Curve Reconstruction, the Traveling Salesman Problem, and Menger's Theorem on Length

We give necessary and sufficient regularity conditions under which the curve reconstruction problem is solved by a traveling salesman tour or path, respectively. For the proof we have to generalize a theorem of Menger [12], [13] on arc lengt

The Quantity Theory Revisited: A New Structural Approach

While the long run relation between money and inflation is well established, empirical evidence on the adjustment to the long run equilibrium is very heterogeneous. In this paper we show, that the development of US consumer price inflation between 1960Q1 and 2005Q4 is strongly driven by money overhang. To this end, we use a multivariate state space framework that substantially expands the traditional vector error correction approach. This approach allows us to estimate the persistent components of velocity and GDP. A sign restriction approach is subsequently used to identify the structural shocks to the signal equations of the state space model, that explain money growth, inflation and GDP growth. We also account for the possibility that measurement error exhibited by simple-sum monetary aggregates causes the consequences of monetary shocks to be improperly identified by using a Divisia monetary aggregate. Our findings suggest that when the money is measured using a reputable index number, the quantity theory holds for the United States.Divisia money, state space decomposition, sign restrictions

Simultaneous Implicit Surface Reconstruction and Meshing

We investigate an implicit method to compute a piecewise linear representation of a surface from a set of sample points. As implicit surface functions we use the weighted sum of piecewise linear kernel functions. For such a function we can partition Rd in such a way that these functions are linear on the subsets of the partition. For each subset in the partition we can then compute the zero level set of the function exactly as the intersection of a hyperplane with the subset

Morphology of ledge patterns during step flow growth of metal surfaces vicinal to fcc(001)

The morphological development of step edge patterns in the presence of meandering instability during step flow growth is studied by simulations and numerical integration of a continuum model. It is demonstrated that the kink Ehrlich-Schwoebel barrier responsible for the instability leads to an invariant shape of the step profiles. The step morphologies change with increasing coverage from a somewhat triangular shape to a more flat, invariant steady state form. The average pattern shape extracted from the simulations is shown to be in good agreement with that obtained from numerical integration of the continuum theory.Comment: 4 pages, 4 figures, RevTeX 3, submitted to Phys. Rev.

Correlations in nano-scale step fluctuations: comparison of simulation and experiments

We analyze correlations in step-edge fluctuations using the Bortz-Kalos-Lebowitz kinetic Monte Carlo algorithm, with a 2-parameter expression for energy barriers, and compare with our VT-STM line-scan experiments on spiral steps on Pb(111). The scaling of the correlation times gives a dynamic exponent confirming the expected step-edge-diffusion rate-limiting kinetics both in the MC and in the experiments. We both calculate and measure the temperature dependence of (mass) transport properties via the characteristic hopping times and deduce therefrom the notoriously-elusive effective energy barrier for the edge fluctuations. With a careful analysis we point out the necessity of a more complex model to mimic the kinetics of a Pb(111) surface for certain parameter ranges.Comment: 10 pages, 9 figures, submitted to Physical Review

Monetary Policy in a World Where Money (Also) Matters

While the long-run relation between money and inflation as predicted by the quantity theory is well established, empirical studies of the short-run adjustment process have been inconclusive at best. The literature regarding the validity of the quantity theory within a given economy is mixed. Previous research has found support for quantity theory within a given economy by combining the P-Star, the structural VAR and the monetary aggregation literature. However, these models lack precise modelling of the short-run dynamics by ignoring interest rates as the main policy instrument. Contrarily, most New Keynesian approaches, while excellently modeling the short-run dynamics transmitted through interest rates, ignore the role of money and thus the potential mid- and long-run effects of monetary policy. We propose a parsimonious and fairly unrestrictive econometric model that allows a detailed look into the dynamics of a monetary policy shock by accounting for changes in economic equilibria, such as potential output and money demand, in a framework that allows for both monetarist and New Keynesian transmission mechanisms, while also considering the Barnett critique. While we confirm most New Keynesian findings concerning the short-run dynamics, we also find strong evidence for a substantial role of the quantity of money for price movements.Während die von der Quantitätstheorie vorhergesagte Langfristbeziehung zwischen Geld und Inflation gut dokumentiert ist, sind die Ergebnisse empirischer Studien zum kurzfristigen Anpassungsprozess wenig aufschlussreich. Die diesbezügliche Literatur, die versucht, die Gültigkeit der Quantitätstheorie mit Zeitreihenmodellen innerhalb eines Landes zu bestätigen, kommt zu gemischten Ergebnissen. Aktuelle Forschungsarbeiten, in denen P-Star-Modelle mit strukturellen VAR-Modellen kombiniert werden und die die Erkenntnisse der Aggregationstheorie bezüglich der relevanten Geldmenge berücksichtigen, bestätigen die Quantitätstheorie. Allerdings vernachlässigen diese Modelle eine präzise Modellierung der kurzfristigen Inflationsdynamik, da die Zinssätze - als wesentliches Politikinstrument - nicht berücksichtigt werden. Im Gegensatz dazu ignorieren die Neukeynesianischen Modelle, die bei der Kurzfristmodellierung sehr gut abschneiden, die Rolle der Geldmenge und vernachlässigen so die denkbaren mittel- und langfristigen Konsequenzen der Geldpolitik. In diesem Papier stellen wir ein übersichtliches und dabei nur wenig restriktives ökonometrisches Modell vor, das einen detaillierten Blick auf die Dynamik nach einem geldpolitischen Schock erlaubt, indem es die Veränderung unbeobachtbarer Gleichgewichtsgrößen wie Produktionspotenzial und Geldnachfrage abbildet. Das ökonometrische Modell erlaubt so die Neukeynesianische wie auch monetaristische Transmission geldpolitischer Schocks und berücksichtigt gleichzeitig die Barnett-Kritik. Die Schätzergebnisse bestätigen einerseits die meisten Neukeynesianischen Effekte für die kurze Frist, deuten aber gleichzeitig stark auf eine langfristig wichtige Rolle der Geldmenge für die Preisentwicklung hin

The Quantity Theory Revisited: A New Structural Approach

While the long run relation between money and inflation is well established, empirical evidence on the adjustment to the long run equilibrium is very heterogeneous. In this paper, we show that the development of US consumer price inflation between 1960Q1 and 2005Q4 is strongly driven by money overhang. To this end, we use a multivariate state space framework that substantially expands the traditional vector error correction approach. This approach allows us to estimate the persistent components of velocity and GDP. A sign restriction approach is subsequently used to identify the structural shocks to the signal equations of the state space model that explain money growth, inflation, and GDP growth. We also account for the possibility that measurement error exhibited by simple-sum monetary aggregates causes the consequences of monetary shocks to be improperly identified by using a Divisia monetary aggregate. Our findings suggest that when the money is measured using a reputable index number, the quantity theory holds for the United States.Im Gegensatz zur weitgehend etablierten Langfristbeziehung zwischen Geldmenge und Preisen ist die empirische Evidenz bezüglich des Anpassungsprozesses hin zu diesem Langfristgleichgewicht durchwachsen. Der vorliegende Beitrag untersucht diesen Zusammenhang für die USA im Zeitraum von 1960 bis 2005. Dazu wird ein multivariates Zustandsraummodell verwendet, das den herkömmlichen Kointegrationsansatz, mit dem diese Frage im Regelfall analysiert wird, deutlich erweitert. Dieser Ansatz erlaubt die Identifikation der persistenten Komponente der Geldumlaufsgeschwindigkeit und des Bruttoinlandsprodukts. Aufbauend auf dem Zustandsraummodell erfolgt über Vorzeichenrestriktionen die Identifikation struktureller Schocks auf die 'Signalgleichungen', welche die Entwicklung von Geldmengenwachstum, Inflation und Wachstum beschreiben. Durch die Verwendung eines so genannten Divisa Geldmengenaggregats wird gleichzeitig der Möglichkeit Rechnung getragen, dass der Zusammenhang zwischen Geld und Preisen durch Messfehler einfacher Geldmengenaggregate verzerrt wird. Die Resultate zeigen, dass ein quantitätstheoretischer Zusammenhang im Sinne eines maßgeblichen Zusammenhangs von Geld und Preisen bei Verwendung eines angemessenen Geldmengenaggregats klar erkennbar ist

Bounds on the k-neighborhood for locally uniform sampled surfaces

Given a locally uniform sample set P of a smooth surface S. We derive upper and lower bounds on the number k of nearest neighbors of a sample point p that have to be chosen from P such that this neighborhood contains all restricted Delaunay neighbors of p. In contrast to the trivial lower bound, the upper bound indicates that a sampling condition that is used in many computational geometry proofs is quite reasonable from a practical point of view