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Malaria is caused by Plasmodium parasites transmitted to humans by the bite of an infected Anopheles mosquito. Plasmodium vivax is distinct from other malaria species in its ability to remain dormant in the liver (as hypnozoites) and activate later to cause further infections (referred to as relapses). For this reason, P. vivax is currently the most geographically widespread malaria-causing parasite resulting in significant associated global morbidity and mortality. As around 79–96% of infections are attributed to relapses from activating hypnozoites, targeting the hypnozoite reservoir (i.e., the collection of dormant parasites) to eliminate P. vivax is crucial. Mathematical models to describe the transmission dynamics of P. vivax have been developed, but most fail to capture realistic hypnozoite dynamics. Models that capture the complexity tend to involve many governing equations, making them difficult to extend to incorporate other important factors for P. vivax, such as treatment status, age, and pregnancy. In this thesis, we have developed a multiscale model (a system of integro-differential equations) that involves a minimal set of equations at the population scale, with an embedded within-host model that captures the dynamics of the hypnozoite reservoir and accounts for superinfection and mosquito seasonality. In this way, we can gain critical insights into the dynamics of P. vivax transmission with a minimum number of equations at the population scale, making this framework readily scalable to incorporate more complexity. We use our multiscale model to study the effect of radical cure (drugs that affect hypnozoites) treatment administered via a mass drug administration (MDA) program accounting for superinfection (infectious bites and/or the activation of hypnozoites can trigger multiple infections). We explicitly model the impact of the radical cure drug on each of the hypnozoites and infections. An optimisation model with different objective functions motiva

To maximise the value of a mining operation and minimise its environmental and social impacts, all processes - from the ore deposit to the final product and waste streams - should be optimised together. However, mining and metallurgical processes are inherently variable and uncertain due to the natural heterogeneity of ore deposits and the limited information and incomplete models available on ore behaviour throughout the process chain. Propagating these effects to geometallurgical models is important because they are used to make decisions with potentially large environmental and economic impacts. In this paper, we describe the need for geometallurgical optimisation routines to account for the effects of uncertainties, and the tools needed to manage them, by summarising the routines that already exist and those that are still missing.

Financial markets continue to see an increase in the share of trades executed by algorithmic trading systems. A key component of an efficient algorithmic trading system is its ability to accurately estimate the probability an order will be executed: the fill probability. This thesis aims to determine whether the dynamics of the order book can be captured accurately by a stochastic model, which subsequently leads to the following research question: Can we accurately compute fill probabilities of limit orders, conditional on the state of the order book? Our research builds upon the stochastic model proposed by Cont, Stoikov and Talreja, which assumes orders and cancellations have unit size and arrive according to independent Poisson processes [12]. There are two main advantages of the model proposed by Cont et al., which include: • Straightforward parameter estimation based on observable order book data, • The possibility to compute various probabilities of interest semi-analytically. These probabilities include the fill probability of limit orders and the direction of the next mid-price move. In this model, the number of orders at each price level in the order book is modelled as a birth-death process, in which births represent an increase in the number of orders and conversely, deaths represent a decrease. The first-passage time is the time it takes for such a process to reach a certain state for the first time. Since the order arrivals follow Poisson processes, we can find an expression for the Laplace transforms of the density functions of the first-passage times. By numerically inverting these Laplace transforms we can calculate the probabilities of interest. The parameters of the Poisson processes that determine the arrivals of orders are calibrated using observable order book data of the Euro-US Dollar currency pair of the foreign exchange (FX) spot market. We extend the model of Cont et al. by integrating spread-dependent arrival rates of orders and cancellati, Applied Mathematics | Financial Engineering

This research extends previous plant modelling using L-systems by means of a novel arrangement comprising synthetic plants and a refined global wheat dataset in combination with a synthetic inference application. The study demonstrates an application with direct recognition of real plant stereotypes, and augmentation via a plant-wide stochastic growth variation structure. The study showed that the automatic annotation and counting of wheat heads using the Global Wheat dataset images provides a time and cost saving over traditional manual approaches and neural networks. This study introduces a novel synthetic inference application using a plant-wide stochastic variation system, resulting in improved structural dataset hierarchy. The research demonstrates a significantly improved L-system that can more effectively and more accurately define and distinguish wheat crop characteristics.

Autonomous robots are often successfully deployed in controlled environments. Operation in uncontrolled situations remains challenging; it is hypothesized that the detection of abstract discrete states (ADS) can improve operation in these circumstances. ADS are high-level system states that are not directly detectable and influence system dynamics. An example of a typical ADS problem that is used in this thesis is that of a wheeled robot driving through puddles of mud that, when entered, alters the velocity of the robot. When the robot is in such a puddle, it is in an ADS 'mud', and when it is not, it is in an ADS 'free'. ADS can be indirectly inferred through the analysis of lower-level data such as the velocity of the robot. The goal of this thesis is to design a general abstract discrete state estimator (ADSE) operating with limited prior knowledge. An ADSE is a hierarchical system for detecting changes in ADS. The ADSE should be general; applicable to multiple ADSE problems. The ADSE should further operate under limited prior knowledge: only assuming that the amount of ADS and the ADS that describes the regular operation are known. The basis for the ADSE designed in this thesis is a Gaussian hidden Markov model (GHMM), a hidden Markov model enhanced with Gaussian emissions. Randomly generated experiments are done on a simple but general ADSE problem. Two unsupervised learning methods derived from Expectation Maximization are evaluated, namely Baum-Welch (BW) and forward extraction (FWE). FWE is introduced in this thesis and is a simpler implementation of Viterbi extraction, leveraging assumptions of ADSE to in theory gain computational efficiency. We found that both BW and FWE exhibit superior performance compared to a likelihood-based baseline estimator when the maximum score of the learning curve is considered. When the final score is considered, in some cases, FWE displays a deteriorating learning curve, resulting in worse final scores com, https://github.com/Wouter-deBoer/adse, Mechanical Engineering | Vehicle Engineering | Cognitive Robotics

Current indoor air quality strategies are based on the measurement and control of carbon dioxide (CO2) indoor concentration. Most educational buildings rely only on natural ventilation, making indoor air quality highly dependent on weather conditions. Therefore, to ensure the safety and well-being of students and teachers, it is necessary to determine the factors influencing CO2 concentration in naturally ventilated spaces. The aim of this paper is to estimate the students’ CO2 emission rates in naturally ventilated classrooms using grey box models., Peer Reviewed, Objectius de Desenvolupament Sostenible::3 - Salut i Benestar, Postprint (published version)

Bleed–feed is a novel technology that allows biomanufacturers to skip bioreactor setups. However, the time at which bleed–feed is performed is important for its successful implementation. In addition, bleed–feed operations involve unique trade-offs that affect the system's throughput. For example, the biomass replenishment amount during bleed–feed affects the expected yield of the system. In this study, we formalise these operational trade-offs and formulate a stochastic optimisation model using renewal reward theory. Our analytical model captures both the biological dynamics and operational trade-offs of bleed–feed decisions to maximise throughput. We present an industry case study to demonstrate the use of our model. Through several practically relevant scenarios, we assess the potential impact of implementing bleed–feed on current practice and develop insights for practitioners. Although our work is primarily motivated by the biomanufacturing industry, our analytical model and insights are applicable to other industries that involve fermentation. Our results show that bleed–feed brings the most benefit for fast-growing cells or high-risk cultures. Although counter-intuitive, our numerical analysis shows that it is optimal not to adopt bleed–feed when biomass accumulation is too slow.

