Crump-Mode-Jagers Branching Process: Modelling and Application for Human Population

2010 Mathematics Subject Classification: 60J85, 92D25.

Assessing the queuing process using data envelopment analysis:an application in health centres

Queuing is one of the very important criteria for assessing the performance and efficiency of any service industry, including healthcare. Data Envelopment Analysis (DEA) is one of the most widely-used techniques for performance measurement in healthcare. However, no queue management application has been reported in the health-related DEA literature. Most of the studies regarding patient flow systems had the objective of improving an already existing Appointment System. The current study presents a novel application of DEA for assessing the queuing process at an Outpatients’ department of a large public hospital in a developing country where appointment systems do not exist. The main aim of the current study is to demonstrate the usefulness of DEA modelling in the evaluation of a queue system. The patient flow pathway considered for this study consists of two stages; consultation with a doctor and pharmacy. The DEA results indicated that waiting times and other related queuing variables included need considerable minimisation at both stages.

Numerical modelling of multimode fibre-optic communication lines

The results of numerical modelling of nonlinear propagation of an optical signal in multimode fibres with a small differential group delay are presented. It is found that the dependence of the error vector magnitude (EVM) on the differential group delay can be reduced by increasing the number of ADC samples per symbol in the numerical implementation of the differential group delay compensation algorithm in the receiver. The possibility of using multimode fibres with a small differential group delay for data transmission in modern digital communication systems is demonstrated. It is shown that with increasing number of modes the strong coupling regime provides a lower EVM level than the weak coupling one.

Modelling markets

Decision makers in marketing are often faced with rather complicated situations in which decisions have to be made. Let us consider the problem of determining the appropriate advertising budget. A brand manager is asked to determine the optimal budget. He knows that increases in advertising may lead to increased sales, but also lead to increased costs. The advertising expenditures in period t, say 1994, may not only lead to increases in sales in t, but also to increases in t + 1 (1995) and possibly may contribute to the value of the brand for a long time period.2 Increases in sales will result in changes in profit. The decision maker is allowed to spend more advertising money if there is more profit and more sales, thus advertising spending depends on past sales and profit performance. In order to account for these and possibly other relationships it is necessary to formalise these relations. This means that the decision maker has to specify which variables influence which other variables and what the directions of causality between these variables are. To this end a model has to be formalised, data have to be collected and the formalised model has to be calibrated.

A virtual species set for robust and reproducible species distribution modelling tests

Predicting species potential and future distribution has become a relevant tool in biodiversity monitoring and conservation.In this data article we present the suitability map of a virtual species generated based on two bioclimatic variables, and a dataset containing more than 700,000 random observations at the extent of Europe. The dataset includes spatial attributes such as: distance to roads, protected areas, country codes, and the habitat suitability of two spatially clustered species (grassland and forest species) and a wide-spread species.

Modelling and linking transformations in EPCIS governing supply chain business processes

Supply chains comprise of complex processes spanning across multiple trading partners. The various operations involved generate large number of events that need to be integrated in order to enable internal and external traceability. Further, provenance of artifacts and agents involved in the supply chain operations is now a key traceability requirement. In this paper we propose a Semantic web/Linked data powered framework for the event based representation and analysis of supply chain activities governed by the EPCIS specification. We specifically show how a new EPCIS event type called "Transformation Event" can be semantically annotated using EEM - The EPCIS Event Model to generate linked data, that can be exploited for internal event based traceability in supply chains involving transformation of products. For integrating provenance with traceability, we propose a mapping from EEM to PROV-O. We exemplify our approach on an abstraction of the production processes that are part of the wine supply chain.

Sensing information modelling for smart city

Sensing technology is a key enabler of the Internet of Things (IoT) and could produce huge volume data to contribute the Big Data paradigm. Modelling of sensing information is an important and challenging topic, which influences essentially the quality of smart city systems. In this paper, the author discusses the relevant technologies and information modelling in the context of smart city and especially reports the investigation of how to model sensing and location information in order to support smart city development.

