Pairwise route synchronization constraints are commonly encountered in the field of service technician routing and scheduling and in the area of mobile care. Pairwise route synchronization refers to constraints that require that two technicians or home care workers visit the same location at exactly the same time. We consider constraints of this type in the context of the well-known vehicle routing problem with time windows and a generic service technician routing and scheduling problem. Different approaches for dealing with the problem of pairwise route synchronization are compared and several ways of integrating a synchronization component into a metaheuristic algorithm tailored to the original problems are analyzed. When applied to benchmark instances from the literature, our algorithm matches almost all available optimal values and it produces several new best results for the remaining instances. This research is motivated by a problem situation commonly encountered in the area of field staff routing and scheduling. It concerns the issue of pairwise route synchronization in both space and time. Many companies plan individual daily tours for each of their field employees since most tasks require only a single staff member. However, both in the service technician field and in the area of mobile care, for some of the tasks to be completed, two staff members are necessary. One example, brought to us by a company from the service technician industry, concerns tasks that demand ladders exceeding a certain size. In this case the second staff member is necessary for both mounting and securing the ladder during the execution of the task. A second example concerns the area of mobile care. For some of the daily hygiene tasks, overweight clients have to be lifted. Also in this case a second staff member is required. Pairwise time and space route synchronization introduces timely interrelationships between all those routes serving a client requiring a synchronized visit. In this paper we evaluate several different ways to deal with such a requirement in the context of a metaheuristic algorithm.In Sect. Route synchronization requirements are not only encountered in the area of mobile care or service technician routing and scheduling; they also exist in fields such as air craft fleet assignment, air borne parcel shipment, ready mixed concrete delivery, snow plowing, ship routing, person transportation, log-truck scheduling and military operations.In the area of mobile care, route synchronization has been addressed by Eveborn et al. , 2009 anMankowska et al.  considerA more generic point of view on routing with temporal dependencies between different routes is taken by Dohn et al. . They coIn the area of field employee routing and scheduling, Li et al.  propose In the context of aircraft fleet assignment, the issue of schedule synchronizations is considered by Ioachim et al. . The proSynchronization requirements are also considered in Armacost et al.  and ArmaIn ready mixed concrete delivery, synchronization issues involve the requirement of a support vehicle to assist in the unloading operations at some of the construction sites. The support vehicle has to arrive before or at the time the first vehicle delivering concrete arrives at the site. In addition, usually, the amount of concrete demanded at each site exceeds the capacities of the vehicles and once the concrete delivery has started it has to be continued (more or less) without interruption. The latter aspect introduces another synchronization requirement into the problem. Schmid et al.  solve thAlso in snow plowing operations, synchronization between vehicles is necessary on specific arcs in the street network . In the following, we denote the first problem as VRPTW with pairwise synchronization (VRPTWPS) and the second problem as STRSP with pairwise synchronization (STRSPPS).V is the set of vertices and A the set of arcs. A given number of locations n has to be served by a given number of routes m. For ease of exposition later on, two vertices are used to denote origin and destination depot of each route k, although they all refer to the same physical location. Thus, the set C or the technicians serving the routes are associated with qualification levels for different skills; in the latter case, k for skill f. The set of customer or task vertices is referred to as Q. Customer or task locations demanding synchronized visits are modeled as two distinct vertices. Then, i, j) costs i, j) is used by route k, and continuous variables i, we are now able to formulate the VRPTWPS:Both problems can be formulated on a directed graph s et al. , not sermentclass2pt{minimk being compatible with vertex i if the required qualification level is met. This can be achieved by setting i and k are incompatible.Replacing constraints  by11\docWe propose an adaptive large neighborhood search (ALNS) algorithm to solve the VRPTWPS and the STRSPPS. The algorithm is very similar to the ALNS developed in Kovacs et al.  for a STIn general, ALNS works as follows. Starting with a first feasible solution, in every iteration, a destroy and a repair operator are employed to the current incumbent solution, hopefully yielding a solution of improved quality. In ALNS, as first proposed by Ropke and Pisinger , a set oThe destroy operators employed in Kovacs et al.  and alsoThe employed repair operators are a greedy insertion, a sequential insertion Solomon , and sevThe initial solution is constructed with the greedy repair heuristic. Since we assume a large enough number of vehicles in the case of the VRPTWPS, and the outsourcing option in the case of the STRSPPS, a feasible solution can always be generated from scratch. In addition, the ALNS is embedded into a simulated annealing framework . Improvements in terms of solution quality of between 2 and 6.8% can be obtained in case of the STRSPPS and of between 3 and 8.5% in case of the VRPTWPS.Summarizing these results, we observe that, as expected, there is value in investing in improving the timing of tasks requiring synchronization. We also observe that approach C  has the largest impact on the solution quality. Adding approaches A and B on top of C does not always lead to additional improvements. In the case of the VRPTWPS, it leads to improvements for instance classes C1, C2, RC1 and RC2. In the case of the STRSPPS, the picture is different. Here it only leads to additional improvements for instance classes C2 and R1. In the case of instance classes C1 and RC1, it even leads to a slight deterioration in solution quality.n”), the average (“Avg.”) and best solution values (“Best”) of our method, their respective percentage deviations from the optimal values (“%”), and the average run time in seconds (column “Time(s)”).Although it is not entirely clear if only approach C or C in combination with A and B should be used, we used the combination of all three approaches in a comparison to optimal solutions. For this purpose, we implemented the previously described models in C++ using concert technology, CPLEX as solver engine and a run time limit of one hour. Since only few of the 100 customer/task instances could be solved to optimality, we also solved instances of reduced size, considering the first 25 and 50 customers of the VRPTWPS instances and the first 50 tasks of the STRSPPS instances. All instances that we were able to solve to optimality are reported in Table Table n), in terms of the number of tasks, the optimal values where known (Opt.), the best results published by Bredström and Rönnqvist  to available benchmark instances from the literature (Bredström and Rönnqvist önnqvist  and by Aönnqvist  (if no rWe observe that our method obtains several new best results and that it matches almost all available optimal values. We note, however, that the method of Afifi et al.  is fasteIn this paper, we have combined a large neighborhood search algorithm with three different approaches to deal with tasks which require visit time synchronization. The first approach is applied with a certain frequency to new solutions encountered during the execution of the ALNS. It tries to iteratively improve the timing of one task requiring a synchronized visit at a time. The second approach takes a more global view. It tries to simultaneously improve the timing of all synchronized tasks. Since this is more time consuming, it is only applied whenever a new best solution is found. The third approach integrates the timing of synchronized tasks into the removal and insertion routine of the LNS. We have evaluated different combinations of these approaches and we have found that the largest impact on solution quality is achieved by the third approach. For the VRPTW with pairwise route synchronization constraints, the best method combines all three approaches. For the STRSP with pairwise route synchronization constraints, the third approach is the best one, very closely followed by the combination of all three approaches. When applied to benchmark instances from the literature, our method obtains several new best solutions and it matches almost all known optimal values. Finally, we have also shown that considerable improvements in terms of solution quality are possible when the timing of tasks requiring synchronized visits is improved during the course of the algorithm. In this paper, we have only investigated problem settings where tasks require up to two persons to be completed and where travel and service times are considered to be deterministic. Future research will involve the consideration of stochastic travel times in combination with synchronization requirements and it should address settings in which more than two persons are necessary to perform a task.