Autoignition risk in initially non-premixed flowing systems, such as premixing ducts, must be assessed to help the development of low-NOx systems and hydrogen combustors. Such situations may involve randomly fluctuating inlet conditions that are challenging to model in conventional mixture-fraction-based approaches. A Computational Fluid Dynamics (CFD)-based surrogate modelling strategy is presented here for fast and accurate predictions of the stochastic autoignition behaviour of a hydrogen flow in a hot air turbulent co-flow. The variability of three input parameters, i.e. inlet fuel and air temperatures and average wall temperature, is first sampled via a space-filling design. For each sampled set of conditions, the CFD modelling of the flame is performed via the Incompletely Stirred Reactor Network (ISRN) approach, which solves the reacting flow governing equations in post-processing on top of a Large Eddy Simulation (LES) of the inert hydrogen plume. An accurate surrogate model, namely a Gaussian Process, is then trained on the ISRN simulations of the burner, and the final quantification of the variability of autoignition locations is achieved by querying the surrogate model via Monte Carlo sampling of the random input quantities. The results are in agreement with the observed statistics of the autoignition locations. The methodology adopted in this work can be used effectively to quantify the impact of fluctuations and assist the design of practical combustion systems., SCOPUS: ar.j, info:eu-repo/semantics/published

DNA methylation occurs predominantly on cytosine-phosphate-guanine (CpG) dinucleotides in the mammalian genome, and the methylation landscape is maintained over mitotic cell division. It has been posited that coupling of maintenance methylation activity among neighbouring CpGs is critical to stability over cellular generations; however, the mechanism is unclear. We used mathematical models and stochastic simulation to analyse data from experiments that probe genome-wide methylation of nascent DNA post-replication in cells. We find that DNA methylation maintenance rates on individual CpGs are locally correlated, and the degree of this correlation varies by genomic regional context. By using theory of protein diffusion along DNA, we show that exponential decay of methylation rate correlation with genomic distance is consistent with enzyme processivity. Our results provide quantitative evidence of genome-wide methyltransferase processivity in vivo. We further developed a method to disentangle different mechanistic sources of kinetic correlations. From the experimental data, we estimate that an individual methyltransferase methylates neighbour CpGs processively if they are 36 basepairs apart, on average. But other mechanisms of coupling dominate for longer inter-CpG distances. Our study demonstrates that quantitative insights into enzymatic mechanisms can be obtained from replication-associated, cell-based genome-wide measurements, by combining data-driven statistical analyses with hypothesis-driven mathematical modelling.

Construction noise monitoring is crucial to assess the impacts of construction noise on the workers and surroundings. However, the existing noise prediction methods are time-consuming in which required laborious work for the computation of noise levels. This study aims to assess the accuracy and reliability of deep learning model (DL) that adopted stochastic modelling and artificial neural network (ANN) in construction noise prediction. The artificial neural network was trained with the output of stochastic modelling. The outcome of noise level prediction using simple prediction chart (SPC) and DL model was discussed and compared to 3 case studies. The case studies were conducted at construction sites located in Semenyih, Selangor, Malaysia. The results of DL model showed high accuracy of predicted noise levels along with an absolute difference of less than 2.3 dBA. Besides, the predicted noise levels are reliable as the R-squared value is higher than 0.992. On that account, DL model is proved to be reliable and accurate in noise level prediction and it has the potential to be utilized as a managerial tool to monitor construction noise more effectively.

Conceptual models are indispensable tools for hydrology. In order to use them for making probabilistic predictions, they need to be equipped with an adequate error model, which, for ease of inference, is traditionally formulated as an additive error on the output (discharge). However, the main sources of uncertainty in hydrological modelling are typically not to be found on the output, but on the input (rain) and in the model structure. Therefore, more reliable error models and probabilistic predictions can be obtained by incorporating those uncertainties directly where they arise, that is, into the model. This, however, leads us to stochastic models, which render traditional inference algorithms such as the Metropolis algorithm infeasible due to their expensive likelihood functions. However, thanks to recent advancements in algorithms and computing power, full-fledged Bayesian inference with stochastic models is no longer off-limit for hydrological applications. We demonstrate this with a case study from urban hydrology, for which we employ a highly efficient Hamiltonian Monte Carlo inference algorithm with a time-scale separation.

Determination of train positions within a railway network must be fail-safe and of high accuracy. This is an essential task to solve to achieve a secure and efficient railway operation. In this paper, we present a method to estimate position and velocity of a train in the track net using given position estimates from an arbitrary information source, and improving the estimate by using geometrical track information. We focus on modelling and exploiting of the geometrical track information including possible uncertainties and examine the impact of uncertainties on the state estimate. We store the track information as a set of supporting points with Gaussian uncertainties and interpolate linearly. The track information is fed into a Kalman filter in form of soft constraints that is modified to account for state-dependent observation noise. A simulated test run shows that the average position and velocity error along track decreases significantly when modelling the uncertainty of the constraints, compared to using a Kalman filter with hard constraints. We evaluate the presented filter for different supporting point and measurement uncertainties and show that the performance within a typical parameter setting for train positioning is improved compared to the unconstrained Kalman filter and the Kalman filter with hard constraints., QC 20221025QC 20230626

Conceptual models are indispensable tools for hydrology. In order to use them for making probabilistic predictions, they need to be equipped with an adequate error model, which, for ease of inference, is traditionally formulated as an additive error on the output (discharge). However, the main sources of uncertainty in hydrological modelling are typically not to be found on the output, but on the input (rain) and in the model structure. Therefore, more reliable error models and probabilistic predictions can be obtained by incorporating those uncertainties directly where they arise, that is, into the model. This, however, leads us to stochastic models, which render traditional inference algorithms such as the Metropolis algorithm infeasible due to their expensive likelihood functions. However, thanks to recent advancements in algorithms and computing power, full-fledged Bayesian inference with stochastic models is no longer off-limit for hydrological applications. We demonstrate this with a case study from urban hydrology, for which we employ a highly efficient Hamiltonian Monte Carlo inference algorithm with a time-scale separation.

