Dynamics of a Quantum Common-Pool Resource Game with Homogeneous Players' Expectations.

In this work, we analyse a common-pool resource game with homogeneous players (both have boundedly rational expectations) and entanglement between players' strategies. The quantum model with homogeneous expectations is a differential approach to the game since, to the best of our knowledge, it has hardly been considered in previous works. The game is represented using a Cournot type payoff functions, limited to the maximum capacity of the resource. The behaviour of the dynamics is studied considering how the fixed points (particularly the Nash equilibrium) and the stability of the system vary depending on the different values of the parameters involved in the model. In the analysis of this game, it is especially relevant to consider the extent to which the resource is exploited, since the output of the players is highly affected by this issue. It is studied in which cases the resource can be overexploited, adjusting the parameters of the model to avoid this scenario when it is possible. The results are obtained from an analytical point of view and also graphically using bifurcation diagrams to show the behaviour of the dynamics.

Complex Dynamics of a Cournot Quantum Duopoly Game with Memory and Heterogeneous Players.

Previous authors tend to consider a certain range of values of the parameters involved in a game, not taking into account other possible values. In this article, a quantum dynamical Cournot duopoly game with memory and heterogeneous players (one of them is boundedly rational and the other one, a naive player) is studied, where the quantum entanglement can be greater than one and the speed of adjustment can be negative. In this context, we analyzed the behavior of the local stability and the profit in those values. Considering the local stability, it is observed that the stability region increases in the model with memory regardless of whether the quantum entanglement is greater than one or whether the speed of adjustment is negative. However, it is also shown that the stability is greater in the negative than in the positive zone of the speed of adjustment and, therefore, it improves the results obtained in previous experiments. This increase of stability enables higher values of speed of adjustment and, as a result of that, the system reaches the stability faster, resulting in a remarkable economic advantage. Regarding the behavior of the profit with these parameters, the principal effect shown is that the application of memory causes a certain delay in the dynamics. Through this article, all these statements are analytically proved and widely supported with several numerical simulations, using different values of the memory factor, the quantum entanglement, and the speed of adjustment of the boundedly rational player.

Vitamin D deficiency in primary health care users at risk in Spain / Deficiencia de vitamina D en usuarios de atención primaria con riesgo en España

Background and objectives: despite long hours of sunlight in Spain, vitamin D deficiency has been rising of late. We aimed to describe vitamin D deficiency and insufficiency in at-risk patients in La Rioja, a region in northern Spain. Methods: a retrospective, cross-sectional study involving 21,490 patients (74.3 % women) aged 14-105 years, who were primary health care (PHC) users in La Rioja, with an available 25-hidroxyvitamin D (25(OH)D) test result corresponding to the first request from January 2013 to October 2015. Vitamin D deficiency, insufficiency, and sufficiency were defined as 25(OH)D levels < 12 ng/mL, 12-20 ng/mL, and ≥ 20 ng/mL, respectively. Hypovitaminosis D was defined considering 2 cut-off points for 25(OH)D: < 20 ng/mL and < 30 ng/mL. Results: mean 25(OH)D levels were 18.3 (SD, 11.6) ng/mL in the whole sample, being lower in men than in women (17.6 vs 18.5 ng/mL, p < 0.001). Significantly higher 25(OH)D levels were found in the groups with 55-59, 60-64, 65-69, and 70-74 years of age (range, 19.4-20.4 ng/mL), and lower levels were found in the groups with 80-85 years and older (16.7 and 14.5 ng/mL), as compared to other groups. Two thirds of the population were vitamin D-deficient (< 12 ng/mL, 30.9 %) or insufficient (12-20 ng/mL, 32.8 %), and only 32.8 % of patients were found to be vitamin D-sufficient (> 20 ng/ml). Hypovitaminosis D rate was higher (89.7 %) when the 25(OH)D cut-off point was set at < 30 ng/mL. A higher hypovitaminosis D rate (< 20 ng/mL) was found in men (67.1 %) vs women (62.6 %) (p < 0.001), and it was more prevalent in patients over 75 years (72.6 %). (AU)

