Interpolation approximations for the steady-state distribution in multi-class resource-sharing systems

International audienceWe consider a single-server multi-class queue that implements relative priorities among customers of the various classes. The discipline might serve one customer at a time in a non-preemptive way, or serve all customers simultaneously. The analysis of the steady-state distribution of the queue-length and the waiting time in such systems is complex and closed-form results are available only in particular cases. We therefore set out to develop approximations for the steady-state distribution of these performance metrics. We first analyze the performance in light traffic. Using known results in the heavy-traffic regime, we then show how to develop an interpolation-based approximation that is valid for any load in the system. An advantage of the approach taken is that it is not model dependent and hence could potentially be applied to other complex queueing models. We numerically assess the accuracy of the interpolation approximation through the first and second moments

Discovering the utility and applicability of probability and statistics using the flipped classroom methodology

“Las estadísticas advierten de que fumar aumenta la probabilidad de cáncer de pulmón” o “La esperanza de vida es mayor en mujeres que en hombres" son frases que escuchamos habitualmente por lo que conviene introducir los conceptos de probabilidad y estadística a los adolescentes. Este artículo presenta una Unidad Didáctica sobre la probabilidad y la estadística a impartir en la asignatura de Matemáticas aplicadas a Ciencias Sociales. El modelo pedagógico se basa en metodologías activas, más concretamente en el llamado flipped-classroom o clase-invertida, una metodología ya bien experimentada que se centra en el alumno permitiéndole marcar el ritmo de estudio.“Statistics state smoking increases the probability of suffering lung cancer” or “Life expectancy is higher in women than in men” are phrases that we hear in everyday life. Hence, the importance of introducing basic probability and statistical concepts to teenagers. This article presents a teaching unit about the probability and statistics to impart in the subject of mathematics applied to Social Sciences in high school. The chosen pedagogical model is based on active methodologies, more precisely, on the so-called flipped classroom, a well-known methodology that focuses on the student, allowing him/her to dictate the pace of study

Sojourn time approximations for a discriminatory-processor-sharing queue

International audienceWe study a multi-class time-sharing discipline with relative priorities known as Discriminatory Processor Sharing (DPS), which provides a natural framework to model service differentiation in systems. The analysis of DPS is extremely challenging and analytical results are scarce. We develop closed-form approximations for the mean conditional (on the service requirement) and unconditional sojourn times. The main benefits of the approximations lie in its simplicity, the fact that it applies for general service requirements with finite second moments, and that it provides insights into the dependency of the performance on the system parameters. We show that the approximation for the mean conditional and unconditional sojourn time of a customer is decreasing as its relative priority increases. We also show that the approximation is exact in various scenarios, and that it is uniformly bounded in the second moments of the service requirements. Finally we numerically illustrate that the approximation for exponential, hyperexponential and Pareto service requirements is accurate across a broad range of parameters

Heavy-traffic analysis of a non-preemptive multi-class queue with relative priorities

International audienceWe study the steady-state queue-length vector in a multi-class single-server queue with relative priorities. Upon service completion, the probability that the next customer to be served is from class k is controlled by class- dependent weights. Once a customer has started service, it is served without interruption until completion. This is a generalization of the random-order-of-service discipline. We investigate the system in a heavy-traffic regime. We first establish a state-space collapse for the scaled queue length vector, that is, in the limit the scaled queue length vector is distributed as the product of an exponentially distributed random variable and a deterministic vector. As a direct consequence, we obtain that the scaled number of customers in the system reduces as classes with smaller mean service requirement obtain relatively larger weights. We then show that the scaled waiting time of a class-k customer is distributed as the product of two exponentially distributed random variables. This allows us to determine the value of the weights that minimize the m-th moment of the scaled waiting time for a customer of arbitrary class. We simulate a system with two different classes of customers in order to numerically verify some of the analytical results

Analysis of statistical graphs made by future primary teachers in open PBL tasks

III Congreso Internacional Virtual de Educación Estadística (CIVEEST), 21-24 febrero de 2019. [www.ugr.es/local/fqm126/civeest.html]En la sociedad actual de las tecnologías de la información y la comunicación se acumula una gran cantidad de datos. Por esta razón, los currículos actuales de matemáticas conceden un lugar específico a la estadística. Trabajar la estadística mediante la metodología aprendizaje basado en problemas con datos reales, contextualizados para el alumnado, es beneficioso de cara a desarrollar el sentido estadístico. Uno de los componentes que definen los estándares (NCTM) es la presentación de la información mediante gráficos. En este artículo se considera una muestra de 50 estudiantes del Grado de Educación Primaria que han llevado a cabo un proyecto de investigación estadístico y se realiza un análisis cualitativo acerca de la representación gráfica de los datos que presentan mediante softwares informáticos. El uso acrítico del software es la mayor fuente de errores.In the current information and communications technology society, a great amount of data is accumulated. For this reason, the recent mathematical curriculums attribute a specific place to statistics. Working statistic by problems based learning methodology with real data, contextualized for the pupils, is beneficial to develop statistical sense. One component that defines the standards (NCTM) is the presentation of the information through graphs. In this article a sample of 50 students of the Primary Education Degree that have carried out a statistical research project is considered. A qualitative analysis of the graphical representation of the data obtained via informatics software is analysed. The acritical use of the software is the largest source of errors