Construction noise monitoring is crucial to assess the impacts of construction noise on the workers and surroundings. However, the existing noise prediction methods are time-consuming in which required laborious work for the computation of noise levels. This study aims to assess the accuracy and reliability of deep learning model (DL) that adopted stochastic modelling and artificial neural network (ANN) in construction noise prediction. The artificial neural network was trained with the output of stochastic modelling. The outcome of noise level prediction using simple prediction chart (SPC) and DL model was discussed and compared to 3 case studies. The case studies were conducted at construction sites located in Semenyih, Selangor, Malaysia. The results of DL model showed high accuracy of predicted noise levels along with an absolute difference of less than 2.3 dBA. Besides, the predicted noise levels are reliable as the R-squared value is higher than 0.992. On that account, DL model is proved to be reliable and accurate in noise level prediction and it has the potential to be utilized as a managerial tool to monitor construction noise more effectively.

The field of finance is an interesting field in which much research takes place. In particular, its sub-field of modeling the dynamics of order books is an interesting field, since it translates into modeling the behaviour of traders on the market. Most of the models proposed in this field can be divided into stochastic models or machine learning models. The problem with the former ones is that they often make assumptions that do not propagate to practical applications, while the problem with the latter is that the models are often incomprehensible, even though they yield good results. This work tries to combine both of those fields to maintain the transparency of stochastic models and the accuracy of machine learning models. We target the limit order book, which is a book used in financial markets to place orders for financial securities in. It is a challenge to both generate realistic order books and predict them as well, since the model should be able to understand the underlying dynamics of order books to do this. We present a deep-learning-based model that is able to generate order books, through the use of a generative adversarial network (GAN) like architecture, and is able to predict order books using a similar architecture for the generator. Our models are able to outperform traditional generative and predictive models in both instances, while it remains transparent in its calculation: it is still able to extract useful and interpretable features from the underlying data set. These features, like the probabilities for up or down movements, or stagnations, or the rates at which the variables within the order book move, can be used by traders or algorithms to make sense out of the predictions. Traders can, for example, ask themselves whether the extracted features are representative of the analyzed asset and can, through this question, build additional confidence in the model. Another use case could be to utilize those features as inputs to other models. To o

Expansions for future demand? How much capacity will be required? Until when the decision can be postponed? When to expand? What should be the magnitude of expansion? What is the position of such an investment? These are the kind of questions which a port authority is subjected to while making a decision to expand or develop a port. The decision to invest in the expansion of the port is based on the anticipation of the market in future. The port authorities try to bridge the gap between “What the port is doing?” and “What the port should be doing?”. The choice of timing and expansion is of extreme importance as it allows the port authority to ensure that the project is financially viable and at the same time they achieve its objectives. During the feasibility stages, while making these decisions, a static discounted cash flow (DCF) model is used to calculate the financial outcomes of the expansion plans. However, such a model gives an impression that the decision-maker is obliged to the expansion decisions and cannot delay or alter their scale of investments. However, the reality is otherwise, the decision-maker is an active manager, who adapts the development/expansion plans to the changes based on the project progress. The current study presents an alternative to the Predict and Control approach of the static DCF model. This is done using Real Options Analysis(ROA). Within the scope of the research, a conceptual framework for ROA for port decision making was derived. The conceptual framework is translated into a mathematical numerical model for a test case in Southeast Africa. The numerical model values the option of multi-stage capacity expansion for the port. Focus is maintained on incorporating flexibility “on” infrastructure based on timing and magnitude under the uncertainty of demand. Through the use of stochastic processes, Monte Carlo simulations, solution algorithm and sensitivity analysis a total of 96 strategies have been evaluated. T

The field of finance is an interesting field in which much research takes place. In particular, its sub-field of modeling the dynamics of order books is an interesting field, since it translates into modeling the behaviour of traders on the market. Most of the models proposed in this field can be divided into stochastic models or machine learning models. The problem with the former ones is that they often make assumptions that do not propagate to practical applications, while the problem with the latter is that the models are often incomprehensible, even though they yield good results. This work tries to combine both of those fields to maintain the transparency of stochastic models and the accuracy of machine learning models. We target the limit order book, which is a book used in financial markets to place orders for financial securities in. It is a challenge to both generate realistic order books and predict them as well, since the model should be able to understand the underlying dynamics of order books to do this. We present a deep-learning-based model that is able to generate order books, through the use of a generative adversarial network (GAN) like architecture, and is able to predict order books using a similar architecture for the generator. Our models are able to outperform traditional generative and predictive models in both instances, while it remains transparent in its calculation: it is still able to extract useful and interpretable features from the underlying data set. These features, like the probabilities for up or down movements, or stagnations, or the rates at which the variables within the order book move, can be used by traders or algorithms to make sense out of the predictions. Traders can, for example, ask themselves whether the extracted features are representative of the analyzed asset and can, through this question, build additional confidence in the model. Another use case could be to utilize those features as inputs to other models. To o

BackgroundSemi-field experiments with human landing catch (HLC) measure as the outcome are an important step in the development of novel vector control interventions against outdoor transmission of malaria since they provide good estimates of personal protection. However, it is often infeasible to determine whether the reduction in HLC counts is due to mosquito mortality or repellency, especially considering that spatial repellents based on volatile pyrethroids might induce both. Due to the vastly different impact of repellency and mortality on transmission, the community-level impact of spatial repellents can not be estimated from such semi-field experiments.MethodsWe present a new stochastic model that is able to estimate for any product inhibiting outdoor biting, its repelling effect versus its killing and disarming (preventing host-seeking until the next night) effects, based only on time-stratified HLC data from controlled semi-field experiments. For parameter inference, a Bayesian hierarchical model is used to account for nightly variation of semi-field experimental conditions. We estimate the impact of the products on the vectorial capacity of the given Anopheles species using an existing mathematical model. With this methodology, we analysed data from recent semi-field studies in Kenya and Tanzania on the impact of transfluthrin-treated eave ribbons, the odour-baited Suna trap and their combination (push–pull system) on HLC of Anopheles arabiensis in the peridomestic area.ResultsComplementing previous analyses of personal protection, we found that the transfluthrin-treated eave ribbons act mainly by killing or disarming mosquitoes. Depending on the actual ratio of disarming versus killing, the vectorial capacity of An. arabiensis is reduced by 41 to 96% at 70% coverage with the transfluthrin-treated eave ribbons and by 38 to 82% at the same coverage with the push–pull system, under the assumption of a similar impact on biting indoors compared to outdoors.Con

Targeted therapies are a mainstay of modern cancer treatments. Rather than harming rapidly dividing cells in general, targeted therapies work by directly interfering with oncogenic molecular pathways present in a tumour. Consequently, a targeted therapy typically has less severe side effects. However, specificity comes at a price as comparatively small changes to the target can render the treatment ineffective. Much like the natural selection among plants and animals, individual cancer cells compete with one another for space and resources. Hence, if a single cancer cell acquires a resistance adaptation, the forces of evolution can turn that advantage in a single cell into an untreatable resistant cancer. This thesis is principally concerned with chronic myeloid leukaemia (CML), characterized by a chromosomal translocation called the Philadelphia chromosome which creates the constitutively active tyrosine kinase Bcr-Abl1. The discovery of tyrosine kinase inhibitors (TKIs) targeting Bcr-Abl1 greatly improved treatment outcomes. Eventually however, resistance emerges. An important mechanism in CML is mutations in the kinase domain of Bcr-Abl1 that affect how well the drugs bind. A number of drugs have been developed that target the mutated kinase to varying degrees, but it is still desirable to prevent drug resistance from occurring in the first place, as the accumulation of multiple mutations is almost certain to create untreatable resistance. The fitness effects of a drug resistance adaptation depend on the drug treatment, so it may be possible to alter the fitness landscape by modifying the treatment. This work examines different approaches, mainly in CML, to delay or prevent the onset of resistance through modifying the treatment protocol. Periodically switching between different TKIs, i.e. drug rotations, was shown through modelling to increase the expected time to resistance and seems to have some protective benefits in vitro. Also apparently promising were drug

