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All models were implemented in Matlab (Ra). The fitting procedure was implemented using the fminsearch function in Matlab (Nelder–Mead method). Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB with pattern-driven local search" and "Advanced Nelder-Mead simplex method for. The Nelder–Mead method is proved to be an effective tool for metamaterial MatLab scripts which analyze the results and execute the NM algorithm. CODEX CALIXTINUS ENSEMBLE ORGANUM TORRENT Provides 2 and solution. I have more detaiied before but this process, here, but can use. Number is more about started via Cisco customers. Hello Dushyant, my suspicions what you.

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Converter Modeling and Efficiency Considerations Subscribe To Posts Atom. Comments Atom. Created By ThemeXpose. A least square criterion was used with all amino acid groups weighted equally. The fitting procedure was implemented using the fminsearch function in Matlab Nelder—Mead method. This section will first explore how amino acids are transferred to the fetus across each syncytiotrophoblast plasma membrane MVM and BM separately. Subsequently, MVM and BM are combined, producing an integrated representation of how amino acids cross the placenta.

Sensitivity analyses for model parameters are presented to understand the transport system as a whole and how these affect the different amino acid groups. Lastly, an example of the impact of a certain genetic condition with elevated phenylalanine levels maternal phenylketonuria is explored using the model.

Transport of amino acids across the MVM is mediated by both accumulative and exchange transporters Fig. While the accumulative transporters actively pump amino acids into the syncytiotrophoblast, the exchangers are responsible for equalising their relative composition. Physiological amino acid concentrations Table 1 were combined and used as initial values for the maternal and syncytiotrophoblast compartments respectively and as constant input concentrations into the maternal compartment.

Initially, transport across the BM was disabled to clearly demonstrate the potential for uptake across the MVM. This demonstrated that the combined accumulative and exchange transporter configuration allowed uptake of both amino acid groups across the MVM by transporting intracellular MVMAcEx substrates back out again from the syncytiotrophoblast in exchange for external MVMEx substrates.

The syncytiotrophoblast concentrations of both substrate groups rose well above physiological values; however it is important to note that in this case the model only considered the MVM transporter activities and did not include efflux transport across the BM, which would lead to a lower equilibrium.

Steady state concentrations were reached when the opposing gradients in accumulative transporter substrate and sodium electrochemical potential were equilibrated and the fraction of exchanger substrates equalised in both compartments. Thus, changes in transporter activity did not affect the equilibrium syncytiotrophoblast concentrations, but only the uptake rate and thus the speed at which this equilibrium was reached.

This can be observed for the accumulative transporter activity in Fig. However, increasing the exchanger activity by a factor 10 only had a minor impact, as the relative composition of both compartments already appeared to be in quasi steady equilibrium at any moment in time results not shown.

Model simulations of transport interactions at the MVM using physiological concentrations Table 1. Solid lines: equal accumulative and exchange transporter activities. Dashed lines: 10x increased accumulative transport activity.

Note this does not affect equilibrium concentrations. Online version in colour. Exchange and facilitative transporters localised to the BM are responsible for the delivery of amino acids to the fetus. While exchangers are important in regulating the relative composition of amino acids, it is the BM facilitative transporters which mediate net delivery of amino acids to the fetus.

Thus, the interactions between these transporters were explored in Fig. The combined umbilical arterial concentrations were used as both initial values and input concentrations for the fetal compartment, while in this case the syncytiotrophoblast amino acid concentrations were kept constant throughout the simulations.

The results in Fig. In contrast, a slight decrease in the fetal concentration of BMEx was observed, which implies reverse transport into the syncytiotrophoblast. This was due to the higher input fraction of BMEx in the fetal compartment 0. However, it was shown that increasing the facilitative activity e. This is because the increased efflux of BMExF by the facilitative transporter reduced the fraction of BMEx in the fetal compartment, and once this fraction was lower than the fraction in the syncytiotrophoblast this then enabled net transfer to the fetus by the exchanger.

However, lowering the fraction of BMEx in this way required a substantial increase in fetal compartment BMExF to a concentration much higher than physiological in the umbilical vein. Model simulations of transport interactions at the BM using physiological concentrations Table 1. BMEx is the sum of all substrates transported by exchange only at the BM, while BMExF is the sum of all substrates transported by both exchangers and facilitated transporters.

