Stabilized reduced order models for low speed flows

This thesis presents the a stabilized projection-based Reduced Order Model (ROM) formulation in low speed fluid flows using a Variational Multi-Scale (VMS) approach. To develop this formulation we use a Finite Element (FE) method for the Full Order Model (FOM) and a Proper Orthogonal Decomposition (POD) to construct the basis. Additional to the ROM formulation, we introduce two techniques that became possible using this approach: a mesh-based hyper-reduction that uses an Adaptive Mesh Refinement (AMR) approach, and a domain decomposition scheme for ROMs. To illustrate and test the proposed formulation we use five different models: a convection–diffusion–reaction, the incompressible Navier–Stokes, a Boussinesq approximation, a low Mach number model, and a three-field incompressible Navier–Stokes.Esta tesis presenta un modelo de orden reducido estabilizado paran fluidos a baja velocidad utilizando un enfoque de multiescala variacional. Para desarrollar esta formulación utilizamos el método de elementos finitos para el modelo no reducido y una descomposición en autovalores del mismo para construir la base. Adicional a la formulación del modelo reducido, presentamos dos técnicas que podemos formular al utilizar este enfoque: una reducción adicional del dominio, basada en la reducción de la malla, donde usamos una técnica de refinamiento adaptativa y un esquema de descomposición de dominio para el modelo reducido. Para ilustrar y probar la formulación propuesta, utilizamos cuatro diferentes modelos fisicos: una ecuación de convección-difusión-reacción, la ecuación de Navier-Stokes para fluidos incompresibles, una aproximación de Boussinesq para la ecuación de Navier-Stokes, y una aproximación para números de Mach bajos de la ecuación de Navier-Stokes

Stabilized reduced order models for low speed flows

This thesis presents the a stabilized projection-based Reduced Order Model (ROM) formulation in low speed fluid flows using a Variational Multi-Scale (VMS) approach. To develop this formulation we use a Finite Element (FE) method for the Full Order Model (FOM) and a Proper Orthogonal Decomposition (POD) to construct the basis. Additional to the ROM formulation, we introduce two techniques that became possible using this approach: a mesh-based hyper-reduction that uses an Adaptive Mesh Refinement (AMR) approach, and a domain decomposition scheme for ROMs. To illustrate and test the proposed formulation we use five different models: a convection–diffusion–reaction, the incompressible Navier–Stokes, a Boussinesq approximation, a low Mach number model, and a three-field incompressible Navier–Stokes.Esta tesis presenta un modelo de orden reducido estabilizado paran fluidos a baja velocidad utilizando un enfoque de multiescala variacional. Para desarrollar esta formulación utilizamos el método de elementos finitos para el modelo no reducido y una descomposición en autovalores del mismo para construir la base. Adicional a la formulación del modelo reducido, presentamos dos técnicas que podemos formular al utilizar este enfoque: una reducción adicional del dominio, basada en la reducción de la malla, donde usamos una técnica de refinamiento adaptativa y un esquema de descomposición de dominio para el modelo reducido. Para ilustrar y probar la formulación propuesta, utilizamos cuatro diferentes modelos fisicos: una ecuación de convección-difusión-reacción, la ecuación de Navier-Stokes para fluidos incompresibles, una aproximación de Boussinesq para la ecuación de Navier-Stokes, y una aproximación para números de Mach bajos de la ecuación de Navier-Stokes

The bHLH transcription factor SPATULA enables cytokinin signaling, and both activate auxin biosynthesis and transport genes at the medial domain of the gynoecium

