Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system

Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here a novel class of tipping points, where a sufficiently rapid change to an input or parameter of a system may cause the system to "tip" or move away from a branch of attractors. Such rate-dependent tipping, or R-tipping, need not be associated with either bifurcations or noise. We present an example of all three types of tipping in a simple global energy balance model of the climate system, illustrating the possibility of dangerous rates of change even in the absence of noise and of bifurcations in the underlying quasi-static system.Comment: 20 pages, 8 figure

Devaluation Crises and the Macroeconomic Consequences of Postponed Adjustment in Developing Countries

This paper develops our analytical model to explore the relationship between the dynamics of macroeconomic adjustment and the timing of the implementation of an adjustment program featuring an official devaluation. The effects of postponing adjustment depend on the source of the original shock, In the case of fiscal expansion, postponement implies a larger eventual official devaluation and greater deviations of macroeconomic variables from their steady-state values. For adverse terms of trade shocks, postponement does not affect the size of the eventual official devaluation, but does magnify the amount of post-devaluation overshooting by key macroeconomic variables.

A practical approach to offset permits in post Kyoto climate policy

International Carbon Offsets from developing countries and emerging economies such as permits from the Clean Development Mechanism (CDM) will potentially play an important role for cost containment in domestic greenhouse gas regulation schemes in industrialised countries. We analyse the potential role of offset permits assuming that major emitters such as the USA, Canada, Japan, Australia and New Zealand install domestic greenhouse gas regulation schemes to achieve the emissions reductions pledged in the Copenhagen Accord and seek cost containment. We estimate a potential demand for offset permits of 627 to 667 MtCO2e p.a. from industrialised countries. To describe the supply structure, we derive marginal abatement cost curves for developing countries and emerging economies. We find that developing countries and emerging economies can supply 627 to 667 MtCO2e p.a. at costs of approximately EUR 10 (in 2004 EUR), neglecting transaction costs and country specific risks. The highest potentials for the generation of carbon offsets are present in China, India and the rest of Asia. --emissions trading,offsets,CDM,marginal abatement costs,climate policy

Measures of Predictive Success for Rating Functions

Aim of our paper is to develop an adequate measure of predictive success and accuracy of rating functions. At first, we show that the common measures of rating accuracy, i.e. area under curve and accuracy ratio, respectively, lack of informative value of single rating classes. Selten (1991) builds up an axiomatic framework for measures of predictive success. Therefore, we introduce a measure for rating functions that fulfills the axioms proposed by Selten (1991). Furthermore, an empirical investigation analyzes predictive power and accuracy of Standard & Poor's and Moody's ratings, and compares the rankings according to area under curve and our measure.Accuracy Measure, Rating Functions, Predictive Success, Discriminative Power

A graph partition problem

Given a graph $G$ on $n$ vertices, for which $m$ is it possible to partition the edge set of the $m$-fold complete graph $mK_n$ into copies of $G$? We show that there is an integer $m_0$, which we call the \emph{partition modulus of $G$}, such that the set $M(G)$ of values of $m$ for which such a partition exists consists of all but finitely many multiples of $m_0$. Trivial divisibility conditions derived from $G$ give an integer $m_1$ which divides $m_0$; we call the quotient $m_0/m_1$ the \emph{partition index of $G$}. It seems that most graphs $G$ have partition index equal to $1$, but we give two infinite families of graphs for which this is not true. We also compute $M(G)$ for various graphs, and outline some connections between our problem and the existence of designs of various types

Deep Directional Statistics: Pose Estimation with Uncertainty Quantification

Modern deep learning systems successfully solve many perception tasks such as object pose estimation when the input image is of high quality. However, in challenging imaging conditions such as on low-resolution images or when the image is corrupted by imaging artifacts, current systems degrade considerably in accuracy. While a loss in performance is unavoidable, we would like our models to quantify their uncertainty in order to achieve robustness against images of varying quality. Probabilistic deep learning models combine the expressive power of deep learning with uncertainty quantification. In this paper, we propose a novel probabilistic deep learning model for the task of angular regression. Our model uses von Mises distributions to predict a distribution over object pose angle. Whereas a single von Mises distribution is making strong assumptions about the shape of the distribution, we extend the basic model to predict a mixture of von Mises distributions. We show how to learn a mixture model using a finite and infinite number of mixture components. Our model allows for likelihood-based training and efficient inference at test time. We demonstrate on a number of challenging pose estimation datasets that our model produces calibrated probability predictions and competitive or superior point estimates compared to the current state-of-the-art