Different Levels Of Resolution Research Articles

Exploring geography and evolutionary history as drivers of variation in floral scent chemistry in western sessile-flowered Trillium using parsimony-constrained phylogenetics.

The sessile-flowered Trillium species from western North America have been challenging to distinguish morphologically due to overlapping characters and intraspecific variation. Molecular phylogenetic analyses, currently inconclusive for this group, have not sampled multiple populations of the different species to account for this. Here, we query the diversity of floral volatile composition to understand its bearings on the taxonomy, distribution and evolution of this group. We explored taxonomic and geographic patterns in average floral volatile composition (105 different compounds) among 42 wild populations of four sessile-flowered Trillium species and the outgroup, Pseudotrillium, in California, Oregon and Washington by means of parsimony-constrained phylogenetic analyses. To assess the influence of character construction, we coded compound abundance in three different ways for the phylogenetic analyses and compared the results with those of statistical analyses using the same dataset and previously published statistical analyses. Different codings of floral volatile composition generated different phylogenetic topologies with different levels of resolution. The different phylogenies provide similar answers to taxonomic questions but support different evolutionary histories. Monophyly of most populations of each taxon suggests that floral scent composition bears phylogenetic signal in the western sessile-flowered Trillium. Lack of correlation between the distribution of populations and their position in scent-based phylogenies does not support a geographic signal in floral scent composition. Floral scent composition is a valuable data source for generating phylogenetic hypotheses. The way scent composition is coded into characters is important. The phylogenetic patterns supported by floral volatile compounds are incongruent with previously reported phylogenies of the western sessile-flowered Trillium obtained using molecular or morphological data. Combining floral scent data with gene sequence data and detailed morphological data from multiple populations of each species in future studies is needed for understanding the evolutionary history of western sessile-flowered Trillium.

Algorithm 1044: PyGenStability, a Multiscale Community Detection Framework with Generalized Markov Stability

We present PyGenStability, a general-use Python software package that provides a suite of analysis and visualization tools for unsupervised multiscale community detection in graphs. PyGenStability finds optimized partitions of a graph at different levels of resolution by maximizing the generalized Markov Stability quality function with the Louvain or Leiden algorithm. The package includes automatic detection of robust graph partitions and allows the flexibility to choose quality functions for weighted undirected, directed, and signed graphs and to include other user-defined quality functions.

Identifying spatially differentiated pathways for rural transformation in Pakistan1

This paper proposes a conceptual and empirical framework to develop rural transformation strategies tailored to the agroecological potential and market access of rural areas in Pakistan. Such a framework allows to move away from stereotypical countrywide policies as in use in Pakistan and many other countries. Using publicly available geospatial measures of vegetation greenness and an urban gravity model to proxy the agricultural market demand, we classify Pakistan’s rural districts into categories with similar comparative advantages and describe dominant livelihood activities. The framework recommends market-based approaches to support commercial agriculture or non-agriculture business development in well-connected areas and where households have accumulated human and physical capital. In areas with less developed agricultural potential or market access, households will benefit from area-based and community-driven development, skill development, and labor programs. Since data collection is often challenging in rural areas, statistical agencies can use such an empirical framework to advise policymakers on prioritizing public investments and tailoring rural transformation pathways. In addition, statistical agencies can also extend the framework at different levels of resolution, from national to local level, and complement it with primary data sources to validate the usefulness of the approach.

Identifying multi-resolution clusters of diseases in ten million patients with multimorbidity in primary care in England

BackgroundIdentifying clusters of diseases may aid understanding of shared aetiology, management of co-morbidities, and the discovery of new disease associations. Our study aims to identify disease clusters using a large set of long-term conditions and comparing methods that use the co-occurrence of diseases versus methods that use the sequence of disease development in a person over time.MethodsWe use electronic health records from over ten million people with multimorbidity registered to primary care in England. First, we extract data-driven representations of 212 diseases from patient records employing (i) co-occurrence-based methods and (ii) sequence-based natural language processing methods. Second, we apply the graph-based Markov Multiscale Community Detection (MMCD) to identify clusters based on disease similarity at multiple resolutions. We evaluate the representations and clusters using a clinically curated set of 253 known disease association pairs, and qualitatively assess the interpretability of the clusters.ResultsBoth co-occurrence and sequence-based algorithms generate interpretable disease representations, with the best performance from the skip-gram algorithm. MMCD outperforms k-means and hierarchical clustering in explaining known disease associations. We find that diseases display an almost-hierarchical structure across resolutions from closely to more loosely similar co-occurrence patterns and identify interpretable clusters corresponding to both established and novel patterns.ConclusionsOur method provides a tool for clustering diseases at different levels of resolution from co-occurrence patterns in high-dimensional electronic health records, which could be used to facilitate discovery of associations between diseases in the future.

