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Objectives. Deoxyelephantopin (DET) is a kind of natural active ingredient extracted from the Chinese herbal medicine Elephantopus scaber L. Many studies have revealed the potential antitumor effect on multiple malignancies. However, the detailed mechanism of its antitumor effect in pancreatic cancer remains unclear. Recently, studies have confirmed that noncoding RNA (ncRNA) plays an important regulatory role in malignancies. This research was performed to explore the relationship between ncRNA and DET-induced tumor inhibition in pancreatic cancer. Methods. Microarray profiling was applied to identify the candidate ncRNAs associated with DET-induced tumor inhibition. Quantitative real-time PCR was used to evaluate the expression of linc00511 in pancreatic cancer cells and tissues. The influence of DET on the cell proliferation, migration, and invasion was assessed by CCK-8, colony formation, wound healing, and Transwell assays. The relationship between lncRNAs, miRNAs, and p21 promoter region was analyzed by bioinformatics and verified by luciferase reporter gene and western blotting. The effect of linc00511 on nuclear translocation of miR-370-5p was explored by cytoplasmic and nuclear RNA purification. Moreover, the effect of DET on tumor growth and metastasis, and the prophylactic effect were investigated by establishing subcutaneous and lung metastatic tumor models. Results. Microarray assay indicated linc00511 was a potential target gene. The antitumor effect of DET in pancreatic cancer depended on downregulating linc00511 expression, and linc00511 might be an oncogene in pancreatic cancer. Silencing linc00511 enhanced the antitumor function of DET; conversely, linc00511 overexpression antagonized the DET cytotoxic effect. Additionally, miR-370-5p could bind to p21 promoter to exert the RNA activation and then promote p21 expression. P21 was a downstream gene of linc00511 and associated with pancreatic cancer progression. Linc00511 regulated p21 expression by blocking miR-370-5p nuclear translocation. Conclusions. To sum up, the present finding confirmed that DET suppressed the malignant biological behavior of pancreatic cancer via linc00511/miR-370-5p/p21 promoter axis.

Deoxyelephantopin (DET) is a kind of natural active ingredient extracted from the Chinese herbal medicineMicroarray profiling was applied to identify the candidate ncRNAs associated with DET-induced tumor inhibition. Quantitative real-time PCR was used to evaluate the expression of linc00511 in pancreatic cancer cells and tissues. The influence of DET on the cell proliferation, migration, and invasion was assessed by CCK-8, colony formation, wound healing, and Transwell assays. The relationship between lncRNAs, miRNAs, and p21 promoter region was analyzed by bioinformatics and verified by luciferase reporter gene and western blotting. The effect of linc00511 on nuclear translocation of miR-370-5p was explored by cytoplasmic and nuclear RNA purification. Moreover, the effect of DET on tumor growth and metastasis, and the prophylactic effect were investigated by establishing subcutaneous and lung metastatic tumor models.Microarray assay indicated linc00511 was a potential target gene. The antitumor effect of DET in pancreatic cancer depended on downregulating linc00511 expression, and linc00511 might be an oncogene in pancreatic cancer. Silencing linc00511 enhanced the antitumor function of DET; conversely, linc00511 overexpression antagonized the DET cytotoxic effect. Additionally, miR-370-5p could bind to p21 promoter to exert the RNA activation and then promote p21 expression.To sum up, the present finding confirmed that DET suppressed the malignant biological behavior of pancreatic cancer via linc00511/miR-370-5p/p21 promoter axis.

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer model at each iteration. We present a new approach that constructs a stochastic correction to the error induced by a reduced model, with the correction improving as the algorithm proceeds. This enables sampling from the correct target distribution at reduced computational cost per iteration, as in existing delayed-acceptance schemes, while avoiding appreciable loss of statistical efficiency that necessarily occurs when using a reduced model. Use of the stochastic correction significantly reduces the computational cost of estimating quantities of interest within desired uncertainty bounds. In contrast, existing schemes that use a reduced model directly as a surrogate do not actually improve computational efficiency in our target applications. We build on recent simplified conditions for adaptive Markov chain Monte Carlo algorithms to give practical approximation schemes and algorithms with guaranteed convergence. The efficacy of this new approach is demonstrated in two computational examples, including calibration of a large-scale numerical model of a real geothermal reservoir, that show good computational and statistical efficiencies on both synthetic and measured data sets.