Conocimiento estadístico del futuro profesorado de educación primaria en la representación de datos

Este artículo analiza si el futuro profesorado de educación primaria distingue las categorías/valores de la variable de las frecuencias absolutas, selecciona y construye el gráfico adecuado según el tipo de variable y cómo justifica tal elección. Así, presentamos un estudio de caso de corte mixto con predominancia cualitativa y carácter exploratorio, con una muestra de 108 futuros docentes en el que se ha diseñado un cuestionario ad-hoc con 4 ítems. Los resultados indican que el futuro profesorado tiene dificultades para distinguir las categorías de una variable cualitativa de sus frecuencias absolutas. Los errores más comunes en la elección del gráfico son realizar gráficos de líneas para variables cualitativas e histogramas para variables cualitativas o cuantitativas discretas sin agrupar. Tanto el grado de corrección en la realización del gráfico como su justificación no es suficiente, lo que evidencia la necesidad de mejorar su alfabetización estadística

Landforms of the lower Hushe Valley (Central Karakoram, Pakistan)

This paper presents a new geomorphological map for the lower Hushe Valley (below 3400 m asl), located to the SE of the Central Karakoram in Baltistan (North Pakistan). Fieldwork and remote sensing were combined to improve understanding of the most recent surface landforms to produce a 1:50,000 scale map. Thirteen landform types associated with glacial, fluvial, gravitational and mass wasting processes were identified and mapped. Particular emphasis was made on currently dynamic processes that could pose a threat to the population. The distribution of the landforms on the valley (reworked tills, alluvial fans, rockfalls, among others) differs between the eastern and the western hillslopes, and from north to south, mainly due to bedrock types, location of geological structures and distribution of lateral tributaries. This map is the first and necessary step towards a deep assessment on geological risk related to external processes in the area.This research was funded by the Basque Government (Eusko Jaurlaritza) through the Humanitarian Action 2018 fund (PRE2018EH/0004) and the Consolidated Research Group IT1029-16. We also thank the University of the Basque Country UPV/EHU for the suppor

Diffusional Behavior of New Insulating Gas Mixtures as Alternatives to the SF6-Use in Medium Voltage Switchgear

Regarding the use of SF6 in medium voltage switchgear (MVS), a review of alternatives was encouraged by the European Parliament in Regulation No 517/2014. This is aimed at a new regulatory change, that is expected soon, which will include its prohibition, similar to what has happened with other fluorinated greenhouse gases in other fields, like refrigeration. Therefore, there is an urgent need to study the physical and chemical properties of alternative gas mixtures to determine if they are suitable to replace SF6. In this context, this work addresses the difusional analysis of new gases. Binary and ternary mixtures made of 1,3,3,3-tetrafluoropropene (C3F4H2) and heptafluoroisopropyl trifluoromethyl ketone (C5F10O), using dry air as a carrier gas, were studied. The mixtures were analyzed using original equipment, composed of UV-Vis spectroscopy technology in a sealed gas chamber, which is similar to MVS. Consequently, an experimental equipment that monitors the concentration of a gas mixture online and a model that predicts the mixing process were designed and tested. The concentration profiles were obtained concerning both the time and position in the gas chamber, and the diffusional and convectional parameters were numerically calculated and optimized in an algorithm created in Scilab.This research was funded by the Basque Government, grant numbers KK-2017/00090 and KK-2019/00017

