Three Hopf algebras and their common simplicial and categorical background

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebras of Goncharov for multiple zeta values, that of Connes--Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, cooperads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretation of known constructions in a large common frameworkPreprin

Grouping Individual Investment Preferences in Retirement Savings: A Cluster Analysis of a USS Members Risk Attitude Survey

Cluster analysis is used to identify homogeneous groups of members of USS in terms of risk attitudes. There are two distinct clusters of members in their 40s and 50s. One had previously ‘engaged’ with USS by making additional voluntary contributions. It typically had higher pay, longer tenure, less interest in ethical investing, lower risk capacity, a higher percentage of males, and a higher percentage of academics than members of the ‘disengaged’ cluster. Conditioning only on the attitude to risk responses, there are 18 clusters, with similar but not identical membership, depending on which clustering method is used. The differences in risk aversion across the 18 clusters could be explained largely by differences in the percentage of females and the percentage of couples. Risk aversion increases as the percentage of females in the cluster increases, while it reduces as the percentage of couples increases because of greater risk sharing within the household. Characteristics that other studies have found important determinants of risk attitudes, such as age, income and (pension) wealth, do not turn out to be as significant for USS members. Further, despite being on average more highly educated than the general population, USS members are marginally more risk averse than the general population, controlling for salary, although the difference is not significant

Shock wave loading and spallation of copper bicrystals with asymmetric Σ3〈110〉tilt grain boundaries

We investigate the effect of asymmetric grain boundaries (GBs) on the shock response of Cu bicrystals with molecular dynamics simulations. We choose a representative Σ3〈110〉tilt GB type, (110)_1/(114)_2, and a grain size of about 15 nm. The shock loading directions lie on the GB plane and are along [001] and [221] for the two constituent crystals. The bicrystal is characterized in terms of local structure, shear strain, displacement, stress and temperature during shock compression, and subsequent release and tension. The shock response of the bicrystal manifests pronounced deviation from planar loading as well as strong stress and strain concentrations, due to GBs and the strong anisotropy in elasticity and plasticity. We explore incipient to full spallation. Voids nucleate either at GBs or on GB-initiated shear planes, and the spall damage also depends on grain orientation

One size fits all: How many default funds does a pension scheme need?

In this paper, we analyse the number of default investment funds appropriate for an occupational defined contribution pension scheme. Using a unique dataset of member risk attitudes and characteristics from a survey of a large UK pension scheme, we apply cluster analysis to identify two distinct groups of members in their 40s and 50s. Further analysis indicated that the risk attitudes of the two groups were not significantly different, allowing us to conclude that a single lifestyle default fund is appropriate

Anisotropic shock response of columnar nanocrystalline Cu

We perform molecular dynamics simulations to investigate the shock response of idealized hexagonal columnar nanocrystalline Cu, including plasticity, local shear, and spall damage during dynamic compression, release, and tension. Shock loading (one-dimensional strain) is applied along three principal directions of the columnar Cu sample, one longitudinal (along the column axis) and two transverse directions, exhibiting a strong anisotropy in the response to shock loading and release. Grain boundaries (GBs) serve as the nucleation sites for crystal plasticity and voids, due to the GB weakening effect as well as stress and shear concentrations. Stress gradients induce GB sliding which is pronounced for the transverse loading. The flow stress and GB sliding are the lowest but the spall strength is the highest, for longitudinal loading. For the grain size and loading conditions explored, void nucleation occurs at the peak shear deformation sites (GBs, and particularly triple junctions); spall damage is entirely intergranular for the transverse loading, while it may extend into grain interiors for the longitudinal loading. Crystal plasticity assists the void growth at the early stage but the growth is mainly achieved via GB separation at later stages for the transverse loading. Our simulations reveal such deformation mechanisms as GB sliding, stress, and shear concentration, GB-initiated crystal plasticity, and GB separation in nanocrystalline solids under shock wave loading

A method for rearing the predaceous mite, Phytoseilus persimilis (Acarina: Phytoseiidae)

The predaceous mite, <i>Phytoseiulus persimilis</i> Athias-Henriot, was reared successfully in a darkened growth chamber on blotting paper on a freezer carton lid floated on water in a plastic saucer. Predators were fed with two-spotted spider mites collected from infested bean leaves with a mite brushing machine

