Lifts, Discrepancy and Nearly Optimal Spectral Gap*

We present a new explicit construction for expander graphs with nearly optimal spectral gap. The construction is based on a series of 2-lift operations. Let G be a graph on n vertices. A 2-lift of G is a graph H on 2n vertices, with a covering map π :H →G. It is not hard to see that all eigenvalues of G are also eigenvalues of H. In addition, H has n “new” eigenvalues. We conjecture that every d-regular graph has a 2-lift such that all new eigenvalues are in the range (if true, this is tight, e.g. by the Alon–Boppana bound). Here we show that every graph of maximal degree d has a 2-lift such that all “new” eigenvalues are in the range for some constant c. This leads to a deterministic polynomial time algorithm for constructing arbitrarily large d-regular graphs, with second eigenvalue . The proof uses the following lemma (Lemma 3.3): Let A be a real symmetric matrix with zeros on the diagonal. Let d be such that the l₁ norm of each row in A is at most d. Suppose that for every x,y ∈{0,1}ⁿ with ‹x,y›=0. Then the spectral radius of A is O(α(log(d/α)+1)). An interesting consequence of this lemma is a converse to the Expander Mixing Lemma. * This research is supported by the Israeli Ministry of Science and the Israel Science Foundation.     

Behavioral modeling in weight loss interventions

Designing systems with human agents is difficult because it often requires models that characterize agents’ responses to changes in the system’s states and inputs. An example of this scenario occurs when designing treatments for obesity. While weight loss interventions through increasing physical activity and modifying diet have found success in reducing individuals’ weight, such programs are difficult to maintain over long periods of time due to lack of patient adherence. A promising approach to increase adherence is through the personalization of treatments to each patient. In this paper, we make a contribution toward treatment personalization by developing a framework for predictive modeling using utility functions that depend upon both time-varying system states and motivational states evolving according to some modeled process corresponding to qualitative social science models of behavior change. Computing the predictive model requires solving a bilevel program, which we reformulate as a mixed-integer linear program (MILP). This reformulation provides the first (to our knowledge) formulation for Bayesian inference that uses empirical histograms as prior distributions. We study the predictive ability of our framework using a data set from a weight loss intervention, and our predictive model is validated by comparison to standard machine learning approaches. We conclude by describing how our predictive model could be used for optimization, unlike standard machine learning approaches that cannot.     

Stimulus-responsive hydrogels made from biosynthetic fibrinogen conjugates for tissue engineering: structural characterization

Nanostructured hydrogels based on "smart" polymer conjugates of poloxamers and protein molecules were developed in order to form stimulus-responsive materials with bioactive properties for 3-D cell culture. Functionalized Pluronic F127 was covalently attached to a fibrinopeptide backbone and cross-linked into a structurally versatile and mechanically stable polymer network endowed with bioactivity and temperature-responsive structural features. Small angle X-ray scattering and transmission electron microscopy combined with rheology were used to characterize the structural and mechanical features of this biosynthetic conjugate, both in solution and in hydrogel form. The temperature at which the chemical cross-linking of F127-fibrinopeptide conjugates was initiated had a profound influence on the mechanical properties of the thermo-responsive hydrogel. The analysis of the scattering data revealed modification in the structure of the protein backbone resulting from increases in ambient temperature, whereas the structure of the polymer was not affected by ambient temperature. The hydrogel cross-linking temperature also had a major influence on the modulus of the hydrogel, which was rationally correlated to the molecular structure of the polymer network. The hydrogel structure exhibited a small mesh size when cross-linked at low temperatures and a larger mesh size when cross-linked at higher temperatures. The mesh size was nicely correlated to the mechanical properties of the hydrogels at the respective cross-linking temperatures. The schematic charts that model this material's behavior help to illustrate the relationship that exists between the molecular structure, the cross-linking temperature, and the temperature-responsive features for this class of protein-polymer conjugates. The precise control over structural and mechanical properties that can be achieved with this bioactive hydrogel material is essential in designing a tissue-engineering scaffold for clinical applications.     

Thermal effects – an alternative mechanism for plasmon-assisted photocatalysis

Recent experiments claimed that the catalysis of reaction rates in numerous bond-dissociation reactions occurs via the decrease of activation barriers driven by non-equilibrium (“hot”) electrons in illuminated plasmonic metal nanoparticles. Thus, these experiments identify plasmon-assisted photocatalysis as a promising path for enhancing the efficiency of various chemical reactions. Here, we argue that what appears to be photocatalysis is much more likely thermo-catalysis, driven by the well-known plasmon-enhanced ability of illuminated metallic nanoparticles to serve as heat sources. Specifically, we point to some of the most important papers in the field, and show that a simple theory of illumination-induced heating can explain the extracted experimental data to remarkable agreement, with minimal to no fit parameters. We further show that any small temperature difference between the photocatalysis experiment and a control experiment performed under external heating is effectively amplified by the exponential sensitivity of the reaction, and is very likely to be interpreted incorrectly as “hot” electron effects.

