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We describe how some differential geometric bifurcation problems can be treated with the MATLAB continuation and bifurcation toolbox pde2path. The basic setup consists in solving the PDEs for the normal displacement of an immersed surface $X\subset\mathbb{R}^3$ and subsequent update of $X$ in each continuation step, combined with bifurcation detection and localization, followed by possible branch switching. Examples treated include some minimal surfaces such as Enneper's surface and a Schwarz-P-family, some non-zero constant mean curvature surfaces such as liquid bridges and nodoids, and some 4th order biomembrane models. In all of these we find interesting symmetry breaking bifurcations. Some of these are (semi)analytically known and thus are used as benchmarks.

Alzheimer's disease and Frontotemporal dementia are common types of neurodegenerative disorders that present overlapping clinical symptoms, making their differential diagnosis very challenging. Numerous efforts have been done for the diagnosis of each disease but the problem of multi-class differential diagnosis has not been actively explored. In recent years, transformer-based models have demonstrated remarkable success in various computer vision tasks. However, their use in disease diagnostic is uncommon due to the limited amount of 3D medical data given the large size of such models. In this paper, we present a novel 3D transformer-based architecture using a deformable patch location module to improve the differential diagnosis of Alzheimer's disease and Frontotemporal dementia. Moreover, to overcome the problem of data scarcity, we propose an efficient combination of various data augmentation techniques, adapted for training transformer-based models on 3D structural magnetic resonance imaging data. Finally, we propose to combine our transformer-based model with a traditional machine learning model using brain structure volumes to better exploit the available data. Our experiments demonstrate the effectiveness of the proposed approach, showing competitive results compared to state-of-the-art methods. Moreover, the deformable patch locations can be visualized, revealing the most relevant brain regions used to establish the diagnosis of each disease.

We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides information about the current material state (i.e., free energy, stress, and the evolution of internal variables) under any given loading scenario without requiring initial data. One advantage of this work is that it bypasses the repetitive Newton iterations needed to solve nonlinear equations in complex material models. Additionally, strategies are provided to reduce the required order of derivative for obtaining the tangent operator. The trained model can be directly used in any finite element package (or other numerical methods) as a user-defined material model. However, challenges remain in the proper definition of collocation points and in integrating several non-equality constraints that become active or non-active simultaneously. We tested this methodology on rate-independent processes such as the classical von Mises plasticity model with a nonlinear hardening law, as well as local damage models for interface cracking behavior with a nonlinear softening law. In order to demonstrate the applicability of the methodology in handling complex path dependency in a three-dimensional (3D) scenario, we tested the approach using the equations governing a damage model for a three-dimensional interface model. Such models are frequently employed for intergranular fracture at grain boundaries. We have observed a perfect agreement between the results obtained through the proposed methodology and those obtained using the classical approach. Furthermore, the proposed approach requires significantly less effort in terms of implementation and computing time compared to the traditional methods.

Accurate segmentation of clustered microcalcifications in mammography is crucial for the diagnosis and treatment of breast cancer. Despite exhibiting expert-level accuracy, recent deep learning advancements in medical image segmentation provide insufficient contribution to practical applications, due to the domain shift resulting from differences in patient postures, individual gland density, and imaging modalities of mammography etc. In this paper, a novel framework named MLN-net, which can accurately segment multi-source images using only single source images, is proposed for clustered microcalcification segmentation. We first propose a source domain image augmentation method to generate multi-source images, leading to improved generalization. And a structure of multiple layer normalization (LN) layers is used to construct the segmentation network, which can be found efficient for clustered microcalcification segmentation in different domains. Additionally, a branch selection strategy is designed for measuring the similarity of the source domain data and the target domain data. To validate the proposed MLN-net, extensive analyses including ablation experiments are performed, comparison of 12 baseline methods. Extensive experiments validate the effectiveness of MLN-net in segmenting clustered microcalcifications from different domains and the its segmentation accuracy surpasses state-of-the-art methods. Code will be available at //github.com/yezanting/MLN-NET-VERSON1.

Nominal assortativity (or discrete assortativity) is widely used to characterize group mixing patterns and homophily in networks, enabling researchers to analyze how groups interact with one another. Here we demonstrate that the measure presents severe shortcomings when applied to networks with unequal group sizes and asymmetric mixing. We characterize these shortcomings analytically and use synthetic and empirical networks to show that nominal assortativity fails to account for group imbalance and asymmetric group interactions, thereby producing an inaccurate characterization of mixing patterns. We propose adjusted nominal assortativity and show that this adjustment recovers the expected assortativity in networks with various level of mixing. Furthermore, we propose an analytical method to assess asymmetric mixing by estimating the tendency of inter- and intra-group connectivities. Finally, we discuss how this approach enables uncovering hidden mixing patterns in real-world networks.

