The SUSY partners of the QES sextic potential revisited

In this paper, the SUSY partner Hamiltonians of the quasi-exactly solvable (QES) sextic potential $V^{\rm qes}(x) = \nu\, x^{6} + 2\, \nu\, \mu\,x^{4} + \left[\mu^2-(4N+3)\nu \right]\, x^{2}$, $N \in \mathbb{Z}^+$, are revisited from a Lie algebraic perspective. It is demonstrated that, in the variable $\tau=x^2$, the underlying $\mathfrak{sl}_2(\mathbb{R})$ hidden algebra of $V^{\rm qes}(x)$ is inherited by its SUSY partner potential $V_1(x)$ only for $N=0$. At fixed $N>0$, the algebraic polynomial operator $h(x,\,\partial_x;\,N)$ that governs the $N$ exact eigenpolynomial solutions of $V_1$ is derived explicitly. These odd-parity solutions appear in the form of zero modes. The potential $V_1$ can be represented as the sum of a polynomial and rational parts. In particular, it is shown that the polynomial component is given by $V^{\rm qes}$ with a different non-integer (cohomology) parameter $N_1=N-\frac{3}{2}$. A confluent second-order SUSY transformation is also implemented for a modified QES sextic potential possessing the energy reflection symmetry. By taking $N$ as a continuous real constant and using the Lagrange-mesh method, highly accurate values ($\sim 20$ s. d.) of the energy $E_n=E_n(N)$ in the interval $N \in [-1,3]$ are calculated for the three lowest states $n=0,1,2$ of the system. The critical value $N_c$ above which tunneling effects (instanton-like terms) can occur is obtained as well. At $N=0$, the non-algebraic sector of the spectrum of $V^{\rm qes}$ is described by means of compact physically relevant trial functions. These solutions allow us to determine the effects in accuracy when the first-order SUSY approach is applied on the level of approximate eigenfunctions.Comment: 25 pages, 20 figure

Classical nn-body system in geometrical and volume variables. I. Three-body case

We consider the classical 3-body system with $d$ degrees of freedom $(d>1)$ at zero total angular momentum. The study is restricted to potentials $V$ that depend solely on relative (mutual) distances $r_{ij}=\mid {\bf r}_i - {\bf r}_j\mid$ between bodies. Following the proposal by J. L. Lagrange, in the center-of-mass frame we introduce the relative distances (complemented by angles) as generalized coordinates and show that the kinetic energy does not depend on $d$, confirming results by Murnaghan (1936) at $d=2$ and van Kampen-Wintner (1937) at $d=3$, where it corresponds to a 3D solid body. Realizing $\mathbb{Z}_2$-symmetry $(r_{ij} \rightarrow -r_{ij})$ we introduce new variables $\rho_{ij}=r_{ij}^2$, which allows us to make the tensor of inertia non-singular for binary collisions. In these variables the kinetic energy is a polynomial function in the $\rho$-phase space. The 3 body positions form a triangle (of interaction) and the kinetic energy is $\mathcal{S}_3$-permutationally invariant wrt interchange of body positions and masses (as well as wrt interchange of edges of the triangle and masses). For equal masses, we use lowest order symmetric polynomial invariants of $\mathbb{Z}_2^{\otimes3} \oplus \mathcal{S}_3$ to define new generalized coordinates, they are called the {\it geometrical variables}. Two of them of the lowest order (sum of squares of sides of triangle and square of the area) are called {\it volume variables}. We study three examples in some detail: (I) 3-body Newton gravity in $d=3$, (II) 3-body choreography in $d=2$ on the algebraic lemniscate by Fujiwara et al where the problem becomes one-dimensional in the geometrical variables, and (III) the (an)harmonic oscillator.Comment: 32 pages, 2 figure

Admixture in Latin America

Latin Americans arguably represent the largest recently admixed populations in the world. This reflects a history of massive settlement by immigrants (mostly Europeans and Africans) and their variable admixture with Natives, starting in 1492. This process resulted in the population of Latin America showing an extensive genetic and phenotypic diversity. Here we review how genetic analyses are being applied to examine the demographic history of this population, including patterns of mating, population structure and ancestry. The admixture history of Latin America, and the resulting extensive diversity of the region, represents a natural experiment offering an advantageous setting for genetic association studies. We review how recent analyses in Latin Americans are contributing to elucidating the genetic architecture of human complex traits

Monitoring synaptic function at the neuromuscular junction of a mouse expressing synaptopHluorin

We monitored presynaptic exocytosis and vesicle recycling at neuromuscular junctions of transgenic mice expressing synaptopHluorin (spH), using simultaneous optical and electrophysiological recordings. Synaptic transmission was indistinguishable from that in wildtype controls. Fluorescence rose during and decayed monotonically after stimulus trains to the nerve, with amplitudes and decay times increasing with the amount of stimulation. The relatively large size of synaptic terminals allowed us to examine the spatial profile of fluorescence changes. We identified hot spots of exocytosis, which were stable with repeated trains. Photobleach experiments showed that spH freshly exposed by nerve stimulation was not preferentially retrieved by compensatory endocytosis; instead, most retrieved spH preexisted in the surface membrane. Finally, we compared fluorescence and electrical [summed end-plate potentials (EPPs)] estimates of exocytosis, which diverged during repeated trains, as fluorescence exceeded summed EPPs, although the average amplitude of miniature EPPs was unchanged. This might reflect exocytosis of spH-containing, acetylcholine-free (“empty”) vesicles or other organelles during intense stimulation

