Uncertain Boundaries Research Articles

The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-CASAM-N): Mathematical Framework

This work presents the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-CASAM-N), which enables the most efficient computation of exactly determined expressions of arbitrarily high-order sensitivities of generic nonlinear system responses with respect to model parameters, uncertain boundaries, and internal interfaces in the model’s phase space. The mathematical framework underlying the nth-CASAM-N is proven to be correct by using mathematical induction. The nth-CASAM-N is formulated in linearly increasing higher-dimensional Hilbert spaces—as opposed to exponentially increasing parameter-dimensional spaces—thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems.

Integration of fuzzy logic and a convolutional neural network in three-way decision-making

With the increase in web usage, opinion mining has become a new trend in analysing opinions. Nevertheless, opinion mining still faces huge challenges, such as uncertainty in opinions which can make opinions difficult to interpret using existing opinion mining models. These models have been developed to automate the opinion mining process of the user; however, extant models which use machine learning algorithms have limitations dealing with uncertainties in opinions such as online customer reviews. Fuzzy models were introduced to solve this problem. However, the fuzzy models have issues in regard to large uncertain boundaries. To address this serious issue, this research introduces a decision framework via which positive, negative and boundary regions are classified using fuzzy concepts. Then, a convolutional neural network (CNN) is used to further classify fuzzy concepts originally allocated to the boundary region. The framework uses formal concepts to represent uncertainties and the CNN classifies the boundary region concepts into either positive or negative opinions. A series of experiments was conducted, the outcomes of which suggest the uncertainties in opinions can be effectively handled using our three-way decision-making framework. Our work contributes to boosting the performance of opinion classification models.

Probabilistic deep learning model as a tool for supporting the fast simulation of a thermal–hydraulic code

Following the Fukushima Daiichi accident, enhancing the safety of nuclear power plants has become the priority mission for the future of nuclear energy. Probabilistic safety assessment (PSA) is a well-known technique to quantify the anticipated risk of nuclear power plants according to the accident scenario. One approach to strengthening nuclear safety is reducing the uncertainty in PSA by analyzing a wide spectrum of accident scenarios. In doing this, massive simulations of thermal–hydraulic (TH) dynamics are required by running TH code. As the computation time for such large-scale simulation is a heavy burden, it is necessary to develop a fast simulation model, but related research has recently begun. For doing this, conditional autoencoder was firstly introduced, however, prediction accuracy can be further improved by exploiting temporal characteristics of simulation data. In this paper, we formalize deep learning-based fast simulation model of TH code, and propose a novel deep learning model, namely ensemble quantile recurrent neural network (eQRNN). By leveraging bi-directional long short-term memory, concatenative positional encoding, quantile regression, and model ensemble, the proposed eQRNN can provide a more accurate prediction on the simulation results and uncertain boundaries of its prediction. Compared to the base RNN model, the proposed eQRNN shows 39% and 28% lower error overall in terms of mean absolute percentage error (MAPE) and mean squared error (MSE). Finally, eQRNN achieved 75%, 79% lower MAPE and MSE than the existing conditional autoencoder-based model.

The uncertainty of boundary can improve the classification accuracy of BI-RADS 4A ultrasound image.

