Computational and analytical studies of the harmonic index on Erdös-Rényi models

A main topic in the study of topological indices is to find bounds of the indices involving several parameters and/or other indices. In this paper we perform statistical (numerical) and analytical studies of the harmonic index H(G), and other topological indices of interest, on Erdos-Rényi (ER) graphs G(n, p) characterized by n vertices connected independently with probability p ∈ (0, 1). Particularly, in addition to H(G), we study here the (−2) sum-connectivity index χ−2(G), the modified Zagreb index MZ(G), the inverse degree index ID(G) and the Randic index R(G). First, to perform the statistical study of these indices, we define the averages of the normalized indices to their maximum value: {H(G)}, {χ−2(G)}, {MZ(G)}, {ID(G)}, {R(G)}. Then, from a detailed scaling analysis, we show that the averages of the normalized indices scale with the product ξ ≈ np. Moreover, we find two different behaviors. On the one hand, hH(G)i and hR(G)i, as a function of the probability p, show a smooth transition from zero to n/2 as p increases from zero to one. Indeed, after scaling, it is possible to define three regimes: a regime of mostly isolated vertices when ξ 10 (H(G), R(G) ≈ n/2). On the other hand, hχ−2(G)i, hMZ(G)i and hID(G)i increase with p until approaching their maximum value, then they decrease by further increasing p. Thus, after scaling the curves corresponding to these indices display bell-like shapes in log scale, which are symmetric around ξ ≈ 1; i.e. the percolation transition point of ER graphs. Therefore, motivated by the scaling analysis, we analytically (i) obtain new relations connecting the topological indices H, χ−2, MZ, ID and R that characterize graphs which are extremal with respect to the obtained relations and (ii) apply these results in order to obtain inequalities on H, χ−2, MZ, ID and R for graphs in ER models.J.A.M.-B. acknowledges financial support from FAPESP (Grant No. 2019/ 06931-2), Brazil, CONACyT (Grant No. 2019-000009-01EXTV-00067) and PRODEP-SEP (Grant No. 511-6/2019.-11821), Mexico. J.M.R. and J.M.S. acknowledge financial support from Agencia Estatal de Investigación (PID2019-106433GB-I00/AEI/ 10.13039/501100011033), Spain

Sustainability and Educational Technology—A Description of the Teaching Self-Concept

The work of teaching is fundamental for achieving Agenda 2030, which defends the importance of improving quality in education (Sustainable Development Goal SDG 4), gender equality (SDG 5) and responsible consumption (SDG 12). Thus, the aim of the present study was to analyse teachers’ self-perceived digital competence as regards their eco-responsible use of technology. A total of 259 teachers in Preschool, Primary and Secondary Education in the Valencian Community (Spain) completed the 14-item questionnaire designed and validated by Barragán et al. (2020). Added to this were two open questions. The data collected then underwent quantitative (descriptive and comparative) and qualitative (conventional and summative content) analysis. Notable among the results were the low levels of knowledge and training regarding the environmental impact of technologies and the use of preventive measures. In addition, differences were found as regards gender, with males having a more positive self-perception, especially those teaching in Secondary Education. The information about training they provided in their narratives supported the quantitative findings. Their voices also led to the uncovering of proposals on how to teach eco-responsible practices and attitudes regarding the use of Information and Communication Technology (ICT). Finally, teacher training was identified as the main problem but also the main solution. All efforts should therefore be directed towards training teachers in the eco-responsible use of ICT following a holistic approach to sustainability.This work was supported by Research Group “GIDU-EDUTIC-IN” (ID: Vigrob-330)

Seismic Activity Rates in the Iberian Peninsula

Evaluating the seismic hazard requires establishing a distribution of the seismic activity rate, irrespective of the methodology used in the evaluation. In practice, how that activity rate is established tends to be the main difference between the various evaluation methods. The traditional procedure relies on a seismogenic zonation and the Gutenberg-Richter (GR) hypothesis. Competing zonations are often compared looking only at the geometry of the zones, but the resulting activity rate is affected by both geometry and the values assigned to the GR parameters. Contour plots can be used for conducting more meaningful comparisons, providing the GR parameters are suitably normalised. More recent approaches for establishing the seismic activity rate forego the use of zones and GR statistics and special attention is paid here to such procedures. The paper presents comparisons between the local activity rates that result for the complete Iberian Peninsula using kernel estimators as well as two seismogenic zonations. It is concluded that the smooth variation of the seismic activity rate produced by zoneless methods is more realistic than the stepwise changes associated with zoned approaches; moreover, the choice of zonation often has a stronger influence on the results than its fairly subjective origin would warrant. It is also observed that the activity rate derived from the kernel approach, related with the GR parameter “a”, is qualitatively consistent with the epicentres in the catalogue. Finally, when comparing alternative zonations it is not just their geometry but the distribution of activity rate that should be compared

