Witten's perturbation on strata with general adapted metrics

Let $M$ be a stratum of a compact stratified space $A$. It is equipped with a general adapted metric $g$, which is slightly more general than the adapted metrics of Nagase and Brasselet-Hector-Saralegi. In particular, $g$ has a general type, which is an extension of the type of an adapted metric. A restriction on this general type is assumed, and then $g$ is called good. We consider the maximum/minimun ideal boundary condition, $d_{\text{\rm max/min}}$, of the compactly supported de~Rham complex on $M$, in the sense of Br\"uning-Lesch. Let $H^*_{\text{\rm max/min}}(M)$ and $\Delta_{\text{\rm max/min}}$ denote the cohomology and Laplacian of $d_{\text{\rm max/min}}$. The first main theorem states that $\Delta_{\text{\rm max/min}}$ has a discrete spectrum satisfying a weak form of the Weyl's asymptotic formula. The second main theorem is a version of Morse inequalities using $H_{\text{\rm max/min}}^*(M)$ and what we call rel-Morse functions. An ingredient of the proofs of both theorems is a version for $d_{\text{\rm max/min}}$ of the Witten's perturbation of the de~Rham complex. Another ingredient is certain perturbation of the Dunkl harmonic oscillator previously studied by the authors using classical perturbation theory. Assume that $A$ is a stratified pseudomanifold, and consider its intersection homology $I^{\bar p}H_*(A)$ with perversity $\bar p$; in particular, the lower and upper middle perversities are denoted by $\bar m$ and $\bar n$, respectively. Then, for any perversity $\bar p\le\bar m$, there is an associated good adapted metric on $M$ satisfying the Nagase isomorphism $H^r_{\text{\rm max}}(M)\cong I^{\bar p}H_r(A)^*$ ($r\in\N$). If $M$ is oriented and $\bar p\ge\bar n$, we also get $H^r_{\text{\rm min}}(M)\cong I^{\bar p}H_r(A)$. Thus our version of the Morse inequalities can be described in terms of $I^{\bar p}H_*(A)$.Comment: 46 pages. A few minor corrections were mad

On Grothendieck Sets

[EN] We call a subset M of an algebra of sets A a Grothendieck set for the Banach space ba (A) of bounded finitely additive scalar-valued measures on A equipped with the variation norm if each sequence fmn g n =1 in ba(A) which is pointwise convergent on M is weakly convergent in ba(A), i. e., if there is m 2 ba (A) such that mn ( A) ! m ( A) for every A 2M then mn ! m weakly in ba(A). A subset M of an algebra of sets A is called a Nikodym set for ba(A) if each sequence fm n g n =1 in ba(A) which is pointwise bounded on M is bounded in ba (A). We prove that if S is a s-algebra of subsets of a set W which is covered by an increasing sequence fS n : n 2 Ng of subsets of S there exists p 2 N such that S p is a Grothendieck set for ba(A). This statement is the exact counterpart for Grothendieck sets of a classic result of Valdivia asserting that if a s-algebra S is covered by an increasing sequence fS n : n 2 Ng of subsets, there is p 2 N such that S p is a Nikodym set for ba (S). This also refines the Grothendieck result stating that for each s -algebra S the Banach space ` (S) is a Grothendieck space. Some applications to classic Banach space theory are given.This research was funded by grant PGC2018-094431-B-I00 of Ministry of Scence, Innovation and universities of Spain.Ferrando, JC.; López Alfonso, S.; López Pellicer, M. (2020). On Grothendieck Sets. Axioms. 9(1):1-7. https://doi.org/10.3390/axioms9010034S1791Valdivia, M. (1979). On certain barrelled normed spaces. Annales de l’institut Fourier, 29(3), 39-56. doi:10.5802/aif.752Ferrando, J. C., López-Alfonso, S., & López-Pellicer, M. (2019). On Nikodým and Rainwater sets for ba (R) and a problem of M. Valdivia. Filomat, 33(8), 2409-2416. doi:10.2298/fil1908409fLópez-Alfonso, S. (2015). On Schachermayer and Valdivia results in algebras of Jordan measurable sets. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 110(2), 799-808. doi:10.1007/s13398-015-0267-xFerrando, J. C., & Ruiz, L. M. S. (2004). A Survey on Recent Advances on the Nikodým Boundedness Theorem and Spaces of Simple Functions. Rocky Mountain Journal of Mathematics, 34(1). doi:10.1216/rmjm/1181069896Valdivia, M. (2012). On Nikodym boundedness property. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 107(2), 355-372. doi:10.1007/s13398-012-0081-7Ferrando, J. C., Ka̧kol, J., & López-Pellicer, M. (2017). On spaces Cb(X) weakly K-analytic. Mathematische Nachrichten, 290(16), 2612-2618. doi:10.1002/mana.201600406Rainwater, J. (1963). Weak convergence of bounded sequences. Proceedings of the American Mathematical Society, 14(6), 999. doi:10.1090/s0002-9939-1963-0155171-9Simons, S. (1972). A convergence theorem with boundary. Pacific Journal of Mathematics, 40(3), 703-708. doi:10.2140/pjm.1972.40.703Drewnowski, L., Florencio, M., & Paúl, P. J. (1994). Barrelled subspaces of spaces with subseries decompositions or Boolean rings of projections. Glasgow Mathematical Journal, 36(1), 57-69. doi:10.1017/s0017089500030548Saxon, S. A. (1972). Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology. Mathematische Annalen, 197(2), 87-106. doi:10.1007/bf0141958

