An Extremal Problem on Degree Sequences of Graphs

 Let G=(I _n ,E) be the graph of the n-dimensional cube. Namely, I _n ={0,1} ⁿ and [x,y]∈E whenever ||x−y||₁=1. For A⊆I _n and x∈A define h _A (x) =#{y∈I _n A|[x,y]∈E}, i.e., the number of vertices adjacent to x outside of A. Talagrand, following Margulis, proves that for every set A⊆I _n of size 2 ⁿ⁻¹ we have for a universal constant K independent of n. We prove a related lower bound for graphs: Let G=(V,E) be a graph with . Then , where d(x) is the degree of x. Equality occurs for the clique on k vertices. Received: January 7, 2000 RID="*" ID="*" Supported in part by BSF and by the Israeli academy of sciences     

Single-walled carbon nanotubes embedded in oriented polymeric nanofibers by electrospinning

The electrospinning process was used successfully to embed single-walled carbon nanotubes (SWCNTs) in a poly(ethylene oxide) (PEO) matrix, forming composite nanofibers. Initial dispersion of SWCNTs in water was achieved by the use of an amphiphilic alternating copolymer of styrene and sodium maleate. The resulting dispersions were stable, having a dark, smooth, ink-like appearance. For electrospinning, the dispersions were mixed with PEO solution in an ethanol/water mixture. The distribution and conformation of the nanotubes in the nanofibers were studied by transmission electron microscopy (TEM). Oxygen plasma etching was used to expose the nanotubes within the nanofibers to facilitate direct observation. Nanotube alignment within the nanofibers was shown to depend strongly on the quality of the initial dispersions. Well-dispersed and separated nanotubes were embedded in a straight and aligned form, while entangled nonseparated nanotubes were incorporated as dense aggregates. X-ray diffraction demonstrated a high degree of orientation of the PEO crystals in the electrospun nanofibers with embedded SWCNTs. This result is in pronounced distinction to the detrimental effect of incorporation of multiwalled carbon nanotubes on polymer orientation in electrospun nanofibers, as reported previously.     

Non-Gaussian noise in quantum wells infrared photodetectors

Non-Gaussian dark current noise has been observed in quantum wells infrared photo detectors. The non-Gaussian component of the noise was ascribed to fluctuations of spatial distribution of electric field in the device. Non-Gaussian noise was found in both n- and p-type QWIPs, however, it was significantly less pronounce. In n-type devices non-Gaussian noise manifests itself only as randomly distributed excess current bursts. In p-type QWIPs the non-Gaussian noise takes form of bias dependent random telegraph-like fluctuations with a finite time of transition between the levels. The lifetime at both levels is Poisson distributed and the average lifetime, together with the level spacing, strongly depend on bias voltage. At low voltages the system stays predominantly in the low current level while at higher voltages the average lifetime of the high current level is longer. The transient time of passing between the states has been related to the charging time constant of the system determined by QWIP capacitance and contacts resistance.     

Elastic scattering of 17, 18O on 12, 13C at Ec.m. = 12.6 – 14.0 MeV

The angular distributions of the elastic scattering of ^{17, 18}O on ^{12, 13}C were measured at c.m. energies between 12.6 to 14.0 MeV. A rise of the cross section at backward angles was observed. Standard optical-model fits were found to reproduce reasonably well the forward part of the cross section, but fail at backward angles. Possible contributions of first-order cluster exchange and compound-nucleus reactions are discussed. Excitation functions of various exit channels in the ¹⁸O + ¹²C system were measured at backward angles in the energy range of 12.0 to 14.8 MeV c.m. No significant correlation was found between any of these cross sections.     

On the variational problem for upper tails in sparse random graphs

What is the probability that the number of triangles in , the Erd?s‐Rényi random graph with edge density p , is at least twice its mean? Writing it as , already the order of the rate function r (n, p ) was a longstanding open problem when p = o (1), finally settled in 2012 by Chatterjee and by DeMarco and Kahn, who independently showed that for ; the exact asymptotics of r (n, p ) remained unknown. The following variational problem can be related to this large deviation question at : for δ > 0 fixed, what is the minimum asymptotic p‐relative entropy of a weighted graph on n vertices with triangle density at least (1 + δ )p ³? A beautiful large deviation framework of Chatterjee and Varadhan (2011) reduces upper tails for triangles to a limiting version of this problem for fixed p . A very recent breakthrough of Chatterjee and Dembo extended its validity to for an explicit α > 0, and plausibly it holds in all of the above sparse regime. In this note we show that the solution to the variational problem is when vs. when (the transition between these regimes is expressed in the count of triangles minus an edge in the minimizer). From the results of Chatterjee and Dembo, this shows for instance that the probability that for has twice as many triangles as its expectation is where . Our results further extend to k‐cliques for any fixed k , as well as give the order of the upper tail rate function for an arbitrary fixed subgraph when . © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 420–436, 2017     