Better queue management in a busy public hospital of a developing country without appointment system::an application using data envelopment analysis

Queuing is a key efficiency criterion in any service industry, including Healthcare. Almost all queue management studies are dedicated to improving an existing Appointment System. In developing countries such as Pakistan, there are no Appointment Systems for outpatients, resulting in excessive wait times. Additionally, excessive overloading, limited resources and cumbersome procedures lead to over-whelming queues. Despite numerous Healthcare applications, Data Envelopment Analysis (DEA) has not been applied for queue assessment. The current study aims to extend DEA modelling and demonstrate its usefulness by evaluating the queue system of a busy public hospital in a developing country, Pakistan, where all outpatients are walk-in; along with construction of a dynamic framework dedicated towards the implementation of the model. The inadequate allocation of doctors/personnel was observed as the most critical issue for long queues. Hence, the Queuing-DEA model has been developed such that it determines the ‘required’ number of doctors/personnel. The results indicated that given extensive wait times or length of queue, or both, led to high target values for doctors/personnel. Hence, this crucial information allows the administrators to ensure optimal staff utilization and controlling the queue pre-emptively, minimizing wait times. The dynamic framework constructed, specifically targets practical implementation of the Queuing-DEA model in resource-poor public hospitals of developing countries such as Pakistan; to continuously monitor rapidly changing queue situation and display latest required personnel. Consequently, the wait times of subsequent patients can be minimized, along with dynamic staff scheduling in the absence of appointments. This dynamic framework has been designed in Excel, requiring minimal training and work for users and automatic update features, with complex technical aspects running in the background. The proposed model and the dynamic framework has the potential to be applied in similar public hospitals, even in other developing countries, where appointment systems for outpatients are non-existent.

A villamos erőművek szén-dioxid-kibocsátásának modellezése reálopciók segítségével = Modelling of the carbon dioxide emissions of a power plant, using real options

A szerző egy, a szennyezőanyag-kibocsátás európai kereskedelmi rendszerében megfelelésre kötelezett gázturbinás erőmű szén-dioxid-kibocsátását modellezi négy termékre (völgy- és csúcsidőszaki áramár, gázár, kibocsátási kvóta) vonatkozó reálopciós modell segítségével. A profitmaximalizáló erőmű csak abban az esetben termel és szennyez, ha a megtermelt áramon realizálható fedezete pozitív. A jövőbeli időszak összesített szén-dioxid-kibocsátása megfeleltethető európai típusú bináris különbözetopciók összegének. A modell keretein belül a szén-dioxid-kibocsátás várható értékét és sűrűségfüggvényét becsülhetjük, az utóbbi segítségével a szén-dioxid-kibocsátási pozíció kockáztatott értékét határozhatjuk meg, amely az erőmű számára előírt megfelelési kötelezettség teljesítésének adott konfidenciaszint melletti költségét jelenti. A sztochasztikus modellben az alaptermékek geometriai Ornstein-Uhlenbeck-folyamatot követnek. Ezt illesztette a szerző a német energiatőzsdéről származó publikus piaci adatokra. A szimulációs modellre támaszkodva megvizsgálta, hogy a különböző technológiai és piaci tényezők ceteris paribus megváltozása milyen hatással van a megfelelés költségére, a kockáztatott értékére. ______ The carbon-dioxide emissions of an EU Emissions Trading System participant, gas-fuelled power generator are modelled by using real options for four underlying instruments (peak and off-peak electricity, gas, emission quota). This profit-maximizing power plant operates and emits pollution only if its profit (spread) on energy produced is positive. The future emissions can be estimated by a sum of European binary-spread options. Based on the real-option model, the expected value of emissions and its probability-density function can be deducted. Also calculable is the Value at Risk of emission quota position, which gives the cost of compliance at a given confidence level. To model the prices of the four underlying instruments, the geometric Ornstein-Uhlenbeck process is supposed and matched to public available price data from EEX. Based on the simulation model, the effects of various technological and market factors are analysed for the emissions level and the cost of compliance.