Seismic Isolation of Liquefied Natural Gas Tanks: a Compartive Assessment

In severe seismic environments, tanks for storage of liquefied natural gas may benefit from seismic isolation. As the design accelerations increase, the inner tank undergoes progressively greater demands and may suffer from corner uplift, elephant’s foot buckling, gross sliding, shell thickness requirements beyond what can be reliably welded and, eventually, global uplift. Some of these problems cause extra costs while others make the construction impossible. The seismic environments at which the previous problems arise are quantified for modern 160,000 m3 tanks, whether supported on shallow or pile foundations, for both a conventional design and one employing seismic isolation. Additionally, by introducing some cost assumptions, comparisons can be made as to the cost of dealing with the seismic threat for each seismic environment and tank design option. It then becomes possible to establish the seismic environments that require seismic isolation, as well as to offer guidance for decisions in intermediate cases

Peligrosidad sísmica en la península ibérica

Se estudia la peligrosidad sísmica en la Península Ibérica con una metodología no paramétrica basada en estimadores de densidad kernel; la tasa de actividad se deduce del catálogo, tanto en cuanto a su dependencia espacial (prescindiendo de zonificación) como en relación con la magnitud (obviando la ley de Gutenberg-Richter). El catálogo es el del Instituto Geográfico Nacional, complementado con otros en zonas periféricas, homogeneizado en su cuantificación de los terremotos y eliminando eventos espacial o temporalmente interrelacionados para mantener un modelo temporal de Poisson. La tasa de actividad sísmica viene determinada por la función kernel, el ancho de banda y los períodos efectivos. La tasa resultante se compara con la obtenida usando estadísticas de Gutenberg-Richter y una metodología zonificada. Se han empleado tres leyes de atenuación: una para terremotos profundos y dos para terremotos superficiales, dependiendo de que su magnitud fuera superior o inferior a 5. Los resultados se presentan en forma de mapas de peligrosidad para diversas frecuencias espectrales y períodos de retorno de 475 y 2475 años, lo que permite construir espectros de peligrosidad uniforme

Down-regulation of heart HFABP and UCP2 gene expression in diet-induced (cafeteria) obese rats.

Long-term exposure to hypercaloric high fat diet induced marked tissue fatty acid accumulation and may influence cell function. Previous results in our laboratory showed that uncoupling proteins (UCPs) and fatty acid-binding protein (FABP) gene expression are changed in adipose tissue and skeletal muscle tissue in diet-induced (cafeteria) obese animals. The aim of this study was to examine heart FABP (HFABP) and UCP2 gene expressions in dietary obese rats. Rats fed on a high-fat diet for 65 days had significantly higher fat stores and body weight than control rats. Interestingly, we found that both HFABP and UCP2 mRNA levels were significantly reduced in cafeteria-obese rats when compared to control animals. Moreover, a statistically significant correlation was observed between the two gene expression levels. The down-regulation of heart HFABP and UCP2 parallels the lower lipid utilization which may account for an enhanced fat deposition. It is plausible that these two genes are regulated by the same family of transcription factors

Differential hypertrophic effects of cardiotrophin-1 on adult cardiomyocytes from normotensive and spontaneously hypertensive rats