The Breast Imaging-Reporting and Data System (BI-RADS) for ultrasound imaging provides a widely used reporting schema for breast imaging. Previous studies have shown that in ultrasound imaging, 90% of BI-RADS 4A tumors are benign lesions after biopsies. Unnecessary biopsy procedures can be avoided by accurate classification of BI-RADS 4A tumors. However, the classification task is challenging and has not been fully investigated by existing studies. For benign and malignant tumors of BI-RADS 4A, the appearances of intra-class tumors are highly variable, the characteristics of inter-class tumors is overall-similar. Discriminative features need to be found to improve classification accuracy of BI-RADS 4A tumors. In this study, we designed the network using the clinical features of BI-RADS 4A tumors to improve the discrimination ability of network. The boundary information is embedded into the input of the network using the uncertainty. A fine-grained data augmentation method is used to find discriminative features in tumor information embedded with boundary information. Two mathematical methods, voting-based and variance-based, are used to define the uncertainty of boundary, and the differences of these two definitions are compared in a classification network. The dataset we used to evaluate our method had 1155 2D grayscale images. Each image represented a unique BI-RADS 4A tumor. Among them, 248 tumors were proven to be malignant by biopsy, and the remaining 907 were benign. A weakly supervised data augmentation network (WS-DAN) was used as the backbone classification network, which showed competitive performance in finding discriminative features. Using the auxiliary input of the uncertain boundaries defined by the voting method, the area under the curve (AUC) value of our method was 0.8347 (sensitivity=0.7774, specificity=0.7459). The AUC value of the variance-based uncertainty was 0.7789. The voting-based uncertainty was higher than the baseline (AUC=0.803), which only inputs the original image. Compared with the classic classification network, our method had a significant effect improvement (p<0.01). Using the uncertain boundaries defined by the voting methods as auxiliary information, we obtained a better performance in the classification of BI-RADS 4A ultrasound images, while variance-based uncertain boundaries had no effect on improving classification performance. Additionally, fine-grained network helped find discriminative features comparing with the commonly used classification networks.

Integration of semantic patterns and fuzzy concepts to reduce the boundary region in three-way decision-making

A three-way decision framework based on fuzzy concepts can better understand uncertain decision boundaries by automatically dividing opinions into three decision regions: positive, negative, and boundary regions. However, when the fuzzy values of the opinions are very close, the boundary regions tend to be large. The difficult problem is how to significantly reduce the boundary regions while maintaining high classification accuracy. The most useful opinion features include fuzzy concepts and semantic features (or patterns). Unlike fuzzy concepts, semantic features are represented by using semantic patterns that frequently appear in opinions. We also observe a low statistical correlation between semantic patterns and fuzzy concepts. Therefore, this paper proposes a novel opinion classification method that integrates semantic patterns with fuzzy concepts in a three-way decision framework. The new method can increase the discriminative power of classifying opinions using features. Experimental results verify that the integration of fuzzy concepts and semantic patterns has better classification performance than using fuzzy concepts alone. This also shows that fusing multiple features is an effective solution to represent opinions more meaningfully, thereby effectively improving classification accuracy and reducing uncertain boundaries in three-way opinion classification.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): II. Paradigm Application to a Bernoulli Model Comprising Uncertain Parameters

This work presents the application of the recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N)” to a simplified Bernoulli model. The 5th-CASAM-N builds upon and incorporates all of the lower-order (i.e., the first-, second-, third-, and fourth-order) adjoint sensitivities analysis methodologies. The Bernoulli model comprises a nonlinear model response, uncertain model parameters, uncertain model domain boundaries and uncertain model boundary conditions, admitting closed-form explicit expressions for the response sensitivities of all orders. Illustrating the specific mechanisms and advantages of applying the 5th-CASAM-N for the computation of the response sensitivities with respect to the uncertain parameters and boundaries reveals that the 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): I. Mathematical Framework

This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

UAV Trajectory Planning With Probabilistic Geo-Fence via Iterative Chance-Constrained Optimization

Chance-constrained optimization provides a promi- sing framework for solving control and planning problems with uncertainties, due to its modeling capability to capture randomness in real-world applications. In this paper, we consider a UAV trajectory planning problem with probabilistic geo-fence, building on the chance-constrained optimization approach. In the considered problem, randomness of the model, such as the uncertain boundaries of geo-fences, is incorporated in the formulation. By solving the formulated chance-constrained optimization with a novel sampling based solution method, the optimal UAV trajectory is achieved while limiting the probability of collision with geo-fences to a prefixed threshold. Furthermore, to obtain a totally collision-free trajectory, i.e., avoiding the collision not only at the discrete time-steps but also within the entire time horizon, we build on the idea of an iterative scheme. That is, to iterate the solving of the chance-constrained optimization until the collision with probabilistic geo-fence is avoided at any time within the time horizon. At last, we validate the effectiveness of our method via numerical simulations.