Incremental Learning from Low-labelled Stream Data in Open-Set Video Face Recognition

[Abstract] Deep Learning approaches have brought solutions, with impressive performance, to general classification problems where wealthy of annotated data are provided for training. In contrast, less progress has been made in continual learning of a set of non-stationary classes, mainly when applied to unsupervised problems with streaming data. Here, we propose a novel incremental learning approach which combines a deep features encoder with an Open-Set Dynamic Ensembles of SVM, to tackle the problem of identifying individuals of interest (IoI) from streaming face data. From a simple weak classifier trained on a few video-frames, our method can use unsupervised operational data to enhance recognition. Our approach adapts to new patterns avoiding catastrophic forgetting and partially heals itself from miss-adaptation. Besides, to better comply with real world conditions, the system was designed to operate in an open-set setting. Results show a benefit of up to 15% F1-score increase respect to non-adaptive state-of-the-art methods.This work has received financial support from the Spanish government (project PID2020-119367RB-I00); from the Xunta de Galicia, Consellaría de Cultura, Educación e Ordenación Universitaria (accreditations 2019-2022 ED431G-2019/04 and ED431G 2019/01, and reference competitive groups 2021-2024 ED431C 2021/48 and ED431C 2021/30), and from the European Regional Development Fund (ERDF). Eric López-López has received financial support from the Xunta de Galicia and the European Union (European Social Fund - ESF)Xunta de Galicia; ED431G-2019/04Xunta de Galicia; and ED431G 2019/01Xunta de Galicia; ED431C 2021/48Xunta de Galicia; ED431C 2021/3

Analysis of Fuzzy Vector Spaces as an Algebraic Framework for Flag Codes

Flag codes are a recent network coding strategy based on linear algebra. Fuzzy vector subspaces extend the notions of classical linear algebra. They can be seen as abstractions of flags to the point that several fuzzy vector subspaces can be identified to the same flag, which naturally induces an equivalence relation on the set of fuzzy vector subspaces. The main contributions of this work are the methodological abstraction of flags and flag codes in terms of fuzzy vector subspaces, as well as the generalisation of three distinct equivalence relations that originated from the fuzzy subgroup theory and study of their connection with flag codes, computing the number of equivalence classes in the discrete case, which represent the number of essentially distinct flags, and a comprehensive analysis of such relations and the properties of the corresponding quotient sets

The Trypanosomatid Pr77-hallmark contains a downstream core promoter element essential for transcription activity of the Trypanosoma cruzi L1Tc retrotransposon

Background: Trypanosomatid genomes are highly colonized by non-LTR retroelements that make up to 5% of the nuclear genome. These elements are mainly accumulated in the strand switch regions (SSRs) where polycistronic transcription is initiated and have a 77nt-long sequence - Pr77 - at their 5' ends. L1Tc is the best represented retrotransposon in the Trypanosoma cruzi genome and is a potentially functional autonomous element that encodes its own retrotransposition machinery. The Pr77of the T. cruzi L1Tc element activates gene transcription via RNA polymerase II, generating abundant, unspliced transcripts which are translated. Results: The present manuscript describes the identification of a downstream core promoter element (DPE) in the L1Tc Pr77sequence. Just four nucleotides long (CGTG), it covers in Pr77positions +25 to +28 of the described L1Tc transcription start site. The Pr77-DPE motif is conserved in terms of sequence composition and position in the Pr77of most trypanosomatid non-LTR retrotransposons, independent of the coding or non-coding capacity of these retroelements. Transcription assays in T. cruzi stable transfectants with vector containing point mutations at 17locations of the Pr77nucleotide sequence evidence that the DPE motif is essential for the promoter function of Pr77. Furthermore, the obtained data show that other nucleotides also contributed to the promoter function of Pr77. In addition, the presented results indicate that parasite nuclear proteins specifically bind to different regions of the Pr77sequence although the strongest binding is to the DPE motif. Moreover, it is shown that the DPE sense single-stranded sequence is being required in DNA-protein recognition of nuclear factors. Conclusions: The Pr77sequence present in most of non-LTR retrotransposons of trypanosomatids contains a downstream core promoter element (DPE) which is conserved in terms of nucleotide composition and location. The Pr77-DPE motif is essential for the transcriptional activity of Pr77although other nucleotides are also involved. DPE has a high affinity binding for nuclear proteins in T. cruzi. The wide retroelement-mediated distribution of Pr77suggests that it may represent an important tool for regulating gene expression in trypanosomatids. © 2016 Macías et al.This work was supported by the Programa Estatal I+D+i (MINECO) via grants SAF2012-35777, SAF2013-48527-R and RTC-2014-2130, by the RICET Tropical Diseases Research Network via grant RD12/0018/0021, and via FEDER funds.Peer reviewe