The stochasticity stems from the updating schedule. Standard updating schedules include the synchronous update, where all the nodes are updated at the same time, and the asynchronous update where a random node is updated at each time step. The former produces a deterministic dynamics while the latter a stochastic dynamics. A more general stochastic setting considers propensity parameters for updating each node. Stochastic Discrete Dynamical Systems (SDDS) are a modeling framework that considers two propensity parameters for updating each node and uses one when the update has a positive impact on the variable, that is, when the update causes the variable to increase its value, and uses the other when the update has a negative impact, that is, when the update causes it to decrease its value. This framework offers additional features for simulations but also adds a complexity in parameter estimation of the propensities. This paper presents a method for estimating the propensity parameters for SDDS. The method is based on adding noise to the system using the Google PageRank approach to make the system ergodic and thus guaranteeing the existence of a stationary distribution. Then with the use of a genetic algorithm, the propensity parameters are estimated. Approximation techniques that make the search algorithms efficient are also presented and Matlab/Octave code to test the algorithms are available at  Mathematical modeling has been widely applied to the study of biological systems with the goal of understanding the important properties of the system and to derive useful predictions about the system. The type of systems of interest ranges from the molecular to ecological systems. At the cellular level, gene regulatory networks (GRN) have been extensively studied to understand the key mechanisms that are relevant for cell function. GRNs represent the intricate relationships among genes, proteins, and other substances that are responsible for the expression levels of mRNA and proteins. The amount of these gene products and their temporal patterns characterize specific cell states or phenotypes  = s1, and fk(x1(t), …, xn(t)) = s2, then xk(t+1) = s2 with probability xi, i = 1, …, n, the probability of changing its value is given byThe stochasticity originates from the propensity parameters x, y ∈ S. The transition from x to y is given byLet Prob(xi → yi) = 0 for all yi ∉ {xi, fi(x)}.Notice that Then the transition matrix is given byaxy, which depend on the propensity values and the update functions. Online software to test examples is available at http://adam.plantsimlab.org/  in the model type).The dynamics of SDDS depends on the transition probabilities axy = p(Xt = x|Xt − 1 = y) represents the probability of being in state x at time t given that system was in state y at time t − 1. If πt = p(Xt = x) represents the probability of being in state x at time t, then we will assume that π is a row vector containing the probabilities of being in state x at time t for all x ∈ S. If π0 is the initial distribution at time t = 0, then at time t = 1,In Markov chain notation, the transition probability If we iterate (Equation 3) and if we get to the point whereIn this section we describe a method for estimating the propensity parameters for SDDS. The approach is based on adding noise to the system using the Google PageRank . 0, For any initial probability vector πA associated with the eigenvalue 1The vector π is the unique probability vector which is an eigenvector of .A proof of Theorem 2.1 can be found in Chapter 10 of Lay .Ak contains only strictly positive entries. However, the transition matrix A of SDDS given in Equation (2) might not be regular. In the following subsection, we use a similar approach to the Google's PageRank algorithm to add noise to the system to obtain a new transition matrix that is regular.Theorem 2.1 ensures a unique stationary distribution π provided that we have a regular transition matrix, that is, if some power fi:S → Si, S = Kn, and |K| = p. Then its transition matrix A given in Equation (2) is a pn × pn matrix. To introduce noise into the system we consider the Google Matrixg is a constant number in the interval  and K is a pn × pn matrix all of whose columns are the vector . The matrix G in Equation (5) is a regular matrix and then we can use Theorem 2.1 to get a stationary distribution for G,For simplicity, consider a SDDS, x∈S can be measured by the size of the corresponding entry πx in the stationary distribution of Equation (6). For instance, for ranking the importance of the states in a Markov chain one can use the size of the corresponding entries in the stationary distribution. We will refer to this entry πx as the PageRank score of x.This stationary distribution reflects the dynamics of the SDDS prop* such that its stationary distribution *. That is, we search for propensity matrices such that the distance between π and π* is minimized,The entries of the stationary distribution π in Equation (6) can also be interpreted as occupation times for each state. Thus, it gives the probability of being at a certain state. Now suppose that we start with a desired stationary distribution http://www.ms.uky.edu/~dmu228/GeneticAlg/Code.html.The pseudocode of this genetic algorithm is given in Algorithm 1 and it has been implemented in Octave/Matlab and our code can be downloaded from x∈S and then with probability g we move to another state y∈S according to axy (see Equation 1) and with probability 1−g we jump to a random node. We repeat this process for a given number of iterations. At the end of a maximum number of iterations, we count how often we visited each state and the normalized frequencies will be the approximated stationary distribution.The genetic algorithm, Algorithm 1, uses the exact stationary distribution through PageRank (see Equation 6) which is computationally expensive for larger models. Here we present an efficient algorithm for estimating the stationary distribution based on a random walk. The expensive part of Algorithm 1 is the calculation of the stationary distribution π in Equation (6). We have implemented an algorithm for estimating the stationary distribution by doing a random walk using SDDS as a generative model; see Algorithm 2. The idea behind Algorithm 2 is to use SDDS for simulating from an initial state according to the transition probabilities given in Equation (5). That is, we initialize the simulation at an initial state http://www.ms.uky.edu/~dmu228/GeneticAlg/Code.html.To make the genetic algorithm more efficient, we used the estimated stationary distribution described in the previous paragraph. Thus, within the fitness function of Algorithm 1, we use the estimated stationary distribution to assess the fitness of the generated propensity matrices. The pseudocode for this new algorithm is the same as Algorithm 1, the only change is in the fitness function. This version of the algorithm has also been implemented in Octave/Matlab and our code can be found in We test our methods using two published models that are appropriate for changing the stationary distribution under the choice of different propensity parameters. The first model is a Boolean network while the second is a multistate model. In both models bistability has been observed but the basin size of one of the attractors under the synchronous update is much larger than the basin of the other attractor, and thus the stationary distribution will be more concentrated in one of the attractors. We will use our methods to change the stationary distribution in favor of the attractor with a smaller basin.Lac-operon network. The lac-operon in E. coli  and s2 =  that represent the state of the operon being OFF and ON, respectively.Example 2.2. g = 0.9 in Equation (5). First we used the propensity values given in Equation (10) where all propensities are fixed to 0.9. This choice of parameters approximates the synchronous dynamics in the sense that each function has a 90% change of being used during the simulations and 10% chance of maintaining its current value. Under this selection of parameters, the fixed point s1 has a PageRank score of 0.3346 while the other fixed point s2 has a score of 0.0463, see Figure s2 and decrease the score of s1. After doing so, we found the propensity parameters given in Equation (11). With this new set of parameters, the fixed point s1 has a score of 0.0199 while s2 has a score of 0.5485, see Figure s2 and the size of the labels of the nodes were scaled according to their PageRank score, see Table To test our method we calculated the stationary distribution of the system using Equation (6) with Equation 0 where aEquation 0 where aEquation 0 where aPhage lambda infection. The outcome of phage lambda infection is another system that has been widely studied over the last decades . CI is fully repressed provided that CRO is active and CII is absent.Example 2.3. This network is a bistable switch between lysis and lysogeny. Lysis is the state where the phage will be replicated, killing the host. Otherwise, the network will transition to a state called lysogeny where the phage will incorporate its DNA into the bacterium and become dormant. These cell fate differences have been attributed to the spontaneous changes in the timing of individual biochemical reaction events . First we used the propensity values given in Equation (12) where all propensities are fixed to 0.9. This choice of parameters approximates the synchronous dynamics in the sense that each function has a 90% change of being used during the simulations and 10% chance of maintaining its current value. Under this selection of parameters, the fixed point 2000 has a PageRank score of 0.2772 while the states of the cycle 0200 and 0300 have scores of 0.2185 and 0.2108, respectively. Notice that this cycle attractor will have an overall score of 0.4293, see Figure To test our method we calculated the stationary distribution of the system using Equation (6) with quation 1 where alquation 1 where alquation 1 where alParameter estimation for stochastic models of biological networks is in general a very hard problem. This paper focuses on a class of stochastic discrete models, which is an extension of Boolean networks. The methods presented here use a well stablished approach for introducing noise into a system in a way that ergodicity and thus the existence of a unique stationary distribution is guaranteed. Then a genetic algorithm for calculating a set of parameters able to approximate a desired stationary distribution was developed. Also, techniques for approximating the stationary distribution at each iteration of the genetic algorithm that make the search process more efficient was applied.One shortcoming of the method is that it is a stochastic method. That is, each time we run the algorithm we get a different result. An exhaustive investigation about the variance of the results is still missing. For the examples that we presented in the results section, the output of the algorithm might vary in about 20% of the reported propensities.In parameter estimation, sometimes, it is useful to identify a smaller set of key parameters to estimate. This problem is out of the scope of the paper. However, for Boolean network models, one way to address this problem could be by using the different network reduction algorithms, for instance see Veliz-Cuba et al.  and Saad10 = 1024) and a multistate network with 4 nodes where each node has 5 states (where the size of the state space is 45 = 625). For each system, we were able to redirect the system toward the attractor with the smaller PageRank score. The method is efficient and for the examples we have shown it can be run in few seconds in a laptop computer. Our code is available at http://www.ms.uky.edu/~dmu228/GeneticAlg/Code.html.In this paper we present an efficient method for estimating the parameters of a stochastic framework. The modeling framework is an extension of Boolean networks that uses propensity parameters for activation and inhibition. Parameter estimation techniques are needed whenever one needs to tune the propensity parameters of the stochastic system to reproduce a desired stationary distribution. For instance, if dealing with a bistable system and if it is desired to have the stationary distribution that have the PageRank score concentrated in one of the attractors of the system, then one needs to estimate the propensity parameters that represent such a desired distribution. Parameter estimation methods for this purpose were not available. In this paper we present a method for estimating propensity parameters given a desired stationary distribution for the system. We tested the method in one Boolean network with 10 nodes (where the size of the state space is 2DM, JM, and AM designed the project. JM developed the genetic algorithm and implemented the Matlab code. AM run simulations for the results section. DM wrote the paper. All authors approved the final version of the manuscript.DM was partially funded by a startup fund from the College of Arts and Sciences at the University of Kentucky.