[EN] Fruits and seeds are the major food source on earth. Both derive from the gynoecium and, therefore, it is crucial to understand the mechanisms that guide the development of this organ of angiosperm species. In Arabidopsis, the gynoecium is composed of two congenitally fused carpels, where two domains: medial and lateral, can be distinguished. The medial domain includes the carpel margin meristem (CMM) that is key for the production of the internal tissues involved in fertilization, such as septum, ovules, and transmitting tract. Interestingly, the medial domain shows a high cytokinin signaling output, in contrast to the lateral domain, where it is hardly detected. While it is known that cytokinin provides meristematic properties, understanding on the mechanisms that underlie the cytokinin signaling pattern in the young gynoecium is lacking. Moreover, in other tissues, the cytokinin pathway is often connected to the auxin pathway, but we also lack knowledge about these connections in the young gynoecium. Our results reveal that cytokinin signaling, that can provide meristematic properties required for CMM activity and growth, is enabled by the transcription factor SPATULA (SPT) in the medial domain. Meanwhile, cytokinin signaling is confined to the medial domain by the cytokinin response repressor ARABIDOPSIS HISTIDINE PHOSPHOTRANSFERASE 6 (AHP6), and perhaps by ARR16 (a type-A ARR) as well, both present in the lateral domains (presumptive valves) of the developing gynoecia. Moreover, SPT and cytokinin, probably together, promote the expression of the auxin biosynthetic gene TRYPTOPHAN AMINOTRANSFERASE OF ARABIDOPSIS 1 (TAA1) and the gene encoding the auxin efflux transporter PIN-FORMED 3 (PIN3), likely creating auxin drainage important for gynoecium growth. This study provides novel insights in the spatiotemporal determination of the cytokinin signaling pattern and its connection to the auxin pathway in the young gynoecium.IRO, VMZM, HHU and PLS were supported by the Mexican National Council of Science and Technology (CONACyT) with a PhD fellowship (210085, 210100, 243380 and 219883, respectively). Work in the SDF laboratory was financed by the CONACyT grants CB-2012-177739, FC-2015-2/1061, and INFR-2015-253504, and NMM by the CONACyT grant CB-2011-165986. SDF, CF and LC acknowledge the support of the European Union FP7-PEOPLE-2009-IRSES project EVOCODE (grant no. 247587) and H2020-MSCARISE-2015 project ExpoSEED (grant no. 691109). SDF also acknowledges the Marine Biological Laboratory (MBL) in Woods Hole for a scholarship for the Gene Regulatory Networks for Development Course 2015 (GERN2015). IE acknowledges the International European Fellowship-METMADS project and the Universita degli Studi di Milano (RTD-A; 2016). Research in the laboratory of MFY was funded by NSF (grant IOS-1121055), NIH (grant 1R01GM112976-01A1) and the Paul D. Saltman Endowed Chair in Science Education (MFY). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Reyes Olalde, J.; Zuñiga, V.; Serwatowska, J.; Chávez Montes, R.; Lozano-Sotomayor, P.; Herrera-Ubaldo, H.; Gonzalez Aguilera, K.... (2017). The bHLH transcription factor SPATULA enables cytokinin signaling, and both activate auxin biosynthesis and transport genes at the medial domain of the gynoecium. PLoS Genetics. 13(4):1-31. https://doi.org/10.1371/journal.pgen.1006726S131134Reyes-Olalde, J. I., Zuñiga-Mayo, V. M., Chávez Montes, R. A., Marsch-Martínez, N., & de Folter, S. (2013). Inside the gynoecium: at the carpel margin. Trends in Plant Science, 18(11), 644-655. doi:10.1016/j.tplants.2013.08.002Alvarez-Buylla, E. 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Reduced order models for thermally coupled low Mach flows

In this paper we present a collection of techniques used to formulate a projection-based reduced order model (ROM) for zero Mach limit thermally coupled Navier–Stokes equations. The formulation derives from a standard proper orthogonal decomposition (POD) model reduction, and includes modifications to improve the drawbacks caused by the inherent non-linearity of the used Navier–Stokes equations: a hyper-ROM technique based on mesh coarsening; an implicit ROM subscales formulation based on a variational multi-scale (VMS) framework; and a Petrov–Galerkin projection necessary in the case of non-symmetric terms. At the end of the article, we test the proposed ROM formulation using 2D and 3D versions of the same example: a differentially heated cavity.Peer Reviewe

Polimorfismo +405G>C del gen del factor de crecimiento de endotelio vascular en población cubana

