arXiv subjects

Khanh Dao Duc

Publications and source records attributed to Khanh Dao Duc.

18 recordsLinked to original sources

arXiv2026

Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality

Efficiently and robustly analyzing shape data is critical across many scientific disciplines. While chirality is a fundamental property in numerous applications - most notably in molecular science - existing shape analysis metrics fail to distinguish between a shape and its mirror image. To address this gap, we introduce a multilinear generalization of the Gromov-Wasserstein objective. Under mild assumptions, this objective yields a distance between shapes, represented as probability distributions quotiented by a symmetry group $G$. In particular, for $G = SO(d)$, we introduce the Chiral Gromov-Wasserstein ($\mathrm{CGW}$) distance, sensitive to chirality. We establish robustness properties for the multilinear Gromov-Wasserstein distances and develop efficient algorithms to compute them, reformulating the underlying optimization problem by projecting couplings onto a low-dimensional space. We derive algorithms for both local and approximate global solutions, yielding a fully polynomial-time approximation scheme for these problems. We validate the framework through numerical experiments that demonstrate the effectiveness of $\mathrm{CGW}$ as a shape metric for chiral objects.

math.OC↗

arXiv2026

Learning the Geometry of Data: A Mathematical Review of Shape Space Analysis

A central objective of machine learning is to identify structure and patterns in data. Advances in data acquisition have increasingly produced datasets whose observations possess rich geometric form, giving rise to shape spaces that encode variability in object geometry. Such datasets arise across a wide range of disciplines, including biology, medicine, anthropology, and computer vision, where subtle geometric differences often carry important scientific information. Traditional machine learning methods, however, are frequently ill-equipped to account for the nonlinear geometric structure underlying these data. This survey synthesizes a rapidly growing body of work on shape space analysis, which provides a mathematical and computational framework for the study of geometric data. Drawing on ideas from differential geometry, statistics, and machine learning, we organize the literature around a common analytical pipeline: shape representation and parameterization, the rigorous construction of robust geodesic metrics, statistical analysis on shape spaces, and geometry-aware learning methods. We discuss how these tools enable the characterization of shape variability, the comparison of geometric objects, and the analysis of structural trajectories across populations and time. To illustrate the breadth of the field, we highlight applications spanning multiple scales of biological organization, including studies of subcellular morphology and primate tooth evolution. Across these and many other domains, researchers face common challenges arising from complex, nonlinear, and often unaligned geometric variation. The review concludes by identifying key theoretical and computational challenges, as well as emerging opportunities driven by increasingly large and diverse geometric datasets.

math.ST↗

arXiv2026

The Joint Gromov Wasserstein Objective for Multiple Object Matching

The Gromov-Wasserstein (GW) distance serves as a powerful tool for matching objects in metric spaces. However, its traditional formulation is constrained to pairwise matching between single objects, limiting its utility in scenarios and applications requiring multiple-to-one or multiple-to-multiple object matching. In this paper, we introduce the Joint Gromov-Wasserstein (JGW) objective and extend the original framework of GW to enable simultaneous matching between collections of objects. Our formulation provides a non-negative dissimilarity measure that identifies partially isomorphic distributions of mm-spaces, with point sampling convergence. We also show that the objective can be formulated and solved for point cloud representations by adapting traditional algorithms in Optimal Transport, including entropic regularization. Our benchmarking with other variants of GW for partial matching indicates superior performance in accuracy and computational efficiency of our method, while experiments on both synthetic and real-world datasets show its effectiveness for multiple shape matching, including geometric shapes and biomolecular complexes, suggesting promising applications for solving complex matching problems across diverse domains, including computer graphics and atomic model building for structural biology.

cs.CV↗

arXiv2026

Scalable Identification and Prioritization of Requisition-Specific Personal Competencies Using Large Language Models