Free-form tumor synthesis in computed tomography images via richer generative adversarial network

The insufficiency of annotated medical imaging scans for cancer makes it challenging to train and validate data-hungry deep learning models in precision oncology. We propose a new richer generative adversarial network for free-form 3D tumor/lesion synthesis in computed tomography (CT) images. The network is composed of a new richer convolutional feature enhanced dilated–gated generator (RicherDG) and a hybrid loss function. The RicherDG has dilated–gated convolution layers to enable tumor-painting and to enlarge perceptive fields; and it has a novel richer convolutional feature association branch to recover multi-scale convolutional features especially from uncertain boundaries between tumor and surrounding healthy tissues. The hybrid loss function, which consists of a diverse range of losses, is designed to aggregate complementary information to improve optimization. We perform a comprehensive evaluation of the synthesis results on a wide range of public CT image datasets covering the liver, kidney tumors, and lung nodules. The qualitative and quantitative evaluations and ablation study demonstrated improved synthesizing results over advanced tumor synthesis methods.

First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Critical Points in Coupled Nonlinear Systems. I: Mathematical Framework

This work presents the novel first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP), which enables the exact and efficient computation of the first-order sensitivities of responses defined at critical points (maxima, minima, saddle points) of coupled nonlinear models of physical systems characterized by imprecisely known parameters underlying the models, boundaries, and interfaces between the coupled systems. Responses defined at critical points are important in many applications, including system optimization, safety analyses and licensing. For the design and licensing of nuclear reactors, such essentially important responses include the maximum temperatures of the fuel and cladding in hot channels. The 1st-CASAM-CP presented in this work makes it possible to determine, using a single large-scale “adjoint” computation, the first-order sensitivities of the magnitude of a response defined at a critical point of a function in the phase-space of the systems’ independent variables. In addition, the 1st-CASAM-CP enables the computation of the sensitivities of the location in phase-space of the critical point at which the respective response is located: one “adjoint” computation is required for each component of the respective critical point in the phase-space of independent variables. By enabling the exact and efficient computation of the sensitivities of responses and of their critical locations to imprecisely known model parameters, boundaries, and interfaces, the 1st-CASAM-CP significantly extends the practicality of analyzing crucially important responses for large-scale systems involving many uncertain parameters, interfaces, and boundaries.

Poe's Fluid, Terraqueous Landscapes: An Archipelagic Rereading of "The Journal of Julius Rodman"

ABSTRACT: In this article, I reread Edgar Allan Poe's "The Journal of Julius Rodman" in an archipelagic mode (Roberts and Stephens). The novel reimagines and remaps American space as a "fluid" and island-studded landscape (Dimock) of shifting identities, blurring timelines, and uncertain boundaries. An archipelagic rereading of "Rodman" extends backwards in time the critical purchase of Roberts and Stephens's ideas to the moment when the continental identity of the United States solidified. But the significance of this rereading goes beyond bringing new materials into—and consequently expanding the interpretive range of—the terraqueous perspective of archipelagic American studies. "Rodman" forms part of a hemispheric archive that must be read archipelagically and continentally. Poe's novel applies this continental-insular doubling dissolutionally and dis-illusionally to the nineteenth-century expansionism of the United States. "Rodman" calls attention to the land- and seascapes (the Glissantian paysages ) of the Americas. Poe narrates American history in "Rodman" as a fluid and terraqueous landscape of coursing rivers that interconnect continents and seas. I conclude the piece by reflecting on the symbolic importance of rivers within the archipelagic Americas.

Anomaly Detection in Videos Using Two-Stream Autoencoder with Post Hoc Interpretability.