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Toward the northwest in El Salvador the northern sliver boundary is marked by a dextral strike-slip fault system active since Late Pleistocene time. To the southeast there is no consensus on what constitutes the northern boundary of the sliver, although a system of active crustal faults has been described in central Costa Rica. Here we propose that the Haciendas-Chiripa fault system serves as the northeastern boundary for the sliver and that the sliver includes most of the Guanacaste volcanic arc, herein the Guanacaste Volcanic Arc Sliver. In this paper we provide constraints on the geometry and kinematics of the boundary of the Guanacaste Volcanic Arc Sliver that are timely and essential to any models aimed at resolving the driving mechanism for sliver motion. Our results are also critical for assessing geological hazards in northwestern Costa Rica.Recent studies have shown that the Nicoya Peninsula of northwestern Costa Rica is moving northwestward ~11 mm a Geodetic work has demonstrated that in northwestern Costa Rica, the Nicoya Peninsula is moving northwestward ~11 mm a−1 relative to eastern Costa Rica11. Forearc motion in El Salvador, to the northwest, is accommodated by a well characterized dextral strike-slip fault system13. The configuration of the sliver to the southeast in the more populous parts of Costa Rica has to date remained unresolved. As a consequence, the scale of the tectonic sliver and the potential roles that it might play in the tectonic, seismologic and volcanic history of Costa Rica are poorly understood. Here we document a fault system that we suggest serves as the northeastern margin of the sliver, and that traverses the Guanacaste volcanic arc. The configuration of this tectonic boundary, herein referred to as the Haciendas-Chiripa fault system, requires that what has previously been described as a forearc sliver10 includes most of the Guanacaste volcanic arc. By documenting the geometry and kinematics of this fault system on the margin of the Guanacaste Volcanic Arc Sliver (GVAS) we provide constraints that are essential for models of sliver motion that aim to disentangle the relative contributions of ridge collision10, oblique subduction2 or trailing edge plate forces14.Ever since forearc slivers were first identified16. Widespread mesoscale faulting in the CCRDB has been attributed to the subduction of rough seafloor at the MAT16. This interpretation is in agreement with the observation that the western edge of the CCRDB meets the Pacific coast at the northeast-trending boundary on the downgoing Cocos plate that separates smooth seafloor to the northwest from rough seafloor to the southeast18. In western Costa Rica the Cocos plate is subducting toward the northeast at ~81 mm a−1 relative to CA, and at a high angle to the MAT2. Recent mapping suggests that locally the CCRDB is being crosscut by the dextral Atirro-Río Sucio fault system that accommodates lateral extrusion of the upper plate in response to Cocos Ridge collision6.Central Costa Rica occupies the southern boundary of the Caribbean plate (CA) where it is in contact with the Panama microplate, and is bounded to the southwest by the Middle America Trench  expose oceanic basement and cover sediments of fluvial and marine origin20. The Costa Rican forearc appears to reflect the influence of lower plate architecture. For example, immediately inboard of the Quepos Plateau  and northward tilting22.Northwestern Costa Rica is dominated by the northwest-trending, extinct ~1.0–2.2 Ma) Monteverde volcanic arc, and the active Guanacaste volcanic arc Fig.  reflecti.0–2.2 Ma8 showed that the Nicoya Peninsula is moving essentially as a rigid block, and that the trench-parallel component of motion diminishes significantly eastward across the Gulf of Nicoya and the area of Lake Arenal  and used HypoDD24 to locate earthquakes precisely and these define a seismic source zone where field observations confirm evidence of active or recent faulting. In Fig. Well-located crustal earthquakes and focal mechanism solutions provide robust constraints on the northeastern GVAS boundary Figs  and 2. Wa  reveal evidence of recent or active faulting along the Haciendas-Chiripa fault system. The northern flank of the Guanacaste volcanic arc in northwestern Costa Rica is marked by a clear topographic lineament Fig.  that inca Fig.  there isa Fig. . The steb  shear planes  step Fig. . Near thd in Fig. d . A local resident reported to us in June of 2016 that he noted changes to the landscape in the immediate aftermath of the 2002 earthquake that are consistent with overall northward motion of the hangingwall – specifically open cracks parallel to the fault trace. The occurrence of thrusting north of the main trace of the Caño Negro segment suggests local partitioning of slip within the fault system.In the eastern sector, the Caño Negro fault is marked by geomorphic expressions of active or recent slip. North of the town of Bijagua 27 and is marked by the west-facing scarp seen at Fig. 26. To the west, the outcrop is cut mostly by normal faults oriented at high angles to the PDZ and that record an average of ~0.6 m of dip separation . The geodetic results would also highlight targets for complementary geomorphology and paleoseismology investigations. More fundamentally, expanded geodetic work spanning northwestern Costa Rica is essential for addressing the mechanisms that drive sliver motion. Outstanding questions include: (1) When did the sliver form? (2) What is the distribution of slip partitioning on the margins of the sliver? and (3) What is the relationship between the sliver and the segmentation of the volcanic arc? If the sliver reflects only Cocos-ridge collision then it should be no older than the first arrival of the ridge at the MAT ~2–3 Ma31. Moreover, the faults accommodating lateral escape might be expected to show an age-progression that reflects northward and radial expansion of the collision zone. This might be reflected by older slip on the Candelaria fault and more recent slip on the San Miguel-Rio Sucio-Atirro fault system  suggest that the current volcanic front of Costa Rica initiated at ~600 Ka, a time of near complete cessation of volcanism in the gap between the Guanacaste Volcanic arc and the Central Volcanic Cordillera  from March 2006 through August 2016 (Supplementary Table 23. After finding the manual locations the events were relocated with a double difference algorithm using HypoDD24 (Supplementary Table The velocity model used for the manual locations is one-dimensional and consists of 6 layers made for the area and with the station corrections obtained with VelestThe configuration for the double difference relocation was for a medium size dataset, with high certainty of the manual picks. The data used consisted of a catalog of P and S arrival manual picks with a maximum distance of 200 km, with a maximum hypocentral separation of 10 km between events, 10 as maximum number of neighbors per event and a minimum of 5 links to define a neighbor. The initial location is from the catalog and the relocation was resolved in two sets of 5 iterations. The weight for P arrivals was set at one for both sets and a weight of −9 and 0.75 for the S arrivals. The residual threshold in seconds for the first set of iterations was not taken into account and a 5 second threshold for the second set of iterations, and a maximum distance between linked pairs was not restricted for the first iteration and a maximum of 3 km for the second set of iterations. The damping factor used for the first and second iterations was set at 50 and 60, respectively.w 3.5 using the program Focmec40 and searching every 5 degrees for best solutions (Supplementary Table Lastly, the new earthquake locations were used to generate focal mechanism solutions. For this we used events with magnitudes greater than MSupplementary Tables S1 and S2


The stochastic simulation algorithm commonly known as Gillespie’s algorithm  is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular level it is often reasonable to assume that times between successive reaction/interaction events are exponentially distributed and can be appropriately modelled as a Markov process and hence simulated by the Gillespie algorithm. However, Gillespie’s algorithm is routinely applied to model biological systems for which it was never intended. In particular, processes in which cell proliferation is important  should not be simulated naively using the Gillespie algorithm since the history-dependent nature of the cell cycle breaks the Markov process. The variance in experimentally measured cell cycle times is far less than in an exponential cell cycle time distribution with the same mean.Here we suggest a method of modelling the cell cycle that restores the memoryless property to the system and is therefore consistent with simulation via the Gillespie algorithm. By breaking the cell cycle into a number of independent exponentially distributed stages, we can restore the Markov property at the same time as more accurately approximating the appropriate cell cycle time distributions. The consequences of our revised mathematical model are explored analytically as far as possible. We demonstrate the importance of employing the correct cell cycle time distribution by recapitulating the results from two models incorporating cellular proliferation  and demonstrating that changing the cell cycle time distribution makes quantitative and qualitative differences to the outcome of the models. Our adaptation will allow modellers and experimentalists alike to appropriately represent cellular proliferation—vital to the accurate modelling of many biological processes—whilst still being able to take advantage of the power and efficiency of the popular Gillespie algorithm. In a well-mixed solution of chemicals undergoing reactions, non-reactive collisions occur far more often than reactive collisions allowing us to neglect the fast dynamics of motion. We can thus assume that the time between reactive collision events is exponentially distributed with rates which are a combinatorial function of the numbers of available reactants  are rate-limiting.However, the