The use of propensity score (PS) methods has become ubiquitous in causal inference. At the heart of these methods is the positivity assumption. Violation of the positivity assumption leads to the presence of extreme PS weights when estimating average causal effects of interest, such as the average treatment effect (ATE) or the average treatment effect on the treated (ATT), which renders invalid related statistical inference. To circumvent this issue, trimming or truncating the extreme estimated PSs have been widely used. However, these methods require that we specify a priori a threshold and sometimes an additional smoothing parameter. While there are a number of methods dealing with the lack of positivity when estimating ATE, surprisingly there is no much effort in the same issue for ATT. In this paper, we first review widely used methods, such as trimming and truncation in ATT. We emphasize the underlying intuition behind these methods to better understand their applications and highlight their main limitations. Then, we argue that the current methods simply target estimands that are scaled ATT (and thus move the goalpost to a different target of interest), where we specify the scale and the target populations. We further propose a PS weight-based alternative for the average causal effect on the treated, called overlap weighted average treatment effect on the treated (OWATT). The appeal of our proposed method lies in its ability to obtain similar or even better results than trimming and truncation while relaxing the constraint to choose a priori a threshold (or even specify a smoothing parameter). The performance of the proposed method is illustrated via a series of Monte Carlo simulations and a data analysis on racial disparities in health care expenditures.

Many researchers have identified distribution shift as a likely contributor to the reproducibility crisis in behavioral and biomedical sciences. The idea is that if treatment effects vary across individual characteristics and experimental contexts, then studies conducted in different populations will estimate different average effects. This paper uses ``generalizability" methods to quantify how much of the effect size discrepancy between an original study and its replication can be explained by distribution shift on observed unit-level characteristics. More specifically, we decompose this discrepancy into ``components" attributable to sampling variability (including publication bias), observable distribution shifts, and residual factors. We compute this decomposition for several directly-replicated behavioral science experiments and find little evidence that observable distribution shifts contribute appreciably to non-replicability. In some cases, this is because there is too much statistical noise. In other cases, there is strong evidence that controlling for additional moderators is necessary for reliable replication.

Computer-assisted diagnostic and prognostic systems of the future should be capable of simultaneously processing multimodal data. Multimodal deep learning (MDL), which involves the integration of multiple sources of data, such as images and text, has the potential to revolutionize the analysis and interpretation of biomedical data. However, it only caught researchers' attention recently. To this end, there is a critical need to conduct a systematic review on this topic, identify the limitations of current work, and explore future directions. In this scoping review, we aim to provide a comprehensive overview of the current state of the field and identify key concepts, types of studies, and research gaps with a focus on biomedical images and texts joint learning, mainly because these two were the most commonly available data types in MDL research. This study reviewed the current uses of multimodal deep learning on five tasks: (1) Report generation, (2) Visual question answering, (3) Cross-modal retrieval, (4) Computer-aided diagnosis, and (5) Semantic segmentation. Our results highlight the diverse applications and potential of MDL and suggest directions for future research in the field. We hope our review will facilitate the collaboration of natural language processing (NLP) and medical imaging communities and support the next generation of decision-making and computer-assisted diagnostic system development.

Breast cancer remains a global challenge, causing over 1 million deaths globally in 2018. To achieve earlier breast cancer detection, screening x-ray mammography is recommended by health organizations worldwide and has been estimated to decrease breast cancer mortality by 20-40%. Nevertheless, significant false positive and false negative rates, as well as high interpretation costs, leave opportunities for improving quality and access. To address these limitations, there has been much recent interest in applying deep learning to mammography; however, obtaining large amounts of annotated data poses a challenge for training deep learning models for this purpose, as does ensuring generalization beyond the populations represented in the training dataset. Here, we present an annotation-efficient deep learning approach that 1) achieves state-of-the-art performance in mammogram classification, 2) successfully extends to digital breast tomosynthesis (DBT; "3D mammography"), 3) detects cancers in clinically-negative prior mammograms of cancer patients, 4) generalizes well to a population with low screening rates, and 5) outperforms five-out-of-five full-time breast imaging specialists by improving absolute sensitivity by an average of 14%. Our results demonstrate promise towards software that can improve the accuracy of and access to screening mammography worldwide.

Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.