Geometric Rényi divergence: A comparative measure with applications to atomic densities

An alternative one-parameter measure of divergence is proposed, quantifying the discrepancy among general probability densities. Its main mathematical properties include (i) comparison among an arbitrary number of functions, (ii) the possibility of assigning different weights to each function according to its relevance on the comparative procedure, and (iii) ability to modify the relative contribution of different regions within the domain. Applications to the study of atomic density functions, in both conjugated spaces, show the versatility and universality of this divergence

Relativistic global and local divergences in hydrogenic systems: A study in position and momentum spaces

Relativistic effects in one-particle densities of hydrogenic systems are quantified by means of global and local density functionals: the Jensen-Shannon and the Jensen-Fisher divergences, respectively. The Schrödinger and Dirac radial densities are compared, providing complementary results in position and momentum spaces. While the electron cloud gets compressed towards the origin in the Dirac case, the momentum density spreads out over its domain, and the raising of minima in position space does not occur in the momentum space. Regarding the dependence on the nuclear charge and the state quantum numbers for all divergences here considered, as well as their mutual interconnection, accurate powerlike laws y˜Cxa are found systematically. The parameters {C,a} defining the respective dependences are extremely sensitive to the closeness of the system to the ground and/or the circular state. Particularly interesting are the analyses of (i) the plane subtended by the Jensen-Shannon and Jensen-Fisher divergences, in a given space (position or momentum), and (ii) either of the above two divergences in the position-momentum plane. These kinds of results show the complementary role of global and local divergences and that of both conjugate spaces

Configuration Complexities of Hydrogenic Atoms

The Fisher-Shannon and Cramer-Rao information measures, and the LMC-like or shape complexity (i.e., the disequilibrium times the Shannon entropic power) of hydrogenic stationary states are investigated in both position and momentum spaces. First, it is shown that not only the Fisher information and the variance (then, the Cramer-Rao measure) but also the disequilibrium associated to the quantum-mechanical probability density can be explicitly expressed in terms of the three quantum numbers (n, l, m) of the corresponding state. Second, the three composite measures mentioned above are analytically, numerically and physically discussed for both ground and excited states. It is observed, in particular, that these configuration complexities do not depend on the nuclear charge Z. Moreover, the Fisher-Shannon measure is shown to quadratically depend on the principal quantum number n. Finally, sharp upper bounds to the Fisher-Shannon measure and the shape complexity of a general hydrogenic orbital are given in terms of the quantum numbers.Comment: 22 pages, 7 figures, accepted i

A numerical method for nonlinear age-structured population models with finite maximum age

AbstractWe propose a new numerical method for the approximation of solutions to a non-autonomous form of the classical Gurtin–MacCamy population model with a mortality rate that is the sum of an intrinsic age-dependent rate that becomes unbounded as the age approaches its maximum value, plus a non-local, non-autonomous, bounded rate that depends on some weighted population size. We prove that our new quadrature based method converges to second-order and we show the results of several numerical simulations

Mean temperature evolution on the Spanish mainland 1916-2015

An analysis of the evolution of annual and seasonal mean temperatures on the Spanish mainland (western Mediterranean basin) was carried out, using the new MOnthly TEmperature Dataset of Spain century (MOTEDAS-century) data set. This data set was developed by combining archives from the National Meteorological Agency and newly digitised legacy data from the Annual Books published between 1916 and 1949. Both the annual and seasonal regional mean temperature series experienced increasing trends during the study period. However, the in-crement was neither constant in time (monotonic) nor homogeneous between seasons. Four main periods were identified in the annual mean regional series. The first 3 corresponded to those previously confirmed in global temperature series (rise-pause-rise); a second pause or hiatus was also detected at the end of the period of analysis. The seasonal regional series followed specific patterns: Winter mean temperature only increased in the second rising period, autumn in the first and spring and summer during the 2 rising periods. Also, negative trends were found in extended areas in the first pause in spring, and to a lesser extent in summer. From the middle of the 1980s, the trends in annual and seasonal mean values were not significant up until 2015. Furthermore, spatial variations were found in the significance of the trends, revealing regional differences in the intensity of warming through the seasons. In comparison with other versions of secular mean temperature series developed for the Spanish mainland, MOTEDAS-century seems to better capture the spatial variability

Spatial variability of maximum and minimum monthly temperature in Spain during 1981–2010 evaluated by correlation decay distance (CDD)

The spatial variability of monthly diurnal and nocturnal mean values of temperature in Spain has been analysed to evaluate the optimal threshold distance between neighbouring stations that make a meteorological network (in terms of stations’ density) well representative of the conterminous land of Spain. To this end, the correlation decay distance has been calculated using the highest quality monthly available temperature series (1981–2010) from AEMet (National Spanish Meteorological Agency). In the conterminous land of Spain, the distance at which couples of stations have a common variance above the selected threshold (50 %, r Pearson ~0.70) for both maximum and minimum temperature on average does not exceed 400 km, with relevant spatial and temporal differences, and in extended areas of Spain, this value is lower than 200 km. The spatial variability for minimum temperature is higher than for maximum, except in cold months when the reverse is true. Spatially, highest values are located in both diurnal and nocturnal temperatures to the southeastern coastland and lower spatial variability is found to the inland areas, and thus the spatial variability shows a clear coastland-to-inland gradient at annual and monthly scale. Monthly analyses show that the highest spatial variability in maximum and minimum temperatures occur in July and August, when radiation is maximum, and in lowland areas, (<200 m o.s.l.), which coincide with the mostly transformed landscapes, particularly by irrigation and urbanization. These results highlight local factors could play a major role on spatial variability of temperature. Being maximum and minimum temperature interstation correlation values highly variable in Spanish land, an average of threshold distance of about 200 km as a limit value for a well representative network should be recommended for climate analyses,