Some specialty crops, such as strawberries and table grapes, are harvested by large crews of pickers who spend significant amounts of time carrying empty and full (with the harvested crop) trays. A step toward increasing harvest automation for such crops is to deploy harvest-aid robots that transport the empty and full trays, thus increasing harvest efficiency by reducing pickers’ non-productive walking times. To that end, this work addresses human-robot collaboration modeling in a harvesting context. First, a modeling framework for all-manual and robot-aided harvesting was developed, which can be used for off-line simulation by system designers, but also as a representation model for robot control, during real-time operation. To serve both functions, the framework utilizes hybrid systems to model picker and robot activities. Finite state machines model discrete operating states, and difference equations describe motion and mass transfer within each discrete state. To capture the variability in human behavior and performance during harvesting, the human activity model utilizes stochastic parameters (e.g., picking time, walking speed) that can be estimated by measurements during harvesting. The stochastic model does not require direct yield measurements, which are not available for most specialty crops. Second, a stochastic simulator was developed based on the developed model. For a given field and crew size, the simulator samples all stochastic parameters to generate many instances of the harvest operation, and estimates metrics such as pickers’ non-productive time and harvest operation efficiency. Part II of this work presents the calibration and evaluation of the simulator based on field data, and a case study that evaluates the effect of various robot scheduling algorithms on harvest efficiency.

Classical Continuous System Simulation (CSS) is restricted to modelling continuous flows, and therefore, cannot correctly realise a conceptual model with discrete objects. The development of Full Potential CSS solves this problem by (1) handling discrete quantities as discrete and continuous matter as continuous, (2) preserving the sojourn time distribution of a stage, (3) implementing attributes correctly, and (4) describing different types of uncertainties in a proper way. In order to apply Full Potential CSS a new software, StochSD, has been developed. This thesis evaluates StochSD's ability to model Full Potential CSS, where the points 1-4 above are included. As a test model a well-defined conceptual epidemic model, which includes all aspects of Full Potential CSS, was chosen. The study was performed by starting with a classical SIR model and then stepwise add the different aspects of the Conceptual Model. The effects of each step were demonstrated in terms of size and duration of the epidemic. Finally, the conceptual model was also realised as an Agent Based Model (ABM). The results from 10 000 replications each of the CSS and ABM models were compared and no statistical differences could be confirmed. The conclusion is that StochSD passed the evaluation.

Some specialty crops, such as strawberries and table grapes, are harvested by large crews of pickers who spend significant amounts of time carrying empty and full (with the harvested crop) trays. A step toward increasing harvest automation for such crops is to deploy harvest-aid robots that transport the empty and full trays, thus increasing harvest efficiency by reducing pickers’ non-productive walking times. To that end, this work addresses human-robot collaboration modeling in a harvesting context. First, a modeling framework for all-manual and robot-aided harvesting was developed, which can be used for off-line simulation by system designers, but also as a representation model for robot control, during real-time operation. To serve both functions, the framework utilizes hybrid systems to model picker and robot activities. Finite state machines model discrete operating states, and difference equations describe motion and mass transfer within each discrete state. To capture the variability in human behavior and performance during harvesting, the human activity model utilizes stochastic parameters (e.g., picking time, walking speed) that can be estimated by measurements during harvesting. The stochastic model does not require direct yield measurements, which are not available for most specialty crops. Second, a stochastic simulator was developed based on the developed model. For a given field and crew size, the simulator samples all stochastic parameters to generate many instances of the harvest operation, and estimates metrics such as pickers’ non-productive time and harvest operation efficiency. Part II of this work presents the calibration and evaluation of the simulator based on field data, and a case study that evaluates the effect of various robot scheduling algorithms on harvest efficiency.

Targeted therapies are a mainstay of modern cancer treatments. Rather than harming rapidly dividing cells in general, targeted therapies work by directly interfering with oncogenic molecular pathways present in a tumour. Consequently, a targeted therapy typically has less severe side effects. However, specificity comes at a price as comparatively small changes to the target can render the treatment ineffective. Much like the natural selection among plants and animals, individual cancer cells compete with one another for space and resources. Hence, if a single cancer cell acquires a resistance adaptation, the forces of evolution can turn that advantage in a single cell into an untreatable resistant cancer. This thesis is principally concerned with chronic myeloid leukaemia (CML), characterized by a chromosomal translocation called the Philadelphia chromosome which creates the constitutively active tyrosine kinase Bcr-Abl1. The discovery of tyrosine kinase inhibitors (TKIs) targeting Bcr-Abl1 greatly improved treatment outcomes. Eventually however, resistance emerges. An important mechanism in CML is mutations in the kinase domain of Bcr-Abl1 that affect how well the drugs bind. A number of drugs have been developed that target the mutated kinase to varying degrees, but it is still desirable to prevent drug resistance from occurring in the first place, as the accumulation of multiple mutations is almost certain to create untreatable resistance. The fitness effects of a drug resistance adaptation depend on the drug treatment, so it may be possible to alter the fitness landscape by modifying the treatment. This work examines different approaches, mainly in CML, to delay or prevent the onset of resistance through modifying the treatment protocol. Periodically switching between different TKIs, i.e. drug rotations, was shown through modelling to increase the expected time to resistance and seems to have some protective benefits in vitro. Also apparently promising were drug

Classical Continuous System Simulation (CSS) is restricted to modelling continuous flows, and therefore, cannot correctly realise a conceptual model with discrete objects. The development of Full Potential CSS solves this problem by (1) handling discrete quantities as discrete and continuous matter as continuous, (2) preserving the sojourn time distribution of a stage, (3) implementing attributes correctly, and (4) describing different types of uncertainties in a proper way. In order to apply Full Potential CSS a new software, StochSD, has been developed. This thesis evaluates StochSD's ability to model Full Potential CSS, where the points 1-4 above are included. As a test model a well-defined conceptual epidemic model, which includes all aspects of Full Potential CSS, was chosen. The study was performed by starting with a classical SIR model and then stepwise add the different aspects of the Conceptual Model. The effects of each step were demonstrated in terms of size and duration of the epidemic. Finally, the conceptual model was also realised as an Agent Based Model (ABM). The results from 10 000 replications each of the CSS and ABM models were compared and no statistical differences could be confirmed. The conclusion is that StochSD passed the evaluation.