The growing interest in deep learning approaches to video surveillance raises concerns about the accuracy and efficiency of neural networks. However, fast and reliable detection of abnormal events is still a challenging work. Here, we introduce a two-stream approach that offers an autoencoder-based structure for fast and efficient detection to facilitate anomaly detection from surveillance video without labeled abnormal events. Furthermore, we present post hoc interpretability of feature map visualization to show the process of feature learning, revealing uncertain and ambiguous decision boundaries in the video sequence. Experimental results on Avenue, UCSD Ped2, and Subway datasets show that our method can detect abnormal events well and explain the internal logic of the model at the object level.

Hard Attention Net for Automatic Retinal Vessel Segmentation.

Automated retinal vessel segmentation is among the most significant application and research topics in ophthalmologic image analysis. Deep learning based retinal vessel segmentation models have attracted much attention in the recent years. However, current deep network designs tend to predominantly focus on vessels which are easy to segment, while overlooking vessels which are more difficult to segment, such as thin vessels or those with uncertain boundaries. To address this critical gap, we propose a new end-to-end deep learning architecture for retinal vessel segmentation: hard attention net (HAnet). Our design is composed of three decoder networks: the first of which dynamically locates which image regions are "hard" or "easy" to analyze, while the other two aim to segment retinal vessels in these "hard" and "easy" regions independently. We introduce attention mechanisms in the network to reinforce focus on image features in the "hard" regions. Finally, a final vessel segmentation map is generated by fusing all decoder outputs. To quantify the network's performance, we evaluate our model on four public fundus photography datasets (DRIVE, STARE, CHASE_DB1, HRF), two recent published color scanning laser ophthalmoscopy image datasets (IOSTAR, RC-SLO), and a self-collected indocyanine green angiography dataset. Compared to existing state-of-the-art models, the proposed architecture achieves better/comparable performances in segmentation accuracy, area under the receiver operating characteristic curve (AUC), and f1-score. To further gauge the ability to generalize our model, cross-dataset and cross-modality evaluations are conducted, and demonstrate promising extendibility of our proposed network architecture.

Rethinking Categories and Dimensions in the DSM.

This paper addresses the role of categories and dimensions in the classification of psychopathology. While psychopathology does not sort itself out neatly into natural categories, we do find rough, symptom-based groupings that, through refinement, become diagnostic categories. Given that these categories suffer from comorbidity, uncertain boundaries, and excessive "unspecified disorder" diagnoses, there has been a move toward refining the diagnoses with dimensional measures. The paper traces efforts both to improve the diagnostic categories with validators that allow at least partial validity and to introduce dimensional measures into the diagnostic manual. Drawing from the philosophical pragmatism of Charles Sanders Peirce, William James, and John Dewey, which emphasizes the practical, effect-sensitive consequences of a theory along with an emphasis on empirical evidence and the progressive, probabilistic character of knowledge, the paper argues that these efforts must be guided both by scientific validity and clinical utility.

Cascade knowledge diffusion network for skin lesion diagnosis and segmentation

Accurate diagnosis and segmentation of skin lesion is critical for early detection and diagnosis of skin cancer. Recent multi-task learning methods require expensive annotations for skin lesion analysis while single-task driven models cannot fully utilize the potential knowledge. The aim of this study is to utilize the neglected knowledge by a flexible architecture in dermoscopy skin lesion classification and segmentation. In this work, we propose a cascade knowledge diffusion network (CKDNet) to transfer and aggregate knowledge learnt from different tasks to simultaneously boost the performances of classification and segmentation. CKDNet consists of a sequence of coarse-level segmentation, classification, and fine-level segmentation networks. We design two novel feature entanglement modules, Entangle-Cls and Entangle-Seg, for classification and segmentation. The Entangle-Cls module aggregates the diffused features from initial segmentation to drive the classification network’s attention to image regions relevant to the disease. The Entangle-Seg module integrates the cascaded context knowledge learnt from classification to benefit fine-level segmentation, especially at uncertain boundaries. The entanglement modules can adaptively control the knowledge that can be diffused from one task to another, which avoids the empirical selection of weights for different learning tasks compared to other multi-task methods. We perform extensive evaluations and comparisons with state-of-the-art methods on skin lesion classification and segmentation with challenge datasets, ISIC2017 and ISIC2018. Our CKDNet demonstrated superior performance without using any ensemble approaches or any external datasets. The effectiveness of each component and loss functions are demonstrated by interpretable results using class activation maps (CAM), t-SNE, and classification and segmentation results.