AI-powered recruitment tools are increasingly adopted in personnel selection, yet they struggle to capture the requisition (req)-specific personal competencies (PCs) that distinguish successful candidates beyond job categories. We propose a large language model (LLM)-based approach to identify and prioritize req-specific PCs from reqs. Our approach integrates dynamic few-shot prompting, reflection-based self-improvement, similarity-based filtering, and multi-stage validation. Applied to a dataset of Program Manager reqs, our approach correctly identifies the highest-priority req-specific PCs with an average accuracy of 0.76, approaching human expert inter-rater reliability, and maintains a low out-of-scope rate of 0.07.

cs.CL↗

arXiv2026

Wasserstein projection distance for fairness testing of regression models

Fairness testing evaluates whether a model satisfies a specified fairness criterion across different groups, yet most research has focused on classification models, leaving regression models underexplored. This paper introduces a framework for fairness testing in regression models, leveraging Wasserstein distance to project data distribution and focusing on expectation-based criteria. Upon categorizing fairness criteria for regression, we derive a Wasserstein projection test statistic from dual reformulation, and derive asymptotic bounds and limiting distributions, allowing us to formulate both a hypothesis-testing procedure and an optimal data perturbation method to improve fairness while balancing accuracy. Experiments on synthetic data demonstrate that the proposed hypothesis-testing approach offers higher specificity compared to permutation-based tests. To illustrate its potential applications, we apply our framework to two case studies on real data, showing (1) statistically significant gender disparities that appear on student performance data across multiple models, and (2) significant unfairness between pollution areas under multiple fairness criteria affecting housing price data, robust to different group divisions, with feature-level analysis identifying spatial and socioeconomic drivers.

cs.LG↗

arXiv2025

CryoSAMU: Enhancing 3D Cryo-EM Density Maps of Protein Structures at Intermediate Resolution with Structure-Aware Multimodal U-Nets

Enhancing cryogenic electron microscopy (cryo-EM) 3D density maps at intermediate resolution (4-8 Å) is crucial in protein structure determination. Recent advances in deep learning have led to the development of automated approaches for enhancing experimental cryo-EM density maps. Yet, these methods are not optimized for intermediate-resolution maps and rely on map density features alone. To address this, we propose CryoSAMU, a novel method designed to enhance 3D cryo-EM density maps of protein structures using structure-aware multimodal U-Nets and trained on curated intermediate-resolution density maps. We comprehensively evaluate CryoSAMU across various metrics and demonstrate its competitive performance compared to state-of-the-art methods. Notably, CryoSAMU achieves significantly faster processing speed, showing promise for future practical applications. Our code is available at https://github.com/chenwei-zhang/CryoSAMU.

cs.CV↗

arXiv2025

Struc2mapGAN: improving synthetic cryo-EM density maps with generative adversarial networks

Generating synthetic cryogenic electron microscopy 3D density maps from molecular structures has potential important applications in structural biology. Yet existing simulation-based methods cannot mimic all the complex features present in experimental maps, such as secondary structure elements. As an alternative, we propose struc2mapGAN, a novel data-driven method that employs a generative adversarial network to produce improved experimental-like density maps from molecular structures. More specifically, struc2mapGAN uses a nested U-Net architecture as the generator, with an additional L1 loss term and further processing of raw training experimental maps to enhance learning efficiency. While struc2mapGAN can promptly generate maps after training, we demonstrate that it outperforms existing simulation-based methods for a wide array of tested maps and across various evaluation metrics.

cs.LG↗

arXiv2024

Optimal control of ribosome population for gene expression under periodic nutrient intake

Translation of proteins is a fundamental part of gene expression that is mediated by ribosomes. As ribosomes significantly contribute to both cellular mass and energy consumption, achieving efficient management of the ribosome population is also crucial to metabolism and growth. Inspired by biological evidence for nutrient-dependent mechanisms that control both ribosome active degradation and genesis, we introduce a dynamical model of protein production, that includes the dynamics of resources and control over the ribosome population. Under the hypothesis that active degradation and biogenesis are optimal for maximizing and maintaining protein production, we aim to qualitatively reproduce empirical observations of the ribosome population dynamics. Upon formulating the associated optimization problem, we first analytically study the stability and global behaviour of solutions under constant resource input, and characterize the extent of oscillations and convergence rate to a global equilibrium. We further use these results to simplify and solve the problem under a quasi-static approximation. Using biophysical parameter values, we find that optimal control solutions lead to both control mechanisms and the ribosome population switching between periods of feeding and fasting, suggesting that the intense regulation of ribosome population observed in experiments allows to maximize and maintain protein production. Finally, we find some range for the control values over which such a regime can be observed, depending on the intensity of fasting.

