The zebrafish is an optimal experimental model to study thyroid hormone (TH) involvement in vertebrate development. The use of state-of-the-art zebrafish genetic tools available for the study of the effect of gene silencing, cell fate decisions and cell lineage differentiation have contributed to a more insightful comprehension of molecular, cellular, and tissue-specific TH actions. In contrast to intrauterine development, extrauterine embryogenesis observed in zebrafish has facilitated a more detailed study of the development of the hypothalamic-pituitary-thyroid axis. This model has also enabled a more insightful analysis of TH molecular actions upon the organization and function of the brain, the retina, the heart, and the immune system. Consequently, zebrafish has become a trendy model to address paradigms of TH-related functional and biomedical importance. We here compilate the available knowledge regarding zebrafish developmental events for which specific components of TH signaling are essential.

Thyroid hormones (THs) regulate tissue remodeling processes during early- and post-embryonic stages in vertebrates. The Mexican axolotl (Ambystoma mexicanum) is a neotenic species that has lost the ability to undergo metamorphosis; however, it can be artificially induced by exogenous administration of thyroxine (T4) and 3,3′,5-triiodo-L-thyronine (T3). Another TH derivative with demonstrative biological effects in fish and mammals is 3,5-diiodo-L-thyronine (3,5-T2). Because the effects of this bioactive TH remains unexplored in other vertebrates, we hypothesized that it could be biologically active in amphibians and, therefore, could induce metamorphosis in axolotl. We performed a 3,5-T2 treatment by immersion and observed that the secondary gills were retracted, similar to the onset stage phenotype; however, tissue regeneration was observed after treatment withdrawal. In contrast, T4 and T3 immersion equimolar treatments as well as a four-fold increase in 3,5-T2 concentration triggered complete metamorphosis. To identify the possible molecular mechanisms that could explain the contrasting reversible or irreversible effects of 3,5-T2 and T3 upon gill retraction, we performed a transcriptomic analysis of differential expression genes in the gills of control, 3,5-T2–treated, and T3-treated axolotls. We found that both THs modify gene expression patterns. T3 regulates 10 times more genes than 3,5-T2, suggesting that the latter has a lower affinity for TH receptors (TRs) or that these hormones could act through different TR isoforms. However, both TH treatments regulated different gene sets known to participate in tissue development and cell cycle processes. In conclusion, 3,5-T2 is a bioactive iodothyronine that promoted partial gill retraction but induced full metamorphosis in higher concentrations. Differential effects on gill retraction after 3,5,-T2 or T3 treatment could be explained by the activation of different clusters of genes related with apoptosis, regeneration, and proliferation; in addition, these effects could be initially mediated by TRs that are expressed in gills. This study showed, for the first time, the 3,5,-T2 bioactivity in a neotenic amphibian.

In the present effort, we revist the Levitron’s dynamics in the line of previous works due to Berry, Dullin and Easton, and Gans. An invariant set in the Eulerian formulation is delivered and a local study is performed which disclose the dynamics on the invariant manifold which coincides to that obtained by Dullin and Easton using the yaw–pitch–roll angles. Moreover, we extend the results of Gans, being able to determine further stable regions for the magnetic levitation of the Levitron. Symmetric and asymmetric trajectories close to an analytical solution are numerically explored. An asymptotic multiscale analysis is also carried out with the aim of studying the nonlinear interaction between the traslational and rotational modes. By recourse to a Hamiltonian approach, we provide the study of the local behavior of the Levitron near an equilibrium point of the system. Also, the existence of invariant regions in phase space corresponding to persistent levitation of the top are detected. The performed numerical studies serve to elucidate the Levitron’s behavior.