Gillespie algorithm is often used inappropriately to represent processes for which the inter-event time is not exponentially distributed. One prevalent example of this is in the simulation of the cell cycle  Stewart . HypoexpRecently, Weber et al.  have sugd Martin  who use d Martin . Bel et d Martin  showed tIn this paper, we consider two special cases of the general hypoexponential distribution: the Erlang and exponentially modified Erlang distribution which, in turn, are special cases of the Gamma and exponentially modified Gamma distributions. For reference, their PDFs  Golubev   into k stages.We divide the cell cycle  that the CCTD is Erlang distributed with scale parameter k. In analogy with the general hypoexponential case, if we decrease k so that C, demonstrating that we can still arbitrarily reduce the variance to match the distribution we are trying to model.The hypoexponential model’s generality is also a significant drawback since it hampers parameter identifiability :32\:32\S, car et al.  write dor et al.  argue thk . As before, we chose the parameter of each stages’ waiting time to ensure we have the same mean proliferation attempt time as in the original model.Next we investigate the effect of incorporating a more realistic model of cell proliferation on the behaviour of a spatially extended individual-level model of cell migration and proliferation ; this results in the cell’s current proliferation stage being incremented by one if the cell is currently in one of the first k) of proliferation and is selected to change stage, then the cell attempts to place a daughter in one of its four neighbouring lattice sites with equal probability. If the chosen site is empty, the cell places a daughter in the empty site and the proliferation stages of both the parent and the daughter are reset to unity. However, if the cell attempts to place a daughter in a site which is already occupied, then that proliferation event is aborted. In the multi-stage model of the cell cycle, we then have two choices:the progression stage of the cell attempting proliferation is reset to unity;kth stage.the cell remains in the In the original model in which Agents undergo a proliferation stage change with rate  Simpson , we willFigure k (black). Under implementation (1), every cell can be found in any stage of the cell cycle so it is hard to distinguish the proliferating rim  generally leads to less dense colonies than implementation (2) since cells do not attempt division as frequently. Under implementation (2) see Fig. e, f, a csee Fig. b, c. Thek independent of the implementation ((1) or (2)). However, the variance in the CCTDs for low-density systems affects the rate of growth with larger values of k (less variance in the CCTD) generally leading to slower growth. This effect can be understood by considering Eqs. k indepenIn Fig. k. The increased variance of cells with fewer stages results in faster population growth.Under implementation (1) see Fig. a–c, evenk at late  times, when the density is higher. Contrastingly, when proliferation is high in comparison with motility  see Fig. d–f, cellsee Fig. f, clustek [exemplified by Eqs.  for fork [exCurrently, many stochastic models which incorporate cell proliferation employ the ubiquitous Gillespie stochastic simulation algorithm (Gillespie We postulate that the general hypoexponential distribution (Zhou and Zhuang We employed our improved model of cell cycle proliferation times on two recent models of real biological processes (Turner et al. The application here of hypoexponentially distributed CCTs built up from a number of intermediary exponential stages assumes that the CCT is not correlated between direct descendants or within a given generation. Whilst there are scenarios in which there is no evidence for a correlation in CCT between related cells (Schultze et al.


With the current proliferation of data, the proficient use of statistical and mining techniques offer substantial benefits to capture useful information from any dataset. As numerous approaches make use of information theory concepts, here, we discuss how Fisher information (FI) can be applied to sustainability science problems and used in data mining applications by analysing patterns in data. FI was developed as a measure of information content in data, and it has been adapted to assess order in complex system behaviour. The main advantage of the approach is the ability to collapse multiple variables into an index that can be used to assess stability and track overall trends in a system, including its regimes and regime shifts. Here, we provide a brief overview of FI theory, followed by a simple step-by-step numerical example on how to compute FI. Furthermore, we introduce an open source Python library that can be freely downloaded from GitHub and we use it in a simple case study to evaluate the evolution of FI for the global-mean temperature from 1880 to 2015. Results indicate significant declines in FI starting in 1978, suggesting a possible regime shift. Thereatlab, and the deployed applications are accessible by contacting the code developer directly  mean (ϑ) is at least 1 − 1/k2′  = 4 × (0.375 + 0.13 + 0 + 0.21 + 0.125) = 4 × 0.534 = 2.136.The probability distribution for the sample data in 1, FI2 and FI3) are averaged, and that average value acts as the representative for all the three consecutive FI values. The averaging is essentially a high frequency filter. Note the number of years including the averaging has to be smaller to capture more accurate trends in dynamic order.In practice, system variables fluctuate such that not all the variables meet the size of state criteria. Therefore, a new parameter called tightening level (TL) is introduced to adjust the binning criteria. The TL adjusts the binning criteria such that a point can be declared to be within a given hyper-rectangle (a particular state of the system) when a certain percentage of the variables meet the size of states criteria . For exa4.t ≈ 0).— A system is considered to be in an orderly dynamic regime when a non-zero FI remains nearly constant over time  and low standard deviation in FI (σFI) [Further, researchers have noted that the actual FI value is not as important as the ability of the system to remain within a desired regime. Accordingly, when comparing different regimes, note that a stable system regime has a relatively high and stable mean FI (FI (σFI) ,21 than Researchers have studied the behaviour of FI in the neighbourhood of a tipping point . While m5.https://github.com/csunlab/fisher-information (accessed 10 July 2016) were used to compute FI for this study.To illustrate the use of FI for assessing system stability, we assessed the evolution of FI as global-mean temperature changed from 1880 to 2015. The data were collected from the National Aeronautics and Space Administration (NASA), Goddard Institute for Space Studies . The data shows the evolution of the global-mean temperature from 1880 to 2015 and figure 4b provides the FI for the corresponding data. A window size of 40 is chosen, a moving window increment of 1 is used and FI is assigned at the end of the window; therefore, the first value reported is for 1919, representing 1880 to 1919. From the figure, we observe a significant change in FI from 1978 with continual decrease since then, suggesting a rapid change in the global-mean temperature. Moreover, the FI for the period of 1919 to 1978 was more stable with an average (µFI) of 5.09 and standard deviation (σFI) of 0.89, than the period of 1979 to 2015 . The decline in FI from 1979 to 2015 represents a 62.62% change indicating significant variation in global temperature patterns.Figure 4Naturally, these analyses are not sufficient to fully capture how the global climate is performing, however, the change in the FI trajectory during the late 1970s corresponds with the period in which our global societal demand  also began to surpass the global biocapacity to supply that demand . Moreove6.atlab with deployed applications available only by contacting the code developer directly. The creation of an open access Python script offers significant opportunities for the general scientific community to facilitate the calculation of FI for any multivariate data. The assessment of global temperature provides a simple case study and suggests that it appears to have destabilized in the latter part of the twentieth century (i.e. since 1978) which corresponds to increasing ecological demand, declining biocapacity, and the initial stages of the new Anthropocene. This case study afforded the ability to demonstrate the power of the index and shows how FI can provide information about trends in complex system behaviour. This effort showcased FI as a viable tool for mining data. By providing public access to the Python script for FI, we hope to expand use of the method to a broader audience who may be interested in methods for detecting hidden trends and identifying signals useful for system evaluation and management.The main objective of this work was to present FI as a useful method for data mining applications by demonstrating its use in assessing patterns in complex system data . FI has


The ultracold atomic gas serving as the quantum reference is a key part of an optical lattice clock, and the temperature of atoms in the optical lattice affects the uncertainty and instability of the optical lattice clocks. Since the carrier spectrum of the clock transition in the lattices reflects the thermal dynamics of cold atoms, the temperature of atoms can be extracted from the carrier spectrum in a non-magic wavelength lattice of ytterbium optical clocks. Furthermore, the temperatures obtained from the carrier spectra are in good agreement with the results obtained by the time-of-flight method and thermometry based on the sideband spectrum. In addition, the heating effects caused by the lattice laser are studied on the basis of the sample temperatures. The best 87Sr clock now achieves an instability of 2.2 × 10−16 at 1 s and a total uncertainty of 2.1 × 10−18 in fractional frequency units12. These state-of-the-art clocks benefit from the great control of ultracold atoms that play the role of quantum references. They are confined in tight optical lattices with the ac Stark shift being eliminated by tuning the lattice laser to the “magic wavelength”14. Although the Doppler and recoil shifts can be reduced by confining the atoms in 1D optical lattices and probing along the lattice axis in the Lamb-Dicke and resolved sideband regimes17, for a finite temperature only a fraction of atoms occupy the motional ground state. The collisional shifts are directly related to this atomic temperature19. So the temperature as one of most important properties of a cold atom sample should be determined accurately. The conventional thermometry techniques of characterization of the cold atoms in optical lattices are time-of-flight (TOF) expansion imaging20 and thermometry based on the sideband spectrum (TSS). The former is realized by measuring the ballistic expansion of atomic clouds released from the trap at different times, while the latter is based on the sideband spectrum, for which the areas of spectrum of blue and red sidebands are different16. TOF is a routine method to determine temperatures of cold atoms in many laboratories, while TSS is developed to determine temperatures of cold ensembles in an optical lattice. These methods have a precision varying from a few percent to several tens of percent which depends on the experimental condition and the signal-to-noise ratio25.In the last decade, research in the field of optical lattice clocks has experienced a