q-bio.SC↗

arXiv2023

Visualizing DNA reaction trajectories with deep graph embedding approaches

Synthetic biologists and molecular programmers design novel nucleic acid reactions, with many potential applications. Good visualization tools are needed to help domain experts make sense of the complex outputs of folding pathway simulations of such reactions. Here we present ViDa, a new approach for visualizing DNA reaction folding trajectories over the energy landscape of secondary structures. We integrate a deep graph embedding model with common dimensionality reduction approaches, to map high-dimensional data onto 2D Euclidean space. We assess ViDa on two well-studied and contrasting DNA hybridization reactions. Our preliminary results suggest that ViDa's visualization successfully separates trajectories with different folding mechanisms, thereby providing useful insight to users, and is a big improvement over the current state-of-the-art in DNA kinetics visualization.

q-bio.BM↗

arXiv2023

ViDa: Visualizing DNA hybridization trajectories with biophysics-informed deep graph embeddings

Visualization tools can help synthetic biologists and molecular programmers understand the complex reactive pathways of nucleic acid reactions, which can be designed for many potential applications and can be modelled using a continuous-time Markov chain (CTMC). Here we present ViDa, a new visualization approach for DNA reaction trajectories that uses a 2D embedding of the secondary structure state space underlying the CTMC model. To this end, we integrate a scattering transform of the secondary structure adjacency, a variational autoencoder, and a nonlinear dimensionality reduction method. We augment the training loss with domain-specific supervised terms that capture both thermodynamic and kinetic features. We assess ViDa on two well-studied DNA hybridization reactions. Our results demonstrate that the domain-specific features lead to significant quality improvements over the state-of-the-art in DNA state space visualization, successfully separating different folding pathways and thus providing useful insights into dominant reaction mechanisms.

q-bio.QM↗

arXiv2023

EMPOT: partial alignment of density maps and rigid body fitting using unbalanced Gromov-Wasserstein divergence

Aligning EM density maps and fitting atomic models are essential steps in single particle cryogenic electron microscopy (cryo-EM), with recent methods leveraging various algorithms and machine learning tools. As aligning maps remains challenging in the presence of a map that only partially fits the other (e.g. one subunit), we here propose a new procedure, EMPOT (EM Partial alignment with Optimal Transport), for partial alignment of 3D maps. EMPOT first finds a coupling between 3D point-cloud representations, which is associated with their so-called unbalanced Gromov Wasserstein divergence, and second, uses this coupling to find an optimal rigid body transformation. Upon running and benchmarking our method with experimental maps and structures, we show that EMPOT outperforms standard methods for aligning subunits of a protein complex and fitting atomic models to a density map, suggesting potential applications of Partial Optimal Transport for improving Cryo-EM pipelines.

q-bio.BM↗

arXiv2023

Quantifying Extrinsic Curvature in Neural Manifolds

The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In this work, we combine topological deep generative models and extrinsic Riemannian geometry to introduce a novel approach for studying the structure of neural manifolds. This approach (i) computes an explicit parameterization of the manifolds and (ii) estimates their local extrinsic curvature--hence quantifying their shape within the neural state space. Importantly, we prove that our methodology is invariant with respect to transformations that do not bear meaningful neuroscience information, such as permutation of the order in which neurons are recorded. We show empirically that we correctly estimate the geometry of synthetic manifolds generated from smooth deformations of circles, spheres, and tori, using realistic noise levels. We additionally validate our methodology on simulated and real neural data, and show that we recover geometric structure known to exist in hippocampal place cells. We expect this approach to open new avenues of inquiry into geometric neural correlates of perception and behavior.