Brain function relies on a precisely coordinated and dynamic balance between the functional integration and segregation of distinct networks. Characterizing the way in which brain regions reconfigure their interactions to give rise to distinct but hidden brain states remains an open challenge. In this paper, we propose a Bayesian method for characterizing community structure-based latent brain states and showcase a novel strategy based on posterior predictive discrepancy using the latent block model to detect transitions between community structures in blood oxygen level-dependent (BOLD) time series. The set of estimated parameters in the model includes a latent label vector that assigns network nodes to communities, and also block model parameters that reflect the weighted connectivity within and between communities. Besides extensive in-silico model evaluation, we also provide empirical validation (and replication) using the Human Connectome Project (HCP) dataset of 100 healthy adults. Our results obtained through an analysis of task-fMRI data during working memory performance show appropriate lags between external task demands and change-points between brain states, with distinctive community patterns distinguishing fixation, low-demand and high-demand task conditions.

Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based dimension reduction method in which the informed subspace does not depend on the data. This permits online–offline computational strategy where the expensive low-dimensional structure of the problem is detected in an offline phase, meaning before observing the data. This strategy is particularly relevant for multiple inversion problems as the same informed subspace can be reused. The proposed approach allows to control the approximation error (in expectation over the data) of the posterior distribution. We also present sampling strategies which exploit the informed subspace to draw efficiently samples from the exact posterior distribution. The method is successfully illustrated on two numerical examples: a PDE-based inverse problem with a Gaussian process prior and a tomography problem with Poisson data and a Besov- B 11 2 prior.

We present a novel offline-online method to mitigate the computational burden of the characterization of posterior random variables in statistical learning. In the offline phase, the proposed method learns the joint law of the parameter random variables and the observable random variables in the tensor-train (TT) format. In the online phase, the resulting order-preserving conditional transport can characterize the posterior random variables given newly observed data in real time. Compared with the state-of-the-art normalizing flow techniques, the proposed method relies on function approximation and is equipped with a thorough performance analysis. The function approximation perspective also allows us to further extend the capability of transport maps in challenging problems with high-dimensional observations and high-dimensional parameters. On the one hand, we present novel heuristics to reorder and/or reparametrize the variables to enhance the approximation power of TT. On the other hand, we integrate the TT-based transport maps and the parameter reordering/reparametrization into layered compositions to further improve the performance of the resulting transport maps. We demonstrate the efficiency of the proposed method on various statistical learning tasks in ordinary differential equations (ODEs) and partial differential equations (PDEs)., Comment: 41 pages

Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest form that requires simulating an accurate computer model at each iteration of the MCMC. The delayed acceptance Metropolis--Hastings MCMC leverages a reduced model for the forward map to lower the compute cost per iteration, though necessarily reduces statistical efficiency that can, without care, lead to no reduction in the computational cost of computing estimates to a desired accuracy. Randomizing the reduced model for the forward map can dramatically improve computational efficiency, by maintaining the low cost per iteration but also avoiding appreciable loss of statistical efficiency. Randomized maps are constructed by a posteriori adaptive tuning of a randomized and locally-corrected deterministic reduced model. Equivalently, the approximated posterior distribution may be viewed as induced by a modified likelihood function for use with the reduced map, with parameters tuned to optimize the quality of the approximation to the correct posterior distribution. Conditions for adaptive MCMC algorithms allow practical approximations and algorithms that have guaranteed ergodicity for the target distribution. Good statistical and computational efficiencies are demonstrated in examples of calibration of large-scale numerical models of geothermal reservoirs and electrical capacitance tomography., This is a pre-print of an article submitted to GEM - International Journal on Geomathematics. arXiv admin note: text overlap with arXiv:1809.03176

Detecting changes in network structure is important for research into systems as diverse as financial trading networks, social networks and brain connectivity. Here we present novel Bayesian methods for detecting network structure change points. We use the stochastic block model to quantify the likelihood of a network structure and develop a score we call posterior predictive discrepancy based on sliding windows to evaluate the model fitness to the data. The parameter space for this model includes unknown latent label vectors assigning network nodes to interacting communities. Monte Carlo techniques based on Gibbs sampling are used to efficiently sample the posterior distributions over this parameter space.

Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge by coupling intractable random variables with tractable reference random variables. This paper generalises the functional tensor-train approximation of the inverse Rosenblatt transport recently developed by Dolgov et al. (Stat Comput 30:603--625, 2020) to a wide class of high-dimensional non-negative functions, such as unnormalised probability density functions. First, we extend the inverse Rosenblatt transform to enable the transport to general reference measures other than the uniform measure. We develop an efficient procedure to compute this transport from a squared tensor-train decomposition which preserves the monotonicity. More crucially, we integrate the proposed order-preserving functional tensor-train transport into a nested variable transformation framework inspired by the layered structure of deep neural networks. The resulting deep inverse Rosenblatt transport significantly expands the capability of tensor approximations and transport maps to random variables with complicated nonlinear interactions and concentrated density functions. We demonstrate the efficiency of the proposed approach on a range of applications in statistical learning and uncertainty quantification, including parameter estimation for dynamical systems and inverse problems constrained by partial differential equations., Comment: Found Comput Math (2021)

Hepatitis B virus (HBV) infection is a risk factor for hepatocellular carcinoma (HCC). HBV X protein (HBx) is an important carcinogen for HBV-induced HCC. When the HBx gene is integrated into the host cell genome, it is difficult to eradicate. The identification of an effective target to inhibit the oncogenic function of HBx is therefore critically important. The present study demonstrated that HBx, particularly truncated HBx, was expressed in several HBV-derived cell lines (e.g., Hep3B and SNU423). By analyzing data from The Cancer Genome Atlas, it was revealed that high expression of high mobility group box 1 (HMGB1) was associated with the process and prognosis of HCC. In vitro experiments confirmed that HBx could regulate the expression of HMGB1 and knockdown of HMGB1 could decrease the ability of HBx to promote cellular proliferation. HBx could also upregulate six transcription factors (GATA binding protein 3, Erb-B2 receptor tyrosine kinase 3, heat shock transcription factor 1, nuclear factor κB subunit 1, TATA-box binding protein and Kruppel-like factor 4), which could directly regulate HMGB1. By analyzing genes that are co-expressed with HMGB1, several signaling pathways associated with the development of HCC were identified. HBx and HMGB1 were revealed to be involved in these pathways, which may be the mechanism by which HBx promotes HCC by regulating HMGB1. These findings suggested that HMGB1 may be an effective target for inhibiting HBV-induced HCC.

We introduce a parallel rejection scheme to give a simple but reliable way to parallelize the Metropolis-Hastings algorithm. This method can be particularly useful when the target density is computationally expensive to evaluate and the acceptance rate of the Metropolis-Hastings is low. We apply the resulting method to quantify uncertainties of inverse problems, in which we aim to calibrate a challenging nonlinear geothermal reservoir model using real measurements from well tests. We demonstrate the parallelized method on various well-test scenarios. In some scenarios, the sample-based statistics obtained by our scheme shows clear advantages in providing robust model calibration and prediction compared with those obtained by nonlinear optimization methods.

Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and large-scale nature of many of these inversions gives rise to some very challenging optimization problems. The inverse problem community has long been developing various techniques for solving such optimization tasks. However, other, seemingly disjoint communities, such as that of machine learning, have developed, almost in parallel, interesting alternative methods which might have stayed under the radar of the inverse problem community. In this survey, we aim to change that. In doing so, we first discuss current state-of-the-art optimization methods widely used in inverse problems. We then survey recent related advances in addressing similar challenges in problems faced by the machine learning community, and discuss their potential advantages for solving inverse problems. By highlighting the similarities among the optimization challenges faced by the inverse problem and the machine learning communities, we hope that this survey can serve as a bridge in bringing together these two communities and encourage cross fertilization of ideas.

