metric graphs with nonlinear point defects

We investigate the existence of normalized ground states for Schr\"odinger equations on noncompact metric graphs in presence of nonlinear point defects, described by nonlinear $\delta$-interactions at some of the vertices of the graph. For graphs with finitely many vertices, we show that ground states exist for every mass and every $L^2$-subcritical power. For graphs with infinitely many vertices, we focus on periodic graphs and, in particular, on $\mathbb{Z}$-periodic graphs and on a prototypical $\mathbb{Z}^2$-periodic graph, the two-dimensional square grid. We provide a set of results unravelling nontrivial threshold phenomena both on the mass and on the nonlinearity power, showing the strong dependence of the ground state problem on the interplay between the degree of periodicity of the graph, the total number of point defects and their dislocation in the graph.Comment: 28 pages, 4 figure

A note on the radial solutions for the supercritical Henon equation

We prove the existence of a positive radial solution for the H\'enon equation with arbitrary growth. The solution is found by means of a shooting method and turns out to be an increasing function of the radial variable. Some numerical experiments suggest the existence of many positive oscillating solutions.Comment: 13 pages, 4 figure

Understanding social relationships in egocentric vision

The understanding of mutual people interaction is a key component for recognizing people social behavior, but it strongly relies on a personal point of view resulting difficult to be a-priori modeled. We propose the adoption of the unique head mounted cameras first person perspective (ego-vision) to promptly detect people interaction in different social contexts. The proposal relies on a complete and reliable system that extracts people\u5f3s head pose combining landmarks and shape descriptors in a temporal smoothed HMM framework. Finally, interactions are detected through supervised clustering on mutual head orientation and people distances exploiting a structural learning framework that specifically adjusts the clustering measure according to a peculiar scenario. Our solution provides the flexibility to capture the interactions disregarding the number of individuals involved and their level of acquaintance in context with a variable degree of social involvement. The proposed system shows competitive performances on both publicly available ego-vision datasets and ad hoc benchmarks built with real life situations

Dimensional crossover with a continuum of critical exponents for NLS on doubly periodic metric graphs

We investigate the existence of ground states for the focusing nonlinear Schroedinger equation on a prototypical doubly periodic metric graph. When the nonlinearity power is below 4, ground states exist for every value of the mass, while, for every nonlinearity power between 4 (included) and 6 (excluded), a mark of $L^2$-criticality arises, as ground states exist if and only if the mass exceeds a threshold value that depends on the power. This phenomenon can be interpreted as a continuous transition from a two-dimensional regime, for which the only critical power is 4, to a one-dimensional behavior, in which criticality corresponds to the power 6. We show that such a dimensional crossover is rooted in the coexistence of one-dimensional and two-dimensional Sobolev inequalities, leading to a new family of Gagliardo-Nirenberg inequalities that account for this continuum of critical exponents.Comment: 17 pages, 2 figure

Existence and multiplicity of peaked bound states for nonlinear Schr\"odinger equations on metric graphs

We establish existence and multiplicity of one-peaked and multi-peaked positive bound states for nonlinear Schr\"odinger equations on general compact and noncompact metric graphs. Precisely, we construct solutions concentrating at every vertex of odd degree greater than or equal to $3$. We show that these solutions are not minimizers of the associated action and energy functionals. To the best of our knowledge, this is the first work exhibiting solutions concentrating at vertices with degree different than $1$. The proof is based on a suitable Ljapunov-Schmidt reduction.Comment: 25 pages, 2 figure

A Novel Concept of a Responsive Transparent Façade Module: Optimization of Energy Performance through Parametric Design

A novel concept of a responsive transparent façade module was developed and analyzed in its energy performance. The module consists of three glazings: a low-E selective glass; a PCM filled double-pane glazing for solar control; an aerogel filled double-pane glazing for thermal insulation. These layers are dynamically combined in response to external conditions so as to minimize the energy consumption for lighting and HVAC systems. The module was applied to a sample room in Turin and the global energy demand was calculated through a parametric design, using DIVA-for-Rhino. Different room orientations and thicknesses of PCM and aerogel layers were analyze

Extensive Evaluation of Transformer-based Architectures for Adverse Drug Events Extraction

Adverse Event (ADE) extraction is one of the core tasks in digital pharmacovigilance, especially when applied to informal texts. This task has been addressed by the Natural Language Processing community using large pre-trained language models, such as BERT. Despite the great number of Transformer-based architectures used in the literature, it is unclear which of them has better performances and why. Therefore, in this paper we perform an extensive evaluation and analysis of 19 Transformer-based models for ADE extraction on informal texts. We compare the performance of all the considered models on two datasets with increasing levels of informality (forums posts and tweets). We also combine the purely Transformer-based models with two commonly-used additional processing layers (CRF and LSTM), and analyze their effect on the models performance. Furthermore, we use a well-established feature importance technique (SHAP) to correlate the performance of the models with a set of features that describe them: model category (AutoEncoding, AutoRegressive, Text-to-Text), pretraining domain, training from scratch, and model size in number of parameters. At the end of our analyses, we identify a list of take-home messages that can be derived from the experimental data

AILAB-Udine@SMM4H 22: Limits of Transformers and BERT Ensembles

This paper describes the models developed by the AILAB-Udine team for the SMM4H 22 Shared Task. We explored the limits of Transformer based models on text classification, entity extraction and entity normalization, tackling Tasks 1, 2, 5, 6 and 10. The main take-aways we got from participating in different tasks are: the overwhelming positive effects of combining different architectures when using ensemble learning, and the great potential of generative models for term normalization.Comment: Shared Task, SMM4H, Transformer