Motivations and Physical Aims of Algebraic QFT

We present illustrations which show the usefulness of algebraic QFT. In particular in low-dimensional QFT, when Lagrangian quantization does not exist or is useless (e.g. in chiral conformal theories), the algebraic method is beginning to reveal its strength.Comment: 40 pages of LateX, additional remarks resulting from conversations and mail contents, removal of typographical error

Data classification methodology for electronic noses using uniform manifold approximation and projection and extreme learning machine

The classification and use of robust methodologies in sensor array applications of electronic noses (ENs) remain an open problem. Among the several steps used in the developed methodologies, data preprocessing improves the classification accuracy of this type of sensor. Data preprocessing methods, such as data transformation and data reduction, enable the treatment of data with anomalies, such as outliers and features, that do not provide quality information; in addition, they reduce the dimensionality of the data, thereby facilitating the tasks of a machine learning classifier. To help solve this problem, in this study, a machine learning methodology is introduced to improve signal processing and develop methodologies for classification when an EN is used. The proposed methodology involves a normalization stage to scale the data from the sensors, using both the well-known min-max approach and the more recent mean-centered unitary group scaling (MCUGS). Next, a manifold learning algorithm for data reduction is applied using uniform manifold approximation and projection (UMAP). The dimensionality of the data at the input of the classification machine is reduced, and an extreme learning machine (ELM) is used as a machine learning classifier algorithm. To validate the EN classification methodology, three datasets of ENs were used. The first dataset was composed of 3600 measurements of 6 volatile organic compounds performed by employing 16 metal-oxide gas sensors. The second dataset was composed of 235 measurements of 3 different qualities of wine, namely, high, average, and low, as evaluated by using an EN sensor array composed of 6 different sensors. The third dataset was composed of 309 measurements of 3 different gases obtained by using an EN sensor array of 2 sensors. A 5-fold cross-validation approach was used to evaluate the proposed methodology. A test set consisting of 25% of the data was used to validate the methodology with unseen data. The results showed a fully correct average classification accuracy of 1 when the MCUGS, UMAP, and ELM methods were used. Finally, the effect of changing the number of target dimensions on the reduction of the number of data was determined based on the highest average classification accuracy.This work was funded in part with resources from the Fondo de Ciencia, Tecnología e Innovación (FCTeI) del Sistema General de Regalías (SGR) from Colombia. The authors express their gratitude to the Administrative Department of Science, Technology, and Innovation–Colciencias with the grant 779–“Convocatoria para la Formación de Capital Humano de Alto Nivel para el Departamento de Boyacá 2017” for sponsoring the research presented herein. This study has been partially funded by the Spanish Agencia Estatal de Investigación (AEI)-Ministerio de Economía, Industria y Competitividad (MINECO), and the Fondo Europeo de Desarrollo Regional (FEDER) through research projects DPI2017-82930-C2-1-R and PGC2018-097257-B-C33; and by the Generalitat de Catalunya through research projects 2017-SGR-388 and 2017-SGR-1278.Peer ReviewedPostprint (published version