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Deep learning based PET image reconstruction methods have achieved promising results recently. However, most of these methods follow a supervised learning paradigm, which rely heavily on the availability of high-quality training labels. In particular, the long scanning time required and high radiation exposure associated with PET scans make obtaining these labels impractical. In this paper, we propose a dual-domain unsupervised PET image reconstruction method based on learned descent algorithm, which reconstructs high-quality PET images from sinograms without the need for image labels. Specifically, we unroll the proximal gradient method with a learnable norm for PET image reconstruction problem. The training is unsupervised, using measurement domain loss based on deep image prior as well as image domain loss based on rotation equivariance property. The experimental results demonstrate the superior performance of proposed method compared with maximum-likelihood expectation-maximization (MLEM), total-variation regularized EM (EM-TV) and deep image prior based method (DIP). 

Inspired by humans’ exceptional ability to master arithmetic and generalize to new problems, we present a new dataset, Handwritten arithmetic with INTegers (HINT), to examine machines’ capability of learning generalizable concepts at three levels: perception, syntax, and semantics. In HINT, machines are tasked with learning how concepts are perceived from raw signals such as images (i.e., perception), how multiple concepts are structurally combined to form a valid expression (i.e., syntax), and how concepts are realized to afford various reasoning tasks (i.e., semantics), all in a weakly supervised manner. Focusing on systematic generalization, we carefully design a five-fold test set to evaluate both the interpolation and the extrapolation of learned concepts w.r.t. the three levels. Further, we design a few-shot learning split to determine whether or not models can rapidly learn new concepts and generalize them to more complex scenarios. To comprehend existing models’ limitations, we undertake extensive experiments with various sequence-to-sequence models, including RNNs, Transformers, and GPT-3 (with the chain of thought prompting). The results indicate that current models struggle to extrapolate to long-range syntactic dependency and semantics. Models exhibit a considerable gap toward human-level generalization when evaluated with new concepts in a few-shot setting. Moreover, we discover that it is infeasible to solve HINT by merely scaling up the dataset and the model size; this strategy contributes little to the extrapolation of syntax and semantics. Finally, in zero-shot GPT-3 experiments, the chain of thought prompting exhibits impressive results and significantly boosts the test accuracy. We believe the HINT dataset and the experimental findings are of great interest to the learning community on systematic generalization. 

Abstract Cyclic degradation in flexible electronic inks remains a key challenge while their deployment in life critical applications is ongoing. The origin of electrical degradation of a screen-printed stretchable conductive ink with silver flakes embedded in a polyurethane binder is investigated under uniaxial monotonic and cyclic stretching, using in-situ confocal microscopy and scanning electron microscopy experiments, for varying ink thickness (1, 2, and 3 layers, each layer around 8–10 μ m) and trace width (0.5, 1, and 2 mm). Cracks form under monotonic stretching, and the evolution of crack pattern (density, length and width) with applied strain is affected by ink thickness such that the 3-layer ink exhibits larger normalized resistance but slightly lower resistance than the 1-layer ink up to strains of 125%. For cyclic stretching, the crack density and length do not evolve with cycling. However, the cracks widen and deepen, leading to an increase in resistance with cycling. There exists a strong correlation between fatigue life, i.e. the number of cycles until a normalized resistance of 100 is reached, and the strain amplitude. The normalized resistance increase rate with respect to cycling is also found to scale with strain amplitude. The rate of change in resistance with cycling decreases with ink thickness and trace width. For practical applications, thicker ( ⩾ 25 μ m) and wider (⩾2 mm) inks should be used to lower resistance increases with repeated deformation. 

The electrical performance of stretchable electronic inks degrades as they undergo cyclic deformation during use, posing a major challenge to their reliability. The experimental characterization of ink fatigue behavior can be a time-consuming process, and models allowing accurate resistance evolution and life estimates are needed. Here, a model is proposed for determining the electrical resistance evolution during cyclic loading of a screen-printed composite conductive ink. The model relies on two input specimen-characteristic curves, assumes a constant rate of normalized resistance increase for a given strain amplitude, and incorporates the effects of both mean strain and strain amplitude. The model predicts the normalized resistance evolution of a cyclic test with reasonable accuracy. The mean strain effects are secondary compared to strain amplitude, except for large strain amplitudes (>10%) and mean strains (>30%). A trace width effect is found for the fatigue behavior of 1 mm vs 2 mm wide specimens. The input specimen-characteristic curves are trace-width dependent, and the model predicts a decrease inN_fby a factor of up to 2 for the narrower trace width, in agreement with the experimental results. Two different methods are investigated to generate the rate of normalized resistance increase curves: uninterrupted fatigue tests (requiring ∼6–7 cyclic tests), and a single interrupted cyclic test (requiring only one specimen tested at progressively higher strain amplitude values). The results suggest that the initial decrease in normalized resistance rate only occurs for specimens with no prior loading. The minimum-rate curve is therefore recommended for more accurate fatigue estimates.