First order comprehensive adjoint sensitivity analysis methodology (1st-casam) for computing efficiently the exact response sensitivities for physical systems with imprecisely known boundaries and parameters: General theory and illustrative paradigm applications

This work presents the novel first-order comprehensive adjoint sensitivity analysis methodology (1st-CASAM) for computing efficiently, exactly, and exhaustively, the first-order response sensitivities for nonlinear physical systems characterized by imprecisely known (uncertain) parameters model and domain boundary parameters. This novel methodology is designed for generic operator-valued model responses, treating scalar-valued responses as particular cases. The 1st-CASAM highlights the conclusion that response sensitivities to the imprecisely known domain boundaries can arise both from the definition of the system’s response as well as from the equations and boundary conditions defining the model on its imprecisely known domain. The application of this new methodology is illustrated on two paradigm models, each admitting exact closed-form expressions for the sensitivities of typical model responses to the model’s imprecisely known (uncertain) model and boundary parameters, as follows: (a) a nonlinear heat conduction equation; and (b) a neutron diffusion equation modeling a subcritical reactor with an external source. Very importantly, the diffusion equation is subject to vacuum boundary conditions on the extrapolated system boundary, thus illustrating the computation of response sensitivities to boundary parameters involving not only imprecisely known geometrical dimensions but also imprecisely known nuclear data. For the nonlinear heat conduction equation, the value of the temperature that would be measured at a point in phase-space is chosen as a representative scalar-valued response, while the temperature distribution in the entire phase-space, having uncertain boundaries, of the model’s independent variable has been chosen as a representative function-valued response. For the neutron diffusion equation, a reaction-rate within the imprecisely known domain boundaries has been chosen as a representative scalar-valued response, and the neutron flux distribution within the imprecisely known domain boundaries has been chosen as a representative function-valued response. The application of the 1st-CASAM for the operator-valued responses is illustrated using: (a) a pseudo-spectral collocation representation for the sensitivities of the temperature distribution response; and (b) a spectral Fourier representation for the sensitivities of the neutron flux distribution response. These paradigm examples highlight the details of applying the general 1st-CASAM methodology, underscoring the effects of imprecisely known domain boundaries on both the system’s state functions and responses. By enabling, in premiere, the exact computations of function-valued response sensitivities to boundary parameters and conditions, the novel adjoint sensitivity analysis methodology presented in this work enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems.

A hybrid interval type-2 semi-supervised possibilistic fuzzy c-means clustering and particle swarm optimization for satellite image analysis

Although satellite images can provide more information about the earth’s surface in a relatively short time and over a large scale, they are affected by observation conditions and the accuracy of the image acquisition equipment. The objects on the images are often not clear and uncertain, especially at their borders. The type-1 fuzzy set based fuzzy clustering technique allows each data pattern to belong to many different clusters through membership function (MF) values, which can handle data patterns with unclear and uncertain boundaries well. However, this technique is quite sensitive to noise, outliers, and limitations in handling uncertainties. To overcome these disadvantages, we propose a hybrid method encompassing interval type-2 semi-supervised possibilistic fuzzy c-means clustering (IT2SPFCM) and Particle Swarm Optimization (PSO) to form the proposed IT2SPFCM-PSO. We experimented on some satellite images to prove the effectiveness of the proposed method. Experimental results show that the IT2SPFCM-PSO algorithm gives accuracy from 98.8% to 99.39% and is higher than that of other matching algorithms including SFCM, SMKFCM, SIIT2FCM, PFCM, SPFCM-W, SPFCM-SS, and IT2SPFCM. Analysis of the results by indicators PC-I, CE-I, D-I, XB-I, t -I, and MSE also showed that the proposed method gives better results in most experiments.

