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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
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Posts
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portfolio
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publications
An investigation into the law of small numbers using R
Published in Ball State University, Mathematics Exchange, 2023
The Law of Small Numbers states that the Binomial distribution converges to the Poisson distribution. Using the programming language R, we investigate the total variation distance between Binomial(n, c/n) and Poisson(c) when we fix c and n individually. We also look at the asymptotics for ndTV for a fixed c, where ndTV is the total variation distance dTV multiplied by increasing values of n. Several properties of dTV are looked at in this paper.
Recommended citation: Barlas, Y., Stark, D. (2023), "An investigation into the law of small numbers using R", Ball State Undergraduate Mathematics Exchange, 17(1):2-14 https://digitalresearch.bsu.edu/mathexchange/wp-content/uploads/2023/12/2023_1_BS.pdf
Dual network structure of the AV node
Published in arXiv preprint arXiv:2405.15841, 2024
Biological systems, particularly the brain, are frequently analyzed as networks, conveying mechanistic insights into their function and pathophysiology. This is the first study of a functional network of cardiac tissue. We use calcium imaging to obtain two functional networks in a subsidiary but essential pacemaker of the heart, the atrioventricular node (AVN). The AVN is a small cellular structure with dual functions: a) to delay the pacemaker signal passing from the sinoatrial node (SAN) to the ventricles, and b) to serve as a back-up pacemaker should the primary SAN pacemaker fail. Failure of the AVN can lead to syncope and death. We found that the shortest path lengths and clustering coefficients of the AVN are remarkably similar to those of the brain. The network is “small-world,” thus optimized for energy use vs transmission efficiency. We further study the network properties of AVN tissue with knock-out of the sodium-calcium exchange transporter. In this case, the average shortest path-lengths remained nearly unchanged showing network resilience, while the clustering coefficient was somewhat reduced, similar to schizophrenia in brain networks. When we removed the global action potential using principal component analysis (PCA) in wild-type model, the network lost its “small-world” characteristics with less information passing efficiency due to longer shortest path lengths but more robust signal propagation resulting from higher clustering. These two wild-type networks (with and without global action potential) may correspond to fast and slow conduction pathways. Lastly, a one-parameter non-linear preferential attachment model is a good fit to all three AVN networks.
Recommended citation: Maltsev, A. V., Barlas, Y. Z., Hazan, A., Zhang, R., Ottolia, M., Goldhaber, J. I. (2024), "Dual network structure of the AV node", arXiv preprint arXiv:2405.15841 https://arxiv.org/pdf/2405.15841
talks
Talk 1 on Relevant Topic in Your Field
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Conference Proceeding talk 3 on Relevant Topic in Your Field
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teaching
DATA70132
Level 7 Postgraduate Master's Module, The University of Manchester, 2025
DATA70132: Statistics & Machine Learning 2: AI, Complex Data, Computationally Intensive Statistics (Semester B, 2024/25 Academic Year)