Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation

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 second part of two papers, we give the general categorical formulation

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

Network Centrality and Delegated Investment Performance

We document a positive relation between network centrality and risk-adjusted performance in a delegated investment management setting. More connected managers take more portfolio risk and receive higher investor flows, consistent with these managers improving their ability to exploit investment opportunities through their network connections. Greater network connections are shown to be particularly important in reducing the diseconomies-of-scale for large managers who are well-connected. We also use the exogenous merger of two investment consultants, which creates a sudden change in the network connections of the managers they oversee, to provide evidence that a greater number of connections translates into better portfolio performance

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.Comment: 14 page

Towards granular hydrodynamics in two-dimensions

We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions compare well with numerical simulations in the nearly elastic limit. It is also seen that the system can achieve a nonequilibrium steady-state with asymmetric velocity distributions, and we discuss the conditions under which such situations occur.Comment: 8 pages, 9 figures, revtex, references added, also available from http://arnold.uchicago.edu/?ebn

Dynamics of the Free Surface of a Conducting Liquid in a Near-Critical Electric Field

Near-critical behavior of the free surface of an ideally conducting liquid in an external electric field is considered. Based on an analysis of three-wave processes using the method of integral estimations, sufficient criteria for hard instability of a planar surface are formulated. It is shown that the higher-order nonlinearities do not saturate the instability, for which reason the growth of disturbances has an explosive character.Comment: 19 page

Smart defaults: Determining the number of default funds in a pension scheme

We propose a new methodology for the smart design of the default investment fund(s) in occupational defined contribution pension schemes based on the observable characteristics of scheme members. Using a unique dataset of member risk attitudes and characteristics from a survey of a large UK pension scheme, we apply factor analysis to identify single factors for risk aversion, risk capacity and ethical investment preferences, and then apply cluster analysis to these factors to identify two distinct groups of members across age cohorts. We find membership of these clusters depends on a number of personal characteristics, with the principal differentiating feature being that one group had previously engaged with the pension scheme, while the other had not. These identified characteristics can be utilised in the design of smart default funds, including appropriate engagement strategies

KP line solitons and Tamari lattices

The KP-II equation possesses a class of line soliton solutions which can be qualitatively described via a tropical approximation as a chain of rooted binary trees, except at "critical" events where a transition to a different rooted binary tree takes place. We prove that these correspond to maximal chains in Tamari lattices (which are poset structures on associahedra). We further derive results that allow to compute details of the evolution, including the critical events. Moreover, we present some insights into the structure of the more general line soliton solutions. All this yields a characterization of possible evolutions of line soliton patterns on a shallow fluid surface (provided that the KP-II approximation applies).Comment: 49 pages, 36 figures, second version: section 4 expande

Selective activation of oxidized PTP1B by the thioredoxin system modulates PDGF-ß receptor tyrosine kinase signaling

The inhibitory reversible oxidation of protein tyrosine phosphatases (PTPs) is an important regulatory mechanism in growth factor signaling. Studies on PTP oxidation have focused on pathways that increase or decrease reactive oxygen species levels and thereby affect PTP oxidation. The processes involved in reactivation of oxidized PTPs remain largely unknown. Here the role of the thioredoxin (Trx) system in reactivation of oxidized PTPs was analyzed using a combination of in vitro and cell-based assays. Cells lacking the major Trx reductase TrxR1 (Txnrd1-/-) displayed increased oxidation of PTP1B, whereas SHP2 oxidation was unchanged. Furthermore, in vivo-oxidized PTP1B was reduced by exogenously added Trx system components, whereas SHP2 oxidation remained unchanged. Trx1 reduced oxidized PTP1B in vitro but failed to reactivate oxidized SHP2. Interestingly, the alternative TrxR1 substrate TRP14 also reactivated oxidized PTP1B, but not SHP2. Txnrd1-depleted cells displayed increased phosphorylation of PDGF-ß receptor, and an enhanced mitogenic response, after PDGF-BB stimulation. The TrxR inhibitor auranofin also increased PDGF-ß receptor phosphorylation. This effect was not observed in cells specifically lacking PTP1B. Together these results demonstrate that the Trx system, including both Trx1 and TRP14, impacts differentially on the oxidation of individual PTPs, with a preference of PTP1B over SHP2 activation. The studies demonstrate a previously unrecognized pathway for selective redox-regulated control of receptor tyrosine kinase signaling