Quasisymmetric embeddings, the observable diameter, and expansion properties of graphs

It is shown that the edges of any n-point vertex expander can be replaced by new edges so that the resulting graph is an edge expander, and such that any two vertices that are joined by a new edge are at distance in the original graph. This result is optimal, and is shown to have various geometric consequences. In particular, it is used to obtain an alternative perspective on the recent algorithm of Arora et al. [Proceedings of the 36th Annual ACM Symposium on the Theory of Computing, 2004, pp. 222-231.] for approximating the edge expansion of a graph, and to give a nearly optimal lower bound on the ratio between the observable diameter and the diameter of doubling metric measure spaces which are quasisymmetrically embeddable in Hilbert space.     

Spectral theory of metastability and extinction in birth-death systems

We suggest a general spectral method for calculating the statistics of multistep birth-death processes and chemical reactions of the type mA-->nA (m and n are positive integers) which possess an absorbing state. The method employs the generating function formalism in conjunction with the Sturm-Liouville theory of linear differential operators. It yields accurate results for the extinction statistics and for the quasistationary probability distribution, including large deviations, of the metastable state. The power of the method is demonstrated on the example of binary annihilation and triple branching 2A--> ?, A-->3A, representative of the rather general class of dissociation-recombination reactions.     

Interaction of scanning probes with semiconductor nanocrystals; physical mechanism and basis for near-field optical imaging

We investigate the modification of photoluminescence (PL) from single semiconductor nanocrystal quantum dots (NCs) in the proximity of metal and semiconducting atomic force microscope (AFM) tips. The presence of the tip alters the radiative decay rate of an emitter via interference and opens efficient nonradiative decay channels via energy transfer to the tip material. These effects cause quenching (or enhancement) of the emitter's PL intensity as a function of its distance from the interacting tip. We take advantage of this highly distance-dependent effect to realize a contrast mechanism for high-resolution optical imaging. AFM tips are optimized as energy acceptors by chemical functionalization with InAs NCs to achieve optical resolution down to 30 nm. The presented experimental scheme offers high-resolution optical information while maintaining the benefits of traditional AFM imaging. We directly measure the PL intensity of single NCs as a function of the tip distance. Our results are in good agreement with calculations made by a classical theoretical model describing an oscillating dipole interacting with a planar mirror.     

Knaster and friends I: closed colorings and precalibers

The productivity of the \(\kappa \)-chain condition, where \(\kappa \) is a regular, uncountable cardinal, has been the focus of a great deal of set-theoretic research. In the 1970s, consistent examples of \(\kappa \)-cc posets whose squares are not \(\kappa \)-cc were constructed by Laver, Galvin, Roitman and Fleissner. Later, \(\textsf {ZFC}\) examples were constructed by Todorcevic, Shelah, and others. The most difficult case, that in which \(\kappa = \aleph _2\), was resolved by Shelah in 1997. In this work, we obtain analogous results regarding the infinite productivity of strong chain conditions, such as the Knaster property. Among other results, for any successor cardinal \(\kappa \), we produce a \(\textsf {ZFC}\) example of a poset with precaliber \(\kappa \) whose \(\omega ^{\mathrm {th}}\) power is not \(\kappa \)-cc. To do so, we carry out a systematic study of colorings satisfying a strong unboundedness condition. We prove a number of results indicating circumstances under which such colorings exist, in particular focusing on cases in which these colorings are moreover closed.     

Dose rate effect of gamma on JFET transistors

Dose rate effects on the noise characteristics of gamma-irradiated junction field effect transistors (JFETs) are presented. The dose rate varied between 0.5 and 19 kGy/h at a constant radiation dose of 600 kGy. Neither obvious nor non-general relationship was identified between noise and dose rate along the total dose rate range. Nevertheless, some explanations have been provided about the resulting effects when the total range was studied, as some partial ranges corresponded to low, medium and high dose rates. This explanation is based on the gamma interaction process in JFET structure and the electronic noise resulted.     