Introduction: The vascular endothelial growth factor (VEGF) is a protein involved in the proliferation and cell migration of the vascular endothelium. In its gene, +405G>C Polymorphism has been reported. There are no population genetic reports of this variant in Cuba that allow the characterization of immunogenetic profiles at a molecular level for its application to allelic association studies. Objective: To describe the genic and genotypic frequencies of the VEGF (+405 G>C) polymorphism in the Cuban population.Material and Methods: A descriptive cross-sectional observational study was carried out from October 2017 to March 2018 in 162 Cuban healthy newborns of both sexes for the neonatal screening for metabolic diseases, whose biological samples were conserved in the DNA bank of the National Center for Medical Genetics. The molecular characterization of the genotypes was carried out using a PCR-ARMS. The GENEPOP 4.4 software and the statistical software package STATISTICA 8.0 were used for the analysis of genic and genotypic frequencies.Results: The population did not adjust to the Hardy-Weinberg equilibrium model for the gene evaluated. The estimated gene frequencies of VEGF +405 G> C polymorphism were 0.33 for the G allele and 0.67 for the C allele. The calculation of the genotypic frequencies resulted in 0.14, 0.37 and 0.49, for the variants GG, GC and CC, respectively.Conclusions: The allelic frequencies of VEGF.C were higher than the frequencies of the VEGF.G allele, being the VEGF GG the least represented genotype in the group studied.Introducción: El factor de crecimiento endotelial vascular (VEGF) es una proteína involucrada en la proliferación y migración celular del endotelio vascular, en cuyo gen se ha reportado el polimorfismo +405G>C. Se reconoce que no existen reportes genéticos poblacionales de esta variante en Cuba, que permitan caracterizar los perfiles inmunogenéticos a nivel molecular, para su aplicación en estudios de asociación alélica.Objetivo: Describir las frecuencias génicas y genotípicas del polimorfismo VEGF (+405 G>C) en la población cubana.Material y Métodos: Se realizó un estudio observacional, descriptivo, transversal, entre octubre de 2017 y marzo de 2018 en 162 neonatos cubanos, de ambos sexos y sanos, para el pesquisaje neonatal de enfermedades metabólicas, cuyas muestras biológicas se conservaban en el banco de ADN del Centro Nacional de Genética Médica. La caracterización molecular de los genotipos fue realizada mediante un PCR-ARMS. Se utilizó el software GENEPOP 4.4 y el paquete estadístico STATISTICA 8.0 para los cálculos de las frecuencias génicas y genotípicas.Resultados: La población no se ajustó al modelo de equilibrio de Hardy Weinberg para el gen evaluado. Las frecuencias génicas estimadas para el polimorfismo VEGF (+405 G>C) fueron de 0,33 para el alelo G y de 0,67 para el alelo C. El cálculo de las frecuencias genotípicas resultó en 0,14, 0,37 y 0,49, para las variantes GG, GC y CC, respectivamente.Conclusiones: Las frecuencias alélicas VEGF.C fueron superiores a la del alelo VEGF.G, siendo el genotipo VEGF.GG el de menor representación en el conjunto estudiado

The auxin transporter <i>PIN3</i> is coordinately activated by cytokinin and SPT.

<p><b>(A-C)</b> PIN3 expression in stage 9 <i>PIN3</i>::<i>PIN3-GFP</i> gynoecia that either received mock (<b>A,</b> transverse section) or BAP treatment for 48 hours (<b>B</b>, transverse section and <b>C</b>, longitudinal view). The inset in <b>(C)</b> shows a magnified view of the proliferating tissue. Arrows indicate the possible auxin flow. <b>(D-F)</b> PIN3 expression in transverse sections of stage 9 <i>PIN3</i>::<i>PIN3-GFP</i> gynoecia in <i>spt-2</i> <b>(D)</b>, <i>35S</i>::<i>SPT</i> <b>(E)</b>, and in <i>spt-2</i> treated for 48 hours with BAP <b>(F)</b>. <b>(G-J)</b> Transverse sections of stage 12 gynoecia of wild-type <b>(G, H)</b> and <i>pin3-4</i> <b>(I, J)</b>. Gynoecia phenotypes after three to four weeks of mock <b>(G, I)</b> or BAP treatment for five days <b>(H, J)</b>. Insets show a scanning electron microscopy image of the gynoecium. <b>(K)</b> Luciferase reporter assay in <i>N</i>. <i>benthamiana</i> leaves co-transformed with <i>35S</i>::<i>ARR1</i> and <i>pPIN3</i>::<i>LUC</i>. Ratio of LUC/REN activity. <b>(L)</b> ChIP experiments against the <i>PIN3</i> promoter regions (indicated by “a” and “b” in the scheme above) using an inducible <i>35S</i>::<i>ARR1ΔDDK</i>:<i>GR</i> line treated with dexamethasone or mock. <i>ACT2/7</i> served as a negative control. <b>(M)</b> Luciferase reporter assay in <i>N</i>. <i>benthamiana</i> leaves co-transformed with <i>35S</i>::<i>SPT</i> and <i>pPIN3</i>::<i>LUC</i>. Ratio of LUC/REN activity. <b>(N)</b> ChIP experiments against the <i>PIN3</i> promoter regions (indicated by “a” and “b” in the scheme above) using a <i>35S</i>::<i>SPT-HA</i> line and wild-type. <i>ACT2/7</i> served as a negative control. Error bars represent the SD for the LUC assays based on three biological replicates. ChIP results of one representative experiment is shown and the error bars represent the SD of the technical replicates. *<i>P</i> < 0.05 (LUC: Student-t test; qPCR: ANOVA). Scale bars: 10 μm (A-F), 100 μm (G-J, G-J insets). Ovule primordium (op).</p

The cytokinin signaling repressors <i>AHP6</i> and <i>ARR16</i> likely block cytokinin responses in lateral tissues.

