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- Methodology article
- Open Access
Efficient parametric analysis of the chemical master equation through model order reduction
- Steffen Waldherr1Email author and
- Bernard Haasdonk2
© Waldherr and Haasdonk; licensee BioMed Central Ltd. 2012
- Received: 3 January 2012
- Accepted: 18 May 2012
- Published: 2 July 2012
Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation.
In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations.
The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.
- Stochastic biochemical network
- Model reduction
- Reduced basis
- Genetic regulatory network
- Computational efficiency
- Parameter estimation
The chemical master equation (CME) is the most basic mathematical description of stochastic biomolecular reaction networks[1, 2]. The CME is a generally infinite-dimensional linear differential equation. It characterizes the temporal development of the probabilities that the network is in any of its possible configurations, where the different configurations are characterized by the molecular copy numbers of the network's chemical species.
Due to its infinite dimension, the CME is usually not directly solvable, not even with numerical methods. A recent breakthrough in the numerical treatment of the CME was the establishment of the finite state projection (FSP) method by Munsky and Khammash[3]. They showed that it is possible to compute a good approximation to the real solution by projecting the CME to a suitable finite subdomain of the network's state space, and solving the resulting finite-dimensional linear differential equation on that domain. Nevertheless, the FSP approach still yields very high-dimensional models which are computationally expensive to simulate, even for small biochemical networks. The efficient simulation of the CME is an area of active research, and recently other simulation methods have been developed that can also be used for larger networks[4, 5].
Despite this progress, the direct simulation of the CME remains a computational bottleneck for common model analysis tasks in systems biology. It is especially problematic for tasks which require the repeated simulation of the model using different parameter values, for example identifiability analysis, parameter estimation, or model sensitivity analysis. Thereby, while a single or a few evaluations of a CME model with the FSP or other approaches may still be computationally feasible, the necessity of many repeated simulations will quickly render higher-level analysis tasks infeasible.
Mathematical methods that approximate the behaviour of a high-dimensional original model through a low-dimensional reduced model are a common way to deal with complex models. Especially for linear differential equations, model order reduction is a well established field and several methods to compute reduced order models are available[6]. Note that the step of generating a reduced model is usually computationally more expensive than a single or even a few simulations of the original high-dimensional model. But the simulation of the resulting reduced models is frequently orders of magnitude faster than the solution of the original model. So, model reduction is worth the effort if many repeated simulations are to be expected. Unfortunately, for analysis tasks which require the repeated model simulation with different parameters, classical model reduction methods are not helpful. With these methods, the reduced model depends on specific parameter values in the original model, and the reduction needs to be redone for different parameter values. Thus, for the mentioned analysis tasks, the model reduction process would have to be repeated for each new parameter value, and no gain in computational efficiency would typically be possible. While classical model reduction techniques have been applied to the CME in the past[7], they are not so suitable for parametric analysis tasks.
Fortunately, model reduction methods where parameters from the original model are retained as adjustable parameters also in the reduced model are now being developed. These methods allow to compute a reduced model which uses the same parameters as the original model, and where the reduced model can directly be simulated with any choice of parameter values[8–11].
The purpose of this paper is to introduce the application of these parametric model reduction methods to finite-state approximations of the chemical master equation, and to show possible usage scenarios of such an approach. The structure is as follows. In the following section, we introduce some background and notation concerning the modelling of chemical reaction networks and parametric model order reduction. We also show how the parametric model order reduction methods can in fact be applied to the CME. Afterwards, we apply the reduction technique on two reaction network models and corresponding parametric analysis tasks.
We start with some preparatory background on the chemical master equation (CME) and parametric model order reduction. This serves in particular to fix the notation used throughout the remainder of the article. Then the application of parametric model order reduction to the CME is introduced.
The chemical master equation
Reversible reactions can always be written in the form (1) by splitting the forward and reverse path into two separate irreversible reactions.
for, i = 1,…,n. As a short-hand notation for (3), we write p(t,x), with.
To avoid needlessly complicated cases, we assume v j ≠ v k for j ≠ k.
for. The CME (7) is subject to an initial condition p(t0,x) = p0(x) for.
Despite being linear, the CME is hard to solve numerically. This is due to the problem that the state space is for most systems infinite-dimensional, since all possible states of the reaction network (1) must in general be considered. Instead of directly solving the CME (7), a number of alternative approaches to study the stochastic dynamics of biochemical reaction networks have been suggested. The most common approach is to generate a simulated realization of the stochastic process described by the reaction network (1), using for example the Gillespie algorithm[13]. In this approach, the probabilities p(t x) for the possible system states are obtained from many simulated realizations. However, since this requires a large number of realizations, it is computationally expensive.
We will frequently omit the parameter dependence of the solution (and other parametric quantities). Hence the solution P(t), as abbreviation of P(t θ), of (10) is an approximation to the solution p(t x) of the orginal CME on the domain Ω. Munsky and Khammash[3] have also derived an upper bound on the error between the solution P(t) computed via the FSP, and the solution of the original CME p(t x) on Ω.
i.e. C = (x(1),…,x(d)) with p = n.
The basic motivation for the model reduction presented here is that we are interested in parametric analysis of the model, where the model (10) has to be solved many times with different values for the parameters θ. Due to the typical high dimensions of the matrix A(θ), already a single simulation is computationally expensive, and analysis tasks requiring many repeated simulations are often computationally infeasible. Thus, the primary goal is to derive a reduced model which is rapidly solvable and provides an approximation to the output y(t), potentially without any consideration of the original state vector P(t).
Order reduction of parametric models
Model order reduction of parametric problems is a very active research field in systems theory, engineering and applied mathematics. We refer to[8, 10, 11] and references therein for more information on the topic.
Here, we apply the reduction technique for parametric problems presented in[9] adopted to our notation. It is based on two biorthogonal global projection matrices with r ≪ d and W T V = Id, where r is the dimension of the reduced model. The matrix V is assumed to span a space that approximates the system state variation for all parameters and times. The construction of such matrices will be detailed in the next subsection.
The gain of computational efficiency in repeated simulations comes from a separation of the simulation task into a computationally expensive "offline" phase and a computationally cheap "online" phase. In the offline phase, suitable projection matrices V and W are computed without fixing specific parameter values. With the projection matrices, a reduced model with the same free parameters as the original model is computed. In the online phase, the reduced model is simulated with the actually chosen parameter values, which is typically several orders of magnitude faster than the simulation of the original model. For analysis tasks with repeated simulations, only the online phase has to be repeated for different choices of the parameter values, yielding an overall gain in computational efficiency.
Decomposition in parametric and non-parametric part
From the reduced state P r (t), an approximate state for the full system can be reconstructed at any desired time by. Also the difference between the approximated output and the output y(t) of the original model can be bounded by so called error estimators. A-posteriori error bounds for the reduced systems as considered here are given in[9].
Basis generation
Different methods for the computation of the projection bases V and W exist. In systems theory, methods like balanced truncation, Hankel-norm approximation or moment matching are applied, that approximate the input-output behaviour of a linear time-invariant system[6]. The resulting reduced models can be applied for varying input signals. Extensions to parametric problems exist, e.g.[8, 11]. As we do not have varying inputs in the problem studied here, we consider snapshot-based approaches to be more suitable. This means, the projection bases are constructed by solution snapshots, i.e. special solutions computed for selected parameter values.
The POD-Greedy procedure which is given in the pseudo-code below, starts with an arbitrary orthonormal initial basis and performs an incremental basis extension. The algorithm repeatedly identifies the currently worst resolved parameter (a), orthogonalizes the corresponding full trajectory with the current reduced space (b), computes a POD of the error trajectory (c), and inserts the dominant mode into the basis (d).
- 1.
- 2.
- (a)
- (b)
- (c)
v N + 1 := POD(E)
- (d)
V N + 1 := [V N ,v N + 1]
- (e)
- (a)
- 3.
end while
Note that the algorithm is implemented such that the simulation of the full model, yielding P(t,θ) in (19), is only performed once for each θ in the training set.
For concluding the basis generation, we set W := V. This satisfies the biorthogonality condition W T V = Id, as V has orthonormal columns by construction. In practice the time-integrals in (18) are realized by a finite sampling of the time interval.
A theoretical underpinning for the POD-Greedy algorithm has recently been provided by the analysis of convergence rates[19]. This is based on the approximation-theoretical notion of the Kolmogorov n-width of a given set, which quantifies how well the set can be approximated by arbitrary N-dimensional linear subspaces of. The convergence statement for the case of exponential convergence then can be summarized as follows: If the set of solutions is compact and has an exponentially decaying Kolmogorov n-width for some M a α > 0 and all, then the error sequence generated by the POD-Greedy procedure (cf. the definition in Step 2. in the pseudo code) also decays with an exponential rate, with suitable constants β c C > 0 depending on M,a,α. Thus, if the set of solutions can be approximated by linear subspaces with an exponentially decaying error term, then the POD-Greedy algorithm will in fact find an approximation with an exponentially decaying error term, though possibly with suboptimal parameters in the error bound.
Extensions of the POD-Greedy algorithm exist, e.g. allowing more than one mode per extension step, performing adaptive parameter and time-interval partitioning, or enabling training-set adaptation[15, 16, 20].
Reduced models of the parametrized chemical master equation
In this section, we describe how to apply the reduction method for parametrized models presented in the previous section to FSP models for the chemical master equation.
More generally, such a decomposition is also possible if reaction rate propensities can be decomposed into the product of two terms, with the first term depending on parameters only, and the second term on molecule numbers only. This case is for example encountered when the temperature-dependance of the reaction rate constant is relevant, and the temperature T is a variable parameter in the Arrhenius equation. Since the output matrix C and the initial condition P0 are usually not depending on parameters in this framework, a decomposition of C and P0 is not considered.
The situation is more difficult for reaction propensities involving for example rational terms with parameters in the denominator. The denominator parameters can not be included in the reduced order model by the decomposition outlined in (20) and (21). If variations in these parameters are however not relevant to the planned analysis, then they can be set to their nominal value, and the decomposition can directly be done as described above. Alternatively, approximation steps can be performed, such as Taylor series expansion or empirical interpolation[22], that generate an approximating parameter-separable expansion.
In this section, we present the study of two example networks with the proposed model reduction method. With these examples, the applicability of the reduced modeling approach especially for analysis tasks requiring repeated simulations with different parameter values is illustrated. The first network is a bistable genetic toggle switch, where cells may switch randomly between two states, based on the model in[23]. For this network, the problem of parameter estimation with a reduced model is studied. The second network is a second-order genetic oscillator, based on[24], where we perform a sensitivity analysis over a wide parameter range.
Parameter estimation in a genetic toggle switch model
Network description
The follicle switch model
Stoichiometry v j
Propensity ν j
Production of X1
Degradation of X1
u 1 x 1
Production of X2
Degradation of X2
u 2 x 2
Parameters for the follicle switch model
k 1
u 1
u 2
In[23], this network was shown to describe a bistable switch with two probability peaks, one close to x(off) = (0,0)T and the other close to.
In the study[23], only the lower probability peak was of interest. Here, we are interested in the transition of the system from x(off) to x(on). Therefore, the system is truncated to a rectangle such that, yielding a good approximation in the finite state projection to the infinite-dimensional chemical master equation.
where A[i], i = 1,…,5 are of dimension 1512 × 1512 = 22801 × 22801.
For the parametric model reduction, we consider only variations in the parameters u1 and u2. These influence both the steady state level of gene activity in the on-state as well as the switching kinetics and are thus of high biological significance in the model. Hence we set as the parametric domain. As final time we choose T = 107 which corresponds to a time range of approximately 19 years, i.e. about three times the half-life time of the off-state estimated in[23].
As typical simulation time for a single trajectory of the full system, we obtain 98.2 seconds on a IBM Lenovo 2.53 GHz Dual Core Laptop.
Basis generation
We generated a reduced basis with the POD-Greedy algorithm, where the training set was chosen as the vertices of a mesh with 92 logarithmically equidistant parameter values over the parameter domain. We set as target accuracy. We use the projection error as error measure, hence precompute the 81 trajectories for construction of the reduced basis. As initial basis we set N0 = 1 and using the parameter independent initial condition.
The final reduced model of dimension 33 can then be simulated in 0.135 seconds, corresponding to a computational speedup factor of more than 700.
Parameter estimation
We exemplify a possible application of the reduced order model in parameter estimation, where we assume that a distorted output y(t) as the expected values E[x1] is available from population-averaged measurements. The task is to estimate the parameter values u1 and u2 from such a noisy measurement.
In such an optimization problem, typically many forward simulations are required for adjusting to the measurement. This is a particular beneficial scenario for reduced order models, as these simulations can be computed rapidly.
In order to gain a deeper insight into the optimization problem (25), we plot the values of the error functional J(θ) over the parameter domain (middle of Figure4). Using the reduced model, the computation of the required 212 = 441 trajectories is realized in less than one minute. This would be a significant computational effort when using a non-reduced model.
From the cost function plot, we observe a narrow area of parameters which seem to produce a similar output as the reference parameter θ ref . This shows that the two model parameters are not simultaneously identifiable from the considered output, and indicates that there may exist a functional dependence between the parameters u1 and u2 such that the model yields similar outputs y(t).
Assuming a functional dependence of u1and u2we now consider the 1-dimensional optimization problem along the line u2 = u2,ref = 0.01. We would like to recover u1from the optimization problem. The corresponding value of the cost function is J(θ ref ) = 3330.68, indicating a significant contribution of the noise. This restricted optimization problem is well conditioned and the optimization with a standard active set algorithm by MATLAB's command fmincon yields the estimated parameter θ est := (u1,est,0.01) with u1,est = 0.0100204, using 27 evaluations of the cost function. This accounts to a relative error in the u1value of 0.204%, hence excellent recovery. We refrain from plotting the recovered output as it is visually indiscriminable from the output in the left of Figure4. Interestingly, the optimization target value J(θ est ) = 3329.56 implies J(θ est ) < J(θ ref ), which may stem from a slight approximation error in the reduced model or from the effects of the measurement noise.
The right plot in Figure4 illustrates another application of reduced parametric models: We incorporated the model in an interactive graphical user interface in RBmatlab, a matlab package for model order reduction, available for download athttp://www.morepas.org. This allows interactive parameter variations and instantaneous simulation response.
Sensitivity analysis in a stochastic oscillator
Network description
The oscillator model
Stoichiometry v j
Propensity ν j
Production of X1
Degradation of X1
k 3 x 1
Production of X2
Degradation of X2
k 7 x 2
Parameters for the oscillator model
k 1
k 2
k 3
k 4
k 5
k 6
k 7
The network model in Table4 shows oscillations only in a stochastic description. The deterministic model has a unique asymptotically stable equilibrium point, but in a stochastic model, fluctuations may push the molecular numbers beyond a certain threshold, inducing a dynamical response along a slow manifold, which corresponds to one oscillatory period[24]. Depending on the noise level, such responses will be initiated more or less often, corresponding to a more or less regular oscillatory pattern.
The system is truncated to the rectangle, which contains the relevant system states for the parameter ranges of interest.
The time scale of interest for the model in (26) is for 0 ≤ t ≤ T = 6. At the end of the interval, the probability distribution seems to approach a steady state.
Basis generation
with and. Note that since only k4 has been varied in the reduction process, the other parameters are no longer present as parameters in the reduced model, but just take their nominal values. While the same basis V could be used to construct another reduced model where all parameters are retained, it is unlikely that this other model will be a good approximation of the original one for varying values of the other parameters.
Sensitivity analysis of the oscillation amplitude
with T = 6 the final time of the simulation. The results are shown in Figure6 and show a clear decay of oscillatory amplitude for increasing values of k4. Due to the significant time savings from the reduced model, this sensitivity curve can be computed with a high resolution.
To evaluate the quality of the reduced model, we also computed the probability (29) using the original model (26) at two points within the considered interval for the parameter k4. As shown in Figure6, the results from the original model are in perfect agreement with the predictions from the reduced model at these points. Since the points at which the original model was evaluated in this experiment were not part of the training set (shown as triangles on the parameter axis in Figure6), this shows that it is in fact possible to extrapolate the reduced model to parameter values that were not used to construct the basis.
In this paper, we have introduced the application of parametric model reduction methods to finite-state approximations of the chemical master equation. We have also presented two case studies where these methods are applied to CME models of different networks in order to make parametric analysis tasks computationally efficient. By this, it has become clear that parametric model reduction methods are a very useful tool for the analysis of stochastic biochemical reaction network described by the CME.
Especially analysis tasks where many repeated simulations of a network with different parameter values are required can profit significantly from parametric model reduction. This includes for example sensitivity analysis or parameter optimization tasks such as identifiability analysis or estimation. Moreover, the significant speedup of the simulation for the reduced model allows an interactive exploration of the network's dynamics within the parameter space within a suitable graphical user interface.
This contribution is just a first step in the application of parametric model reduction methods to the CME. One particularly important aspect that we have not discussed here is the computation of error estimates for certifying that the simulation output of the reduced model is within some tolerance of the corresponding simulation output of the original model. To maintain computational efficiency, the error estimation should be done without actually simulating the original model. Error estimation methods have been developed for parametric model reduction of generic models[9], but tighter estimates could likely be obtained by taking into account the special structure of the CME models. Recent work for example refined the previous generic error bounds for stable models[25].
Authors contributions
SW and BH conceived of the study, performed the study, and wrote the manuscript. Both authors read and approved the final manuscript.
We thank Wolfgang Halter for programming support in the oscillator case study. The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology at the University of Stuttgart. BH also acknowledges the Baden-Württemberg Stiftung gGmbH for funding. This work was also supported by the German Research Foundation (DFG) within the funding programme Open Access Publishing.
Authors' Affiliations
- Gillespie DT: A rigorous derivation of the chemical master equation. Physica A: Statist Theor Phys 1992,188(1-3):404-425. [http://www.sciencedirect.com/science/article/B6TVG-46FX396-7N/2/a0537c1efc0f5c330fa05b5e4ae61b98] [] 10.1016/0378-4371(92)90283-VView ArticleGoogle Scholar
- van Kampen NG: Stochastic Processes in Physics and Chemistry. Amsterdam, The Netherlands: North-Holland; 1981.Google Scholar
- Munsky B, Khammash M: The finite state projection algorithm for the solution of the chemical master equation. J Chem Phys 2006,124(4):044104. [http://dx.doi.org/10.1063/1.2145882] [] 10.1063/1.2145882View ArticleGoogle Scholar
- Jahnke T, Huisinga W: A Dynamical Low-Rank Approach to the Chemical Master Equation. Bull Math Biol 2008, 70: 2283-2302. 10.1007/s11538-008-9346-xView ArticleGoogle Scholar
- Hegland M, Hellander A, Lötstedt P: Sparse grids and hybrid methods for the chemical master equation. BIT Numerical Mathematics 2008, 48: 265-283. 10.1007/s10543-008-0174-zView ArticleGoogle Scholar
- Antoulas AC: Approximation of Large-Scale Dynamical Systems. Philadelphia, USA: SIAM; 2005.View ArticleGoogle Scholar
- Munsky B, Khammash M: The Finite State Projection Approach for the Analysis of Stochastic Noise in Gene Networks. Automatic Control, IEEE Transactions on 2008,53(Special Issue):201-214.View ArticleGoogle Scholar
- Baur U, Benner P: Parametrische Modellreduktion mit dünnen Gittern. GMA-Fachausschuss 1.30, Modellbildung, Identifizierung und Simulation in der Automatisierungstechnik, Salzburg ISBN 978-3-9502451-3-4 2008, 262-271.Google Scholar
- Haasdonk B, Ohlberger M: Efficient Reduced Models and A-Posteriori Error Estimation for Parametrized Dynamical Systems by Offline/Online Decomposition. MCMDS, Mathematical and Computer Modelling of Dynamical Systems 2011,17(2):145-161. 10.1080/13873954.2010.514703View ArticleGoogle Scholar
- Daniel L, Siong O, Chay L, Lee K, White J: Multi-parameter moment-matching model-reduction approach for generating geometrically parameterized interconnect performance models. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 2004,23(5):678-693. 10.1109/TCAD.2004.826583View ArticleGoogle Scholar
- Moosmann C, Rudnyi E, Greiner A, Korvink J, Hornung M: Parameter Preserving Model Order Reduction of a Flow Meter. Technical Proceedings of Nanotech 2005 2005.Google Scholar
- Higham DJ: Modeling and Simulating Chemical Reactions. SIAM Rev 2008,50(2):347-368. [http://link.aip.org/link/?SIR/50/347/1] [] 10.1137/060666457View ArticleGoogle Scholar
- Gillespie DT: Exact stochastic simulation of coupled chemical reactions. J Phys Chem 1977,81(25):2340-2361. [http://pubs.acs.org/cgibin/abstract.cgi/jpchax/1977/81/i25/f-pdf/f_j100540a008.pdf] [] 10.1021/j100540a008View ArticleGoogle Scholar
- Haasdonk B, Ohlberger M: Reduced Basis Method for Finite Volume Approximations of Parametrized Linear Evolution Equations. M2AN, Math Model Numer Anal 2008,42(2):277-302. 10.1051/m2an:2008001View ArticleGoogle Scholar
- Eftang JL, Knezevic DJ, Patera AT: An hp Certified Reduced Basis Method for Parametrized Parabolic Partial Differential Equations. MCMDS, Mathematical and Computer Modelling of Dynamical Systems 2011,17(4):395-422. 10.1080/13873954.2011.547670View ArticleGoogle Scholar
- Knezevic D, Patera A: A Certified Reduced Basis Method for the Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow. SIAM Journal of Scientific Computing 2010,32(2):793-817. 10.1137/090759239View ArticleGoogle Scholar
- Volkwein S: Model Reduction using Proper Orthogonal Decomposition. 2011.http://www.uni-graz.at/imawww/volkwein/publist.html []. [Lecture Notes, University of Constance]Google Scholar
- Jolliffe IT: Principal Component Analysis. New York, USA: Springer-Verlag; 2002.Google Scholar
- Haasdonk B: Convergence Rates of the POD-Greedy Method. 2011.Google Scholar
- Haasdonk B, Dihlmann M, Ohlberger M: A Training Set and Multiple Bases Generation Approach for Parametrized Model Reduction Based on Adaptive Grids in Parameter Space. MCMDS, Mathematical and Computer Modelling of Dynamical Systems 2011,17(4):423-442. 10.1080/13873954.2011.547674View ArticleGoogle Scholar
- Wu J, Vidakovic B, Voit EO: Constructing stochastic models from deterministic process equations by propensity adjustment. BMC Syst Biol 2011, 5: 187. [http://dx.doi.org/10.1186/1752-0509-5-187] [] 10.1186/1752-0509-5-187View ArticleGoogle Scholar
- Barrault M, Maday Y, Nguyen N, Patera A: An 'empirical interpolation' method: application to efficient reduced-basis discretization of partial differential equations. C R Math Acad Sci Paris Series I 2004, 339: 667-672. 10.1016/j.crma.2004.08.006View ArticleGoogle Scholar
- Waldherr S, Wu J, Allgöwer F: Bridging time scales in cellular decision making with a stochastic bistable switch. BMC Syst Biol 2010, 4: 108. [http://www.biomedcentral.com/1752-0509/4/108] [] 10.1186/1752-0509-4-108View ArticleGoogle Scholar
- El-Samad H, Khammash M: Coherence resonance: a mechanism for noise induced stable oscillations in gene regulatory networks. In Proc. of the 45th Conf. Dec. Contr. (CDC). San Diego, USA; 2006:2382-2387.Google Scholar
- Hasenauer J, Löhning M, Khammash M, Allgöwer F: Dynamical optimization using reduced order models: A method to guarantee performance. 2012.Google Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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|Linux & Solaris
tar xvzf gpstk.tar.gz
$ ./build.sh [-h] [-cdeusxtpv] [-b ] [-i ] [-j ] [-P ]
-h Display this help message.
-b <build_path> Specify the cmake build directory to use.
-i <install_prefix> Install the build to the given path.
-j <num_threads> Number of threads to have make use. Defauts to $num_threads on host
-c Clean out any files in the build dir prior to running cmake.
-d Build documentation, including generate dependency graphs
using GraphViz (.DOT and .PDF files).
-e GPSTk has several parts: core, ext, and python/swig bindings.
See README.txt for details.
Default (without -e) will build only core
Optional (with -e) will build core, ext, and swig
-u Install the build to the path in the \$gpstk environment variable.
If this variable is not set, it will be installed to
-s Install the build into $system_install_prefix and the python
bindings to the default system location. Make sure the build path
is writable by root.
-x Disable building the python bindings. Default is to build them
if -e is specified.
-P <python_exe> Python executable used to help determine with python system libraries
will be used when building python extension package.
-t Build and run tests.
-p Build supported packages (source, binary, deb, ...)
-v Include debugging output.
Remember to add user and non-standard locations to your environment. Eg:
$ export LD_LIBRARY_PATH=/tmp/test/gpstk/lib:\$LD_LIBRARY_PATH
$ export PYTHONPATH=/tmp/test/lib/python2.7/site-packages:\$PYTHONPATH
|Linux & Solaris
tar xvzf gpstk.tar.gz
mkdir build
cmake ../To install to a different directory, the install directory must be set-up when CMake configures the makefiles, add the following command:
-DCMAKE_INSTALL_PREFIX:PATH=/path/to/installTo build GPSTk with Ext, in addition to Core, add the following command:
-DBUILD_EXT=ONTo turn on processing of python extension package, add the following command:
-DBUILD_PYTHON=ONTo turn on test mode, add the following command:
-DTEST_SWITCH=ONExample - Command for building GPSTk with core, ext, python, and test code and installing to sytem library in /usr/local:
cmake -DBUILD_EXT=ON -DBUILD_PYTHON=ON -DTEST_SWITCH=ON ../
make test
make install


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Breton Hat
Description: Breton hat of deep red fur felt. The cylindrical crown is flattened at top, and is encircled at the base by a wide band of horizontally pleated peau de soie silk satin. The wide brim is curved out and up around the crown, and is lined/faced with same fur, while the part of the brim facing the crown is faced with deep red fabric. The crown is unlined, with an inner deep red grosgrain ribbon hatband. Designer's label inside: "Styled by / Coralie" Stamp inside crown of the maker of the felt body: "Selene / HB / Body made in Italy"
Date: [1955..1959]
Creator: Coralie
Item Type: Refine your search to only Physical Object


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STOCKTON - San Joaquin County Superintendent of Schools Mick Founts thought back to his days as a high school English teacher in the 1990s and fondly recalled an annual assignment he gave his students called an I-Search paper.
STOCKTON - San Joaquin County Superintendent of Schools Mick Founts thought back to his days as a high school English teacher in the 1990s and fondly recalled an annual assignment he gave his students called an I-Search paper.
No, the I-Search was not any sort of official precursor to iPods or any of the genius marketing terms that Apple Computer executives have used to put the Internet into your pocket.
However, in many ways, it is the precursor to something else, Founts said. The idea behind the I-Search assignments that prompted students of the past to make a hypothesis about a subject, then dig deep and research that subject to the point where they became experts and could write papers and give speeches about those topics, is the basic philosophy of the new Common Core standards to which public schools are now moving.
"Only now we can do it so much faster," Founts said. "I remember vividly one kid that did his I-Search on the Holocaust and how he had to go find textbooks and printed materials and how much he had to go through."
Take an I-Search and add an Internet-equipped iMac, and students can learn more, faster. The philosophy of Common Core has been around for decades, Founts said, but technology is the linchpin to making it teachable on a large scale.
Common Core standards are being implemented in all of the state's public school districts, replacing the No Child Left Behind act, which many educators felt promoted short-term memorization of many lessons over students being able to go in-depth to learn and master fewer topics.
What that means in general terms is that schoolchildren will be tested based on their ability to read, write and explain their answers - some of it computer-based - instead of filling out multiple-choice bubbles with a No. 2 pencil.
School campuses are equipped with Wi-Fi, and new computers are on order. Some schools already are piloting the programs, and others are readying for the full transition.
Educators are excited.
"The new expectations have a foundation in higher-level thinking skills and demand relevance and the application of knowledge. Knowledge is seen as a means to an end, not an end in and of itself," said Randy Malandro, who was principal at McAuliffe Middle School during a Common Core pilot program before recently being promoted to an administrative position in the Lodi Unified School District.
"The Common Core includes greater collaboration and student problem-solving in an engaging atmosphere, where we honor and support the struggle rather than providing answers with the requisite student memorization," Malandro said.
During a recent parent introduction to Common Core at McAuliffe, Malandro and his staff showed how the new curriculum will work and how many online resources are being made available to parents and their children.
Quotes from McAuliffe students were shown a screen in the form of complaints, such as, "It's more complex and harder. I do not like this because it makes me think."
Teachers see that and smile. Yet they have challenges ahead, too, in the way of being retrained to teach the standards.
Ten years from now, those who went through Common Core will be more well-rounded and more ready for the work force, teachers and administrators say.
"We keep hearing from colleges that kids aren't coming in with the requisite knowledge. They know a slim piece of info, but not the whole concept," Manteca Unified Director of Secondary Education Clara Schmiedt said. "We're going to spend a lot of time and energy to produce a student that is much more well-rounded, can think critically, can face issues from everyday life and can be more career-ready than they have been."
In San Joaquin County, there's a new push for career readiness over college readiness. College readiness is shifting more toward simply being part of a longer path to the work force, Founts said.
"This Common Core is a bridge to the future and a foreshadowing of the flexibility we are going to need to have to respond to ever-changing world - one that changes so quickly that kids need to be nimble, and educators need to be nimble," Founts said.
Contact reporter Keith Reid at (209) 546-8257 or firstname.lastname@example.com. Follow him at recordnet.com/edublog and on Twitter @kreidme.


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ServicesYour gift to Three Rivers College, made in any of the following ways, does make a difference. You can direct the way in which your gift is to be used, or the gift can be unrestricted and with your permission, we will use it for our current greatest need. All gifts made to the Three Rivers Endowment Trust Fund are tax deductible. We would be pleased to work with your tax advisor to implement a gift that takes advantage of available tax benefits and reflects your generous spirit.
Planned Giving
Leave a legacy gift to Three Rivers College. It can be designed to benefit you and your family, as well as Three Rivers.
Securities and Property
Your gift of appreciated securities or property has real advantages to you and Three Rivers College.
Memorial and Honor Gifts
Numerous opportunities exist to make gifts to Three Rivers College to honor a loved one.


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Zebra Wall Decal
Wall decals are growing in popularity. They are the perfect way to add a unique look to any room in very little time. Once applied, decals give a painted look. They will not damage walls upon removal, making them perfect for homeowners and renters. Our personalized decals will add a special touch to nurseries and kid's rooms. Our decals also make the perfect wedding, baby shower, housewarming, and anniversary gifts.
- We use the highest quality thin matte vinyl paired with the best vinyl cutters to create a product we're sure you'll love.
- Decal measurements include the entire decal.
- Our decals do NOT have any clear film around them, once applied, all that will be on your wall is the letters/design.
- Easily removable without damaging walls.
- Decals are meant for a one time use, they are not reusable.
- Vinyl may be gently cleaned and will last for many years.
Proudly made in the USA


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If you are looking for wheelchair ramp construction in New Jersey, Wheel Chair Ramp Pros can help. Wood wheelchair ramps are a great lower cost alternative and provide years of freedom. The all natural wood ramps add a warmth to any home. We can construct and design the perfect wood ramp for your home or business. The most affordable all-natural wheelchair ramp solution.
From adding a ramp to your deck to installations and repairs we can help. Fill out the short form on this page, tell us about your wheelchair ramp needs in New Jersey, and we will get right back to you with estimates and the best options.
Contact us today to learn more about all of the wheel chair ramp contractor services we provide. Get a free quote for service now when you fill out the form.


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jpace necesitaba un nuevo diseño de camiseta y lanzó un concurso de diseño en 99designs.
Un ganador ha sido elegido entre 20 diseños de 5 diseñadores freelance.
Levatino|Pace LLP /www.lpfirm.com
We are a young Austin, Texas based law firm. We regularly participate in various cycling adventures including helping to raise money for the Multiple Sclerosis Society and its annual MS150 Charity Rides. Normally we just wear whatever, but this time we want to stand out, and help brand our new business with an exciting and unique jersey and shorts design. We have used 99designs for almost all of our print media including our logo and website so we're really excited to do this again. We have a good logo and good colors and need help with a design because, well. . . . we're lawyers not graphic designers. If that part of our brains functioned properly we wouldn't be doing this law thing, now would we. HELP!!!! We will be selling these to help raise money and to help promote our firm. We want something really unique and cool that is not just like everyone else's stuff. We are using a Company called Champion Systems to actually manufacturer the stuff. They need vector graphic ready stuff which is over our heads. We are three attorneys, one assistant and a law clerk. However, our team for the race is much larger and we hope to sell a lot of jerseys.
Our target market is really just what looks good to us and those to whom we may sell this stuff too. We tend to market towards younger businesses and individuals as far as our work. This project really doesn't have a target audience because we are the client and target for the most part.
We need a design for a cycling jersey and matching cycling shorts (called bibs). The design templates provided by Champion Systems are available at http://champ-sys.com/custom/cycling…dtemplates (we are using short sleeve, raglan, with side panel and **NEW** Short / Bib Short U-Panel Full Wrap). That will show you the layout for each. For more information check out their website:www.champ-sys.com/gallery/us.
We would like the firm logo - the large "LP" used prominently on the design. We also want the full name "Levatino|Pace LLP" used on at least the side panels of the jersey and on the shorts. We would like our website (http://www.lpfirm.com) to be used on the jersey collar and on the sleeve ends. The "LP" symbol and main logo are attached as vector graphic files. We would like to maintain a blue color pallatte. However, feel free to experiment with the different blue colors and complimentary colors. We like black, grey, silver as complimentary colors.
I have also attached several jersey examples that have good design elements that we like. These are just starting points for you.
We will have at least two additional sponsors that will go on the back pockets. Those are Catholic Charities and a group called Mobile Loaves & Fishes (they feed the homeless). In the end we need: vector graphic with layers and all necessary colors and graphics included for each piece


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Push- / Pull Unit PTT3
with Pivot Bearing for fix connected Heavy Load Trailers
At applications, at which single customer's non-driven heavy load trailers need to be pushed / pulled always by the same Push- / Pull Unit PTT3, it is recommended to connect the Push- / Pull Unit PTT3 to the trailer permanently by means of a pivot bearing. As this type of connection is extremely able to work under pressure, it is recommended specially for bigger load weights of more than 20 tons.
This combination of customer's heavy load trailer (upon request it also can be produced by Hedin Lagan AB) and the Push- / Pull Unit PTT3 creates a 3-wheeled transport cart, similar to the universal transport cart UTW type 2 or the pallet truck PTW type 2.
The Push- / Pull Unit PTT3 is an all purpose transportation device which, basing on its multiple possibilities of combinations can serve a wide field of applications.
Please inform us about your inhouse transport tasks. We are prepared to provide you with a suitable and very interesting offer.
If you will have questions regarding our Push- / Pull Unit PTT3 with pivot bearing, we will be at your disposal for clarification at any time. Please do not hesitate to contact us:
|+49 2156 419193
|+49 2156 4979325


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Tim Kern is a rotten carny bastard. A seventh-generation twin, he was born in a state of Misery... Half-cooked and with a lazy eye. Over the years, he has developed a passion for human oddities, prestidigitation, and serial killers. Tim has been a tattoo artist since 1995, and works at No Hope No Fear Tattoo in Portland.
For information about scheduling appointments, see the Contact page.


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Berenson Brenda Collection Pulls
Berenson's Brenda pull collection has a formal and balanced design featuring patterns and detailed accents. Shapes are soft with smooth edges that blend together seamlessly. Click on the related families tab below for a link to matching knobs.
Shipping : All orders are shipped in 24 hours
Item #: SC832$0.11
Item #: AMEROCK TEMPLATE$4.43
Write Your Own Review


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Related Suppliers
Shop Floor Automations offers its Predator DNC Enterprise software for controlling and managing network-based CNCs. The program uses an 801.11 B/G wireless CNC adapter for faster communication to machine tools with RJ45 network connectors and DB25 serial ports. The software closes the communication loop to reduce errors and improve overall efficiency, the company says.
The company will also demonstrate its Scytec Data Exchange program for machine monitoring and data collection, the USB Connect device for adding a memory stick to CNC controls, and a USB to Floppy Emulator device for transferring programs to a USB drive without retrofitting the controller.


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We are unable to find very much information on this incident.
If anyone has any information that we could add, please let us know, by going to our CONTACT US page. Please advise us how you came across this information (personal knowledge, newspaper article, web page, etc).
Your name and your contact information will NOT be posted, or released to anyone.
We simply feel that the victims of these crimes deserve more acknowledgement than just their name and a piece or two of information.


text: Hello all. As I'm sure you have read PBT recently lost a sweet, loving, and goofy canine member, Hoyden's Petey, to cancer We are all heart broken for Hoyden and her family. If you would like to help out with cremation costs we still have some to cover. Please PM SisMorphine on how to donate straight to the vet's office.


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May 4, 2012
Martin Marietta Materials made a significant contribution to the Museum's Phase IA construction project in Frisco in the form of ballast at a greatly reduced cost. The material was provided by their Frisco facility which is located just across the BNSF main line from the Museum's new site. Ballast is the rock that is applied to track for drainage and stability. This material is worked underneath new track construction and also fills the spaces between crossties.
Martin Marietta made 2,600 tons of crushed granite available to the Museum at a greatly reduced cost. Granite is commonly used on mainline railroad tracks and is preferred due to its longevity and appearance. The City of Frisco, through its Public Works Department, generously provided transportation of the material to the site.
The Museum is very grateful to Martin Marietta and the City of Frisco for their generosity and support of track construction at the new facility. It is gratifying to have contributions from Frisco-based industries that have the ability to advance construction through in-kind contributions. Many thanks to Martin Marietta for becoming a stakeholder in the Museum's success in the Frisco community and North Texas.


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Visit our main website at www.StDavids.com
Amy Scholten, MPH
Syphilis is a sexually transmitted disease (STD). If left untreated, syphilis can cause brain, nerve, tissue damage, and death. Fortunately, syphilis can be treated with antibiotics.
Syphilis is caused by specific bacteria. It is transmitted through direct contact with a syphilis lesion. This may occur when:
Factors that may increase your chance of getting syphilis include:
Symptoms will depend on what stage the syphilis is in. There are 4 main stages.
A single lesion will usually appear. It will occur in the area where the infection was originally passed. Common sites include the genitals, rectum, tongue, inside of the mouth, or lips.
It will start as a raised and painless lesion. It will gradually break down to form an ulcer. The ulcer is painless at first with raised edges. It usually lasts for 3-6 weeks. The ulcer will heal on its own.
Without treatment, the infection may move to the secondary stage. This can happen even if the ulcers are no longer visible.
Copyright © Nucleus Medical Media, Inc.
This stage is marked by the appearance of a non-itchy rash. This rash may appear as rough, red, or reddish brown spots on the palms of the hands or soles of the feet. It is also possible for different rashes to appear in other places on the body. These rashes may appear as:
The rash may be accompanied by flu-like symptoms, such as:
Untreated secondary symptoms will disappear within a few weeks, but there may be repeated episodes during the next few years.
The infection is still present but there are no symptoms. It may or may not progress to the third stage. Blood tests for syphilis will be positive during this stage.
This stage may begin years after the initial infection. This stage has become rare in developed countries. In this stage, the infection begins to damage:
Damage can be serious enough to cause death. Symptoms include the following:
Babies born with this infection can have problems, such as deafness, cataracts, brain and nerve damage, and seizures. It can also cause premature births or stillbirths.
You will be asked about your symptoms and medical history. A physical exam will be done.
Your bodily fluids will be tested. This can be done with:
Syphilis testing is part of routine prenatal care. This is done to treat and prevent congenital syphilis.
All people who have syphilis should also be tested for HIV.
Syphilis can be treated with antibiotics. The type of antibiotic and length of treatment will depend on how long you have been infected. Half of those being treated for syphilis will have fever with headache, muscle aches, and other symptoms during the first 24 hours of treatment.
If you have syphilis of any stage, avoid sexual contact until treatment is complete and the infection is gone. All sex partners should be notified. They will need to be treated as well.
To reduce your chance of getting syphilis:
It may not be obvious that a sex partner has syphilis. Do not assume your partner is healthy just because you do not see lesions.
Please be aware that this information is provided to supplement the care provided by your physician. It is neither intended nor implied to be a substitute for professional medical advice. CALL YOUR HEALTHCARE PROVIDER IMMEDIATELY IF YOU THINK YOU MAY HAVE A MEDICAL EMERGENCY. Always seek the advice of your physician or other qualified health provider prior to starting any new treatment or with any questions you may have regarding a medical condition.
Copyright © EBSCO Publishing. All rights reserved.
Women's Center of Texas12221 N. Mopac Expwy.Austin, TX 78758Telephone: (512) 478-3627Map & Directions


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Gary Mabbutt confirms Paul Gascoigne in intensive care in Arizona but on road to recovery
Gary Mabbutt has confirmed Paul Gascoigne is in intensive care in Arizona but his condition is not life-threatening.
Last Updated: 10/02/13 11:26am
Gascoigne flew out to the United States last week and was admitted to the Cottonwood rehabilitation centre for treatment for alcohol addiction.
However the 45-year-old former England international suffered a reaction when undergoing a detox programme and was taken to a hospital in Tucson where his condition could be monitored.
Mabbutt, who has talked to Gascoigne regularly in recent weeks, told Sky Sports News on Sunday morning: "The first part of the treatment was the detox and unfortunately Paul had a very bad reaction to the detox which meant that as a precaution he was moved from the clinic to a hospital where he was put in intensive care so that they could monitor him.
"But I spoke to his medical team here in the UK who spoke to Paul this morning. It's not a life-threatening situation and Paul is back on the road to recovery and hopefully soon he will be back into the clinic to continue his rehab.
"Over the years he has had a lot of support from the football family, but of course it could be a long road to recovery. Now Paul's asked for the help we can focus on getting through this."
The rehab centre had earlier refused to comment on Gascoigne's condition, while his former England team mate Gary Lineker tweeted at 1am on Sunday morning: "Gazza is struggling, Let's hope he can hang on in there. Others have generously offered to help."
And current England forward Wayne Rooney said of Gascoigne's plight: "He was a hero of mine growing up and it's sad for everyone to see and read about.
"My best wishes are with him and hopefully he can get himself out of this situation. I'm sure everyone, every England fan and every Paul Gascoigne fan, wishes him the best of luck."
Gascoigne earned 57 England caps, playing a starring role in their run to the semi-finals of the 1990 World Cup, and represented Newcastle, Tottenham, Lazio, Rangers, Middlesbrough and Everton at club level.