Woong Kook

Chankyu Joung, Mijin Kim, Taejin Paik et al.

Accurate delineation of key waveforms in an ECG is a critical step in extracting relevant features to support the diagnosis and treatment of heart conditions. Although deep learning based methods using segmentation models to locate P, QRS, and T waves have shown promising results, their ability to handle arrhythmias has not been studied in any detail. In this paper we investigate the effect of arrhythmias on delineation quality and develop strategies to improve performance in such cases. We introduce a U-Net-like segmentation model for ECG delineation with a particular focus on diverse arrhythmias. This is followed by a post-processing algorithm which removes noise and automatically determines the boundaries of P, QRS, and T waves. Our model has been trained on a diverse dataset and evaluated against the LUDB and QTDB datasets to show strong performance, with F1-scores exceeding 99% for QRS and T waves, and over 97% for P waves in the LUDB dataset. Furthermore, we assess various models across a wide array of arrhythmias and observe that models with a strong performance on standard benchmarks may still perform poorly on arrhythmias that are underrepresented in these benchmarks, such as tachycardias. We propose solutions to address this discrepancy.

Younng-Jin Kim, Woong Kook

A harmonic cycle $λ$, also called a discrete harmonic form, is a solution of the Laplace's equation with the combinatorial Laplace operator obtained from the boundary operators of a chain complex. By the combinatorial Hodge theory, harmonic spaces are isomorphic to the homology groups with real coefficients. In particular, if a cell complex has a one dimensional reduced homology, it has a unique harmonic cycle up to scalar, which we call the \emph{standard harmonic cycle}. In this paper, we will present a formula for the standard harmonic cycle $λ$ of a cell complex based on a high-dimensional generalization of cycletrees. Moreover, by using duality, we will define the standard harmonic cocycle $λ^*$, and show intriguing combinatorial properties of $λ$ and $λ^*$ in relation to (dual) spanning trees, (dual) cycletrees, winding numbers $w(\cdot)$ and cutting numbers $c(\cdot)$ in high dimensions.

Jea Kwon, Dong-Kyum Kim, Jiwon Kim et al.

Memory formation is fundamental to intelligence, yet whether deep neural networks preserve identifiable memory traces analogous to biological memory units remains an open question. This work introduces a geometric framework to identify such "AI engrams" by formalizing the neuroscientific criteria of specificity, reactivation, sufficiency, and necessity into a constrained inverse problem. We derive a closed-form estimator that isolates individual memory traces from globally entangled parameters, and show that this biologically-derived solution corresponds to a natural gradient update on the parameter manifold. AI engrams enable surgical manipulation of learned knowledge: any subset of memories can be composed or erased through linear arithmetic, without iterative optimization. Experiments ranging from simple MLPs to LLMs demonstrate the causal validity and substantial scalability of AI engrams. Together, these results bridge theories of biological memory and artificial representation learning and offer geometric insight into how deep networks simultaneously support functional specificity within distributed storage.