On Canonical Subfield Preserving Polynomials

Explicit monoid structure is provided for the class of canonical subfield preserving polynomials over finite fields. Some classical results and asymptotic estimates will follow as corollaries.Comment: (To appear in Acta Arithmetica

A Deep Generative Model for Fragment-Based Molecule Generation

Molecule generation is a challenging open problem in cheminformatics. Currently, deep generative approaches addressing the challenge belong to two broad categories, differing in how molecules are represented. One approach encodes molecular graphs as strings of text, and learns their corresponding character-based language model. Another, more expressive, approach operates directly on the molecular graph. In this work, we address two limitations of the former: generation of invalid and duplicate molecules. To improve validity rates, we develop a language model for small molecular substructures called fragments, loosely inspired by the well-known paradigm of Fragment-Based Drug Design. In other words, we generate molecules fragment by fragment, instead of atom by atom. To improve uniqueness rates, we present a frequency-based masking strategy that helps generate molecules with infrequent fragments. We show experimentally that our model largely outperforms other language model-based competitors, reaching state-of-the-art performances typical of graph-based approaches. Moreover, generated molecules display molecular properties similar to those in the training sample, even in absence of explicit task-specific supervision

Compositional generative mapping for tree-structured data - Part II: Topographic projection model

We introduce GTM-SD (Generative Topographic Mapping for Structured Data), which is the first compositional generative model for topographic mapping of tree-structured data. GTM-SD exploits a scalable bottom-up hidden-tree Markov model that was introduced in Part I of this paper to achieve a recursive topographic mapping of hierarchical information. The proposed model allows efficient exploitation of contextual information from shared substructures by a recursive upward propagation on the tree structure which distributes substructure information across the topographic map. Compared to its noncompositional generative counterpart, GTM-SD is shown to allow the topographic mapping of the full sample tree, which includes a projection onto the lattice of all the distinct subtrees rooted in each of its nodes. Experimental results show that the continuous projection space generated by the smooth topographic mapping of GTM-SD yields a finer grained discrimination of the sample structures with respect to the state-of-the-art recursive neural network approach

Graph Mixture Density Networks

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph representation learning, we address a broader class of challenging conditional density estimation problems that rely on structured data. In this respect, we evaluate our method on a new benchmark application that leverages random graphs for stochastic epidemic simulations. We show a significant improvement in the likelihood of epidemic outcomes when taking into account both multimodality and structure. The empirical analysis is complemented by two real-world regression tasks showing the effectiveness of our approach in modeling the output prediction uncertainty. Graph Mixture Density Networks open appealing research opportunities in the study of structure-dependent phenomena that exhibit non-trivial conditional output distributions

Theoretically Expressive and Edge-aware Graph Learning

We propose a new Graph Neural Network that combines recent advancements in the field. We give theoretical contributions by proving that the model is strictly more general than the Graph Isomorphism Network and the Gated Graph Neural Network, as it can approximate the same functions and deal with arbitrary edge values. Then, we show how a single node information can flow through the graph unchanged

CVD nano-coating of carbon composites for space materials atomic oxygen shielding

The present work analyzes the possibility to employ carbon nanostructures as a basic material to prevent the erosion effects of atomic oxygen suffered by the carbon fiber reinforced polymeric material used in low earth orbit space environment. The application of thin protecting coatings to base materials is a widely used method for preventing the atomic oxygen induced erosion, and thus degradation. The generic purpose is to integrate carbon nanostructures onto carbon composites surface in order to develop the basic substrate of advanced nanocomposite for atomic oxygen protection. The final goal is the characterization of carbon nanostructures-reinforced carbon composites by means of on-ground atomic oxygen simulation facility, with the future objective to assess and optimize the process of carbon-multiscale advanced composites production. With such an aim, a wide investigation on the methane chemical vapor deposition (CVD) over catalyzed carbon fiber-based substrates has been carried out. The as grown nanostructures have been analyzed in terms of morphology, as well as regarding the main features of the resulting growth (yield, purity, homogeneity, coating uniformity, etc.) and the influence of the deposition route operating parameters (catalyst typology, gas flowing rate, growth time/temperature, etc.). A high degree of reproducibility in terms of the relationship between the carbon deposit type/yield and the main process variables (catalyst and protocol) has been thus obtained. Finally, atomic oxygen ground tests have been conducted in order to evaluate the coating process effectiveness. The on-ground test in atomic oxygen environment, with respect to the performances of the reference carbon composites (in terms of total mass loss and atomic oxygen rate of erosion), showed a worsening for the disordered carbon deposit, while an intriguing improvement was achieved by the high-yield carbon nano-filaments deposition

