Metric structures in : dimension, snowflakes, and average distortion

We study the metric properties of finite subsets of L₁. The analysis of such metrics is central to a number of important algorithmic problems involving the cut structure of weighted graphs, including the Sparsest Cut Problem, one of the most compelling open problems in the field of approximation algorithms. Additionally, many open questions in geometric non-linear functional analysis involve the properties of finite subsets of L₁.We present some new observations concerning the relation of L₁ to dimension, topology, and Euclidean distortion. We show that every n-point subset of L₁ embeds into L₂ with average distortion , yielding the first evidence that the conjectured worst-case bound of is valid. We also address the issue of dimension reduction in L_p for p(1,2). We resolve a question left open by M. Charikar and A. Sahai [Dimension reduction in the ℓ₁ norm, in: Proceedings of the 43rd Annual IEEE Conference on Foundations of Computer Science, ACM, 2002, pp. 251–260] concerning the impossibility of dimension reduction with a linear map in the above cases, and we show that a natural variant of the recent example of Brinkman and Charikar [On the impossibility of dimension reduction in ℓ₁, in: Proceedings of the 44th Annual IEEE Conference on Foundations of Computer Science, ACM, 2003, pp. 514–523], cannot be used to prove a lower bound for the non-linear case. This is accomplished by exhibiting constant-distortion embeddings of snowflaked planar metrics into Euclidean space.     

The dynamics of endohedral complex formation in surface pick-up scattering as probed by kinetic energy distributions: experiment and model calculation for Cs@C60+

Endohedral Cs@C60 molecules were formed by implanting low energy (E0 = 30-220 eV) Cs+ ions into C60 molecules adsorbed on gold. Both growth and etching experiments of the surface deposited C(60) layer provide clear evidence for a submonolayer coverage. The Cs+ penetration and Cs@C60 ejection stages are shown to be a combined, single collision event. Thermal desorption measurements did not reveal any Cs@C60 left on the surface following the Cs+ impact. The Cs@C60 formation/ejection event therefore constitutes a unique example of a pick-up scattering by endocomplex formation. Kinetic energy distributions (KEDs) of the outgoing Cs@C60+ were measured for two different Cs+ impact energies under field-free conditions. The most striking observation is the near independence of the KEDs on the Cs+ impact energy. Both KEDs peak around 1.2 eV with similar line shapes. A simple model for the formation/ejection/fragmentation dynamics of the endohedral complex is proposed. The model leads to a strong correlation between the vibrational and kinetic energy of the outgoing Cs@C60. The KEDs are calculated taking into account the competition between the various decay processes: fragmentation and delayed ionization of the neutral Cs@C60 emitted from the surface, fragmentation of the Cs@C60+ ion, and radiative cooling. It is concluded that the measured KEDs are heavily biased by the experimental breakdown function. Good agreement between experimental and calculated KEDs is obtained.     

Environment Polarity in Proteins Mapped Noninvasively by FTIR Spectroscopy

The polarity pattern of a macromolecule is of utmost importance to its structure and function. For example, one of the main driving forces for protein folding is the burial of hydrophobic residues. Yet polarity remains a difficult property to measure experimentally, due in part to its non-uniformity in the protein interior. Herein, we show that FTIR linewidth analysis of noninvasive 1-(13)C=(18)O labels can be used to obtain a reliable measure of the local polarity, even in a highly multi-phasic system, such as a membrane protein. We show that in the Influenza M2 H(+) channel, residues that line the pore are located in an environment that is as polar as fully solvated residues, while residues that face the lipid acyl chains are located in an apolar environment. Taken together, FTIR linewidth analysis is a powerful, yet chemically non-perturbing approach to examine one of the most important properties in proteins - polarity.