A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Cell Attention Networks

Since their introduction, graph attention networks achieved outstanding results in graph representation learning tasks. However, these networks consider only pairwise relationships among nodes and then they are not able to fully exploit higher-order interactions present in many real world data-sets. In this paper, we introduce Cell Attention Networks (CANs), a neural architecture operating on data defined over the vertices of a graph, representing the graph as the 1-skeleton of a cell complex introduced to capture higher order interactions. In particular, we exploit the lower and upper neighborhoods, as encoded in the cell complex, to design two independent masked self-attention mechanisms, thus generalizing the conventional graph attention strategy. The approach used in CANs is hierarchical and it incorporates the following steps: i) a lifting algorithm that learns {\it edge features} from {\it node features}; ii) a cell attention mechanism to find the optimal combination of edge features over both lower and upper neighbors; iii) a hierarchical {\it edge pooling} mechanism to extract a compact meaningful set of features. The experimental results show that CAN is a low complexity strategy that compares favorably with state of the art results on graph-based learning tasks.Comment: Preprint, under revie

A diagrammatic view of differential equations in physics

Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm mathematical footing, while also systematizing a broadly applicable framework to reason formally about systems of equations and their solutions. Our main mathematical tools are category-theoretic diagrams, which are well known, and morphisms between diagrams, which have been less appreciated. As an application of the diagrammatic framework, we show how complex, multiphysical systems can be modularly constructed from basic physical principles. A wealth of examples, drawn from electromagnetism, transport phenomena, fluid mechanics, and other fields, is included.Comment: 69 page

A mathematical programming approach to SVM-based classification with label noise

The authors of this research acknowledge financial support by the Spanish Ministerio de Ciencia y Tecnologia, Agencia Estatal de Investigacion and Fondos Europeos de Desarrollo Regional (FEDER) via project PID2020114594GB-C21. The authors also acknowledge partial support from projects FEDER-US-1256951, Junta de Andalucía P18-FR-1422, CEI-3-FQM331, NetmeetData: Ayudas Fundación BBVA a equipos de investigación científica 2019. The first author was also supported by projects P18-FR-2369 (Junta de Andalucía) and IMAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033. (Spanish Ministerio de Ciencia y Tecnologia).In this paper we propose novel methodologies to optimally construct Support Vector Machine-based classifiers that take into account that label noise occur in the training sample. We propose different alternatives based on solving Mixed Integer Linear and Non Linear models by incorporating decisions on relabeling some of the observations in the training dataset. The first method incorporates relabeling directly in the SVM model while a second family of methods combines clustering with classification at the same time, giving rise to a model that applies simultaneously similarity measures and SVM. Extensive computational experiments are reported based on a battery of standard datasets taken from UCI Machine Learning repository, showing the effectiveness of the proposed approaches.Spanish Ministerio de Ciencia y Tecnologia, Agencia Estatal de Investigacion and Fondos Europeos de Desarrollo Regional (FEDER) via project PID2020114594GB-C21FEDER-US-1256951Junta de Andalucía P18-FR-1422CEI-3-FQM331NetmeetData: Ayudas Fundación BBVA a equipos de investigación científica 2019Project P18-FR-2369 Junta de AndalucíaIMAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033. (Spanish Ministerio de Ciencia y Tecnologia

Progettazione multidisciplinare ottimizzata nelle microturbine a gas

Optimized multidisciplinary design in micro-gasturbine

Quality management approach of product data models for shipbuilding

A quality management approach to manage the quality of ship product model data is discussed. It aims to improve and to automate product data model control to make the design and production processes more reliable. This approach is supporting an efficient correction of decient structural designs under visual guidance towards the identied problems. Two international standards ISO STEP-59 and ISO/PAS 26183:2006 are utilized in this thesis

Thermal Calculation of Rotational Electrical Machines Using Thermal Network

Práce se zabývá konstrukcí a využitím tepelných sítí k simulaci oteplení elektrických motorů velkých výkonú. Po úvodu do termiky a teorie proudění je popsána konstrukce tří různých typů sítí pro odlišné ventilační schémata motoru. Dále jsou popsány optimalizační metody a jejich možnosti k tepelné optimalizaci motorů. Je vybrána a vysvělena Marquard-Levenbergova metoda a na konkrétním případě je vysvětleno její použití a výhody pro optimalizaci chlazení elektrického motoru. V závěru se práce zabývá také citlivostí teplotních sití na jednotlivé vstupní parametry, porovnáním simulací s měřenými výsledky a také vlivem teplotních závislosti jenotlivých prvků sítě.The work deals with construction and usage of thermal networks to simulate the temperature rise in electrical motors of high power. After the introduction into heat transfer and flow theory, the construction of three different thermal networks is explained. Further the work handles different optimization methods and their usage for thermal optimization of electrical motors. The Levenberg-Marquard method is chosen and on the example is explained the procedure and an advantage against other methods for optimizing electrical motors. In the conclusion the thesis points out the most important input parameters of the thermal networks and their general sensitivity. It compares the results of the simulation with the results of tests obtained in test field. Another point of concern is the thermal dependence of various elements in the network.