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Peer Reviewed
See detailBatch control of the master equation: a linear programming approach
Goncalves, Jorge UL; Martins, N.

Scientific Conference (2008)

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See detailA Bayesian framework to identify random parameter fields based on the copula theorem and Gaussian fields: Application to polycrystalline materials
Rappel, Hussein UL; Wu, Ling; Noels, Ludovic et al

in Journal of Applied Mechanics (in press)

For many models of solids, we frequently assume that the material parameters do not vary in space, nor that they vary from one product realization to another. If the length scale of the application ... [more ▼]

For many models of solids, we frequently assume that the material parameters do not vary in space, nor that they vary from one product realization to another. If the length scale of the application approaches the length scale of the micro-structure however, spatially fluctuating parameter fi elds (which vary from one realization of the fi eld to another) can be incorporated to make the model capture the stochasticity of the underlying micro-structure. Randomly fluctuating parameter fields are often described as Gaussian fields. Gaussian fi elds however assume that the probability density function of a material parameter at a given location is a univariate Gaussian distribution. This entails for instance that negative parameter values can be realized, whereas most material parameters have physical bounds (e.g. the Young's modulus cannot be negative). In this contribution, randomly fluctuating parameter fi elds are therefore described using the copula theorem and Gaussian fi elds, which allow di fferent types of univariate marginal distributions to be incorporated, but with the same correlation structure as Gaussian fields. It is convenient to keep the Gaussian correlation structure, as it allows us to draw samples from Gaussian fi elds and transform them into the new random fields. The bene fit of this approach is that any type of univariate marginal distribution can be incorporated. If the selected univariate marginal distribution has bounds, unphysical material parameter values will never be realized. We then use Bayesian inference to identify the distribution parameters (which govern the random fi eld). Bayesian inference regards the parameters that are to be identi fied as random variables and requires a user-defi ned prior distribution of the parameters to which the observations are inferred. For the homogenized Young's modulus of a columnar polycrystalline material of interest in this study, the results show that with a relatively wide prior (i.e. a prior distribution without strong assumptions), a single specimen is su ciffient to accurately recover the distribution parameter values. [less ▲]

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See detailBayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights
Rappel, Hussein UL; Beex, Lars UL; Hale, Jack UL et al

E-print/Working paper (n.d.)

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material ... [more ▼]

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material parameters. For this purpose a single spring is considered, for which the stress-strain curves are artificially created. Besides offering a didactic introduction to BI, this paper proposes an approach to incorporate statistical errors both in the measured stresses, and in the measured strains. It is assumed that the uncertainty is only due to measurement errors and the material is homogeneous. Furthermore, a number of possible misconceptions on BI are highlighted based on the purely elastic case. [less ▲]

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See detailBayesian inference to identify parameters in viscoelasticity
Rappel, Hussein UL; Beex, Lars UL; Bordas, Stéphane UL

in Mechanics of Time-Dependent Materials (2017)

This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are: (i) to show that the prior has a substantial influence for viscoelasticity, (ii ... [more ▼]

This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are: (i) to show that the prior has a substantial influence for viscoelasticity, (ii) to show that this influence decreases for an increasing number of measurements and (iii) to show how different types of experiments influence the identified parameters and their uncertainties. The standard linear solid model is the material description of interest and a relaxation test, a constant strain-rate test and a creep test are the tensile experiments focused on. The experimental data are artificially created, allowing us to make a one-to-one comparison between the input parameters and the identified parameter values. Besides dealing with the aforementioned issues, we believe that this contribution forms a comprehensible start for those interested in applying BI in viscoelasticity. [less ▲]

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See detailA Bayesian inversion approach to recovering material parameters in hyperelastic solids using dolfin-adjoint
Hale, Jack UL; Farrell, Patrick E.; Bordas, Stéphane UL

Presentation (2015, July 01)

In the first part of the talk I will describe in general terms the link between classical optimisation techniques and the Bayesian approach to statistical inversion as outlined in the seminal book of ... [more ▼]

