Number Of Possible Models Research Articles

Inferring Biologically Relevant Models: Nested Canalyzing Functions

Inferring dynamic biochemical networks is one of the main challenges in systems biology. Given experimental data, the objective is to identify the rules of interaction among the different entities of the network. However, the number of possible models fitting the available data is huge, and identifying a biologically relevant model is of great interest. Nested canalyzing functions, where variables in a given order dominate the function, have recently been proposed as a framework for modeling gene regulatory networks. Previously, we described this class of functions as an algebraic toric variety. In this paper, we present an algorithm that identifies all nested canalyzing models that fit the given data. We demonstrate our methods using a well-known Boolean model of the cell cycle in budding yeast.

Constraining the interior of extrasolar giant planets with the tidal Love numberk2using the example of HAT-P-13b

Transit and radial velocity observations continuously discover an increasing number of exoplanets. However, when it comes to the composition of the observed planets the data are compatible with several interior structure models. Thus, a planetary parameter sensitive to the planet's density distribution could help constrain this large number of possible models even further. We aim to investigate to what extent an exoplanet's interior can be constrained in terms of core mass and envelope metallicity by taking the tidal Love number k_2 into account as an additional possibly observable parameter. Because it is the only planet with an observationally determined k_2, we constructed interior models for the Hot Jupiter exoplanet HAT-P-13b by solving the equations of hydrostatic equilibrium and mass conservation for different boundary conditions. In particular, we varied the surface temperature and the outer temperature profile, as well as the envelope metallicity within the widest possible parameter range. We also considered atmospheric conditions that are consistent with nongray atmosphere models. For all these models we calculated the Love number k_2 and compared it to the allowed range of k_2 values that could be obtained from eccentricity measurements of HAT-P-13b. We use the example of HAT-P-13b to show the general relationships between the quantities temperature, envelope metallicity, core mass, and Love number of a planet. For any given k_2 value a maximum possible core mass can be determined. For HAT-P-13b we find Mcore < 27 ME, based on the latest eccentricity measurement. We are able to constrain both the envelope and bulk metallicity of HAT-P-13b to 1 -- 11 times stellar metallicity and the extension of the isothermal layer in the planet's atmosphere to 3 -- 44 bar. Assuming equilibrium tidal theory, we find lower limits on the tidal Q consistent with 10^3 - 10^5.

A Parallel Algorithm for Reverse Engineering Gene Regulatory Networks

Dynamic biological systems, such as gene regulatory networks (GRNs) and protein signaling networks, are often represented as systems of ordinary differential equations. Such equations can be utilized in reverse engineering these biological networks, specifically since identifying these networks is challenging due to the cost of the necessary experiments growing with at least the square of the size of the system. Moreover, the number of possible models, proportional to the number of directed graphs connecting nodes representing the variables in the system, suffers from combinatorial explosion as the size of the system grows. Therefore, exhaustive searches for systems of nontrivial complexity are not feasible. Here we describe a practical and scalable algorithm for determining candidate network interactions based on decomposing an N-dimensional system into N one-dimensional problems. The algorithm was tested on in silico networks based on known biological GRNs. The computational complexity of the network identification is shown to increase as N2 while a parallel implementation achieves essentially linear speedup with the increasing number of processing cores. For each in silico network tested, the algorithm successfully predicts a candidate network that reproduces the network dynamics. This approach dramatically reduces the computational demand required for reverse engineering GRNs and produces a wealth of exploitable information in the process. Moreover, the candidate network topologies returned by the algorithm can be used to design future experiments aimed at gathering informative data capable of further resolving the true network topology.

Ranking Docked Models of Protein-Protein Complexes Using Predicted Partner-Specific Protein-Protein Interfaces: A Preliminary Study.

Computational protein-protein docking is a valuable tool for determining the conformation of complexes formed by interacting proteins. Selecting near-native conformations from the large number of possible models generated by docking software presents a significant challenge in practice. We introduce a novel method for ranking docked conformations based on the degree of overlap between the interface residues of a docked conformation formed by a pair of proteins with the set of predicted interface residues between them. Our approach relies on a method, called PS-HomPPI, for reliably predicting protein-protein interface residues by taking into account information derived from both interacting proteins. PS-HomPPI infers the residues of a query protein that are likely to interact with a partner protein based on known interface residues of the homo-interologs of the query-partner protein pair, i.e., pairs of interacting proteins that are homologous to the query protein and partner protein. Our results on Docking Benchmark 3.0 show that the quality of the ranking of docked conformations using our method is consistently superior to that produced using ClusPro cluster-size-based and energy-based criteria for 61 out of the 64 docking complexes for which PS-HomPPI produces interface predictions. An implementation of our method for ranking docked models is freely available at: http://einstein.cs.iastate.edu/DockRank/.