A new advanced railgun system for debris impact study

The growing quantity of debris in Earth orbit poses a danger to users of the orbital environment, such as spacecraft. It also increases the risk that humans or manmade structures could be impacted when objects reenter Earth's atmosphere. During the design of a spacecraft, a requirement may be specified for the surviv-ability of the spacecraft against Meteoroid / Orbital Debris (M/OD) impacts throughout the mission; further-more, the structure of a spacecraft is designed to insure its integrity during the launch and, if it is reusable, during descent, re-entry and landing. In addition, the structure has to provide required stiffness in order to allow for exact positioning of experiments and antennas, and it has to protect the payload against the space environment. In order to decrease the probability of spacecraft failure caused by M/OD, space maneuver is needed to avoid M/OD if the M/OD has dimensions larger than 10cm, but for M/OD with dimensions less than 1cm M/OD shields are needed for spacecrafts. It is therefore necessary to determine the impact-related failure mechanisms and associated ballistic limit equations (BLEs) for typical spacecraft components and subsys-tems. The methods that are used to obtain the ballistic limit equations are numerical simulations and la-borato-ry experiments. In order to perform an high energy ballistic characterization of layered structures, a new ad-vanced electromagnetic accelerator, called railgun, has been assembled and tuned. A railgun is an electrically powered electromagnetic projectile launcher. Such device is made up of a pair of parallel conducting rails, which a sliding metallic armature is accelerated along by the electromagnetic effect (Lorentz force) of a cur-rent that flows down one rail, into the armature and then back along the other rail, thanks to a high power pulse given by a bank of capacitors. A tunable power supplier is used to set the capacitors charging voltage at the desired level: in this way the Rail Gun energy can be tuned as a function of the desired bullet velocity. This facility is able to analyze both low and high velocity impacts. A numerical simulation is also performed by using the Ansys Autodyn code in order to analyze the damage. The experimental results and numerical simulations show that the railgun-device is a good candidate to perform impact testing of materials in the space debris energy range

Fully Configurable Electromagnetic Wave Absorbers by Using Carbon Nanostructures

The configurable electromagnetic wave absorber (CEMA) defines a new method for the full design of layered carbon-based nanocomposites able to quasi-perfectly reproduce any kind of EM reflection coefficient (RC) profile. The method involves three main factors: (a) nanofillers-like carbon nanotube (CNT), carbon nanofiber (CNF), graphene nanoplatelet (GNP), and polyaniline (PANI) in different concentration versus the matrix; (b) the dielectric parameters of the nanoreinforced materials in the microwave range 2–18 GHz; (c) a numerical technique based on particle swarm optimization (PSO) algorithm within the MATLAB code of the EM propagation engine. Output is the layering of the wave absorber, that is, number of layers and material/thickness of each layer and the reflection/transmission simulated profiles. The frequency selective behavior is due to the multilayered composition, thanks to the direct/reflected wave combination tuning at interfaces. The dielectric characterization of the employed nanocomposites is presented in details: these materials constitute the database for the optimization code running toward the multilayer optimal solution. A FEM analysis is further proposed to highlight the EM propagation within the material’s bulk at different frequencies. The mathematical model of layered materials, the PSO objective function used for RC target fitting, and some results are reported in the text