Moreover, we utilize amino acid replacement matrices for the diffusion forward process, encoding the biologically meaningful prior knowledge of amino acids from their spatial and sequential neighbors as well as themselves, which reduces the sampling space of the generative process.

This paper investigates the design of joint adaptive sampling and clustering algorithms in networks whose structure follows the celebrated Stochastic Block Model (SBM). To extract hidden clusters, the interaction between edges (pairs of nodes) may be sampled sequentially, in an adaptive manner.

China figured out how to sell EVs. Now it has to bury their batteries. As early electric cars age out, hundreds of thousands of used batteries are flooding the market, fueling a gray recycling economy even as Beijing and big manufacturers scramble to build a more orderly system. In August 2025, Wang Lei decided it was finally time to say goodbye to his electric vehicle. Wang, who is 39, had bought the car in 2016, when EVs still felt experimental in Beijing. It was a compact Chinese brand.

Protein inverse folding, the design of an amino acid sequence based on a target 3D structure, is a fundamental problem of computational protein engineering. Existing methods either generate sequences without leveraging external knowledge or relying on protein language models (PLMs). The former omits the evolutionary information stored in protein databases, while the latter is parameter-inefficient and inflexible to adapt to ever-growing protein data. To overcome the above drawbacks, in this paper we propose a novel method, called r etrieval-a ugmented d enoising diff usion (RadDiff), for protein inverse folding. Given the target protein backbone, RadDiff uses a hierarchical search strategy to efficiently retrieve structurally similar proteins from large protein databases. The retrieved structures are then aligned residue-by-residue to the target to construct a position-specific amino acid profile, which serves as an evolutionary-informed prior that conditions the denoising process. A lightweight integration module is further designed to incorporate this prior effectively. Experimental results on the CA TH, PDB, and TS50 datasets show that RadDiff consistently outperforms existing methods, improving sequence recovery rate by up to 19%. Experimental results also demonstrate that RadDiff generates highly foldable sequences and scales effectively with database size. Proteins are the molecular machines of life, executing a vast array of biological functions dictated by their three-dimensional (3D) structures (Koehler Leman et al., 2023).

Where the constraint ensures that the solution is unique.

The COVID-19 pandemic has highlighted the need for quantitative modeling and analysis to understand real-world disease dynamics. In particular, post hoc analyses using compartmental models offer valuable insights into the effectiveness of public health interventions, such as vaccination strategies and containment policies. However, such compartmental models like SIR (Susceptible-Infectious-Recovered) often face limitations in directly incorporating noisy observational data. In this work, we employ Physics-Informed Neural Networks (PINNs) to solve the inverse problem of the SIR model using infection data from the Robert Koch Institute (RKI). Our main contribution is a fine-grained, spatio-temporal analysis of COVID-19 dynamics across all German federal states over a three-year period. We estimate state-specific transmission and recovery parameters and time-varying reproduction number (R_t) to track the pandemic progression. The results highlight strong variations in transmission behavior across regions, revealing correlations with vaccination uptake and temporal patterns associated with major pandemic phases. Our findings demonstrate the utility of PINNs in localized, long-term epidemiological modeling.