The Tandem Duplication Distance Is NP-Hard

In computational biology, tandem duplication is an important biological phenomenon which can occur either at the genome or at the DNA level. A tandem duplication takes a copy of a genome segment and inserts it right after the segment - this can be represented as the string operation AXB ? AXXB. Tandem exon duplications have been found in many species such as human, fly or worm, and have been largely studied in computational biology. The Tandem Duplication (TD) distance problem we investigate in this paper is defined as follows: given two strings S and T over the same alphabet, compute the smallest sequence of tandem duplications required to convert S to T. The natural question of whether the TD distance can be computed in polynomial time was posed in 2004 by Leupold et al. and had remained open, despite the fact that tandem duplications have received much attention ever since. In this paper, we prove that this problem is NP-hard, settling the 16-year old open problem. We further show that this hardness holds even if all characters of S are distinct. This is known as the exemplar TD distance, which is of special relevance in bioinformatics. One of the tools we develop for the reduction is a new problem called the Cost-Effective Subgraph, for which we obtain W[1]-hardness results that might be of independent interest. We finally show that computing the exemplar TD distance between S and T is fixed-parameter tractable. Our results open the door to many other questions, and we conclude with several open problems

International Macroeconomic Policy: When Wealth Affects People's Impatience

Under a modified neo-classical framework, this paper reexamined the effect of international macroeconomic policies by rejecting the routine assumption of a constant rate of time preference. In the model presented here, we suppose the holdings of real financial wealth will affect people's impatience which has far-reaching implications towards various core issues in international macroeconomics. The introducing of wealth into instantaneous discounting function yields intriguing dynamics of consumption, real balances, and foreign bond holdings. One interesting feature of our model is that stationary rate of time preference no longer necessarily equals real interest rate. We also find that central bank's foreign exchange intervention is not super-neutral even if households capitalize all transfers from the government, which contradicts Obstfeld(1981) in that the distribution of the economy¡¯s claims on the rest of the world between the public and the central bank is relevant to the economic performance. The monetary policy affects the real factors, but how the economy behaves in the long run and in the short run differs a lot from Uzawa(1968) and Obstfeld(1981).international macroeconomic policy, impatience, foreign exchange, monetary policy

When Wealth Affects People's Impatience

Zou [1994] has proved that the spirit of capitalism will cause endogenous growth using the AK model. We find that this conclusion needs to be reexamined under our endogenous time preference model. Contrastingly different patterns of growth will obtain under our framework.

Capital Accumulation And Present-biased Preference

This paper reexamines the capital accumulation within a neo-classical growth model under the assumption of hyperbolic discounting as well as endogenous preference, finding that 1) two kinds of Naifs¡¯ behavior coincides under log utility; 2) increasing marginal impatience due to capital accumulation itself will negatively affect the steady state locus of consumption and capital; 3) the effect of hyperbolic settings through effective rate of preference is still ambiguous; 4) we prove the saddle-point equilibrium property for the steady state under various assumptions about individual¡¯s preference. Our model also justifies Max Weber's idea that although spirit of capitalism is an engine to capital accumulation, the subsequent growing wealth will damage this engine.hyperbolic discounting, time-inconsistent, capital accumulation, spirit of capitalism