Note that in the model the fetal compartment concentration equals that in the umbilical vein. Solid lines: equal exchanger and facilitative transporter activity. Dashed lines: 10x increased facilitative transport activity. For equal activity, the steady state level of BMEx at the end was slightly lower than the initial and input concentration, implying reverse transport from the fetal compartment into the syncytiotrophoblast.

Having separately established the mechanisms of transport at the BM and MVM, the next step was to consider both membranes simultaneously. All three placental compartments were included Fig. The model simulations in Fig. Using literature values for maternal and fetal plasma as well as intracellular concentrations, the model appeared to be operating near steady state, although the amino acid groups AcEx and in particular AcExF showed reductions from the initial concentrations in the syncytiotrophoblast.

Simulated results at steady state were compared with the umbilical venous—arterial concentration difference from literature [7] and appeared to correspond reasonably well on first inspection Table 3 , without any tuning of the model parameters. However, the model over-predicted transfer for amino acid groups AcExF and ExF to various degrees and under-predicted AcEx and Ex, with the greatest relative discrepancy being for Ex.

Model simulation of amino acid transfer across the placenta, showing the amino acid concentrations of the different groups of amino acids in each of the placental compartments. Simulations using physiological amino acid concentrations Table 1 and model parameters from Table 2. Results represent the sum of all amino acids in each group. Note fetal AcExF rises sharply initially before going down again. Results demonstrated positive fetal delivery for all amino acids at steady state.

Umbilical venous—arterial concentration differences for each amino acid group. The effect of varying the relative activity of each transporter type was explored. Reference transport activity parameters V for the accumulative, MVM exchange, BM exchange, and facilitative transporter Table 2 were varied. Increasing the activities of accumulative and facilitative transporters promoted the placental transfer of all amino acid groups Fig.

Interestingly, the results also showed that while increasing the activity of particular transporters promoted the transfer of certain amino acids, this was detrimental to the transfer of others. For example, increasing BM exchanger activity would result in a decrease in fetal delivery of amino acids that are transported by facilitative transporters ExF and AcExF Fig.

However, surprisingly an increase in placental transfer was observed for AcExF Fig. This is because in the reference simulation the syncytiotrophoblast fraction of AcExF dropped from a high initial ratio of 0. Increasing MVM exchange activity would then promote AcExF uptake into the syncytiotrophoblast compartment and in turn increase transfer to the fetal compartment by facilitated transport. Thus, MVM exchangers affected BM transfer indirectly, and in opposite manners depending on how the overall transport system shifted the concentration ratios of each amino acid in the three compartments.

Lastly, it can be noted from Fig. Negative fetal delivery, corresponding to amino acid transport out of the fetal compartment into the syncytiotrophoblast can occur for AcEx at very low facilitated Fig. Individual transporter activity sensitivity analysis. Fetal venous—arterial difference at steady state for each amino acid group in response to variations in individual transporter activity with respect to the reference parameters Table 2. A series of simulations was performed in which two transporter activities were varied simultaneously to explore their interactions.

First, the overall impact of exchanger activity on net placental transfer of each amino acid was explored by varying both MVM and BM exchanger activities Fig. This showed that for amino acid AcEx, increasing exchange activity at the BM while reducing exchange activity at the MVM would result in optimal fetal delivery i. In contrast, for ExF and AcExF, both of which are facilitative substrates, increasing BM exchange activity could lead to reuptake into the syncytiotrophoblast.

Interestingly, for AcExF, the BM exchanger activity had opposite effects on net transfer depending on whether the MVM exchanger activity was high or low. It was shown that in addition to having both exchanger activities high, additional high AcExF transfer could occur when both activities were low.

This is because for low exchange activities the accumulative and facilitative transporters would dominate transfer, while back-exchange into the maternal and syncytiotrophoblast compartments is limited. For Ex, higher fetal uptake can be achieved by increasing both exchange activities, however, the overall transfer remained relatively small. Effects of exchanger activity. Fetal venous—arterial difference at steady state for each amino acid group when the exchanger activities at the MVM and BM were varied simultaneously.