Justificación y objetivos: a pesar de las largas horas de exposición solar en España, la deficiencia de vitamina D ha ido en aumento. Nuestro objetivo fue describir la deficiencia e insuficiencia de vitamina D en pacientes de riesgo en La Rioja, España. Métodos: estudio transversal retrospectivo en el que participaron 21.490 pacientes (74,3 % mujeres), usuarios de Atención Primaria (APS) en La Rioja, con resultado de prueba de 25-hidroxivitamina D (25(OH) D) disponible, correspondiente a las solicitudes efectuadas entre enero de 2013 y octubre de 2015. La deficiencia, insuficiencia y suficiencia de vitamina D se definieron como niveles de 25(OH)D < 12 ng/mL, = 12-20 ng/mL y ≥ 20 ng/mL, respectivamente. La hipovitaminosis D se definió considerando 2 puntos de corte de 25(OH)D: < 20 ng/mL y < 30 ng/mL. Resultados: los valores medios de 25(OH)D fueron de 18,3 (DE: 11,6) ng/mL en toda la muestra, siendo menores en los hombres que en las mujeres (17,6 vs. 18,5 ng/mL, p < 0,001). Se encontraron niveles de 25(OH)D significativamente más altos en los grupos de 55-59, 60-64, 65-69 y 70-74 años (rango, 19,4-20,4 ng/mL), y más bajos en los grupos de 80-85 años y mayores (16,7 y 14,5 ng/mL) en comparación con otros grupos. Dos tercios de la población presentaban deficiencia de vitamina D (< 12 ng/mL, 30,9 %) o insuficiencia (12-20 ng/mL, 32,8 %), y solo el 32,8 % de los pacientes presentaban niveles suficientes de vitamina D (> 20 ng/mL). La hipovitaminosis D fue mayor (89,7 %) cuando el punto de corte de 25(OH)D se estableció en < 30 ng/mL. Se encontró una mayor tasa de hipovitaminosis D (< 20 ng/mL) en los hombres (67,1 %) que en las mujeres (62,6 %) (p < 0,001), y dicha hipovitaminosis fue más prevalente en los pacientes mayores de 75 años (72,6 %). La prevalencia de la hipovitaminosis D siguió un patrón estacional que varió del 51,8 % al 76,5 %. (AU)

Vitamin D deficiency in primary health care users at risk in Spain.

INTRODUCTION: Background and objectives: despite long hours of sunlight in Spain, vitamin D deficiency has been rising of late. We aimed to describe vitamin D deficiency and insufficiency in at-risk patients in La Rioja, a region in northern Spain. Methods: a retrospective, cross-sectional study involving 21,490 patients (74.3 % women) aged 14-105 years, who were primary health care (PHC) users in La Rioja, with an available 25-hidroxyvitamin D (25(OH)D) test result corresponding to the first request from January 2013 to October 2015. Vitamin D deficiency, insufficiency, and sufficiency were defined as 25(OH)D levels < 12 ng/mL, 12-20 ng/mL, and ≥ 20 ng/mL, respectively. Hypovitaminosis D was defined considering 2 cut-off points for 25(OH)D: < 20 ng/mL and < 30 ng/mL. Results: mean 25(OH)D levels were 18.3 (SD, 11.6) ng/mL in the whole sample, being lower in men than in women (17.6 vs 18.5 ng/mL, p < 0.001). Significantly higher 25(OH)D levels were found in the groups with 55-59, 60-64, 65-69, and 70-74 years of age (range, 19.4-20.4 ng/mL), and lower levels were found in the groups with 80-85 years and older (16.7 and 14.5 ng/mL), as compared to other groups. Two thirds of the population were vitamin D-deficient (< 12 ng/mL, 30.9 %) or insufficient (12-20 ng/mL, 32.8 %), and only 32.8 % of patients were found to be vitamin D-sufficient (> 20 ng/ml). Hypovitaminosis D rate was higher (89.7 %) when the 25(OH)D cut-off point was set at < 30 ng/mL. A higher hypovitaminosis D rate (< 20 ng/mL) was found in men (67.1 %) vs women (62.6 %) (p < 0.001), and it was more prevalent in patients over 75 years (72.6 %). The prevalence of hypovitaminosis D followed a seasonal pattern ranging from 51.8 % to 76.5 %; the lowest 25(OH)D levels were found in winter, and the highest in summer, with levels above 20 ng/mL in all age groups except for patients over 75 years (17.7 ng/mL). Patients over 75 years exhibited high rates of deficiency or insufficiency across all seasons of the year. Conclusions: in La Rioja, Spain, hypovitaminosis D was highly prevalent among PHC users, and especially in older age groups and during the winter months.

