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Abstract The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 in [Freedman, Kitaev, Nayak, Slingerland, Walker, and Wang, J. Geom. Topol.9(2005), 2303–2317]. We prove an analogous result for 2‐complexes, and show that the universal pairing does not detect the difference between simple homotopy equivalence and 3‐deformations. The question of whether these two equivalence relations are different for 2‐complexes is the subject of the Andrews–Curtis conjecture. We also discuss the universal pairing for higher dimensional complexes and show that it is not positive. 

In this study, we present a preliminary investigation focused on determining cumulative fission yields for short-lived fission products. Our analysis involves examining gamma spectra from the irradiated samples of 235 U and 239 Pu using the High Flux Isotope Reactor. The motivation stems from the observed discrepancy in the antineutrino energy spectrum within the range of 5 to 7 MeV. While several hypotheses have been proposed, a thorough analysis of fission yields provides an additional way of gaining insight into this unexplained phenomenon. Our study suggests that the measured gamma rays from 100 Nb, 140 Cs and 95 Sr are consistent with the expected values. However, 93 Rb, 96 Y, 97 Y and 142 Cs cannot be quantified due to insufficient statistics, interference from other gamma rays and the Compton scattering background. Additionally, the calculated cumulative fission yields based on the measured 140 Cs and 95 Sr are found to be consistent with the JEFF3.3 fission yield library. The present work shows that the potential of improving gamma-ray spectroscopy in the fission yields as a means to improve our understanding of the antineutrino spectrum. 

Abstract Antiferromagnets hosting structural or magnetic order that breaks time reversal symmetry are of increasing interest for “beyond von Neumann” computing applications because the topology of their band structure allows for intrinsic physical properties, exploitable in integrated memory and logic function. One such group are the noncollinear antiferromagnets. Essential for domain manipulation is the existence of small net moments found routinely when the material is synthesized in thin film form and attributed to symmetry breaking caused by spin canting, either from the Dzyaloshinskii–Moriya interaction or from strain. Although the spin arrangement of these materials makes them highly sensitive to strain, there is little understanding about the influence of local strain fields caused by lattice defects on global properties, such as magnetization and anomalous Hall effect. This premise is investigated by examining noncollinear antiferromagnetic films that are either highly lattice mismatched or closely matched to their substrate. In either case, edge dislocation networks are generated and for the former case, these extend throughout the entire film thickness, creating large local strain fields. These strain fields allow for finite intrinsic magnetization in seemingly structurally relaxed films and influence the antiferromagnetic domain state and the intrinsic anomalous Hall effect. 

Abstract We prove that the homology groups of a principal ample groupoid vanish in dimensions greater than the dynamic asymptotic dimension of the groupoid (as a side‐effect of our methods, we also give a new model of groupoid homology in terms of the Tor groups of homological algebra, which might be of independent interest). As a consequence, the K‐theory of the ‐algebras associated with groupoids of finite dynamic asymptotic dimension can be computed from the homology of the underlying groupoid. In particular, principal ample groupoids with dynamic asymptotic dimension at most two and finitely generated second homology satisfy Matui's HK‐conjecture. We also construct explicit maps from the groupoid homology groups to the K‐theory groups of their ‐algebras in degrees zero and one, and investigate their properties. 

AbstractOne‐dimensional (1D) cardiovascular models offer a non‐invasive method to answer medical questions, including predictions of wave‐reflection, shear stress, functional flow reserve, vascular resistance and compliance. This model type can predict patient‐specific outcomes by solving 1D fluid dynamics equations in geometric networks extracted from medical images. However, the inherent uncertainty inin vivoimaging introduces variability in network size and vessel dimensions, affecting haemodynamic predictions. Understanding the influence of variation in image‐derived properties is essential to assess the fidelity of model predictions. Numerous programs exist to render three‐dimensional surfaces and construct vessel centrelines. Still, there is no exact way to generate vascular trees from the centrelines while accounting for uncertainty in data. This study introduces an innovative framework employing statistical change point analysis to generate labelled trees that encode vessel dimensions and their associated uncertainty from medical images. To test this framework, we explore the impact of uncertainty in 1D haemodynamic predictions in a systemic and pulmonary arterial network. Simulations explore haemodynamic variations resulting from changes in vessel dimensions and segmentation; the latter is achieved by analysing multiple segmentations of the same images. Results demonstrate the importance of accurately defining vessel radii and lengths when generating high‐fidelity patient‐specific haemodynamics models.image Key pointsThis study introduces novel algorithms for generating labelled directed trees from medical images, focusing on accurate junction node placement and radius extraction using change points to provide haemodynamic predictions with uncertainty within expected measurement error.Geometric features, such as vessel dimension (length and radius) and network size, significantly impact pressure and flow predictions in both pulmonary and aortic arterial networks.Standardizing networks to a consistent number of vessels is crucial for meaningful comparisons and decreases haemodynamic uncertainty.Change points are valuable to understanding structural transitions in vascular data, providing an automated and efficient way to detect shifts in vessel characteristics and ensure reliable extraction of representative vessel radii.