Graph Zeta Function and Gauge Theories

Along the recently trodden path of studying certain number theoretic properties of gauge theories, especially supersymmetric theories whose vacuum manifolds are non-trivial, we investigate Ihara's Graph Zeta Function for large classes of quiver theories and periodic tilings by bi-partite graphs. In particular, we examine issues such as the spectra of the adjacency and whether the gauge theory satisfies the strong and weak versions of the graph theoretical analogue of the Riemann Hypothesis.Comment: 35 pages, 7 Figure

M2-Branes and Fano 3-folds

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.Comment: 128 pages, 39 figures, 42 table

Reproductive inequality in humans and other mammals

Data, Materials, and Software Availability: All study data are included in the article and/or supporting information available online at https://www.pnas.org/lookup/doi/10.1073/pnas.2220124120#supplementary-materials .Copyright © 2023 the Author(s). To address claims of human exceptionalism, we determine where humans fit within the greater mammalian distribution of reproductive inequality. We show that humans exhibit lower reproductive skew (i.e., inequality in the number of surviving offspring) among males and smaller sex differences in reproductive skew than most other mammals, while nevertheless falling within the mammalian range. Additionally, female reproductive skew is higher in polygynous human populations than in polygynous nonhumans mammals on average. This patterning of skew can be attributed in part to the prevalence of monogamy in humans compared to the predominance of polygyny in nonhuman mammals, to the limited degree of polygyny in the human societies that practice it, and to the importance of unequally held rival resources to women’s fitness. The muted reproductive inequality observed in humans appears to be linked to several unusual characteristics of our species—including high levels of cooperation among males, high dependence on unequally held rival resources, complementarities between maternal and paternal investment, as well as social and legal institutions that enforce monogamous norms.This work was conducted as a part of the “Emergence of Hierarchy and Leadership in Mammalian Societies” group at the National Institute for Mathematical and Biological Synthesis, supported by NSF Award DBI-1300426 and the University of Tennessee, Knoxville. It was supported by NSF awards SMA-1329089 and SMA-1743019, and the Santa Fe Institute, as well as the Max Planck Institute for Evolutionary Anthropology, Department of Human Behavior, Ecology and Culture. S.G. was supported by the US Army Research Office grants W911NF-14-1-0637, W911NF-17-1-0150, and the Office of Naval Research grant W911NF-18-1-0138. Additional funding for data collection was provided by the Wenner-Gren Foundation for Anthropological Research awards: 8913 and 7970, by NSF awards: BCS-0924630, BCS-0925910, BCS-0848360, BCS-0514559, BCS-0613226, BCS-0827277, SES-9870429, and DDRIG-1357209, by the National Geographic Society awards: HJ-099R-17, 20113909, 8671-09, and 7968-06, by the Kone Foundation awards: 086809, 088423, and 088423, and by the Jacobs Foundation, the UCSB Broom Center for Demography, and the UCSB Department of Anthropology