Some Second Thoughts on Monopolistic Distortions and Endogenous Growth

The most fundamental proposition about growth and competition is that there is a tradeoff between static welfare and long-term growth. This paper reconsiders this basic proposition in an increasing product variety endogenous growth model with competitive markets for “old” innovative products and for a traditional good. We shed light on some implications of monopolistic distortions which tend to be ignored by standard models. First, no growth may be better than some growth, since modest positive growth potentially requires sizeable static welfare losses. Second, the economy may converge to a steady state with zero growth, even though another (saddle-point stable) steady state with positive growth exists if the initial share of “cheap” competitive markets is sufficiently high, as this implies a relatively low demand for “expensive” innovative goods. Third, such a “no-growth trap” may happen in a world economy made up of several countries engaged in free trade with each other. The policy implications are that growth-enhancing policies may be misguided and that quick deregulation as well as quick trade liberalization can lead to stagnation in the long term.endogenous growth, competition, deregulation, poverty trap, trade liberalization

Attraction and ionic correlations between charged stiff polyelectrolytes

We use Molecular Dynamics simulations to study attractive interactions and the underlying ionic correlations between parallel like-charged rods in the absence of additional salt. For a generic bulk system of rods we identify a reduction of short range repulsions as the origin of a negative osmotic coefficient. The counterions show signs of a weak three-dimensional order in the attractive regime only once the rod-imposed charge-inhomogeneities are divided out. We also treat the case of attraction between a single pair of rods for a few selected line charge densities and rod radii. Measurements of the individual contributions to the force between close rods are studied as a function of Bjerrum length. We find that even though the total force is always attractive at sufficiently high Bjerrum length, the electrostatic contribution can ultimately become repulsive. We also measure azimuthal and longitudinal correlation functions to answer the question how condensed ions are distributed with respect to each other and to the neighboring rod. For instance, we show that the prevalent image of mutually interlocked ions is qualitatively correct, even though modifications due to thermal fluctuations are usually strong.Comment: 14 pages, 14 figures, REVTeX4 styl

Electrostatics in Periodic Slab Geometries I

We propose a new method to sum up electrostatic interactions in 2D slab geometries. It consists of a combination of two recently proposed methods, the 3D Ewald variant of Yeh and Berkowitz, J. Chem. Phys. 111 (1999) 3155, and the purely 2D method MMM2D by Arnold and Holm, to appear in Chem. Phys. Lett. 2002. The basic idea involves two steps. First we use a three dimensional summation method whose summation order is changed to sum up the interactions in a slab-wise fashion. Second we subtract the unwanted interactions with the replicated layers analytically. The resulting method has full control over the introduced errors. The time to evaluate the layer correction term scales linearly with the number of charges, so that the full method scales like an ordinary 3D Ewald method, with an almost linear scaling in a mesh based implementation. In this paper we will introduce the basic ideas, derive the layer correction term and numerically verify our analytical results.Comment: 10 pages, 7 figure

Electrostatics in Periodic Slab Geometries II

In a previous paper a method was developed to subtract the interactions due to periodically replicated charges (or other long-range entities) in one spatial dimension. The method constitutes a generalized "electrostatic layer correction" (ELC) which adapts any standard 3D summation method to slab-like conditions. Here the implementation of the layer correction is considered in detail for the standard Ewald (EW3DLC) and the PPPM mesh Ewald (PPPMLC) methods. In particular this method offers a strong control on the accuracy and an improved computational complexity of O(N log N) for mesh-based implementations. We derive anisotropic Ewald error formulas and give some fundamental guidelines for optimization. A demonstration of the accuracy, error formulas and computation times for typical systems is also presented.Comment: 14 pages, 7 figure

