Woong Kook

We combinatorially interpret the spectra of discrete Laplace operators from the boundary maps in the simplicial complex of independent sets of a matroid. The interpretation follows from a surprising orthogonal decomposition of the simplicial chain groups. This decomposition is in general finer than the spectral decomposition. As a consequence, the spectra are integral. One corollary to our combinatorial interpretation may be paraphrased as stating that one can “hear" the characteristic polynomia

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 intr

Given a finite connected graph G=(V(G),E(G)) and a basis ∂ for a hyperplane in the cycle space of G, define λ=∑Ydet(CY,∂)·CY summing over all connected spanning subgraphs Y of G such that |E(Y)|=|V(G)| with CY denoting the unique cycle in Y. We will show that λ is an element of the harmonic space ker(∂1t∂1+∂∂t) where ∂1 is the incidence matrix of G by establishing an inner product formula λ∘z=det(z,∂)k(G) for the cycles z and the tree number k(G) of G. Several examples and applications of these

see the abstract in the attached pdf