Review of mathematical representations for biomolecular data.
problem Complexity and high dimensionality of biomolecular datasets hinder ML applications.
method Developed low-dimensional and scalable mathematical representations using algebraic topology, differential geometry, and graph theory.
result Mathematical representations improve protein-ligand binding predictions and other biomolecular applications.
Physics-informed machine learning models improve biomolecular system simulations.
problem Modeling unresolved interactions beyond classical force fields.
method Physics-informed neural networks and operator learning.
result Accurate, mechanistic, generalizable models for long-timescale kinetics.
Tabular in-context learners perform well on biomolecular tasks, but performance depends on the representation used.
problem Predicting biomolecular properties from limited labeled data.
method Evaluating tabular in-context learners on protein fitness regression and small-molecule classification tasks.
result Tabular in-context learners are competitive for protein fitness regression but not for small-molecule classification.
Design of experiments improves validation of biomolecular networks.
problem Efficiently validate non-machine learning designed biomolecular networks.
method Use Gaussian processes and Bayesian optimization to select experimental points.
result Developed a stopping criterion based on discrepancy metric and uncertainty.
Optimizes biomolecular simulations by ranking adaptive sampling policies.
problem Efficiently sampling biomolecular systems to capture complex dynamical behaviors.
method Metric-driven ranking of adaptive sampling policies to identify the optimal policy for each round.
result Different adaptive sampling policies lead to faster convergence and improved sampling performance.
Unified mathematical theory for analyzing biomolecular geometry and flexibility.
problem Lack of a unified mathematical theory for analyzing biomolecular geometry and flexibility.
method Introducing de Rham-Hodge theory, Helmholtz-Hodge decomposition, and discrete exterior calculus.
result Unified framework for predicting macromolecular flexibility and natural modes.
As deep Variational Auto-Encoder (VAE) frameworks become more widely used for modeling biomolecular simulation data, we emphasize the capability of the VAE architecture to concurrently maximize the timescale of the latent space while inferring a reduced coordinate, which assists in finding slow processes as according t…
A deep learning model organizes RNA graphs to reveal folding patterns and properties.
problem Organizing and understanding the complex folding patterns of RNA secondary structures.
method Geometric scattering autoencoder (GSAE) network for learning graph embeddings.
result GSAE accurately reflects bistable RNA structures and can sample new folding trajectories.
Cryo-em images are found to be low-dimensional.
problem Understanding the geometric structure of cryo-em data.
method Applied manifold learning techniques to CryoSBI representations.
result Cryo-em data inherently populate low-dimensional manifolds.
Equivariant networks improve geometric prediction without scalar approximations.
problem Efficiently predicting geometric tensors in real-world scenarios.
method Equivariant networks for geometric prediction.
result Equivariant networks can generalize to unseen systems for geometric prediction.
Pipeline learns topological features for protein stability prediction.
problem Predicting protein stability using topological features.
method Data-driven method to learn topological features, comparing with expert features.
result Topological features achieve 92%-99% of SME-based models' performance.
Framework integrates Markov and causal models for accurate counterfactual inference.
problem Lack of counterfactual inference in Markov models and identification in causal models.
method Defines structural causal models in terms of Markov process parameters and equilibrium dynamics, enabling consistent counterfactual inference.
result Proposed framework alleviates identifiability issues and improves accuracy of counterfactual inference.
Enhanced diffusion sampling improves rare event sampling in biomolecular simulations.
problem Efficiently sampling rare transition events in biomolecular systems.
method Quantitative steering protocols to generate biased ensembles and exact reweighting.
result Fast, accurate, and scalable estimation of equilibrium properties.
Enhanced diffusion sampling tackles rare event sampling in biomolecular simulations.
problem Efficiently sampling rare transition events in biomolecular simulations.
method Quantitative steering protocols to generate biased ensembles, followed by exact reweighting.
result Fast, accurate, and scalable estimation of equilibrium properties for folding free energies.