Constructing Light Spanners Deterministically in Near-Linear Time

Graph spanners are well-studied and widely used both in theory and practice. In a recent breakthrough, Chechik and Wulff-Nilsen [Shiri Chechik and Christian Wulff-Nilsen, 2018] improved the state-of-the-art for light spanners by constructing a (2k-1)(1+epsilon)-spanner with O(n^(1+1/k)) edges and O_epsilon(n^(1/k)) lightness. Soon after, Filtser and Solomon [Arnold Filtser and Shay Solomon, 2016] showed that the classic greedy spanner construction achieves the same bounds. The major drawback of the greedy spanner is its running time of O(mn^(1+1/k)) (which is faster than [Shiri Chechik and Christian Wulff-Nilsen, 2018]). This makes the construction impractical even for graphs of moderate size. Much faster spanner constructions do exist but they only achieve lightness Omega_epsilon(kn^(1/k)), even when randomization is used. The contribution of this paper is deterministic spanner constructions that are fast, and achieve similar bounds as the state-of-the-art slower constructions. Our first result is an O_epsilon(n^(2+1/k+epsilon\u27)) time spanner construction which achieves the state-of-the-art bounds. Our second result is an O_epsilon(m + n log n) time construction of a spanner with (2k-1)(1+epsilon) stretch, O(log k * n^(1+1/k) edges and O_epsilon(log k * n^(1/k)) lightness. This is an exponential improvement in the dependence on k compared to the previous result with such running time. Finally, for the important special case where k=log n, for every constant epsilon>0, we provide an O(m+n^(1+epsilon)) time construction that produces an O(log n)-spanner with O(n) edges and O(1) lightness which is asymptotically optimal. This is the first known sub-quadratic construction of such a spanner for any k = omega(1). To achieve our constructions, we show a novel deterministic incremental approximate distance oracle. Our new oracle is crucial in our construction, as known randomized dynamic oracles require the assumption of a non-adaptive adversary. This is a strong assumption, which has seen recent attention in prolific venues. Our new oracle allows the order of the edge insertions to not be fixed in advance, which is critical as our spanner algorithm chooses which edges to insert based on the answers to distance queries. We believe our new oracle is of independent interest

Empty promises and nonincorporation in Mercosur

Why do the member states of the world’s fourth-largest trading block incorporate only about two-thirds of all policies they adopt? This article argues that empty promises are an important reason for Mercosur’s incorporation problems and that Mercosur’s institutional design furthers such a defective behavior. Member governments easily sign agreements whenever they are rewarded for the mere act of doing so. However, if they expect high costs from implementing these policies, they try to avoid incorporation. Since only the last state to incorporate a policy triggers its overall legal validity, Mercosur’s members can easily veto any agreement ex post. In addition to empty promises, mismanaged drafting and incorporation and the abuse of negotiation power also pose important obstacles to incorporation. Free riding, however, does not play a role. Due to the incorporation rules, there can be no externalities that incentivize unilateral defection. The article substantiates the arguments empirically with the multivariate analysis of the complete incorporation record of 1,033 policies adopted between 1994 and 2008

A Model for Optimal Human Navigation with Stochastic Effects

We present a method for optimal path planning of human walking paths in mountainous terrain, using a control theoretic formulation and a Hamilton-Jacobi-Bellman equation. Previous models for human navigation were entirely deterministic, assuming perfect knowledge of the ambient elevation data and human walking velocity as a function of local slope of the terrain. Our model includes a stochastic component which can account for uncertainty in the problem, and thus includes a Hamilton-Jacobi-Bellman equation with viscosity. We discuss the model in the presence and absence of stochastic effects, and suggest numerical methods for simulating the model. We discuss two different notions of an optimal path when there is uncertainty in the problem. Finally, we compare the optimal paths suggested by the model at different levels of uncertainty, and observe that as the size of the uncertainty tends to zero (and thus the viscosity in the equation tends to zero), the optimal path tends toward the deterministic optimal path

Radiation therapy calculations using an on-demand virtual cluster via cloud computing

Computer hardware costs are the limiting factor in producing highly accurate radiation dose calculations on convenient time scales. Because of this, large-scale, full Monte Carlo simulations and other resource intensive algorithms are often considered infeasible for clinical settings. The emerging cloud computing paradigm promises to fundamentally alter the economics of such calculations by providing relatively cheap, on-demand, pay-as-you-go computing resources over the Internet. We believe that cloud computing will usher in a new era, in which very large scale calculations will be routinely performed by clinics and researchers using cloud-based resources. In this research, several proof-of-concept radiation therapy calculations were successfully performed on a cloud-based virtual Monte Carlo cluster. Performance evaluations were made of a distributed processing framework developed specifically for this project. The expected 1/n performance was observed with some caveats. The economics of cloud-based virtual computing clusters versus traditional in-house hardware is also discussed. For most situations, cloud computing can provide a substantial cost savings for distributed calculations.Comment: 12 pages, 4 figure