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     

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...     

The two-neutron transfer reactions (O, O) with O, C and Mg targets

Excitation functions, angular distributions and differential ranges were measured for the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction at ¹⁸O beam energies of 20–45 MeV. Excitation functions only were measured for the reactions ¹⁴C(¹⁸O, ¹⁹O)¹³C, ¹⁴C(¹⁸O, ¹⁶O)¹⁶C, ¹⁴C(¹⁸O, ²⁰O)¹²C, ¹⁴C(¹⁸O, ¹⁵N)¹⁷N and ¹⁸O(¹⁸O, ¹⁹O)¹⁷O, ¹⁸O(¹⁸O, ¹⁶O)²⁰O, ¹⁸O(¹⁸O, ¹⁵N)²¹F at ¹⁸O beam energies of 13–41 MeV. We have identified these as direct reactions in which a single neutron, a two-neutron cluster, a deuteron and a triton are transferred between projectile and target.

The cross sections for two-neutron transfer reactions were found to be relatively high and those for the ¹⁸O+¹⁸O and the ¹⁴C+¹⁸O reactions were higher than the ones of single-neutron transfers over most of the energy range.

Attempts were made to apply the theory of Buttle and Goldfarb for single-neutron transfer to the case of two-neutron transfer in the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction below the Coulomb barrier. It is shown that for those reactions for which the assumptions, implicit in the model, are valid, good agreement is obtained with experiment. We also tried to apply the diffraction model of Dar and Kozlovsky to the calculation of the angular distribution of these reactions. A good fit to the experimental results could be obtained if quite different sets of parameters were used in the calculations for the two bombarding energies.     

Quasi‐polynomial mixing of critical two‐dimensional random cluster models

We study the Glauber dynamics for the random cluster (FK) model on the torus with parameters (p,q), for q ∈ (1,4] and p the critical point p_c. The dynamics is believed to undergo a critical slowdown, with its continuous‐time mixing time transitioning from for p ≠ p_c to a power‐law in n at p = p_c. This was verified at p ≠ p_c by Blanca and Sinclair, whereas at the critical p = p_c, with the exception of the special integer points q = 2,3,4 (where the model corresponds to the Ising/Potts models) the best‐known upper bound on mixing was exponential in n. Here we prove an upper bound of at p = p_c for all q ∈ (1,4], where a key ingredient is bounding the number of nested long‐range crossings at criticality.     

Cycle Factors and Renewal Theory

For which values of k does a uniformly chosen 3‐regular graph G on n vertices typically contain n/k vertex‐disjoint k ‐cycles (a k ‐cycle factor)? To date, this has been answered for k = n and for k ? log n ; the former, the Hamiltonicity problem, was finally answered in the affirmative by Robinson and Wormald in 1992, while the answer in the latter case is negative since with high probability (w.h.p.) most vertices do not lie on k ‐cycles. A major role in our study of this problem is played by renewal processes without replacement, where one wishes to estimate the probability that in a uniform permutation of a given set of positive integers, the partial sums hit a designated target integer. Using sharp tail estimates for these renewal processes, which may be of independent interest, we settle the cycle factor problem completely: the “threshold” for a k ‐cycle factor in G as above is κ ₀ log₂ n with . To be precise, G contains a k ‐cycle factor w.h.p. if and w.h.p. does not contain one if . Thus, for most values of n the threshold concentrates on the single integer K ₀(n ). As a byproduct, we confirm the “comb conjecture,” an old problem concerning the embedding of certain spanning trees in the random graph (n,p ).© 2015 Wiley Periodicals, Inc.