Contractions and expansion

Let A be a finite set of reals and let K >= 1 be a real number. Suppose that for each a in A we are given an injective map f_a : A -> R which fixes a and contracts other points towards it in the sense that |a - f_a(x)| <= |a - x|/K for all x in A, and such that f_a(x) always lies between a and x. Then the union of the f_a(A) has cardinality >= K|A|/10 - O_K(1). An immediate consequence of this is the estimate |A + K.A| >= K|A|/10 - O_K(1), which is a slightly weakened version of a result of Bukh.Comment: 6 pages, submitted to special volume of EJC in honour of Yahya Hamidoun

The duration of business cycle expansions and contractions: Are there change-points in duration dependence?

The issue of whether the likelihood of an expansion or contraction ending is dependent on its age, i.e whether they are duration dependent, is widely addressed in the business cycles literature and evidence of positive duration dependence is found in several studies. However, there is an important issue that has not been explored in this literature yet: the presence of change-points in duration dependence. All the studies in this field depart from the assumption that the magnitude of duration dependence is the same over time. However, we conjecture that the degree of likeliness of an expansion or contraction ending as it gets older might change after a specific duration. To test for that possibility, this paper will allow for the presence of a change-point in the analysis of the duration of expansions and contractions for a group of 13 European and Non-European industrial countries over the period 1948-2009. The evidence provided by the estimation of a continuous-time Weibull duration model shows strong support for the presence of positive duration dependence, which is stronger for contractions than for expansions. Results also show that contractions have become longer over time and that their length is negatively a¤ected by the length of the previous expansion. Most importantly, this paper provides quite interesting evidence for the presence of a change-point in duration dependence for expansions, but not for contractions. Results show that the magnitude of the duration dependence parameter decreases signi.cantly when an expansion surpasses 10 years of duration. In particular, evidence of positive duration dependence is no longer found when an expansion surpasses that threshold.business cycles; expansions; contractions; duration dependence.

The duration of business cycle expansions and contractions: Are there change-points in duration dependence?

The issue of whether the likelihood of an expansion or contraction ending is dependent on its age,i.e whether they are duration dependent, is widely addressed in the business cycles literature and evidence of positive duration dependence is found in several studies. However, there is an important issue that has not been explored in this literature yet: the presence of change-points in duration dependence. All the studies in this field depart from the assumption that the magnitude of duration dependence is the same over time. However, we conjecture that the degree of likeliness of an expansion or contraction ending as it gets older might change after a specific duration. To test for that possibility, this paper will allow for the presence of a change-point in the analysis of the duration of expansions and contractions for a group of 13 European and Non-European industrial countries over the period 1948-2009. The evidence provided by the estimation of a continuous-time Weibull duration model shows strong support for the presence of positive duration dependence, which is stronger for contractions than for expansions. Results also show that contractions have become longer over time and that their length is negatively affected by the length of the previous expansion. Most importantly, this paper provides quite interesting evidence for the presence of a change-point in duration dependence for expansions, but not for contractions. Results show that the magnitude of the duration dependence parameter decreases significantly when an expansion surpasses 10 years of duration. In particular, evidence of positive duration dependence is no longer found when an expansion surpasses that threshold.business cycles; expansions; contractions; duration dependence.

Expansions of algebras and superalgebras and some applications

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the Inonu-Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).Comment: Invited lecture delivered at the 'Deformations and Contractions in Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches Forschungsinstitut Oberwolfach, German

Financial Sector Ups and Downs and the Real Sector: Up by the stairs, down by the parachute

We examine how financial expansion and contraction cycles affect the broader economy through their impact on real economic sectors in a panel of countries over 1960–2005. Periods of accelerated growth of the financial sector are more likely to be followed by abrupt financial contractions than are periods of slower financial sector growth. Sharp fluctuations in the financial sector have strongly asymmetric effects, with the majority of real sectors adversely affected by contractions, but not helped by expansions. The adverse effects of financial contractions are transmitted almost exclusively through the financial openness channel, with precautionary foreign exchange reserve holdings serving as a key buffer.

Simple Mathematical Model Of Pathologic Microsatellite Expansions: When Self-Reparation Does Not Work

We propose a simple model of pathologic microsatellite expansion, and describe an inherent self-repairing mechanism working against expansion. We prove that if the probabilities of elementary expansions and contractions are equal, microsatellite expansions are always self-repairing. If these probabilities are different, self-reparation does not work. Mosaicism, anticipation and reverse mutation cases are discussed in the framework of the model. We explain these phenomena and provide some theoretical evidence for their properties, for example the rarity of reverse mutations

Financial sector ups and downs and the real sector : big hindrance, little help

This paper examines how financial expansion and contraction cycles affect the broader economy through their impact on eight real economic sectors in a panel of 28 countries over 1960-2005, paying particular attention to large, or sharp, contractions and magnifying and mitigating factors. Overall, the construction sector is the most responsive to financial sector growth, with a number of others -- such as government, public utilities, and transportation -- also exhibiting significant sensitivity to lagged financial sector growth. Sharp fluctuations in the financial sector have asymmetric effects, with the majority of real sectors adversely affected by contractions but not helped by expansions. The adverse effects of financial contractions are transmitted almost exclusively by the financial openness channel with foreign reserves mitigating these effects with a sizeable (10 to 15 times greater) impact during sharp financial contractions. Both effects are magnified during particularly large financial contractions (with coefficients on interaction terms two to three times greater than when all contractions are considered). Consequent upon a financial contraction, the most severe real sector contractions occur in countries with high financial openness; relative predominance of construction, manufacturing, and wholesale and retail sectors; and low international reserves. Finally, the analysis finds that abrupt financial contractions are more likely to follow periods of accelerated growth, indicative of"up by the stairs, down by the elevator dynamics."Economic Theory&Research,Achieving Shared Growth,Emerging Markets,Currencies and Exchange Rates,Debt Markets

Domain wall dynamics in expanding spaces

We study the effects on the dynamics of kinks due to expansions and contractions of the space. We show that the propagation velocity of the kink can be adiabatically tuned through slow expansions/contractions, while its width is given as a function of the velocity. We also analyze the case of fast expansions/contractions, where we are no longer on the adiabatic regime. In this case the kink moves more slowly after an expansion-contraction cycle as a consequence of loss of energy through radiation. All these effects are numerically studied in the nonlinear Klein-Gordon equations (both for the sine-Gordon and for the phi^4 potential), and they are also studied within the framework of the collective coordinate evolution equations for the width and the center of mass of the kink. These collective coordinate evolution equations are obtained with a procedure that allows us to consider even the case of large expansions/contractions.Comment: LaTeX, 18 pages, 2 figures, improved version to appear in Phys Rev

Discordant City Employment Cycles

The national economy is often described as having a business cycle over which aggregate output enters and exits distinct expansion and recession phases. Analogously, national employment cycles in and out of its own expansion and contraction phases, which are closely related to the business cycle. This paper estimates city-level employment cycles for 58 large U.S. cities and documents the substantial cross-city variation in the timing, lengths, and frequencies of their employment contractions. It also shows how the spread of city-level contractions associated with U.S. recessions has tended to follow recession-specific geographic patterns. In addition, cities within the same state or region have tended to have similar employment cycles. There is no evidence, however, that similarities in employment cycles are related to similarities in industry mix. This suggests that the U.S. employment and business cycles has a spatial dimension that is independent of broad industry-level fluctuations.