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Vadim Savin
Vadim Savin

Problem Solving And Uncertainty Modeling Throug... ^HOT^



The mindsets of great problem solvers are just as important as the methods they employ. A mindset that encourages curiosity, embraces imperfection, rewards a dragonfly-eye view of the problem, creates new data from experiments and collective intelligence, and drives action through compelling show-and-tell storytelling creates radical new possibilities under high levels of unpredictability. Of course, these approaches can be helpful in a broad range of circumstances, but in times of massive uncertainty, they are essential.




Problem Solving and Uncertainty Modeling throug...



This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well.


Those examples illustrate how difficult strategic decisions can be at level 4, but they also underscore their transitory nature. Greater political and regulatory stability has turned decisions about whether to enter Russian markets into level 3 problems for the majority of industries today. Similarly, uncertainty about strategic decisions in the consumer multimedia market will migrate to level 3 or to level 2 as the industry begins to take shape over the next several years.


Our experience suggests that at least half of all strategy problems fall into levels 2 or 3, while most of the rest are level 1 problems. But executives who think about uncertainty in a binary way tend to treat all strategy problems as if they fell into either level 1 or level 4. And when those executives base their strategies on rigorous analysis, they are most likely to apply the same set of analytic tools regardless of the level of residual uncertainty they face. For example, they might attempt to use standard, quantitative market-research techniques to forecast demand for data traffic over wireless communications networks as far out as ten years from now.


Uncertainty demands a more flexible approach to situation analysis. The old one-size-fits-all approach is simply inadequate. Over time, companies in most industries will face strategy problems that have varying levels of residual uncertainty, and it is vitally important that the strategic analysis be tailored to the level of uncertainty.


IU may interact with existing vulnerability in depression in several ways. First, IU may act as a moderating variable for rumination, which may explain heightened IU among persons with depression symptoms. Watkins and Baracaia [36] found that many patients with depression perceive rumination as beneficial for understanding, and perhaps ameliorating, their symptoms. Paradoxically, rumination appears to inhibit effective problem solving and emotion regulation through increasing uncertainty [37]. Indeed, rumination, IU, and depressive symptoms appear significantly interrelated among dysphoric (those showing elevated symptoms of depression not reaching clinical threshold) and non-dysphoric participants [38].


Rumination mediated the relationship between IU and depression in both Study 1 (cross-sectionally) and Study 2 (longitudinally). The brooding and reflection rumination subtypes both mediated the association between IU and depression; however, brooding yielded a stronger indirect effect on the IU-depression relationship compared to reflection. There were minor differences in the estimates of the mediational effect across both our studies; specifically, rumination only partially mediated the IU-depression relationship in Study 1, whereas full mediation was found in all three models in Study 2. The current results replicated previous cross-sectional results [39, 40] and provide the first evidence of temporal precedence; that is, high levels of IU appeared to support the development of depression symptoms over time through the engagement in heightened rumination. The longitudinal results are consistent with the notion that rumination, and especially brooding, is a maladaptive coping strategy that intensifies the relationship between cognitive vulnerability factors and the associated negative psychological outcomes. Individuals who are intolerant of uncertainty may lack sufficient problem-solving skills, which in turn is associated with higher levels of distress [40]. Spasojević and Alloy [52] indicated that individuals with cognitive vulnerabilities for depression, such as IU, tended to engage in rumination to cope with negative emotions associated with perceived uncertainty [36,66]. Rumination may intensify negative emotions associated with uncertain situations rather than reduce the ability to engage in problem-solving strategies [5,39], increasing vulnerability to depressive symptoms [66].


Results from the current study contrast previous cross-sectional results [24,39,40] by evidencing reflection as mediating the relationship between IU and depression; however, the mediating effect was larger for brooding than for reflection. Brooding is a passive coping strategy associated with poor decision making, less effective problem solving, and higher depression symptoms over time (e.g., [9,36,67]); in contrast, reflection is conceptualized as an active coping strategy [24,68] associated with lower depression symptoms over time [24,53]. The relative benefits of reflection may be context dependent [25] or mitigated by IU which negatively biases attention and information processing of ambiguous events [69]. IU may facilitate negative thoughts, providing opportunities for individuals engaging in reflection to elaborate on negative cognitions, further facilitating heightened depressogenic beliefs. Overall, it appears that the association between IU and depression may be explained through subcomponents of rumination. Additional longitudinal research is needed to delineate the interplay between components of rumination, IU, and depression.


To approach problem solving successfully, you need to establish consistent processes that help you evaluate, explore solutions, prioritize execution, and measure success. In many ways, it should be similar to how you review business performance through a monthly plan review. You work through the same documentation, look for gaps, dig deeper to identify the root cause, and hash out options. Without this process, you simply cannot expect to solve problems efficiently or effectively.


In fact, it has been found that groups that show greater diversity were better at solving problems than groups made up specifically of highly skilled problem solvers. So whoever you bring in to help you problem-solve, resist the urge to surround yourself with people who already agree with you about everything.


The reconstruction and analysis of genome-scale metabolic models constitutes a powerful systems biology approach, with applications ranging from basic understanding of genotype-phenotype mapping to solving biomedical and environmental problems. However, the biological insight obtained from these models is limited by multiple heterogeneous sources of uncertainty, which are often difficult to quantify. Here we review the major sources of uncertainty and survey existing approaches developed for representing and addressing them. A unified formal characterization of these uncertainties through probabilistic approaches and ensemble modeling will facilitate convergence towards consistent reconstruction pipelines, improved data integration algorithms, and more accurate assessment of predictive capacity.


Our ability to assess and communicate the sources of uncertainty associated with a model can have great impact on the relevance of predictions and on the degree to which these predictions can be constructively used for follow-up studies, as has been noted for the field of systems biology in general [22]. This review is not an introduction to genome-scale metabolic modeling or a survey of its applications, as these topics have been covered elsewhere [5, 11, 23]. Rather, we hope that this text will serve as a roadmap facilitating the development of methods that further formalize a unified characterization of uncertainty in GEM reconstruction and analysis.


In this review, we highlighted methods that use probabilistic approaches and ensemble modeling to represent the uncertainty associated with constraint-based reconstruction and analysis of GEMs. Formalizing the representation of uncertainty in GEMs would improve confidence in modeling results. Although we concede that this is a difficult task, we hope that this review will serve as a roadmap for how this issue can be further addressed. We maintain that ensemble approaches (which are in essence discrete representations of probability distributions) provide a strong framework that naturally captures the uncertainty arising from the many possible outcomes in each step of the reconstruction and flux analysis process (Fig. 1). A practical step moving forward is the development of a unified metabolic network reconstruction and analysis framework that provides a probabilistic ensemble of results. Such a framework would require further development of methods for the representation and analysis of GEM ensembles, such as the MEDUSA package [190], and continued development and integration of approaches that represent uncertainty encountered in each stage of the GEM reconstruction and analysis process. In future development of ensemble models of GEMs, one should keep in mind that this approach is not a panacea [191]. It will be important to accurately account for uncertainty in each step to avoid potential pitfalls, such as an increase in false positive predictions given the sparse nature of the stoichiometric matrix. For example, when incorporating de novo predicted reactions into network gap-filling algorithms, the probabilistic weighting of these reactions would need to be carefully tuned. Additionally, it will be important to further explore correlations between the results of the different steps in the reconstruction and analysis process to fully understand uncertainty in this framework. For example, probabilistic genome annotation and ensemble gap-filling can work synergistically to identify candidate genes for orphan metabolic reactions. Conversely, uncertainty in metabolic network structure could be propagated through methods that use the network structure to infer the biomass formulation (such as BOFdat) or environment specification (such as reverse ecology). It is also important to focus on understanding the sensitivity of modeling results to uncertainty in specific parameters or steps in the pipeline. Generating an ensemble of results can provide insight into which results are robust to uncertainty in different parameters or model choices. Furthermore, clustering and classifying ensembles of results with machine learning algorithms can provide insight into which areas of genome-scale modeling are particularly sensitive and should be targeted for uncertainty reduction [192]. Ultimately, capturing all of the uncertainty in GEM reconstruction and analysis in a single pipeline will be a difficult task, and an emphasis should be placed on transparency and reproducibility such that all of the assumptions employed by a particular approach can be easily accounted for [193]. The standardization of model quality control provided by MEMOTE is an important contribution in this direction [194]. A similar community-effort towards standardized assessment and reporting of GEM uncertainties, as has been recently suggested by Carey et al., would be similarly highly beneficial [195]. 041b061a72


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