Cryo-electron microscopy (cryo-EM) is an emerging experimental method to characterize the structure of large biomolecular assemblies. Single particle cryo-EM records 2D images (so-called micrographs) of projections of the three-dimensional particle, which need to be processed to obtain the three-dimensional reconstruct…
Bayesian model clusters diverse 'omics data for disease subtyping.
problem Clustering diverse 'omics datasets conflates multiple structures.
method Multi-view Bayesian mixture model with semi-supervised learning.
result Identifies distinct clusters of patients for stratified medicine.
Method scales up ML science by measuring multiple molecules at once.
problem Scaling up ML-driven science with wet lab experiments.
method Neural extension of compressed sensing for function space.
result Proves orders-of-magnitude gains in information density.
Generative model tailors anticancer drugs based on transcriptomic data.
problem Designing effective anticancer drugs considering genetic profiles.
method RL framework using pretrained VAEs to generate compounds conditioned on transcriptomic data.
result Generative model produces molecules with high predicted inhibitory effects.
This review explores the use of machine learning in discovering collective variables for biomolecular dynamics.
problem Understanding the conformational dynamics and molecular recognition in biomolecules.
method Statistical analysis of high-dimensional spatiotemporal data generated from molecular dynamics simulations.
result Machine learning algorithms can be used to discover abstract collective variables that describe biomolecular dynamics.
We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system for generating atomic potentials through machine learning (ML). Tests on the QM7, QM7b and GDB9 biom…
Extend CPS to non-exchangeable settings with observation-specific permutation weights
problem Calibrated predictive bands under distributional shifts
method Encoding distributional shifts through observation-specific permutation weights
result Shift-aware predictive systems remain valid
Enhanced coloring invariant distinguishes folded molecular chain topologies.
problem Apparent indistinguishability of folded chain topologies using current coloring invariants.
method Introduced Boltzmann weights to improve the resolving power of quandle colorings.
result Improved resolution in distinguishing folded chain topologies.
Develops methods for spectral estimation and rare-event prediction in complex systems.
problem Challenges in understanding dynamics in complex systems with many degrees of freedom.
method Inexact iterative numerical linear algebra methods for spectral estimation and rare-event prediction.
result Demonstrates methods on low-dimensional and high-dimensional models, showing their effectiveness.
Develops an MS-inspired algorithm for regression mode finding and space partitioning.
problem Finding local modes of regression functions and partitioning input space.
method Mean-shift-inspired algorithm for iterative gradient ascent.
result Proves convergence and rates of convergence for estimated local modes.
There is an increasing demand for computing the relevant structures, equilibria and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension red…
Macromolecular and biomolecular folding landscapes typically contain high free energy barriers that impede efficient sampling of configurational space by standard molecular dynamics simulation. Biased sampling can artificially drive the simulation along pre-specified collective variables (CVs), but success depends crit…
Paper uses transfer learning and Bayesian optimization to reduce DNA sequence design experiments.
problem Designing many similar DNA sequences for specific applications is expensive and time-consuming.
method Combines transfer learning with Bayesian optimization to reduce experiment count.
result Total number of experiments can be significantly reduced by sharing information between tasks.
We address the problem of analyzing sets of noisy time-varying signals that all report on the same process but confound straightforward analyses due to complex inter-signal heterogeneities and measurement artifacts. In particular we consider single-molecule experiments which indirectly measure the distinct steps in a b…
Diffusion maps are a nonlinear manifold learning technique based on harmonic analysis of a diffusion process over the data. Out-of-sample extensions with computational complexity O(N), where N is the number of points comprising the manifold, frustrate applications to online learning applications requiring…
Adapts safe policies for exploration in high-risk settings.
problem Balancing safety and exploration in high-risk environments.
method Uses conformal calibration on a safe reference policy to determine aggressive action limits.
result Safe exploration improves performance without requiring model class identification or hyperparameter tuning.
The modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long-time kinetics from molecular…
This abstract reviews recent methods for predicting protein-ligand binding affinity.
problem Predicting protein-ligand binding affinity for various applications in life sciences.
method Traditional and deep learning models for binding affinity prediction.
result Improved predictive performance of AI-driven models.