q-bio.NC↗

arXiv2022

Testing geometric representation hypotheses from simulated place cell recordings

Hippocampal place cells can encode spatial locations of an animal in physical or task-relevant spaces. We simulated place cell populations that encoded either Euclidean- or graph-based positions of a rat navigating to goal nodes in a maze with a graph topology, and used manifold learning methods such as UMAP and Autoencoders (AE) to analyze these neural population activities. The structure of the latent spaces learned by the AE reflects their true geometric structure, while PCA fails to do so and UMAP is less robust to noise. Our results support future applications of AE architectures to decipher the geometry of spatial encoding in the brain.

q-bio.NC↗

arXiv2022

Defining an action of SO(d)-rotations on images generated by projections of d-dimensional objects: Applications to pose inference with Geometric VAEs

Recent advances in variational autoencoders (VAEs) have enabled learning latent manifolds as compact Lie groups, such as $SO(d)$. Since this approach assumes that data lies on a subspace that is homeomorphic to the Lie group itself, we here investigate how this assumption holds in the context of images that are generated by projecting a $d$-dimensional volume with unknown pose in $SO(d)$. Upon examining different theoretical candidates for the group and image space, we show that the attempt to define a group action on the data space generally fails, as it requires more specific geometric constraints on the volume. Using geometric VAEs, our experiments confirm that this constraint is key to proper pose inference, and we discuss the potential of these results for applications and future work.

cs.CV↗

arXiv2021

ICLR 2021 Challenge for Computational Geometry & Topology: Design and Results

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstats and Giotto-TDA. The challenge attracted 16 teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

cs.CG↗

arXiv2020

EGGTART: A computational tool to visualize the dynamics of biophysical transport processes under the inhomogeneous $\ell$-TASEP

The totally asymmetric simple exclusion process (TASEP), which describes the stochastic dynamics of interacting particles on a lattice, has been actively studied over the past several decades and applied to model important biological transport processes. Here we present a software package, called EGGTART (Extensive GUI gives TASEP-realization in real time), which quantifies and visualizes the dynamics associated with a generalized version of the TASEP with an extended particle size and heterogeneous jump rates. This computational tool is based on analytic formulas obtained from deriving and solving the hydrodynamic limit of the process. It allows an immediate quantification of the particle density, flux, and phase diagram, as a function of a few key parameters associated with the system, which would be difficult to achieve via conventional stochastic simulations. Our software should therefore be of interest to biophysicists studying general transport processes, and can in particular be used in the context of gene expression to model and quantify mRNA translation of different coding sequences.

physics.bio-ph↗

arXiv2020

The key parameters that govern translation efficiency

Translation of mRNA into protein is a fundamental yet complex biological process with multiple factors that can potentially affect its efficiency. Here, we study a stochastic model describing the traffic flow of ribosomes along the mRNA (namely, the inhomogeneous $\ell$-TASEP), and identify the key parameters that govern the overall rate of protein synthesis, sensitivity to initiation rate changes, and efficiency of ribosome usage. By analyzing a continuum limit of the model, we obtain closed-form expressions for stationary currents and ribosomal densities, which agree well with Monte Carlo simulations. Furthermore, we completely characterize the phase transitions in the system, and by applying our theoretical results, we formulate design principles that detail how to tune the key parameters we identified to optimize translation efficiency. Using ribosome profiling data from S. cerevisiae, we shows that its translation system is generally consistent with these principles. Our theoretical results have implications for evolutionary biology, as well as synthetic biology.

math-ph↗

arXiv2017

Operator Norm Inequalities between Tensor Unfoldings on the Partition Lattice

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order-$k$ tensor, which are in one-to-one correspondence with the set of partitions of $\{1,\ldots,k\}$. We derive general inequalities between the $l^p$-norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm ($p=2$) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.

math.NA↗