On the topology of some hyperspaces of convex bodies associated to tensor norms

For every tuple $d_1,\dots, d_l\geq 2,$ let $\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_l}$ denote the tensor product of $\mathbb{R}^{d_i},$ $i=1,\dots,l.$ Let us denote by $\mathcal{B}(d)$ the hyperspace of centrally symmetric convex bodies in $\mathbb{R}^d,$ $d=d_1\cdots d_l,$ endowed with the Hausdorff distance, and by $\mathcal{B}_\otimes(d_1,\dots,d_l)$ the subset of $\mathcal{B}(d)$ consisting of the convex bodies that are closed unit balls of reasonable crossnorms on $\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_l}.$ It is known that $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is a closed, contractible and locally compact subset of $\mathcal{B}(d).$ The hyperspace $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is called the space of tensorial bodies. In this work we determine the homeomorphism type of $\mathcal{B}_\otimes(d_1,\dots,d_l).$ We show that even if $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is not closed with respect to the Minkowski sum, it is an absolute retract homeomorphic to $\mathcal{Q}\times\mathbb{R}^p,$ where $\mathcal{Q}$ is the Hilbert cube and $p=\frac{d_1(d_1+1)+\cdots+d_l(d_l+1)}{2}.$ Among other results, the relation between the Banach-Mazur compactum and the Banach-Mazur type compactum associated to $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is examined.Comment: 28 pages. Among others, in this version we added an illustrative figure for the proof of Lemma 2.6. A gap on the selection of $r$ in the proof of lemma 2.6 was corrected. We provide a new sentence for Proposition 5.2. This new statement improves the resul

Decays Z' -> \gamma\gamma\gamma{} and Z -> \gamma\gamma\gamma{} in the minimal 331 model

The possibility of a significant effect of exotic particles on the Z'->\gamma\gamma\gamma{} and Z->\gamma\gamma\gamma{} decays is investigated in the context of the minimal 331 model. This model, which is based in the SU_C(3)xSU_L(3)xU_X(1) gauge group, predicts the existence of many exotic charged particles that can significantly enhance the decay widths. It is found that the standard model prediction for the Z->\gamma\gamma\gamma{} decay remains essentially unchanged, as the new physics effects quickly decouples. On the other hand, it is found that the contributions of the new exotic quarks and gauge bosons predicted by this model lead to a branching fraction for the Z'->\gamma\gamma\gamma{} decay of about 10^(-6), which is about three orders of magnitude larger than that of the Z->\gamma\gamma\gamma{} decay.Comment: 20 pages and 20 figure

Nonlinear Control of Underactuated Systems using a 3-D Virtual Laboratory

Control of underactuated mechanical systems is currently one of the most active fields in research due to the diverse applications of these systems in real-life. The aim of this article is focused on the application of nonlinear control techniques for underactuated systems and the virtual simulation of their dynamics behavior. The main contribution of this research is related with the applications of balancing controllers designed with linearization techniques, and including swing-up control using energy based methods for two of the most typical underactuated systems used for testing nonlinear control: The cart-pole and the rotating pendulum systems. The second contribution relies in the development of a virtual laboratory for testing this algorithms and also with a great feature included; the platform is not tied to specific embedded controllers, the users can proof their own control techniques, adding control equations using a graphical user interface developed for that purpose. Finally, the analytical results will be validated via numerical solutions implemented on Matlab-Simulink toolbox, comparing the controllers and the simulation capabilities through several test cases

RNA-seq analysis of the Rhizobium tropici CIAT 899 Transcripitome shows similarites in the activation patterns of symbiotic genes in the presence of apigenin and salt.

Rhizobium tropici strain CIAT 899 establishes effective symbioses with several legume species, including Phaseolus vulgaris and Leucaena leucocephala. This bacterium synthesizes a large variety of nodulation factors in response to nod-gene inducing flavonoids and, surprisingly, also under salt stress conditions. The aim of this study was to identify differentially expressed genes in the presence of both inducer molecules, and analyze the promoter regions located upstream of these genes. Results obtained by RNA-seq analyses of CIAT 899 induced with apigenin, a nod gene-inducing flavonoid for this strain, or salt allowed the identification of 19 and 790 differentially expressed genes, respectively. Fifteen of these genes were up-regulated in both conditions and were involved in the synthesis of both Nod factors and indole-3-acetic acid. Transcription of these genes was presumably activated through binding of at least one of the five NodD proteins present in this strain to specific nod box promoter sequences when the bacterium was induced by both apigenin and salt. Finally, under saline conditions, many other transcriptional responses were detected, including an increase in the transcription of genes involved in trehalose catabolism, chemotaxis and protein secretion, as well as ribosomal genes, and a decrease in the transcription of genes involved in transmembrane transport. To our knowledge this is the first time that a transcriptomic study shows that salt stress induces the expression of nodulation genes in the absence of flavonoids. Thus, in the presence of both nodulation inducer molecules, apigenin and salt, R. tropici CIAT 899 up-regulated the same set of symbiotic genes. It could be possible that the increases in the transcription levels of several genes related to nodulation under saline conditions could represent a strategy to establish symbiosis under abiotic stressing conditions

Regulatory nodD1 and nodD2 genes of Rhizobium tropici strain CIAT 899 and their roles in the early stages of molecular signaling and host-legume nodulation.