Dynamic programming procedure for searching optimal models to estimate substitution rates based on the maximum-likelihood method

The substitution rate in a gene can provide valuable information for understanding its functionality and evolution. A widely used method to estimate substitution rates is the maximum-likelihood method implemented in the CODEML program in the PAML package. A limited number of branch models, chosen based on a priori information or an interest in a particular lineage(s), are tested, whereas a large number of potential models are neglected. A complementary approach is also needed to test all or a large number of possible models to search for the globally optional model(s) of maximum likelihood. However, the computational time for this search even in a small number of sequences becomes impractically long. Thus, it is desirable to explore the most probable spaces to search for the optimal models. Using dynamic programming techniques, we developed a simple computational method for searching the most probable optimal branch-specific models in a practically feasible computational time. We propose three search methods to find the optimal models, which explored O(n) (method 1) to O(n(2)) (method 2 and method 3) models when the given phylogeny has n branches. In addition, we derived a formula to calculate the number of all possible models, revealing the complexity of finding the optimal branch-specific model. We show that in a reanalysis of over 50 previously published studies, the vast majority obtained better models with significantly higher likelihoods than the conventional hypothesis model methods.

Confirmatory analysis for phase III population pharmacokinetics

Population pharmacokinetics (POPPK) has many important uses at various stages of drug development and approval. At the phase III stage, one of the major uses of POPPK is to identify covariate influences on human pharmacokinetics, which is important for potential dose adjustment and drug labeling. One common analysis approach is nonlinear mixed-effect modeling, which typically involves time-consuming extensive search for best fits among a large number of possible models. We propose that the analysis goal can be better achieved with a more standard confirmatory statistical analysis approach, which uses a prespecified primary analysis and additional sensitivity analyses. We illustrate this approach using a phase III study data set and compare the result with that calculated using the common exploratory approach. We argue that the confirmatory approach not only substantially reduces analysis time but also yields more accurate and interpretable results. Some aspects of this confirmatory approach may also be extended to data analysis in earlier stages of clinical drug development, i.e. phase II and phase I.

A parallel algorithm for reverse engineering of biological networks.

Dynamic biological systems, such as gene regulatory networks (GRNs) and protein signaling networks, are often represented as systems of ordinary differential equations. Such equations can be utilized in reverse engineering these biological networks, specifically since identifying these networks is challenging due to the cost of the necessary experiments growing with at least the square of the size of the system. Moreover, the number of possible models, proportional to the number of directed graphs connecting nodes representing the variables in the system, suffers from combinatorial explosion as the size of the system grows. Therefore, exhaustive searches for systems of nontrivial complexity are not feasible. Here we describe a practical and scalable algorithm for determining candidate network interactions based on decomposing an N-dimensional system into N one-dimensional problems. The algorithm was tested on in silico networks based on known biological GRNs. The computational complexity of the network identification is shown to increase as N(2) while a parallel implementation achieves essentially linear speedup with the increasing number of processing cores. For each in silico network tested, the algorithm successfully predicts a candidate network that reproduces the network dynamics. This approach dramatically reduces the computational demand required for reverse engineering GRNs and produces a wealth of exploitable information in the process. Moreover, the candidate network topologies returned by the algorithm can be used to design future experiments aimed at gathering informative data capable of further resolving the true network topology.

Qualitative modelling of invasive species eradication on subantarctic Macquarie Island

Summary1. Invaded ecosystems present complex management issues. This problem is exacerbated in many situations by a lack of knowledge about the ecosystem. However, delaying conservation action to collect further data and so reduce such uncertainty is often either impractical or inadvisable.2. The Macquarie Island Pest Eradication Project, currently underway, is attempting to eradicate rabbits, rats, and mice from the island. We undertook qualitative modelling of this project, examining a range of likely outcomes and their possible ecological consequences. The results were aggregated across a large number of possible models, in order to account for uncertainty concerning interactions within the ecosystem.3. The results strongly support the current actions of simultaneous eradication of all three pest species, as simulated eradications of only one or two generally led to continued impacts on the island’s native biota. The results also provided support for the anticipated positive outcomes of the project, with predicted recoveries of tall tussock vegetation, and burrow‐ and surface‐nesting seabirds.4. However, the model predictions also highlighted potential risks: the eradication of mice from the island may not succeed, due in part to the structural position of this species within the ecosystem. Successful eradication of all three target species could potentially release the self‐introduced, non‐native redpolls and starlings, allowing expansion of their populations, with possible impacts on macro‐invertebrates and vegetation.5. Synthesis and applications. These results demonstrate that qualitative modelling approaches can in some cases deliver consistent results, despite high levels of uncertainty regarding interactions within the underlying ecosystem. Such outcomes can provide assistance in the development of strategic contingency plans and ongoing future management action.

Dynamic causal modeling with genetic algorithms

In the last years, dynamic causal modeling has gained increased popularity in the neuroimaging community as an approach for the estimation of effective connectivity from functional magnetic resonance imaging (fMRI) data. The algorithm calls for an a priori defined model, whose parameter estimates are subsequently computed upon the given data. As the number of possible models increases exponentially with additional areas, it rapidly becomes inefficient to compute parameter estimates for all models in order to reveal the family of models with the highest posterior probability. In the present study, we developed a genetic algorithm for dynamic causal models and investigated whether this evolutionary approach can accelerate the model search. In this context, the configuration of the intrinsic, extrinsic and bilinear connection matrices represents the genetic code and Bayesian model selection serves as a fitness function. Using crossover and mutation, populations of models are created and compared with each other. The most probable ones survive the current generation and serve as a source for the next generation of models. Tests with artificially created data sets show that the genetic algorithm approximates the most plausible models faster than a random-driven brute-force search. The fitness landscape revealed by the genetic algorithm indicates that dynamic causal modeling has excellent properties for evolution-driven optimization techniques.

Statistical decisions under ambiguity

This article provides unified axiomatic foundations for the most common optimality criteria in statistical decision theory. It considers a decision maker who faces a number of possible models of the world (possibly corresponding to true parameter values). Every model generates objective probabilities, and von Neumann–Morgenstern expected utility applies where these obtain, but no probabilities of models are given. This is the classic problem captured by Wald’s (Statistical decision functions, 1950) device of risk functions. In an Anscombe–Aumann environment, I characterize Bayesianism (as a backdrop), the statistical minimax principle, the Hurwicz criterion, minimax regret, and the “Pareto” preference ordering that rationalizes admissibility. Two interesting findings are that c-independence is not crucial in characterizing the minimax principle and that the axiom which picks minimax regret over maximin utility is von Neumann–Morgenstern independence.

Testing properties of the Galactic center black hole using stellar orbits

The spin and quadrupole moment of the supermassive black hole at the Galactic center can in principle be measured via astrometric monitoring of stars orbiting at milliparsec (mpc) distances, allowing tests of general relativistic "no-hair" theorems (Will 2008). One complicating factor is the presence of perturbations from other stars, which may induce orbital precession of the same order of magnitude as that due to general relativistic effects. The expected number of stars in this region is small enough that full N-body simulations can be carried out. We present the results of a comprehensive set of such simulations, which include a post-Newtonian treatment of spin-orbit effects. A number of possible models for the distribution of stars and stellar remnants are considered. We find that stellar perturbations are likely to obscure the signal due to frame-dragging for stars beyond ~0.5 mpc from the black hole, while measurement of the quadrupole moment is likely to require observation of stars inside ~0.2 mpc. A high fraction of stellar remnants, e.g. 10-Solar-mass black holes, in this region would make tests of GR problematic at all radii. We discuss the possibility of separating the effects of stellar perturbations from those due to GR.

Le Conseil économique et l’impact régional de la politique commerciale

Given that there are a number of possible models of the regional impact of a tariff, one would have hoped that the Council would have attempted to test the standard ones and/or to have developed new and better ones. After almost forty years Mackintosh's model is still probably the most persuasive model of the long run impact of the tariff in Canada. The Council in its main report has been largely content to repeat and to some extent to confuse elements of the conventional wisdom on the subject. Interesting points have been made in some of the background studies, particularly, among the studies reviewed, by Postner and by Dauphin. At a general level, the Council has failed to integrate its recommendations concerning tariff policy into the general framework of regional policy in this country. Specifically, the Council fails to consider explicitly that on "second best" grounds the elimination of tariffs may not lead to an improvement in resource allocation, nor does it consider in any detail policies which would be preferable to tariffs to achieve regional (and other) objectives which require intervention by the government. For a study which suggests that free trade would bring gains of at least five per cent of GNP, or over $8 billion per year at current levels of production, it would be unfortunate if a certain naïveté in exposition of the free trade case were to consign the document to the political dust-bin.

