Bulletin of the American Physical Society
Mid-Atlantic Section 2022 Meeting
Volume 67, Number 20
Friday–Sunday, December 2–4, 2022; University Park, PA, Pennsylvania State University
Session D02: Bio II |
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Chair: Bekele Gurmessa, Bucknell University Room: Pennsylvania State University Osmond 104 |
Saturday, December 3, 2022 11:00AM - 11:35AM |
D02.00001: Phenotype control in biological systems Invited Speaker: Reka Z Albert My group is using network science and dynamic modeling to understand the emergent properties of biological systems. For example, we think of cell phenotypes as attractors of a system of interacting molecules. We collaborate with wet-bench biologists to develop and validate dynamic models of the processes that underlie cellular phenotypes. We have found that network-based discrete dynamic modeling is very useful in synthesizing causal interaction information into a predictive model. We use the accumulated knowledge gained from specific models to draw general conclusions that connect a network's structure and dynamics. Such a general connection is our identification of stable motifs, which are self-sustaining cyclic interaction structures that determine trap spaces of the system's state space. We have elucidated a system's decision-making as a choice between two mutually exclusive stable motifs and have shown that the control of stable motifs can guide the system into a desired phenotype. We have recently developed the software library pystablemotifs, which implements efficient algorithms to determine and control any Boolean system's attractor repertoire. Stable motif - based phenotype control can form the foundation of therapeutic strategies on a wide application domain. |
Saturday, December 3, 2022 11:35AM - 12:10PM |
D02.00002: Thermodynamics of complex networks and other discrete systems from non-equilibrium ensembles of random walks Invited Speaker: Alexandre V Morozov Large-scale networks represent a broad spectrum of systems in nature, science, and technology. Computer networks such as the World Wide Web and the Internet, social networks such as Twitter and Facebook, and knowledge-sharing online platforms such as Wikipedia exert considerable influence on our everyday lives. Many of these networks are very large and evolve with time, making investigation of their statistical properties a challenging task. I will describe a novel methodology, based on random walks, for the inference of statistical properties of complex networks with weighted or unweighted edges [1]. I will show how this formalism can yield reliable estimates of various network statistics, such as the network size, after only a small fraction of network nodes has been explored. I will introduce two novel algorithms for partitioning network nodes into non-overlapping communities - a key step in revealing network modularity and hierarchical organization [2]. These clustering tools will be applied to various benchmarks, including a large-scale map of roads and intersections in the state of Colorado. Finally, I will demonstrate how these ideas can be extended to computing various thermodynamic quantities in discrete systems such as spin glasses from small non-equilibrium samples of states. In summary, I will demonstrate how random walks can be used to reveal modular organization and global structure of complex networks and infer key statistical mechanics quantities that are otherwise not easily accessible. |
Saturday, December 3, 2022 12:10PM - 12:22PM |
D02.00003: Predicting cascading extinctions and efficient restoration strategies in ecological networks Fatemehsadat Fateminasrollahi, Colin Campbell, Reka Albert The ecologically important task of predicting the severity of cascading extinctions is made challenging by the complexity of ecological networks. In this work, we study an ensemble of network models that describe mutualistic inter-species interactions by Boolean threshold functions. We demonstrate that identifying generalized positive feedback loops (stable motifs) helps pinpoint the species whose extinction leads to catastrophic damage to the whole community. We compare stable motif-based results with previously studied network structural measures and show that stable motifs can identify certain crucial species that the other measures fail to find. We also use the stable motifs of the Boolean model to propose mitigation measures to 1. prevent the damage to the community by protecting a subset of the species, 2. restore the community after the damage by restoring a subset of species. The analysis in this work indicates that the stable motifs predict the most fruitful strategies to manage ecological systems. This approach can also be implemented in other complex systems to achieve the desired outcome. |
Saturday, December 3, 2022 12:22PM - 12:57PM |
D02.00004: Integrability and Chaos in Replicator Dynamics from Signed Interaction Networks Invited Speaker: Christopher H Griffin Complete odd tournaments are frequently used as abstract models of micro and macroscopic ecological systems via replicator dynamics. In these models, the payoff matrix is a skew-symmetric +1/-1 matrix and all species interactions result in a non-zero interaction payoff. These matrices correspond to directed graphs with species as vertices and edge direction giving the sign of the corresponding matrix entries. A circulant tournament is defined by a graph in which every vertex has the same in/out degree and the matrix is also circulant. It is known that the replicator dynamics derived from these tournaments admit polynomial conserved quantities. In this talk we extend this result to show that these circulant tournaments produce quasi-periodic dynamics and are Liouville-Arnold integrable by showing they commute under the action of a non-linear Poisson bracket (related to the Nambu bracket). Furthermore, we show that all tournaments constructed by embeddings are Liouville-Arnold integrable. By an embedding we mean a tournament constructed by recursively replacing vertices in an outer circulant tournament with other circulant tournaments and adding appropriate edges. We numerically illustrate that tournaments not constructed in this manner produce chaotic dynamics and classify all dynamics generated by any tournament with up to seven species. |
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