A Polish group without Lie sums

We construct a Polish group with an invariant metric in which Lie sums and Lie brackets do not exist. The construction of the group and the proof of the main theorem use some facts of combinatorial nature about the free group with two generators equipped with a Graev metric. The second author acknowledges the United States NSF grant DMS-0501039 for the support of his research.     

The approximability of three-dimensional assignment problems with bottleneck objective

We discuss two special cases of the three-dimensional bottleneck assignment problem where a certain underlying cost function satisfies the triangle inequality. We present polynomial time 2-approximation algorithms for the broadest class of these special cases, and we prove that (unless P = NP) this factor 2 is best possible even in the highly restricted setting of the Euclidean plane.     

Discovery of a Highly Potent and Broadly Effective Epidermal Growth Factor Receptor and HER2 Exon 20 Insertion Mutant Inhibitor

Exon 20 insertion (Ex20Ins) mutations are the third most prevalent epidermal growth factor receptor (EGFR) activating mutation and the most prevalent HER2 mutation in non‐small cell lung cancer (NSCLC). Novel therapeutics for the patients with Ex20Ins mutations are urgently needed, due to their poor responses to the currently approved EGFR and HER2 inhibitors. Here we report the discovery of highly potent and broadly effective EGFR and HER2 Ex20Ins mutant inhibitors. The co‐crystal structure of compound 1 b in complex with wild type EGFR clearly revealed an additional hydrophobic interaction of 4‐fluorobenzene ring within a deep hydrophobic pocket, which has not been widely exploited in the development of EGFR and HER2 inhibitors. As compared with afatinib, compound 1 a exhibited superior inhibition of proliferation and signaling pathways in Ba/F3 cells harboring either EGFR or HER2 Ex20Ins mutations, and in the EGFR P772_H773insPNP patient‐derived lung cancer cell line DFCI127. Our study identifies promising strategies for development of EGFR and HER2 Ex20Ins mutant inhibitors.     

Stability of a three‐station fluid network

This paper studies the stability of a three‐station fluid network. We show that, unlike the two‐station networks in Dai and Vande Vate [18], the global stability region of our three‐station network is not the intersection of its stability regions under static buffer priority disciplines. Thus, the “worst” or extremal disciplines are not static buffer priority disciplines. We also prove that the global stability region of our three‐station network is not monotone in the service times and so, we may move a service time vector out of the global stability region by reducing the service time for a class. We introduce the monotone global stability region and show that a linear program (LP) related to a piecewise linear Lyapunov function characterizes this largest monotone subset of the global stability region for our three‐station network. We also show that the LP proposed by Bertsimas et al. [1] does not characterize either the global stability region or even the monotone global stability region of our three‐station network. Further, we demonstrate that the LP related to the linear Lyapunov function proposed by Chen and Zhang [11] does not characterize the stability region of our three‐station network under a static buffer priority discipline. This revised version was published online in June 2006 with corrections to the Cover Date.     

Topographical and functional characterization of the ssDNA probe layer generated through EDC-mediated covalent attachment to nanocrystalline diamond using fluorescence microscopy

The covalent attachment method for DNA on nanocrystalline diamond (NCD), involving the introduction of COOH functionalities on the surface by photoattachment of 10-undecenoic acid (10-UDA), followed by the 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide (EDC)-mediated coupling to NH 2-labeled ssDNA, is evaluated in terms of stability, density, and functionality of the resulting biological interface. This is of crucial importance in DNA biosensor development. The covalent nature of DNA attachment will infer the necessary stability and favorable orientation to the ssDNA probe molecules. Using confocal fluorescence microscopy, the influence of buffer type for the removal of excess 10-UDA and ssDNA, the probe ssDNA length, the probe ssDNA concentration, and the presence of the COOH-linker on the density and functionality of the ssDNA probe layer were investigated. It was determined that the most homogeneously dense and functional DNA layer was obtained when 300 pmol of short ssDNA was applied to COOH-modified NCD samples, while H-terminated NCD was resistant for DNA attachment. Exploiting this surface functionality dependence of the DNA attachment efficiency, a shadow mask was applied during the photochemical introduction of the COOH-functionalities, leaving certain regions on the NCD H-terminated. The subsequent DNA attachment resulted in a fluorescence pattern corresponding to the negative of the shadow mask. Finally, NCD surfaces covered with mixtures of the 10-UDA linker molecule and a similar molecule lacking the COOH functionality, functioning as a lateral spacer, were examined for their suitability in preventing nonspecific adsorption to the surface and in decreasing steric hindrance. However, purely COOH-modified NCD samples, patterned with H-terminated regions and treated with a controlled amount of probe DNA, proved the most efficient in fulfilling these tasks.     

