Curves in the Lorentz-Minkowski plane with curvature depending on their position

Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propound the same question in the Lorentz-Minkowski plane, focusing on spacelike and timelike curves. In this article, we study those curves in 2 whose curvature depends on the Lorentzian pseudodistance from the origin, and those ones whose curvature depends on the Lorentzian pseudodistance through the horizontal or vertical geodesic to a fixed lightlike geodesic. Making use of the notions of geometric angular momentum (with respect to the origin) and geometric linear momentum (with respect to the fixed lightlike geodesic), respectively, we get two abstract integrability results to determine such curves through quadratures. In this way, we find out several new families of Lorentzian spiral, special elastic and grim-reaper curves whose intrinsic equations are expressed in terms of elementary functions. In addition, we provide uniqueness results for the generatrix curve of the Enneper surface of second kind and for Lorentzian versions of some well-known curves in the Euclidean setting, like the Bernoulli lemniscate, the cardioid, the sinusoidal spirals and some nondegenerate conics. We are able to get arc-length parametrizations of them and they are depicted graphically.European Union (EU) Spanish Government MTM2017-89677-PMECD FPU16/0309

Helicoidal minimal surfaces in the 3-sphere: An approach via spherical curves

We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous function depending on the distance to its axis. As an application in the case of vanishing mean curvature, it is shown that the well-known conjugation between the belicoid and the catenoid in Euclidean three-space extends naturally to the 3-sphere to their spherical versions and determine in a quite explicit way their associated surfaces in the sense of Lawson. As a key tool, we use the notion of spherical angular momentum of the spherical curves that play the role of profile curves of the minimal helicoidal surfaces in the 3-sphere.Comment: 22 pages, 4 figure

Genus 1 minimal k-noids and saddle towers in H-2 x R

The authors would like to express their gratitude to Magdalena Rodriguez for her valuable comments during the preparation of this manuscript, as well as to the anonymous referee for the thorough revision of the manuscript, which has greatly improved the final presentation. This research was supported by MINECO-FEDER project MTM2017-89677-P and by MCIN/AEI project PID2019-111531GA-I00. The first author is also supported by the FPU programme from MICINN and by MCIN/AEI project PID2020-117868GB-I00. The second author is also supported by EBM/FEDER UJA 2020 project 1380860.For each k >= 3, we construct a 1-parameter family of complete properly Alexandrov-embedded minimal surfaces in the Riemannian product space H-2 x R with genus 1 and k embedded ends asymptotic to vertical planes. We also obtain complete minimal surfaces with genus 1 and 2k ends in the quotient of H-2 x R by an arbitrary vertical translation. They all have dihedral symmetry with respect to k vertical planes, as well as finite total curvature -4k pi. Finally, we provide examples of complete properly Alexandrov-embedded minimal surfaces with finite total curvature with genus 1 in quotients of H-2 x R by the action of a hyperbolic or parabolic translation.Spanish Government MTM2017-89677-P MCIN/AEI project PID2019-111531GA-I00 PID2020-117868GB-I00FPU programme from MICINNEBM/FEDER UJA 2020 project 138086

Maestras de la antropología en España: una aproximación a través del relato de vida

Portada, créditos, sumario y biografía de las autoras. Libro disponible en la Editorial ComaresEste libro recoge los testimonios de catorce antropólogas pioneras de la universidad española nacidas en la primera mitad del siglo XX. En él se narran sus experiencias de vida, su acercamiento a la Antropología o los logros científicos y académicos que han alcanzado dentro de esta disciplina. Cada capítulo de esta obra está realizado por un/a investigador/a que entrevista a aquella maestra con la que tiene más afinidad académica y, a veces, un conocimiento personal de años de colaboración. Esta metodología nos permite decir que este libro es mucho más que un recopilatorio de biografías o una genealogía al uso, pues cada capítulo que lo compone está impregnado de una confidencialidad, cuando no de cierta complicidad, entre entrevistada y entrevistador/a que lo hace singular, permitiendo al lector acercarse de manera amena tanto a la vida de estas brillantes académicas, como a la historia de la Antropología del siglo XX en España desde las narrativas de sus protagonistas. Maestras de la Antropología en España. Una aproximación a través del relato de vida se ha dispuesto en dieciséis capítulos. Tras la introducción y un primer capítulo de contextualización histórica se estructuran catorce capítulos en dos partes tituladas Centro y periferia y Descentralizando el conocimiento, en los que se recogen respectivamente las narrativas de las doctoras y profesoras, Dolores Juliano - recientemente fallecida-, Teresa San Román, María Jesús Buxó, María Cátedra, Virginia Maquieira, Mercedes Fernández-Martorell, Aurora González, Teresa del Valle Murga, Pilar Sanchiz, Carmen Diez, Alida Carloni, Josepa Cucó, María de las Mercedes Cano y Dolors Comas