Targeted therapies are a mainstay of modern cancer treatments. Rather than harming rapidly dividing cells in general, targeted therapies work by directly interfering with oncogenic molecular pathways present in a tumour. Consequently, a targeted therapy typically has less severe side effects. However, specificity comes at a price as comparatively small changes to the target can render the treatment ineffective. Much like the natural selection among plants and animals, individual cancer cells compete with one another for space and resources. Hence, if a single cancer cell acquires a resistance adaptation, the forces of evolution can turn that advantage in a single cell into an untreatable resistant cancer. This thesis is principally concerned with chronic myeloid leukaemia (CML), characterized by a chromosomal translocation called the Philadelphia chromosome which creates the constitutively active tyrosine kinase Bcr-Abl1. The discovery of tyrosine kinase inhibitors (TKIs) targeting Bcr-Abl1 greatly improved treatment outcomes. Eventually however, resistance emerges. An important mechanism in CML is mutations in the kinase domain of Bcr-Abl1 that affect how well the drugs bind. A number of drugs have been developed that target the mutated kinase to varying degrees, but it is still desirable to prevent drug resistance from occurring in the first place, as the accumulation of multiple mutations is almost certain to create untreatable resistance. The fitness effects of a drug resistance adaptation depend on the drug treatment, so it may be possible to alter the fitness landscape by modifying the treatment. This work examines different approaches, mainly in CML, to delay or prevent the onset of resistance through modifying the treatment protocol. Periodically switching between different TKIs, i.e. drug rotations, was shown through modelling to increase the expected time to resistance and seems to have some protective benefits in vitro. Also apparently promising were drug

Targeted therapies are a mainstay of modern cancer treatments. Rather than harming rapidly dividing cells in general, targeted therapies work by directly interfering with oncogenic molecular pathways present in a tumour. Consequently, a targeted therapy typically has less severe side effects. However, specificity comes at a price as comparatively small changes to the target can render the treatment ineffective. Much like the natural selection among plants and animals, individual cancer cells compete with one another for space and resources. Hence, if a single cancer cell acquires a resistance adaptation, the forces of evolution can turn that advantage in a single cell into an untreatable resistant cancer. This thesis is principally concerned with chronic myeloid leukaemia (CML), characterized by a chromosomal translocation called the Philadelphia chromosome which creates the constitutively active tyrosine kinase Bcr-Abl1. The discovery of tyrosine kinase inhibitors (TKIs) targeting Bcr-Abl1 greatly improved treatment outcomes. Eventually however, resistance emerges. An important mechanism in CML is mutations in the kinase domain of Bcr-Abl1 that affect how well the drugs bind. A number of drugs have been developed that target the mutated kinase to varying degrees, but it is still desirable to prevent drug resistance from occurring in the first place, as the accumulation of multiple mutations is almost certain to create untreatable resistance. The fitness effects of a drug resistance adaptation depend on the drug treatment, so it may be possible to alter the fitness landscape by modifying the treatment. This work examines different approaches, mainly in CML, to delay or prevent the onset of resistance through modifying the treatment protocol. Periodically switching between different TKIs, i.e. drug rotations, was shown through modelling to increase the expected time to resistance and seems to have some protective benefits in vitro. Also apparently promising were drug

Targeted therapies are a mainstay of modern cancer treatments. Rather than harming rapidly dividing cells in general, targeted therapies work by directly interfering with oncogenic molecular pathways present in a tumour. Consequently, a targeted therapy typically has less severe side effects. However, specificity comes at a price as comparatively small changes to the target can render the treatment ineffective. Much like the natural selection among plants and animals, individual cancer cells compete with one another for space and resources. Hence, if a single cancer cell acquires a resistance adaptation, the forces of evolution can turn that advantage in a single cell into an untreatable resistant cancer. This thesis is principally concerned with chronic myeloid leukaemia (CML), characterized by a chromosomal translocation called the Philadelphia chromosome which creates the constitutively active tyrosine kinase Bcr-Abl1. The discovery of tyrosine kinase inhibitors (TKIs) targeting Bcr-Abl1 greatly improved treatment outcomes. Eventually however, resistance emerges. An important mechanism in CML is mutations in the kinase domain of Bcr-Abl1 that affect how well the drugs bind. A number of drugs have been developed that target the mutated kinase to varying degrees, but it is still desirable to prevent drug resistance from occurring in the first place, as the accumulation of multiple mutations is almost certain to create untreatable resistance. The fitness effects of a drug resistance adaptation depend on the drug treatment, so it may be possible to alter the fitness landscape by modifying the treatment. This work examines different approaches, mainly in CML, to delay or prevent the onset of resistance through modifying the treatment protocol. Periodically switching between different TKIs, i.e. drug rotations, was shown through modelling to increase the expected time to resistance and seems to have some protective benefits in vitro. Also apparently promising were drug

Pollution build-up and wash-off processes are often included in urban stormwater quality models. However, these models are often unreliable and have poor performance at large scales and in complicated catchments. This study tried to improve stormwater quality models by adopting the genetic programming (GP) approach to generate new build-up algorithms for three different pollutants (total suspend solids – TSS, total phosphorus – TP and total nitrogen – TN). This was followed by testing of the new models (also traditional build-up and wash-off models as benchmark) using data collected from different catchments in Australia and the USA. The GP approach informed new sets of build-up algorithms with the inclusion of not just the typical antecedent dry weather period (ADWP), but also other less ‘traditional’ variables - previous rainfall depth for TSS and maximum air temperatures for TP and TN simulation. The traditional models had relatively poor performance (Nash-Sutcliffe coefficient, E < 0.0), except for TP at Gilby Road (GR) (E = 0.21 in calibration and 0.43 in validation). Improved performance was observed using the models with new build-up algorithms informed by GP. Taking TP at GR for example, the best performing model had E of 0.46 in calibration and 0.54 in validation. The best performing models for TSS, TP, and TN are often different, suggesting that specific models shall be used for different pollutants. Insights into further improvements possible for stormwater quality models were given. It is recommended that in addition to the typical build-up and wash-off process, new generations of stormwater quality models should be able to account for the non-conventional pollutant sources (e.g. cross-connections, septic tank leakage, illegal discharges) through stochastic approaches. Emission inventories with information like intensity-frequency-duration (IFD) of pollutant loads from each type of non-conventional source are suggested to be built for stochastic model

Uganda is using a strategy called treatment as prevention where as many individuals as possible that are infected with HIV receive treatment. As a result, the number of newly infected individuals has decreased significantly. However, there is a discussion about a potential problem regarding transmitted drug resistance. This work aims to investigate if this in fact will be a problem in the future, and to estimate the costs for different scenarios. Through developing a population-based mathematical model that describes transmission dynamics of HIV in Uganda, stochastic simulations are made for different conditions. Through analysing our simulations, we can see that Uganda may have to change their approach to HIV treatment., För att minska smittoriskerna av HIV nyttjar Uganda en strategi som syftar till att behandla så många smittade personer som möjligt. Detta har lett till en signifikant minskning av antalet smittade personer. Det har dock uppstått en diskussion angående om läkemedels-resistent smitta kan komma att utgöra ett problem. Detta arbete syftar till att undersöka om detta kan utgöra ett problem i framtiden samt till att uppskatta de kostnader som kan uppstå i olika typer av scenarion. Under olika förutsättningar genomförs stokastiska simuleringar med hjälp av en matematisk populationsmodell framtagen för att beskriva spridningen av HIV i Uganda. Genom att analysera resultaten från olika simuleringar dras slutsatsen att Uganda kan behöva omvärdera sitt tillvägagångssätt gällande behandling av HIV.