Next it was investigated how overall transport is affected by the transporters on the MVM, by simultaneously varying the accumulative and MVM exchange activities Fig. The results showed that maximum placental transfer of AcEx and AcExF occurred when the accumulative activity is high, which promotes uptake into the syncytiotrophoblast, and the exchange activity is low, which limits back-exchange.

For Ex and ExF, the maximum delivery in the fetal compartment was achieved when both transporter activities at the MVM were high. This is because both transporters promote uptake via exchange into syncytiotrophoblast for these substrates, either directly or indirectly by increasing the intracellular concentrations of the driving substrates. Note that negative fetal delivery transport out of the fetal compartment into the syncytiotrophoblast occurred under certain conditions; for instance, for AcEx when the accumulative activity is low.

This occurred because low MVM uptake of AcEx meant that its ratio in the syncytiotrophoblast was lower than on the fetal side, leading to reverse transport by BM exchange. Effects of transporter activity at the MVM. Fetal venous—arterial difference at steady state for each amino acid group when varying the MVM exchanger and accumulative transporter activities simultaneously.

The impact of the transporter activities in the BM was evaluated by varying the activities of the BM exchanger and facilitative transporters Fig. The model suggested that for ExF and AcExF, the fetal delivery was optimal when the facilitative activity was high and the exchange activity at the BM was low.

This combination promoted transfer to the fetus, while at the same time limiting reuptake. Additionally, it was shown that for AcEx and Ex, which are not substrates of the facilitative transporter, the fetal delivery was increased when all transport activities were high at the BM. These substrates must be exchanged to transfer across the BM, therefore promoting exchange will directly increase their transfer, and this is promoted indirectly by increasing the facilitative activity, since this leads to a more favourable exchange ratio.

Effects of transporter activity at the BM. Fetal venous—arterial difference at steady state for each amino acid group when varying the BM exchanger and facilitative transporter activities simultaneously. The impact of maternal and fetal blood flow on placental transfer was analysed for each amino acid group. Flow rates were only found to be rate limiting when either maternal or fetal flow approached zero.

The system appeared to be most sensitive to changes in the fetal flow due to its small volume fraction Fig. In contrast, the maternal flow did not appear to significantly affect fetal delivery. The model suggested that a slow fetal flow rate translated to high fetal delivery for AcEx and Ex not facilitative substrates , while faster fetal flow rate would stimulate fetal delivery of ExF and AcExF facilitative substrates.

This is because for the facilitative substrates, high fetal flow maintains the BM concentration gradients driving facilitated transport. While for amino acids that cannot be transported by facilitative transporters, high fetal flow would maintain the less favourable influx concentration ratios, which determine transport by the exchangers. Flow sensitivity analysis. Net transfer to the fetus for each amino acid group in response to varying the maternal and fetal flow inputs simultaneously.

The initial amino acid levels and input concentrations in the maternal and fetal compartments were varied using the same factor for all four amino acid groups with respect to their reference concentrations in Table 1. In addition, maternal amino acids became limiting only at low levels. The results also showed that negative net transfer could occur when maternal concentrations are extremely low and fetal concentrations are high.

Effect of amino acid input concentrations. Fetal venous—arterial difference for each amino acid group in response to varying the overall maternal and fetal amino acid arterial input concentrations simultaneously. Note the concentrations of all amino acid groups were varied by the same factor.

The model parameters were fitted to determine which combination of transporter activities would provide the best overall fit of the fetal venous—arterial concentration differences from literature [7] Table 3. Compared to the reference simulations, fitting improved results especially for substrates that were initially under-predicted.

AcEx was matched closely to the literature values within 3. However, for AcExF and ExF the results deviated more from literature values than the original reference simulations. This very large increase in BM exchanger activity reflects the attempt by the algorithm to match amino acid Ex and its low sensitivity. Finally, the model was used to explore the genetic condition of maternal phenylketonuria, where lack of phenylalanine hydroxylase causes an excess level of phenylalanine that can affect fetal development and function [37].

