Simultaneous sensitive and cost-effective detection of multiple tumor markers has shown great potential for cancer diagnostics. Herein, we reported a simple enzyme-free parallel catalytic hairpin assembly (CHA) amplification strategy with Nmethyl mesoporphyrin IX (NMM) and quantum dots (QDs) as signal reporters for the homogeneous fluorescent simultaneous detection of alpha-fetoprotein (AFP) and glypican-3 (GPC3). Upon selective binding, the released single-stranded DNA (ssDNA) from the two-aptamer double-stranded DNA (dsDNA) probes triggers CHA amplification, further releasing the G-quadruplex sequence and Ag + from the C−Ag + −C structures at the same time. Then, NMM and CdTe QDs selectively recognize G-quadruplex and Ag + , respectively. Under optimized conditions, limits of detections (LODs) as low as 3 fg/mL for AFP and 0.25 fg/mL for GPC3 were achieved using fluorescence readout. Using color-and distance-based visual readouts, an LOD of 1 fg/mL for GPC3 was reached. This method was applied to quantitatively analyze AFP and GPC3 in 41 clinical serum samples of hepatocellular carcinoma (HCC) patients. The quantitative test results for AFP and GPC3 were consistent with those obtained using the electrochemiluminescence immunoassay (ECL-IA) clinical kit and correlated with radiological and pathological findings. The results of clinical tests demonstrated the potential of GPC3 as a tumor biomarker, and we propose a cut-off value of 2 ng/mL GPC3 for HCC.

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For systems with only known pixels, it is difficult to identify its dynamics, especially with a linear operator. In this work, we present a convolutional neural network (CNN) based on the Koopman operator (CKNet) to identify the latent dynamics from raw pixels. CKNet learned an encoder and decoder to play the role of the Koopman eigenfunctions and modes, respectively. The Koopman eigenvalues can be approximated by the eigenvalues of the learned system matrix. We present the deterministic and variational approaches to realize the encoder separately. Because CKNet is trained under the constraints of the Koopman theory, the identified dynamics is linear, controllable and physically-interpretable. Besides, the system matrix and control matrix are trained as trainable tensors. To improve the performance, we propose the auxiliary weight term for multistep linearity and prediction losses. Experiments select two classic forced dynamical systems with continuous action space, and the results show that identified dynamics with 32-dim can predict validly 120 steps and generate clear images.

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