Time-series of cosmogenic radionuclides stored in natural archives such as ice cores and tree rings are a proxy for solar magnetic activity on multi-millennial time-scales. Radionuclides data exhibit a number of interesting features such as intermittent stable cycles of high periods and Grand Minima. Although a lot of effort has gone into the development of sound physically based stochastic solar dynamo models, it is still largely unclear what are the underlying mechanisms that lead to the observed phenomena. Answering these questions requires quantitatively calibrating the models to the data and comparing performances of different models with the associated uncertainties in model parameters and predictions. Bayesian statistics is a consistent framework for parameter inference where knowledge about model parameters is expressed through probability distributions and updated using measured data. However, Bayesian inference with non-linear stochastic models can become computationally extremely expensive and it is therefore hardly ever applied. In recent years, sophisticated and scalable algorithms have emerged, which have the potential of making Bayesian inference for complex stochastic models feasible. We intend to investigate the power of Approximate Bayesian Computation (ABC) and Hamiltonian Monte Carlo (HMC) algorithms. We present our first inference results with stochastic solar dynamo models.

This study examines a method for a stochastic beach width prediction with a process-based morphodynamic model. This is carried out by a case study at the Hondsbossche Dunes, after a beach nourishment in March 2018. Stochastic forcing conditions are generated for the location of the Hondsbossche Dunes. These stochastic forcing conditions consist of time series with significant wave heights, peak wave periods, wave directions, and water levels. The basis of the method for generating these stochastic forcing conditions are Autoregressive-Moving Average (ARMA) models. The morphological change of the beach width due to these stochastic forcing conditions is modelled using an XBeach model. This results in a range of the possible development of the beach width, with the probability of occurrence. With the method examined in this study, a more realistic idea of the possible future beach width development can be given., Civil Engineering

[EN] The aim of this paper is to show a methodology, based on the so-called Lognormal Model, to describe the dynamics of underlying assets by taking into account the uncertainty of nancial markets. In spite of its simple formulation, the Lognormal Model is a valuable tool from a formative standpoint becauseit provides an excellent basis to study more advanced models. The proposed approach has been put into practice by the authors in their teaching in both undergraduate and postgraduate studies. We present the model and its application to describe the dynamics of real data of an asset traded in the Spanish stock market index IBEX35., [ES] El objetivo de este trabajo es mostrar una metodología estocástica, basada en el denominado Modelo Lognormal, para modelizar la dinámica de subyacentes cotizados teniendo en cuenta la incertidumbre de los mercados financieros. Se trata de un modelo sencillo desde el punto de vista de su formulación, pero de gran valor formativo porque constituye la base de otros modelos avanzados que son objeto de investigación actual. La modelización que se presenta ha sido puesta en práctica por los autores en su labor docente en estudios tanto de Grado como de Posgrado universitario. Presentamos una aproximación docente al modelo y su aplicación a datos reales de un activo financiero que cotiza en el mercado español IBEX35.

[EN] The aim of this paper is to show a methodology, based on the so-called Lognormal Model, to describe the dynamics of underlying assets by taking into account the uncertainty of nancial markets. In spite of its simple formulation, the Lognormal Model is a valuable tool from a formative standpoint becauseit provides an excellent basis to study more advanced models. The proposed approach has been put into practice by the authors in their teaching in both undergraduate and postgraduate studies. We present the model and its application to describe the dynamics of real data of an asset traded in the Spanish stock market index IBEX35., [ES] El objetivo de este trabajo es mostrar una metodología estocástica, basada en el denominado Modelo Lognormal, para modelizar la dinámica de subyacentes cotizados teniendo en cuenta la incertidumbre de los mercados financieros. Se trata de un modelo sencillo desde el punto de vista de su formulación, pero de gran valor formativo porque constituye la base de otros modelos avanzados que son objeto de investigación actual. La modelización que se presenta ha sido puesta en práctica por los autores en su labor docente en estudios tanto de Grado como de Posgrado universitario. Presentamos una aproximación docente al modelo y su aplicación a datos reales de un activo financiero que cotiza en el mercado español IBEX35.

Time-series of cosmogenic radionuclides stored in natural archives such as ice cores and tree rings are a proxy for solar magnetic activity on multi-millennial time-scales. Radionuclides data exhibit a number of interesting features such as intermittent stable cycles of high periods and Grand Minima. Although a lot of effort has gone into the development of sound physically based stochastic solar dynamo models, it is still largely unclear what are the underlying mechanisms that lead to the observed phenomena. Answering these questions requires quantitatively calibrating the models to the data and comparing performances of different models with the associated uncertainties in model parameters and predictions. Bayesian statistics is a consistent framework for parameter inference where knowledge about model parameters is expressed through probability distributions and updated using measured data. However, Bayesian inference with non-linear stochastic models can become computationally extremely expensive and it is therefore hardly ever applied. In recent years, sophisticated and scalable algorithms have emerged, which have the potential of making Bayesian inference for complex stochastic models feasible. We intend to investigate the power of Approximate Bayesian Computation (ABC) and Hamiltonian Monte Carlo (HMC) algorithms. We present our first inference results with stochastic solar dynamo models.

This study examines a method for a stochastic beach width prediction with a process-based morphodynamic model. This is carried out by a case study at the Hondsbossche Dunes, after a beach nourishment in March 2018. Stochastic forcing conditions are generated for the location of the Hondsbossche Dunes. These stochastic forcing conditions consist of time series with significant wave heights, peak wave periods, wave directions, and water levels. The basis of the method for generating these stochastic forcing conditions are Autoregressive-Moving Average (ARMA) models. The morphological change of the beach width due to these stochastic forcing conditions is modelled using an XBeach model. This results in a range of the possible development of the beach width, with the probability of occurrence. With the method examined in this study, a more realistic idea of the possible future beach width development can be given., Civil Engineering

Uganda is using a strategy called treatment as prevention where as many individuals as possible that are infected with HIV receive treatment. As a result, the number of newly infected individuals has decreased significantly. However, there is a discussion about a potential problem regarding transmitted drug resistance. This work aims to investigate if this in fact will be a problem in the future, and to estimate the costs for different scenarios. Through developing a population-based mathematical model that describes transmission dynamics of HIV in Uganda, stochastic simulations are made for different conditions. Through analysing our simulations, we can see that Uganda may have to change their approach to HIV treatment., För att minska smittoriskerna av HIV nyttjar Uganda en strategi som syftar till att behandla så många smittade personer som möjligt. Detta har lett till en signifikant minskning av antalet smittade personer. Det har dock uppstått en diskussion angående om läkemedels-resistent smitta kan komma att utgöra ett problem. Detta arbete syftar till att undersöka om detta kan utgöra ett problem i framtiden samt till att uppskatta de kostnader som kan uppstå i olika typer av scenarion. Under olika förutsättningar genomförs stokastiska simuleringar med hjälp av en matematisk populationsmodell framtagen för att beskriva spridningen av HIV i Uganda. Genom att analysera resultaten från olika simuleringar dras slutsatsen att Uganda kan behöva omvärdera sitt tillvägagångssätt gällande behandling av HIV.