We numerically integrate the equations of motion of the Levitron in its twofold fashion, i.e. in terms of the Eulerian description of the spinning top’s motion as well as those in a different set of angular coordinates, the yaw-pitch-roll angles, in order to avoid the singularity posed by the vanishing of the angle describing the top’s nutation. We not only extend both set of equations to include dissipation for a more realistic model of the Levitron, but we introduce two types of mechanical forcing to inject energy into the system to prevent the prompt falling of the spinning top as well. A systematic study of the flying time as a function of the perturbation parameters is performed, and detailed bifurcation diagrams are obtained exhibiting an Arnold’s tongues structure. A very similar structure is obtained when the stability analysis is carried out by recourse to a fast method to compute the maximum Lyapunov exponent, namely the Mean Exponential Growth factor of Nearby Orbits (MEGNO). Our numerical experiments confirmed that the MEGNO serves as an early indicator of the stability of the Levitron’s flights, regular solutions being good candidates to allow for very long flying times.

The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work proposes a new method to compute high-order periodic orbits in twist maps without the use of symmetries. The method is a combination of the parameterization method in Fourier space and a Newton–Gauss multiple shooting scheme. The parameterization method has been successfully used in the past to compute quasi-periodic invariant circles. However, this is the first time that this method is used in the context of periodic orbits. Numerical examples are presented showing the accuracy and efficiency of the proposed method. The method is also applied to verify the renormalization prediction of the residues’ convergence at criticality (extensively studied in reversible maps) in the relatively unexplored case of maps without symmetries.

C. E. Garza-Hume Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas Universidad Nacional Autónoma de México Ciudad de México, México clara@mym.iimas.unam.mx, M. C. Jorge Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas Universidad Nacional Autónoma de México Ciudad de México, México y A. Olvera Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas Universidad Nacional Autónoma de México Ciudad de México, México

In contrast to mammalian adults, myelination in teleosts occurs throughout their lifespan and most of the progenitor cells are originated in the cerebellum. To understand the role that thyroid hormones (THs) play in juvenile cerebellar myelination in teleosts, we identified and localised the expression of genes involved in TH signalling (mct8, oatp1c1, dio2, dio3, thraa and l-thrb1) and analysed the effects of the two bioactive THs, T2 and T3, upon their regulation, as well as upon some structural components of the myelination process. Ex vivo approaches using organotypic cerebellar cultures followed by FISH and qPCR showed gene-specific localisation and regulation of TH signalling genes in the cerebellar nuclei. In vivo approaches using methimazole (MMI)-treated juvenile tilapias replaced with low doses of T3 and T2 showed by immunofluorescence that myelin fibres in the cerebellum are more abundant in the granular layer and that their visible size is reduced after MMI treatment but partially restored with TH replacement, suggesting that low doses of TH promote the re-myelination process in an altered condition. Together, our data support the idea that T2 and T3 promote myelination via different pathways and prompt T2 as a target for further analysis as a promising therapy for hypomyelination.