Characterization of the different behaviours exhibited by juvenile flathead grey mullet (Mugil cephalus Linnaeus, 1758) under rearing conditions

Aim of study: To describe the common behaviour of flathead grey mullet (Mugil cephalus) under rearing conditions. Area of study: Tepic, Mexico. Material and methods: Behaviours exhibited by mullets were videorecorded with submersible cameras installed inside of three tanks. A total of 690 min per day (07:30 - 18:30 h) were recorded per tank during a week. Afterwards, the different behaviours exhibited by juvenile M. cephalus were described, identified and characterized in an ethogram and grouped into two categories: a) locomotion, including three different observed behaviours (resting, swimming and fast swimming) and b) feeding, including three behaviours (surface feeding, bottom feeding and rubbing). Each of the behavioural variables were quantified. Main results: M. cephalus is a species with a constant locomotion associated to feeding, since fish showed continuous movement during most of day light period. On the contrary, fish exhibited reduced movement during dark periods. Mullets were observed to be a non-aggressive fish species under conditions of the present study, since the absence of dominance and aggression towards conspecifics was observed, which suggested a high predisposition for adaptation to captivity. Finally, behavioural frequencies of grey mullet juveniles were similar among the three tanks for most of the behavioural variables analysed (p>0.05) except for the variable bottom feeding (p=0.02). Research highlights: Results from this study could be of interest for the aquaculture industry to optimize rearing techniques and welfare for the production of grey mullet.info:eu-repo/semantics/publishedVersio

Improved calibration of the human mitochondrial clock using ancient genomes

Reliable estimates of the rate at which DNA accumulates mutations (the substitution rate) are crucial for our understanding of the evolution and past demography of virtually any species. In humans, there are considerable uncertainties around these rates, with substantial variation among recent published estimates. Substitution rates have traditionally been estimated by associating dated events to the root (e.g. the divergence between humans and chimpanzees) or to internal nodes in a phylogenetic tree (e.g. first entry into the Americas). The recent availability of ancient mtDNA sequences allows for a more direct calibration by assigning the age of the sequenced samples to the tips within the human phylogenetic tree. But studies also vary greatly in the methodology employed and in the sequence panels analysed, making it difficult to tease apart the causes for the differences between previous estimates. To clarify this issue, we compiled a comprehensive dataset of 350 ancient and modern human complete mtDNA genomes, among which 146 were generated for the purpose of this study, and estimated substitution rates using calibrations based both on dated nodes and tips. Our results demonstrate that, for the same dataset, estimates based on individual dated tips are far more consistent with each other than those based on nodes and should thus be considered as more reliable

Discerning the ancestry of European Americans in genetic association studies

European Americans are often treated as a homogeneous group, but in fact form a structured population due to historical immigration of diverse source populations. Discerning the ancestry of European Americans genotyped in association studies is important in order to prevent false-positive or false-negative associations due to population stratification and to identify genetic variants whose contribution to disease risk differs across European ancestries. Here, we investigate empirical patterns of population structure in European Americans, analyzing 4,198 samples from four genome-wide association studies to show that components roughly corresponding to northwest European, southeast European, and Ashkenazi Jewish ancestry are the main sources of European American population structure. Building on this insight, we constructed a panel of 300 validated markers that are highly informative for distinguishing these ancestries. We demonstrate that this panel of markers can be used to correct for stratification in association studies that do not generate dense genotype data

What did Hughes teach us about repairing surgical defects in the lower eyelid?

La reconstrucción del párpado inferior sigue siendo un reto, especialmente la reparación de defectos que abarcan más de la mitad de su superficie horizontal. El colgajo de Hughes del párpado superior ipsilateral es la técnica quirúrgica de elección para los tumores de gran tamaño del párpado inferior. Presentamos el caso de una paciente con carcinoma basocelular superficial de párpado inferior izquierdo que fue intervenida con extirpación del tumor con margen de seguridad y reparación del defecto primario mediante este colgajo. Describimos la técnica de Hughes paso a paso, sus potenciales complicaciones, así como los puntos clave en su ejecución para conseguir unos resultados satisfactorios.Lower eyelid reconstrution remains a challenge, especially the repair of defects that cover more than a half of its horizontal surface. The Hughes flap of the ipsilateral upper eyelid is the surgical technique of choice for large tumors of the lower eyelid. We present the case of a patient with superficial basal cell carcinoma of the lower left eyelid who underwent surgery with excision of the tumor with margin of safety and repair of the primary defect using this flap. We describe the Hughes technique step by step, its potential complications, as well as the key points in its execution to achieve satisfactory results

Short-term impact of noise, other air pollutants and meteorological factors on emergency hospital mental health admissions in the Madrid region

A number of environmental factors, such as air pollution, noise in urbanised settings and meteorological-type variables, may give rise to important effects on human health. In recent years, many studies have confirmed the relation between various mental disorders and these factors, with a possible impact on the increase in emergency hospital admissions due to these causes. The aim of this study was to analyse the impact of a range of environmental factors on daily emergency hospital admissions due to mental disorders in the Madrid Autonomous Region (MAR), across the period 2013–2018