[EN] The aim of this paper is to show a methodology, based on the so-called Lognormal Model, to describe the dynamics of underlying assets by taking into account the uncertainty of nancial markets. In spite of its simple formulation, the Lognormal Model is a valuable tool from a formative standpoint becauseit provides an excellent basis to study more advanced models. The proposed approach has been put into practice by the authors in their teaching in both undergraduate and postgraduate studies. We present the model and its application to describe the dynamics of real data of an asset traded in the Spanish stock market index IBEX35., [ES] El objetivo de este trabajo es mostrar una metodología estocástica, basada en el denominado Modelo Lognormal, para modelizar la dinámica de subyacentes cotizados teniendo en cuenta la incertidumbre de los mercados financieros. Se trata de un modelo sencillo desde el punto de vista de su formulación, pero de gran valor formativo porque constituye la base de otros modelos avanzados que son objeto de investigación actual. La modelización que se presenta ha sido puesta en práctica por los autores en su labor docente en estudios tanto de Grado como de Posgrado universitario. Presentamos una aproximación docente al modelo y su aplicación a datos reales de un activo financiero que cotiza en el mercado español IBEX35.

Dynamic frequency tuning of the 40.67 GHz intermode beat frequency of a 1255 nm emitting 1 mm long monolithic self mode-locked single section optical frequency comb InAs/InGaAs quantum dot laser across 70 MHz is experimentally demonstrated by fine-delay dual-cavity controlled all optical self-injection. Fiber-based macroscopic optical delay lengths are 9.4 m (round-trip time of 62.7 ns) and 16.5 m (round-trip time of 110.1 ns), the maximum studied microscopic delay tuning times are 40 ps and the optical self-injection strengths are below 0.02%. For selected delay times, the lowest intermode beat frequency line width amounts to 2 kHz indicating an improvement of carrier phase coherence by a factor of 700 as compared to the free-running laser. We validate these experimental results by a simple and universal stochastic time-domain model which is applied for the first time to model a self mode-locked quantum dot laser subject to optical self-injection. Modeling results are in good quantitative agreement.

[EN] The aim of this paper is to show a methodology, based on the so-called Lognormal Model, to describe the dynamics of underlying assets by taking into account the uncertainty of nancial markets. In spite of its simple formulation, the Lognormal Model is a valuable tool from a formative standpoint becauseit provides an excellent basis to study more advanced models. The proposed approach has been put into practice by the authors in their teaching in both undergraduate and postgraduate studies. We present the model and its application to describe the dynamics of real data of an asset traded in the Spanish stock market index IBEX35., [ES] El objetivo de este trabajo es mostrar una metodología estocástica, basada en el denominado Modelo Lognormal, para modelizar la dinámica de subyacentes cotizados teniendo en cuenta la incertidumbre de los mercados financieros. Se trata de un modelo sencillo desde el punto de vista de su formulación, pero de gran valor formativo porque constituye la base de otros modelos avanzados que son objeto de investigación actual. La modelización que se presenta ha sido puesta en práctica por los autores en su labor docente en estudios tanto de Grado como de Posgrado universitario. Presentamos una aproximación docente al modelo y su aplicación a datos reales de un activo financiero que cotiza en el mercado español IBEX35.

[EN] The aim of this paper is to show a methodology, based on the so-called Lognormal Model, to describe the dynamics of underlying assets by taking into account the uncertainty of nancial markets. In spite of its simple formulation, the Lognormal Model is a valuable tool from a formative standpoint becauseit provides an excellent basis to study more advanced models. The proposed approach has been put into practice by the authors in their teaching in both undergraduate and postgraduate studies. We present the model and its application to describe the dynamics of real data of an asset traded in the Spanish stock market index IBEX35., [ES] El objetivo de este trabajo es mostrar una metodología estocástica, basada en el denominado Modelo Lognormal, para modelizar la dinámica de subyacentes cotizados teniendo en cuenta la incertidumbre de los mercados financieros. Se trata de un modelo sencillo desde el punto de vista de su formulación, pero de gran valor formativo porque constituye la base de otros modelos avanzados que son objeto de investigación actual. La modelización que se presenta ha sido puesta en práctica por los autores en su labor docente en estudios tanto de Grado como de Posgrado universitario. Presentamos una aproximación docente al modelo y su aplicación a datos reales de un activo financiero que cotiza en el mercado español IBEX35.

[Abstract] Cell fate determination, the process through which cells commit to differentiated states is commonly mediated by gene regulatory motifs with mutually exclusive expression states. The classical deterministic picture for cell fate determination includes bistability and hysteresis, which enables the persistence of the acquired cellular state after withdrawal of the stimulus, ensuring a robust cellular response. However, stochasticity inherent to gene expression dynamics is not compatible with hysteresis, since the stationary solution of the governing Chemical Master Equation does not depend on the initial conditions. We provide a quantitative description of a transient hysteresis phenomenon reconciling experimental evidence of hysteretic behaviour in gene regulatory networks with inherent stochasticity: under sufficiently slow dynamics hysteresis is transient. We quantify this with an estimate of the convergence rate to the equilibrium and introduce a natural landscape capturing system’s evolution that, unlike traditional cell fate potential landscapes, is compatible with coexistence at the microscopic level.

[Resumen] Las herramientas de decisión y planificación automáticas pueden aumentar la eficacia de las operaciones de búsqueda y rescate en el mar. Por ese motivo, la comunidad científica y las empresas del sector desarrollan e incorporan a sus herramientas nuevos algoritmos de modelado probabilístico y de optimización de las trayectorias de los vehículos involucrados en la misión. El objetivo de este artículo es describir las características principales de una nueva herramienta que está siendo desarrollada para este fin por AIRBUS e investigadores de la UCM, y que incorpora diferentes estrategias de evaluación, optimiza las trayectorias del vehículo con algoritmos genéticos y el movimiento del sensor electro-óptico utilizado para la búsqueda con temple simulado, y que permite al operador comparar y seleccionar la solución más adecuada en función de diferentes criterios., [Abstract] Automated decision and planning tolos can increment the effectiveness of maritime Search And Rescue (SAR) operations. Hence, the scientific community and companies are developing new probabillistic modelling and vehiche-trajectory optimization algorithms to be integrated in their mission systems. The objective of this work is to describe the main features of a new maritime SAR tool developed by AIRBUS and UCM researchers, which incorporates several evaluation strategies, optimizes the vehicle trajectory with genetic algorithms and the movement of the electro-optic sensor (used in the search) with simmulated annealing, and allows the operator to compare and select the best solutions according to different critera.

