The distributional consequences of tax reforms under capital-skill complementarity

This paper analyses wage inequality and the welfare effects of changes in capital and labour income tax rates for different types of agents. To achieve this, we develop a model that allows for capital–skill complementarity given non-uniform distributions of asset holdings and labour skills. We find that capital tax reductions lead to the highest aggregate welfare gains but are skill-biased and thus increase inequality. However, our analysis also shows that the inequality effects of capital tax reductions are lower over the transition period compared with the long run

The semi-discrete AKNS system: Conservation laws, reductions and continuum limits

In this paper, the semi-discrete Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy is shown in spirit composed by the Ablowitz-Ladik flows under certain combinations. Furthermore, we derive its explicit Lax pairs and infinitely many conservation laws, which are non-trivial in light of continuum limit. Reductions of the semi-discrete AKNS hierarchy are investigated to include the semi-discrete Korteweg-de Vries (KdV), the semi-discrete modified KdV, and the semi-discrete nonlinear Schr\"odinger hierarchies as its special cases. Finally, under the uniform continuum limit we introduce in the paper, the above results of the semi-discrete AKNS hierarchy, including Lax pairs, infinitely many conservation laws and reductions, recover their counterparts of the continuous AKNS hierarchy

A Recipe for State Dependent Distributed Delay Differential Equations

We use the McKendrick equation with variable ageing rate and randomly distributed maturation time to derive a state dependent distributed delay differential equation. We show that the resulting delay differential equation preserves non-negativity of initial conditions and we characterise local stability of equilibria. By specifying the distribution of maturation age, we recover state dependent discrete, uniform and gamma distributed delay differential equations. We show how to reduce the uniform case to a system of state dependent discrete delay equations and the gamma distributed case to a system of ordinary differential equations. To illustrate the benefits of these reductions, we convert previously published transit compartment models into equivalent distributed delay differential equations.Comment: 28 page

Higher dimensional Kaluza-Klein Monopoles

It is well known that the Kaluza-Klein monopole of Sorkin, Gross and Perry can be obtained from the Euclidean Taub-NUT solution with an extra compact fifth spatial dimension via Kaluza-Klein reduction. In this paper we consider Taub-NUT-like solutions of the vacuum Einstein field equations, with or without cosmological constant, in five dimensions and higher, and similarly perform Kaluza-Klein reductions to obtain new magnetic KK brane solutions in higher dimensions, as well as further sphere reductions to magnetic monopoles in four dimensions. In six dimensions we also employ spatial and timelike Hopf dualities to untwist the circle fibration characteristic to these spaces and obtain charged strings. A variation of these methods in ten dimensions leads to a non-uniform electric string in five-dimensions.Comment: 28 pages, Latex, v.2 Typos corrected, references added. To appear in Nucl. Phys.

The First-Order Theory of Ground Tree Rewrite Graphs

We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.Comment: accepted for Logical Methods in Computer Scienc

Pseudo-random generators and structure of complete degrees

It is shown that, if there exist sets in E (the exponential complexity class) that require 2Ω(n)-sized circuits, then sets that are hard for class P (the polynomial complexity class) and above, under 1-1 reductions, are also hard under 1-1 size-increasing reductions. Under the assumption of the hardness of solving the RSA (Rivest-Shamir-Adleman, 1978) problem or the discrete log problem, it is shown that sets that are hard for class NP (nondeterministic polynomial) and above, under many-1 reductions, are also hard under (non-uniform) 1-1 and size-increasing reductions

New Insights on the (Non-)Hardness of Circuit Minimization and Related Problems

The Minimum Circuit Size Problem (MCSP) and a related problem (MKTP) that deals with time-bounded Kolmogorov complexity are prominent candidates for NP-intermediate status. We show that, under very modest cryptographic assumptions (such as the existence of one-way functions), the problem of approximating the minimum circuit size (or time-bounded Kolmogorov complexity) within a factor of n^{1 - o(1)} is indeed NP-intermediate. To the best of our knowledge, these problems are the first natural NP-intermediate problems under the existence of an arbitrary one-way function. We also prove that MKTP is hard for the complexity class DET under non-uniform NC^0 reductions. This is surprising, since prior work on MCSP and MKTP had highlighted weaknesses of "local" reductions such as NC^0 reductions. We exploit this local reduction to obtain several new consequences: * MKTP is not in AC^0[p]. * Circuit size lower bounds are equivalent to hardness of a relativized version MKTP^A of MKTP under a class of uniform AC^0 reductions, for a large class of sets A. * Hardness of MCSP^A implies hardness of MKTP^A for a wide class of sets A. This is the first result directly relating the complexity of MCSP^A and MKTP^A, for any A