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1. Equilibrium effects of intraday order-splitting benchmarks

   https://doi.org/10.1007/s11579-020-00278-7  

   Choi, Jin Hyuk; Larsen, Kasper; Seppi, Duane J. (March 2021, Mathematics and Financial Economics)

   null (Ed.)
2. Surprising effects of cascading higher order interactions

   https://doi.org/10.1038/s41598-022-23763-z  

   Hsieh, Hsun-Yi; Vandermeer, John; Perfecto, Ivette (November 2022, Scientific Reports)

   Abstract Most species are embedded in multi-interaction networks. Consequently, theories focusing on simple pair-wise interactions cannot predict ecological and/or evolutionary outcomes. This study explores how cascading higher-order interactions (HOIs) would affect the population dynamics of a focal species. Employing a system that involves a myrmecophylic beetle, a parasitic wasp that attacks the beetle, an ant, and a parasitic fly that attacks the ant, the study explores how none, one, and two HOIs affect the parasitism and the sex ratio of the beetle. We conducted mesocosm experiments to examine these HOIs on beetle survival and sex ratio and found that the 1st degree HOI does not change the beetle’s survival rate or sex ratio. However, the 2nd degree HOI significantly reduces the beetle’s survival rate and changes its sex ratio from even to strongly female-biased. We applied Bayes’ theorem to analyze the per capita survival probability of female vs. male beetles and suggested that the unexpected results might arise from complex eco-evolutionary dynamics involved with the 1st and 2nd degree HOIs. Field data suggested the HOIs significantly regulate the sex ratio of the beetle. As the same structure of HOIs appears in other systems, we believe the complexity associated with the 2nd degree HOI would be more common than known and deserve more scientific attention. 

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3. Polarization effects in higher-order guiding-centre Lagrangian dynamics

   https://doi.org/10.1017/S0022377824000096  

   Brizard, Alain J. (February 2024, Journal of Plasma Physics)

   The extended guiding-centre Lagrangian equations of motion are derived by the Lie-transform perturbation method under the assumption of time-dependent and inhomogeneous electric and magnetic fields that satisfy the standard guiding-centre space–time orderings. Polarization effects are introduced into the Lagrangian dynamics by the inclusion of the polarization drift velocity in the guiding-centre velocity and the appearance of finite-Larmor-radius corrections in the guiding-centre Hamiltonian and guiding-centre Poisson bracket. 

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4. High-Order Anharmonicities Shape Phonon Hydrodynamic Effects in Graphene

   https://doi.org/10.1021/acs.nanolett.5c00855  

   Tur-Prats, Jordi; Han, Zherui; Beardo, Albert; Ruan, Xiulin; Alvarez, F Xavier (July 2025, Nano Letters)
5. Abstract Interpretation of Temporal Safety Effects of Higher Order Programs

   https://doi.org/10.1145/3763140  

   Nicola, Mihai; Agarwal, Chaitanya; Koskinen, Eric; Wies, Thomas (October 2025, Proceedings of the ACM on Programming Languages)

   This paper describes a new abstract interpretation-based approach to verify temporal safety properties of recursive, higher-order programs. While prior works have provided theoretical impact and some automation, they have had limited scalability. We begin with a new automata-based abstract effect domain for summarizing context-sensitive dependent effects, capable of abstracting relations between the program environment and the automaton control state. Our analysis includes a new transformer for abstracting event prefixes to automatically computed context-sensitive effect summaries, and is instantiated in a type-and-effect system grounded in abstract interpretation. Since the analysis is parametric on the automaton, we next instantiate it to a broader class of history/register (or accumulator) automata, beyond finite state automata to express some context-free properties, input-dependency, event summation, resource usage, cost, equal event magnitude, etc. We implemented a prototype evDrift that computes dependent effect summaries (and validates assertions) for OCaml-like recursive higher-order programs. As a basis of comparison, we describe reductions to assertion checking for higher-order but effect-free programs, and demonstrate that our approach outperforms prior tools Drift, RCaml/Spacer, MoCHi, and ReTHFL. Overall, across a set of 23 benchmarks, Drift verified 12 benchmarks, RCaml/Spacer verified 6, MoCHi verified 11, ReTHFL verified 18, and evDrift verified 21; evDrift also achieved a 6.3x, 5.3x, 16.8x, and 6.4x speedup over Drift, RCaml/Spacer, MoCHi, and ReTHFL, respectively, on those benchmarks that both tools could solve. 

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