A simple Arrhenius-based theory of heating, rather than “hot electrons”, can reproduce some high-profile photocatalysis experimental results to remarkable accuracy. Flaws in temperature measurement may have led to wrong conclusions.     

HPTLC coupled to ESI-Tandem MS for identifying phospholipids associated to membrane proteins in photosynthetic purple bacteria

High-performance thin-layer chromatography (HPTLC)-densitometry was directly combined with electrospray (ESI) tandem mass spectrometry for obtaining rapid and relevant structural identification of phospholipids (PL) species associated to membrane proteins (MP), in non-sulfur, purple bacteria having photosynthetic activity. Thus, species belonging to phosphatidylcholines (PC), phosphatidylethanolamines (PE), cardiolipins (CL) and phosphatidylglycerols (PG) associated to MP were investigated in bacterial membrane extracts from Rhodobacter (Rb.) blasticus, Rhodospirillum (R.) rubrum and Rhodobaca (Rbc.) bogoriensis, as well as those which are bound to a purified MP-photosynthetic complex from Rbc. bogoriensis.

PL-classes were separated using a 7-step gradient-solvent sequence with a previous acid plate preconditioning, using Automated Multiple Development. Band zones of the plate corresponding to PL classes were selected to ensure their direct transfer to ion-trap MS equipment through an elution-based interface.

Under the studied conditions, ESI⁺-MS spectra of PC and CL mostly showed sodium adducts ([M?+?Na]⁺) and [M-2H?+?3Na]⁺, respectively, when recorded from the plate. The respective sodium adducts were fragmented in the ion-trap, and sodium remained as the charge of the fragment ions, thus being useful for their structural identification through MS/MS. ESI^--MS and MS/MS spectra of CL were also obtained as [M-2H]^2?, as well as those of PE and PG species as [M-H]^- and [M]^?, respectively.

In this way, relative composition profiles of each studied PL-class by ESI-MS, and further identification of individual PL and the molecular species belonging to each of them by MS/MS were obtained.     

Law of corresponding states and thermal-diffusion factor of He-Ar mixtures from two-bulb measurements

Experimental data of the thermal diffusion factor for low density He-Ar mixtures are given. The measurement apparatus is a two-bulb operated at T_H = 308 K and T_C = 77.6 K, the mean temperature being T = 148 K. It is concluded that the extended law of corresponding states proposed by Kestin, Ro and Wakeham is able to predict in a correct way the obtained results.     

Diffusion of buffer layer assisted grown gold nanoclusters on Ru(100) and p(1 x 2)-O/Ru(100) surfaces

Patterning of metallic clusters on surfaces is demonstrated by utilizing a buffer layer assisted laser patterning technique (BLALP). This method has been employed in order to measure the diffusion of AFM and STM characterized size selected gold nanoclusters (5-10 nm diameter), over Ru(100) and p(1 x 2)-O/Ru(100) surfaces. Optical linear diffraction from gold cluster coverage gratings was utilized for the macroscopic diffusion measurements. The clusters were found to diffuse on the surface intact without significant coalescence or sintering. The barrier for metastable gold nanocluster diffusion on the surface is thought to be lower than the energy required for surface wetting. The apparent activation energy for diffusion was found to depend on the cluster size, increasing from 6.2 +/- 0.4 kcal/mol for 5 nm clusters to 10.6 +/- 0.5 kcal/mol for 9 nm clusters. The macroscopic diffusion of gold nanoclusters has been studied on the p(1 x 2)-O/Ru(100) surface as well, where surface diffusion was found to be rather insensitive to the clusters size with activation energy of 5.5 +/- 1 kcal/mol. The difference between the two surfaces is discussed in terms of a better commensurability (higher level of friction) of the gold facets at the contact area with the clean Ru(100) than in the case of the oxidized surface.     

A Dynamic Nuclear Polarization spectrometer at 95 GHz/144 MHz with EPR and NMR excitation and detection capabilities

A spectrometer specifically designed for systematic studies of the spin dynamics underlying Dynamic Nuclear Polarization (DNP) in solids at low temperatures is described. The spectrometer functions as a fully operational NMR spectrometer (144 MHz) and pulse EPR spectrometer (95 GHz) with a microwave (MW) power of up to 300 mW at the sample position, generating a MW B(1) field as high as 800 KHz. The combined NMR/EPR probe comprises of an open-structure horn-reflector configuration that functions as a low Q EPR cavity and an RF coil that can accommodate a 30-50 μl sample tube. The performance of the spectrometer is demonstrated through some basic pulsed EPR experiments, such as echo-detected EPR, saturation recovery and nutation measurements, that enable quantification of the actual intensity of MW irradiation at the position of the sample. In addition, DNP enhanced NMR signals of samples containing TEMPO and trityl are followed as a function of the MW frequency. Buildup curves of the nuclear polarization are recorded as a function of the microwave irradiation time period at different temperatures and for different MW powers.