Giuseppe Cervi, Guillaume Jacobe y las relaciones entre la "Regia Sociedad de Medicina y demás Ciencias de Sevilla" y la "Royal Society of London" en 1736

El siglo XVIII fue el siglo de las instituciones científicas. Nuestro país no fue ajeno a este proceso, encontrándose entre las instituciones de más temprana creación la Regia Sociedad de Medicina y demás Ciencias de Sevilla que, aunque fundada a principios de siglo, adquirió carta de naturaleza realmente en la década de los años treinta. En este resurgimiento tuvo una influencia decisiva Giuseppe Cervi, primer médico de Felipe V y uno de los personajes más relevantes del panorama médico español de la época. Este artículo estudia las circunstancias que marcaron el nombramiento de Cervi como miembro de la Royal Society, en particular las debidas a la intervención de Guillaume Jacobe, médico francés contratado como anatómico por la Regia Sociedad, durante una estancia de trabajo en París, de quien se estudia la vinculación con la Sociedad sevillana

La investigación para ahorrar costes en programas de comunicación efectivos: buscando cambios de actitud en un hospital escuela, a través de la comunicación interna

Desde su creación hace más de doscientos años, la Universidad de Guadalajara fue creada en paralelo con la instalación del primer Hospital Civil Fray Antonio Alcalde y Barriga y desde entonces el vínculo Universidad y Hospital ha permitido el avance del servicio prestado en la entidad. Se une a este esfuerzo otro hospital Escuela: el Juan. I. Menchaca (JIM) que concentra un banco de ojos que provee de tejidos oculares a esos y otros hospitales de la región. Bajo esta perspectiva, la Universidad de Guadalajara, por medio de su Dirección de Prensa y comunicaciones, vista como un área de desarrollo corporativo, brinda asesoría a aquellas instituciones que están íntimamente ligadas con esta casa de estudios como es el caso del nosocomio Juan I. Menchaca. Ante la imperante necesidad de contar con tejidos oculares para el Banco de Órganos y Tejidos Oculares, (BOTO), ubicado en el JIM se trabajó para aumentar la donación de córneas y así satisfacer la demanda actual que rebasa los 1,334 pacientes en lista de espera, cifra que incluye además las necesidades de tres hospitales públicos con capacidad de realizar este tipo de trasplante. La obtención de tejidos por parte del BOTO durante el 2004 fue sola de una cornea, muy por debajo de su necesidad, lo que comparándolo con el Banco de Ojos para el tratamiento de la ceguera, ubicado en la clínica Barraquer de Barcelona, se puede observar una gestión de corneas de 841 (2003), considerablemente normal a la demanda. Es pues evidente el número de tejidos que se deben importar a Guadalajara con un costo elevado y sin la óptima calidad y sin satisfacer aún las necesidades, a pesar de que a diario fallecen entre cinco y siete pacientes en el JIM, Marco Tulio Flores y Carlos Manuel López 323 Luego de aplicar una metodología de investigación basada en estudios cualitativos y cuantitativos se propuso a la titular del BOTO un plan de comunicación que permitiese sanear este problema, para lo que se partió de la hipótesis de que la sociedad no estaba acostumbrada a donar sus órganos y tejidos, por lo que se pensó en una campaña publicitaria que cambiase la cultura de donación de órganos entre la población, sin embargo tras largos estudios se concluyó: 1. La capacidad real de transplantes de corneas en la entidad que es diferente a la necesidad de las listas de espera 2. La verdadera razón por la que no se obtienen los tejidos potencialmente posibles que es por no solicitar el consentimiento a los familiares de pacientes fallecidos 3. Existe una verdadera cultura de donación de órganos en la entidad 4. Necesidades comunicativas reales intramuros para aumentar la obtención de córneas y tejidos oculares Lo anterior nos permitió proponer: 1. La cancelación de una costosa campaña publicitaria 2. Un programa informativo de rehumanización para informar la situación real sobre la obtención de tejidos y los procedimientos adecuados 3. Un programa integral de comunicación interna para difundir las acciones del BOTO y buscar la integración de públicos hacia la institución 4. Acciones complementarias para fortalecer el plan y extenderlo a públicos secundarios Esto permite ver, no solo la importancia de la investigación en las campañas de comunicación, sino que además, en ocasiones, las relaciones públicas y otras técnicas de comunicación son más efectivas y económicas que la publicidad

Classifying Topologies through G-Bases

[EN] We classify several topological properties of a Tychonoff space $X$ by means of certain locally convex topologies $\mathcal{T}$ with a $\mathfrak{G}$-base located between the pointwise topology $\tau _{p}$ and the bounded-open topology $\tau _{b}$ of the real-valued continuous function space $C\left( X\right)$.This research was funded in part by grant PGC2018-094431-B-I00 of Ministry of Science, Innovation and Universities of Spain.Ferrando, JC.; López Pellicer, M. (2022). Classifying Topologies through G-Bases. Axioms. 11(12):1-7. https://doi.org/10.3390/axioms1112074417111