arXiv subjects

Betul Orcan-Ekmekci

Publications and source records attributed to Betul Orcan-Ekmekci.

3 recordsLinked to original sources

arXiv2026

BioKERN: Biological Kernel Regularization for Histology-to-Transcriptomics Neighborhood Retrieval

Spatially resolved biology requires representations that preserve biological neighborhood structure rather than only exact cross-modal correspondences. Existing histology--transcriptomics objectives can emphasize instance-level matching even when non-paired spots share molecular or spatial context. We introduce BioKERN, a multimodal spatial representation-learning framework that incorporates biological structure as an explicit, learnable inductive bias. BioKERN constructs a training-time biological kernel by combining transcriptomic similarity and spatial proximity, then uses it to provide graded neighborhood supervision and regularize embedding geometry. Evaluation uses a fixed, model-independent biological neighborhood definition shared by all methods. Across Mouse Brain Visium and Human Liver GSE240429, BioKERN consistently improves biological-neighborhood retrieval over BLEEP in both single- and multi-scale settings. Controlled shared-architecture experiments show that most of the improvement arises from biological-kernel regularization rather than increased model capacity. These results support explicit biological geometry as an interpretable inductive bias for multimodal learning in spatial biology.

cs.LG↗

arXiv2024

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the NMR autocorrelation function for intramolecular dipole pairs assume single-exponential decay, yet the calculated autocorrelation of realistic systems display a rich, multi-exponential behavior resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational and translational diffusion in the same framework. We recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker-Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction, and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole-pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict NMR dipole-dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Pad{é}-Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.

physics.chem-ph↗

arXiv2016

Blowup with vorticity control for a 2D model of the Boussinesq equations

We propose a system of equations with nonlocal flux in two space dimensions which is closely modeled after the 2D Boussinesq equations in a hyperbolic flow scenario. Our equations involve a simplified vorticity stretching term and Biot-Savart law and provide insight into the underlying intrinsic mechanisms of singularity formation. We prove stable, controlled finite time blowup involving upper and lower bounds on the vorticity up to the time of blowup for a wide class of initial data.

math.AP↗