Oxygen isotopes of fuel pellets from the fifth collaborative materials exercise and uranium oxides reference materials determined by continuous flow laser fluorination mass spectrometry for nuclear forensic applications

Journal of Radioanalytical and Nuclear Chemistry - Uranium oxides are essential materials in the production process of nuclear fuel for civilian or military applications. As such, identifying their...     

Photobleaching pathways in single-molecule FRET experiments

To acquire accurate structural and dynamical information on complex biomolecular machines using single-molecule fluorescence resonance energy transfer (sm-FRET), a large flux of donor and acceptor photons is needed. To achieve such fluxes, one may use higher laser excitation intensity; however, this induces increased rates of photobleaching. Anti-oxidant additives have been extensively used for reducing acceptor's photobleaching. Here we focus on deciphering the initial step along the photobleaching pathway. Utilizing an array of recently developed single-molecule and ensemble spectroscopies and doubly labeled Acyl-CoA binding protein and double-stranded DNA as model systems, we study these photobleaching pathways, which place fundamental limitations on sm-FRET experiments. We find that: (i) acceptor photobleaching scales with FRET efficiency, (ii) acceptor photobleaching is enhanced under picosecond-pulsed (vs continuous-wave) excitation, and (iii) acceptor photobleaching scales with the intensity of only the short wavelength (donor) excitation laser. We infer from these findings that the main pathway for acceptor's photobleaching is through absorption of a short wavelength photon from the acceptor's first excited singlet state and that donor's photobleaching is usually not a concern. We conclude by suggesting the use of short pulses for donor excitation, among other possible remedies, for reducing acceptor's photobleaching in sm-FRET measurements.     

Energy transfer between manganese(II) and thulium(III) in transition-metal fluoride glasses

Lead zinc gallium fluoride glass containing 2 mole% TmF₃ is shown to luminesce from ¹I₆ (35200 cm⁻¹), ¹D₂(28000), ¹G₄ (21500) and ³H₄ (12800) to several lower J levels. When the 24 mole% ZnF₂ is replaced by MnF₂ in the absence of thulium, the (broad band) quartet-to-sextet (ground state) emission at 16800cm⁻¹ has a mean lifetime of 1 ms. If 2 mole% TmF₃ is added to the latter glass, energy transfer decreases the lifetime to below 0.03 ms. The high critical radius R₀ (above 20 Å) is rationalized by Mn-Mn energy migration (concomitant with a lifetime shortened from 24 ms) to be compared with R₀≈ 8 Å for low Mn(II) concentration, almost identical with energy transfer between 1 mole% each of MnF₂ and NdF₃ previously studied in an analogous glass.     

Electrospun polymer nanofibers: Mechanical and thermodynamic perspectives

This article reviews and discusses some open problems concerning polymer materials of reduced sizes and dimensions. Such objects exhibit exceptional physical properties when compared with their macroscopic counterparts. More specifically, abrupt increases in polymer nanofiber elastic modulus have been observed when diameters drop below a certain value. In addition, temperature dependence of elastic modulus is highly influenced by fiber diameter. Mechanical (macroscopic) analyses have failed to provide satisfactory explanations for the mechanisms ruling such features, calling for detailed microscopic examination of the systems in question. A hypothesis bridging the current knowledge gaps is presented. The key element of this hypothesis is based on confinement of the supermolecular microstructure of polymer nanofibers and its dominant role in the deformation process. This suggestion challenges the commonly held view suggesting that surface effects are the most significant parameters impacting mechanical and thermodynamic nanofiber behaviors. The review will focus on the mechanical and thermodynamic properties of electrospun polymer nanofibers, selected as representatives of nanoscale polymer objects. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011