Identifying Biological Network Structure, Predicting Network Behavior, and Classifying Network State With High Dimensional Model Representation (HDMR)

This work presents an adapted Random Sampling - High Dimensional Model Representation (RS-HDMR) algorithm for synergistically addressing three key problems in network biology: (1) identifying the structure of biological networks from multivariate data, (2) predicting network response under previously unsampled conditions, and (3) inferring experimental perturbations based on the observed network state. RS-HDMR is a multivariate regression method that decomposes network interactions into a hierarchy of non-linear component functions. Sensitivity analysis based on these functions provides a clear physical and statistical interpretation of the underlying network structure. The advantages of RS-HDMR include efficient extraction of nonlinear and cooperative network relationships without resorting to discretization, prediction of network behavior without mechanistic modeling, robustness to data noise, and favorable scalability of the sampling requirement with respect to network size. As a proof-of-principle study, RS-HDMR was applied to experimental data measuring the single-cell response of a protein-protein signaling network to various experimental perturbations. A comparison to network structure identified in the literature and through other inference methods, including Bayesian and mutual-information based algorithms, suggests that RS-HDMR can successfully reveal a network structure with a low false positive rate while still capturing non-linear and cooperative interactions. RS-HDMR identified several higher-order network interactions that correspond to known feedback regulations among multiple network species and that were unidentified by other network inference methods. Furthermore, RS-HDMR has a better ability to predict network response under unsampled conditions in this application than the best statistical inference algorithm presented in the recent DREAM3 signaling-prediction competition. RS-HDMR can discern and predict differences in network state that arise from sources ranging from intrinsic cell-cell variability to altered experimental conditions, such as when drug perturbations are introduced. This ability ultimately allows RS-HDMR to accurately classify the experimental conditions of a given sample based on its observed network state

Thermal uncertainty quantification in frequency responses of laminated composite plates

The propagation of thermal uncertainty in composite structures has significant computational challenges. This paper presents the thermal, ply-level and material uncertainty propagation in frequency responses of laminated composite plates by employing surrogate model which is capable of dealing with both correlated and uncorrelated input parameters. The present approach introduces the generalized high dimensional model representation (GHDMR) wherein diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression is utilized to ensure the hierarchical orthogonality of high dimensional model representation component functions. The stochastic range of thermal field includes elevated temperatures up to 375 K and sub-zero temperatures up to cryogenic range of 125 K. Statistical analysis of the first three natural frequencies is presented to illustrate the results and its performance

A comparison of approximation techniques for variance-based sensitivity analysis of biochemical reaction systems

<p>Abstract</p> <p>Background</p> <p>Sensitivity analysis is an indispensable tool for the analysis of complex systems. In a recent paper, we have introduced a thermodynamically consistent variance-based sensitivity analysis approach for studying the robustness and fragility properties of biochemical reaction systems under uncertainty in the standard chemical potentials of the activated complexes of the reactions and the standard chemical potentials of the molecular species. In that approach, key sensitivity indices were estimated by Monte Carlo sampling, which is computationally very demanding and impractical for large biochemical reaction systems. Computationally efficient algorithms are needed to make variance-based sensitivity analysis applicable to realistic cellular networks, modeled by biochemical reaction systems that consist of a large number of reactions and molecular species.</p> <p>Results</p> <p>We present four techniques, derivative approximation (DA), polynomial approximation (PA), Gauss-Hermite integration (GHI), and orthonormal Hermite approximation (OHA), for <it>analytically </it>approximating the variance-based sensitivity indices associated with a biochemical reaction system. By using a well-known model of the mitogen-activated protein kinase signaling cascade as a case study, we numerically compare the approximation quality of these techniques against traditional Monte Carlo sampling. Our results indicate that, although DA is computationally the most attractive technique, special care should be exercised when using it for sensitivity analysis, since it may only be accurate at low levels of uncertainty. On the other hand, PA, GHI, and OHA are computationally more demanding than DA but can work well at high levels of uncertainty. GHI results in a slightly better accuracy than PA, but it is more difficult to implement. OHA produces the most accurate approximation results and can be implemented in a straightforward manner. It turns out that the computational cost of the four approximation techniques considered in this paper is orders of magnitude smaller than traditional Monte Carlo estimation. Software, coded in MATLAB^®, which implements all sensitivity analysis techniques discussed in this paper, is available free of charge.</p> <p>Conclusions</p> <p>Estimating variance-based sensitivity indices of a large biochemical reaction system is a computationally challenging task that can only be addressed via approximations. Among the methods presented in this paper, a technique based on orthonormal Hermite polynomials seems to be an acceptable candidate for the job, producing very good approximation results for a wide range of uncertainty levels in a fraction of the time required by traditional Monte Carlo sampling.</p

Forward uncertainty quantification with special emphasis on a Bayesian active learning perspective

Uncertainty quantification (UQ) in its broadest sense aims at quantitatively studying all sources of uncertainty arising from both computational and real-world applications. Although many subtopics appear in the UQ field, there are typically two major types of UQ problems: forward and inverse uncertainty propagation. The present study focuses on the former, which involves assessing the effects of the input uncertainty in various forms on the output response of a computational model. In total, this thesis reports nine main developments in the context of forward uncertainty propagation, with special emphasis on a Bayesian active learning perspective. The first development is concerned with estimating the extreme value distribution and small first-passage probabilities of uncertain nonlinear structures under stochastic seismic excitations, where a moment-generating function-based mixture distribution approach (MGF-MD) is proposed. As the second development, a triple-engine parallel Bayesian global optimization (T-PBGO) method is presented for interval uncertainty propagation. The third contribution develops a parallel Bayesian quadrature optimization (PBQO) method for estimating the response expectation function, its variable importance and bounds when a computational model is subject to hybrid uncertainties in the form of random variables, parametric probability boxes (p-boxes) and interval models. In the fourth research, of interest is the failure probability function when the inputs of a performance function are characterized by parametric p-boxes. To do so, an active learning augmented probabilistic integration (ALAPI) method is proposed based on offering a partially Bayesian active learning perspective on failure probability estimation, as well as the use of high-dimensional model representation (HDMR) technique. Note that in this work we derive an upper-bound of the posterior variance of the failure probability, which bounds our epistemic uncertainty about the failure probability due to a kind of numerical uncertainty, i.e., discretization error. The fifth contribution further strengthens the previously developed active learning probabilistic integration (ALPI) method in two ways, i.e., enabling the use of parallel computing and enhancing the capability of assessing small failure probabilities. The resulting method is called parallel adaptive Bayesian quadrature (PABQ). The sixth research presents a principled Bayesian failure probability inference (BFPI) framework, where the posterior variance of the failure probability is derived (not in closed form). Besides, we also develop a parallel adaptive-Bayesian failure probability learning (PA-BFPI) method upon the BFPI framework. For the seventh development, we propose a partially Bayesian active learning line sampling (PBAL-LS) method for assessing extremely small failure probabilities, where a partially Bayesian active learning insight is offered for the classical LS method and an upper-bound for the posterior variance of the failure probability is deduced. Following the PBAL-LS method, the eighth contribution finally obtains the expression of the posterior variance of the failure probability in the LS framework, and a Bayesian active learning line sampling (BALLS) method is put forward. The ninth contribution provides another Bayesian active learning alternative, Bayesian active learning line sampling with log-normal process (BAL-LS-LP), to the traditional LS. In this method, the log-normal process prior, instead of a Gaussian process prior, is assumed for the beta function so as to account for the non-negativity constraint. Besides, the approximation error resulting from the root-finding procedure is also taken into consideration. In conclusion, this thesis presents a set of novel computational methods for forward UQ, especially from a Bayesian active learning perspective. The developed methods are expected to enrich our toolbox for forward UQ analysis, and the insights gained can stimulate further studies

Modeling mechanical response of heterogeneous materials

Heterogeneous materials are ubiquitous in nature and as synthetic materials. These materials provide unique combination of desirable mechanical properties emerging from its heterogeneities at different length scales. Future structural and technological applications will require the development of advanced light weight materials with superior strength and toughness. Cost effective design of the advanced high performance synthetic materials by tailoring their microstructure is the challenge facing the materials design community. Prior knowledge of structure-property relationships for these materials is imperative for optimal design. Thus, understanding such relationships for heterogeneous materials is of primary interest. Furthermore, computational burden is becoming critical concern in several areas of heterogeneous materials design. Therefore, computationally efficient and accurate predictive tools are highly essential. In the present study, we mainly focus on mechanical behavior of soft cellular materials and tough biological material such as mussel byssus thread. Cellular materials exhibit microstructural heterogeneity by interconnected network of same material phase. However, mussel byssus thread comprises of two distinct material phases. A robust numerical framework is developed to investigate the micromechanisms behind the macroscopic response of both of these materials. Using this framework, effect of microstuctural parameters has been addressed on the stress state of cellular specimens during split Hopkinson pressure bar test. A voronoi tessellation based algorithm has been developed to simulate the cellular microstructure. Micromechanisms (microinertia, microbuckling and microbending) governing macroscopic behavior of cellular solids are investigated thoroughly with respect to various microstructural and loading parameters. To understand the origin of high toughness of mussel byssus thread, a Genetic Algorithm (GA) based optimization framework has been developed. It is found that two different material phases (collagens) of mussel byssus thread are optimally distributed along the thread. These applications demonstrate that the presence of heterogeneity in the system demands high computational resources for simulation and modeling. Thus, Higher Dimensional Model Representation (HDMR) based surrogate modeling concept has been proposed to reduce computational complexity. The applicability of such methodology has been demonstrated in failure envelope construction and in multiscale finite element techniques. It is observed that surrogate based model can capture the behavior of complex material systems with sufficient accuracy. The computational algorithms presented in this thesis will further pave the way for accurate prediction of macroscopic deformation behavior of various class of advanced materials from their measurable microstructural features at a reasonable computational cost