[EN] The aim of this paper is to show a methodology, based on the so-called Lognormal Model, to describe the dynamics of underlying assets by taking into account the uncertainty of nancial markets. In spite of its simple formulation, the Lognormal Model is a valuable tool from a formative standpoint becauseit provides an excellent basis to study more advanced models. The proposed approach has been put into practice by the authors in their teaching in both undergraduate and postgraduate studies. We present the model and its application to describe the dynamics of real data of an asset traded in the Spanish stock market index IBEX35., [ES] El objetivo de este trabajo es mostrar una metodología estocástica, basada en el denominado Modelo Lognormal, para modelizar la dinámica de subyacentes cotizados teniendo en cuenta la incertidumbre de los mercados financieros. Se trata de un modelo sencillo desde el punto de vista de su formulación, pero de gran valor formativo porque constituye la base de otros modelos avanzados que son objeto de investigación actual. La modelización que se presenta ha sido puesta en práctica por los autores en su labor docente en estudios tanto de Grado como de Posgrado universitario. Presentamos una aproximación docente al modelo y su aplicación a datos reales de un activo financiero que cotiza en el mercado español IBEX35.

The purpose of this study is to investigate a pharmacokinetic model of levodopa concentration in patients with Parkinson's disease by introducing stochasticity so that inter-individual variability may be separated into measurement and system noise. It also aims to investigate whether the stochastic differential equations (SDE) model provide better fits than its ordinary differential equations (ODE) counterpart, by using a real data set. Westin et al. developed a pharmacokinetic-pharmacodynamic model for duodenal levodopa infusion described by four ODEs, the first three of which define the pharmacokinetic model. In this study, system noise variables are added to the aforementioned first three equations through a standard Wiener process, also known as Brownian motion. The R package PSM for mixed-effects models is used on data from previous studies for modelling levodopa concentration and parameter estimation. First, the diffusion scale parameter, σ, and bioavailability are estimated with the SDE model. Second, σ is fixed to integer values between 1 and 5, and bioavailability is estimated. Cross-validation is performed to determine whether the SDE based model explains the observed data better or not by comparingthe average root mean squared errors (RMSE) of predicted levodopa concentration. Both ODE and SDE models estimated bioavailability to be about 88%. The SDE model converged at different values of σ that were signicantly different from zero while estimating bioavailability to be about 88%. The average RMSE for the ODE model wasfound to be 0.2980, and the lowest average RMSE for the SDE model was 0.2748 when σ was xed to 4. Both models estimated similar values for bioavailability, and the non-zero σ estimate implies that the inter-individual variability may be separated. However, the improvement in the predictive performance of the SDE model turned out to be rather small, compared to the ODE model.

The addition of photovoltaics (PV) to a grid impacts the performance of that grid in a number of ways. These impacts limit how much PV can be connected, termed ‘hosting capacity (HC)’. The impacts include overvoltage and overloading. Mitigation of impacts can be achieved in different ways: in this paper, upgrade of service cable and feeder cable has been considered, one of the classical solutions. Cable size upgrades to 16, 25 and 35 mm2 from 10 mm2 have been studied to mitigate overvoltages in a 28-customer Swedish suburban grid. A stochastic planning-based approach has been used to obtain a performance parameter that can be used to compare the mitigation methods. The results showed an improvement in overvoltage and hosting capacity with cable upgrade. The hosting capacity is also shown to be sensitive to the risk chosen and to the PV size.

The purpose of this study is to investigate a pharmacokinetic model of levodopa concentration in patients with Parkinson's disease by introducing stochasticity so that inter-individual variability may be separated into measurement and system noise. It also aims to investigate whether the stochastic differential equations (SDE) model provide better fits than its ordinary differential equations (ODE) counterpart, by using a real data set. Westin et al. developed a pharmacokinetic-pharmacodynamic model for duodenal levodopa infusion described by four ODEs, the first three of which define the pharmacokinetic model. In this study, system noise variables are added to the aforementioned first three equations through a standard Wiener process, also known as Brownian motion. The R package PSM for mixed-effects models is used on data from previous studies for modelling levodopa concentration and parameter estimation. First, the diffusion scale parameter, σ, and bioavailability are estimated with the SDE model. Second, σ is fixed to integer values between 1 and 5, and bioavailability is estimated. Cross-validation is performed to determine whether the SDE based model explains the observed data better or not by comparingthe average root mean squared errors (RMSE) of predicted levodopa concentration. Both ODE and SDE models estimated bioavailability to be about 88%. The SDE model converged at different values of σ that were signicantly different from zero while estimating bioavailability to be about 88%. The average RMSE for the ODE model wasfound to be 0.2980, and the lowest average RMSE for the SDE model was 0.2748 when σ was xed to 4. Both models estimated similar values for bioavailability, and the non-zero σ estimate implies that the inter-individual variability may be separated. However, the improvement in the predictive performance of the SDE model turned out to be rather small, compared to the ODE model.

The purpose of this study is to investigate a pharmacokinetic model of levodopa concentration in patients with Parkinson's disease by introducing stochasticity so that inter-individual variability may be separated into measurement and system noise. It also aims to investigate whether the stochastic differential equations (SDE) model provide better fits than its ordinary differential equations (ODE) counterpart, by using a real data set. Westin et al. developed a pharmacokinetic-pharmacodynamic model for duodenal levodopa infusion described by four ODEs, the first three of which define the pharmacokinetic model. In this study, system noise variables are added to the aforementioned first three equations through a standard Wiener process, also known as Brownian motion. The R package PSM for mixed-effects models is used on data from previous studies for modelling levodopa concentration and parameter estimation. First, the diffusion scale parameter, σ, and bioavailability are estimated with the SDE model. Second, σ is fixed to integer values between 1 and 5, and bioavailability is estimated. Cross-validation is performed to determine whether the SDE based model explains the observed data better or not by comparingthe average root mean squared errors (RMSE) of predicted levodopa concentration. Both ODE and SDE models estimated bioavailability to be about 88%. The SDE model converged at different values of σ that were signicantly different from zero while estimating bioavailability to be about 88%. The average RMSE for the ODE model wasfound to be 0.2980, and the lowest average RMSE for the SDE model was 0.2748 when σ was xed to 4. Both models estimated similar values for bioavailability, and the non-zero σ estimate implies that the inter-individual variability may be separated. However, the improvement in the predictive performance of the SDE model turned out to be rather small, compared to the ODE model.