Related papers: Proofreading through spatial gradients
This paper presents novel methods for estimating certified radii in randomized smoothing, a technique crucial for certifying the robustness of neural networks against adversarial perturbations. Our proposed techniques significantly improve…
As deep learning models and datasets rapidly scale up, network training is extremely time-consuming and resource-costly. Instead of training on the entire dataset, learning with a small synthetic dataset becomes an efficient solution.…
Molecular dynamics simulations are widely used across chemistry, physics, and biology, providing quantitative insight into complex processes with atomic detail. However, their limited timescale of a few microseconds is a significant…
Several enzymes exhibit enhanced diffusion in the presence of a substrate. One explanation of this enhancement arises from fluctuating dimer models, which suggest that enzymes have a higher diffusion constant when interacting with…
It is a long-standing question in origin-of-life research whether the information content of replicating molecules can be maintained in the presence of replication errors. Extending standard quasispecies models of non-enzymatic replication,…
The widespread deployment of high-fidelity generative models has intensified the need for reliable mechanisms for provenance and content authentication. In-processing watermarking, embedding a signature into the generative model's synthesis…
Sub-diffusion in biological systems is conventionally treated as anomalous, requiring fractional derivatives, heavy-tailed waiting times, or fitted memory kernels. We argue that this anomaly is an artifact of an incomplete phase space.…
Designing enzyme backbones with substrate-specific functionality is a critical challenge in computational protein engineering. Current generative models excel in protein design but face limitations in binding data, substrate-specific…
Protein function often involves changes between different conformations. Central questions are how these conformational changes are coupled to the binding or catalytic processes during which they occur, and how they affect the catalytic…
The velocity solution of the incompressible Stokes equations is not affected by changes of the right hand side data in form of gradient fields. Most mixed methods do not replicate this property in the discrete formulation due to a…
Although DNA foundation models have advanced the understanding of genomes, they still face significant challenges in the limited scale and diversity of genomic data. This limitation starkly contrasts with the success of natural language…
The molecular motor protein kinesin plays a key role in fundamental cellular processes such as intracellular transport, mitotic spindle formation, and cytokinesis, with important implications for neurodegenerative and cancer disease…
Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active…
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine…
Understanding and modeling enzyme-substrate interactions is crucial for catalytic mechanism research, enzyme engineering, and metabolic engineering. Although a large number of predictive methods have emerged, they do not incorporate prior…
Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological steering} to determine the optimal pathway by which a…
Accurate estimation of spatial derivatives from discrete and noisy data is central to scientific machine learning and numerical solutions of PDEs. We extend kinetic-based regularization (KBR), a localized multidimensional kernel regression…
The kinetics of collective rearrangements in solution, such as protein folding and nanocrystal phase transitions, often involve free energy barriers that are both long and rough. Applying methods of transition path sampling to harvest…
Synthetic data has been increasingly used to train frontier generative models. However, recent studies raise key concerns that iteratively retraining a generative model on its self-generated synthetic data may keep deteriorating model…