In the first part of the talk I will describe in general terms the link between classical optimisation techniques and the Bayesian approach to statistical inversion as outlined in the seminal book of [Kaipio and Somersalo, 2005]. Under the assumption of an additive Gaussian noise model, a Gaussian prior distribution and a linear parameter-to-observable map, it is possible to uniquely characterise the Bayesian posterior as Gaussian with the maximum aposteriori (MAP) point equal to the minimum of a classic regularised minimisation problem and covariance matrix equal to the inverse of the Hessian of the functional evaluated at the MAP point. I will also discuss techniques that can be used when these assumptions break down. In the second part of the talk I will describe a method implemented within dolfin-adjoint [Funke and Farrell, arXiv 2013] to quantify the uncertainty in the recovered material parameters of a hyperelastic solid from partial and noisy observations of the displacement field in the domain. The finite element discretisation of the adjoint and higher-order adjoint (Hessian) equations are derived automatically from the high-level UFL representation of the problem. The resulting equations are solved using PETSc. I will concentrate on finding the eigenvalue decomposition of the posterior covariance matrix (Hessian). The eigenvectors associated with the lowest eigenvalues of the Hessian correspond with the directions in parameter space least constrained by the observations [Flath et al. 2011]. This eigenvalue problem is tricky to solve efficiently because the Hessian is very large (on the order of the number of parameters) and dense (meaning that only its action on a vector can be calculated, each involving considerable expense). Finally, I will show some illustrative examples including the uncertainty associated with deriving the material properties of a 3D hyperelastic block with a stiff inclusion with knowledge only of the displacements on the boundary of the domain. J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, vol. 160. New York: Springer-Verlag, 2005. S. W. Funke and P. E. Farrell, “A framework for automated PDE-constrained optimisation,” arXiv:1302.3894 [cs], Feb. 2013. H. P. Flath, L. C. Wilcox, V. Akçelik, J. Hill, B. van Bloemen Waanders, and O. Ghattas, “Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations,” SIAM J. Sci. Comput., vol. 33, no. 1, pp. 407–432, Feb. 2011. [less ▲]

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See detailBayesian statistical inference on the material parameters of a hyperelastic body
Hale, Jack UL; Farrel, Patrick E.; Bordas, Stéphane UL

in Proceedings of the ACME-UK 2016 24th Conference on Computational Mechanics (2016, March 31)

We present a statistical method for recovering the material parameters of a heterogeneous hyperelastic body. Under the Bayesian methodology for statistical inverse problems, the posterior distribution ... [more ▼]

We present a statistical method for recovering the material parameters of a heterogeneous hyperelastic body. Under the Bayesian methodology for statistical inverse problems, the posterior distribution encodes the probability of the material parameters given the available displacement observations and can be calculated by combining prior knowledge with a finite element model of the likelihood. In this study we concentrate on a case study where the observations of the body are limited to the displacements on the surface of the domain. In this type of problem the Bayesian framework (in comparison with a classical PDE-constrained optimisation framework) can give not only a point estimate of the parameters but also quantify uncertainty on the parameter space induced by the limited observations and noisy measuring devices. There are significant computational and mathematical challenges when solving a Bayesian inference problem in the case that the parameter is a field (i.e. exists infinite-dimensional Banach space) and evaluating the likelihood involves the solution of a large-scale system of non-linear PDEs. To overcome these problems we use dolfin-adjoint to automatically derive adjoint and higher-order adjoint systems for efficient evaluation of gradients and Hessians, develop scalable maximum aposteriori estimates, and use efficient low-rank update methods to approximate posterior covariance matrices. [less ▲]

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See detailBearing capacity of steel fiber reinforced concrete flat slabs
Michels, Julien UL

Doctoral thesis (2009)

Detailed reference viewed: 164 (9 UL)
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See detailA Big Data Demand Estimation Framework for Modelling of Urban Congested Networks
Cantelmo, Guido UL; Viti, Francesco UL

in CSUM 2018, AISC 879 proceedings (2019)

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See detailBimodal and hysteretic expression in mammalian cells from a synthetic gene circuit
May, T.; Eccleston, L. J.; Markusic, D. et al

in Public Library of Science ONE (2008), 3(6),

In order to establish cells and organisms with predictable properties, synthetic biology makes use of controllable, synthetic genetic devices. These devices are used to replace or to interfere with ... [more ▼]

