Right triangles with algebraic sides and elliptic curves over number fields

Given any positive integer n, we prove the existence of infinitely many right triangles with area n and side lengths in certain number fields. This generalizes the famous congruent number problem. The proof allows the explicit construction of these triangles; for this purpose we find for any positive integer n an explicit cubic number field Q(\lambda) (depending on n) and an explicit point P_\lambda of infinite order in the Mordell-Weil group of the elliptic curve Y^2=X^3-n^2*X over Q(\lambda).Comment: To appear in Math. Slovac

Holocene fossil woods from the Caldera de Taburiente National Park (Canary Islands, Spain)

The study of 39 Pinus canariensis Holocene fossil woods from the Caldera de Taburiente is presente

Hospital volume and outcomes for acute pulmonary embolism: Multinational population based cohort study

[Objectives] To evaluate the association between experience in the management of acute pulmonary embolism, reflected by hospital case volume, and mortality.[Design] Multinational population based cohort study using data from the Registro Informatizado de la Enfermedad TromboEmbólica (RIETE) registry between 1 January 2001 and 31 August 2018.[Setting] 353 hospitals in 16 countries.[Participants] 39 257 consecutive patients with confirmed diagnosis of acute symptomatic pulmonary embolism.[Main] outcome measure Pulmonary embolism related mortality within 30 days after diagnosis of the condition.[Results] Patients with acute symptomatic pulmonary embolism admitted to high volume hospitals (>40 pulmonary embolisms per year) had a higher burden of comorbidities. A significant inverse association was seen between annual hospital volume and pulmonary embolism related mortality. Admission to hospitals in the highest quarter (that is, >40 pulmonary embolisms per year) was associated with a 44% reduction in the adjusted odds of pulmonary embolism related mortality at 30 days compared with admission to hospitals in the lowest quarter (<15 pulmonary embolisms per year; adjusted risk 1.3% v 2.3%; adjusted odds ratio 0.56 (95% confidence interval 0.33 to 0.95); P=0.03). Results were consistent in all sensitivity analyses. All cause mortality at 30 days was not significantly reduced between the two quarters (adjusted odds ratio 0.78 (0.50 to 1.22); P=0.28). Survivors showed little change in the odds of recurrent venous thromboembolism (odds ratio 0.76 (0.49 to 1.19)) or major bleeding (1.07 (0.77 to 1.47)) between the low and high volume hospitals.[Conclusions] In patients with acute symptomatic pulmonary embolism, admission to high volume hospitals was associated with significant reductions in adjusted pulmonary embolism related mortality at 30 days. These findings could have implications for management strategies.Peer reviewe

Stable thrust on a finite-sized magnet above a Meissner superconducting torus

Forces and torques exerted by a superconducting torus on a permanent magnet have been mapped. It is demonstrated that stable orbits exist. Moreover, provided that the magnet remains in any of these orbits, the first critical field in the superconductor is never overpassed and the superconductor remains in the Meissner state. The consequent absence of hysteresis makes these kinds of device perfect candidates for non-frictional bearings or gyroscopes.Comment: accepted versio

Metastable Resting State Brain Dynamics

Metastability refers to the fact that the state of a dynamical system spends a large amount of time in a restricted region of its available phase space before a transition takes place, bringing the system into another state from where it might recur into the previous one. beim Graben and Hutt (2013) suggested to use the recurrence plot (RP) technique introduced by Eckmann et al. (1987) for the segmentation of system's trajectories into metastable states using recurrence grammars. Here, we apply this recurrence structure analysis (RSA) for the first time to resting-state brain dynamics obtained from functional magnetic resonance imaging (fMRI). Brain regions are defined according to the brain hierarchical atlas (BHA) developed by Diez et al. (2015), and as a consequence, regions present high-connectivity in both structure (obtained from diffusion tensor imaging) and function (from the blood-level dependent-oxygenation—BOLD—signal). Remarkably, regions observed by Diez et al. were completely time-invariant. Here, in order to compare this static picture with the metastable systems dynamics obtained from the RSA segmentation, we determine the number of metastable states as a measure of complexity for all subjects and for region numbers varying from 3 to 100. We find RSA convergence toward an optimal segmentation of 40 metastable states for normalized BOLD signals, averaged over BHA modules. Next, we build a bistable dynamics at population level by pooling 30 subjects after Hausdorff clustering. In link with this finding, we reflect on the different modeling frameworks that can allow for such scenarios: heteroclinic dynamics, dynamics with riddled basins of attraction, multiple-timescale dynamics. Finally, we characterize the metastable states both functionally and structurally, using templates for resting state networks (RSNs) and the automated anatomical labeling (AAL) atlas, respectively.SR would like to acknowledge Ikerbasque (The Basque Foundation for Science) and moreover, this research is supported by the Basque Government through the BERC 2018-2021 program and by the Spanish State Research Agency through BCAM Severo Ochoa excellence accreditation SEV2017-0718 and through project RTI2018-093860-B- C21 funded by (AEI/FEDER, UE) and acronym MathNEURO. JC acknowledges financial support from Ikerbasque, Ministerio Economia, Industria y Competitividad (Spain) and FEDER (grant DPI2016-79874-R) and the Department of Economical Development and Infrastructure of the Basque Country (Elkartek Program, KK-2018/00032). Finally, PG acknowledges BCAM’s hospitality during a visiting fellowship in fall 2017