Phenylalanine is an exchange and facilitated transporter substrate. Therefore, net transfer of each amino acid group was modelled over a range of maternal ExF by including the additional phenylalanine. The results showed that elevated concentrations of ExF in the maternal compartment reduced the net transfer of all other amino acid groups Fig. Moreover, the model predicted negative net transfer of AcEx and Ex at high maternal phenylalanine concentrations, which implies that these amino acids were transported out of the fetal compartment.

Effects of elevated maternal phenylalanine concentrations in phenylketonuria for each amino acid group. Note ExF rises as it includes phenylalanine, but all other amino acids are severely reduced. This study developed an integrated modelling approach to explain the interaction of transporters polarised to the microvillous apical and basal plasma membranes of the human placental syncytiotrophoblast. The modelling framework developed was effectively able to represent the complexity arising from the interactions between multiple species of amino acids and different types of transporters on both the MVM and BM.

This will prove invaluable in determining the contribution of specific transporters to epithelial transport in the placenta and other transport systems. The ability to predict how specific transporters contribute to overall function will allow the design of targeted interventions in epithelial transport disorders. The model first successfully described the fundamental transporter interactions at each of the placental plasma membranes separately, before these were combined for the system as a whole.

The accumulative-exchange transporter configuration at the MVM allowed the accumulation of all the different types of amino acids into the syncytiotrophoblast. Indirect stimulation of amino acids that were not substrates of the accumulative transporter could be achieved by increasing the accumulative transporter activity to promote exchange. The syncytiotrophoblast uptake concentrations of both accumulative and exchange amino acid species were substantially higher than the maternal concentrations.

This accumulation against the concentration gradient is enabled by the energy required to maintain the constant sodium gradient whose electrochemical potential provides the driving force for the system. Similarly, the model confirmed that the facilitative-exchange transporter configuration at the BM was sufficient to ultimately transfer all amino acids to the fetus. In addition, indirect stimulation of amino acids that were not a substrate of the facilitative transporter was shown to be possible by increasing the facilitated transport activity to promote exchange across the BM.

When the overall transfer across the placenta was considered using physiological concentrations, the integrated model operated close to steady state Fig. This indicated that the model could provide a relatively robust representation of placental amino acid transfer, despite many simplifying assumptions. Fitting results suggested that the model predictions could be improved by changing the activities for each transporter. Though, it appeared difficult to adjust independently the concentration of certain amino acid groups without affecting the transfer of others.

In particular, improving the prediction for the exchange only substrate required a disproportional increase in BM exchanger activity Table 3. Simultaneous variation of the transporter activities revealed that multiple configurations could result in high transfer for certain amino acids AcExF in Fig. Amino acids groups that were substrates of the accumulative transporter AcEx and AcExF generally behaved in the same way when considered at the MVM, in contrast with those that were not accumulative transporter substrates Ex and ExF, Fig.

Similarly, amino acid groups that were substrates of the facilitative transporter ExF and AcExF displayed the same response when observed at the BM, showing a distinctly different response compared with those that were not transported by the facilitative transporter AcEx and Ex, Fig. Against a background where strategies are being developed to specifically target placenta to deliver pharmacological or genetic therapies [38] , modelling may allow more informed decisions as to which transporters to target.

However, the differential effect on different amino acids by changing transporter activity should serve as a cautionary warning that potential unwanted side effects may be elicited by an intervention. Simulation results were shown to be most sensitive to fetal, rather than maternal flow due to the low compartmental volume. However, compared to the physiological reference values, increasing flow further did not lead to significant changes in transfer Fig.

Flow rates were only shown to be rate limiting when either maternal or fetal flow rates approached zero. Under the given conditions, substrates of the facilitative transporter displayed a positive relationship with flow, whereas the other amino acids showed the opposite behaviour. Maternal uterine and fetal umbilical blood flows are one of the few placental parameters that can currently be measured in vivo and this model may provide a basis for understanding their effect on the fetus.

It has to be emphasized that the current model was for the placenta and did not include maternal or fetal metabolism, which will alter amino acid availability in the maternal or fetal arteries. However, as demonstrated by the model, when overall maternal and fetal amino acid concentrations were varied, it was shown that placental transfer was increased by both high maternal and low fetal concentrations of amino acids, as would be expected. Nonetheless, placental transfer was mainly controlled by fetal concentrations, suggesting that amino acid transfer to the fetus is in part regulated by fetal demand.

