Kramers-restricted self-consistent 2-spinor fields for heavy-element chemistry

The relativistic pseudopotential (PP) method is one of the most common and successful approximations in computational quantum chemistry. If suitably parameterized -- e.g., fitted to atomic valence total energies from highly accurate relativistic reference calculations --, atomic PPs provide effective (spin�orbit) 1-electron operators mimicking the chemically inert atomic core subsystem, which thus is excluded from explicit considerations. This work deals with the development of a Kramers-restricted, 2-component PP Hartree�Fock SCF program based on the spin-restricted, 1-component HF SCF modules of the "Quantum Objects Library" of C++ program modules at the Dolg and Hanrath groups at Cologne University. Kramers' restriction, i.e. time reversal symmetry, is addressed at the lowest hierarchical level of the (formally complexified) matrix algebra modules. PP matrix elements are computed using PP integral subroutines of the ARGOS program, which are interfaced to the existing structure. On this basis, a set of spin-restricted, 1-component (all-electron and) spin-free PP, and Kramers-restricted, 2-component spin--orbit PP HF SCF programs is implemented. "Optimal damping" and initial guess density matrices constructed from atomic densities are shown to improve SCF convergence significantly. As first steps towards correlated 2-component calculation schemes, a modular structure for matrix--matrix multiplication-driven 4-index integral transformations to the Fockian eigenbasis is developed, and preliminary 2-component MP2 calculations are presented

Proximity-sensors on GPS collars reveal fine-scale predator-prey behavior during a predation event: A case study from Scandinavia

Although the advent of high-resolution GPS tracking technology has helped increase our understanding of individual and multispecies behavior in wildlife systems, detecting and recording direct interactions between free-ranging animals remains difficult. In 2023, we deployed GPS collars equipped with proximity sensors (GPS proximity collars) on brown bears (Ursus arctos) and moose (Alces alces) as part of a multispecies interaction study in central Sweden. On 6 June, 2023, a collar on an adult female moose and a collar on an adult male bear triggered each other's UHF signal and started collecting fine-scale GPS positioning data. The moose collar collected positions every 2 min for 89 min, and the bear collar collected positions every 1 min for 41 min. On 8 June, field personnel visited the site and found a female neonate moose carcass with clear indications of bear bite marks on the head and neck. During the predation event, the bear remained at the carcass while the moose moved back and forth, moving toward the carcass site about five times. The moose was observed via drone with two calves on 24 May and with only one remaining calf on 9 June. This case study describes, to the best of our knowledge, the first instance of a predation event between two free ranging, wild species recorded by GPS proximity collars. Both collars successfully triggered and switched to finer-scaled GPS fix rates when the individuals were in close proximity, producing detailed movement data for both predator and prey during and after a predation event. We suggest that, combined with standard field methodology, GPS proximity collars placed on free-ranging animals offer the ability for researchers to observe direct interactions between multiple individuals and species in the wild without the need for direct visual observation

Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery

Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields and it forms the basis of constraint-based causal discovery. Oftentimes, CI testing relies on strong, rather unrealistic assumptions. One of these assumptions is homoskedasticity, in other words, a constant conditional variance is assumed. We frame heteroskedasticity in a structural causal model framework and present an adaptation of the partial correlation CI test that works well in the presence of heteroskedastic noise, given that expert knowledge about the heteroskedastic relationships is available. Further, we provide theoretical consistency results for the proposed CI test which carry over to causal discovery under certain assumptions. Numerical causal discovery experiments demonstrate that the adapted partial correlation CI test outperforms the standard test in the presence of heteroskedasticity and is on par for the homoskedastic case. Finally, we discuss the general challenges and limits as to how expert knowledge about heteroskedasticity can be accounted for in causal discovery