Cyclotomic and simplicial matroids

Two naturally occurring matroids representable over Q are shown to be dual: the {\it cyclotomic matroid} $\mu_n$ represented by the $n^{th}$ roots of unity $1,\zeta,\zeta^2,...,\zeta^{n-1}$ inside the cyclotomic extension $Q(\zeta)$, and a direct sum of copies of a certain simplicial matroid, considered originally by Bolker in the context of transportation polytopes. A result of Adin leads to an upper bound for the number of $Q$-bases for $Q(\zeta)$ among the $n^{th}$ roots of unity, which is tight if and only if $n$ has at most two odd prime factors. In addition, we study the Tutte polynomial of $\mu_n$ in the case that $n$ has two prime factors.Comment: 9 pages, 1 figur

Factorizations of some weighted spanning tree enumerators

We give factorizations for weighted spanning tree enumerators of Cartesian products of complete graphs, keeping track of fine weights related to degree sequences and edge directions. Our methods combine Kirchhoff's Matrix-Tree Theorem with the technique of identification of factors.Comment: Final version, 12 pages. To appear in the Journal of Combinatorial Theory, Series A. The paper has been reorganized, and the proof of Theorem 4 shortened, in light of a more general result appearing in reference [6

The role of the exchange rate for adjustment in boom and bust episodes

Numerous countries have experienced boom-bust episodes in asset prices in the past 20 years. This study looks at stylised facts and conducts statistical and econometric analysis for such episodes, distinguishing between industrialised countries that experienced external adjustment (via real effective exchange rate depreciation during busts) and those that relied on an internal adjustment process (and experienced no depreciation). The study finds that different adjustment experiences are correlated with the degree of macroeconomic imbalances and balance sheet problems. Internal adjustment seems more prevalent when financial vulnerabilities, excess demand and competitiveness loss remain relatively contained in the boom. In the bust, internal adjusters experience more protracted but less deep downturns than external adjusters as imbalances unwind more slowly. Some Central and East European EU Member States are currently experiencing strong credit and asset price growth in conjunction with rapid economic expansion. Against this background the experience of other countries may raise awareness of related policy challenges. JEL Classification: E32, E63, E65Booms and busts, competitiveness, Exchange Rates, external and internal adjustment, financial imbalances

Regulatory reforms in selected EU network industries

In the course of the 1990s, the EU has embarked on an ambitious regulatory reform programme for a number of European network industries, such as telecommunications, energy and transport. This paper analyses the potential benefits of successful reforms in these sectors with a focus on the price effects of regulatory reforms. Following a review of the existing empirical literature in this field, the paper discusses the evolution of the current regulatory framework for network industries in the EU. An empirical analysis of the main determinants of recent price developments in these industries provides evidence that regulatory reform measures had a substantial downward impact on prices in the four sectors under review.Network Industries, Panel Data, Price effects, Regulatory Reforms.

Real convergence in Central and Eastern European EU Member States: which role for exchange rate volatility?

This paper analyzes the relation between exchange rate volatility and several macroeconomic variables, namely real per capita output growth, the credit cycle, the stock of inward foreign direct investment (FDI) and the current account balance, in the Central and Eastern European EU Member States. Using panel estimations for the period between 1995 and 2006, we find that lower exchange rate volatility is associated with higher growth (for relatively less financially developed economies), higher stocks of FDI (for relatively more open economies), higher current account deficits, and a more volatile development of the credit to GDP ratio. JEL Classification: F3, F4, F5Catching-up, Convergence, credit, current account, EU, Exchange rate volatility, FDI, Growth

EU-Regionalpolitik: Reform oder Stillstand?

--

Pseudodeterminants and perfect square spanning tree counts

The pseudodeterminant $\textrm{pdet}(M)$ of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If $\partial$ is a symmetric or skew-symmetric matrix then $\textrm{pdet}(\partial\partial^t)=\textrm{pdet}(\partial)^2$. Whenever $\partial$ is the $k^{th}$ boundary map of a self-dual CW-complex $X$, this linear-algebraic identity implies that the torsion-weighted generating function for cellular $k$-trees in $X$ is a perfect square. In the case that $X$ is an \emph{antipodally} self-dual CW-sphere of odd dimension, the pseudodeterminant of its $k$th cellular boundary map can be interpreted directly as a torsion-weighted generating function both for $k$-trees and for $(k-1)$-trees, complementing the analogous result for even-dimensional spheres given by the second author. The argument relies on the topological fact that any self-dual even-dimensional CW-ball can be oriented so that its middle boundary map is skew-symmetric.Comment: Final version; minor revisions. To appear in Journal of Combinatoric

Emulating the one-dimensional Fermi-Hubbard model by a double chain of qubits

The Jordan-Wigner transformation maps a one-dimensional (1D) spin- 1 / 2 system onto a fermionic model without spin degree of freedom. A double chain of quantum bits with X X and Z Z couplings of neighboring qubits along and between the chains, respectively, can be mapped on a spin-full 1D Fermi-Hubbard model. The qubit system can thus be used to emulate the quantum properties of this model. We analyze physical implementations of such analog quantum simulators, including one based on transmon qubits, where the Z Z interaction arises due to an inductive coupling and the X X interaction due to a capacitive interaction. We propose protocols to gain confidence in the results of the simulation through measurements of local operators