Aggregate and Individual Price Adjustment

macroeconomics, price adjustment, wages, Keynes, rigidities

The Beveridge Curve

macroeconomics, Beveridge Curve

The Price of Connectivity for Vertex Cover

The vertex cover number of a graph is the minimum number of vertices that are needed to cover all edges. When those vertices are further required to induce a connected subgraph, the corresponding number is called the connected vertex cover number, and is always greater or equal to the vertex cover number. Connected vertex covers are found in many applications, and the relationship between those two graph invariants is therefore a natural question to investigate. For that purpose, we introduce the {\em Price of Connectivity}, defined as the ratio between the two vertex cover numbers. We prove that the price of connectivity is at most 2 for arbitrary graphs. We further consider graph classes in which the price of connectivity of every induced subgraph is bounded by some real number $t$. We obtain forbidden induced subgraph characterizations for every real value $t \leq 3/2$. We also investigate critical graphs for this property, namely, graphs whose price of connectivity is strictly greater than that of any proper induced subgraph. Those are the only graphs that can appear in a forbidden subgraph characterization for the hereditary property of having a price of connectivity at most $t$. In particular, we completely characterize the critical graphs that are also chordal. Finally, we also consider the question of computing the price of connectivity of a given graph. Unsurprisingly, the decision version of this question is NP-hard. In fact, we show that it is even complete for the class $\Theta_2^P = P^{NP[\log]}$, the class of decision problems that can be solved in polynomial time, provided we can make $O(\log n)$ queries to an NP-oracle. This paves the way for a thorough investigation of the complexity of problems involving ratios of graph invariants.Comment: 19 pages, 8 figure

A search for muon-catalysed dd fusion in a deuterated organic crystal

Summary in English.Bibliography: pages 82-83.The possibility of muon-catalysed dd fusion via a Vesman-type mechanism in an organic crystal of deuterated anthracene is considered. In order to test this possibility the production of muons by 200 Me V protons incident on a 1mm Pb target is investigated. Two experiments to search for evidence of muon-catalysed fusion in a cylindrical deuterated anthracene crystal (9 mm diameter by l20 mm length) are described. The results indicate, tentatively, a fusion rate of 0.2 - 1.1 per incident μ-

A combined HST/CFH12k/XMM survey of X-ray luminous clusters of galaxies at z~0.2

We describe a project to study a sample of X-ray luminous clusters of galaxies at redshift z~0.2 at several scales (with HST/WFPC2 and CFHT/CFH12k) and wavebands (optical and X-ray). The main aims of the project are (i) to determine the mass profiles of the clusters on scales ranging from ~10 kpc/h to >1.5 Mpc/h using weak and strong lensing, thereby testing theoretical predictions of a ``universal mass profile'', and (ii) to calibrate the M_tot - T_X relation in view of future application in the study of the evolution of the cluster mass function at higher redshift.Comment: 4 pages, 2 figures, Proceedings of the XXth Moriond Astrophysics Meeting ``Cosmological Physics with Gravitational Lensing'', J.-P. Kneib, Y. Mellier, M. Moniez and J. Tran Thanh Van eds., 200