Nodulation and symbiotic nitrogen fixation are mediated by several genes, both of the host legume and of the bacterium. The rhizobial regulatory nodD gene plays a critical role, orchestrating the transcription of the other nodulation genes. Rhizobium tropici strain CIAT 899 is an effective symbiont of several legumes?with an emphasis on common bean (Phaseolus vulgaris)?and is unusual in carrying multiple copies of nodD, the roles of which remain to be elucidated. Results: Phenotypes, Nod factors and gene expression of nodD1 and nodD2 mutants of CIAT 899 were compared with those of the wild type strain, both in the presence and in the absence of the nod-gene-inducing molecules apigenin and salt (NaCl). Differences between the wild type and mutants were observed in swimming motility and IAA (indole acetic acid) synthesis. In the presence of both apigenin and salt, large numbers of Nod factors were detected in CIAT 899, with fewer detected in the mutants. nodC expression was lower in both mutants; differences in nodD1 and nodD2 expression were observed between the wild type and the mutants, with variation according to the inducing molecule, and with a major role of apigenin with nodD1 and of salt with nodD2. In the nodD1 mutant, nodulation was markedly reduced in common bean and abolished in leucaena (Leucaena leucocephala) and siratro (Macroptilium atropurpureum), whereas a mutation in nodD2 reduced nodulation in common bean, but not in the other two legumes. Conclusion: Our proposed model considers that full nodulation of common bean by R. tropici requires both nodD1 and nodD2, whereas, in other legume species that might represent the original host, nodD1 plays the major role. In general, nodD2 is an activator of nod-gene transcription, but, in specific conditions, it can slightly repress nodD1. nodD1 and nodD2 play other roles beyond nodulation, such as swimming motility and IAA synthesis

Structure and function of the alfa-rhizobia non-coding transcriptome investigated by RNAseq

Conferencia presentada en: I Spanish-Portuguese Congress on Beneficial Plant-Microbe Interactions (BeMiPlant) and XVIII National Meeting of the Spanish Society of Nitrogen Fixation (XVIII SEFIN). Oeiras, Portugal, 17-19 octubre (2022)This work was supported by grants BFU2017-82645-P and PID2020-114782GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” (BFU2017-82645-P), and grant P20_00185 funded by Junta de Andalucía PAIDI/FEDER/EU, awarded to J.I.J.-Z., and by grant US-1250546 funded by FEDER/Universidad de Sevilla to J.M.V

STUDIA: una aplicación para apoyar el conteo de carbohidratos simulando la dinámica de la glucosa

Contexto: El conteo de carbohidratos se ha considerado la forma ideal de calcular la insulina prandial, por ende se han propuesto varias formas de mejorarlo. Objetivo: Proponemos refinar el conteo de carbohidratos utilizando una simulación, la cual se presenta en una aplicación móvil, STUDIA, que simula en tiempo real la glucosa postprandial. Métodos: Utilizamos un fenomenológico del tracto gastrointestinal, acoplado al modelo mínimo para la glucosa postprandial en personas con diabetes mellitus tipo 1 (DM1). Las funciones y requisitos técnicos se definieron mediante un sistema de adquisición de requerimientos. Para la caracterización de usuarios, utilizamos una aproximación basada en el individuo. El ecosistema de datos se evaluó mediante el criterio UX/UI, la curva de aprendizaje, flexibilidad y la posibilidad de ejecutar modelos matemáticos. Utilizamos datos de un paciente con DM1 para ejemplificar el uso de la aplicación y los datos del monitoreo continuo de glucosa para comparación. Resultados: STUDIA fue construida en Android Studio® con una interfaz de usuario y un módulo administrativo basado en la web conectado a AWS®. Permite similar la glucosa basado en el conteo de carbohidratos para su refinamiento. Se utilizan los parámetros del paciente y los datos históricos de la glucosa para el ajuste de la aplicación. Esta aplicación puede ser utilizada tanto por los pacientes para comparar diferentes escenarios al igual que en la investigación clínica. Conclusiones: Presentamos la primera aplicación para simular la glucosa postprandial basada en un modelo fenomenológico del tracto gastrointestinal para pacientes con DM1. STUDIA se probará con datos históricos de pacientes y en un ensayo clínico

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio