1,720,983 research outputs found
Probabilistic uncertainty quantification and experiment design for nonlinear models: Applications in systems biology
Full text linkDespite the ever-increasing interest in understanding biology at the system level, there are several factors that hinder studies and analyses of biological systems. First, unlike systems from other applied fields whose parameters can be effectively identified, biological systems are usually unidentifiable, even in the ideal case when all possible system outputs are known with high accuracy. Second, the presence of multivariate bifurcations often leads the system to behaviors that are completely different in nature. In such cases, system outputs (as function of parameters/inputs) are usually discontinuous or have sharp transitions across domains with different behaviors. Finally, models from systems biology are usually strongly nonlinear with large numbers of parameters and complex interactions. This results in high computational costs of model simulations that are required to study the systems, an issue that becomes more and more problematic when the dimensionality of the system increases. Similarly, wet-lab experiments to gather information about the biological model of interest are usually strictly constrained by research budget and experimental settings. The choice of experiments/simulations for inference, therefore, needs to be carefully addressed. The work presented in this dissertation develops strategies to address theoretical and practical limitations in uncertainty quantification and experimental design of non-linear mathematical models, applied in the context of systems biology. This work resolves those issues by focusing on three separate but related approaches: (i) the use of probabilistic frameworks for uncertainty quantification in the face of unidentifiability (ii) the use of behavior discrimination algorithms to study systems with discontinuous model responses and (iii) the use of effective sampling schemes and optimal experimental design to reduce the computational/experimental costs. This cumulative work also places strong emphasis on providing theoretical foundations for the use of the proposed framework: theoretical properties of algorithms at each step in the process are investigated carefully to give more insights about how the algorithms perform, and in many cases, to provide feedback to improve the performance of existing approaches. Through the newly developed procedures, we successfully created a general probabilistic framework for uncertainty quantification and experiment design for non-linear models in the face of unidentifiability, sharp model responses with limited number of model simulations, constraints on experimental setting, and even in the absence of data. The proposed methods have strong theoretical foundations and have also proven to be effective in studies of expensive high-dimensional biological systems in various contexts
Optimal parameter estimation for long-term prediction in the presence of model mismatch applied to a two-link flexible joint robot
No full textFor nonlinear multi-input multi-output (MIMO) systems such as multi-link robotic manipulators, finding a correct, physically-derived model structure is almost impossible, so that significant model mismatch is nearly inevitable. Though Lagrange equation gives us a systematic way to build a dynamic model based on the laws of physics, the accuracy of the model as a long-term predictor for multi-link robotic manipulators is often not good enough for model-dependent precision control techniques and computer simulation. Moreover, in the presence of model mismatch, the use of least-squares minimization of the one-step-ahead prediction error (residual error) to estimate unknown parameters in a given model structure often leads to model predictions that are extremely inaccurate beyond a short time interval. In this work, for better model accuracy, a MIMO nonlinear autoregressive moving average with exogenous inputs (NARMAX) model with more mathematical degrees of freedom is constructed partly based on the Lagrangian model. For more accurate parameter estimation in the presence of significant model mismatch, a method of optimal parameter estimation for accurate long-term prediction models is developed in this research. For many practical cases where a correct model and the correct number of degrees of freedom for a given model structure are unknown, we combine the use of long-term prediction error with frequency-based regularization to produce more accurate long-term prediction models for actual MIMO nonlinear systems. When the proposed Fourier-regularized optimal parameter estimation (OPE) method was used to estimate the parameters of the MIMO NARMAX model, the identified high-order model showed significantly better model accuracy compared to the Lagrangian model. Though the Fourier-regularization was very helpful to avoid overfitting and yield more accurate parameter estimation, the high-order MIMO NARMAX model was composed of many redundant regressors with a large number of parameters. To find an optimal model structure of the MIMO NARMAX model, L1 regularization method is used in this research to yield sparse model structures and overcome the ill-posedness of parameter estimation due to the redundant model structure. Though the L1 and L 2 regularization methods are useful to solve ill-posed inverse problems, the simulation results of identified models with L1 /L2 - regularized parameters showed significant model discrepancy between actual outputs and simulated outputs. Since the L1 and L2 regularization methods try to minimize both residual error and the L1/L2 norm of a parameter vector, these methods do not guarantee accurate long-term prediction models in the presence of significant model mismatch. For more accurate parameter estimation for the sparse models obtained by the L1 regularization, parameters were re-estimated by the proposed method of Fourier-regularized optimal parameter estimation using simulation error. The identified sparse models with the parameters reestimated using the OPE method showed comparable long-term prediction accuracy with a significantly fewer number of regressors compared to the high-order model
Existence and stability of traveling wave solutions in a simplified model of cardiac tissue
No full textWe introduce a simplified two-variable model of cardiac tissue. The model captures key features of cardiac behavior, including electrical alternans, while also allowing for analytical investigations into the propagation of electrical impulses. We examine the existence and stability of traveling wave front and traveling pulse solutions
High Speed Imaging Via Advanced Modeling
No full textThere is an increasing need to accurately image objects at a high temporal resolution for different applications in order to analyze the underlying physical, chemical, or biological processes. In this thesis, we use advanced models exploiting the image structure and the measurement process in order to achieve an improved temporal resolution. The thesis is divided into three chapters, each corresponding to a different imaging application.In the first chapter, we propose a novel method to localize neurons in fluorescence microscopy images. Accurate localization of neurons enables us to scan only the neuron locations instead of the full brain volume and thus improve the temporal resolution of neuron activity monitoring. We formulate the neuron localization problem as an inverse problem where we reconstruct an image that encodes the location of the neuron centers. The sparsity of the neuron centers serves as a prior model, while the forward model comprises of shape models estimated from training data.In the second chapter, we introduce multi-slice fusion, a novel framework to incorporate advanced prior models for inverse problems spanning many dimensions such as 4D computed tomography (CT) reconstruction. State of the art 4D reconstruction methods use model based iterative reconstruction (MBIR), but it depends critically on the quality of the prior modeling. Incorporating deep convolutional neural networks (CNNs) in the 4D reconstruction problem is difficult due to computational difficulties and lack of high-dimensional training data. Multi-Slice Fusion integrates the tomographic forward model with multiple low dimensional CNN denoisers along different planes to produce a 4D regularized reconstruction. The improved regularization in multi-slice fusion allows each time-frame to be reconstructed from fewer measurements, resulting in an improved temporal resolution in the reconstruction. Experimental results on sparse-view and limited-angle CT data demonstrate that Multi-Slice Fusion can substantially improve the quality of reconstructions relative to traditional methods, while also being practical to implement and train.In the final chapter, we introduce CodEx, a synergistic combination of coded acquisition and a non-convex Bayesian reconstruction for improving acquisition speed in computed tomography (CT). In an ideal “step-and-shoot” tomographic acquisition, the object is rotated to each desired angle, and the view is taken. However, step-and-shoot acquisition is slow and can waste photons, so in practice the object typically rotates continuously in time, leading to views that are blurry. This blur can then result in reconstructions with severe motion artifacts. CodEx works by encoding the acquisition with a known binary code that the reconstruction algorithm then inverts. The CodEx reconstruction method uses the alternating direction method of multipliers (ADMM) to split the inverse problem into iterative deblurring and reconstruction sub-problems, making reconstruction practical. CodEx allows for a fast data acquisition leading to a good temporal resolution in the reconstruction
Modeling, analysis, and control of Syk-mediated signaling events for B cells and associated cellular response for B cells
