Minimum Convex Partitions and Maximum Empty Polytopes

Let $S$ be a set of $n$ points in $\mathbb{R}^d$. A Steiner convex partition is a tiling of ${\rm conv}(S)$ with empty convex bodies. For every integer $d$, we show that $S$ admits a Steiner convex partition with at most $\lceil (n-1)/d\rceil$ tiles. This bound is the best possible for points in general position in the plane, and it is best possible apart from constant factors in every fixed dimension $d\geq 3$. We also give the first constant-factor approximation algorithm for computing a minimum Steiner convex partition of a planar point set in general position. Establishing a tight lower bound for the maximum volume of a tile in a Steiner convex partition of any $n$ points in the unit cube is equivalent to a famous problem of Danzer and Rogers. It is conjectured that the volume of the largest tile is $\omega(1/n)$. Here we give a $(1-\varepsilon)$-approximation algorithm for computing the maximum volume of an empty convex body amidst $n$ given points in the $d$-dimensional unit box $[0,1]^d$.Comment: 16 pages, 4 figures; revised write-up with some running times improve

Regional Debt in Monetary Unions: Is it Inflationary?

This paper studies the inflationary implications of interest bearing regional debt in a monetary union. Is this debt simply backed by future taxation with no inflationary consequences? Or will the circulation of region debt induce monetization by a central bank? We argue here that both outcomes can arise in equilibrium. In the model economy, there are multiple equilibria which reflect the perceptions of agents regarding the manner in which the debt obligations will be met. In one equilibrium, termed Ricardian, the future obligations are met with taxation by a regional government while in the other, termed Monetization, the central bank is induced to print money to finance the region's obligations. The multiplicity of equilibria reflects a commitment problem of the central bank. A key indicator of the selected equilibrium is the distribution of the holdings of the regional debt. We show that regional governments, anticipating central bank financing of their debt obligations, have an incentive to create excessively large deficits. We use the model to assess the impact of policy measures within a monetary union.Monetary Union ; Inflation tax ; Seigniorage ; Public debt.

Insulation impossible: monetary policy and regional fiscal spillovers in a federation

This paper studies the effects of monetary policy rules in a fiscal federation, such as the European Union. The focus of the analysis is the interaction between the fiscal policy of member countries (regions) and the monetary authority. Each of the countries structures its fiscal policy (spending and taxes) with the interests of its citizens in mind. Ricardian equivalence does not hold due to the presence of monetary frictions, modeled here as reserve requirements. When capital markets are integrated, the fiscal policy of one country influences equilibrium wages and interest rates. Under certain rules, monetary policy may respond to the price variations induced by regional fiscal policies. Depending on the type of rule it adopts, interventions by the monetary authority affect the magnitude and nature of the spillover from regional fiscal policy.Monetary Union, Inflation tax, Seigniorage, monetary rules, public debt.

Monetary rules and the spillover of regional fiscal policies in a federation.

This paper studies the effects of monetary policy rules in a fiscal federation, such as the European Union. The focus of the analysis is the interaction between the fiscal policy of member countries (regions) and the monetary authority. Each of the countries structures its fiscal policy (spending and taxes) with the interests of its citizens in mind. Ricardian equivalence does not hold due to the presence of monetary frictions, modelled here as reserve requirements. When capital markets are integrated, the fiscal policy of one country influences equilibrium wages and interest rates. Under certain rules, monetary policy may respond to the price variations induced by regional fiscal policies. Depending on the type of rule it adopts, interventions by the monetary authority affect the magnitude and nature of the spillover from regional fiscal policy.Monetary Union ; Inflation tax ; Seigniorage ; monetary rules ; public debt.

Near-Perfect Correlation of the Resistance Components of Mesoscopic Samples at the Quantum Hall Regime

We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the $\nu=2$ and the $\nu=1$ quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall components of the resistance. These correlated fluctuations appear in a magnetic-field range for which the two-terminal resistance of the samples is quantized. We discuss these findings in light of edge-state transport models of the quantum Hall effect. We also show that our results lead to an ambiguity in the determination of the width of quantum Hall transitions.Comment: As publishe

On commutativity based edge lean search

Exploring a graph through search is one of the most basic building blocks of various applications. In a setting with a huge state space, such as in testing and verification, optimizing the search may be crucial. We consider the problem of visiting all states in a graph where edges are generated by actions and the (reachable) states are not known in advance. Some of the actions may commute, i.e., they result in the same state for every order in which they are taken (this is the case when the actions are performed independently by different processes). We show how to use commutativity to achieve full coverage of the states while traversing considerably fewer edges

A reduced semantics for deciding trace equivalence using constraint systems

Many privacy-type properties of security protocols can be modelled using trace equivalence properties in suitable process algebras. It has been shown that such properties can be decided for interesting classes of finite processes (i.e., without replication) by means of symbolic execution and constraint solving. However, this does not suffice to obtain practical tools. Current prototypes suffer from a classical combinatorial explosion problem caused by the exploration of many interleavings in the behaviour of processes. M\"odersheim et al. have tackled this problem for reachability properties using partial order reduction techniques. We revisit their work, generalize it and adapt it for equivalence checking. We obtain an optimization in the form of a reduced symbolic semantics that eliminates redundant interleavings on the fly.Comment: Accepted for publication at POST'1

Allocating Security Expenditures under Knightian Uncertainty: an Info-Gap Approach

We apply the information gap approach to resource allocation under Knightian (non-probabilistic) uncertainty in order to study how best to allocate public resources between competing defense measures. We demonstrate that when determining the level and composition of defense spending in an environment of extreme uncertainty vis-a-vis the likelihood of armed conflict and its outcomes, robust-satisficing expected utility will usually be preferable to expected utility maximization. Moreover, our analysis suggests that in environments with unreliable information about threats to national security and their consequences, a desire for robustness to model misspecification in the decision making process will imply greater expenditure on certain types of defense measures at the expense of others. Our results also provide a positivist explanation of how governments seem to allocate security expenditures in practice

Allocating Security Expenditures under Knightian Uncertainty: an Info-Gap Approach

We apply the information gap approach to resource allocation under Knightian (non-probabilistic) uncertainty in order to study how best to allocate public resources betweencompeting defense measures. We demonstrate that when determining the level and composi-tion of defense spending in an environment of extreme uncertaintyvis-a-visthe likelihood ofarmed conflict and its outcomes, robust-satisficing expected utility will usually be preferableto expected utility maximisation. Moreover, our analysis suggests that in environments withunreliable information about threats to national security and their consequences, a desirefor robustness to model misspecification in the decision making process will imply greaterexpenditure on certain types of defense measures at the expense of others. Our results alsoprovide a positivist explanation of how governments seem to allocate security expendituresin practice