New method for causal discovery in high dimensions with confounder blanket assumption.
problem Inferring causal relationships from observational data in high dimensions.
method Relaxes parametric restrictions and sparsity constraints, focusing on confounder blanket.
result Provable sound and complete structure learning algorithm with finite sample error control.
Study limits of circadian synchronization under different light signals.
problem Disruption of circadian rhythms due to misalignment with external light signals.
method Matrix-free approach for locating periodic steady states, numerical continuation, bifurcation diagrams, unsupervised learning.
result Limits of circadian synchronization to external light signals of different frequency and duty cycle.
Energy-based diffusion models improve molecular sampling and simulation.
problem Inconsistency between diffusion model scores and equilibrium distributions.
method Fokker-Planck regularization to enforce consistency.
result Improved consistency and efficient sampling of biomolecular systems.
Continuous-depth Evoformer reduces protein folding prediction time and resource usage.
problem Efficient protein structure prediction with reduced computational costs.
method Continuous-depth formulation of Evoformer using Neural Ordinary Differential Equations (Neural ODEs).
result The continuous-time Evoformer achieves constant memory cost and improved efficiency.
K-Models clusters functional data with ordinal constraints for better interpretability.
problem Challenges in extracting meaningful insights from functional data due to lack of interpretability.
method Integrates ordinal constraints into clustering to improve interpretability and structure identification.
result Enhances interpretability of clustering results while maintaining performance.
GDML learns effective CG models from all-atom data.
problem Learning effective coarse-grained force fields efficiently.
method Ensemble learning with stratified sampling and GDML.
result GDML yields smaller free energy error than neural networks.
BIDIFAC integrates multi-platform, multi-cohort data for shared and unique patterns.
problem Integration of multi-platform, multi-cohort data for shared and unique patterns.
method BIDIFAC integrates bidimensionally linked matrices into four components: globally shared, row-shared, column-shared, and single-matrix structural components.
result BIDIFAC reveals shared and unique patterns of variability in multi-platform, multi-cohort data.
Unified framework for sampling and approximating high-dimensional energy landscapes.
problem Sampling and approximating complex energy landscapes in physical systems with constraints and energy barriers.
method Formulates a minimax optimization problem that jointly adapts surrogate approximation and adaptive sampling.
result Demonstrates effectiveness in biomolecular systems with up to 30 collective variables.
Introduce a thermodynamically informed, temperature-transferable MLCG framework for proteins.
problem Temperature transferability of MLCG models for proteins.
method Explicit decomposition of CG potential into energetic and entropic components.
result Reproduces temperature-dependent quantities like heat capacity.
Machine learning generates coarse-grained force fields for molecular dynamics.
problem Creating thermodynamically consistent coarse-grained models for larger systems.
method Hybrid architecture using graph neural networks to learn molecular features.
result Framework reproduces thermodynamics for small biomolecular systems.
In this thesis we present the novel semi-supervised network-based algorithm P-Net, which is able to rank and classify patients with respect to a specific phenotype or clinical outcome under study. The peculiar and innovative characteristic of this method is that it builds a network of samples/patients, where the nodes …
Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.
problem Characterize surfaces with constant ratio of principal curvatures in different geometries.
method Differential geometry, line geometry, Lie sphere geometry, ordinary differential equations, algebraic geometry.
result Characterized various types of surfaces like rotational, channel, ruled, helical, and translational.
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwe…
We define (p,q) hermitian geometry as the target space geometry of the two dimensional (p,q) supersymmetric sigma model. This includes generalised Kähler geometry for (2,2), generalised hyperkähler geometry for (4,2), strong Kähler with torsion geometry for (2,1) and strong hyperkähler with torsion geometry f…
A car's motion shows flat parabolic geometry.
problem Understanding the geometry of a car's motion.
method Analyzing a car as a nonholonomic system.
result Shows a car's motion as a flat parabolic geometry.
Hessian geometry explains special geometries in N=2 theories.
problem Explaining special geometries in N=2 theories. method Formulating N=2 theories in terms of Hessian structures. result Hessian geometry relates special geometries of vector multiplets to hypermultiplet geometries.