Motifs for processes on networks and their applications in data science

Complexity Speaker Series

###### Alice Schwarze

Postdoctoral Research Affiliate, Dartmouth College

The study of motifs in networks can help researchers uncover links between the structure and function of networks in biology, sociology, economics, and many other areas. Empirical studies of networks have identified feedback loops, feedforward loops, and several other small structures as “motifs” that occur frequently in real-world networks and may contribute by various mechanisms to important functions in these systems. However, these mechanisms are unknown for many of these motifs. We propose to distinguish between “structure motifs” (i.e., graphlets) in networks and “process motifs” (which we define as structured sets of walks) on networks and consider process motifs as building blocks of processes on networks. Using the steady-state covariances and steady-state correlations in a multivariate Ornstein-Uhlenbeck process on a network as examples, we demonstrate that the distinction between structure motifs and process motifs makes it possible to gain quantitative insights into mechanisms that contribute to important functions of dynamical systems on networks.

About the speaker

About the speaker

Alice Schwarze is an applied mathematician with interests in mathematical modeling, networks, complex systems, and data science. She received her DPhil (PhD) in mathematics from the University of Oxford in 2019, and has subsequently conducted postdoctoral research at the Department of Biology at the University of Washington (2019-2021) and at the Department of Mathematics at Dartmouth College (2021- present). At the core of her research program lies the question 'How can mathematical thinking advance our understanding of real-world complex systems?' Encoding structural information about networks in matrices (e.g., an adjacency matrix, Laplace matrix, or Hashimoto matrix) establishes a firm connection between network science and linear algebra. Combining the study of matrix powers and spectra with concepts from dynamical systems, control theory, and random-matrix theory, Alice Schwarze aims contribute to the collective understanding of how structure, dynamics, and function of networks are related and how these relationships can be used to control, infer, or predict attributes of complex systems and their change over time. Alice Schwarze is committed to improving diversity, equity, and inclusion in academia and higher education. Since 2020, she has convened the Women in Network Science seminar to improve the visibility of women researchers in network science and further recognition for their work. In 2021, she was elected president of the Women in Network Science Society. She joined the board of the Network Science Society in 2023.

Alice Schwarze is an applied mathematician with interests in mathematical modeling, networks, complex systems, and data science. She received her DPhil (PhD) in mathematics from the University of Oxford in 2019, and has subsequently conducted postdoctoral research at the Department of Biology at the University of Washington (2019-2021) and at the Department of Mathematics at Dartmouth College (2021- present). At the core of her research program lies the question 'How can mathematical thinking advance our understanding of real-world complex systems?' Encoding structural information about networks in matrices (e.g., an adjacency matrix, Laplace matrix, or Hashimoto matrix) establishes a firm connection between network science and linear algebra. Combining the study of matrix powers and spectra with concepts from dynamical systems, control theory, and random-matrix theory, Alice Schwarze aims contribute to the collective understanding of how structure, dynamics, and function of networks are related and how these relationships can be used to control, infer, or predict attributes of complex systems and their change over time. Alice Schwarze is committed to improving diversity, equity, and inclusion in academia and higher education. Since 2020, she has convened the Women in Network Science seminar to improve the visibility of women researchers in network science and further recognition for their work. In 2021, she was elected president of the Women in Network Science Society. She joined the board of the Network Science Society in 2023.

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