We study analytically and numerically the possible shapes and areas of planar irregular polygons with prescribed side-lengths. We give an a lgorithm and a computer program to construct the cyclic configuration with its circum circle and hence the maximum possible area. We study quadrilaterals with a self-intersection and prove that not all area minimizers are cyclic. We cla ssify quadrilaterals into four classes related to the possibility of reversing orienta tion by deforming continuously. We study the possible shapes of polygons with prescribed side-lengths and prescribed area. In this paper we carry out an analytical and numerical study of the possib le shapes and areas of general planar irregular polygons with prescrib d side-lengths. We explain a way to construct the shape with maximum area, which is known to be the cyclic configuration. We write a transcendental equation whose roo t is the radius of the circumcircle and give an algorithm to compute the root. We provid e an algorithm and a corresponding computer program that actually computes the circumcircle and draws the shape with maximum area, which can then be defor med as needed. We study quadrilaterals with a self-intersection, which are the o nes that achieve minimum area and we prove that area minimizers are not necessa rily cyclic, as mentioned in the literature ([4]). We also study the possible shapes of polygons with prescribed side-length s and prescribed area. For areas between the minimum and the maximum, there are two possible configurations for quadrilaterals and an infinite number for polyg ons with more than four sides. The work was motivated by the study of two Codices, ancient documents fro m central Mexico written around 1540 by a group called the Acolhua ([9],[1 0] or online [3]). The codices contain drawings of polygonal fields, with their s idelengths in one section and their areas in another. We had to find out if the pro posed areas were correct and to confirm the location of some of the fields. The fields are not drawn to scale and it is not known how the Acolhua computed (or measured) areas. There are no angles or diagonals therefo re w could not compute the actual areas but one thing we could do was compute maximum and minimum possible areas for the given side-lengths and say the areas in the do cuments were feasible if they were between those two values. Maxima are easy to Publication Date: January 17, 2018. Communicating Editor: Paul Yiu. We thank Ana Ṕerez Arteaga and Ramiro Ch ávez Tovar for computational support, figures and animations. This work was supported by Conacyt Project 133036-F.. 18 C. E. Garza-Hume, M. C. Jorge, and A. Olvera find for quadrilaterals by applying Brahmagupta’s formula ([5], [6]) bu t we could not find in the literature a formula for the maximum possible area of polygons with more than four sides. There are some results in [8] but not a formula. We c ould also not find a complete treatment of minima in the literature. The study of the documents also required an analysis of the possible shape s of polygons with prescribed side-lengths and area to try to localize the fields. F or polygons with more than four sides there is no easily available, explicit formula for this. We explain the mathematics of the problem, provide an algorithm to find the possible shapes and a computer implementation in javascript of the algorithm. Observe that finding areas of polygons is just an application of calculus if the coordinates of the vertices are known but the problem we are addressin g here is, what can be done when only side-lengths are known, not angles, diago nals r coordinates. The question is relevant in surveying, architecture, home dec orating, gardening and carpentry to name but a few. For some quadrilaterals it is possible to change orientation by deforming continuously and in others it is necessary to perform a reflection. This obser vation led to a classification of quadrilaterals into four classes. The case of triangles is special because they are the only rigid polygons, that is, the shape and area are determined by the side-lengths. Also, all triangles c an be inscribed in a circle whose center is located at the intersection of the perpen dicular bisectors. If the side-lengths are called a, b, c the area is given by Heron’s Formula, AH(a, b, c) = √ s(s− a)(s− b)(s− c) (1) wheres = 1 2 (a + b + c) is the semi-perimeter. In what follows we will discuss polygons with more than three sides. 1. Computing the shape with maximum area for any polygon In this section we will describe how to compute the maximum possible area of a planar polygon withn sides and how to construct the shape with maximum area given its ordered side-lengths. It is well-known that no side-length can b e larger than the sum of the others if they are to form a closed polygon. We will call this the compatibility condition. It was proved in [4] that the configuration with maximum possible area is given by the cyclic polygon, that is, the configuration that can be inscribed in a circle. The problem is that we do not know whichcircle; we do not know its center or its radius. We will solve this problem in the present section. We will first give an analytical solution for quadrilaterals and then describ e an iterative method that works for any polygon and its numerical implementation. Analytic solution for n=4: Circle-Line construction. For n = 4, Bretschneider’s formula gives the (unoriented) area A of a quadrilateral with side-lengths a, b, c, d and opposite angles α andγ as

We all learn at a young age how to calculate areas of squares or rectangles, but areas of irregular quadrilaterals are seldom mentioned. However, irregular quadrilaterals often appear in the real world. For instance, in a house, computing the area of walls, floors, or ceilings might be necessary to determine the amount of material needed for painting, tiling, and so on. Knowing the areas of backyards or fields is necessary for planting and computing yields. City personnel must determine areas of properties to compute prices and taxes. In our own research, computing areas of irregular quadrilaterals was needed for the interpretation of an ancient Aztec document that discussed surveying (see Jorge y Jorge et al. 2011). In this article, we talk about a formula deduced by Bretschneider in the mid-nineteenth century that not only allows the computation of areas of planar quadrilaterals, regular and irregular, but also provides a more thorough understanding of the geometry of such figures.