Evaluation of climate change scenarios based on aquatic food web modelling

In the years 2004 and 2005 we collected samples of phytoplankton, zooplankton and macroinvertebrates in an artificial small pond in Budapest. We set up a simulation model predicting the abundance of the cyclopoids, Eudiaptomus zachariasi and Ischnura pumilio by considering only temperature as it affects the abundance of population of the previous day. Phytoplankton abundance was simulated by considering not only temperature, but the abundance of the three mentioned groups. This discrete-deterministic model could generate similar patterns like the observed one and testing it on historical data was successful. However, because the model was overpredicting the abundances of Ischnura pumilio and Cyclopoida at the end of the year, these results were not considered. Running the model with the data series of climate change scenarios, we had an opportunity to predict the individual numbers for the period around 2050. If the model is run with the data series of the two scenarios UKHI and UKLO, which predict drastic global warming, then we can observe a decrease in abundance and shift in the date of the maximum abundance occurring (excluding Ischnura pumilio, where the maximum abundance increases and it occurs later), whereas under unchanged climatic conditions (BASE scenario) the change in abundance is negligible. According to the scenarios GFDL 2535, GFDL 5564 and UKTR, a transition could be noticed.

Analysis of climate change scenarios based on modelling of the seasonal dynamics of a Danubian copepod species

Climate change is one of the most crucial ecological problems of our age with great influence. Seasonal dynamics of aquatic communities are — among others — regulated by the climate, especially by temperature. In this case study we attempted the simulation modelling of the seasonal dynamics of a copepod species, Cyclops vicinus, which ranks among the zooplankton community, based on a quantitative database containing ten years of data from the Danube’s Göd area. We set up a simulation model predicting the abundance of Cyclops vicinus by considering only temperature as it affects the abundance of population. The model was adapted to eight years of daily temperature data observed between 1981 and 1994 and was tested successfully with the additional data of two further years. The model was run with the data series of climate change scenarios specified for the period around 2070- 2100. On the other hand we looked for the geographically analogous areas with the Göd region which are mostly similar to the future climate of the Göd area. By means of the above-mentioned points we can get a view how the climate of the region will change by the end of the 21st century, and the way the seasonal dynamics of a chosen planktonic crustacean species may follow this change. According to our results the area of Göd will be similar to the northern region of Greece. The maximum abundance of the examined species occurs a month to one and a half months earlier, moreover larger variances are expected between years in respect of the abundance. The deviations are expected in the direction of smaller or significantly larger abundance not observed earlier.

Trends in research on the possible effects of climate change concerning aquatic ecosystems with special emphasis on the modelling approach

Knowledge on the expected effects of climate change on aquatic ecosystems is defined by three ways. On the one hand, long-term observation in the field serves as a basis for the possible changes; on the other hand, the experimental approach may bring valuable pieces of information to the research field. The expected effects of climate change cannot be studied by empirical approach; rather mathematical models are useful tools for this purpose. Within this study, the main findings of field observations and their implications for future were summarized; moreover, the modelling approaches were discussed in a more detailed way. Some models try to describe the variation of physical parameters in a given aquatic habitat, thus our knowledge on their biota is confined to the findings based on our present observations. Others are destined for answering special issues related to the given water body. Complex ecosystem models are the keys of our better understanding of the possible effects of climate change. Basically, these models were not created for testing the influence of global warming, rather focused on the description of a complex system (e. g. a lake) involving environmental variables, nutrients. However, such models are capable of studying climatic changes as well by taking into consideration a large set of environmental variables. Mostly, the outputs are consistent with the assumptions based on the findings in the field. Since synthetized models are rather difficult to handle and require quite large series of data, the authors proposed a more simple modelling approach, which is capable of examining the effects of global warming. This approach includes weather dependent simulation modelling of the seasonal dynamics of aquatic organisms within a simplified framework.

Analyzing interrelated stochastic trend and seasonality on the example of energy trading data

The correct modelling of long- and short-term seasonality is a very interesting issue. The choice between the deterministic and stochastic modelling of trend and seasonality and their implications are as relevant as the case of deterministic and stochastic trends itself. The study considers the special case when the stochastic trend and seasonality do not evolve independently and the usual differencing filters do not apply. The results are applied to the day-ahead (spot) trading data of some main European energy exchanges (power and natural gas).

Analyzing interrelated stochastic trend and seasonality on the example of energy trading data

The correct modelling of long- and short-term seasonality is a very interesting issue. The choice between the deterministic and stochastic modelling of trend and seasonality and their implications are as relevant as the case of deterministic and stochastic trends itself. The study considers the special case when the stochastic trend and seasonality do not evolve independently and the usual differencing filters do not apply. The results are applied to the day-ahead (spot) trading data of some main European energy exchanges (power and natural gas).