Physics-Informed Deep Learning Approach for Reintroducing Atomic Detail in Coarse-Grained Configurations of Multiple Poly(lactic acid) Stereoisomers.

Multiscale modeling of complex molecular systems, such as macromolecules, encompasses methods that combine information from fine and coarse representations of molecules to capture material properties over a wide range of spatiotemporal scales. Being able to exchange information between different levels of resolution is essential for the effective transfer of this information. The inverse problem of reintroducing atomistic degrees of freedom in coarse-grained (CG) molecular configurations is particularly challenging as, from a mathematical point of view, it is an ill-posed problem; the forward mapping from the atomistic to the CG description is typically defined via a deterministic operator ("one-to-one" problem), whereas the reversed mapping from the CG to the atomistic model refers to creating one representative configuration out of many possible ones ("one-to-many" problem). Most of the backmapping methods proposed so far balance accuracy, efficiency, and general applicability. This is particularly important for macromolecular systems with different types of isomers, i.e., molecules that have the same molecular formula and sequence of bonded atoms (constitution) but differ in the three-dimensional configurations of their atoms in space. Here, we introduce a versatile deep learning approach for backmapping multicomponent CG macromolecules with chiral centers, trained to learn structural correlations between polymer configurations at the atomistic level and their corresponding CG descriptions. This method is intended to be simple and flexible while presenting a generic solution for resolution transformation. In addition, the method is aimed to respect the structural features of the molecule, such as local packing, capturing therefore the physical properties of the material. As an illustrative example, we apply the model on linear poly(lactic acid) (PLA) in melt, which is one of the most popular biodegradable polymers. The framework is tested on a number of model systems starting from homopolymer stereoisomers of PLA to copolymers with randomly placed chiral centers. The results demonstrate the efficiency and efficacy of the new approach.

Assessing the adequacy of an aggregated vegetation classification: A test in semi‐arid Australia

AbstractVegetation classifications are a valuable tool for guiding management decisions. Vegetation can be classified at different levels of resolution for different purposes. Aggregating finer‐resolution classification units to simplify planning and decision‐making is becoming more common in land management. However, little is known about which resolution or scale of aggregation is appropriate for specific land management practices and the factors to consider when aggregating vegetation classification units. There is a risk that aggregated classification units may overlook vital floristic and structural differences between communities and not accurately represent the patterns of variation in vegetation. This may lead to unanticipated adverse outcomes from management actions. We compared three classification systems to test how well each represented patterns of variation in the vegetation of a semi‐arid region in Victoria, Australia: (a) a finer‐level classification system; (b) a coarser‐resolution system that aggregated finer compositional resolution units for fire management purposes; and (c) a coarser‐resolution classification based on Climate Zones. We conducted floristic and vegetation structure surveys at 249 sites stratified across a climate gradient. Sites were assigned to vegetation classifications based on mapped data layers and checked by ground truthing prior to inclusion. The classification based on a finer compositional resolution best represented variation in both the floristic and structural patterns of the vegetation across this region. This was not unexpected, because accuracy is traded‐off against simplicity when aggregating vegetation classification units. However, the aggregated classification also performed poorly in representing patterns of vegetation when compared with a simple scheme based on Climate Zones. Assessing the adequacy of aggregated vegetation classification units is important, yet often overlooked. To be effective, aggregated vegetation classes must reflect the underlying factors that drive patterns of variation in the vegetation to ensure they support intended management outcomes.

Characteristics of <i>Bacillus cereus</i> complex Group Strains Isolated from Permafrost in Yakutia for Assessment of Microbiological Risks During Climate Change

Strains of Bacillus genus were isolated from soil samples in the permafrost region (Yakutia, Russia). The phenotypic characteristics of the strains are given. The analysis of the obtained data made it possible to assign them to the group Bacillus cereus complex. PCR analysis made it possible to determine the profile of B. cereus toxin synthesis genes in the genomes of the studied strains. Genetic characterization was obtained by RAPD genotyping and using MLVA loci used for genotyping of the anthrax pathogen. The results of genotyping at different levels of resolution made it possible to differentiate the studied strains from the B. anthracis species, to show their intraspecific genetic differences and the degree of relationship. Whole genome sequencing was carried out, based on the data of which MLST genotyping was carried out, which revealed 2 known sequence types and one new one, described for the first time in this work. The results obtained are of practical importance and are extremely interesting from the point of view of the evolution and phylogeography of the B. cereus complex group, since the fact that strains were isolated from permafrost suggests that their age may be much older than expected.

Comparison of Brucella abortus population structure based on genotyping methods with different levels of resolution

Numerous genotyping techniques based on different principles and with different costs and levels of resolution are currently available for understanding the transmission dynamics of brucellosis worldwide. We aimed to compare the population structure of the genomes of 53 Brazilian Brucella abortus isolates using eight different genotyping methods: multiple-locus variable-number tandem-repeat analysis (MLVA8, MLVA11, MLVA16), multilocus sequence typing (MLST9, MLST21), core genome MLST (cgMLST) and two techniques based on single nucleotide polymorphism (SNP) detection (parSNP and NASP) from whole genomes. The strains were isolated from six different Brazilian states between 1977 and 2008 and had previously been analyzed using MLVA8, MLVA11, and MLVA16. Their whole genomes were sequenced, assembled, and subjected to MLST9 MLST21, cgMLST, and SNP analyses. All the genotypes were compared by hierarchical grouping method based on the average distances between the correlation matrices of each technique. MLST9 and MLST21 had the lowest level of resolution, both revealing only four genotypes. MLVA8, MLVA11, and MLVA16 had progressively increasing levels of resolution as more loci were analyzed, identifying 6, 16, and 44 genotypes, respectively. cgMLST showed the highest level of resolution, identifying 45 genotypes, followed by the SNP-based methods, both of which had 44 genotypes. In the assessed population, MLVA was more discriminatory than MLST and was easier and cheaper to perform. SNP techniques and cgMLST provided the highest levels of resolution and the results from the two methods were in close agreement. In conclusion, the choice of genotyping technique can strongly affect one's ability to make meaningful epidemiological conclusions but is dependent on available resources: while the VNTR based techniques are more indicated to high prevalence scenarios, the WGS methods are the ones with the best discriminative power and therefore recommended for outbreaks investigation.

Modeling Massive Highly Multivariate Nonstationary Spatial Data with the Basis Graphical Lasso

We propose a new modeling framework for highly multivariate spatial processes that synthesizes ideas from recent multiscale and spectral approaches with graphical models. The basis graphical lasso writes a univariate Gaussian process as a linear combination of basis functions weighted with entries of a Gaussian graphical vector whose graph is estimated from optimizing an l 1 penalized likelihood. This article extends the setting to a multivariate Gaussian process where the basis functions are weighted with Gaussian graphical vectors. We motivate a model where the basis functions represent different levels of resolution and the graphical vectors for each level are assumed to be independent. Using an orthogonal basis grants linear complexity and memory usage in the number of spatial locations, the number of basis functions, and the number of realizations. An additional fusion penalty encourages a parsimonious conditional independence structure in the multilevel graphical model. We illustrate our method on a large climate ensemble from the National Center for Atmospheric Research’s Community Atmosphere Model that involves 40 spatial processes. Supplementary materials for this article are available online.

TreeTerminus —creating transcript trees using inferential replicate counts

A certain degree of uncertainty is always associated with the transcript abundance estimates. The uncertainty may make many downstream analyses, such as differential testing, difficult for certain transcripts. Conversely, gene-level analysis, though less ambiguous, is often too coarse-grained. We introduce TreeTerminus, a data-driven approach for grouping transcripts into a tree structure where leaves represent individual transcripts and internal nodes represent an aggregation of a transcript set. TreeTerminus constructs trees such that, on average, the inferential uncertainty decreases as we ascend the tree topology. The tree provides the flexibility to analyze data at nodes that are at different levels of resolution in the tree and can be tuned depending on the analysis of interest. We evaluated TreeTerminus on two simulated and two experimental datasets and observed an improved performance compared to transcripts (leaves) and other methods under several different metrics.

Evaluation of the optimal ground motion intensity measure in the prediction of the seismic vulnerability of earth dams

The large majority of existing earth dams were designed with old standards, which often accounted for the effects of earthquakes in a simplified manner. As a result, seismic re-evaluation of these structures is now becoming increasingly important for dam owners. The seismic performance of earth dams can be evaluated at different levels of resolution, typically ranging from simple sliding block analysis, to the use of advanced numerical models. Seismic inputs for these models are typically chosen using code-based or site-specific probabilistic seismic hazard analysis (PSHA). In this study, we analyze the seismic vulnerability of two major earth dams located in Southern Italy, a seismically active area. The two dam systems have different geotechnical characteristics: one of them is founded on potentially liquefiable materials, whereas the other one is not susceptible to liquefaction. Our analyses are based on finite difference numerical simulations using both simplified and advanced constitutive models. Seismic vulnerability of both dams is analyzed by means of analytical fragility functions for various damage mechanisms and ground motion intensity measures (IMs). Such fragility functions are based on nonlinear deformation analyses within the multiple stripe analysis framework. We analyze efficiency and predictability of various IMs in predicting different damage levels and mechanisms. We show that the cumulative absolute velocity is overall the optimal IM in predicting vulnerability of both earth dams. We also analyze the relative importance of PSHA inputs (i.e. alternative ground motion and earthquake rupture forecast models; GMMs and ERFMs, respectively) and numerical models (simplified vs advanced) in the seismic analysis of earth dams by means of tornado diagrams. We show that the choice of GMMs and ERFMs is always more important than that of the constitutive model. However, for dams prone to liquefaction, the choice of the constitutive model has a higher importance than for non-liquefiable earth dams.

On Inclusive Growth: An Economic Growth Time-Frequency Analysis of the Democratic Republic of Congo from 1975-2016

This paper focuses on fluctuations in the inclusiveness of economic growth (in terms of its participatory aspect) in the Democratic Republic of Congo at different time scales. We investigate the extent to which variations in economic growth are explained by variations in the unemployment rate, the agricultural sector, and the mining sector, using an econometric model known as Auto-Regressive Distributed Lag model which will give us both short and long-term impulse responses in order to identify the dynamics of our variables (endogenous and exogenous). In the same vein, we show that the development of a structural economic policy is imperative to overcome the problem of the non-resilience of the Congolese economy, in particular through the promotion of growth-catalyzing sectors in order to generate more wealth to be equitably redistributed to each segment of the Congolese population as well as to the pro-poor sectors. Moreover, knowing that the Congolese economy has been confronted with multiple shocks (supply and demand) to the point of damaging its sustainability, the information contained in the fluctuations of economic growth informs us about the state of inclusive growth in its entirety relative to the interference of the Congolese state. Thus, the cyclical movements of economic growth are extracted using a multi-resolution analysis (or wavelet decomposition) that spreads a time series at different levels of resolution.

Systematic population-wide ecological analysis of regional variability in disease prevalence

The prevalence of diseases often varies substantially from region to region. Besides basic demographic properties, the factors that drive the variability of each prevalence are to a large extent unknown. Here we show how regional prevalence variations in 115 different diseases relate to demographic, socio-economic, environmental factors and migratory background, as well as access to different types of health services such as primary, specialized and hospital healthcare. We have collected regional data for these risk factors at different levels of resolution; from large regions of care (Versorgungsregion) down to a 250 by 250 m square grid. Using multivariate regression analysis, we quantify the explanatory power of each independent variable in relation to the regional variation of the disease prevalence. We find that for certain diseases, such as acute heart conditions, diseases of the inner ear, mental and behavioral disorders due to substance abuse, up to 80% of the variance can be explained with these risk factors. For other diagnostic blocks, such as blood related diseases, injuries and poisoning however, the explanatory power is close to zero. We find that the time needed to travel from the inhabited center to the relevant hospital ward often contributes significantly to the disease risk, in particular for diabetes mellitus. Our results show that variations in disease burden across different regions can for many diseases be related to variations in demographic and socio-economic factors. Furthermore, our results highlight the relative importance of access to health care facilities in the treatment of chronic diseases like diabetes.

Machine-guided path sampling to discover mechanisms of molecular self-organization

Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Here we present an autonomous path sampling algorithm that integrates deep learning and transition path theory to discover the mechanism of molecular self-organization phenomena. The algorithm uses the outcome of newly initiated trajectories to construct, validate and—if needed—update quantitative mechanistic models. Closing the learning cycle, the models guide the sampling to enhance the sampling of rare assembly events. Symbolic regression condenses the learned mechanism into a human-interpretable form in terms of relevant physical observables. Applied to ion association in solution, gas-hydrate crystal formation, polymer folding and membrane-protein assembly, we capture the many-body solvent motions governing the assembly process, identify the variables of classical nucleation theory, uncover the folding mechanism at different levels of resolution and reveal competing assembly pathways. The mechanistic descriptions are transferable across thermodynamic states and chemical space.

On equilibrating non-periodic molecular dynamics samples for coupled particle-continuum simulations of amorphous polymers

In the context of fracture simulations of polymers, the molecular mechanisms in the vicinity of the crack tip are of particular interest. Nevertheless, to keep the computational cost to a minimum, a coarser resolution must be used in the remaining regions of the numerical sample. For the specific case of amorphous polymers, the Capriccio method bridges the gap between the length and time scales involved at the different levels of resolution by concurrently coupling molecular dynamics (MD) with the finite element method (FEM). Within the scope of the Capriccio approach, the coupling to the molecular MD region introduces non-periodic, so-called stochastic boundary conditions (SBC). In similarity to typical simulations under periodic boundary conditions (PBC), the SBC MD simulations must reach an equilibrium state before mechanical loads are exerted on the coupled systems. In this contribution, we hence extensively study the equilibration properties of non-periodic MD samples using the Capriccio method. We demonstrate that the relaxation behavior of an MD-FE coupled MD domain utilizing non-periodic boundary conditions is rather insensitive to the specific coupling parameters of the method chosen to implement the boundary conditions. The behavior of an exemplary system equilibrated with the parameter set considered as optimal is further studied under uniaxial tension and we observe some peculiarities in view of creep and relaxation phenomena. This raises important questions to be addressed in the further development of the Capriccio method.

A multimodal critical discourse analysis of city as text: investigation of meaning metafunctions of Rasht’s Imam Khomeini Street

Studying the city as text is influenced by a phenomenon called the linguistic turn. This is because the text of the city is composed of different semiotic systems. This study employs multimodal discourse analysis as its theoretical framework. Through a close examination of the organizational, interactional and representational metafunction of the city text, the authors aim to highlight its characteristics as a communicational resource to provide a multimodal reading of the city. They demonstrate how applying a social semiotic approach to the physical dimensions of a street contributes to a particular understanding of how this public space is used or navigated and how the formal management of the flow of cars and people is materialized. Here the city is classified into different levels of resolution based on urban morphology’s description of the urban tissue. The text of the city is constructed through dialogue among meaning metafunctions on one level and among different levels. Examining different aspects of meaning in the text of Imam Khomeini Street and the city of Rasht indicates how, in such a text, the producers and participants communicate through the material aspect of the city. Uses of semiotic materials are ideological and their affordances have evolved in specific socio-political moments. In this street, the city as an institution and as a place of authority having the biggest share in the production of this text persuades other participants to follow and reproduce a certain narration of the reality. Controlling and training the body, on one hand, and using the urban space for advertising the dominant discourse, on the other hand, are the boldest motives of this street’s design, and the formation of the different dimensions of meaning is somehow at the service of the consolidation of a particular kind of everyday life.

Validation of hierarchical taxonomy in a clinical sample.

Quantitatively derived dimensional models of psychopathology enjoy overwhelming empirical support, and a large and active community of psychopathology researchers has been establishing an empirically based dimensional hierarchical taxonomy of psychopathology (or HiTOP) as a strong candidate replacement for the current categorical classification system. The hierarchical nature of this taxonomy implies that different levels of resolution are likely to be optimal for different purposes. Our aim was to identify which level of detail is likely to provide optimal validity and explanatory power with regard to relevant clinical variables. In the present report from the Rhode Island Methods to Improve Diagnostic Assessment and Services project, we used data from a sample of 2900 psychiatric outpatients to compare different levels from a bass-ackwards model of psychopathology in relation to psychosocial impairment across different domains (global functioning, inability to work, social functioning, suicidal ideation, history of suicide attempts, history of psychiatric hospitalization). All functioning indices were significantly associated with general psychopathology, but more complex levels provided significant incremental validity. The optimal level of complexity varied across functioning indices, suggesting that there is no single 'best' level for understanding relations between psychopathology and functioning. Results support the hierarchical organization of psychopathology dimensions with regard to validity considerations and downstream implications for applied assessment. It would be fruitful to develop and implement measurement of these dimensions at the appropriate level for the purpose at hand. These findings can be used to guide HiTOP-consistent assessment in other research and clinical settings.