<p><b>(A-D)</b> Expression of the transcriptional reporter <i>AHP6</i>::<i>GFP</i> in transverse sections of stage 7, 8, 9, and 12 gynoecia. <b>(E, F)</b> Expression of the cytokinin response reporter <i>TCS</i>::<i>GFP</i> in transverse sections of stage 9 and 12 gynoecia in an <i>ahp6-1</i> mutant background. Arrowheads indicate the absence of GFP signal in the epidermis of the valves. <b>(G, H)</b> Phenotypes of wild-type (G) and <i>ahp6-1</i> (H) gynoecia one week after receiving BAP treatment for two weeks. <b>(I-L)</b> Expression of the transcriptional reporter <i>ARR16</i>::<i>GUS</i> (type-A <i>ARR</i>) in transverse sections of stage 7, 8, 9, and 12 gynoecia. Scale bars: 10 μm (A-C, E), 20 μm (D, F), 1 mm (G, H), 100 μm (I-L).</p

Overview of the gynoecium and SPT is necessary for cytokinin signaling in the young gynoecium.

<p></p><p><b>(</b></p><b>A)</b> Schematic overview and false-coloured transverse section of a stage 8 and of a stage 12 <i>Arabidopsis thaliana</i> gynoecium (pistil). The medial (M) and lateral (L) domains of the gynoecium are indicated. The CMM in the medial domain (stage 8 gynoecium; left side) is indicated and its derived structures can be seen in a stage 12 gynoecium (right side). L, lateral domain; M, medial domain. Orange, abaxial valve (abv); blue, adaxial valve (adv); white, abaxial replum (abr); pink, adaxial replum (adr); green, ovule primordium (op); red, septum primordium (sp); CMM, carpel margin meristem; septum (S); replum (R); transmitting tract (TT); ovule (O); funiculus (F). <b>(B-M)</b> Expression of the cytokinin response reporter <i>TCS</i>::<i>GFP</i> in transverse sections of gynoecia at stage 7, 8, 9, and 12 of wild-type <b>(B-E)</b>, <i>spt-2</i> <b>(F-I)</b>, and <i>35S</i>::<i>SPT</i> <b>(J-M)</b>.<b>(N-U)</b> Expression of the reporter <i>TCS</i>::<i>GFP</i> in transverse sections of gynoecia at stage 7, 8, 9, and 12, after 48 hours of 6-benzylaminopurine (BAP; a synthetic cytokinin) treatment in wild-type <b>(N-Q)</b> and <i>spt-2</i> <b>(R-U)</b>. Scale bars: 20 μm (E, I, M, Q, U), 10 μm (B-D, F-H, J-L, N-P, R-T).<p></p

SPT enables cytokinin responses during early gynoecium development and regulates type-B <i>ARR</i> gene expression.

<p><b>(A)</b> Phenotypes of wild-type, <i>arr1</i>, <i>arr10</i>, <i>arr12</i>, <i>arr1 arr10</i>, <i>arr10 arr12</i>, <i>arr1 arr12</i>, <i>arr1 arr10 arr12</i>, and <i>spt-2</i> gynoecia three to four weeks after receiving BAP treatment for five to ten days. (<b>B-E)</b> Scanning electron microscopy image of wild-type and <i>spt-2</i> stage 12 gynoecia one day after either receiving mock <b>(B, C)</b> or BAP treatment for only 48 hours <b>(D, E)</b>. Insets show a transverse section of the ovary. (<b>F</b>) Expression analysis by qRT-PCR of <i>ARR1</i>, <i>ARR10</i>, and <i>ARR12</i> in wild-type and <i>spt-12</i> dissected gynoecia. (<b>G-J</b>) <i>In situ</i> hybridization of type-B <i>ARR1</i> mRNA in wild-type <b>(G, H)</b> and <i>spt-2</i> <b>(I, J)</b> floral buds at stages 9 and 12. Arrowheads indicate the detected expression in wild-type and the absence in <i>spt-2</i>. <b>(K</b>) Luciferase reporter assay in <i>N</i>. <i>benthamiana</i> leaves co-transformed with <i>35S</i>::<i>SPT</i> and <i>pARR1</i>::<i>LUC</i>. Ratio of firefly luciferase (LUC) to Renilla luciferase (REN) activity. <b>(L)</b> ChIP experiments against the <i>ARR1</i> promoter region (indicated by “a” in the scheme above) using a <i>35S</i>::<i>SPT-HA</i> line and wild-type. <i>ACT2/7</i> served as a negative control. For the LUC assays and qRT-PCR experiments error bars represent the SD based on three biological replicates. ChIP results of one representative experiment are shown; error bars represent the SD of the technical replicates. *<i>P</i> < 0.05 (LUC: Student-t test; qRT-PCR and qPCR: ANOVA). Scale bars: 500 μm (A), 100 μm (B-E, H, J), 50 μm (insets in B-E, G, I).</p