Geometric properties of 2-dimensional minimal surfaces in a sub-Riemannian manifold which models the Visual Cortex

In this paper we study the notion of degree forsubmanifolds embedded in an equiregular sub-Riemannian manifold and we provide the definition of their associated area functional. In this setting we prove that the Hausdorff dimension of a submanifold coincides with its degree, as stated by Gromov. Using these general definitions we compute the first variation for surfaces embedded in low dimensional manifolds and we obtain the partial differential equation associated to minimal surfaces. These minimal surfaces have several applications in the neurogeometry of the visual cortex.

Sub-wavelength resonators as seismic Rayleigh waves shield

We explore the thesis that tall structures can be protected by means of seismic metamaterials. Seismic metamaterials can be built as some elements are created over soil layer with different shapes, dimensions, patterns and from different materials. Resonances in these elements are acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. Analytically we proved that if we put infinite chain of SDOF resonator over the soil layer as an elastic, homogeneous and isotropic material, vertical component of Rayleigh wave, longitudinal resonance of oscillators will couple with each other, they would create a Rayleigh bandgap frequency, and wave will experience attenuation before it reaches the structure. As it is impossible to use infinite chain of resonators over soil layer, we considered finite number of resonators throughout our simulations. Analytical work is interpreted using finite element simulations that demonstrates the observed attenuation is due to bandgaps when oscillators are arranged at sub-wavelength scale with respect to the incident Rayleigh wave. For wavelength less than 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when impedance of oscillators matches impedance of soil. Since longitudinal resonance of SDOF resonator are proportional to its length inversely, a formed array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground. Optimum number of vertical pillars and their interval spacing called effective area of resonators are investigated. For 10 pillars with effective area of 1 meter and resonance frequency of 4.9 Hz, bandgap frequency causes attenuation and a sinusoidal impulsive force illustrate wave steering down phenomena. Simulation results proved analytical findings of this work.

Bayesian Linear Regression for estimation of the Fractal Dimension of the Cerebral Cortex

The cerebral cortex presents self-similarity in a proper interval of spatial scales, a property typical of natural objects exhibiting fractal geometry. Its complexity therefore can be characterized by the value of its fractal dimension (FD). In the computation of this metric, it has usually been employed a frequentist approach to probability, with point estimator methods yielding only the optimal values of the FD. In our study, we aimed at retrieving a more complete evaluation of the FD by utilizing a Bayesian model for the linear regression analysis of the box-counting algorithm. We used T1-weighted MRI data of 86 healthy subjects (age 44.2 ± 17.1 years, mean ± standard deviation, 48% males) in order to gain insights into the confidence of our measure and investigate the relationship between mean Bayesian FD and age. Our approach yielded a stronger and significant (P < .001) correlation between mean Bayesian FD and age as compared to the previous implementation. Thus, our results make us suppose that the Bayesian FD is a more truthful estimation for the fractal dimension of the cerebral cortex compared to the frequentist FD.

Model-Based Contrastive Explanations for XAIP: Towards a General Model and Prototype

Planning is an important sub-field of artificial intelligence (AI) focusing on letting intelligent agents deliberate on the most adequate course of action to attain their goals. Thanks to the recent boost in the number of critical domains and systems which exploit planning for their internal procedures, there is an increasing need for planning systems to become more transparent and trustworthy. Along this line, planning systems are now required to produce not only plans but also explanations about those plans, or the way they were attained. To address this issue, a new research area is emerging in the AI panorama: eXplainable AI (XAI), within which explainable planning (XAIP) is a pivotal sub-field. As a recent domain, XAIP is far from mature. No consensus has been reached in the literature about what explanations are, how they should be computed, and what they should explain in the first place. Furthermore, existing contributions are mostly theoretical, and software implementations are rarely more than preliminary. To overcome such issues, in this thesis we design an explainable planning framework bridging the gap between theoretical contributions from literature and software implementations. More precisely, taking inspiration from the state of the art, we develop a formal model for XAIP, and the software tool enabling its practical exploitation. Accordingly, the contribution of this thesis is four-folded. First, we review the state of the art of XAIP, supplying an outline of its most significant contributions from the literature. We then generalise the aforementioned contributions into a unified model for XAIP, aimed at supporting model-based contrastive explanations. Next, we design and implement an algorithm-agnostic library for XAIP based on our model. Finally, we validate our library from a technological perspective, via an extensive testing suite. Furthermore, we assess its performance and usability through a set of benchmarks and end-to-end examples.

Non-line-of-sight localization with frequency-selective metasurfaces

An emerging technology, that Smart Radio Environments rely on to improve wireless link quality, are Reconfigurable Intelligent Surfaces (RISs). A RIS, in general, can be understood as a thin layer of EM composite material, typically mounted on the walls or ceilings of buildings, which can be reconfigured even after its deployment in the network. RISs made by composing artificial materials in an engineered way, in order to obtain unconventional characteristics, are called metasurfaces. Through the programming of the RIS, it is possible to control and/or modify the radio waves that affect it, thus shaping the radio environment. To overcome the limitations of RISs, the metaprism represents an alternative: it is a passive and non-reconfigurable frequency-selective metasurface that acts as a metamirror to improve the efficiency of the wireless link. In particular, using an OFDM (Orthogonal Frequency-Division Multiplexing) signaling it is possible to control the reflection of the signal, suitably selecting the sub-carrier assigned to each user, without having to interact with the metaprism or having to estimate the CSI. This thesis investigates how OFDM signaling and metaprism can be used for localization purposes, especially to extend the coverage area at low cost, in a scenario where the user is in NLoS (Non-line-of-sight) conditions with respect to the base station, both single antenna. In particular, the paper concerns the design of the analytical model and the corresponding Matlab implementation of a Maximum Likelihood (ML) estimator able to estimate the unknown position, behind an obstacle, from which a generic user transmits to a base station, exploiting the metaprism.