Localization, Stability, and Resolution of Topological Derivative Based Imaging Functionals in Elasticity

The focus of this work is on rigorous mathematical analysis of the topological derivative based detection algorithms for the localization of an elastic inclusion of vanishing characteristic size. A filtered quadratic misfit is considered and the performance of the topological derivative imaging functional resulting therefrom is analyzed. Our analysis reveals that the imaging functional may not attain its maximum at the location of the inclusion. Moreover, the resolution of the image is below the diffraction limit. Both phenomena are due to the coupling of pressure and shear waves propagating with different wave speeds and polarization directions. A novel imaging functional based on the weighted Helmholtz decomposition of the topological derivative is, therefore, introduced. It is thereby substantiated that the maximum of the imaging functional is attained at the location of the inclusion and the resolution is enhanced and it proves to be the diffraction limit. Finally, we investigate the stability of the proposed imaging functionals with respect to measurement and medium noises.Comment: 38 pages. A new subsection 6.4 is added where we consider the case of random Lam\'e coefficients. We thought this would corrupt the statistical stability of the imaging functional but our calculus shows that this is not the case as long as the random fluctuation is weak so that Born approximation is vali

Target Identification Using Dictionary Matching of Generalized Polarization Tensors

The aim of this paper is to provide a fast and efficient procedure for (real-time) target identification in imaging based on matching on a dictionary of precomputed generalized polarization tensors (GPTs). The approach is based on some important properties of the GPTs and new invariants. A new shape representation is given and numerically tested in the presence of measurement noise. The stability and resolution of the proposed identification algorithm is numerically quantified.Comment: Keywords: generalized polarization tensors, target identification, shape representation, stability analysis. Submitted to Foundations of Computational Mathematic

Toward Learning Model-Agnostic Explanations for Deep Learning-Based Signal Modulation Classifiers

Recent advances in deep learning (DL) have brought tremendous gains in signal modulation classification. However, DL-based classifiers lack transparency and interpretability, which raises concern about model's reliability and hinders the wide deployment in real-word applications. While explainable methods have recently emerged, little has been done to explain the DL-based signal modulation classifiers. In this work, we propose a novel model-agnostic explainer, Model-Agnostic Signal modulation classification Explainer (MASE), which provides explanations for the predictions of black-box modulation classifiers. With the subsequence-based signal interpretable representation and in-distribution local signal sampling, MASE learns a local linear surrogate model to derive a class activation vector, which assigns importance values to the timesteps of signal instance. Besides, the constellation-based explanation visualization is adopted to spotlight the important signal features relevant to model prediction. We furthermore propose the first generic quantitative explanation evaluation framework for signal modulation classification to automatically measure the faithfulness, sensitivity, robustness, and efficiency of explanations. Extensive experiments are conducted on two real-world datasets with four black-box signal modulation classifiers. The quantitative results indicate MASE outperforms two state-of-the-art methods with 44.7% improvement in faithfulness, 30.6% improvement in robustness, and 44.1% decrease in sensitivity. Through qualitative visualizations, we further demonstrate the explanations of MASE are more human interpretable and provide better understanding into the reliability of black-box model decisions

3D phase field modeling of multi-dendrites evolution in solidification and validation by synchrotron x-ray tomography

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. In this paper, the dynamics of multi-dendrite concurrent growth and coarsening of an Al-15 wt.% Cu alloy was studied using a highly computationally efficient 3D phase field model and real-time synchrotron X-ray micro-tomography. High fidelity multi-dendrite simulations were achieved and the results were compared directly with the time-evolved tomography datasets to quantify the relative importance of multi-dendritic growth and coarsening. Coarsening mechanisms under different solidification conditions were further elucidated. The dominant coarsening mechanisms change from small arm melting and interdendritic groove advancement to coalescence when the solid volume fraction approaches ~0.70. Both tomography experiments and phase field simulations indicated that multi-dendrite coarsening obeys the classical Lifshitz–Slyozov–Wagner theory Rn − Rn0=kc(t − t0), but with a higher constant of n = 4.3

