Another of our papers for teens and pre-teens came out in final form today. Here are some details.
Title: The Waiting-Time Paradox
Authors: Naoki Masuda and Mason A. Porter
Abstract: Suppose that you are going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer—possibly much longer—than what you might guess from looking at a bus schedule. This phenomenon, which is called the waiting-time paradox, has a purely mathematical origin. In this article, we explore the waiting-time paradox, explain why it occurs, and discuss some of its implications (beyond the possibility of being late for school).
My name is Mason Porter. I am a Professor in the Department of Mathematics at UCLA. Previously I was Professor of Nonlinear and Complex Systems in the Mathematical Institute at University of Oxford. I was also a Tutorial Fellow of Somerville College.
Thursday, February 25, 2021
Monday, February 15, 2021
RIP Dame Fiona Caldicott (1941–2021)
Today I once again have woken up to awful news: Dame Fiona Caldicott, who I know from her role as Principal of Somerville College, died today.
A tribute has been posted on the UK government page.
Here is her Wikipedia entry.
A tribute has been posted on the UK government page.
Here is her Wikipedia entry.
Tuesday, February 09, 2021
"Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases"
Our article for teens and preteens about modeling the spread of infectious diseases just came out in final form. Here are some details.
Title: Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases
Authors: Heather Z. Brooks, Unchitta Kanjanasaratool, Yacoub H. Kureh, and Mason A. Porter
Abstract: The COVID-19 pandemic has led to significant changes in how people are currently living their lives. To determine how to best reduce the effects of the pandemic and start reopening communities, governments have used mathematical models of the spread of infectious diseases. In this article, we introduce a popular type of mathematical model of disease spread. We discuss how the results of analyzing mathematical models can influence government policies and human behavior, such as encouraging mask wearing and physical distancing to help slow the spread of a disease.
Title: Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases
Authors: Heather Z. Brooks, Unchitta Kanjanasaratool, Yacoub H. Kureh, and Mason A. Porter
Abstract: The COVID-19 pandemic has led to significant changes in how people are currently living their lives. To determine how to best reduce the effects of the pandemic and start reopening communities, governments have used mathematical models of the spread of infectious diseases. In this article, we introduce a popular type of mathematical model of disease spread. We discuss how the results of analyzing mathematical models can influence government policies and human behavior, such as encouraging mask wearing and physical distancing to help slow the spread of a disease.
Friday, February 05, 2021
"Models of Continuous-Time Networks with Tie Decay, Diffusion, and Convection"
Another of my papers just came out in final form today. Here are some details.
Title: Models of Continuous-Time Networks with Tie Decay, Diffusion, and Convection
Authors: Xinzhe Zuo and Mason A. Porter
Abstract: The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. However, for many complex systems, it is useful to develop continuous-time models of networks and to compare them to associated discrete models. In this paper, we study several continuous-time network models and examine discrete approximations of them both numerically and analytically. To consider continuous-time networks, we associate each edge in a graph with a time-dependent tie strength that can take continuous non-negative values and decays in time after the most recent interaction. We investigate how the moments of the tie strength evolve with time in several models, and we explore—both numerically and analytically—criteria for the emergence of a giant connected component in some of these models. We also briefly examine the effects of the interaction patterns of continuous-time networks on the contagion dynamics of a susceptible–infected–recovered model of an infectious disease.
Title: Models of Continuous-Time Networks with Tie Decay, Diffusion, and Convection
Authors: Xinzhe Zuo and Mason A. Porter
Abstract: The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. However, for many complex systems, it is useful to develop continuous-time models of networks and to compare them to associated discrete models. In this paper, we study several continuous-time network models and examine discrete approximations of them both numerically and analytically. To consider continuous-time networks, we associate each edge in a graph with a time-dependent tie strength that can take continuous non-negative values and decays in time after the most recent interaction. We investigate how the moments of the tie strength evolve with time in several models, and we explore—both numerically and analytically—criteria for the emergence of a giant connected component in some of these models. We also briefly examine the effects of the interaction patterns of continuous-time networks on the contagion dynamics of a susceptible–infected–recovered model of an infectious disease.
Thursday, February 04, 2021
"Persistent Homology of Geospatial Data: A Case Study with Voting"
A new paper of mine is out in final form today. Here are some details.
Title: Persistent Homology of Geospatial Data: A Case Study with Voting
Authors: Michelle Feng and Mason A. Porter
Abstract: A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object (which, in our case, is a simplicial complex). Software packages for computing persistent homology typically construct Vietoris–Rips or other distance-based simplicial complexes on point clouds because they are relatively easy to compute. We investigate alternative methods of constructing simplicial complexes and the effects of making associated choices during simplicial-complex construction on the output of persistent-homology algorithms. We present two new methods for constructing simplicial complexes from two-dimensional geospatial data (such as maps). We apply these methods to a California precinct-level voting data set, and we thereby demonstrate that our new constructions can capture geometric characteristics that are missed by distancebased constructions. Our new constructions can thus yield more interpretable persistence modules and barcodes for geospatial data. In particular, they are able to distinguish short-persistence features that occur only for a narrow range of distance scales (e.g., voting patterns in densely populated cities) from short-persistence noise by incorporating information about other spatial relationships between regions.
Title: Persistent Homology of Geospatial Data: A Case Study with Voting
Authors: Michelle Feng and Mason A. Porter
Abstract: A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object (which, in our case, is a simplicial complex). Software packages for computing persistent homology typically construct Vietoris–Rips or other distance-based simplicial complexes on point clouds because they are relatively easy to compute. We investigate alternative methods of constructing simplicial complexes and the effects of making associated choices during simplicial-complex construction on the output of persistent-homology algorithms. We present two new methods for constructing simplicial complexes from two-dimensional geospatial data (such as maps). We apply these methods to a California precinct-level voting data set, and we thereby demonstrate that our new constructions can capture geometric characteristics that are missed by distancebased constructions. Our new constructions can thus yield more interpretable persistence modules and barcodes for geospatial data. In particular, they are able to distinguish short-persistence features that occur only for a narrow range of distance scales (e.g., voting patterns in densely populated cities) from short-persistence noise by incorporating information about other spatial relationships between regions.