Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra 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, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework, which is presented step-by-step with examples throughout. In this first part of two papers, we concentrate on the simplicial and operadic aspects.Comment: This replacement is part I of the final version of the paper, which has been split into two parts. The second part is available from the arXiv under the title "Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation" arXiv:2001.0872

Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra 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, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework, which is presented step-by-step with examples throughout. In this first part of two papers, we concentrate on the simplicial and operadic aspectsPeer ReviewedPostprint (author's final draft

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

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

Amine, Amido, and Imido Complexes of Tantalum Supported by a Pyridine-Linked Bis(phenolate) Pincer Ligand: Ta−N π-Bonding Influences Pincer Ligand Geometry

A series of tantalum imido and amido complexes supported by a pyridine-linked bis(phenolate) ligand has been synthesized. Characterization of these complexes via X-ray crystallography reveals both C_s and C_2 binding modes of the bis(phenolate)pyridine ligand, with complexes containing two or fewer strong π-donor interactions from ancillary ligands giving C_s symmetry, whereas three strong π-donor interactions (e.g., three amido ligands or one amido ligand and one imido ligand) give C_2-symmetric binding of the bis(phenolate)pyridine ligand. DFT calculations and molecular orbital analyses of the complexes have revealed that the preference for C_s-symmetric ligand binding is a result of tantalum−phenolate π-bonding, whereas in cases where tantalum−phenolate π-bonding is overridden by stronger Ta−N π-bonding, C_2-symmetric ligand binding is preferred, likely because conformationally this is the lowest-energy arrangement. This electronically driven change in geometry indicates that, unlike analogous metallocene systems, the bis(phenolate)pyridine pincer ligand is not a strong enough π-donor to exert dominant control over the electronic and geometric properties of the complex

Homophilic binding of PTP mu, a receptor-type protein tyrosine phosphatase, can mediate cell-cell aggregation

The receptor-like protein tyrosine phosphatase, PTPmu, displays structural similarity to cell-cell adhesion molecules of the immunoglobulin superfamily. We have investigated the ability of human PTPmu to function in such a capacity. Expression of PTPmu, with or without the PTPase domains, by recombinant baculovirus infection of Sf9 cells induced their aggregation. However, neither a chimeric form of PTPmu, containing the extracellular and transmembrane segments of the EGF receptor and the intracellular segment of PTPmu, nor the intracellular segment of PTPmu expressed as a soluble protein induced aggregation. PTPmu mediates aggregation via a homophilic mechanism, as judged by lack of incorporation of uninfected Sf9 cells into aggregates of PTPmu-expressing cells. Homophilic binding has been demonstrated between PTPmu-coated fluorescent beads (Covaspheres) and endogenously expressed PTPmu on MvLu cells. Additionally the PTPmu-coated beads specifically bound to a bacterially expressed glutathione-S-transferase fusion protein containing the extracellular segment of PTPmu (GST/PTPmu) adsorbed to petri dishes. Covaspheres coated with the GST/PTPmu fusion protein aggregated in vitro and also bound to PTPmu expressed endogenously on MvLu cells. These results suggest that the ligand for this transmembrane PTPase is another PTPmu molecule on an adjacent cell. Thus homophilic binding interactions may be an important component of the function of PTPmu in vivo

Test of a Jastrow-type wavefunction for a trapped few-body system in one dimension

For a system with interacting quantum mechanical particles in a one-dimensional harmonic oscillator, a trial wavefunction with simple structure based on the solution of the corresponding two-particle system is suggested and tested numerically. With the inclusion of a scaling parameter for the distance between particles, at least for the very small systems tested here the ansatz gives a very good estimate of the ground state energy, with the error being of the order of ~1% of the gap to the first excited state

The risk assessment of ERTMS-based railway systems from a cyber security perspective: Methodology and lessons learned

The impact that cyber issues might have on the safety and resilience of railway systems has been studied for more than five years by industry specialists and government agencies. This paper presents some of the work done by Adelard in this area, ranging from an analysis of potential vulnerabilities in the ERTMS specifications through to a high-level cyber security risk assessment of a national ERTMS implementation and detailed analysis of particular ERTMS systems on behalf of the GB rail industry. The focus of the paper is on our overall methodology for security-informed safety and hazard analysis. Lessons learned will be presented but of course our detailed results remain proprietary or sensitive and cannot be published