In order to establish cells and organisms with predictable properties, synthetic biology makes use of controllable, synthetic genetic devices. These devices are used to replace or to interfere with natural pathways. Alternatively, they may be interlinked with endogenous pathways to create artificial networks of higher complexity. While these approaches have been already successful in prokaryotes and lower eukaryotes, the implementation of such synthetic cassettes in mammalian systems and even animals is still a major obstacle. This is mainly due to the lack of methods that reliably and efficiently transduce synthetic modules without compromising their regulation properties. To pave the way for implementation of synthetic regulation modules in mammalian systems we utilized lentiviral transduction of synthetic modules. A synthetic positive feedback loop, based on the Tetracycline regulation system was implemented in a lentiviral vector system and stably integrated in mammalian cells. This gene regulation circuit yields a bimodal expression response. Based on experimental data a mathematical model based on stochasticity was developed which matched and described the experimental findings. Modelling predicted a hysteretic expression responsewhich was verified experimentally. Thereby supporting the idea that the system is driven by stochasticity. The results presented here highlight that the combination of three independent tools/methodologies facilitate the reliable installation of synthetic gene circuits with predictable expression characteristics in mammalian cells and organisms. [less ▲]

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See detailBiomechanical properties of five different currently used implants for open-wedge high tibial osteotomy
Diffo Kaze, Arnaud UL; Maas, Stefan UL; Waldmann, Danièle UL et al

in Journal of Experimental Orthopaedics (2015), 2(14),

Background: As several new tibial osteotomy plates recently appeared on the market, the aim of the present study was to compare mechanical static and fatigue strength of three newly designed plates with ... [more ▼]

Background: As several new tibial osteotomy plates recently appeared on the market, the aim of the present study was to compare mechanical static and fatigue strength of three newly designed plates with gold standard plates for the treatment of medial knee joint osteoarthritis. Methods: Sixteen fourth-generation tibial bone composites underwent a medial open-wedge high tibial osteotomyn(HTO) according to standard techniques, using five TomoFix standard plates, five PEEKPower plates and six iBalance implants. Static compression load to failure and load-controlled cyclic fatigue failure tests were performed. Forces, horizontal and vertical displacements were measured; rotational permanent plastic deformations, maximal displacement ranges in the hysteresis loops of the cyclic loading responses and dynamic stiffness were determined. Results: Static compression load to failure tests revealed that all plates showed sufficient stability up to 2400 N without any signs of opposite cortex fracture, which occurred above this load in all constructs at different load levels. During the fatigue failure tests, screw breakage in the iBalance group and opposite cortex fractures in all constructs occurred only under physiological loading conditions (<2400 N). The highest fatigue strength in terms of maximal load and number of cycles performed prior to failure was observed for the ContourLock group followed by the iBalance implants, the TomoFix standard (std) and small stature (sm) plates. The PEEKPower group showed the lowest fatigue strength. Conclusions: All plates showed sufficient stability under static loading. Compared to the TomoFix and the PEEKPower plates, the ContourLock plate and iBalance implant showed a higher mechanical fatigue strength during cyclic fatigue testing. These data suggest that both mechanical static and fatigue strength increase with a wider proximal T-shaped plate design together with diverging proximal screws as used in the ContourLock plate or a closed-wedge construction as in the iBalance design. Mechanical strength of the bone-implant constructs decreases with a narrow T-shaped proximal end design and converging proximal screws (TomoFix) or a short vertical plate design (PEEKPower Plate). Whenever high mechanical strength is required, a ContourLock or iBalance plate should be selected. [less ▲]

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See detailBiomechanik neuer Implantate für die HTO
Pape, Dietrich; Diffo Kaze, Arnaud UL; Hoffmann, Alexander et al

in Orthopade (Der) (2017), 46(7), 583-595

Biomechanical characteristics of 5 tibial osteotomy plates for the treatment of medial knee joint osteoarthritis were examined. Fourth-generation tibial bone composites underwent a medial open-wedge high ... [more ▼]

