Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.Preprin

Etapas del ciclo de vida en el desarrollo del turismo religioso: una comparación de estudios de caso

The religious tourism is a strategic development option for many destinations. It requires a tourism orientation, significant private and public capital investment, and a willingness on the part of religious authorities to adapt to visitor needs. The aim of this article is to examine the development of Catholic tourism in different Mexican and European regions and assess related life-cycle implications. Recommendations are made for developing the potential of the Mexican religious regions, and for advancement of the religious tourism destination life-cycle concept.El turismo religioso es una opción estratégica de desarrollo para muchos destinos. Requiere orientación al turismo, importante inversión de capital privado y público, y predisposición de las autoridades eclesiásticas para adaptarse a las necesidades del visitante. Este artículo examina el turismo religioso de carácter católico en distintos lugares de México y Europa y valora implicaciones relacionadas con el ciclo de vida. Finalmente, se hacen recomendaciones para desarrollar el potencial de los lugares analizados, y para el avance del concepto de ciclo de vida de destinos turísticos religiosos

Molecular Segmentation of the Spinal Trigeminal Nucleus in the Adult Mouse Brain

© 2021. The authors. This document is made available under the CC-BY 4.0 license http://creativecommons.org/licenses/by /4.0/ This document is the Published version of a Published Work that appeared in final form in Frontiers in Neuroanatomy. To access the final edited and published work see https://doi.org/10.3389/fnana.2021.785840The trigeminal column is a hindbrain structure formed by second order sensory neurons that receive afferences from trigeminal primary (ganglionic) nerve fibers. Classical studies subdivide it into the principal sensory trigeminal nucleus located next to the pontine nerve root, and the spinal trigeminal nucleus which in turn consists of oral, interpolar and caudal subnuclei. On the other hand, according to the prosomeric model, this column would be subdivided into segmental units derived from respective rhombomeres. Experimental studies have mapped the principal sensory trigeminal nucleus to pontine rhombomeres (r) r2-r3 in the mouse. The spinal trigeminal nucleus emerges as a plurisegmental formation covering several rhombomeres (r4 to r11 in mice) across pontine, retropontine and medullary hindbrain regions. In the present work we reexamined the issue of rhombomeric vs. classical subdivisions of this column. To this end, we analyzed its subdivisions in an AZIN2-lacZ transgenic mouse, known as a reference model for hindbrain topography, together with transgenic reporter lines for trigeminal fibers. We screened as well for genes differentially expressed along the axial dimension of this structure in the adult and juvenile mouse brain. This analysis yielded genes from multiple functional families that display transverse domains fitting the mentioned rhombomeric map. The spinal trigeminal nucleus thus represents a plurisegmental structure with a series of distinct neuromeric units having unique combinatorial molecular profiles

Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem

Consider the Restricted Planar Circular 3 Body Problem. If the trajectory of the body of zero mass is defined for all time, it can have the following four types of asymptotic motion when time tends to infinity forward or backward in time: bounded, parabolic (goes to infinity with asymptotic zero velocity), hyperbolic (goes to infinity with asymptotic positive velocity) or oscillatory (the position of the body is unbounded but goes back to a compact region of phase space for a sequence of arbitrarily large times). We consider realistic mass ratio for the Sun-Jupiter pair and Jacobi constant which allows the massless body to cross Jupiter's orbit. This is a non-perturbative regime. We prove the existence of all possible combinations of past and future final motions. In particular, we obtain the existence of oscillatory motions. All the constructed trajectories cross the orbit of Jupiter but avoid close encounters with it. The proof relies on analyzing the stable and unstable invariant manifolds of infinity and their intersections. We construct orbits shadowing these invariant manifolds by the method of correctly aligned windows. The proof is computer assisted.M. C. has been partially supported by the NCN grant 2018/29/B/ST1/00109 2M. G. has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 757802). M. G. is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2019. P. M. has been partially supported by the Spanish MINECO-FEDER Grant PGC2018-100928-B-I00 and the Catalan grant 2017SGR1049 T. S. has been also partly supported by the Spanish MINECO-FEDER Grant PGC2018-098676-B100 (AEI/FEDER/UE), the Catalan grant 2017SGR1049 and by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2019. P. Z. has been partially supported by the NCN grant 2019/35/B/ST1/00655Peer ReviewedPostprint (author's final draft

A Sustained Increase in Intracellular Ca2+ Is Required for the Acrosome Reaction in Sea Urchin Sperm

AbstractThe acrosome reaction (AR), necessary for fertilization in many species, requires an increase in intracellular Ca2+ ([Ca2+]i). In sea urchin sperm, the AR is triggered by an egg-jelly factor: the associated [Ca2+]i elevation lasts minutes and involves two Ca2+ permeable channels. Both the opening of the second channel and the onset of the AR occur ∼5 s after treatment with egg factor, suggesting that these events are linked. In agreement, removal of Ca2+ from sea water or addition of Ca2+ channel blockers at the time when opening of the second channel is first detected inhibits AR and causes a “rapid” (t1/2 = 3–15 s) decrease in [Ca2+]i and partial inhibition of the intracellular pH change associated with the AR. Simultaneous addition of NH4Cl and either EGTA, Co2+, or Ni2+ 5 s after egg factor prevents the partial inhibition of the evoked pHi change observed but does not reverse AR inhibition. Therefore, the sustained increase in [Ca2+]i caused by the second Ca2+ channel is needed for the sperm AR. Experiments with agents that induce capacitative Ca2+ uptake (thapsigargin and cyclopiazonic acid) suggest that the second channel opened during the AR could be a store-operated Ca2+ channel