2030 Agendako helburuetatik lurra-ura hartzera

The 2030 Agenda includes objectives in three dimensions (economic, social and environmental). To these three, we must add the territory where the action plans are implemented. Hence, as researchers working in hydrology we must generate knowledge towards the resilience of dynamic territories combining Water and Land. Thus, this article analyses the need to establish a basin-perspective in water management instead of the usual river-perspective, considering the basin as the basic bio-physical unit for territorial planning. Climate change mitigation and adaptation policies converge in the basin, facilitating the identification of synergies and trade-offs between both strategies. In fact, global mitigation policies focus, largely, on carbon sequestration through reforestation, neglecting its side-effects on adaptation. The hydrological functions of the territory affect the quantity, quality, location and timing of water, by accumulating, moving and transforming it. Therefore, accepting this water regulatory function would imply a change in the way of understanding the management of water resources and an improvement in the integration of hydrological services in the territorial planning. For this purpose, local knowledge and knowledge on trade-offs and synergies between different objectives are needed. In this era of uncertainties, we should focus our main research strategies towards minimization of uncertainties in order to properly manage them and make knowledge-informed decisions, thus, changing the management paradigm. We need, therefore, socio-political will to redirect territorial dynamics, incorporating a development model adapted to local ecosystem services limitations, placing Land and Water in the centre of the territory, anywhere in the world; Garapen Iraunkorrerako 2030 Agendaren hiru dimentsioei (ekonomikoa, soziala eta ingurumenarena) lurraldearena gehitu behar zaie, ekintza-planak gauzatzeko ezinbesteko ingurune fisikoa baita. Hortik dator hidrologiatik ari garen ikertzaileok iraunkortasunari egin diezaiokegun ekarpena: ura eta lurra uztartuta lurralde dinamikoak erresiliente egiteko bidean ezagutza sortzea, erabakietan eragiteko. Iraunkortasuna zutabe hartuta, uraren kudeaketan ohikoa den ibai-ikuspegia aldatu eta arro-ikuspegia ezarri beharra dugu, eta ibai-arroa (ura + lurraldea) lurralde-antolamenduaren oinarrizko unitate biofisiko bihurtu. Hala, klima-aldaketaren aurrean ezartzen diren arintze- eta egokitze-politiken bateragune bihurtzen da ibai-arroa, bi estrategia horien arteko sinergiak eta helburu-gatazkak identifikatzea errazten duen heinean. Izan ere, klima-aldaketarekin lotutako mundu mailako arintze-politiken oinarriak karbonoa bahitzea eta horri lotuta lurraldea basotzea dira neurri handi batean, basotzeak klima-aldaketara egokitzeko ekar ditzakeen albo-kalteak kontuan izan gabe. Lurraldearen funtzio hidrologikoek eragina dute uraren kantitatean, kalitatean, kokapenean eta denboran, zeren eta ura metatzen, mugitzen etaeraldatzen baitute. Beraz, lurraldeak uraren erregulatzaile gisa duen funtzioa onartuz gero, baliabide hidrologikoen kudeaketa ulertzeko modua aldatuko litzateke, baita egokitzera bidean lurraldearen kudeaketan zerbitzu hidrologikoak barneratzea erraztuko ere. Horretarako, beharrezkoa da tokiko eskalari lotutako ezagutzen eta helburuen arteko gatazkak eta sinergiak zein diren jakitea. Alde horretatik, bizi dugun ziurgabetasun-aroan, auzi horiek argitzera bideratu behar genituzke ikerketa-bide nagusiak, haiek egoki kudeatzeko eta ezagutzak informatutako erabakiak hartzeko, ohiko inertziak gaindituta, kudeaketa-paradigma aldatuta. Hortaz, lurralde-dinamikak birbideratzeko borondate soziopolitikoa behar da, eta naturak lekuan-lekuan eskaintzen dituen zerbitzu ekosistemikoen mugetara egokituriko garapen-eredu bat barneratu, lurra eta ura lurraldearen ardatzean jarrita, munduko edozein herrialdetan

Cerebrospinal Fluid 7-Ketocholesterol Level is Associated with Amyloid-β42 and White Matter Microstructure in Cognitively Healthy Adults

Background:Abnormal cholesterol metabolism changes the neuronal membrane and may promote amyloidogenesis. Oxysterols in cerebrospinal fluid (CSF) are related to Alzheimer’s disease (AD) biomarkers in mild cognitive impairment and dementia. Cholesterol turnover is important for axonal and white matter (WM) microstructure maintenance. Objective:We aim to demonstrate that the association of oxysterols, AD biomarkers, and WM microstructure occurs early in asymptomatic individuals. Methods:We studied the association of inter-individual variability of CSF 24-hydroxycholesterol (24-OHC), 27-hydroxycholesterol (27-OHC), 7-ketocholesterol (7-KC), 7β-hydroxycholesterol (7β-OHC), amyloid-β42 (Aβ42), total-tau (t-tau), phosphorylated-tau (p-tau), neurofilament (NfL), and WM microstructure using diffusion tensor imaging, generalized linear models and moderation/mediation analyses in 153 healthy adults. Results:Higher 7-KC levels were related to lower Aβ42, indicative of greater AD pathology (p = 0.041) . Higher 7-KC levels were related to lower fractional anisotropy (FA) and higher mean (MD), axial (AxD), and radial (RD) diffusivity. 7-KC modulated the association between AxD and NfL in the corpus callosum splenium (B = 39.39, p = 0.017), genu (B = 68.64, p = 0.000), and fornix (B = 10.97, p = 0.000). Lower Aβ42 levels were associated to lower FA and higher MD, AxD, and RD in the fornix, corpus callosum, inferior longitudinal fasciculus, and hippocampus. The association between AxD and Aβ42 was moderated by 7K-C (p = 0.048). Conclusion:This study adds clinical evidence to support the role of 7K-C on axonal integrity and the involvement of cholesterol metabolism in the Aβ42 generation process