fast development, especially the clocks based on cold nz = 0). We assume the atoms are not cold enough to degenerate, so they still satisfy the Boltzmann distribution which results in the expression as16kB is the Boltzmann constant. The longitudinal temperature Tz can be calculated directly from equation  of the carrier line shape, 25 to map temperature of atoms or molecules in optical lattices via a differential spectroscopic light shift. TCS is limited to the narrow spectral lines of atoms or molecules confined tightly in optical lattices, which is suitable for the optical lattice clocks. We apply TCS to determine the temperature of cold ensembles in an ytterbium optical lattice clock. And we demonstrate the TCS method in an ytterbium optical lattice clock which is different from the experiment in ref.25. On the other hand, we show that the TCS method is an alternative method to map the temperature of cold ensembles in an optical lattice clock. From the accurately determined temperature it is possible to calculate the cold atom distributions and acquire such information as the light shift caused by thermal contributions and thermal line pulling. In this paper, we firstly present the clock transition spectrum including the carrier, the first-order and second-order sidebands spectrum. We then show the temperatures obtained by the three above mentioned methods. In conclusion the heating effects caused by the lattice laser are discussed.In this paper, we show another thermometry technique based on the carrier spectrum (TCS), which is consistent with TOF and TSS. As is well known, TOF is no longer reliable due to low particle numbers or a lack of cycling transitions, and it needs two samples of cold atoms for probing different radii at different times, during which the cold atom samples are destroyed by the probe laser. TSS is based on the ratio of integrated sideband absorption and there is no contribution from the red sideband mentclass2pt{minim17. Normally, the first-order sidebands are easily observed when the motional state is excited to the increased and decreased motional state by 1. The relative size of the sidebands is not only proportional to the Rabi frequency but has also other factors that influence the sideband intensities. The effective Rabi frequency of the lth order sidebands is proportional to ηl, where η is the Lamb-Dicke parameter that can be expressed as fz is the trap frequency and 26. In the Lamb-Dicke regime η < 1, the sideband intensity shrinks drastically with increasing sideband order, which makes their detection problematic. The atoms in the optical lattice are not cold enough to degenerate and still satisfy the Boltzmann distribution, so there are still a number of atoms that populate a high motional state. This, in turn, means the second-order sidebands  may be observed. Here we not only obtain the carrier and first-order sidebands spectrum, but also for the first time observe the second-order sidebands in the ytterbium optical lattice clock experiments, which is shown in Fig. 16, according to the harmonic approximation model, the first-order longitudinal energy gap is given asAfter preparing ultracold ytterbium atoms and loading into the optical lattice (see Methods), the atoms are probed along the lattice axis in the Lamb-Dicke and resolved sideband regimes with the clock laser at 578 nm. As shown in Fig. We can write the second-order longitudinal energy gap as28, accordingly the lattice trap depth of the excited and ground state is different due to the linear relation to the polarizability. The different polarizabilities lead to the ac Stark shift which can be expressed as 171Yb in optical lattices, the polarizability of the excited state is larger than the polarizability of the ground state 14. Considering the polarizability as the dominant term, the light shift is positive for The optical lattice clock is operated at the magic wavelength, where the polarizability of the excited and ground states is equal and the ac Stark shift is eliminated. When operating the optical lattice at a non-magic wavelength, the polarizability of the excited and ground state is no longer the samenz motional state deviates from the nominal clock frequency ν0 by a value of nzdν. Here dν is the difference between the excited state and ground state trap frequencies. With the Boltzmann distribution of cold atoms in the lattice, the spectrum of the carrier can be considered as a superposition of all the motional states and the line shape of a single transition between two motional states is a Lorentzian form with the weight of the occupation probability 25 as Due to different lattice trap depths of the excited and ground state at a non-magic wavelength, the carrier transition frequency of the m by a lattice photon with wavelength λL. For the thermometry experiments, the trap depth U0 = 450ER is obtained from the spectrum including the carrier and first-order sidebands.We measure the temperature of cold atoms in the lattice with a trap depth characterized by the recoil energy, t1, t2 are the times after the lattice laser is shut, a(t1), a(t2) are the expansion radii of the atom clouds released from the optical lattice trap at time of t1 and t2, which can be directly read out from the images. The temperatures are plotted for three different intensities of 556 nm laser (the second cooling laser) in Fig. 30 as 394,798.33(0.01) GHz. The unbroadened carrier linewidth is about 6.9 Hz, approaching the Fourier-limited linewidth with a 150 ms interrogation time31. The temperatures in Fig. nz ≥ 2, which means a higher temperature34. Although only the longitudinal temperature is determined from the first-order sideband spectrum and equation  at 5 ms and 10 ms after the lattice laser is shut and the atom clouds emit fluorescent light when the C and α′/α can be determined from the carrier spectrum as shown in Fig. α′/α can be extrapolated by the expression of W0 is the nonthermal light shift caused by the lattice laser25. It follows from equation (α′/α (see Methods). The theoretical spectroscopic line shape of equation . Its frequency is locked to the build-in cavity and can be measured by a wavemeter with the 10-MHz uncertainty.Figure 25 asδEi is a differential light shift. The equation (u is zero as δEi = 0, which corresponds to zero light shifts. So the nonthermal light shift is the zero point of the line shape function. The fitting parameters yield the nonthermal light shift as W0/h = c/b.The line shape of the carrier can be expressed


SAM) under real‐life conditions in Germany. Database: Administrative data  for all individuals in Germany insured with the Statutory Health Insurance. Basic population: individuals 18 years and older who have been insured continually from 2009 to 2011 . Data access is provided by the German Institute of Medical Documentation and Information, DIMDI) according to the Data Transparency Regulation of 2012. Statins: identification with the ATC–Codes: C10AA, C10BA and C10BX. Study population: incident statin users in 2010 with a diagnosis of lipid disorders  in the first statin prescription quarter or in one of the three following quarters. The first event is considered for the incidence estimate. The daily doses included in a package were classified as “days under therapy” (by assuming one DDD) and taken as exposition time. SAM was found in 1.9% of 531 672 incident statin users. The percentage differs according to the patterns of statin use: the lowest incidence is observed in those with only one prescription (1.3%), the highest incidence with 5.0% is observed in those who not only stopped the treatment within 365 days, but who also had their statin changed. Administrative data including diagnoses from ambulatory care provide a realistic estimate of SAM frequency in every day practice.Aim of the study was to assess the incidence of statin‐associated myopathy ( ATCAnatomical Therapeutic Chemical (ATC) classification systemCKcreatine kinaseCTTCholesterol Treatment TrialistsDaTraVInformation system health care dataDDDDefined Daily DoseDIMDIGerman Institute of Medical Documentation and InformationICD 10 GMInternational classification of Diseases‐ German ModificationPADperipheral arterial diseaseSAMstatin associated myopathySHIstatutory health insuranceWHOWord Health Organisation1Statin therapy has great importance in the treatment of lipid metabolic disorders and in the prevention of cardiovascular events and therefore is recommended as the therapy of first choice in international and domestic guidelines, along with lifestyle changes.Statin treatment generally represents long‐term therapy, but there are strong indications of insufficient adherence and premature discontinuation of treatment.Since there is no information for Germany on the frequency of statin‐associated myopathy (SAM) under everyday conditions, the goal of the study was to develop a method to report SAM based on routine data from the statutory health insurers and to make an estimate of the frequency of statin‐induced myopathy based on that data. There are different definitions of SAM in the literature.22.1Deutsches Institut für Medizinische Dokumentation und Information, DIMDI) (hereinafter referred to as DaTraV data). This database of approx. 70 million SHI insured persons out of 80.8 million inhabitants, which was established based on a statutory provision, has been available since February 2014.Bundesversicherungsamt, BVA). The DIMDI is receiving this insured person‐based pseudonymized data with sociodemographic information on the insured persons  and information on the diagnoses coded in the outpatient and inpatient sector (according to ICD 10‐GM) as well as the drugs dispensed in the outpatient sector and reimbursed by the SHI. For analyses of this database, an SQL analysis script was submitted on 3 August 2015. Before the result sets are transmitted, an intensive review is conducted by the DIMDI to determine whether the insured person's identity is protected. A cell population of at least n = 30 is required for this. It is also reviewed whether, as a result of dependencies within the results table or even due to dependencies between the results tables, for example, through subtraction or comparisons of marginal totals, cell populations below the above‐cited minimum case number of n = 30 can also be approximately calculated. After repeated aggregation of the results tables by the applicant and intensive review by the DIMDI, the result sets were transmitted in compliance with data privacy law on 22 Dec. 2016).The analysis was conducted on a Germany‐wide statutory health insurance (SHI) data set, the so‐called “Health Care Data Information System”, which is located at the German Institute of Medical Documentation and Information  could be made. For the inpatient stays, it is only documented in which month the hospital stay took place.2.2These are calculated in the data set based on the Anatomic‐Therapeutic‐Chemical‐Classification (ATC code) C10AA for monosubstances and C10BA as well as C10BX for combinations (ATC Version 2012).2.3The population consists of all continuously insured persons of the SHI for the period 2009 to 2011 who are 18 years and older . The study population is incidental statin recipients from 2010 with documented lipid metabolic disorder. A statin recipient was defined as incidental if in the data set, before the first statin prescription in 2010, no statin prescription was documented in 2008 and 2009. This means a therapy‐free period of at least 2 years.2.3.1The presence of a lipid metabolic disorder was assumed if one of the following diagnoses‐according to ICD 10‐GM 2.4Since there is no specific coding for this, SAM must be determined indirectly from the SHI data. We assume SAM in cases where SAM is documented for the first time in new users of statins (in the prescription quarter or in one of the three following quarters) and where no documentation of SAM is found during the eight quarters before starting statins. Myopathies that were documented after the end of the statin therapy were not included in the analysis. Muscle pain was recorded here with following ICD 10‐GM‐coded diagnoses: G72.0: Drug‐induced myopathy, G72.8: Other specified myopathies, G72.9: Myopathy, unspecified, M60.8: Other myositis, M60.9: Myositis, unspecified, M79.1: Myalgia. The WHO Code M62.82 Rhabdomyolysis is not available in the German Modification. In each case, the first event with exposure is considered.2.5Estimation of the SAM requires that the exposure time, ie, the period of treatment with statins, be determined for every statin recipient. In the SHI routine data, there is no information on the prescribed dose from which the range of coverage of the prescribed package could be determined. For this reason, the daily doses included in a package were classified for this as “days under therapy”. This approach was established as a quasi‐standard for the secondary data analysis of SHI routine data.In the case of insured persons who are given a lower dose than one daily dose per day and for whom, consequently, the range of coverage of the package would be longer, when a DDD is used to calculate the range of coverage of the package, there are interruptions in therapy due to methodological reasons. This calculative therapeutic gap was “closed” if the number of days was smaller than the range of coverage of the last package. In terms of the calculation, this means a doubling of the range of coverage and thus halving the daily dose for the last prescribed package before the interruption. If the therapy gap, in contrast, was longer than the number of daily doses included in the package, only the single daily dose was taken as the range of coverage, and an interruption in therapy was identified. For the calculation of the range of coverage, combination drugs had to be recoded into the individual active substances, for example, the combination drug of simvastatin and ezetimibe (ATC code C10BA02) into simvastatin C10AA01 and ezetimibe ATC code C10AX09. For the calculation of the duration of therapy, the daily dose of the combination drug was transferred to both individual substances. If the combination drug contained 50 daily doses, for example, then each of the two monosubstance shares was also entered with 50 daily doses into the calculation of the duration of the range of coverage.Based on the pattern of use, different populations can be seen with respect to (i) the duration of therapy (end of therapy within 364 days), (ii) the continuity of treatment (no follow‐up prescription after a gap according to the number of daily doses of the last prescription) as well as (iii) with respect to the occurrence of a change in the statin.The frequency of SAM is determined for all insured persons with incidental statin prescription as well as for populations that are differentiated by the (i) duration of the statin treatment, (ii) continuity of the therapy and (iii) by a change in the statin therapy. In an additional analysis, the share with SAM is determined for the subgroup of incidental statin recipients in whom a change in the statin with subsequent discontinuation of therapy could be observed. Included here were insured persons with first‐time statin therapy with the following active substances : Atorvastatin, fluvastatin, lovastatin, pitavastatin, pravastatin, rosuvastatin, simvastatin in which a change to a second statin as well as a therapy discontinuation of the second statin and no additional statin therapy were observed within the investigation period of 365 days after the index date.2.6Frequency estimates are made in percentage values. The calculation was made with SQL Server 2016 under Windows Server 2016.3Using the definition for the study population, results in 531 672 incidental statin recipients with a lipid metabolic disorder in 2010  Duration of prescription, (ii) Continuity of treatment and (iii) Type of therapy, ie, with or without change in the statin. In the next step, the analysis of the documentation of an SAM is made overall (according to the type of SAM) as well as according to the previously described prescription pattern.The analysis of the prescription duration shows that roughly one quarter of the statin recipients received only a one‐time prescription without a follow‐up prescription in the course of the first 12 months after an incidental statin prescription. In another quarter, the therapy was ended within 364 days. Just under half of the statin recipients (49.1%), in contrast, were still treated after 365 days; 33.6% were treated continuously for 1 year. A change in statin was observed in around 14 000 incidental statin recipients in the period of 364 days after the first prescription, with such a change occurring already in more than one‐third of the statin recipients within the first 91 days. In the last quarter, a statin change was observed only in just under 18%.Table 3.1In the 1‐year follow‐up period of 531 672 incidental statin recipients, myopathy according to the included diagnoses was documented in 10 250 persons (1.93%). Myalgia (ICD 10‐GM: M79.1) was documented in almost 94% of the cases . Consistent with other authors,With respect to patients who were given continuous treatment without statin changes and were diagnosed with SAM, our interpretation is that the muscle pain occurring under therapy was discussed and documented in the doctor‐patient contact in the outpatient sector. A dose reduction might have been made. However, this was not able to be investigated using the available database.If the different diagnoses that are subsumed under SAM are broken down individually, at first glance, it is confusing that “drug‐induced myopathy” is named as a diagnosis, and also that unspecific diagnoses are supplemented with the description “unspecified”. However, in Germany, this is consistent with the general diagnosis coding behavior in the outpatient sector. Here, the emphasis is on continued treatment and not the clarification of possible causality.Thus, just as there are different definitions for the diagnosis of statin intolerance and SAM,There are some international studies that address estimating the frequency of SAM using administrative data,Chang et al. As our analysis of the continuity of statin therapy showed, just under half of the patients were still on therapy after 365 days; an interruption of therapy was observed in 29% (54% if one‐time prescriptions are included). Data on the persistence of statin therapy have, like the estimates of the frequency of statin intolerance, a broad range.NICE guideline Schulman et al. In our view, SAM or statin intolerance cannot necessarily be concluded from the discontinuation rates. The estimates for SAM that we calculated are conservative, since unreported dose reductions or even therapy interruptions—as specified in treatment recommendations—may occur without documentation of a diagnosis of SAM. Even a change in the statin does not necessarily have to be associated with SAM. This may also be caused by regulatory drug policies (feedback to physicians concerning their adherence to simvastatin and pravastatin as lead compounds) or through marketing measures of pharmaceutical companies .4.1Some limitations must be kept in mind when interpreting the results. Due to the database, only prescriptions that are charged to the SHI are reported, not the actual ingestion by the patient. This means that the exposure time is a result of the prescription pattern, with assumptions of the daily dose  having to be made. Statin intolerance was limited in this study to SAM using ICD‐10 GM‐coded inpatient and outpatient “muscle diagnoses”. These diagnoses cannot be validated externally, eg, through chart review or laboratory data. Our analysis is based on a single citation of the diagnosis. Since this is not a chronic disease (the complaints should subside after discontinuation or reducing the dose of the statins), we abstained from additional internal validation steps, such as multiple citations or citation by other, different doctor groups.To our knowledge, for doctors in private practices, there are no economic incentives for documentation of a diagnosis in this area; therefore, we rather assume a potential under‐reporting instead of over‐reporting. Authors who had the options for validation consider the administrative data for reporting statin intolerance suitable We cannot rule out, that we might overestimate SAM as we did not apply a control group design. Our study design followed clinical practice, that is, the co‐occurrence of incident myopathy together with incident statin use would be rated as SAM by physicians and patients in every day practice.As a further limitation we have to mention that we did not analyze different dosages of the statins with regard to any dose effect relationship for myopathy. We lack information on the daily doses prescribed by the physician, which is a prerequisite for such an analysis. When evaluating the results, documentation customs and billing rules  must be taken into account. It must also be considered that muscle pain is perceived differently according to the individual, and even physicians tolerate a CK value increase in their patients to different degrees.4.2The strengths of the study are that, as a database, the entire SHI population in Germany was made available for the first time. Based on Germany's population, only around 12% (insured privately or uninsured) were not included. An important advantage compared to clinical studies is that an unselected patient group can be observed in an everyday care setting. Without selection and recall bias and a nonresponder rate of 0%, all statin recipients can be investigated with reference to the population. Another special feature is that the documentation of the SAM was described for different populations according to their pattern of treatment and not only for patients with statin changes. Thus, it appears that the SAM frequency differs substantially.5Compared to studies that use only hospitalizations due to SAM, the results reported here, by including the outpatient sector, also include milder cases of muscle complaints and give a realistic idea of SAM under everyday conditions. Depending on the observed pattern of treatment, the shares found in the study are between 1.3% and 5.0% and thus certainly do not represent a rare event in everyday health care. On the one hand, the results show that a not insignificant share of patients tolerate the therapy despite myalgia, since the statin therapy was continued for these patients without interruptions and without changing to an alternative statin. On the other hand, for patients who do not tolerate statins but need them due to their cardiovascular risk profile, an alternative treatment strategy must be found. There are recommendations for approaches to this issue.The study was financed by an unrestricted grant to the PMV forschungsgruppe from Sanofi‐Aventis.Franz‐Werner Dippel is employee of Sanofi Aventis. Peter Ihle and Ingrid Schubert have no competing interest to declare.PI, IS, and FWD designed the study, PI managed and analyzed the data, PI and IS prepared the draft of the manuscript, FWD reviewed the paper and all authors approved the final version of the manuscript. IS had full access to all the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.


Low field NMR has been used to investigate water status in various plant tissues. In plants grown in controlled conditions, the method was shown to be able to monitor leaf development as it could detect slight variations in senescence associated with structural modifications in leaf tissues. The aim of the present study was to demonstrate the potential of NMR to provide robust indicators of the leaf development stage in plants grown in the field, where leaves may develop less evenly due to environmental fluctuations. The study was largely motivated by the need to extend phenotyping investigations from laboratory experiments to plants in their natural environment.The mobile NMR laboratory was developed, enabling characterization of oilseed rape leaves throughout the canopy without uprooting the plant. The measurements made on the leaves of plants grown and analyzed in the field were compared to the measurements on plants grown in controlled conditions and analyzed in the laboratory.The approach demonstrated the potential of the method to assess the physiological status of leaves of plants in their natural environment. Comparing changes in the patterns of NMR signal evolution in plants grown under well-controlled laboratory conditions and in plants grown in the field shows that NMR is an appropriate method to detect structural modifications in leaf tissues during senescence progress despite plant heterogeneity in natural conditions. Moreover, the specific effects of the environmental factors on the structural modifications were revealed.The present study is an important step toward the selection of genotypes with high tolerance to water or nitrogen depletion that will be enabled by further field applications of the method. In the context of the increasing world population and the move towards more sustainable development, there is a need to increase agricultural productivity and to reduce the ecological footprint of plant production. To achieve these aims, genotypes need to be selected that can better adapt to environmental stresses using water and nutrients applied to the soil more efficiently, so plants can be grown with limited inputs. Large-scale phenotyping has been developed to assist such selection, as it allows characterization of plant adaptative traits in different agricultural systems. Studies have been conducted on a large number of plants with, for example, bulk methods of canopy spectral reflectance and absorbance . On the Plant response to the environment may differ in controlled and field conditions because of soil-climate and canopy architecture variability . There i2), which is particularly sensitive to variations in water properties in plant tissues, was used to study changes in cell water status and distribution. As demonstrated in different plant tissues including leaves, differences in the physical and chemical properties of water in different compartments and the relatively slow diffusion exchange of water molecules between compartments are reflected by the multi-exponential relaxation times [The potential of nuclear magnetic resonance (NMR) relaxometry to finely evaluate the cell and tissue structure of oilseed rape leaves was recently demonstrated –9. The Non times . Appliedon times –9. This on times –9.® [Until now, the great majority of NMR and magnetic resonance imaging (MRI) studies on plants have been performed under controlled conditions in the laboratory. Current trends in the further development of the NMR/MRI method, largely motivated by phenotyping needs, are to extend investigations to in situ experiments  rather than to transport plants to the laboratory where the equipment is located. Relatively recent important technological advancements have been reported in mobile NMR devices. A single-sided open NMR sensor equipped with a permanent magnet for near surface studies, which allows free access to large objects, known as NMR MOUSE® , was dev® , 13, suc®  and to d® . Another®  with a m®  and used® . Another®  equipped® , 20. Rec® . Finally® , 22–24.Only a limited number of NMR/MRI studies have been performed on plants in their natural environment. Capitani et al. used NMR relaxometry to investigate the water status of rockrose and holm oak leaves growing in sand dunes . Okada e2 values measured [The development of outdoor NMR and MRI measurements has faced two major challenges. The first concerns the NMR/MRI device itself and the effects of the environmental conditions on it. The system needs to be portable and easy to handle in different conditions. Further, the temperature drift of the magnet, the lack of homogeneity of the magnetic field and the variations in sample temperature can make it difficult to distinguish variations in the signal due to the biological changes under study from variations due to the system or measurement conditions. Some applications require accurate measurements and exploitation of the complete NMR signal. For example, in the specific case of characterization of the progress of senescence in oilseed rape leaves based on slight variations in multi-exponential relaxation parameters , 9, smalmeasured . The secThe objective of this study was to demonstrate the potential of NMR to access information about the status and sub-cellular distribution of water in leaves from plants grown in natural conditions, thereby providing robust indicators of the stage of development directly in the field. To this end, a mobile NMR lab was designed for in situ measurements of the relaxation times of leaves from plants in their natural environment. A commercially available NMR spectrometer similar to that previously used for investigations of oilseed rape leaves –9 was usTransverse relaxation measurements were performed using a mobile NMR lab specifically set up for this purpose Fig. . A comme2. The recycle delay for each sample was adjusted after measurement of the longitudinal relaxation time (T1) with a fast-saturation-recovery sequence. The measurement time for T2 (including spectrometer adjustments and T1 measurement) was about 10 min per sample.The transverse relaxation times was measured using the Carr–Purcell–Meiboom–Gill (CPMG) sequence. The signal was acquired with the 90°–180° pulse spacing of 0.2 ms. Data were averaged over 64 acquisitions. The number of successive echoes recorded was adjusted for each sample according to its T2 values, while peak areas correspond to the intensity of the T2 components. Signal intensity was expressed through the specific leaf water weight of the ith signal component (LWW) expressed in g m−2. LWW of each CPMG component was calculated according to the equation:0Ri is the relative intensity of the ith signal component expressed as a percentage of the total CPMG signal intensity, mw is the water mass of the leaf discs used for NMR (in g) and A is the leaf disc area (in m2).The CPMG signal was fitted using Scilab software according to the maximum entropy method (MEM) , which pBrassica napus L., genotype Aviso) plants were grown in a field trial in Le Rheu, France  during the 2014–2015 cropping season. The seeds were sown on the 10th of September, 2014 in plots measuring 6.75 m2  at a density of 45 seeds m−2 and were grown under an optimal N regime. Four plots were used for this experiment corresponding to four repetitions. Measurements were made between the 23rd and the 26th of March 2015, at the end of the stem elongation stage . The chlorophyll content of each leaf was estimated as the average of six independent measurements.Leaf discs were kept in the closed NMR tubes until the end of the NMR experiment each day. The samples were transferred in the laboratory and water content was then determined by weighing before (fresh weight) and after drying (dry weight) in an oven at 70 °C for 48 h. Water content is expressed as a percentage of fresh weight.32 non-vernalized oilseed rape plants of Tenor genotype, details are reported in 20 vernalized oilseed rape plants of Aviso genotype, details are reported in The outdoor NMR measurements made in the present study were compared with the NMR measurements performed on plants grown under controlled conditions and analyzed in the laboratory . TheLike in the outdoor experiment, the NMR device used for transverse relaxation times in controlled conditions was a 20 MHz spectrometer . The CPMG measurements were performed at 18 °C with the 90°–180° pulse spacing of 0.1 ms and 64 signal averages.2 signal component measured in the mature leaves to target leaves at the same developmental stage. In this representation, leaf rank zero is assigned to the leaf of the last leaf rank in which the split occurred, the subsequent leaf rank is numbered 1, etc. According to this scale, the older the leaf, the higher its rank, while negative ranks represent young leaves in which split has not yet occurred. This NMR split scale makes it possible to average values from data obtained in leaves located at different positions in the canopy. The NMR split scale is used in all the following figures.Both NMR results and parameters describing physiological status measured were represented according to the NMR split scale. It was previously shown  that it 2 component corresponding to the vacuolar water was centered at 150–200 ms, which correspond to slightly higher values than those measured in the controlled conditions  of the transverse relaxation time distribution for two leaf development stages (leaf ranks −2 and 0) are shown in Fig. ons Fig. a. This c2 spectra shown in (a) and (c), respectively. The first one was centered at a few ms and represented a small percent of the water amount. It was always observed in the youngest leaves (leaf rank −2), disappeared with leaf age and was consequently observed only in some leaves of leaf rank 0. The second component was centered at about 15 ms and represented less than 20% of the water amount for all leaf ranks. Under field conditions, the signal differed from what was expected according to these results. Actually, the number of components detected in the T2 range 0–30 ms varied between one and three. In the case of two components , the same general frame was found as that observed under controlled conditions  and LWW (b) values of the NMR signal components (4 and 5) associated with the vacuole during leaf ageing in plants grown in the field. Data from plants grown in controlled environment conditions extracted from [2 values were reproducible over the whole leaf rank scale in all three growing conditions  was the same in the different experiments (about 200 ms per leaf