GABAergic deficits in absence of LPA1 receptor, associated anxiety-like and coping behaviors, and amelioration by interneuron precursor transplants into the dorsal hippocampus

Defects in GABAergic function can cause anxiety- and depression-like behaviors among other neuropsychiatric disorders. Therapeutic strategies using the transplantation of GABAergic interneuron progenitors derived from the medial ganglionic eminence (MGE) into the adult hippocampus reversed the symptomatology in multiple rodent models of interneuron-related pathologies. In turn, the lysophosphatidic acid receptor LPA has been reported to be essential for hippocampal function. Converging evidence suggests that deficits in LPA receptor signaling represent a core feature underlying comparable hippocampal dysfunction and behaviors manifested in common neuropsychiatric conditions. Here, we first analyzed the GABAergic interneurons in the hippocampus of wild-type and maLPA-null mice, lacking the LPA receptor. Our data revealed a reduction in the number of neurons expressing GABA, calcium-binding proteins, and neuropeptides such as somatostatin and neuropeptide Y in the hippocampus of maLPA-null mice. Then, we used interneuron precursor transplants to test links between hippocampal GABAergic interneuron deficit, cell-based therapy, and LPA receptor-dependent psychiatric disease-like phenotypes. For this purpose, we transplanted MGE-derived interneuron precursors into the adult hippocampus of maLPA-null mice, to test their effects on GABAergic deficit and behavioral symptoms associated with the absence of the LPA receptor. Transplant studies in maLPA-null mice showed that grafted cells were able to restore the hippocampal host environment, decrease the anxiety-like behaviors and neutralize passive coping, with no abnormal effects on motor activity. Furthermore, grafted MGE-derived cells maintained their normal differentiation program. These findings reinforce the use of cell-based strategies for brain disorders and suggest that the LPA receptor represents a potential target for interneuron-related neuropsychiatric disorders.This work was supported by grants from the Spanish Ministry of Science, Innovation and Universities, co-funded by the European Regional Development Fund (ERDF, EU), (PSI2017-82604R, to LJS; PSI2017-83408-P to CP; SAF09-07746, to MAD; PI16/01510, to GET) and Andalusian Regional Ministries of Economy, Knowledge, Business and University (SEJ-4515 -to LJS; SEJ1863 to CP) and of Health and Families (Nicolas Monardes Programme to GET)

GABAergic deficits in absence of LPA1 receptor, associated anxiety-like and coping behaviors, and amelioration by interneuron precursor transplants into the dorsal hippocampus

Defects in GABAergic function can cause anxiety- and depression-like behaviors among other neuropsychiatric disorders. Therapeutic strategies using the transplantation of GABAergic interneuron progenitors derived from the medial ganglionic eminence (MGE) into the adult hippocampus reversed the symptomatology in multiple rodent models of interneuron-related pathologies. In turn, the lysophosphatidic acid receptor LPA1 has been reported to be essential for hippocampal function. Converging evidence suggests that deficits in LPA1 receptor signaling represent a core feature underlying comparable hippocampal dysfunction and behaviors manifested in common neuropsychiatric conditions. Here, we first analyzed the GABAergic interneurons in the hippocampus of wild-type and maLPA1-null mice, lacking the LPA1 receptor. Our data revealed a reduction in the number of neurons expressing GABA, calcium-binding proteins, and neuropeptides such as somatostatin and neuropeptide Y in the hippocampus of maLPA1-null mice. Then, we used interneuron precursor transplants to test links between hippocampal GABAergic interneuron deficit, cell-based therapy, and LPA1 receptor-dependent psychiatric disease-like phenotypes. For this purpose, we transplanted MGE-derived interneuron precursors into the adult hippocampus of maLPA1-null mice, to test their effects on GABAergic deficit and behavioral symptoms associated with the absence of the LPA1 receptor. Transplant studies in maLPA1-null mice showed that grafted cells were able to restore the hippocampal host environment, decrease the anxiety-like behaviors and neutralize passive coping, with no abnormal effects on motor activity. Furthermore, grafted MGE-derived cells maintained their normal differentiation program. These findings reinforce the use of cell-based strategies for brain disorders and suggest that the LPA1 receptor represents a potential target for interneuron-related neuropsychiatric disorders

Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers

This article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane 2 whose curvature is expressed in terms of the Lorentzian pseudodistance to fixed geodesics. In this way, we get a complete description of all the elastic curves in 2 and provide the Lorentzian versions of catenaries and grim-reaper curves. We show several uniqueness results for them in terms of their geometric linear momentum. In addition, we are able to get arc-length parametrizations of all the aforementioned curves and they are depicted graphically