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We study the impact of nonconvexity on the complexity of nonsmooth optimization, emphasizing objectives such as piecewise linear functions, which may not be weakly convex. We focus on a dimension-independent analysis, slightly modifying a 2020 black-box algorithm of Zhang-Lin-Jegelka-Sra-Jadbabaie that approximates an ϵ-stationary point of any directionally differentiable Lipschitz objective using [Formula: see text] calls to a specialized subgradient oracle and a randomized line search. Seeking by contrast a deterministic method, we present a simple black-box version that achieves [Formula: see text] for any difference-of-convex objective and [Formula: see text] for the weakly convex case. Our complexity bound depends on a natural nonconvexity modulus that is related, intriguingly, to the negative part of directional second derivatives of the objective, understood in the distributional sense. Funding: This work was supported by the National Science Foundation [Grant DMS-2006990]. 

Synopsis What are the implications of misunderstanding sex as a binary, and why is it essential for scientists to incorporate a more expansive view of biological sex in our teaching and research? This roundtable will include many of our symposium speakers, including biologists and intersex advocates, to discuss these topics and visibilize the link between ongoing reification of dyadic sex within scientific communities and the social, political, and medical oppression faced by queer, transgender, and especially intersex communities. As with the symposium as a whole, this conversation is designed to bring together empirical research and implementation of equity, inclusion, and justice principles, which are often siloed into separate rooms and conversations at academic conferences. Given the local and national attacks on the rights of intersex individuals and access to medical care and bodily autonomy, this interdisciplinary discussion is both timely and urgent. 

Abstract Neutron-capture cross sections of neutron-rich nuclei are calculated using a Hauser–Feshbach model when direct experimental cross sections cannot be obtained. A number of codes to perform these calculations exist, and each makes different assumptions about the underlying nuclear physics. We investigated the systematic uncertainty associated with the choice of Hauser-Feshbach code used to calculate the neutron-capture cross section of a short-lived nucleus. The neutron-capture cross section for$$^{73}\hbox {Zn}$$ ${}^{73}\text{Zn}$(n,$$\gamma $$ $\gamma$)$$^{74}\hbox {Zn}$$ ${}^{74}\text{Zn}$was calculated using three Hauser-Feshbach statistical model codes: TALYS, CoH, and EMPIRE. The calculation was first performed without any changes to the default settings in each code. Then an experimentally obtained nuclear level density (NLD) and$$\gamma $$ $\gamma$-ray strength function ($$\gamma \hbox {SF}$$ $\gamma \text{SF}$) were included. Finally, the nuclear structure information was made consistent across the codes. The neutron-capture cross sections obtained from the three codes are in good agreement after including the experimentally obtained NLD and$$\gamma \hbox {SF}$$ $\gamma \text{SF}$, accounting for differences in the underlying nuclear reaction models, and enforcing consistent approximations for unknown nuclear data. It is possible to use consistent inputs and nuclear physics to reduce the differences in the calculated neutron-capture cross section from different Hauser-Feshbach codes. However, ensuring the treatment of the input of experimental data and other nuclear physics are similar across multiple codes requires a careful investigation. For this reason, more complete documentation of the inputs and physics chosen is important.