Partial duals of plane graphs, separability and the graphs of knots

There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While every plane graph arises as a Tait graph of a unique link diagram, not every embedded graph represents a link diagram. Furthermore, although a Tait graph describes a unique link diagram, the same embedded graph can represent many different link diagrams. One is then led to ask which embedded graphs represent link diagrams, and how link diagrams presented by the same embedded graphs are related to one another. Here we answer these questions by characterizing the class of embedded graphs that represent link diagrams, and then using this characterization to find a move that relates all of the link diagrams that are presented by the same set of embedded graphs.Comment: v2: major change

The risk-free rate in heterogeneous-agent, incomplete-insurance economies

Includes bibliographical references (p. 16-18)

The apparatus of digital archaeology

Digital Archaeology is predicated upon an ever-changing set of apparatuses – technological, methodological, software, hardware, material, immaterial – which in their own ways and to varying degrees shape the nature of Digital Archaeology. Our attention, however, is perhaps inevitably more closely focussed on research questions, choice of data, and the kinds of analyses and outputs. In the process we tend to overlook the effects the tools themselves have on the archaeology we do beyond the immediate consequences of the digital. This paper introduces cognitive artefacts as a means of addressing the apparatus more directly within the context of the developing archaeological digital ecosystem. It argues that a critical appreciation of our computational cognitive artefacts is key to understanding their effects on both our own cognition and on the creation of archaeological knowledge. In the process, it defines a form of cognitive digital archaeology in terms of four distinct methods for extracting cognition from the digital apparatus layer by layer

Reuse remix recycle: repurposing archaeological digital data

Preservation of digital data is predicated on the expectation of its reuse, yet that expectation has never been examined within archaeology. While we have extensive digital archives equipped to share data, evidence of reuse seems paradoxically limited. Most archaeological discussions have focused on data management and preservation and on disciplinary practices surrounding archiving and sharing data. This article addresses the reuse side of the data equation through a series of linked questions: What is the evidence for reuse, what constitutes reuse, what are the motivations for reuse, and what makes some data more suitable for reuse than others? It concludes by posing a series of questions aimed at better understanding our digital engagement with archaeological data

Skeptical Notes on a Physics of Passage

This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question of the paper is whether the existing representation of time is adequate, or whether it can or should be supplemented: especially, do we need a physics incorporating some kind of `dynamical passage' of time? The paper argues that the existing mathematical framework is resistant to such changes, and might have to be rejected by anyone seeking a physics of passage. Then it rebuts two common arguments for incorporating passage into physics, especially the claim that it is an element of experience. Finally the paper investigates whether, as has been claimed, `causal set theory' provides a physics of passage.Comment: 14 page

When are Comparative Dynamics Monotone?

A common problem in dynamic economic theory is to determine when an increase in a parameter and/or an initial condition increases the future dynamics of a theoretical economy. This paper provides conditions that are necessary and sufficient for making statements of this type. The result is applicable to situations with a single agent or with many agents in the presence or absence of uncertainty. The result holds for general notions of what it means for a parameter, an initial condition or even the dynamics of a model to be increasing.

Human Capital and Earnings Distribution Dynamics

Earnings heterogeneity plays a crucial role in modern macroeconomics. We document that mean earnings and measures of earnings dispersion and skewness all increase in US data over most of the working life-cycle for a typical cohort as the cohort ages. We show that a human capital model can replicate these properties from the right distribution of initial human capital and learning ability, while producing the key properties of the cross-section distribution. We also show that learning ability differences are essential to produce the increase in earnings dispersion over the life cycle and that these differences account for the bulk of the variation in the present value of earnings across agents. These findings emphasize the need to further understand the role and origins of initial conditions in macro models.Precautionary wealth, earnigs risk, multi-period models

Out of Nowhere: Spacetime from causality: causal set theory

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian W\"uthrich and under contract with Oxford University Press. (More information at www.beyondspacetime.net.) This chapter introduces causal set theory and identifies and articulates a 'problem of space' in this theory.Comment: 29 pages, 5 figure