Chromatic polynomials of complements of bipartite graphs

Bicliques are complements of bipartite graphs; as such each consists of two cliques joined by a number of edges. In this paper we study algebraic aspects of the chromatic polynomials of these graphs. We derive a formula for the chromatic polynomial of an arbitrary biclique, and use this to give certain conditions under which two of the graphs have chromatic polynomials with the same splitting field. Finally, we use a subfamily of bicliques to prove the cubic case of the $\alpha +n$ conjecture, by showing that for any cubic integer $\alpha$, there is a natural number $n$ such that $\alpha +n$ is a chromatic root.Comment: 15 pages; significantly revised and expanded (with thanks to the referees). To appear in Graphs and Combinatoric

The slippage paradox

Buying or selling assets leads to transaction costs for the investor. On one hand, it is well know to all market practionaires that the transaction costs are positive on average and present therefore systematic loss. On the other hand, for every trade, there is a buy side and a sell side, the total amount of asset and the total amount of cash is conserved. I show, that the apparently paradoxical observation of systematic loss of all participants is intrinsic to the trading process since it corresponds to a correlation of outstanding orders and price changes

Topological interactions between ring polymers: Implications for chromatin loops

Chromatin looping is a major epigenetic regulatory mechanism in higher eukaryotes. Besides its role in transcriptional regulation, chromatin loops have been proposed to play a pivotal role in the segregation of entire chromosomes. The detailed topological and entropic forces between loops still remain elusive. Here, we quantitatively determine the potential of mean force between the centers of mass of two ring polymers, i.e. loops. We find that the transition from a linear to a ring polymer induces a strong increase in the entropic repulsion between these two polymers. On top, topological interactions such as the non-catenation constraint further reduce the number of accessible conformations of close-by ring polymers by about 50%, resulting in an additional effective repulsion. Furthermore, the transition from linear to ring polymers displays changes in the conformational and structural properties of the system. In fact, ring polymers adopt a markedly more ordered and aligned state than linear ones. The forces and accompanying changes in shape and alignment between ring polymers suggest an important regulatory function of such a topology in biopolymers. We conjecture that dynamic loop formation in chromatin might act as a versatile control mechanism regulating and maintaining different local states of compaction and order.Comment: 12 pages, 11 figures. The article has been accepted by The Journal Of Chemical Physics. After it is published, it will be found at http://jcp.aip.or

Public Finance under Political Instability and Debt Conditionality

This paper presents an intertemporal political economy model of sustainable public finance relevant for many developing or transition countries: instability is inherent to the political structure and foreign debt is a crucial source of government revenue. The main results are: First, political instability causes myopic government behaviour as it induces higher debt levels, but it does not lead to an increase in inflation taxation as in Cukierman, et al. (1992). Second, debt conditionality aiming at monetary stability is particularly effective in heterogeneous societies with unstable governments. Third, it is shown that IMF policies requiring debtor countries to achieve both monetary and fiscal stability are suboptimal.

The Sustainability of Fiscal Policy in the United States

The paper examines the sustainability of U.S. fiscal policy, finding substantial evidence in favor. I summarize the U.S. fiscal record from 1792-2003, critically review sustainability conditions and their testable implications, and apply them to U.S. data. I particularly emphasize the ramifications of economic growth. A “growth dividend” has historically covered the entire interest bill on the U.S. debt. Unit root tests on real series, unscaled by GDP, are distorted by the series’ severe heteroskedasticity. The most credible evidence in favor of sustainability is the robust positive response of primary surpluses to fluctuations in the debt-GDP ratio.public debt, sustainability, primary surplus, unit root

Greed, Impatience and Exchange Rate Determination

This paper offers a theoretical explanation for the determination of exchange rates under specific conditions which can/could be found in some OECD and newly industrialised countries. In an Obstfeld (1994) framework extended to incorporate government expropriation reneging on a fixed exchange rate promise unambiguously produces short term benefits, but long term losses. The choice of exchange rate regime depends on the combined effect of greediness (expropriation) and impatience (political instability), though not straightforwardly. In particular, similarly stable countries may choose different exchange rate regimes due to different levels of rent-seeking, for instance Mexico and Chile in the 1980s.exchange rate regime, monetary policy, fiscal policy, expropriation, political instability, political economy

The slippage paradox

Buying or selling assets leads to transaction costs for the investor. On one hand, it is well know to all market practionaires that the transaction costs are positive on average and present therefore systematic loss. On the other hand, for every trade, there is a buy side and a sell side, the total amount of asset and the total amount of cash is conserved. I show, that the apparently paradoxical observation of systematic loss of all participants is intrinsic to the trading process since it corresponds to a correlation of outstanding orders and price changes.