ACMD Seminar: The Concept of Effective Resistance in a Directed Network

Fern Hunt
Scientist Emeritus, Applied & Computational Mathematics Division, NIST

Tuesday, May 20, 2025, 3:00-4:00 PM ET (1:00-2:00 PM MT)

In-person at Bldg. 101 Rm. B-111* with VTC to Boulder 1-4072
Online at: Zoom Gov (email seminar chairs for link to talk)

Abstract: A network is a collection of individual units or agents that interact with each other. The prediction and description of the collective behavior of a network is a fundamental goal. The mathematical modeling of networks centers on a graph. A graph consists of a set of nodes representing the agents, and edges— directed arcs that connect nodes. These edges indicate the directed influence of one node upon another. In the so-called undirected case, the influence between connected nodes is bidirectional and of equal strength. In 1984 Doyle and Snell popularized an analogy between random walks on a graph and the flow of an electrical current through a network of resistors. This idea, significantly deepened and extended by mathematicians and computers scientists is now e.g. the foundation of the nearly linear time Laplace equation solvers used in machine learning algorithms and optimization problems.. There have been several attempts to extend effective resistance to directed graphs. The speaker will discuss an extension due to Sato and Sugihara that has very useful properties. Their results will be used to discuss first passage (first hitting times) for random walks in a network.

Bio: Fern Y. Hunt is a research associate and scientist emeritus in the Applied and Computational Mathematics Division of the Information Technology. Dr. Hunt’s interests are the dynamics of Markov chains and dynamical systems. Hunt received an under graduate degree in Mathematics from Bryn Mawr College and graduate degrees from New York University’s Courant Institute of Mathematical Sciences.

Host: Leroy Jia

Note: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

*Safety Precaution: The hallway leading from the Courtyard to the exit closest to B-111 and B-113 will be used by contractors to move debris, machinery, and other supplies, as well as will be heavily trafficked by the contractors throughout the process. Be aware of the safety precautions posted during this time.

Note: Visitors from outside NIST must contact Meliza Lane at least 24 hours in advance.