Full text linkUnderstanding the immune system and its responses to foreign threats (antigens) is a matter of understanding the immune cells involved, their individual responses, and chemicals responsible for intracellular and intercellular communication. The overall immune response is driven by individual actions of neutrophils, antigen-presenting cells, and lymphocytes (T cells and B cells), among other cells. Intercellular communication is the means by which immune cells develop coordinated response while intracellular signals determine responses within a cell; both depend on systems of chemical reactions at their respective scales. The perspective taken in this dissertation is that of understanding B cells at the intracellular scale and the signaling molecules responsible for its responses. B cells, a type of white blood cell in the immune system, identify antigens by binding to them via B cell receptors (BCRs). After identifying an antigen, mechanisms in the B cell membrane initiate a system of chemical interactions that propagate an intracellular signal and thereby determining the cell\u27s response. In the first part of this thesis, we present a model for B cell signaling using dynamical systems and motivated by the desire to understand the role of the protein Syk. Syk is intricately involved in the early signaling events and is required for proper response to an antigen. The importance of this protein has led to mutant variants being genetically engineered to manipulate its impact. This mutant variant is one of the primary novelties of our model, and allows us to investigate the role of feedback loops involving Syk in producing responses. This mutant model is used to develop testable hypothesis regarding the B cell mutant kinase known as Syk-AQL. It is often difficult to resolve questions regarding complicated biological systems through experimentation alone; this has led to the rise in the use of mathematical modeling in systems biology. Experimentation is still important, however, as data is needed to refine models, and designing experiments to most efficiently refine models is an important topic of research. This is a motivation for an interest in model-based experimental design, where experiments can be systematically chosen to reduce dynamic uncertainty in a given model. In the second part of this thesis, we provide background on methods of experiment design and discuss the Maximal Informative Next Experiment (MINE) method in greater detail. In particular, we provide a theoretical foundation for this method and prove a convergence result for MINE with nonlinear models. Design criteria have been developed to sequentially provide maximal reduction in uncertainty and one criterion has been rigorously justified. We will extend this analysis to other design criteria and in more general contexts. Experimental design results will be useful for work on B cell modeling as well as other applications. This project is a step towards better understanding cellular response and creating tools useful modeling biological systems
A Supervised Learning Approach for Dynamic Sampling (SLADS)
Full text linkSparse sampling schemes can broadly be classified in to two main categories: static sampling where the sampling pattern is predetermined, and dynamic sampling where each new measurement location is selected based on information obtained from previous measurements. Dynamic sampling methods are particularly appropriate for point-wise imaging methods in which pixels are measured sequentially in arbitrary order. Examples of point-wise imaging schemes include certain implementations of atomic force microscopy (AFM), electron back scatter diffraction (EBSD), and Scanning Electron Microscopy (SEM). In these point-wise imaging applications, dynamic sparse sampling methods have the potential to dramatically reduce the number of measurements required to achieve a desired level of fidelity. However, existing dynamic sampling methods tend to be computationally expensive and are therefore too slow for many practical applications. In this dissertation, we present a framework for dynamic sampling based on machine learning techniques, which we call a supervised learning approach for dynamic sampling (SLADS). In each step of SLADS, the objective is to find the pixel that maximizes the expected reduction in distortion (ERD) given previous measurements. SLADS is fast because we use a simple regression function to compute the ERD, and it is accurate because the regression function is trained using data sets that are representative of the specific application. In addition, we introduce an approximate method to terminate dynamic sampling at a desired level of distortion. We then extend our algorithm to incorporate multiple measurements at each step, which we call group-wise SLADS. We then present simulation results on computationally-generated synthetic data and experimentally-collected data to demonstrate a dramatic improvement over state-of-the-art static sampling methods. Next, we present implementations of SLADS for Scanning Electron Microscopy (SEM), Raman Imaging, Energy Dispersive Spectroscopy (EDS) and synchrotron X-ray imaging. In these imaging techniques, a measurement acquired at a pixel location may be a scalar or a vector, and therefore, to directly apply the SLADS framework we pre-process the measurements to convert them to scalar labels, using various classification techniques. We finally present results from SLADS implementations and simulations for these imaging techniques