Exhaustive Enumeration of Kinetic Model Topologies for the Analysis of Time-Resolved RNA Folding

Unlike protein folding, the process by which a large RNA molecule adopts a functionally active conformation remains poorly understood. Chemical mapping techniques, such as Hydroxyl Radical (·OH) footprinting report on local structural changes in an RNA as it folds with single nucleotide resolution. The analysis and interpretation of this kinetic data requires the identification and subsequent optimization of a kinetic model and its parameters. We detail our approach to this problem, specifically focusing on a novel strategy to overcome a factorial explosion in the number of possible models that need to be tested to identify the best fitting model. Previously, smaller systems (less than three intermediates) were computationally tractable using a distributed computing approach. However, for larger systems with three or more intermediates, the problem became computationally intractable. With our new enumeration strategy, we are able to significantly reduce the number of models that need to be tested using non-linear least squares optimization, allowing us to study systems with up to five intermediates. Furthermore, two intermediate systems can now be analyzed on a desktop computer, which eliminates the need for a distributed computing solution for most medium-sized data sets. Our new approach also allows us to study potential degeneracy in kinetic model selection, elucidating the limits of the method when working with large systems. This work establishes clear criteria for determining if experimental ·OH data is sufficient to determine the underlying kinetic model, or if other experimental modalities are required to resolve any degeneracy.

Discriminating the native structure from decoys using scoring functions based on the residue packing in globular proteins.

BackgroundSetting the rules for the identification of a stable conformation of a protein is of utmost importance for the efficient generation of structures in computer simulation. For structure prediction, a considerable number of possible models are generated from which the best model has to be selected.ResultsTwo scoring functions, Rs and Rp, based on the consideration of packing of residues, which indicate if the conformation of an amino acid sequence is native-like, are presented. These are defined using the solvent accessible surface area (ASA) and the partner number (PN) (other residues that are within 4.5 Å) of a particular residue. The two functions evaluate the deviation from the average packing properties (ASA or PN) of all residues in a polypeptide chain corresponding to a model of its three-dimensional structure. While simple in concept and computationally less intensive, both the functions are at least as efficient as any other energy functions in discriminating the native structure from decoys in a large number of standard decoy sets, as well as on models submitted for the targets of CASP7. Rs appears to be slightly more effective than Rp, as determined by the number of times the native structure possesses the minimum value for the function and its separation from the average value for the decoys.ConclusionTwo parameters, Rs and Rp, are discussed that can very efficiently recognize the native fold for a sequence from an ensemble of decoy structures. Unlike many other algorithms that rely on the use of composite scoring function, these are based on a single parameter, viz., the accessible surface area (or the number of residues in contact), but still able to capture the essential attribute of the native fold.

Using Correlation Proximity Graphs to Study Phenotypic Integration

Characterizing and comparing the covariance or correlation structure of phenotypic traits lies at the heart of studies concerned with multivariate evolution. I describe an approach that represents the geometric structure of a correlation matrix as a type of proximity graph called a Correlation Proximity graph. Correlation Proximity graphs provide a compact representation of the geometric relationships inherent in correlation matrices, and these graphs have simple and intuitive properties. I demonstrate how this framework can be used to study patterns of phenotypic integration by employing this approach to compare phenotypic and additive genetic correlation matrices within and between species. I also outline a graph-based method for testing whether an inferred correlation proximity graph is one of a number of possible models that are consistent with a “soft” biological hypothesis.

Numerical Analysis of the 650,000 m2 Åknes Rock Slope based on Measured Displacements and Geotechnical Data

The unstable 650,000 m2 Aknes rock slope (Western Norway) poses a hazard, as a sudden failure may cause a destructive tsunami in the fjord. In this study the slope was divided into blocks based on displacements measured at the slope surface. Discontinuous deformation analysis (DDA) showed that three or four blocks in the upper half may be considered as potential subareas that may fail catastrophically. The lower half may be divided into two or three blocks, but more limited data introduces more uncertainty into block definition. The Universal Distinct Element code (UDEC) was used for two-dimensional (2D) stability analyses. By varying fracture geometry, fracture friction, and groundwater conditions within reasonable limits based on site-specific data a number of possible models were compared. The conclusions show that models that were unstable to great depths were in closer agreement with shear strength parameters derived from an earlier study than models that were unstable to smaller depths. The length (depth) of the outcropping fracture, along which shear displacements are shown to occur, plays an important role. A (shallow) slide at 30 m, in which displacements have been documented by borehole measurements, will reduce the stability at greater depths. Increased groundwater pressure is demonstrated to be less critical for very deep slope instability. The results of the DDA and UDEC modelling will be useful for planning of future investigations, interpretation of the subsequent results, further development of the early warning system and in the tsunami modelling.