CONTRIBUCIÓN DEL CAPITAL SOCIAL EN LA MICROEMPRESA RURAL

The present study research identified the level of social capital in a small enterprise and its impact in the company itself. In Latin America, the importance of this concept lies in its relevance because diverse disciplines uses it as a reference setting, today it is used not only as part of political science and sociology, but also as part of the organization theory, economics, human behavior and management. It put emphasis in the relationships among people, among organizations and not in the individuals as isolated subjects. One of its advantages is that the social capital can contribute in the analysis of the small local communities from a social perspective and economical development. Because of the nature of the data handled in this study a qualitative design was adopted, and it was used the method case study, selecting for that matter the small enterprise Koolel Kab S. de R.L. Mi. The results of the study show that the origin of enterprise was an initiative of the partners who share the same objectives. It was verified the presence of social capital, which has permitted them to access to new information, to improve its commercialization, to obtain more funds, to develop new products and improve its production and sales. Based on these, we can conclude that social capital has contributed mainly to improve aspects such as learning and knowledge generation, innovation and management processes.Social capital, small enterprise, social development, network, learning, knowledge generation and innovation., Agribusiness,

Immunometabolism is a key factor for the persistent spontaneous elite control of HIV-1 infection

Approximately 25% of elite controllers (ECs) lose their virological control by mechanisms that are only partially known. Recently, immunovirological and proteomic factors have been associated to the loss of spontaneous control. Our aim was to perform a metabolomic approach to identify the underlying mechanistic pathways and potential biomarkers associated with this loss of control. Methods: Plasma samples from EC who spontaneously lost virological control (Transient Controllers, TC, n=8), at two and one year before the loss of control, were comparedwith a control group of ECwho persistently maintained virological control during the same follow-up period (Persistent Controllers, PC, n=8). The determination of metabolites and plasma lipids was performed by GC-qTOF and LC-qTOF using targeted and untargeted approaches. Metabolite levels were associated with the polyfunctionality of HIV-specific CD8+T-cell response. Findings: Our data suggest that, before the loss of control, TCs showed a specific circulating metabolomic profile characterized by aerobic glycolytic metabolism, deregulated mitochondrial function, oxidative stress and increased immunological activation. In addition, CD8+ T-cell polyfunctionality was strongly associated with metabolite levels. Finally, valine was the main differentiating factor between TCs and PCs. Interpretation: All these metabolomic differences should be considered not only as potential biomarkers but also as therapeutic targets in HIV infection.Instituto Carlos III PI10/02635 PI13/00796 PI16/00503 PI12/02283 PI16/00684 CPII014/00025 FI14/00431 FI17/00186 INT11/240 INT12/282 INT15/226Fondos Europeos para el Desarrollo Regional PI10/02635 PI13/00796 PI16/00503 PI12/02283 PI16/00684 CPII014/00025 FI14/00431 FI17/00186FEDER PI10/02635 PI13/00796 PI16/00503 PI12/02283 PI16/00684 CPII014/00025 FI14/00431 FI17/00186FEDER PI10/02635 PI13/00796 PI16/00503 PI12/02283 PI16/00684 CPII014/00025 FI14/00431 FI17/00186Programa de Suport als Grups de Recerca 2017SGR948 2014SGR250Gilead Fellowship Program GLD14/293 GLD17/00299Red de Investigación en Sida RD12/0017/0005 RD16/0025/0006 RD12/0017/0029 RD16/0025/0020Junta de Andalucía C-0032/17Generalitat de Catalunya PERIS SLT002/16/0010

External validity of docetaxel triplet trials in advanced gastric cancer: are there patients who still benefit?

Bayesian model; Docetaxel; Gastric cancerModel bayesià; Docetaxel; Càncer gàstricModelo bayesiano; Docetaxel; Cáncer gástricoBackground The purpose of our study was to develop an online calculator to estimate the effect of docetaxel triplets (DPF) in first line of advanced gastric cancer (AGC), and to assess the external validity of docetaxel trials in individual patients. Methods The study includes patients with HER2(-) AGC treated with platin and fluoropyrimidine (PF) or with DPF in first line. Treatment effect and interactions were assessed using Bayesian accelerated failure time models. Result The series comprises 1376 patients; 238 treated with DPF and 1138 with PF between 2008 and 2019. DPF was associated with increased progression-free survival (PFS) and overall survival (OS) with time ratio (TR) 1.27 (95% credible interval [CrI], 1.15–1.40), and TR 1.19 (95% CrI, 1.09–1.27), respectively. Serious adverse events were more common with DPF, particularly hematological effects (32% vs 22%). Younger participants received greater DPF dose density without achieving greater disease control, while severe toxicity was likewise higher. DPF yielded superior OS in Lauren intestinal (TR 1.27, 95% CrI, 1.08–1.11) vs diffuse subtype (TR 1.17, 95% CrI, 1.09–1.24) and the probability of increasing OS > 15% was 90% vs 67% in each subtype, respectively. The effect dwindles over time, which can be attributed to pathological changes and clinical practice changes. Conclusion Our study confirms the effect of DPF is highly dependent on several clinical–pathological variables, with discreet and gradually declining benefit over platinum doublets in later years, at the expense of increased toxicity. These results may help to underpin the idea that external validity of AGC trials should be revised regularly