arXiv subjects

Kristofor E. Pas

Publications and source records attributed to Kristofor E. Pas.

3 recordsLinked to original sources

arXiv2026

FlowLOT: Linearized Optimal Transport for Flow Cytometry Analysis

Multiparameter flow cytometry generates high-dimensional, unordered single-cell mea- surement data for disease diagnosis and monitoring, yet analysis often remains dependent on manual gating, limiting scalability and reproducibility. Existing machine-learning ap- proaches can reduce annotation burden but frequently require large training cohorts and offer limited interpretability. To address these challenges, we introduce FlowLOT , an optimal-transport-based framework that models the single-cell measurement data of a pa- tient sample as an empirical cellular distribution and maps it directly into a fixed-length feature vector. Within a single transparent architecture, FlowLOT unifies high-dimensional classification, interpretable visualization, and continuous quantitative inference. In few-shot regimes, using as few as 16 patients per class on FlowCAP-II and 8 patients per class on BLAST110, it accurately distinguishes healthy from acute myeloid leukemia (AML) sam- ples, reaching 94.3% and 98.0% balanced accuracy, respectively. The underlying embedding exposes marker-level variation driving disease-associated population shifts and enables quantitative measurable residual disease (MRD) estimation, achieving a Pearson correlation of 0.82 on held-out samples and 0.79 under cross-dataset transfer. Furthermore, at the clinically relevant 0.1% threshold for leukemia-associated immunophenotype (LAIP) residual disease, FlowLOT detects positivity with 72% sensitivity at 100% specificity. By replacing subjective manual gating and black-box deep learning with a distribution-aware framework, FlowLOT offers a sample-efficient, scalable, and interpretable solution for high- dimensional cytometry under realistic clinical and experimental constraints.

q-bio.QM↗

arXiv2026

Reduced Order Modeling of One-Dimensional Conservative PDEs via the Cumulative Distribution Transform

We propose a reduced order modeling (ROM) framework for 1D conservative PDEs based on the cumulative distribution transform (CDT). The CDT maps nonnegative, equal-mass states into a Hilbert space in which 1D Wasserstein distances become weighted $L^2$ distances and translations become affine shifts. This makes the transform especially suited for transport-dominated dynamics, where Eulerian linear-subspace ROMs often suffer from slow decay of Kolmogorov widths. We study this phenomenon for scalar conservative dynamics by analyzing the solution manifold in CDT coordinates. For linear transport, the transformed solution manifold is contained in the 2-dimensional space spanned by the transformed initial datum and the constant function, and has zero Kolmogorov $2$-width. For nonlinear hyperbolic conservation laws, we prove two complementary types of estimates: robust $O(n^{-1})$ bounds that rely only on the conservative transport structure and remain meaningful after shock formation, and sharper $O(n^{-2})$ bounds in smooth pre-shock regimes. For conservative advection-diffusion, we show that the CDT trajectory remains within distance $O(\sqrt{DT})$ of the pure-transport plane, and we also obtain sharper $O(D^2T^2)$ estimates under additional regularity or away from initial layers. In both cases, the zero 2-width behavior of linear transport is recovered as the diffusion coefficient tends to zero. Motivated by these estimates, we develop a CDT-POD numerical scheme: snapshots are mapped to CDT space, Proper Orthogonal Decomposition (POD) is performed in transformed coordinates, and the inverse CDT is used to reconstruct physical states. Numerical experiments for several transport-dominated dynamics show that CDT-POD can capture solution manifolds with substantially fewer modes than Eulerian POD.

math.AP↗

arXiv2025

An Efficient Transport-Based Dissimilarity Measure for Time Series Classification under Warping Distortions

Time Series Classification (TSC) is an important problem with numerous applications in science and technology. Dissimilarity-based approaches, such as Dynamic Time Warping (DTW), are classical methods for distinguishing time series when time deformations are confounding information. In this paper, starting from a deformation-based model for signal classes we define a problem statement for time series classification problem. We show that, under theoretically ideal conditions, a continuous version of classic 1NN-DTW method can solve the stated problem, even when only one training sample is available. In addition, we propose an alternative dissimilarity measure based on Optimal Transport and show that it can also solve the aforementioned problem statement at a significantly reduced computational cost. Finally, we demonstrate the application of the newly proposed approach in simulated and real time series classification data, showing the efficacy of the method.

cs.IT↗