Nonlinear softening as a predictive precursor to climate tipping

Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious in the presence of noisy disturbances. We consider an underlying potential, as defined theoretically for a saddle-node fold and (via averaging) for a Hopf bifurcation. Close to a stable state, this potential has a parabolic form; but approaching a jump it becomes increasingly dominated by softening nonlinearities. If we have already detected a decrease in the linear decay rate, nonlinear information allows us to estimate the propensity for early tipping due to noise. We argue that one needs to extract information about the nonlinear features (a "softening") of the underlying potential from the time series to judge the probability and timing of tipping. This analysis is the logical next step if one has detected a decrease of the linear decay rate. If there is no discernable trend in the linear analysis, nonlinear softening is even more important in showing the proximity to tipping. After extensive normal form calibration studies, we check two geological time series from paleo-climate tipping events for softening of the underlying well. For the ending of the last ice age, where we find no convincing linear precursor, we identify a statistically significant nonlinear softening towards increasing temperature. The analysis has thus successfully detected a warning of the imminent tipping event.Comment: 22 pages, 11 figures, changed title back, corrected smaller mistakes, updated reference

A short note on the multiplier ideals of monomial space curves

Thompson (2014) exhibits a formula for the multiplier ideal with multiplier lambda of a monomial curve C with ideal I as an intersection of a term coming from the I-adic valuation, the multiplier ideal of the term ideal of I, and terms coming from certain specified auxiliary valuations. This short note shows it suffices to consider only one auxiliary valuation. This improvement is achieved through a more intrinsic approach, reduction to the toric case.Comment: This version adds Corollary 10 and fixes several typo

Land Law – The fight against gazumping

Professor M.P. Thompson (University of Leicester) considers the background and needs for the government review of conveyancing procedures in England and Wales which has focussed on stamping out the practice of gazumping. Note published in Amicus Curiae - Journal of the Institute of Advanced Legal Studies and its Society for Advanced Legal Studies. The Journal is produced by the Society for Advanced Legal Studies at the Institute of Advanced Legal Studies, University of London

Is the Internet a Viable Threat to Representative Democracy?

The Internet, despite its relatively recent advent, is critical to millions of Americans’ way of life. Although the Internet arguably opens new opportunities for citizens to become more directly involved in their government, some scholars fear this direct involvement poses a risk to one of the Constitution’s most precious ideals: representative democracy. This iBrief explores whether the constitutional notion of representation is vulnerable to the Internet’s capacity to open new vistas for a more direct democracy by analyzing statistics and theories about why voters in the United States do or do not vote and by examining the inherent qualities of the Internet itself. This iBrief concludes that the Constitution will adapt to the Internet and the Internet to the Constitution, such that even if there are advances in direct democracy, representative democracy will not be unduly threatened

AdS Solutions of 2D Type 0A

We present a two-parameter family of AdS solutions to the two-dimensional type 0A effective action.Comment: 9 page

Wittgenstein's Contributions to Philosophy

Any discussion of Wittgenstein's philosophical thought would be incomplete without taking notice of the method he employs. Often criticized for his style and organization, many feel that they are indicative of his state of mind; that such a lack of rigid argumentation betrays an inadequacy within the arguments themselves. However, criticism of Wittgenstein along these lines only serves to demonstrate a superficial reading of his texts. Not simply content (or even able) to just present us with the results of his investigations, Wittgenstein coaxes the reader into taking up an investigation of his own by means of an open dialogue. As a dialogue, we are not confronted with a traditional argumentative structure, i.e. the stating of theses and their subsequent defense. Rather, Wittgenstein attempts to draw the reader away from the obvious by means of an indirect method of discourse

Toric singularities revisited

In [Kat94b], Kato defined his notion of a log regular scheme and studied the local behavior of such schemes. A toric variety equipped with its canonical logarithmic structure is log regular. And, these schemes allow one to generalize toric geometry to a theory that does not require a base field. This paper will extend this theory by removing normality requirements.Comment: new longer introduction, other minor improvements, 35 page