High-Enthalpy Geothermal Simulation with Continuous Localization in Physics

Simulation of heat production in high-enthalpy geothermal systems is associated with a complex physical process in which cold water invades steam-saturated control volumes. The fully implicit, fully coupled numerical strategy is commonly adopted to solve the governing system composed of mass and energy conservation equations. A conventional nonlinear solver is generally challenged by the strong nonlinearity present during phase transition because of a huge contrast of thermodynamics between hot steam and cool water. In the process of solution, due to the steam condensation, the reduction in fluid volume reduces the pressure in the control volume. This generates multiple local minima in the physical parameter space, which indicates the Newton initial guess should be carefully selected to guarantee the nonlinear convergence. Otherwise, the Newton iteration will approach a local minimum and the solution based on Newton’s update cannot converge and needs to be repeated for a smaller timestep. This problem brings simulation to the stalling behavior where a nonlinear solver wastes a lot of computations and performs at a very small timestep. To tackle this problem, we formulated continuous localization of Newton’s method based on an Operator-Based Linearization (OBL) approach. In OBL, the physical space can be parameterized in terms of operators with supporting points at different levels of resolution. During the simulation, the operator values at supporting points are obtained through reference physics and the remaining part of the space is interpolated. In this way, the nonlinear physical parameter space can be flexibly characterized with different degrees of accuracy. In our proposed approach, the nonlinear Newton iterations are performed in parameter space with different resolutions from coarse to fine. Specifically, the Newton solution under coarser resolution is taken as the initial guess for that under finer resolution. A coarser parameter space represents more linear physics, under which the nonlinear solver quickly converges to a localized solution near the true solution. With refinement in physics, the Newton iteration will approach the true solution and the stalling behaviour in the simulation is avoided. Therefore, a larger timestep can be utilized in the simulation compared with the conventional nonlinear solvers.

A comprehensive suite of earthquake catalogues for the 2016-2017 Central Italy seismic sequence

The protracted nature of the 2016-2017 central Italy seismic sequence, with multiple damaging earthquakes spaced over months, presented serious challenges for the duty seismologists and emergency managers as they assimilated the growing sequence to advise the local population. Uncertainty concerning where and when it was safe to occupy vulnerable structures highlighted the need for timely delivery of scientifically based understanding of the evolving hazard and risk. Seismic hazard assessment during complex sequences depends critically on up-to-date earthquake catalogues—i.e., data on locations, magnitudes, and activity of earthquakes—to characterize the ongoing seismicity and fuel earthquake forecasting models. Here we document six earthquake catalogues of this sequence that were developed using a variety of methods. The catalogues possess different levels of resolution and completeness resulting from progressive enhancements in the data availability, detection sensitivity, and hypocentral location accuracy. The catalogues range from real-time to advanced machine-learning procedures and highlight both the promises as well as the challenges of implementing advanced workflows in an operational environment.

Probabilistic model checking of cancer metabolism

Cancer cell metabolism is often deregulated as a result of adaption to meeting energy and biosynthesis demands of rapid growth or direct mutation of key metabolic enzymes. Better understanding of such deregulation can provide new insights on targetable vulnerabilities, but is complicated by the difficulty in probing cell metabolism at different levels of resolution and under different experimental conditions. We construct computational models of glucose and glutamine metabolism with focus on the effect of IDH1/2-mutations in cancer using a combination of experimental metabolic flux data and patient-derived gene expression data. Our models demonstrate the potential of computational exploration to reveal biologic behavior: they show that an exogenously-mutated IDH1 experimental model utilizes glutamine as an alternative carbon source for lactate production under hypoxia, but does not fully-recapitulate the patient phenotype under normoxia. We also demonstrate the utility of using gene expression data as a proxy for relative differences in metabolic activity. We use the approach of probabilistic model checking and the freely-available Probabilistic Symbolic Model Checker to construct and reason about model behavior.