The conserved immunoglobulin domain controls the subcellular localization of the homophilic adhesion receptor protein-tyrosine phosphatase mu

The receptor protein-tyrosine phosphatase mu (PTPmu) is a homophilic adhesion protein thought to regulate cell-cell adhesion in the vascular endothelium through dephosphorylation of cell junction proteins. In subconfluent cell cultures, PTPmu resides in an intracellular membrane pool; however, as culture density increases and cell contacts form, the phosphatase localizes to sites of cell-cell contact, and its expression level increases. These characteristics of PTPmu, which are consistent with a role in cell-cell adhesion, suggest that control of subcellular localization is an important mechanism to regulate the function of this phosphatase. To gain a better understanding of how PTPmu is regulated, we examined the importance of the conserved immunoglobulin domain, containing the homophilic binding site, in control of the localization of the enzyme. Deletion of the immunoglobulin domain impaired localization of PTPmu to the cell-cell contacts in endothelial and epithelial cells. In addition, deletion of the immunoglobulin domain affected the distribution of PTPmu in subconfluent endothelial cells when homophilic binding to another PTPmu molecule on an apposing cell was not possible, resulting in an accumulation of the mutant phosphatase at the cell surface with a concentration at the cell periphery in the region occupied by focal adhesions. This aberrant localization correlated with reduced survival and alterations in normal focal adhesion and cytoskeleton morphology. This study therefore illustrates the critical role of the immunoglobulin domain in regulation of the localization of PTPmu and the importance of such control for the maintenance of normal cell physiology

Deformation and spallation of shocked Cu bicrystals with Σ3 coherent and symmetric incoherent twin boundaries

We perform molecular dynamics simulations of Cu bicrystals with two important grain boundaries (GBs), Σ3 coherent twin boundaries (CTB), and symmetric incoherent twin boundaries (SITB) under planar shock wave loading. It is revealed that the shock response (deformation and spallation) of the Cu bicrystals strongly depends on the GB characteristics. At the shock compression stage, elastic shock wave can readily trigger GB plasticity at SITB but not at CTB. The SITB can induce considerable wave attenuation such as the elastic precursor decay via activating GB dislocations. For example, our simulations of a Cu multilayer structure with 53 SITBs (∼1.5-μm thick) demonstrate a ∼80% elastic shock decay. At the tension stage, spallation tends to occur at CTB but not at SITB due to the high mobility of SITB. The SITB region transforms into a threefold twin via a sequential partial dislocation slip mechanism, while CTB preserves its integrity before spallation. In addition, deformation twinning is a mechanism for inducing surface step during shock tension stage. The drastically different shock response of CTB and SITB could in principle be exploited for, or benefit, interface engineering and materials design

Left-right loading dependence of shock response of (111)//(112) Cu bicrystals: Deformation and spallation

We investigate with molecular dynamics the dynamic response of Cu bicrystals with a special asymmetric grain boundary (GB), (111)//(112)〈110〉, and its dependence on the loading directions. Shock loading is applied along the GB normal either from the left or right to the GB. Due to the structure asymmetry, the bicrystals demonstrate overall strong left-right loading dependence of its shock response, including compression wave features, compression and tensile plasticity, damage characteristics (e.g., spall strength), effective wave speeds and structure changes, except that spallation remains dominated by the GB damage regardless of the loading directions. The presence or absence of transient microtwinning also depends on the loading directions

Dynamic response of phenolic resin and its carbon-nanotube composites to shock wave loading

We investigate with nonreactive molecular dynamics simulations the dynamic response of phenolic resin and its carbon-nanotube (CNT) composites to shock wave compression. For phenolic resin, our simulations yield shock states in agreement with experiments on similar polymers except the “phase change” observed in experiments, indicating that such phase change is chemical in nature. The elastic–plastic transition is characterized by shear stress relaxation and atomic-level slip, and phenolic resin shows strong strain hardening. Shock loading of the CNT-resin composites is applied parallel or perpendicular to the CNT axis, and the composites demonstrate anisotropy in wave propagation, yield and CNT deformation. The CNTs induce stress concentrations in the composites and may increase the yield strength. Our simulations suggest that the bulk shock response of the composites depends on the volume fraction, length ratio, impact cross-section, and geometry of the CNT components; the short CNTs in current simulations have insignificant effect on the bulk response of resin polymer