Design technologies for eco-industrial parks: From unit operations to processes, plants and industrial networks

© 2016 Elsevier Ltd. The concept of eco-industrial park (EIP) has recently become the subject of a great deal of attention from industry and academic research groups. This paper proposes a series of systematic approaches for multi-level modelling and optimisation in EIPs. The novelties of this work include, (1) building a four-level modelling framework (from unit level to process level, plant level and industrial network level) for EIP research, (2) applying advanced mathematical modelling methods to describe each level operation, (3) developing efficient methodologies for solving optimisation problems at different EIP levels, (4) considering symbiotic relations amongst the three networks (material, water and energy networks) at the top EIP level with the boundary conditions of economic, social and legal requirements. For methodology demonstration, two cases at process level and industrial network level respectively are tested and solved with the developed modelling and optimisation strategies. Finally, the challenges and applications in future EIP research are also discussed, including data collection, the extension of the current networks to EIPs, and the feasibility of the proposed methodologies for complex EIP problems. The extended EIPs include the combination of material exchanges, energy systems and waste-water treatment networks. The aspects considered for future industrial ecology are carbon emission, by-product reuse, water consumption, and energy consumption. The main object of this paper is to explain the detailed model construction process and the development of optimisation approaches for a complex EIP system. In future work, this system is expected to share services, utility, and product resources amongst industrial plants to add value, reduce costs, improve environment, and consequently achieve sustainable development in a symbiosis community

Uncertainty Quantification for Electromagnetic Analysis via Efficient Collocation Methods.

Electromagnetic (EM) devices and systems often are fraught by uncertainty in their geometry, configuration, and excitation. These uncertainties (often termed “random variables”) strongly and nonlinearly impact voltages and currents on mission-critical circuits or receivers (often termed “observables”). To ensure the functionality of such circuits or receivers, this dependency should be statistically characterized. In this thesis, efficient collocation methods for uncertainty quantification in EM analysis are presented. First, a Stroud-based stochastic collocation method is introduced to statistically characterize electromagnetic compatibility and interference (EMC/EMI) phenomena on electrically large and complex platforms. Second, a multi-element probabilistic collocation (ME-PC) method suitable for characterizing rapidly varying and/or discontinuous observables is presented. Its applications to the statistical characterization of EMC/EMI phenomena on electrically and complex platforms and transverse magnetic wave propagation in complex mine environments are demonstrated. In addition, the ME-PC method is applied to the statistical characterization of EM wave propagation in complex mine environments with the aid of a novel fast multipole method and fast Fourier transform-accelerated surface integral equation solver -- the first-ever full-wave solver capable of characterizing EM wave propagation in hundreds of wavelengths long mine tunnels. Finally, an iterative high-dimensional model representation technique is proposed to statistically characterize EMC/EMI observables that involve a large number of random variables. The application of this technique to the genetic algorithm based optimization of EM devices is presented as well.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/100086/1/acyucel_1.pd

Novel approaches for dynamic modelling of E. coli and their application in Metabolic Engineering

PhD thesis in BioengineeringOne of the trends of modern societies is the replacement of chemical processes by biochemical ones, with new compounds being synthesized by engineered microorganisms, while some waste products are also being degraded by biotechnological means. Biotechnology holds the promise of creating a more profitable and environmental friendly industry, with a reduced number of waste products, when contrasted with the traditional chemical industry. However, in an era in which genomes are sequenced at a faster pace than ever before, and with the advent omic measurements, this information is not directly translated into the targeted design of new microorganisms, or biological processes. These experimental data in isolation do not explain how the different cell constituents interact. Reductionist approaches that dominated science in the last century study cellular entities in isolation as separate chunks, without taking into consideration interactions with other molecules. This leads to an incomplete view of biological processes, which compromises the development of new knowledge. To overcome these hurdles, a formal systems approach to Biology has been surging in the last thirty years. Systems biology can be defined as the conjugation of different fields (such as Mathematics, Computer Science, Biology), to describe formally and non-ambiguously the behavior of the different cellular systems and their interactions, using to models and simulations. Metabolic Engineering takes advantage of these formal specifications, using mathematically based methods to derive strategies to optimize the microbial metabolism, in order to achieve a desired goal, such as the increase of the production of a relevant industrial compound. In this work, we develop a mechanistic dynamic model based on ordinary differential equations, comprised by elementary mass action descriptions of each reaction, from an existing model of Escherichia coli in the literature. We also explore different calibration processes for these reaction descriptions. We also contribute to the field of strain design by utilizing evolutionary algorithms with a new representation scheme that allows to search for enzyme modulations, in continuous or discrete scales, as well as reaction knockouts, in existing dynamic metabolic models, aiming at the maximization of product yields. In the bioprocess optimization field, we extended the Dynamic Flux Balance Analysis formulation to incorporate the possibility to simulate fed-batch bioprocesses. This formulation is also enhanced with methods that possess the capacity to design feed profiles to attain a specific goal, such as maximizing the bioprocess yield or productivity. All the developed methods involved some form of sensitivity and identifiability analysis, to identify how model outputs are affected by their parameters. All the work was constructed under a modular software framework (developed during this thesis), that permits the interaction of distinct algorithms and languages, being a flexible tool to utilize in a cluster environment. The framework is available as an open-source software package, and has appeal to systems biologists describing biological processes with ordinary differential equations.Uma das tendências na nossa sociedade actual é a substituição de processos químicos por processos bioquímicos, e a síntese de novos compostos por microrganismos, bem como a degradação de resíduos por meios biotecnológicos. A Biotecnologia tem, assim, a promessa de criar uma indústria mais rentavél e mais amiga do ambiente, com um número reduzido de resíduos, contrastando com a indústria química. No entanto, numa era em que os genomas são sequenciados a um ritmo nunca visto, assim como as medições de dados ómicos, esta informação não é diretamente traduzida no desenho de estirpes microbianas ou processos biológicos. Estes dados experimentais em isolamento não explicam como os diferentes componentes celulares interagem. As abordagens reducionistas que dominaram a ciência no século passado, estudam os constituintes celulares em isolamento, como pedaços isolados, sem tomar em consideração as interacções com outras moléculas, o que traduz uma visão incompleta do mundo, que compromete o desenvolvimento de novo conhecimento. Para superar estes obstáculos, uma nova abordagem à Biologia tem emergido nos últimos trinta anos. A Biologia de Sistemas pode ser definida como a conjugação de diferentes áreas (como a Matemática, Ciência da Computação, Biologia), para descrever formalmente e de forma não ambígua o comportamento dos diferentes sistemas celulares e as suas interações utilizando a modelação. A Engenharia Metabólica tira partido destas especificações formais, utilizando métodos matemáticos para derivar estratégias tendo em vista a optimização do metabolismo de microrganismos, de forma a atingir um objetivo definido como por exemplo o aumento da produção de um composto relevante a nível industrial. Neste trabalho, desenvolvemos um modelo dinâmico mecanístico baseado em equações diferenciais ordinárias, composto por descrições ação de massas elementares para cada reacção, partindo de um modelo já existente da Escherichia coli na literatura. Utilizamos também algoritmos evolucionários com um novo esquema de representação que permite pesquisar por modulações enzimáticas, numa escala contínua ou discreta, assim como eliminar reações em modelos metabólicos existentes de forma a maximizar o rendimento ou a produtividade. Todos os métodos desenvolvidos envolveram alguma forma de análise de sensibilidade ou identifiabilidade, de forma a verificar como as saídas do modelo são afetados pelos parâmetros. Todo o trabalho foi construído de acordo com uma plataforma de software modular (desenvolvida durante esta tese) que permite a interação de algoritmos e linguagens distintos, sendo uma ferramenta flexível para utilizar em ambientes de cluster. A plataforma encontra-se disponível como um pacote de software de código aberto e tem utilidade para biólogos de sistemas que pretendam descrever processos com equações diferencias ordinárias