On the Maximum Number of Edges in Topological Graphs with no Four Pairwise Crossing Edges

A topological graph is called k -quasi-planar if it does not contain k pairwise crossing edges. It is conjectured that for every fixed k, the maximum number of edges in a k-quasi-planar graph on n vertices is O(n). We provide an affirmative answer to the case k=4.     

Circulating spatial solitons

A class of optical spatial solitons exhibiting propagation in a closed-loop orbit in a two-dimensional plane is presented. A closed-form particlelike model is derived, indicating that the quasi-centrifugal force acting on these solitons can be balanced by an inhomogeneity in the nonlinear index of refraction. Specifically, a circular-shaped nonlinear interface is shown to facilitate stable orbital propagation of solitons that carve their own circular cavity for a wide range of nonlinearity parameters.     

Upper bound imposed on responsivity of optical modulators

I study theoretically the responsivity of optical modulators. For the case of a linear response, by using perturbation theory I find an upper bound imposed on the responsivity. For the case of a two-mode modulator I find a lower bound imposed on the optical path required for achieving full modulation when the maximum birefringence strength is given.     

Enzymatic/Immunoassay Dual‐Biomarker Sensing Chip: Towards Decentralized Insulin/Glucose Detection

Performing bioassay formats based on enzyme and antibody recognition reactions with a single detection chip remains an unmet challenge owing to the different requirements of such bioassays. Herein, we describe a dual‐marker biosensor chip, integrating enzyme and antibody‐based assays for simultaneous electrochemical measurements of insulin (I) and glucose (G). Simultaneous G/I sensing has been realized by addressing key fabrication and operational challenges associated with the different assay requirements and surface chemistry. The I immunosensor relies on a peroxidase‐labeled sandwich immunoassay, while G is monitored through reaction with glucose oxidase. The dual diabetes biomarker chip offers selective and reproducible detection of picomolar I and millimolar G concentrations in a single microliter sample droplet within less than 30 min, including direct measurements in whole blood and saliva samples. The resulting integrated enzymatic‐immunoassay biosensor chip opens a new realm in point‐of‐care multiplexed biomarker detection.     

Analytic Hessian derivation for the quasi-one-dimensional Euler equations

The Hessian for the quasi-one-dimensional Euler equations is derived. A pressure minimization problem and a pressure matching inverse problem are considered. The flow sensitivity, adjoint sensitivity, gradient and Hessian are calculated analytically using a direct approach that is specific to the model problems. For the pressure minimization problem we find that the Hessian exists and it contains elements with significantly larger values around the shock location. For the pressure matching inverse problem we find at least one case for which the gradient as well as the Hessian do not exist. In addition, two formulations for calculating the Hessian are proposed and implemented for the given problems. Both methods can be implemented in industrial applications such as large scale aerodynamic optimization.     

Spatial averaging of oceanic rainfall variability using underwater sound: Ionian Sea rainfall experiment 2004

An experiment to evaluate the inherent spatial averaging of the underwater acoustic signal from rainfall was conducted in the winter of 2004 in the Ionian Sea southwest of Greece. A mooring with four passive aquatic listeners (PALs) at 60, 200, 1000, and 2000 m was deployed at 36.85 degrees N, 21.52 degrees E, 17 km west of a dual-polarization X-band coastal radar at Methoni, Greece. The acoustic signal is classified into wind, rain, shipping, and whale categories. It is similar at all depths and rainfall is detected at all depths. A signal that is consistent with the clicking of deep-diving beaked whales is present 2% of the time, although there was no visual confirmation of whale presence. Co-detection of rainfall with the radar verifies that the acoustic detection of rainfall is excellent. Once detection is made, the correlation between acoustic and radar rainfall rates is high. Spatial averaging of the radar rainfall rates in concentric circles over the mooring verifies the larger inherent spatial averaging of the rainfall signal with recording depth. For the PAL at 2000 m, the maximum correlation was at 3-4 km, suggesting a listening area for the acoustic rainfall measurement of roughly 30-50 km(2).     

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.     

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