Operando study of the dynamic evolution of multiple Fe-rich intermetallics of an Al recycled alloy in solidification by synchrotron X-ray and machine learning

Using synchrotron X-ray diffraction, tomography and machine-learning enabled phase segmentation strategy, we have studied under operando conditions the nucleation, co-growth and dynamic interplays among the dendritic and multiple intermetallic phases of a typical recycled Al alloy (Al5Cu1.5Fe1Si, wt.%) in solidification with and without ultrasound. The research has revealed and elucidated the underlying mechanisms that drive the formation of the very complex and convoluted Fe-rich phases with rhombic dodecahedron and 3D skeleton networks (the so-called Chinese-script type morphology). Through statistical microstructural analyses and numerical modelling of the ultrasound melt processing, the research has demonstrated that a short period of ultrasound processing of just 7 s in the liquid state is able to reduce the average size of the α-Al dendrites and the Fe-containing intermetallic phases by ∼5 times compared to the cases without ultrasound. For the first time, this work has revealed fully the nucleation and growth dynamics of the convoluted morphology of the Fe-containing intermetallic phases in 4D domain. The research has also demonstrated clearly the beneficial effects of applying ultrasound to control the Fe phases' morphology in recycled Al alloys and it is one of the most effective and green processing strategies

CMRxRecon: An open cardiac MRI dataset for the competition of accelerated image reconstruction

Cardiac magnetic resonance imaging (CMR) has emerged as a valuable diagnostic tool for cardiac diseases. However, a limitation of CMR is its slow imaging speed, which causes patient discomfort and introduces artifacts in the images. There has been growing interest in deep learning-based CMR imaging algorithms that can reconstruct high-quality images from highly under-sampled k-space data. However, the development of deep learning methods requires large training datasets, which have not been publicly available for CMR. To address this gap, we released a dataset that includes multi-contrast, multi-view, multi-slice and multi-coil CMR imaging data from 300 subjects. Imaging studies include cardiac cine and mapping sequences. Manual segmentations of the myocardium and chambers of all the subjects are also provided within the dataset. Scripts of state-of-the-art reconstruction algorithms were also provided as a point of reference. Our aim is to facilitate the advancement of state-of-the-art CMR image reconstruction by introducing standardized evaluation criteria and making the dataset freely accessible to the research community. Researchers can access the dataset at https://www.synapse.org/#!Synapse:syn51471091/wiki/.Comment: 14 pages, 8 figure

Substrate-Dependent Sensitivity of SIRT1 to Nicotinamide Inhibition

SIRT1 is the most extensively studied human sirtuin with a broad spectrum of endogenous targets. It has been implicated in the regulation of a myriad of cellular events, such as gene transcription, mitochondria biogenesis, insulin secretion as well as glucose and lipid metabolism. From a mechanistic perspective, nicotinamide (NAM), a byproduct of a sirtuin-catalyzed reaction, reverses a reaction intermediate to regenerate NAD+ through “base exchange”, leading to the inhibition of the forward deacetylation. NAM has been suggested as a universal sirtuin negative regulator. Sirtuins have evolved different strategies in response to NAM regulation. Here, we report the detailed kinetic analysis of SIRT1-catalyzed reactions using endogenous substrate-based synthetic peptides. A novel substrate-dependent sensitivity of SIRT1 to NAM inhibition was observed. Additionally, SIRT1 demonstrated pH-dependent deacetylation with normal solvent isotope effects (SIEs), consistent with proton transfer in the rate-limiting step. Base exchange, in contrast, was insensitive to pH changes with no apparent SIEs, indicative of lack of proton transfer in the rate-limiting step. Consequently, NAM inhibition was attenuated at a high pH in proteated buffers. Our study provides new evidence for “activation by de-repression” as an effective sirtuin activation strategy