INTRODUCCIÓN: Justificación y objetivos: a pesar de las largas horas de exposición solar en España, la deficiencia de vitamina D ha ido en aumento. Nuestro objetivo fue describir la deficiencia e insuficiencia de vitamina D en pacientes de riesgo en La Rioja, España. Métodos: estudio transversal retrospectivo en el que participaron 21.490 pacientes (74,3 % mujeres), usuarios de Atención Primaria (APS) en La Rioja, con resultado de prueba de 25-hidroxivitamina D (25(OH) D) disponible, correspondiente a las solicitudes efectuadas entre enero de 2013 y octubre de 2015. La deficiencia, insuficiencia y suficiencia de vitamina D se definieron como niveles de 25(OH)D < 12 ng/mL, = 12-20 ng/mL y ≥ 20 ng/mL, respectivamente. La hipovitaminosis D se definió considerando 2 puntos de corte de 25(OH)D: < 20 ng/mL y < 30 ng/mL. Resultados: los valores medios de 25(OH)D fueron de 18,3 (DE: 11,6) ng/mL en toda la muestra, siendo menores en los hombres que en las mujeres (17,6 vs. 18,5 ng/mL, p < 0,001). Se encontraron niveles de 25(OH)D significativamente más altos en los grupos de 55-59, 60-64, 65-69 y 70-74 años (rango, 19,4-20,4 ng/mL), y más bajos en los grupos de 80-85 años y mayores (16,7 y 14,5 ng/mL) en comparación con otros grupos. Dos tercios de la población presentaban deficiencia de vitamina D (< 12 ng/mL, 30,9 %) o insuficiencia (12-20 ng/mL, 32,8 %), y solo el 32,8 % de los pacientes presentaban niveles suficientes de vitamina D (> 20 ng/mL). La hipovitaminosis D fue mayor (89,7 %) cuando el punto de corte de 25(OH)D se estableció en < 30 ng/mL. Se encontró una mayor tasa de hipovitaminosis D (< 20 ng/mL) en los hombres (67,1 %) que en las mujeres (62,6 %) (p < 0,001), y dicha hipovitaminosis fue más prevalente en los pacientes mayores de 75 años (72,6 %). La prevalencia de la hipovitaminosis D siguió un patrón estacional que varió del 51,8 % al 76,5 %. Los niveles más bajos de 25(OH)D se encontraron en invierno y los más altos en verano, con niveles por encima de 20 ng/mL en todos los grupos de edad excepto en los pacientes mayores de 75 años (17,7 ng/mL). Los pacientes mayores de 75 años presentaron altas tasas de deficiencia o insuficiencia durante todas las estaciones del año. Conclusiones: en La Rioja, España, la hipovitaminosis D fue altamente prevalente entre los usuarios de APS y, especialmente, en los grupos de mayor edad y durante los meses de invierno.

A quantum Samaritan's dilemma cellular automaton.

The dynamics of a spatial quantum formulation of the iterated Samaritan's dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e. with local and synchronous interaction. The game is assessed in fair and unfair contests, in noiseless scenarios and with disrupting quantum noise.

Spatial correlated games.

This article studies correlated two-person games constructed from games with independent players as proposed in Iqbal et al. (2016 R. Soc. open sci.3, 150477. (doi:10.1098/rsos.150477)). The games are played in a collective manner, both in a two-dimensional lattice where the players interact with their neighbours, and with players interacting at random. Four game types are scrutinized in iterated games where the players are allowed to change their strategies, adopting that of their best paid mate neighbour. Particular attention is paid in the study to the effect of a variable degree of correlation on Nash equilibrium strategy pairs.

Rebuilding Iberian motorways with slime mould.

Plasmodium of a cellular slime mould Physarum polycephalum is a unique living substrate proved to be efficient in solving many computational problems with natural spatial parallelism. The plasmodium solves a problem represented by a configuration of source of nutrients by building an efficient foraging and intra-cellular transportation network. The transportation networks developed by the plasmodium are similar to transport networks built by social insects and simulated trails in multi-agent societies. In the paper we are attempting to answer the question "How close plasmodium of P. polycephalum approximates man-made motorway networks in Spain and Portugal, and what are the differences between existing motorway structure and plasmodium network of protoplasmic tubes?". We cut agar plates in a shape of Iberian peninsula, place oat flakes at the sites of major urban areas and analyse the foraging network developed. We compare the plasmodium network with principle motorways and also analyse man-made and plasmodium networks in a framework of planar proximity graphs.

Spatial order prevails over memory in boosting cooperation in the iterated prisoner's dilemma.

This paper presents some results on a spatial version of the iterated prisoner's dilemma in which every player imitates in any iteration the optimal strategy of its neighbors. Neighbors are defined with different degrees of random variation (initial rewiring) based on a square lattice, and optimal is defined with different degrees of memory, ranging from only the single preceding iteration up to all preceding iterations. It is concluded that memory notably stimulates cooperation in the iterated prisoner's dilemma played in ordered lattices, but it is unable to boost cooperation as the wiring network becomes highly disordered.

Memory versus spatial disorder in the support of cooperation.

In the conventional spatial formulation of the iterated prisoner's dilemma only the results generated in the last round are taken into account in deciding the next choice. Historic memory can be implemented by featuring players with a summary of their previous winnings and moves. The effect of memory as a mechanism of supporting cooperation versus spatial disorder is assessed when the players are allowed for continuous degree of cooperation, not the mere binary cooperation/defection disjunctive.