A Selective Cucurbit[8]uril-Peptide Beacon Ensemble for the Ratiometric Fluorescence Detection of Peptides

A convenient supramolecular strategy for constructing a ratiometric fluorescent chemosensing ensemble, consisting of a macrocyclic host (cucurbit[8]uril CB[8]), and a pyrene-tagged amphiphilic peptide beacon (AP 1), is reported. AP 1 unfolds upon encapsulation of the pyrene termini into the hydrophobic CB[8] cavity. This changes pyrene excimer to monomer emission. Substrates with higher affinity for the CB[8] cavity can displace AP 1 from the ensemble. The released AP 1 folds again to form a pyrene excimer, which allows for the ratiometric fluorescence monitoring of the substrate. In this report, the ensemble capacity for ratiometric fluorescence monitoring of biological substrates, such as amino acid derivatives, specific peptides, and proteins, in aqueous media is demonstrated.     

Long-range electronic-to-vibrational energy transfer from nanocrystals to their surrounding matrix environment

A radiationless transition process of long-range, resonance interconversion of electronic-to-vibrational energy transfer (EVET) is discovered between the band-gap excitation of nanocrystal quantum dots to matrix vibrational overtone modes using fluorescence lifetime measurements. A theoretical analysis based on long-range dipole-dipole nonadiabatic couplings, being distinct from the traditional adiabatic or "static-coupling" pictures, is given and is in qualitative agreement with experiments. EVET should be considered in matrix choices for near-infrared optoelectronic applications of nanocrystals.     

Variational multiple-tensor fitting of fiber-ambiguous diffusion-weighted magnetic resonance imaging voxels

Partial volume effects are often experienced in diffusion-weighted MRI of biologic tissue. This is when the signal attenuation reflects a mixture of diffusion processes, originating from different tissue compartments, residing in the same voxel. Decomposing the mixture requires elaborated models that account for multiple compartments, yet the fitting problem for those models is usually ill posed. We suggest a novel approach for stabilizing the fitting problem of the multiple-tensors model by a variational framework that adds biologically oriented assumption of neighborhood alignments. The framework is designed to address fiber ambiguity caused by a number of neuronal fiber compartments residing in the same voxel. The method requires diffusion data acquired by common, clinically feasible MRI sequences, and is able to derive familiar tensor quantities for each compartment. Neighborhood alignment is performed by adding piece-wise smooth regularization constraints to an energy function. Minimization with the gradient descent method produces a set of diffusion-reaction partial differential equations that describe a tensor-preserving flow towards a best approximation of the data while maintaining the constraints. We analyze fiber compartment separation capabilities on a synthetic model of crossing fibers and on brain areas known to have crossing fibers. We compare the results with diffusion tensor imaging analysis and discuss applications for the framework.     

Morphological and Interaction Characteristics of Surface-Active Ionic Liquids and Palmitic Acid in Mixed Monolayers

A series of water soluble, surface-active ionic liquids (SAILs), namely, 1-alkyl-3-methyl imidazolium chlorides ([C_n-mim]Cl) and their mixtures with palmitic acid (PA) are investigated in Langmuir monolayers and Langmuir–Blodgett films. It is inferred from the surface pressure-area isotherms that C₁₆-mim-IL mixes non-ideally with PA and stabilizes the binary mixed films. In addition, the residence of mim-IL at the water surface is enhanced as a function of the increasing alkyl side chain length. Generally, the compressional moduli values decrease upon increasing the content of the mim-ILs over a wide range of compositions. Furthermore, film relaxation measurements indicate that the IL component is selectively excluded from the mixed films upon achieving a certain target pressure. Brewster angle microscope images demonstrate minimal changes on the PA domains in the presence of either C₄- and C₈-mim-ILs, whereas presence of the hexadecyl counterpart results in the formation of condensed sheets. Atomic force microscopy imaging of deposited films show the formation of propeller-like aggregates when C₈- or C₁₆-mim-IL is present in the mixed films.