A New Determination of the High‐Redshift Type Ia Supernova Rates with theHubble Space TelescopeAdvanced Camera for Surveys

We present a new measurement of the volumetric rate of SNe Ia up to a redshift of 1.7, using the HST GOODS data combined with an additional HST data set covering the GOODS-North field collected in 2004. We employ a novel technique that does not require spectroscopic data for identifying SNe Ia (although spectroscopic measurements of redshifts are used for over half the sample); instead, we employ a Bayesian approach using only photometric data to calculate the probability that an object is an SN Ia. This Bayesian technique can easily be modified to incorporate improved priors on SN properties, and it is well-suited for future high-statistics SN searches in which spectroscopic follow-up of all candidates will be impractical. Here the method is validated on both ground- and space-based SN data having some spectroscopic follow-up. We combine our volumetric rate measurements with low-redshift SN data and fit to a number of possible models for the evolution of the SN Ia rate as a function of redshift. The data do not distinguish between a flat rate at redshift >0.5 and a previously proposed model, in which the Type Ia rate peaks at redshift ~1 due to a significant delay from star formation to the SN explosion. Except for the highest redshifts, where the signal-to-noise ratio is generally too low to apply this technique, this approach yields uncertainties that are smaller than or comparable to previous work.

Bayesian Model Averaging for Spatial Econometric Models

We extend the literature on Bayesian model comparison for ordinary least‐squares regression models to include spatial autoregressive and spatial error models. Our focus is on comparing models that consist of different matrices of explanatory variables. A Markov Chain Monte Carlo model composition methodology labeled MC3 by Madigan and York is developed for two types of spatial econometric models that are frequently used in the literature. The methodology deals with cases where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. Estimates and inferences are produced by averaging over models using the posterior model probabilities as weights, a procedure known as Bayesian model averaging. We illustrate the methods using a spatial econometric model of origin–destination population migration flows between the 48 U.S. states and the District of Columbia during the 1990–2000 period.

Simultaneous X-ray and infrared variability in the quasar 3C273 - II. Confirmation of the correlation and X-ray lag

The X-ray emission from quasars such as 3C273 is generally agreed to arise from Compton scattering of low energy seed photons by relativistic electrons in a relativistic jet oriented close to the line of sight. However there are a number of possible models for the origin of the seed photons. In Paper I (McHardy et al 1999) we showed that the X-ray and IR variability from 3C273 was highly correlated in 1997, with the IR flux leading the X-rays by ~0.75 +/- 0.25 days. The strong correlation, and lag, supports the Synchrotron Self-Compton (SSC) model, where the seed photons are synchroton photons from the jet itself. The previous correlation was based on one moderately well sampled flare and another poorly sampled flare, so the possibility of chance correlated variability exists. Here we report on further X-ray and IR observations of 3C273 which confirm the behaviour seen in Paper I. During a 2 week period of observations we see a flare of amplitude ~25%, lasting for ~5 days, showing a high correlation between IR and X-ray variations, with the X-rays lagging by ~1.45+/- 0.15 days. These observations were not scheduled at any special time, implying that the same mechanism - almost certainly SSC - dominates the X-ray emission on most occasions and that the structure of the emission region is similar in most small flares.

Computer models of musical creativity

In this original and provocative study of computational creativity in music, David Cope asks whether computer programs can effectively model creativity -- and whether computer programs themselves can create. Defining musical creativity, and distinguishing it from creativity in other arts, Cope presents a series of experimental models that illustrate salient features of musical creativity. He makes the case that musical creativity results from a process that he calls inductive association, and he contends that such a computational process can in fact produce music creatively. Drawing on the work of many other scholars and musicians -- including Douglas Hofstadter, Margaret Boden, Selmer Bringsjord, and Kathleen Lennon -- Cope departs from the views expressed by most with his contentions that computer programs can create and that those who do not believe this have probably defined creativity so narrowly that even humans could not be said to create. After examining the foundations of creativity and musical creativity, Cope describes a number of possible models for computationally imitating human creativity in music. He discusses such issues as recombinance and pattern matching, allusions, learning, inference, analogy, musical hierarchy, and influence, and finds that these experimental models solve only selected aspects of creativity. He then describes a model that integrates these different aspects -- an inductive-association computational process that can create music. Cope's writing style is lively and nontechnical; the reader needs neither knowledge of computer programming nor specialized computer hardware or software to follow the text. The computer programs discussed in the text, along with MP3 versions of all the musical examples, are available at the author's website, http://arts.ucsc.edu/faculty/cope.