We investigate the use of the randomize-then-optimize (RTO) method as a proposal distribution for sampling posterior distributions arising in nonlinear, hierarchical Bayesian inverse problems. Specifically, we extend the hierarchical Gibbs sampler for linear inverse problems to nonlinear inverse problems by embedding RTO-MH within the hierarchical Gibbs sampler. We test the method on a nonlinear inverse problem arising in differential equations.

Inference of genetic network is an important task to explore and predict the regulatory mechanism inside the cell. Although a number of algorithms have been designed to reverse-engineer regulatory networks effective, it is still a challenge to introduce non-linearity into mathematical models effectively. To address this issue, this work proposes a novel framework to infer genetic networks with non-linearity. A new mathematical model using exponential ordinary differential equations is introduced to realize the non-linearity. Using the hematopoietic stem cell fate determination as the test problem, this work successfully reconstructs two networks for erythroid and granulocyte differentiation respectively, each of which includes 11 genes. Numerical results suggest that our new framework is able to provide accurate realizations of the system states. This work provide new ideas to infer regulatory networks effectively and explore novel regulatory mechanisms.

We present a new technique, based on semivariogram methodology, for obtaining point estimates for use in prior modeling for solving Bayesian inverse problems. This method requires a connection between Gaussian processes with covariance operators defined by the Mat\'ern covariance function and Gaussian processes with precision (inverse-covariance) operators defined by the Green's functions of a class of elliptic stochastic partial differential equations (SPDEs). We present a detailed mathematical description of this connection. We will show that there is an equivalence between these two Gaussian processes when the domain is infinite -- for us, $\mathbb{R}^2$ -- which breaks down when the domain is finite due to the effect of boundary conditions on Green's functions of PDEs. We show how this connection can be re-established using extended domains. We then introduce the semivariogram method for estimating the Mat\'ern covariance parameters, which specify the Gaussian prior needed for stabilizing the inverse problem. Results are extended from the isotropic case to the anisotropic case where the correlation length in one direction is larger than another. Finally, we consider the situation where the correlation length is spatially dependent rather than constant. We implement each method in two-dimensional image inpainting test cases to show that it works on practical examples.

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a h eterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters., United States. Department of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0009297)

Estimating statistics of model outputs with the Monte Carlo method often requires a large number of model evaluations. This leads to long runtimes if the model is expensive to evaluate. Importance sampling is one approach that can lead to a reduction in the number of model evaluations. Importance sampling uses a biasing distribution to sample the model more efficiently, but generating such a biasing distribution can be difficult and usually also requires model evaluations. A different strategy to speed up Monte Carlo sampling is to replace the computationally expensive high-fidelity model with a computationally cheap surrogate model; however, because the surrogate model outputs are only approximations of the high-fidelity model outputs, the estimate obtained using a surrogate model is in general biased with respect to the estimate obtained using the high-fidelity model. We introduce a multifidelity importance sampling (MFIS) method, which combines evaluations of both the high-fidelity and a surrogate model. It uses a surrogate model to facilitate the construction of the biasing distribution, but relies on a small number of evaluations of the high-fidelity model to derive an unbiased estimate of the statistics of interest. We prove that the MFIS estimate is unbiased even in the absence of accuracy guarantees on the surrogate model itself. The MFIS method can be used with any type of surrogate model, such as projection-based reduced-order models and data-fit models. Furthermore, the MFIS method is applicable to black-box models, i.e., where only inputs and the corresponding outputs of the high-fidelity and the surrogate model are available but not the details of the models themselves. We demonstrate on nonlinear and time-dependent problems that our MFIS method achieves speedups of up to several orders of magnitude compared to Monte Carlo with importance sampling that uses the high-fidelity model only., United States. Department of Energy. Office of Advanced Scientific Computing Research. Applied Mathematics Program (award DE-FG02-08ER2585), United States. Department of Energy. Office of Advanced Scientific Computing Research. Applied Mathematics Program (award DE-SC0009297)