Fekete's lemma for componentwise subadditive functions of two or more real variables

We prove an analogue of Fekete's subadditivity lemma for functions of several real variables which are subadditive in each variable taken singularly. This extends both the classical case for subadditive functions of one real variable, and a result in a previous paper by the author. While doing so, we prove that the functions with the property mentioned above are bounded in every closed and bounded subset of their domain. The arguments follows those of Chapter 6 in E. Hille's 1948 textbook.Comment: 22 pages. Revised and expanded. Longer introduction, more detailed background, statement of main theorem extende

Path Integrals on Euclidean Space Forms

In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel Hilbert space. A definition of the Feynman propagator, based on the reproducing property of this space, is proposed. In the $\mathbb{R}^n$ case the obtained results coincide with the known expressions

DocEmul: a Toolkit to Generate Structured Historical Documents

We propose a toolkit to generate structured synthetic documents emulating the actual document production process. Synthetic documents can be used to train systems to perform document analysis tasks. In our case we address the record counting task on handwritten structured collections containing a limited number of examples. Using the DocEmul toolkit we can generate a larger dataset to train a deep architecture to predict the number of records for each page. The toolkit is able to generate synthetic collections and also perform data augmentation to create a larger trainable dataset. It includes one method to extract the page background from real pages which can be used as a substrate where records can be written on the basis of variable structures and using cursive fonts. Moreover, it is possible to extend the synthetic collection by adding random noise, page rotations, and other visual variations. We performed some experiments on two different handwritten collections using the toolkit to generate synthetic data to train a Convolutional Neural Network able to count the number of records in the real collections.Comment: In Proceedings of the 14th International Conference on Document Analysis and Recognition (ICDAR), 201

Multidimensional cellular automata and generalization of Fekete's lemma

Fekete's lemma is a well known combinatorial result on number sequences: we extend it to functions defined on $d$-tuples of integers. As an application of the new variant, we show that nonsurjective $d$-dimensional cellular automata are characterized by loss of arbitrarily much information on finite supports, at a growth rate greater than that of the support's boundary determined by the automaton's neighbourhood index.Comment: 6 pages, no figures, LaTeX. Improved some explanations; revised structure; added examples; renamed "hypercubes" into "right polytopes"; added references to Arratia's paper on EJC, Calude's book, Cook's proof of Rule 110 universality, and arXiv paper 0709.117

S-AVE Semantic Active Vision Exploration and Mapping of Indoor Environments for Mobile Robots

Semantic mapping is fundamental to enable cognition and high-level planning in robotics. It is a difficult task due to generalization to different scenarios and sensory data types. Hence, most techniques do not obtain a rich and accurate semantic map of the environment and of the objects therein. To tackle this issue we present a novel approach that exploits active vision and drives environment exploration aiming at improving the quality of the semantic map

Quantitative risk assessment on a hydrogen refuelling station

The Directive 2014/94/UE (DAFI, Alternative Fuel Initiative Directive) on the deployment of alternative fuels (i.e. hydrogen) infrastructures has been recently transposed into national law in Italy. Consequently, the technical regulation on fire prevention for H2fuelling stations has been updated, in order to consider the current maximum delivery pressure (700 bar) of gaseous hydrogen for road vehicles. This technical regulation establishes the prescriptive safety distance from a piece of equipment. In the case of a new station, an assessment of the frequency of the event and its potential consequences is necessary. This is to understand which risk can reasonably be mitigated by a safety distance or whether additional mitigation or prevention measures should be taken. This paper presents the quantitative risk assessment (QRA) study on a hydrogen station planned to be installed, study which aims at determining the safety distances. Such study utilizes the Sandia-developed QRA tool, Hydrogen Risk Analysis Model (HyRAM), to calculate risk values when developing risk-equivalent plans. HyRAM combines reduced order deterministic models that characterize hydrogen release and flame behavior with probabilistic risk models to quantify risk values. Thanks to HyRAM tool it is possible to estimate physical effects and consequences on people and structures and plants, related to risk scenarios, by means of a damage model library. Use of risk assessment may allow station owners and designers to flexibly define station-specific mitigations, with the purpose of achieving equal or better levels of safety with respect to prescriptive recommendation levels, as suggested by ISO19880-1 (2018)