Biomechanical characteristics of 5 tibial osteotomy plates for the treatment of medial knee joint osteoarthritis were examined. Fourth-generation tibial bone composites underwent a medial open-wedge high tibial osteotomy, using TomoFix™ standard, PEEKPower®, ContourLock®, TomoFix™ small stature plates, and iBalance® implants. Static compression load to failure and load-controlled cyclic fatigue failure tests were performed. All plates had sufficient stability up to 2400 N in the static compression load to failure tests. Screw breakage in the iBalance® group and opposite cortex fractures in all constructs occurred at lower loading conditions. The highest fatigue strength in terms of maximal load and number of cycles performed prior to failure was observed for the ContourLock® group followed by the iBalance® implants, the TomoFix™ standard and small stature plates. PEEKPower® had the lowest fatigue strength. All plates showed sufficient stability under static loading. Compared to the TomoFix™ and the PEEKPower® plates, the ContourLock® plate and iBalance® implant showed a higher mechanical fatigue strength during cyclic fatigue testing, suggesting that both mechanical static and fatigue strength increase with a wider proximal T‑shaped plate design together with diverging proximal screws. Mechanical strength of the bone–implant constructs decreases with a narrow T‑shaped proximal end design and converging proximal screws (TomoFix™) or a short vertical plate design (PEEKPower®). Published results indicate high fusion rates and good clinical results with the TomoFix™ plate, which is contrary to our findings. A certain amount of interfragmentary motion rather than high mechanical strength and stiffness seem to be important for bone healing which is outside the scope of this paper. [less ▲]

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See detailBiopharm - the Influence of Macro-substrates & Conditioning on Pharmaceutical Removal Rates by Moving Bed Biofilm Reactors
Köhler, Christian UL

Doctoral thesis (2015)

Organic micropollutants with endocrine disruptive properties are present in the aquatic environment. A major part of their emission is caused by municipal wastewater treatment plants (WWTPs). For this ... [more ▼]

Organic micropollutants with endocrine disruptive properties are present in the aquatic environment. A major part of their emission is caused by municipal wastewater treatment plants (WWTPs). For this reason, a vast amount of research has been undertaken to remove xenobiotics from municipal wastewater by developing post-treatment technologies with some success. However, these technologies cause considerable environmental costs due their high demand for electrical energy implicating an increase in CO2 emissions. Consequently, existing biological treatments need first to be better understood and subsequently optimized regarding xenobiotic removal before post-treatments are employed. The study focused on the fate of xenobiotics during biological wastewater treatment. In particular, metabolic strategies of bacteria degrading pharmaceuticals were investigated within moving bed biofilm reactor (MBBR) processes. Two main objectives were tracked. On the one hand, it was to unfold the impact of macro-substrates in terms of type and molecular complexity on the activity of microorganisms and consequently pharmaceutical degradation performance. On the other hand, the study was set out to explore the adaptation of metabolic means regarding exoenzymes and consortia structure during continuous (long-term) exposure to pharmaceuticals. Accordingly, the ability to increase microbial competences during pharmaceutical short-term pulses was the general target of investigation. Both conditions continuous substance flow and short-term peak loads of xenobiotics are believed to occur in urban WWTPs. A pilot MBBR was set up next to a domestic WWTP. The pilot treated municipal sewage and served as inoculation reservoir for biofilm carriers used for in-depth laboratory experiments. The latter comprised six lab-scale MBBRs featuring flow through operation under controlled conditions regarding temperature, dissolved oxygen, pH, influent flow and influent load. The reactors were conditioned over four weeks with a synthetic sewage providing substrates and micro-nutrients in a similar manner as expected under real conditions. Biofilm was monitored by respirometry and a series of enzyme assays using fluorogenic substrates to capture esterase, phosphatase, alpha- and beta-glucosidase and aminopeptidase activity. All enzymes are essential during organic carbon metabolism. An array of macro-substrates with different molecular complexity was triggering individual enzyme activity profiles. After conditioning, 12 pharmaceuticals being subject to a range of anticipated metabolic pathways and degradation rates were spiked into the MBBRs. Their degradation kinetics were measured by liquid chromatography coupled with tandem mass spectrometry (LC MS/MS). Pseudo first-order kinetics revealed substrate related fingerprints and showed that readily biodegradable substrate leads generally to good pharmaceutical degradation performance compared to synthetic sewage with a mixture of several high molecular organic substrates. The latter was designed to induce the greatest metabolic effort of tested substrates before microbial uptake occurs. However, single substrates triggering exoenzyme activity in a more targeted manner such as maltose and cellobiose showed positive impact on the pseudo first-order rate coefficients of particular pharmaceuticals such as atenolol and diclofenac. Accordingly, alpha-glucosidase activity was found to be directly proportional to atenolol degradation kinetics. Phylogenetic characterisation of DNA and RNA involving state-of-the-art 16S ribosomal rRNA gene amplification and sequencing techniques was used to explore community structures. Prokaryote diversity in lab-scale MBBRs was in agreement to previous studies which investigated microbial consortia in full-scale systems. Multivariate analysis revealed that bacteria are adapting their active gene pool when the beta-blocker atenolol is continuously present with a concentration in ug/L range. Differential analysis unfolded that the prokaryotic genera Delftia and Lysobacter were thereby exclusively benefiting from the exposure to atenolol. Yet, compared to the influence of macro-substrates, biomass conditioning (training) with atenolol and diclofenac had no notable impact on the degradation performance of pharmaceutical short-term pulses. The outstanding comprehensive character of the study which encompassed sophisticated experimental design and powerful analytical tools from different scientific domains uncovered some interesting insights in xenobiotic degradation processes. The results finally show how biomass is reacting towards the presence of primary carbon sources and organic micro-pollutants. The outcomes highlight the importance of WWTP influent characterization being indicative of metabolic activity and therefore degradation capacity of xenobiotics. The study further suggests that xenobiotic metabolism and co-metabolism co-exist during biological treatment processes. Co-metabolism is the decisive actor when adaption time is relatively short as it was the case during the lab-scale experiments compared to real conditions. Further, the study indicates some potential of process enhancement of WWTPs ranging from straightforward implementations such as external carbon sources to more elaborated processes of bioaugmentation. [less ▲]