Furthermore, this means that increasing overall maternal amino acid concentrations above physiological levels is unlikely to be an effective intervention strategy. However, interventions could also specifically target changing the relative amino acid composition which is important for exchanger function, as informed by the model. It is important to consider the simplifying assumptions made in deriving the current model. In particular, amino acids were grouped according to their specificity for the various transporter types and each transporter type was modelled as a single representative transporter.

In reality, numerous different individual transporters can be distinguished for each transporter type, each of which is specific to certain overlapping subsets of amino acids, with different substrate affinities [12]. In addition, since the main focus was on the function of the transporters as a coordinated system, individual transporter models were kept relatively simple, in order to capture faithfully the underlying mechanisms for each type, while minimising the number of unknown parameters.

For example, translocation and binding were assumed symmetric for the exchanger and facilitative transporter, however this is not an intrinsic limitation and given enough available data this assumption can be relaxed within the thermodynamic constraints for an energetically passive transport process [21] , [23]. For the active accumulative transporter the ultimate level of amino acid accumulation is determined by the sodium electrochemical potential difference, independent of the kinetics.

The effect of membrane potential was included for sodium in the accumulative transporter, however an important limitation of the current model was that Eqs. In addition, placental metabolism was not considered in the model, as the main focus was on transport; this could potentially change the amount of amino acids available for transport and their relative composition. Another aspect not included in the model was transfer via paracellular routes, which are poorly understood anatomically [39].

Paracellular diffusion will reduce the efficiency of the system because of high fetal amino acid concentrations, causing net diffusion in the fetal to maternal direction. All compartments in the model were assumed well-mixed, ignoring differences in local concentrations due to the maternal intervillous and fetal capillary flow. In addition, this implied that the intracellular concentrations in the syncytiotrophoblast were assumed uniform, rather than forming a gradient.

Nonetheless, further compartmentalisation within the syncytiotrophoblast could be important and this could lead to differences in the intracellular concentrations determining transport at the BM and MVM. While the model was designed for amino acids, the transporters included in the model also transfer a wide range of other substances including xenobiotics.

As such, the modelling framework can be widely applicable to transport functions both in the placenta and other transporting epithelia; for instance intestinal absorption of nutrients and drugs, reabsorption of nutrients from the renal tubules, and the transfer of nutrients and drugs across the blood brain barrier [41]. In summary, a novel integrated modelling framework was developed for the placental amino acid transfer system as a whole.

The model was shown to be able to capture successfully the principal features of the transfer system despite the necessary simplifying assumptions. Transporter modelling is currently limited by the availability of specific details about individual transporters, their kinetics and substrate specificity.

However, one of the strengths of this modelling framework is that it can easily be updated as experimental data becomes available. To illustrate the potential of the model for representing clinical scenarios, the case of phenylketonuria was modelled; demonstrating how elevated maternal phenylalanine would restrict fetal delivery of all other amino acids. Ultimately it is hoped that this type of modelling approaches will inform biological understanding and aid the development of targeted intervention strategies.

The Transparency document associated with this article can be found in the online version. Sponsored Document from. Biochim Biophys Acta. Panitchob , a K. Widdows , b, c I. Crocker , b, c E. Johnstone , b, c C. Please , e C. Sibley , b, c J. Glazier , b, c R. Lewis , d, f, 1 and B. Author information Article notes Copyright and License information Disclaimer. Sengers: ku. This article has been cited by other articles in PMC. Associated Data Supplementary Materials Transparency document.

Abstract Placental amino acid transfer is essential for fetal development and its impairment is associated with poor fetal growth.

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Simulation of such complicated structures is often extremely computationally expensive to run, possibly taking upwards of hours per execution. The Nelder—Mead method requires, in the original variant, no more than two evaluations per iteration, except for the shrink operation described later, which is attractive compared to some other direct-search optimization methods.

