Extension of Arrow's theorem to symmetric sets of tournaments

Arrow's impossibility theorem [K.J. Arrow, Social Choice and Individual Values, Wiley, New York, NY, 1951] shows that the set of acyclic tournaments is not closed to non-dictatorial Boolean aggregation. In this paper we extend the notion of aggregation to general tournaments and we show that for tournaments with four vertices or more any proper symmetric (closed to vertex permutations) subset cannot be closed to non-dictatorial monotone aggregation and to non-neutral aggregation. We also demonstrate a proper subset of tournaments that is closed to parity aggregation for an arbitrarily large number of vertices. This proves a conjecture of Kalai [Social choice without rationality, Reviewed NAJ Economics 3(4)] for the non-neutral and the non-dictatorial and monotone cases and gives a counter example for the general case.     

On the number of rectangulations of a planar point set

We investigate the number of different ways in which a rectangle containing a set of n noncorectilinear points can be partitioned into smaller rectangles by n (nonintersecting) segments, such that every point lies on a segment. We show that when the relative order of the points forms a separable permutation, the number of rectangulations is exactly the (n+1)st Baxter number. We also show that no matter what the order of the points is, the number of guillotine rectangulations is always the nth Schröder number, and the total number of rectangulations is O(n²⁰/n⁴).     

Electrospun fibers of functional nanocomposites composed of single‐walled carbon nanotubes,fullerene derivatives,and poly(3‐hexylthiophene)

Electrospinning of fibers composed of poly(3‐hexylthiophene) (P3HT), fullerene derivative, phenyl‐C₆₁‐butyric acid methyl ester (PCBM), and single‐walled carbon nanotubes (SWNT) is reported. While of great promise for photovoltaic applications, morphological control of functional structures is a great challenge for most processing methods. It is demonstrated that the use of a tailor‐made block‐copolymer for dispersion of individual SWNT enables the preparation of stable dispersions of individual tubes that may be further cospun from chloroform solutions with PCBM and P3HT into submicron fibers. The block copolymer used to mediate the colloidal and interfacial interactions in the combined system enables the spinning of centimeters long and uniform fibers. Structural characterization indicates a high degree of ordering and alignment within the fibers and absorption and quenching of the photoluminescence indicate significant interactions among the components. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1263–1268, 2011     

The welfare effects of public opinion polls

This paper presents an experimental study of the effects of polls on voters’ welfare. The analysis shows that polls have a different effect on closely divided and lopsided divided electorates. The data show that in closely divided electorates (and only for these electorates) the provision of information on the voters’ distribution of preferences significantly raises the participation of subjects supporting the slightly larger team relative to the smaller team. This causes a substantial increase on the frequency of electoral victories of the larger team. As a consequence, we observe a steep decrease in the welfare of the members of the smaller team because they vote more often and yet they loose the elections more frequently. Polls are detrimental to aggregate welfare in closely divided electorates because the decrease in the payoffs of the minority is stronger than the increase in the payoffs of the majority. In lopsided divided electorates polls don’t have a significant different effect on the voters’ turnout conditional on their team size. We do observe an increase on the frequency of electoral victories of the larger team after the provision of information, but this is in part due to smaller teams’ members voting less frequently and saving the participation costs. As a consequence, while polls have a negative effect on the relative payoffs of the minority for these electorates as well, they have a positive effect on total welfare.     

There Are Not Too Many Magic Configurations

A finite planar point set P is called a magic configuration if there is an assignment of positive weights to the points of P such that, for every line l determined by P, the sum of the weights of all points of P on l equals 1. We prove a conjecture of Murty from 1971 and show that if a set of n points P is a magic configuration, then P is in general position, or P contains n−1 collinear points, or P is a special configuration of 7 points. The research by Rom Pinchasi was supported by a Grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.     

Über neue Hexafluoroaluminate(III)

On New Hexafluoroaluminates (III) Due to Guinier-Simon powder photographs we obtained by heating mixtures of binary fluorides in a closed system 15 hitherto unknown cubic, colourless Elpasolithes. Cs₂AgAIF₆ crystallizes hexagonal in the Cs₂NaCrF₆-type of structure, but at high pressure conditions (p = 60 kbar) cubic as an Elpasolithe. The Madelung Part of Lattice Energy, MAPLE, is calculated and discussed.     

Declining valuations in sequential auctions

We analyze an independent private values model where a number of objects are sold in sequential first- and second-price auctions. Bidders have unit demand and their valuation for an object is decreasing in the rank number of the auction in which it is sold. We derive efficient equilibria if prices are announced after each auction or if no information is given to bidders. We show that the sequence of prices constitutes a supermartingale. Even if we correct for the decrease in valuations for objects sold in later auctions we find that average prices are declining.Received June 2004We are grateful to Christian Groh, Wolfgang Köhler and Benny Moldovanu for helpful suggestions. Financial support from the German Science Foundation through SFB 504 and SFB/TR 15 at the University of Mannheim and the University of Bonn is gratefully acknowledged.     

Long term behavior of lithographically prepared in vitro neuronal networks

We measured the long term spontaneous electrical activity of neuronal networks with different sizes, grown on lithographically prepared substrates and recorded with multi-electrode-array technology. The time sequences of synchronized bursting events were used to characterize network dynamics. All networks exhibit scale-invariant Lévy distributions and long-range correlations. These observations suggest that different-size networks self-organize to adjust their activities over many time scales. As predictions of current models differ from our observations, this calls for revised models.     

Hasse invariants for Hilbert modular varieties

Given a totally real fieldL of degreeg, we constructg Hasse invariants on Hilbert modular varieties in characteristicp and characterize their divisors. We show that these divisors give the type stratification defined by the action of on theα _p -elementary subgroup. Under certain conditions, involving special values of zeta functions, the product of these Hasse invariants is the reduction of an Eisenstein series of weightp−1