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See detailBlock Backstepping, NDI and Related Cascade Designs for Efficient Development of Nonlinear Flight Control Laws
Thunberg, Johan UL; Robinson, J.W.C.

in Proceedings of the AIAA Guidance, Navigation and Control Conference and Exhibit 2008 (2008)

A common feature of many aircraft configurations is that the actuation mainly effects the moments, and thereby the angular accelerations, whereas the desired normal acceleration is achieved by adjusting ... [more ▼]

A common feature of many aircraft configurations is that the actuation mainly effects the moments, and thereby the angular accelerations, whereas the desired normal acceleration is achieved by adjusting the location of the velocity vector in body coordinates. Thus, the main desired effects of the actuators appear after one integration, and if the actuators have dynamics the effect of the primary control variable occurs after more than one integration. This inherent cascade structure of many aircraft control problems is exploited in e.g. nonlinear dynamic inversion via time scale separation (NDI-TSS) to yield a powerful nonlinear design method. In the present work we present a family of multivariable (three axis) nonlinear cascade design techniques for flight control law design which includes block backstepping and NDI-TSS as special cases and we show that this family can offer a large design flexibility and excellent performance as well as short design cycles. We show stability for the family of techniques and illustrate the theory using simulations based on the ADMIRE model which is a realistic nonlinear model of an agile fighter with delta-canard configuration. [less ▲]

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See detailBlood flow simulation using smoothed particle hydrodynamics: application to thrombus generation
AL-SAAD, Mohammed; Kulasegaram, Sivakumar; Bordas, Stéphane UL

Scientific Conference (2016, March 31)

Blood flow rheology is considered to be a complex phenomenon. In order to understand the characteristics of blood flow, it is important to identify key parameters those influence the flow behaviour of ... [more ▼]

Blood flow rheology is considered to be a complex phenomenon. In order to understand the characteristics of blood flow, it is important to identify key parameters those influence the flow behaviour of blood. Further, the characterisation of blood flow will also enable us to understand flow parameters associated with physiological conditions such as atherosclerosis. Thrombosis plays a crucial role in atherosclerosis, or to stop bleeding when a blood vessel is injured. This article focuses on using meshless particle-based Lagrangian numerical technique named smoothed particles hydrodynamic (SPH) method to study the flow behaviour of blood and to explore flow condition that induces formation of thrombus in a blood vessel. Due its simplicity and effectiveness, the SPH method is employed here to simulate the process of thrombogenesis under the influence of various blood flow parameters. In the present SPH simulation, blood is modelled by particles that have characteristics of plasma and of platelets. To simulate coagulation of platelets which forms thrombus, the adhesion and aggregation process of platelets are modelled by an effective inter-particle force model. With these models, platelet motion in the flowing blood and platelet adhesion and aggregation are effectively coupled with viscous blood flow. In this study, the adhesion and aggregation of blood particles are performed on a bifurcated artery under a various low Reynolds number scenarios. The results are compared with experimental results and a good agreement is found between the simulated and experimental results. [less ▲]

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See detailBMS revisited
Aucher, Guillaume UL

in Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge (2009)

The insight of the BMS logical framework (proposed by Baltag, Moss and Solecki) is to represent how an event is perceived by several agents very similarly to the way one represents how a static situation ... [more ▼]