Parallel Computational Methods for Model-Based Tomographic Reconstruction and Coherent Imaging
No full textNon-destructive imaging modalities for evaluating the internal properties of materials can be formulated as physics-driven inverse problems. Model-based Iterative reconstruction (MBIR) methods that integrate a forward model of the imaging system and a prior model of the object being imaged can provide superior reconstruction quality relative to conventional methods. However, making MBIR feasible for practical applications faces two key challenges. First, we require efficient computational methods for MBIR that allow large-scale reconstructions in real-time. Second, we must develop forward models that accurately capture the physics and geometry of the imaging system, and, support the use of advanced denoisers that enhance image quality as prior models.This thesis attempts to address the aforementioned challenges and is divided into three main chapters, each corresponding to a different inverse imaging application.In the first chapter of this thesis, we propose a novel 4D model-based iterative reconstruction (MBIR) algorithm for low-angle coherent-scatter X-ray Diffraction (XRD) tomography that can substantially increase the SNR. Our forward model is based on a Poisson photon counting model that incorporates a spatial point-spread function, detector energy response and energy-dependent attenuation correction. Our prior model uses a Markov random field (MRF) together with a reduced spectral bases set determined using non-negative matrix factorization. Our algorithm efficiently computes the Bayesian estimate by exploiting the sparsity of the measurement data. We demonstrate the ability of our method to achieve sufficient spatial resolution from sparse photon-starved measurements and also discriminate between materials of similar densities with real datasets.In the second chapter of this thesis, we propose a multi-agent consensus equilibrium (MACE) algorithm for distributing both the computation and memory of MBIR for Computed Tomographic (CT) reconstruction across a large number of parallel nodes. In MACE, each node stores only a sparse subset of views and a small portion of the system matrix, and each parallel node performs a local sparse-view reconstruction, which based on repeated feedback from other nodes, converges to the global optimum. Our distributed approach can also incorporate advanced denoisers as priors to enhance reconstruction quality. In this case, we obtain a parallel solution to the serial framework of Plug-n-play (PnP) priors, which we call MACE-PnP. In order to make MACE practical, we introduce a partial update method that eliminates nested iterations and prove that it converges to the same global solution. Finally, we validate our approach on a distributed memory system with real CT data. We also demonstrate an implementation of our approach on a massive supercomputer that can perform large-scale reconstruction in real-time.In the third chapter of this thesis, we propose a method that makes MBIR feasible for real-time single-shot holographic imaging through deep turbulence. Our method uses surrogate optimization techniques to simplify and speedup the reflectance and phase-error updates in MBIR. Further, our method accelerates computation of the surrogate-updates by leveraging cache-prefetching and SIMD vector processing units on a single CPU core. We analyze the convergence and real CPU time of our method using simulated datasets, and demonstrate its dramatic speedup over the original MBIR approach
From Flies to Fish: Model-Based Design of Experiments and Multi-Objective Optimization for Understanding Complex Biological Systems
No full textBiological systems are complex, consisting of a vast number of components interacting in a nonlinear fashion with processes that vary both temporally and spatially across multiple scales. Along with that, biological data is discrete and sparse, not complete for all unknown components of the system and available in many different types. Systems biology provides a theoretical framework that integrates as much information as possible from all functional levels to understand the system. Mathematical and computational analysis tools are key to formally merge current biological knowledge and hypotheses underlying the mechanism of these systems. The models that encode this knowledge, through mathematical equations and dynamical or spatial rates, are informed by experimental data through a relationship between various system inputs and outputs. One of the biggest challenges of these models is the uncertainty in the precise model structures and parameters. This thesis discusses computational tools developed to acquire and integrate biological information. Model-based design of experiments (MBDOE) capitalizes on the uncertainty in the models to investigate how to perturb the real system to maximize the information obtained from experiments. MBDOE identifies