Radial and tangential migration of telencephalic somatostatin neurons originated from the mouse diagonal area

The telencephalic subpallium is the source of various GABAergic interneuron cohorts that invade the pallium via tangential migration. Based on genoarchitectonic studies, the subpallium has been subdivided into four major domains: striatum, pallidum, diagonal area and preoptic area (Puelles et al. 2013; Allen Developing Mouse Brain Atlas), and a larger set of molecularly distinct progenitor areas (Flames et al. 2007). Fate mapping, genetic lineage-tracing studies, and other approaches have suggested that each subpallial subdivision produces specific sorts of inhibitory interneurons, distinguished by differential peptidic content, which are distributed tangentially to pallial and subpallial target territories (e.g., olfactory bulb, isocortex, hippocampus, pallial and subpallial amygdala, striatum, pallidum, septum). In this report, we map descriptively the early differentiation and apparent migratory dispersion of mouse subpallial somatostatin-expressing (Sst) cells from E10.5 onward, comparing their topography with the expression patterns of the genes Dlx5, Gbx2, Lhx7-8, Nkx2.1, Nkx5.1 (Hmx3), and Shh, which variously label parts of the subpallium. Whereas some experimental results suggest that Sst cells are pallidal, our data reveal that many, if not most, telencephalic Sst cells derive from de diagonal area (Dg). Sst-positive cells initially only present at the embryonic Dg selectively populate radially the medial part of the bed nucleus striae terminalis (from paraseptal to amygdaloid regions) and part of the central amygdala; they also invade tangentially the striatum, while eschewing the globus pallidum and the preoptic area, and integrate within most cortical and nuclear pallial areas between E10.5 and E16.5.This work was funded by the Spanish Ministry of Science and Innovation grant BFU2008-04156, and SENECA Foundation contract 0458/GERM/06-10891 to L.P.; and the Local Government of Castilla-La Mancha grant PII1I09-0065-8194 to C.D. Infrastructure support provided by the University of Murcia and Castilla-La Mancha is also acknowledged

3D 360° surface morphometric analysis of pounding stone tools used by Hadza foragers of Tanzania: A new methodological approach for studying percussive stone artefacts

Surface morphometry comprises a relevant set of techniques that provide objective tools to identify, map, and understand use wear patterns in stone tools. Thus far, these techniques have been applied mainly to 2D or 2.5D data, but their application to 3D 360° data is promising and still underdeveloped. Here, we apply new 3D techniques to calculate morphometric variables and to analyse surficial features and changes in pounding stone tools used for baobab processing among Hadza foragers of Tanzania. Baobab pounding stones were collected after use by Hadza foragers for processing the plant food and then 3D point clouds were acquired from laser scanners and SfM photogrammetry. Morphometry was conducted directly on 3D point clouds to avoid time-consuming and surface modifications related to more complex 3D data, such as meshing. Several morphometric variables were computed for the complete pieces (360° sphere) providing fast and accurate data to identify the detailed morphometric features of the artefacts. Additionally, stone surface changes due to baobab processing were measured by comparing the stone surface before and after use, thus enabling calculation of spatial abrasion patterns. Data were interpreted using multivariate exploratory statistical analysis. Differences in the effect of processing on surface morphology are likely explained by variations in raw source material and use. Results suggest that the traces produced by baobab processing on stone tools should be detectable in the archaeological record

Insight of lichens as ideal models for astrobiological studies analyzed by Raman spectroscopy

Exposure experiments of different species to space conditions are essential because real space conditions with different radiation sources like ionizing radiation, UV-radiation, X-rays, gamma-ray from even galactic radiation, vacuum and space weathering by micro-dust cannot simultaneously be simulated in parallel even in our best simulation chambers on Earth. We need results from experiments under real space conditions to enable the development of appropriate predictions about the stability of organisms and their constituent organic parts. The extremophile lichen Circinaria gyrosa is one of the selected species within the BIOMEX (Biology and Mars Experiment) experiment and in this work we compare the previous Raman results obtained in this lichen [1] with the corresponding Raman results on the lichen Xanthoparmelia hueana. Both species have been exposed to space and simulated Mars-like conditions in planetary chambers and we have studied and identified possible degradation process in different layers and biomarkers. The analysis by Raman spectroscopy of simulated Space and Mars exposed samples confirm alterations and damages of the photobiont part of the lichen and changes related to the molecular structure of whewellite. The conclusions of this work will be important to understand what are the effects to consider when biological systems are exposed to space or Mars-like conditions and to expand our knowledge of how life survives in most extreme conditions that is a prerequisite in future planetary exploration projects.Acknowledgment Support for this work was provided by the Spanish Ministry of Economy, Industry and Competitiveness (MINECO), by the project BIOindicadores en MARTE y Espacio (BIOMARSS) (PID2019-109448RB-I00) and by INTA. References [1] M.R. Lopez Ramirez, L.G Sancho, J. P. de Vera, M. Baqué, U. Böttcher, E. Rabbow, J. Martínez-Frías, R. de la Torre Noetzel. Spectrochimica Acta, Part A. 261 (2021) 120046.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec