Sampling Of Parameter Space Research Articles

Estimation of biochemical network parameter distributions in cell populations

Populations of heterogeneous cells play an important role in many biological systems. In this paper we consider systems where each cell can be modelled by an ordinary differential equation. To account for heterogeneity, parameter values are different among individual cells, subject to a distribution function which is part of the model specification.Experimental data for heterogeneous cell populations can be obtained from flow cytometric fluorescence microscopy. We present a heuristic approach to use such data for estimation of the parameter distribution in the population. The approach is based on generating simulation data for samples in parameter space. By convex optimisation, a suitable probability density function for these samples is computed.To evaluate the proposed approach, we consider artificial data from a simple model of the tumor necrosis factor (TNF) signalling pathway. Its main characteristic is a bimodality in the TNF response: a certain percentage of cells undergoes apoptosis upon stimulation, while the remaining part stays alive. We show how our modelling approach allows to identify the reasons that underly the differential response.

Characterizing and predicting species distributions across environments and scales: Argentine ant occurrences in the eye of the beholder

ABSTRACTAim Species distribution models (SDMs) or, more specifically, ecological niche models (ENMs) are a useful and rapidly proliferating tool in ecology and global change biology. ENMs attempt to capture associations between a species and its environment and are often used to draw biological inferences, to predict potential occurrences in unoccupied regions and to forecast future distributions under environmental change. The accuracy of ENMs, however, hinges critically on the quality of occurrence data. ENMs often use haphazardly collected data rather than data collected across the full spectrum of existing environmental conditions. Moreover, it remains unclear how processes affecting ENM predictions operate at different spatial scales. The scale (i.e. grain size) of analysis may be dictated more by the sampling regime than by biologically meaningful processes. The aim of our study is to jointly quantify how issues relating to region and scale affect ENM predictions using an economically important and ecologically damaging invasive species, the Argentine ant (Linepithema humile).Location California, USA.Methods We analysed the relationship between sampling sufficiency, regional differences in environmental parameter space and cell size of analysis and resampling environmental layers using two independently collected sets of presence/absence data. Differences in variable importance were determined using model averaging and logistic regression. Model accuracy was measured with area under the curve (AUC) and Cohen's kappa.Results We first demonstrate that insufficient sampling of environmental parameter space can cause large errors in predicted distributions and biological interpretation. Models performed best when they were parametrized with data that sufficiently sampled environmental parameter space. Second, we show that altering the spatial grain of analysis changes the relative importance of different environmental variables. These changes apparently result from how environmental constraints and the sampling distributions of environmental variables change with spatial grain.Conclusions These findings have clear relevance for biological inference. Taken together, our results illustrate potentially general limitations for ENMs, especially when such models are used to predict species occurrences in novel environments. We offer basic methodological and conceptual guidelines for appropriate sampling and scale matching.

Mass and Orbit Determination from Transit Timing Variations of Exoplanets

The timing variations of transits of an exoplanet provide means of detecting additional planets in the system. The short-period and resonant variations of the transit signal are probably the most diagnostic of the perturbing planet's mass and orbit. The method can be sensitive to small perturbing masses near the transiting planet and for orbits at mean motion resonances. It is not evident, however, how the mass and orbit of the perturbing planet can be determined from the observed variations of transit times. This is a difficult inverse problem. Direct N-body integrations are computationally too expensive to provide an adequate sampling of parameter space. Here we develop an alternative method based on analytic perturbation theory. We find that this new method is typically ~104 times faster than direct N-body integrations. The perturbation theory that we use here has an adequate precision to predict timing variations for most planetary orbits except those with very large eccentricities where the expansion of the disturbing function is divergent. By applying the perturbation method to the inverse problem we determine the number and precision of the measured transit times that are required for the unique and correct characterization of the perturbing planet. We find that the required precision is typically a small fraction (~15%-30%) of the full transit timing variation amplitude. Very high precision observations of transits will therefore be needed. We discuss the optimal observation strategy to characterize a planetary system from the transit timing variations. We find that the timing of secondary transits, if measured with adequate precision, can help to alleviate the problem with the degeneracy of solutions of the inverse problem.

Memory Switches in Chemical Reaction Space

Just as complex electronic circuits are built from simple Boolean gates, diverse biological functions, including signal transduction, differentiation, and stress response, frequently use biochemical switches as a functional module. A relatively small number of such switches have been described in the literature, and these exhibit considerable diversity in chemical topology. We asked if biochemical switches are indeed rare and if there are common chemical motifs and family relationships among such switches. We performed a systematic exploration of chemical reaction space by generating all possible stoichiometrically valid chemical configurations up to 3 molecules and 6 reactions and up to 4 molecules and 3 reactions. We used Monte Carlo sampling of parameter space for each such configuration to generate specific models and checked each model for switching properties. We found nearly 4,500 reaction topologies, or about 10% of our tested configurations, that demonstrate switching behavior. Commonly accepted topological features such as feedback were poor predictors of bistability, and we identified new reaction motifs that were likely to be found in switches. Furthermore, the discovered switches were related in that most of the larger configurations were derived from smaller ones by addition of one or more reactions. To explore even larger configurations, we developed two tools: the “bistabilizer,” which converts almost-bistable systems into bistable ones, and frequent motif mining, which helps rank untested configurations. Both of these tools increased the coverage of our library of bistable systems. Thus, our systematic exploration of chemical reaction space has produced a valuable resource for investigating the key signaling motif of bistability.

Tidal Disruption of Protoclusters in Giant Molecular Clouds

We study the collapse of protoclusters within a giant molecular cloud (GMC) to determine the conditions under which collapse is significantly disrupted. Motivated by observations of star-forming regions which exhibit flattened cloud structures, this study considers collapsing protoclusters with disk geometries. The collapse of a 103 M☉ protocluster initially a distance of 2-10 pc from a 103-106 M☉ point mass is numerically calculated. Simulations with zero initial relative velocity between the two are completed, as well as simulations with relative velocities consistent with those observed in GMCs. The results allow us to define the conditions under which it is safe to assume that protocluster collapse proceeds as if in isolation. For instance, we find that the collapse of a 103 M☉ protocluster will be significantly disrupted if it is within 2-4 pc of a 104 M☉ point mass. Thus, the collapse of a 103 M☉ protocluster can be considered to proceed as if in isolation if it is more than ~4 pc away from a 104 M☉ compact object. In addition, in no portion of the sampled parameter space does the gravitational interaction between the protocluster disk and the massive particle significantly disperse the disk into the background GMC. We discuss the distribution of clusters of young stellar objects within the Perseus and Mon R2 star-forming regions, which are consistent with the results of our simulations and the limitations of our results in gas dominated regions such as the Orion cloud.

Improved Monte Carlo inversion of surface wave data

ABSTRACTInversion of surface wave data suffers from solution non‐uniqueness and is hence strongly biased by the initial model. The Monte Carlo approach can handle this non‐uniqueness by evidencing the local minima but it is inefficient for high dimensionality problems and makes use of subjective criteria, such as misfit thresholds, to interpret the results. If a smart sampling of the model parameter space, which exploits scale properties of the modal curves, is introduced the method becomes more efficient and with respect to traditional global search methods it avoids the subjective use of control parameters that are barely related to the physical problem. The results are interpreted drawing inference by means of a statistical test that selects an ensemble of feasible shear wave velocity models according to data quality and model parameterization. Tests on synthetic data demonstrate that the application of scale properties concentrates the sampling of model parameter space in high probability density zones and makes it poorly sensitive to the initial boundary of the model parameters. Tests on synthetic and field data, where boreholes are available, prove that the statistical test selects final results that are consistent with the true model and which are sensitive to data quality. The implemented strategies make the Monte Carlo inversion efficient for practical applications and able to effectively retrieve subsoil models even in complex and challenging situations such as velocity inversions.

Sampling and sensitivity analyses tools (SaSAT) for computational modelling

SaSAT (Sampling and Sensitivity Analysis Tools) is a user-friendly software package for applying uncertainty and sensitivity analyses to mathematical and computational models of arbitrary complexity and context. The toolbox is built in Matlab®, a numerical mathematical software package, and utilises algorithms contained in the Matlab® Statistics Toolbox. However, Matlab® is not required to use SaSAT as the software package is provided as an executable file with all the necessary supplementary files. The SaSAT package is also designed to work seamlessly with Microsoft Excel but no functionality is forfeited if that software is not available. A comprehensive suite of tools is provided to enable the following tasks to be easily performed: efficient and equitable sampling of parameter space by various methodologies; calculation of correlation coefficients; regression analysis; factor prioritisation; and graphical output of results, including response surfaces, tornado plots, and scatterplots. Use of SaSAT is exemplified by application to a simple epidemic model. To our knowledge, a number of the methods available in SaSAT for performing sensitivity analyses have not previously been used in epidemiological modelling and their usefulness in this context is demonstrated.

A Theory of Automatic Parameter Selection for Feature Extraction With Application to Feature-Based Multisensor Image Registration

This paper generalizes the previously developed automated edge-detection parameter selection algorithm of Yitzhaky and Peli. We generalize the approach to arbitrary multidimensional, continuous or discrete parameter spaces, and feature spaces. This generalization enables use of the parameter selection approach with more general image features, for use in feature-based multisensor image registration applications. We investigate the problem of selecting a suitable parameter space sampling density in the automated parameter selection algorithm. A real-valued sensitivity measure is developed which characterizes the effect of parameter space sampling on feature set variability. Closed-form solutions of the sensitivity measure for special feature set relationships are derived. We conduct an analysis of the convergence properties of the sensitivity measure as a function of increasing parameter space sampling density. For certain parameter space sampling sequence types, closed-form expressions for the sensitivity measure limit values are presented. We discuss an approach to parameter space sampling density selection which uses the sensitivity measure convergence behavior. We provide numerical results indicating the utility of the sensitivity measure for selecting suitable parameter values.

Permeability, Transport, and Metabolism of Solutes in Caco-2 Cell Monolayers: A Theoretical Study

We explored the properties of a catenary model that includes the basolateral (B), apical (A), and cellular compartments via simulations under linear and nonlinear conditions to understand the asymmetric observations arising from transporters, enzymes, and permeability in Caco-2 cells. The efflux ratio (EfR; P(app,B-->A)/P(app,A-->B)), obtained from the effective permeability from the A-->B and B-->A direction under linear conditions, was unity for passively permeable drugs whose transport does not involve transporters; the value was unaffected by cellular binding or metabolism, but increased with apical efflux. Metabolism was asymmetric, showing lesser metabolite accrual for the B-->A than A-->B direction because of inherent differences in the volumes for A and B. Moreover, the net flux (total - passive permeation) due to saturable apical efflux, absorption, or metabolism showed nonconformity to simple Michaelis-Menten kinetics against C(D,0), the loading donor concentration. EfR values differed with saturable apical efflux and metabolism (>1), as well as apical absorption (EfRs <1), but approached unity with high passive diffusive clearance (CL(d)) and increasing C(D,0) at a higher degree of saturation of the process. The J(max) (apparent V(max) estimated for the carrier system) and K(m)(') [or the K(m)('') based on a modified equation with the Hill coefficient (beta)] estimates from the Eadie-Hofstee plot revealed spurious correlations with the assigned V(max) and K(m). The sampling time, CL(d), and parameter space of K(m) and V(max) strongly influenced both the correlation and accuracy of estimates. Improved correlation was found for compounds with high CL(d). These observations showed that the catenary model is appropriate in the description of transport and metabolic data in Caco-2 cells.

Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation

Inspiraling compact-object binary systems are promising gravitational wave sources for ground and space-based detectors. The time-dependent signature of these sources is a well-characterized function of a relatively small number of parameters; thus, the favored analysis technique makes use of matched filtering and maximum likelihood methods. As the parameters that characterize the source model vary, so do the templates against which the detector data are compared in the matched filter. For small variations in the parameters, the filter responses are closely correlated. Current analysis methodology samples a bank of filters whose parameter values are chosen so that the correlation between successive samples from successive filters in the bank is 97%. Correspondingly, the additional information available with each successive template evaluation is, in a real sense, only 3% of that already provided by the nearby templates. The reason for such a dense coverage of parameter space is to minimize the chance that a real signal, near the detection threshold, will be missed by the parameter space sampling. Here we investigate the use of Chebyshev interpolation for reducing the number of templates that must be evaluated to obtain the same analysis sensitivity. Additionally, rather than focus on the ``loss'' of signal-to-noise associated with the finite number of filters in the template bank, we evaluate the receiver operating characteristic (ROC) as a measure of the effectiveness of an analysis technique. The ROC relates the false alarm probability to the false dismissal probability of an analysis, which are the quantities that bear most directly on the effectiveness of an analysis scheme. As a demonstration, we compare the present ``dense sampling'' analysis methodology with the ``interpolation'' methodology using Chebyshev polynomials, restricted to one dimension of the multidimensional analysis problem by plotting the ROC curves. We find that the interpolated search can be arranged to have the same false alarm and false dismissal probabilities as the dense sampling strategy using 25% fewer templates. Generalized to the two-dimensional space used in the computationally limited current analyses, this suggests a factor of 2 increase in computational efficiency; generalized to the full seven-dimensional parameter space that characterizes the signal associated with an eccentric binary system of spinning neutron stars or black holes, it suggests an order of magnitude increase in computational efficiency. Since the computational cost of the analysis is driven almost exclusively by the matched filter evaluations, a reduction in the number of template evaluations translates directly into an increase in computational efficiency; additionally, since the computational cost of the analysis is large, the increased efficiency translates also into an increase in the size of the parameter space that can be analyzed and, thus, the science that can be accomplished with the data.

A semi-static approach to mapping dynamic iterative tasks onto heterogeneous computing systems

Minimization of the execution time of an iterative application in a heterogeneous parallel computing environment requires an appropriate mapping scheme for matching and scheduling the subtasks of a given application onto the processors. Often, some of the characteristics of the application subtasks are unknown a priori or change from iteration to iteration during execution-time based on the inputs being processed. In such a scenario, it may not be feasible to use the same off-line-derived mapping for each iteration of the application. One possibility is to employ a semi-static methodology that starts with an initial mapping but dynamically performs remapping between application iterations by observing the effects of the changing characteristics of the application's input data, called dynamic parameters, on the application's execution time. A contribution in this paper is to implement and evaluate a semi-static methodology involving the on-line use of off-line-derived mappings. The off-line phase is based on a genetic algorithm (GA) to generate high-quality mappings for a range of values for the dynamic parameters. A dynamic parameter space partitioning and sampling scheme is proposed that partitions the parameter space into a number of hyper-rectangles, within which the “best” mapping for each hyper-rectangle is stored in a mapping table. During the on-line phase, the actual dynamic parameters are observed and the off-line-derived mapping table is referenced to choose the most suitable mapping. Experimental results indicate that the semi-static approach outperforms a dynamic on-line approach and performs reasonably close to an infeasible on-line GA approach. Furthermore, the semi-static approach considerably outperforms the method of using the same mapping for all iterations.

Prediction in Multilevel Models

Multilevel modeling is an increasingly popular technique for analyzing hierarchical data. This article addresses the problem of predicting a future observable y*j in thej th group of a hierarchical data set. Three prediction rules are considered and several analytical results on the relative performance of these prediction rules are demonstrated. In addition, the prediction rules are assessed by means of a Monte Carlo study that extensively covers both the sample size and parameter space. Specifically, the sample size space concerns the various combinations of Level 1 (individual) and Level 2 (group) sample sizes, while the parameter space concerns different intraclass correlation values. The three prediction rules employ OLS, prior, and multilevel estimators for the Level 1 coefficientsβj The multilevel prediction rule performs the best across all design conditions, and the prior prediction rule degrades as the number of groups, J, increases. Finally, this article investigates the robustness of the multilevel prediction rule to misspecifications of the Level 2 model.

Combining Global and Local Optimization Techniques for Automatic History Matching Production and Seismic Data

SummaryGradient-based optimization techniques are increasingly adopted by oil industries for computer-aided history matching because of the great timesaving they can offer over conventional trial-anderror approaches. However, these methods lead to the identification of a single set of parameters, thus neglecting the inherent nonuniqueness of the solution of the underlying inverse problem. In this paper we propose a new approach that couples a chaotic sampling of parameter space with a local minimization technique. Through the evolution of a nonlinear dynamical system, we identify several points to be successively used as initial guesses for a local gradient-based optimizer. This provides a series of alternative matched models with different production forecasts that improve the understanding of the possible reservoir behaviors. The validity of this approach has been proven on a synthetic reservoir derived from a real west Africa field.

Neural networks for microwave modeling: Model development issues and nonlinear modeling techniques

Artificial neural networks (ANN) recently gained attention as a fast and flexible vehicle to microwave modeling and design. Fast neural models trained from measured/simulated microwave data can be used during microwave design to provide instant answers to the task they have learned. We review two important aspects of neural-network-based microwave modeling, namely, model development issues and nonlinear modeling. A systematic description of key issues in neural modeling approach such as data generation, range and distribution of samples in model input parameter space, data scaling, etc., is presented. Techniques that pave the way for automation of neural model development could be of immense interest to microwave engineers, whose knowledge about ANN is limited. As such, recent techniques that could lead to automatic neural model development, e.g., adaptive controller and adaptive sampling, are discussed. Neural modeling of nonlinear device/circuit characteristics has emerged as an important research area. An overview of nonlinear techniques including small/large signal neural modeling of transistors and dynamic recurrent neural network (RNN) modeling of circuits is presented. Practical microwave examples are used to illustrate the reviewed techniques. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 4–21, 2001.

Probing CdS Nanocrystal Surfaces with Laser-Polarized Xenon

This paper describes the application of optically pumped xenon NMR to probe the surface of semiconductor nanocrystals by physisorption at 123 K. These experiments were made possible by using highly spin ordered [sup 129]Xe, prepared by optical pumping and spin exchange of a rubidium xenon gas mixture, to increase the NMR signal strength. CdS nanocrystals were prepared by regulated growth in inverse micelles and precipitated by surface derivatization with thiophenol. Nanocrystals of 11.8, 12.8, and [angstrom] radii with 26%, 63%, and 57% thiophenol surface coverage, respectively, were characterized. Within this sample parameter space, the [sup 129]Xe spectra, recorded at varying xenon coverages, depended strongly on thiophenol surface coverage but were not sensitive to the crystallite size. In addition, the nanocrystals with low thiophenol coverage yielded a xenon line shape consisting of two components, interpreted as xenon signals arising from district surface domains. 23 refs., 4 figs., 1 tab.

Hypocentre location: genetic algorithms incorporating problem-specific information

SUMMARY This paper shows how the performance of a fully non-linear earthquake location scheme can be improved by taking advantage of problem-specific information in the location procedure. The genetic algorithm is best viewed as a method of parameter space sampling that can be used for optimization problems. It has been applied successfully in regional and teleseismic earthquake location when the network geometry is favourable. However, on a series of test events with unfavourable network geometries the performance of the genetic algorithm is found to be poor. We introduce a method to separate the spatial and temporal parameters in such a way that problems related to the strong trade-off between depth and origin time are avoided. Our modified algorithm has been applied to several test events. Performance over the unmodified algorithm is improved substantially and the computational cost is reduced. The algorithm is better suited to the determination of hypocentral location whether using arrival times, array information (slowness and azimuth) or a combination of both. A second type of modification is introduced which exploits the weak correlation between the epicentral parameters and depth. This algorithm also improves performance over the standard genetic algorithm search, except in circumstances where the depth and epicentre are not weakly correlated, which occurs when the azimuthal coverage is very poor, or when azimuth and slowness information are incorporated. On a shallow nuclear explosion with only teleseismic P arrivals available, the algorithm consistently converged to a depth very close to the true depth, indicating superior depth estimation for shallow earthquake locations over the unmodified algorithm.

Most stringent and maximin tests as solutions of linear programming problems

The problem to obtain the most stringent size-α test ϕ * is formulated as a linear programming problem of type II (Section 2). If sample space and parameter space are finite, then we obtain a discrete linear programming problem (Section 4). The well-known results for this special case, and the results of Krafft and Witting for the maximin size-α test, point out how to formulate the dual problem of type I in the general case and how to develop the corresponding duality theory (Sections 5 and 6). It turns out that ϕ * can be determined completely by the solution of the dual type I problem, which solution may be characterized by means of a least favorable pair $$(\tilde \lambda ,\tilde v)$$ of probability measures over Ω H and Ω K respectively (Section 7). Statistical interpretation shows further that ϕ * can also be characterized by means of a least favorable distribution $$\tilde v$$ over Ω K alone (Section 8).