ABSTRACTExtracellular nucleotides and nucleosides have emerged as important elements regulating tissue homeostasis. Acting through specific receptors, have the ability to control gene expression patterns to direct cellular fate. We observed that SKOV‐3 cells express the ectonucleotidases: ectonucleotide pyrophosphatase 1 (ENPP1), ecto‐5′‐nucleotidase (NT5E), and liver alkaline phosphatase (ALPL). Strikingly, in pulse and chase experiments supplemented with ATP, SKOV‐3 cells exhibited low catabolic efficiency in the conversion of ADP into AMP, but they were efficient in converting AMP into adenosine. Since these cells release ATP, we proposed that the conversion of ADP into AMP is a regulatory node associated with the migratory ability and the mesenchymal characteristics shown by SKOV‐3 cells under basal conditions. The landscape of gene expression profiles of SKOV‐3 cell cultures treated with apyrase or adenosine demonstrated similarities (e.g., decrease FGF16 transcript) and differences (e.g., the negative regulation of Wnt 2, and 10B by adenosine). Thus, in SKOV‐3 we analyzed the migratory ability and the expression of epithelium to mesenchymal transition (EMT) markers in response to apyrase. Apyrase‐treatment favored the epithelial‐like phenotype, as revealed by the re‐location of E‐cadherin to the cell to cell junctions. Pharmacological approaches strongly suggested that the effect of Apyrase involved the accumulation of extracellular adenosine; this notion was strengthened when the incubation of the SKOV‐3 cell with α,β‐methylene ADP (CD73 inhibitor) or adenosine deaminase was sufficient to abolish the effect of apyrase on cell migration. Overall, adenosine signaling is a fine tune mechanism in the control of cell phenotype in cancer. J. Cell. Biochem. 118: 4468–4478, 2017. © 2017 Wiley Periodicals, Inc.

A non-autonomous version of the standard map with a periodic variation of the parameter is introduced and studied. Symmetry properties in the variables and parameters of the map are found and used to find relations between rotation numbers of invariant sets of the autonomous realization of the period-two case of the map. The role of the nonautonomous dynamics on period-one orbits, stability and bifurcation is studied. The critical boundaries for the global transport and the destruction of invariant circles with fixed rotation number are studied in detail using direct computation and a continuation method. In the case of global transport, the critical boundary has a particular symmetrical horn shape. The results are contrasted with similar calculations found in the literature.

Although 3,5,3′-triiodothyronine (T3) is considered to be the primary bioactive thyroid hormone (TH) due to its high affinity for TH nuclear receptors (TRs), new data suggest that 3,5-diiodothyronine (T2) can also regulate transcriptional networks. To determine the functional relevance of these bioactive THs, RNA-seq analysis was conducted in the cerebellum, thalamus-pituitary and liver of tilapia treated with equimolar doses of T2 or T3. We identified a total of 169, 154 and 2863 genes that were TH-responsive (FDR < 0.05) in the tilapia cerebellum, thalamus-pituitary and liver, respectively. Among these, 130, 96 and 349 genes were uniquely regulated by T3, whereas 22, 40 and 929 were exclusively regulated by T2 under our experimental paradigm. The expression profiles in response to TH treatment were tissue-specific, and the diversity of regulated genes also resulted in a variety of different pathways being affected by T2 and T3. T2 regulated gene networks associated with cell signalling and transcriptional pathways, while T3 regulated pathways related to cell signalling, the immune system, and lipid metabolism. Overall, the present work highlights the relevance of T2 as a key bioactive hormone, and reveals some of the different functional strategies that underpin TH pleiotropy.

The stability of the magnetic levitation showed by the Levitron was studied by M.V. Berry as a six degrees of freedom Hamiltonian system using an adiabatic approximation. Further, H.R. Dullin found critical spin rate bounds where the levitation persists and R.F. Gans et al. offered numerical results regarding the initial conditions’ manifold where this occurs. In the line of this series of works, first, we extend the equations of motion to include dissipation for a more realistic model, and then introduce a mechanical forcing to inject energy into the system in order to prevent the Levitron from falling. A systematic study of the flying time as a function of the forcing parameters is carried out which yields detailed bifurcation diagrams showing an Arnold’s tongues structure. The stability of these solutions were studied with the help of a novel method to compute the maximum Lyapunov exponent called MEGNO. The bifurcation diagrams for MEGNO reproduce the same Arnold’s tongue structure.

Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherent structures. Numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.

Introduccion . Implementar una cultura positiva de segu- ridad del paciente previene la aparicion de eventos adver- sos e incidentes, permite aprender de los errores, busca la causa raiz y modifica los procedimientos con el fin de evitar la reaparicion de los errores. La evaluacion de la seg- uridad del paciente se lleva a cabo a partir de la aplicacion de encuestas las cuales tienen varios bene-ficios. Para esta evaluacion se cuenta con el Cuestio-nario Sobre la Segu- ridad del Paciente en los Hospitales, desarrollado por la Agency for Healthcare Research and Quality de los EUA . La encuesta se ha utilizado para evaluar un extenso nume- ro de hospitales en diferentes paises, incluyendo a Mexico. Sin embargo, durante las evaluaciones previas, no se ha hecho diferencia, ni se han comparado los resultados en- tre el personal medico de base y los medicos internos. Material y metodos. Se realizo la aplicacion de la encuesta Cuestionario Sobre la Seguridad del Paciente en los Hospitales a 327 medicos pasantes del servicio social, enfocada en la experiencia que tuvieron durante el internado medico de pregrado. Resultados. La percepcion global de seguridad fue de 6.8 en una escala del 1 al 10. La dimension mas baja fue dotacion de personal (32.07%) y la mas alta trabajo en equipo en la unidad/servicio (70.69%). Conclusiones. Es fundamental analizar la infor- macion en este estudio, para poder observar donde se encuentran los puntos debiles dentro de la cultura de seguridad del paciente y asi poder planear e implemen- tar programas con la finalidad de acercarse a cumplir los objetivos en materia de seguridad del paciente.

We study weakly nonlinear spatially localized solutions of a Fermi-Pasta-Ulam model describing a unidimensional chain of particles interacting with a number of neighbors that can vary from site to site. The interaction potential contains quadratic and quartic terms, and is derived from a nonlinear elastic network model proposed by Juanico et al. [1]. The FPU model can be also derived for arbitrary dimensions, under a small angular displacement assumption. The variable interaction range is a consequence of the spatial inhomogeneity in the equilibrium particle distribution. We here study some simple one-dimensional examples with only a few, well defined agglomeration regions. These agglomerations are seen to lead to spatially localized linear modes and gaps in the linear spectrum, which in turn imply a normal form that has spatially localized periodic orbits.

Introduction. Create a positive culture of patient’s safety prevents adverse events and incidents, it allows to learn from mistakes, searches the root cause and modifies procedures with the purpose of not making mistakes again. The Patient’s Safety Evaluation in Hospitals, developed by the Agency for Healthcare Research and Quality in USA, which has a lot of benefices, is used for this evaluation.

Renormalization group has become a standard tool for describing universal properties of different routes to chaos-period-doubling in unimodal maps, quasiperiodic transitions in circle maps, dynamics on the boundaries of Siegel disks, destruction of invariant circles of area-preserving twist maps, and others. The universal scaling exponents for each route are related to the properties of the corresponding renormalization operators.We propose a Principle of Approximate Combination of Scaling Exponents (PACSE) that organizes the scaling exponents for different transitions to chaos. Roughly speaking, if the combinatorics of a transition is a composition of two simpler combinatorics, then the scaling exponents of the combined combinatorics is approximately equal to the product of the scaling exponents, both in the parameter space and in the configuration space, corresponding to each of these two combinatorics. We state PACSE quantitatively as precise asymptotics of the scaling exponents for combined combinatorics, and give convincing numerical evidence for it for each of the four dynamical systems mentioned above.We propose an explanation of PACSE in terms of the dynamical properties of the renormalization operators-in particular, as a consequence of certain transversal intersections of the stable and unstable manifolds of the operators corresponding to different transition to chaos.