The insight of the BMS logical framework (proposed by Baltag, Moss and Solecki) is to represent how an event is perceived by several agents very similarly to the way one represents how a static situation is perceived by them: by means of a Kripke model. There are however some differences between the definitions of an epistemic model (representing the static situation) and an event model. In this paper we restore the symmetry. The resulting logical framework allows, unlike any other one, to express statements about ongoing events and to model the fact that our perception of events (and not only of the static situation) can also be updated due to other events. We axiomatize it and prove its decidability. Finally, we show that it embeds the BMS one if we add common belief operators. [less ▲]

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See detailBoard Game Prototyping to Co-Design a Better Location-Based Digital Game
Jones, Catherine UL; Liapis; Lykourentzou, Ioanna et al

in Abstract book of the 2017 CHI Conference Extended Abstracts on Human Factors in Computing Systems - CHI EA '17 (2017)

In this case study we describe the iterative process of paper prototyping, using a board game, to co-design a location-based mobile application. The end goal of the application is to motivate reflection ... [more ▼]

In this case study we describe the iterative process of paper prototyping, using a board game, to co-design a location-based mobile application. The end goal of the application is to motivate reflection on historical topics about migration. The board game serves to capture the core concerns of this application by simulating movement through the city. Three play tests highlighted the users' interest and issues with the historical content, the way this content is represented, and the players' responses to the interactions and motivating mechanisms of the application. Results show that the board game helped capture important design preferences and problems, ensuring the improvement of our scenario. This feedback can help reduce development effort and implement a future technology prototype closer to the needs of our end users. [less ▲]

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See detailA Boolean Approach for Disentangling the Roles of Submodules to the Global Properties of a Biomodel
Czeizler, Elena; Mizera, Andrzej UL; Petre, Ion

in Fundamenta Informaticae (2012), 116(1-4), 51-63

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See detailA boolean control network approach to pursuit evasion problems in polygonal environments
Thunberg, Johan UL; Ogren, P.; Hu, X.

in Proceedings of the 2011 IEEE International Conference on Robotics and Automation (ICRA) (2011)

In this paper, the multi pursuer version of the pursuit evasion problem in polygonal environments is addressed. This problem is NP-hard, and therefore we seek good enough, but not optimal solutions. By ... [more ▼]

In this paper, the multi pursuer version of the pursuit evasion problem in polygonal environments is addressed. This problem is NP-hard, and therefore we seek good enough, but not optimal solutions. By modeling the problem as a Boolean Control Network, we can efficiently keep track of which regions are cleared, and which are not, while the input nodes of the network are used to represent the motion of the pursuers. The environment is partitioned into a set of convex regions, where each region correspond to a set of nodes in the network. The method is implemented in ANSI C, and efficiently solves complex environments containing multiple loops and requiring so-called recontamination. The provided examples demonstrate the effectiveness of the method in terms of computational time. [less ▲]

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See detailCalculating the Malliavin derivative of some stochastic mechanics problems
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

in PLoS ONE (2017), 12(12), 0189994

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to ... [more ▼]

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. [less ▲]

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See detailCalibration of a microscopic simulation model for emission calculation
Li, Jie; Van Zuylen, Henk J.; Chen, Yusen et al

in Transportation Research. Part C : Emerging Technologies (2013), 31

Emissions by road traffic can be reduced by optimising traffic control. The impact of this optimisation on emission can be analysed ex ante by simulation. The simulation programs used for this analysis ... [more ▼]

Emissions by road traffic can be reduced by optimising traffic control. The impact of this optimisation on emission can be analysed ex ante by simulation. The simulation programs used for this analysis should be valid with respect to the traffic characteristics that determine the emissions. Thus calibration of the parameters is a prerequisite. In most cases, volumes, travel times and queues are used to calibrate simulation models, rather than detailed driving characteristics such as speed and acceleration patterns. However, these driving behaviour parameters determine the vehicular emissions to a great extent. A study was carried out in which the driving behaviour parameters in a microscopic simulation model (VISSIM) were calibrated using real trajectories collected by image processing at an intersection in Rotterdam. The sensitivity of the simulation results for driving behaviour parameters was investigated. The most influential parameters were identified and adjusted to ensure that the simulation results were consistent with the observed traffic and could provide valid estimations of the total production of emissions. [less ▲]

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