Cardiotrophin-1 (CT-1) produces longitudinal elongation of neonatal cardiomyocytes, but its effects in adult cardiomyocytes are not known. Recent observations indicate that CT-1 may be involved in pressure overload left ventricular hypertrophy (LVH). We investigated whether the hypertrophic effects of CT-1 are different in cardiomyocytes isolated from adult normotensive and spontaneously hypertensive rats (SHR). Hypertrophy was evaluated by planimetry and confocal microscopy, contractile proteins were quantified by Western blotting and real-time RT-PCR, and intracellular pathways were analyzed with specific chemical inhibitors. CT-1 increased c-fos and ANP expression (p<0.01) and cell area (p<0.01) in cardiomyocytes from both rat strains. In Wistar cells, CT-1 augmented cell length (p<0.01) but did not modify either the transverse diameter or cell depth. In SHR cells, CT-1 increased cell length (p<0.05), cell width (p<0.01) and cell depth, augmented the expression of myosin light chain-2v (MLC-2v) and skeletal alpha-actin (p<0.01) and enhanced MLC-2v phosphorylation (p<0.01). The blockade of gp130 or LIFR abolished CT-1-induced growth in the two cell types. All distinct effects observed in cardiomyocytes from SHR were mediated by STAT3. Baseline angiotensinogen expression was higher in SHR cells, and CT-1 induced a 1.7-fold and 3.2-fold increase of angiotensinogen mRNA in cardiomyocytes from Wistar rats and SHR respectively. In addition, AT1 blockade inhibited the specific effects of CT-1 in SHR cells. Finally, ex vivo determinations revealed that adult SHR exhibited enhanced myocardial CT-1 (mRNA and protein, p<0.01), increased cell width (p<0.01) and concentric LVH compared with pre-hypertensive SHR. These findings reveal a specific cell-broadening effect of CT-1 in cardiomyocytes from adult SHR and suggest that the hypertensive phenotype of these cells may influence the hypertrophic effects of CT-1, probably by means of an exaggerated induction of angiotensinogen expression. We suggest that CT-1 might facilitate LVH in genetic hypertension through a cross-talk with the renin-angiotensin system

Association of increased plasma cardiotrophin-1 with inappropriate left ventricular mass in essential hypertension

Inappropriate left ventricular mass is present when the value of left ventricular mass exceeds individual needs to compensate hemodynamic load imposed by increased blood pressure. The goal of this study was to investigate whether plasma concentration of cardiotrophin-1, a cytokine that induces exaggerated hypertrophy in cardiomyocytes with hypertensive phenotype, is related to inappropriate left ventricular mass in patients with essential hypertension. The study was performed in 118 patients with never-treated hypertension and without prevalent cardiac disease. The left ventricular mass prediction from stroke work (systolic blood pressurexDoppler stroke volume), sex, and height (in meters(2.7)) was derived. An observed left ventricular mass/predicted left ventricular mass value >128% defined inappropriate left ventricular mass. Plasma cardiotrophin-1 was measured by an enzyme-linked immunosorbent assay. The studies were repeated in a group of 45 patients after 1 year of antihypertensive treatment. At baseline 67 and 51 patients presented with appropriate and inappropriate left ventricular mass, respectively. Plasma cardiotrophin-1 was higher (P<0.001) in patients with inappropriate mass than in patients with appropriate mass and normotensive controls. A direct correlation was found between cardiotrophin-1 and observed left ventricular mass/predicted left ventricular mass ratio (r=0.330, P<0.001) in all hypertensive patients. After treatment, plasma cardiotrophin-1 decreased and increased in patients in which inappropriate left ventricular mass regressed and persisted, respectively, despite a similar reduction of blood pressure in the 2 subgroups of patients. Albeit descriptive in nature, these results suggest the hypothesis that an excess of cardiotrophin-1 may contribute to inappropriate left ventricular growth in hypertensive patients

Fibrosis in hypertensive heart disease: role of the renin-angiotensin-aldosterone system

Structural homogeneity of cardiac tissue is governed by mechanical and humoral factors that regulate cell growth, apoptosis, phenotype, and extracellular matrix turnover. ANGII has endocrine, autocrine, and paracrine properties that influence the behavior of cardiac cells and matrix by AT1 receptor binding. Various paradigms have been suggested, including ANGII-mediated up-regulation of collagen types I and III formation and deposition in cardiac conditions, such as HHD. A growing body of evidence, however, deals with the potential role of aldosterone, either local or systemic, in inducing cardiac fibrosis. Aldosterone might also mediate the profibrotic actions of ANGII. To reduce the risk of heart failure that accompanies HHD, its adverse structural remodeling (eg, myocardial hypertrophy and fibrosis) must be targeted for pharmacologic intervention. Cardioprotective agents must reverse not only the exaggerated growth of cardiac cells, but also regress existing abnormalities in fibrillar collagen. Available experimental and clinical data suggest that agents interfering with ACE, the AT1 receptor, or the mineralocorticoid receptor may provide such a cardioprotective effect