the optimal conditions for stimuli and measurements that yield the most information about the system given practical limitations such as experimental cost and time, feasible inputs and measurements. We use multi-objective optimization (MOO) to investigate how a single model could be used to fit multiple systems by changing parameters. The MOO platform provides a framework to study how a Bone morphogenic protein (BMP) mechanism differs or how it is similar in vastly different organisms, in this case, Drosophila (an arthropod) and zebrafish (a vertebrate). These tools address generalized models used in systems biology, considering both dynamical and spatial distribution of the biological molecules with ordinary and partial differential equations. As a consequence, these methods can be broadly applied to a wide variety of biological applications as demonstrated in this work
Methods for Ultrasound Imaging of Multi- Layered Objects Based on Collimated Beam Systems
No full textNon-destructive characterization of multi-layered structures that can be accessed from only a single side is important for applications such as well-bore integrity inspection. Collimated beam ultrasound systems are a technology for imaging inside multi-layered structures such as geothermal wells. These systems work by using a collimated narrow-band ultrasound transmitter that can penetrate through multiple layers of heterogeneous material. A series of measurements can then be made at multiple transmit frequencies. However, commonly used reconstruction algorithms such as Synthetic Aperture Focusing Technique (SAFT) tend to produce poor quality reconstructions for these systems both because they do not model collimated beam systems and they do not jointly reconstruct the multiple frequencies.In this thesis, we first propose a multi-frequency ultrasound model-based iterative reconstruction (UMBIR) algorithm designed for multi-frequency collimated beam ultrasound systems. The combined system targets reflective imaging of heterogeneous, multi-layered structures. For each transmitted frequency band, we introduce a physics-based forward model to accurately account for the propagation of the collimated narrow-band ultrasonic beam through the multi-layered media. We then show how the joint multi-frequency UMBIR reconstruction can be computed by modeling the direct arrival signals, detector noise, and incorporating a spatially varying image prior.We also propose a ringing artifact reduction method for ultrasound image reconstruction that uses a multi-agent consensus equilibrium (RARE-MACE) framework. Our approach integrates a physics-based forward model that accounts for the propagation of a collimated ultrasonic beam in multi-layered media, a spatially varying image prior, and a denoiser designed to suppress the ringing artifacts that are characteristic of reconstructions from high-fractional bandwidth ultrasound sensor data.Results using both simulated and experimental data indicate that multi-frequency UMBIR reconstruction yields much higher reconstruction quality than either single frequency UMBIR or SAFT. In addition, our results demonstrate the capability of our RARE-MACE method to suppress ringing artifacts and substantially improve the image quality over single frequency UMBIR and SAFT
Persistent homoclinic tangencies and infinitely many sinks for automorphisms of C('2).
No full textIn the study of surface diffeomorphisms, an important and initially surprising result was Newhouse's discovery of diffeomorphisms having persistent homoclinic tangencies. More precisely, he showed the existence of a compact manifold M and a C\sp2 diffeomorphism o/ of M together with a neighborhood U of o/ in the C\sp2 topology such that each diffeomorphism in a dense subset of U has a homoclinic tangency; i.e., a tangency between the stable and unstable manifolds of a periodic point. By abuse of language we say that o/ has persistent homoclinic tangencies. Using this he was able to show the existence of a diffeomorphism of M having infinitely many attracting periodic points, or sinks. In this paper, this result is extended to the space of holomorphic automorphisms of \doubc\sp2. That is, there is an automorphism F of \doubc\sp2, a neighborhood U of F in the space of automorphisms, and a compact set K in \doubc\sp2, such that each automorphism in some dense subset of U has a homoclinic tangency contained in K. Moreover, there is another dense subset of U such that each automorphism in this subset has infinitely many sinks contained in K. In the real 2-dimensional case, this problem essentially reduces to the intersection of two dynamically defined Cantor sets in the line. Here, the problem reduces to the intersection of two Cantor sets in the plane. The central observation is to use holomorphicity to obtain a good understanding of how these Cantor sets change under small perturbations of the original map and to show that these two sets will intersect for all small perturbations.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104440/1/9527593.pdfDescription of 9527593.pdf : Restricted to UM users only
- …