One-Dimensional p-Adic Subanalytic Sets

In this paper we extend two theorems from [2] on p-adic subanalyticsets, where p is a fixed prime number, Q_p is the field of p-adicnumbers and Z_p is the ring of p-adic integers. One of thesetheorems [2, 3.32] says that each subanalytic subset of Z_p issemialgebraic. This is extended here as follows.     

Fraction auctions: The tradeoff between efficiency and running time

This paper studies the sales of a single indivisible object where bidders have continuous valuations. In Grigorieva et al. [14] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show the existence of an ex-post equilibrium, called bluff equilibrium, in which bidders behave truthfully except for particular constellations of observed bids at which it is optimal to pretend a slightly higher valuation. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders, when bidders choose to play the bluff equilibrium. We discuss the running time and the efficiency in the bluff equilibrium. We show that by changing the parameter c of the auction we can trade off efficiency against running time.     

On the real exponential field with restricted analytic functions

The model-theoretic structure (ℝ_an, exp) is investigated as a special case of an expansion of the field of reals by certain families ofC ^∞-functions. In particular, we use methods of Wilkie to show that (ℝ_an, exp) is (finitely) model complete and O-minimal. We also prove analytic cell decomposition and the fact that every definable unary function is ultimately bounded by an iterated exponential function. An erratum to this article is available at .     

Sensitivity of Saturation Transfer Electron Spin Resonance Extended to Extremely Slow Mobility in Glassy Materials

A novel extension of the saturation transfer (ST) ESR technique that enables the determination of extremely long rotational correlation times of nitroxide spin labels up to values around 10⁴s is proposed. The method is based on the observation that the integral of ST-ESR spectra is sensitive to the spin–lattice relaxation time of the electron of the spin label, which in turn is directly dependent upon the rotational correlation time. The method is applied to the spin label TEMPOL (4-hydroxy-2,2,6,6-tetramethylpiperidine-N-oxyl) in glycerol. From the known viscosity data and the related rotational correlation times of the TEMPOL spin label in glycerol, the rotational correlation times of unknown samples can be determined. The method is especially applicable to systems with a very high viscosity, such as glassy materials. The method is applied to a 20 wt% glucose–water mixture in the glassy state, giving a value for the highest limiting rotational correlation time of about 10³s at a temperature of 45 K below the glass transition temperature of this system. This is an extension by six decades for the rotational correlation time, as compared to the current application of ST-ESR.     

Stochastic dominance equilibria in two-person noncooperative games

Two-person noncooperative games with finitely many pure strategies are considered, in which the players have linear orderings over sure outcomes but incomplete preferences over probability distributions resulting from mixed strategies. These probability distributions are evaluated according to t-degree stochastic dominance. A t-best reply is a strategy that induces a t-degree stochastically undominated distribution, and a t-equilibrium is a pair of t-best replies. The paper provides a characterization and an existence proof of t-equilibria in terms of representing utility functions, and shows that for large t behavior converges to a form of max–min play. Specifically, increased aversion to bad outcomes makes each player put all weight on a strategy that maximizes the worst outcome for the opponent, within the supports of the strategies in the limiting sequence of t-equilibria.The paper has benefitted from the comments of four referees and an associate editor.