Variability of maximum and minimum monthly mean air temperatures over mainland Spain and their relationship with low-variability atmospheric patterns for period 1916–2015

The analysis of monthly air temperature trends over mainland Spain during 1916–2015 shows that warming has not been constant over time nor generalized among different months; it has not been synchronous for maximum and minimum air temperatures; and it has been heterogeneous in space. Temperature rose during two characteristic pulses separated by a pause around the middle of the 20th century in some months. In other months, only the second rising period is identified, or no warming can be found. In all months, and both for maximum and minimum air temperatures, a stagnation of the increasing trend is observed in the last two decades of the study period. High spatial variability exists in trend signal and significance, and two contrasting temporal patterns of advance over the study area are identified for maximum and minimum air temperatures. These patterns can be related to prevalent flow directions and relief disposition with respect to the flows associated with low-variability meteorological patterns North Atlantic Oscillation (NAO) and Western Mediterranean Oscillation (WEMO). The results show that warming is a complex phenomenon at regional and sub-regional scales that can only be analysed using high-spatial-resolution data and considering global and local factors

Post-antibiotic effect of three quinolones against gram negative isolates from urine

he post-antibiotic effect (PAE) is defined as the bacterial growth suppression which persists after a limited exposure to an antimicrobial agent. The PAE and the bactericidal effect of the quinolones ciprofloxacin, norfloxacin and nalidixic acid have been studied against several urinary isolates of Gram-negative bacteria. The PAE was determined after one hour's exposure to the antimicrobial agent using an initial inoculum of 10(5) to 10(6) cfu/ml; the drug was rapidly removed by a 10(-2) dilution technique in antibiotic-free medium. When ciprofloxacin was used at four times its MIC the PAEs were 1.37 +/- 0.09; 2.45 +/- 0.63 and 2.86 +/- 0.15 h against Esch. coli, Klebs. pneumoniae and Pseudomonas aeruginosa, respectively. We found lower values for norfloxacin under the same conditions, and nalidixic acid did not induce a significative PAE. These results could support changes in dosing intervals of norfloxacin and ciprofloxacin, with possibly greater intervals between doses

Variaciones temporales de las tendencias en la serie de temperatura de inglaterra central

Variations in trend rates of annual values of the Central England Temperature series (CET) over the period 1659-2017 were analysed using moving windows of different length, to identify the minimum period in which the trend expresses a climate signal not hidden by the noise produced by natural variability. Trend rates exhibit high variability and irregular shifting from positive to negative values unless very long window lengths (of 100 years or more) are used. In general, as the duration of the length of the temporal window analysed increases, the absolute range of the trend rates decreases and the signal-to-noise (S/N) ratio increases. The relationship between the S/N ratio and the window length also depended on the total length of the series, so high S/N values are achieved faster when shorter time series are considered. This prevents suggesting a minimum window length for undertaking trend analyses. A comparison between CET and the average continental series in the Berkeley Earth Surface Temperature (BEST) database in their common period (17532017) repeats the patterns described for 1659-2017, although the average values of the rates, ranges and the “threshold period” in years change, and are more variable in CET than in BEST. Analysis of both series suggests that the recent warming started early and can be linked to the recovery of temperatures after the Little Ice Age. This process has characterised by progressively increasing trend rates, but also includes periods of deceleration or even negative trends spanning less than 50 years. The behaviour of the two long-term temperature records analysed agrees with a long-term persistence (LTP) process. We estimated the Hurst exponent of the CET series to be around 0.72 and 0.8, which reinforces the LTP hypothesis. This implies that the currently widespread statistical framework assuming a stationary, short-memory process in which departures from the norm can be easily assessed by monotonic trend analysis should not be accepted for long climatic series. In brief, relevant questions relative to the recent evolution of temperatures such as the distinction between natural variability and departures from stationarity; attribution of the causes of variability at different time scales; determination of the shortest window length to detect a trend; and other similar ones have still not been answered and may require adoption of an alternative analytical framework

High-resolution spatio-temporal analyses of drought episodes in the western Mediterranean basin (Spanish mainland, Iberian Peninsula)

The purpose of this research was to identify major drought events on the Spanish mainland between 1961 and 2014 by means of two drought indices, and analyze the spatial propagation of drought conditions. The indices applied were the standardized precipitation index (SPI) and the standardized evaporation precipitation index (SPEI). The first was calculated as standardized anomalies of precipitation at various temporal intervals, while the second examined the climatic balance normalized at monthly scale, incorporating the relationship between precipitation and the atmospheric water demand. The daily meteorological data from Spanish Meteorological Archives (AEMet) were used in performing the analyses. Within the framework of the DESEMON project, original data were converted into a high spatial resolution grid (1.1 km2) following exhaustive quality control. Values of both indices were calculated on a weekly scale and different timescales (12, 24 and 36 months). The results show that during the first half of the study period, the SPI usually returned a higher identification of drought areas, while the reverse was true from the 1990s, suggesting that the effect from atmospheric evaporative demand could have increased. The temporal propagation from 12- to 24-month and 36-month timescales analyzed in the paper seems to be a far from straightforward phenomenon that does not follow a simple rule of time lag, because events at different temporal scales can overlap in time and space. Spatially, the propagation of drought events affecting more than 25% of the total land indicates the existence of various spatial gradients of drought propagation, mostly east–west or west–east, but also north–south have been found. No generalized episodes were found with a radial pattern, i.e., from inland to the coast