First-Order Comprehensive Adjoint Method for Computing Operator-Valued Response Sensitivities to Imprecisely Known Parameters, Internal Interfaces and Boundaries of Coupled Nonlinear Systems: I. Mathematical Framework

This work presents the first-order comprehensive adjoint sensitivity analysis methodology (1st-CASAM) for computing efficiently the first-order sensitivities (i.e., functional derivatives) of operator-valued responses (i.e., model results) of general models of coupled nonlinear physical systems characterized by imprecisely known or and/or uncertain parameters, external boundaries, and internal interfaces between the coupled systems. The explicit mathematical formalism developed within the 1st-CASAM for computing the first-order sensitivities of operator-valued response to uncertain internal interfaces and external boundaries in the models’ phase–space enables this methodology to generalize all of the previously published methodologies for computing first-order response sensitivities. The computational resources needed for using forward versus adjoint operators in conjunction with spectral versus collocation methods for computing the response sensitivities are analyzed in detail. By enabling the exact computations of operator-valued response sensitivities to internal interfaces and external boundary parameters and conditions, the 1st-CASAM presented in this work makes it possible, inter alia, to quantify the effects of manufacturing tolerances on operator-valued responses of physical and engineering systems.

Thematic Classification Accuracy Assessment with Inherently Uncertain Boundaries: An Argument for Center-Weighted Accuracy Assessment Metrics

Accuracy assessment is one of the most important components of both applied and research-oriented remote sensing projects. For mapped classes that have sharp and easily identified boundaries, a broad array of accuracy assessment methods has been developed. However, accuracy assessment is in many cases complicated by classes that have fuzzy, indeterminate, or gradational boundaries, a condition which is common in real landscapes; for example, the boundaries of wetlands, many soil map units, and tree crowns. In such circumstances, the conventional approach of treating all reference pixels as equally important, whether located on the map close to the boundary of a class, or in the class center, can lead to misleading results. We therefore propose an accuracy assessment approach that relies on center-weighting map segment area to calculate a variety of common classification metrics including overall accuracy, class user’s and producer’s accuracy, precision, recall, specificity, and the F1 score. This method offers an augmentation of traditional assessment methods, can be used for both binary and multiclass assessment, allows for the calculation of count- and area-based measures, and permits the user to define the impact of distance from map segment edges based on a distance weighting exponent and a saturation threshold distance, after which the weighting ceases to grow. The method is demonstrated using synthetic and real examples, highlighting its use when the accuracy of maps with inherently uncertain class boundaries is evaluated.

Seeking Credibility from Uncertainty: How Formal Cooptation Institution Unleashes Outspoken NGOs

Uncertain political boundaries and formal cooptation institutions often make NGOs in China self-censor on sensitive issues. A growing body of literature has focused on various strategies NGOs proactively adopt to circumvent formal restrictions and manage the risk of participation. However, a comparative case study from a four-month fieldwork in this paper reveals a previously neglected aspect of state-NGO interaction, i.e., how do NGOs perceive and process the information they get? We find that endorsement outside of the formal institution—a retired official in our case—is not perceived as credible because the retired official does not have to bear the consequence of miscalculation. On the contrary, endorsement from local supervision institution is perceived as credible. Paradoxically, the credibility comes from the institutional design that originally intends to make restriction and monitoring effective. Our study suggests that while NGOs have various ways to seek endorsement, not all of them are perceived as credible. State, as the creator of uncertainty in the first place, is also the ultimate solution for it.