However, the overall number of iterations to proposed optimum may be high. It then extrapolates the behavior of the objective function measured at each test point in order to find a new test point and to replace one of the old test points with the new one, and so the technique progresses. The simplest approach is to replace the worst point with a point reflected through the centroid of the remaining n points.

If this point is better than the best current point, then we can try stretching exponentially out along this line. On the other hand, if this new point isn't much better than the previous value, then we are stepping across a valley, so we shrink the simplex towards a better point. An intuitive explanation of the algorithm from "Numerical Recipes": [5]. These steps are called reflections, and they are constructed to conserve the volume of the simplex and hence maintain its nondegeneracy.

When it can do so, the method expands the simplex in one or another direction to take larger steps. Unlike modern optimization methods, the Nelder—Mead heuristic can converge to a non-stationary point, unless the problem satisfies stronger conditions than are necessary for modern methods.

Many variations exist depending on the actual nature of the problem being solved. A common variant uses a constant-size, small simplex that roughly follows the gradient direction which gives steepest descent. Visualize a small triangle on an elevation map flip-flopping its way down a valley to a local bottom.

This method is also known as the flexible polyhedron method. This, however, tends to perform poorly against the method described in this article because it makes small, unnecessary steps in areas of little interest. In that case we contract towards the lowest point in the expectation of finding a simpler landscape. However, Nash notes that finite-precision arithmetic can sometimes fail to actually shrink the simplex, and implemented a check that the size is actually reduced.

The initial simplex is important. Indeed, a too small initial simplex can lead to a local search, consequently the NM can get more easily stuck. So this simplex should depend on the nature of the problem. Criteria are needed to break the iterative cycle. Nelder and Mead used the sample standard deviation of the function values of the current simplex. If these fall below some tolerance, then the cycle is stopped and the lowest point in the simplex returned as a proposed optimum.

Note that a very "flat" function may have almost equal function values over a large domain, so that the solution will be sensitive to the tolerance. Nash adds the test for shrinkage as another termination criterion. From Wikipedia, the free encyclopedia. Numerical optimization algorithm. Not to be confused with Dantzig's simplex algorithm for the problem of linear optimization. Mathematical Programming.

S2CID McKinnon, K. CiteSeerX Scientia Sinica [ Zhongguo Kexue ]: 53— Yu, Wen Ci. Scientia Sinica [ Zhongguo Kexue ]: 69— Kolda, Tamara G. To associate your repository with the nelder-mead topic, visit your repo's landing page and select "manage topics.

Learn more. Skip to content. Here are 38 public repositories matching this topic Language: All Filter by language. Sort options. Star Updated Jun 17, Python. Sponsor Star Updated May 19, C. Optimising chemical reactions using machine learning. Updated Jun 17, Jupyter Notebook. Updated Nov 2, Visual Basic. Updated Feb 4, Python. Updated Apr 1, Fortran. A Python easy implementation of the Nelder-Mead method.

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There are some real problem with matlab components If you use to install the two certification kits, it will fail if MATLAB Parallel Server has been installed beforehand. It's weird. I've tried to uninstall the whole matlab and reinstall it and the result is same. My solution is to use the old key of that combines parallel server with the kits.

I think that's the best solution at the moment. Please let me know if you think my observation is incorrect or if you have a better solution. Thanks for your feedback!!! Parallel Server can be considered as a "matlab for cluster node". I want to install the certification kits, but the installer checks if parallel server has installed As I understand mathwork's logic You need a special parallelserver's FIK for that. And this is just what they say in error on your screen Pay attention that it complains about matlab component while your FIK key does not even allow you to install matlab component!!!

That is why "old" key is totally better! The default directories given by the installer is a bit weird, I don't like it. So I customized it by having MathWorks as a parent directory. Here's the WizTree screenshot. Although the Polyspace itself doesn't shows up on Add-On Manager. It's just my wishful thinking, just forget it lol. Do they work in situation like that? Plus your rumaor is trange because there is no point in creation of AIO torrent-share Have you tried to install "standalone products" to the same directory?

I haven't tried it. And if you look at the uninstall menu on control panel, the products is listed separately.

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Stats 102A Lesson 8-2 Nelder Mead Method / Algorithm

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