Employing isomorphisms between their ambient rings, we propose new definitions of equivalence and isometry for skew polycyclic codes that will lead to tighter classifications than existing ones. This reduces the number of previously known isometry and equivalence classes. In the process, we classify classes of skew (f,σ,δ)-polycyclic codes with the same performance parameters, to avoid duplicating already existing codes, and state precisely when different notions of equivalence coincide.The generator of a skew polycyclic code is in one-one correspondence with the generator of a principal left ideal in its nonassociative unital ambient ring. By allowing the ambient rings to be nonassociative, we eliminate the need on restrictions on the length of the codes. Ring isomorphisms that preserve the Hamming distance (called isometries) map generators of principal left ideals to generators of principal left ideals and preserve length, dimension, and Hamming distance of the corresponding isometric skew polycyclic codes.
By work of Howlett and Muraleedaran–Taylor, a parabolic subgroup of a real or complex reflection group always admits a complement in its normalizer. In this note, we investigate this phenomenon for quaternionic reflection groups. Here, in contrast to the real and complex setting, we find that complements of parabolic subgroups do not exist in general. Indeed, there are infinitely many examples of quaternionic reflection groups in arbitrary rank greater than 2 with a parabolic subgroup that does not admit a complement in its normalizer. We give a full classification of parabolic subgroups of irreducible quaternionic reflection groups and describe their complements, if the latter exist.
Exponential Runge-Kutta methods are a well-established tool for the numerical integration of parabolic evolution equations. However, these schemes are typically developed under the assumption of homogeneous boundary conditions. In this paper, we extend classical convergence results to the case of non-homogeneous boundary conditions. Since non-homogeneous boundary conditions typically cause order reduction, we introduce a correction strategy based on smooth extensions of the boundary data. This results in a reformulation as a homogeneous problem with modified source term, to which standard exponential integrators can be applied. For linear problems, we prove that the corrected schemes recover the expected convergence order, and hat higher orders can be attained with suitable quadrature rules, reaching order 2s for s-stage Gauss collocation methods. For semilinear problems, our approach preserves the convergence orders guaranteed by exponential Runge-Kutta methods satisfying the corresponding stiff order conditions. Numerical experiments validate the theoretical findings.
Support for political violence is often shaped by ideological alignment, with individuals tending to endorse aggression by actors perceived as ideologically similar while rejecting violence by opposing actors. However, some individuals may show a broader tendency to endorse violence across opposing sides of a conflict. Two studies examined whether Dark Tetrad personality traits—narcissism, Machiavellianism, psychopathy, and sadism—are associated with support for violent actions by both Israel and Hamas (Ns = 257 and 470). Across both studies, support for violence by Israel and Hamas was negatively correlated, indicating actor-specific endorsement patterns. Psychopathy and sadism were consistently associated with support for violent actions by both actors, whereas narcissism and Machiavellianism showed weaker and less consistent associations. Interest in militarism and moral disengagement partially accounted for the associations between psychopathy and sadism and support for Israeli violent actions, but not for Hamas-related outcomes. Overall, the findings suggest that while ideological alignment structures actor-specific support for political violence, psychopathy and sadism are associated with a broader tendency to endorse violence across opposing actors. These results highlight the importance of considering both ideological and dispositional factors in understanding support for political violence.
This work presents NEVU, a benchmark for actor-conditioned, event-centric, and direction-aware human value recognition in news-domain texts. NEVU evaluates whether models can infer values from event-structured evidence, attribute them to the correct social actors, and determine their aligned or contradictory direction. Built from 2865 English news articles, NEVU represents news at four semantic levels, from subevents to composite events and full articles. Using a hierarchical taxonomy of 54 fine-grained and 20 coarse-grained values, the benchmark contains 46,589 semantic units, 72,905 annotated unit–actor pairs, and 168,061 directed value instances. NEVU is constructed through a staged LLM-assisted annotation and verification pipeline, with targeted human verification for unresolved cases. Candidate-level acceptance and agreement are further examined through a multi-group assessment. The experiments show that prompting-only models remain limited, whereas LoRA-tuned open-weight models substantially improve performance, with overall Micro-F1 gains of 29.77 and 8.21 percentage points over the strongest prompting-only open-weight and proprietary baselines, respectively. These gains primarily reflect learnability under the NEVU reference-label setting. NEVU provides a structured benchmark for systematic evaluation and supervised adaptation of actor-conditioned human value recognition in English news.