rank). However, while this maximum rate followed the appearance of the fifth component in plants grown in field conditions, it was delated for leaves from [2(5) increased at the maximum rate between leaf ranks +5 and +7.Figure ted from , 8 are smponents  and 5 as2(4) with ageing of the leaf. Considering differences in genotypes, vernalization and environmental factors between plant growing conditions, Fig. 2 values describing structural leaf changes appeared to be more affected by environmental conditions.Note that in the case of the field measurements, it was possible to analyze leaves characterized by leaf ranks up to −15, corresponding to very young leaves. This made it possible to confirm the increasing trend in the value of T2 with ageAccording to –9, the NChanges in physiological traits during leaf development were described through general parameters Fig.  i.e. chlThe results of the present study show that a mobile NMR lab makes it possible to successfully perform outdoor NMR measurements under controlled conditions usually obtained in the laboratory that ensure optimum measurement accuracy. Using this approach, it was possible to compare the NMR signal from plants grown under well-controlled conditions (growth cabinet) with the signal from the plants grown in the field.2 value of the longest component corresponding to vacuolar water appears to have been initiated while the chlorophyll and dry matter content were still high.The trend in the transverse relaxation times associated with vacuolar water revealing changes in leaf structure during senescence was very similar to that previously measured on plants grown under controlled conditions. This shows that, despite the great variability of the environmental factors during plant growth and throughout the canopy , the NMR method can provide robust indicators of the leaf development stage of plants grown in the field. The results of the present outdoor study, confirmed previous data –9 showinWithin the common framework of changes in relaxation times, some differences in the NMR parameters measured on plants grown under different conditions were observed and are discussed in the following paragraph.2 of the signal component associated with vacuolar water before the split (leaf rank 0) was very similar, a difference was observed in the leaf ranks at which the maximum rate of the increase in the T2 value occurred. This indicated that changes in the vacuolar volume associated with the T2(5) increase [As mentioned above, some differences were observed in the NMR parameters measured on plants grown under different conditions Fig. a, b. Theincrease  were preth the T2 increaseThe environment perceived by plants has an effect on the progress of leaf senescence but not necessarily on the onset of senescence . It is w2, the total amount of the vacuolar water expressed by LWW (4 + 5) decreased in senescing leaves.The young leaves from the vernalized plants (present experiment and ) were ch2 range up to 30 ms), very similar results were obtained in the field experiment and in the experiments conducted under controlled conditions in about 50% of the leaves analyzed. In the remaining leaves, the number of components detected in this T2 range was one or three, instead of two components as expected from [2 peaks corresponded to the same water pools (apoplastic water and water inside starch granules and chlorophyll) as proposed in [2 values in all cases. It will be interesting to clarify this point in further experiments, although this is not crucial for the purpose of phenotyping.Concerning the NMR signal components corresponding to water in cell compartments other than vacuoles (Tted from , 8. ConsConsidering a negative shift of five leaf ranks for the chlorophyll content curve Fig. a corresp2 and peak amplitudes change with temperaure, and are thus a possible source of interpretation errors.Until now, only a few mobile NMR  and MRI Malone et al.  isolatedIn the present study, the effects of the environmental conditions on both the device and the sample were controlled. The operating temperature of the benchtop NMR device magnet was maintained through a magnet heating system. The stable temperature of the sample was ensured by a variable temperature control units within 0.1 °C. The NMR mobile laboratory therefore made it possible to perform measurements in exactly the same controlled conditions throughout the experiment, despite the fact the measurements were performed in an environment with no temperature regulation.As described in “The mobile NMR laboratory developed in this study was shown to be able to perform accurate outdoor characterization of oilseed rape leaves throughout the canopy. The approach used enabled in situ assessment of physiological status of leaves from plants grown in their natural environment without disturbing the plants themselves. The study enabled the comparison between the patterns of NMR signal evolution from plants grown under well-controlled conditions and plants grown in the field. The method described here provides new opportunities for fine phenotyping and monitoring of plant development in the natural environment. It can be used for the selection of oilseed rape genotypes with high tolerance to water or nitrogen depletion. Future investigations should extend the method to other crops.


SystemaMurphy has noted that the analytical blank may be considered the “Achilles Heel” in chemical analysis . FrequenIn this note, we limit our focus to the effect of chemical blanks and chemical yields on the accuracy of chemical measurements. Their effect on both accuracy and precision will be discussed in more detail in a later paper.For this discussion the term chemical yield is synonymous with the term recovery which refers to the fractional amount of a substance reclaimed from a purification process. We will take the following as an operational definition of the chemical blank: the chemical blank is the sum of all sources of the element or compound being determined that is not indigenous to the sample but is measured by the detector. Chemical species other than the analyte of interest that give the same response in the detector are not considered chemical blank.T is the true value and cM is the corrected experimentally measured value given by one of the following two relations:iB and jY are the chemical blanks and chemical yields which are subject to the boundary conditions:An accurate measurement is one which obeys the following condition:n -step separation process. During the dissolution step the sample picks up a reagent blank, BR, and at each successive separation step the sample is subject to a blank iB. After the chemical separation process the sample encounters an instrumental blank or loading blank inherent to the measurement system designated as BL. We will consider the case which is encountered in most instances in chemical analysis in which both sample and blank are lost together for a two-step (n =2) separation process.Chemical techniques can be grouped into two broad categories. For convenience, we will refer to techniques that have an internal standard as internal techniques whereas those that require external standards as external techniques. An example of an internal technique is isotope dilution in which an enriched or radioactive isotope of the element of interest is added to the sample. After dissolution of the sample and separation of the element of interest from the matrix the isotopic ratio of the mixture is then measured. Examples of the external techniques are the many spectroscopic techniques that compare the response of the sample to that of a standard. We wish to consider the functional form of several blank corrections and compare these to the exact blank corrections to ascertain the magnitude of the bias that is introduced. We will assume that measuring devices in both the internal and external cases are perfect and introduce no error. We will assume that both techniques must dissolve the sample and chemically separate the element of interest by an n = 2 the following:For the external case the measured value is given in general by the following relation:M, is given in general by the following:n=2 the following for the true value, T:For the internal case the measured value, T= 10, BR=1, B1=2, B2=2, BL=0.1 and Y0=1.A simple way of illustrating the differences between the two methods is to consider the case which is often encountered in trace determinations where the blank approaches the size of the analyte of interest. For illustration let us assume that Y1. Because Y2 only appears as a coefficient of BL, the measured value is not strongly influenced by the value of Y2 [see Y2. As Y2 becomes smaller the line moves to lower values.In f Y2 see . The meaBT=BR+ΣBi+BL, is subtracted from the measured value, M. This gives for the external and internal techniques the following two equations which are plotted in Y2= 1:External TechniqueInternal TechniqueFrom inspection of Mc⩽T for all values of iB, whereas the converse (Mc⩾T) is true for the internal case. As Y2 becomes smaller the external line drops to lower and lower values whereas the internal line is essentially unchanged due to the small dependence of Y2. It is clear from iB and jY.This is the type of correction that is frequently used by chemists and is referred to as a straight blank correction. In this case the total chemical blank, n =2, if one knows the iB’s, and determines the chemical yield after step 1, this allows the following approximate blank correction to be used:Y0=1 is a function of only BL and the chemical yields. Since the coefficients of B1 and BL are positive Mc⩾T. Y1=2Y=0.5 T + 2BL.It should be noted that with isotope dilution it is possible to measure the chemical yield at any point in the chemical separation for each sample by adding another isotope to the sample. For the case of n ⩾ 1. If chemical yields cannot be determined, they should be bounded. The number of separation steps should be kept as small as possible because the number of unknowns is equal to 2n+4. For n=2, a nearly exact solution can be used in isotope dilution determinations which is not true for the external method case because the yields must be determined in parallel experiments and cannot easily be determined on an individual sample.The important point is that all approximations to the blank and yield correction introduce a systematic error into the final result whose magnitude will depend on the Sample/Blank ratio, the chemical yields, and blanks for individual steps in the separation process for