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     

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     

Using the near-field coupling of a sharp tip to tune fluorescence-emission fluctuations during quantum-dot blinking

We demonstrate that the cycling between internal states of quantum dots during fluorescence blinking can be used to tune the near-field coupling with a sharp tip. In particular, the fluorescence emission from states with high quantum yield is quenched due to energy transfer, while that from low-yield states is elevated due to field enhancement. Thus, as a quantum dot blinks, its emission fluctuations are progressively suppressed upon approach of a tip.     

Structural elucidation of amino amide‐type local anesthetic drugs and their main metabolites in urine by LC‐MS after derivatization and its application for differentiation between positional isomers of prilocaine

The demand for clinical toxicology analytical methods for identifying drugs of abuse and medicinal drugs is steadily increasing. Structural elucidation of amino amide‐type local anesthetic drugs and their main metabolites by GC‐EI‐MS and LC‐ESI‐MS/MS is of great analytical challenge. These compounds exhibit only/mostly fragments/product ions representing the amine‐containing residue, while the aromatic amide moiety remains unidentified. This task becomes even more complicated when discrimination between positional isomers of such compounds is required. Here, we report the development of a derivatization procedure for the differentiation and structural elucidation of a mixture of local anesthetic drugs and their metabolites that possess tertiary and secondary amines in water and urine. A method based on two sequential “in‐vial” instantaneous derivatization processes at ambient temperature followed by LC‐ESI‐MS/MS analysis was developed. 2,2,2‐Trichloro‐1,1‐dimethylethyl chloroformate (TCDMECF) was utilized to selectively convert the secondary amines into their carbamate derivatives, followed by hydrogen peroxide addition to produce the corresponding tertiary amine oxides. The resulting derivatives exhibited rich fragmentation patterns, enabling improved structural elucidation of the original compounds. The developed method was successfully applied to the differentiation and structural elucidation of prilocaine and its four positional isomers, which all possess similar GC and LC retention times and four of them exhibit almost identical EI‐MS and ESI‐MS/MS spectra, enabling their structural elucidation in a single LC‐ESI‐MS/MS analysis. The developed technique is fast and simple and enables discrimination between isomers based on different diagnostic ions/fragmentation patterns.     

The Langlands parameter of a simple supercuspidal representation: symplectic groups

The Ramanujan Journal - Let $$\pi $$ be a simple supercuspidal representation of the symplectic group $${\mathrm {Sp}}_{2l}(F)$$, over a p-adic field F. In this work, we explicitly compute the...     

On the maximum number of edges in quasi-planar graphs

A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [P.K. Agarwal, B. Aronov, J. Pach, R. Pollack, M. Sharir, Quasi-planar graphs have a linear number of edges, Combinatorica 17 (1) (1997) 1-9] proved that these graphs have a linear number of edges. We give a simple proof for this fact that yields the better upper bound of 8n edges for n vertices. Our best construction with 7n−O(1) edges comes very close to this bound. Moreover, we show matching upper and lower bounds for several relaxations and restrictions of this problem. In particular, we show that the maximum number of edges of a simple quasi-planar topological graph (i.e., every pair of edges have at most one point in common) is 6.5n−O(1), thereby exhibiting that non-simple quasi-planar graphs may have many more edges than simple ones.     

Use of sol-gel entrapment techniques for the resolution of itaconic acid biosynthetic pathway in Aspergillus terreus

A new technique of investigation of labile metabolic pathways using immobilization of the pathway in sol-gel derived silicate matrices was demonstrated. The biosynthetic pathway of itaconic acid in Aspergillus terreus is believed to proceed through decarboxylation of cis-aconitate catalyzed by an unstable enzyme aconitate decarboxylase, E.C. 4.1.1.6. Stabilization of this pathway in sol-gel derived silicate matrix enabled the elucidation of the correct sequence of biosynthetic steps. The decarboxylation of cis-aconitate does not lead directly to itaconate, but rather to citraconate. The latter is then isomerized to itaconate by a previously unknown enzyme.