Destroying cycles in digraphs

For a simple directed graph G with no directed triangles, let β(G) be the size of the smallest subset X ∈ E(G) such that G\X has no directed cycles, and let γ(G) denote the number of unordered pairs of nonadjacent vertices in G. Chudnovsky, Seymour, and Sullivan showed that β(G) ≤ γ(G), and conjectured that β(G) ≤ $\tfrac{{\gamma (G)}} {2}$\tfrac{{\gamma (G)}} {2} . In this paper we prove that β(G)<0.88γ(G).     

Deformation and breakup of micro- and nanoparticle stabilized droplets in microfluidic extensional flows

Using a microfluidic flow-focusing device, monodisperse water droplets in oil were generated and their interface populated by either 1 μm or 500 nm amine modified silica particles suspended in the water phase. The deformation and breakup of these Pickering droplets were studied in both pure extensional flow and combined extensional and shear flow at various capillary numbers using a microfluidic hyperbolic contraction. The shear resulted from droplet confinement and increased with droplet size and position along the hyperbolic contraction. Droplet deformation was found to increase with increasing confinement and capillary number. At low confinements and low capillary numbers, the droplet deformation followed the predictions of theory. For fully confined droplets, where the interface was populated by 1 μm silica particles, the droplet deformation increased precipitously and two tails were observed to form at the rear of the droplet. These tails were similar to those seen for surfactant covered droplets. At a critical capillary number, daughter droplets were observed to stream from these tails. Due to the elasticity of the particle-laden interface, these drops did not return to a spherical shape, but were observed to buckle. Although increases in droplet deformation were observed, no tail streaming occurred for the 500 nm silica particle covered droplets over the range of capillary numbers studied.     

Basic characteristics of interference image obtained using spatially phase-modulated mirror array

Single-shot full-field optical coherence tomography (OCT) using spatially phase-modulated reference light has been proposed to achieve a higher sensitivity.16) The reference light can be generated by a spatially phase-modulated mirror array (SPMA). The basic characteristics of an interference image using SPMA have been demonstrated using a superluminescent diode (SLD) with a center wavelength of 840 nm as a popular low-coherence light source. SPMA consisted of a small mirror of 10 × 10 mm² and had a full area of 5 × 5mm². The magnifications in the reference arm were 3, 2, and 1. The corresponding magnifications in the signal arm were 18.1, 12.2, and 5.2. The ratios of the interference area to the full CCD area were 0.68, 0.32, and 0.13. Visibilities and ratios for calculations were measured at 0.38 (54%), 0.19 (28%), and 0.062 (8.2%). The periodical background noise was high owing to interferences with scattered lights from SPMA. From the spectra of signal intensity profiles in the subtracted image between two interference images, it was confirmed that the optical phase in the reference light was spatially and periodically modulated by SPMA.     

Cost-effective interrogation of single nucleotide polymorphisms using the mismatch amplification mutation assay and capillary electrophoresis

The ability to characterize SNPs is an important aspect of many clinical diagnostic, genetic and evolutionary studies. Here, we designed a multiplexed SNP genotyping method to survey a large number of phylogenetically informative SNPs within the genome of the bacterium Bacillus anthracis. This novel method, CE universal tail mismatch amplification mutation assay (CUMA), allows for PCR multiplexing and automatic scoring of SNP genotypes, thus providing a rapid, economical and higher throughput alternative to more expensive SNP genotyping techniques. CUMA delivered accurate B. anthracis SNP genotyping results and, when multiplexed, saved reagent costs by more than 80% compared with TaqMan real-time PCR. When real-time PCR technology and instrumentation is unavailable or the reagents are cost-prohibitive, CUMA is a powerful alternative for SNP genotyping.     

Stability of electrostatic ion cyclotron waves in a multi-ion plasma

We have studied the stability of the electrostatic ion cyclotron wave in a plasma consisting of isotropic hydrogen ions (H⁺) and temperature-anisotropic positively (O⁺) and negatively (O⁻) charged oxygen ions, with the electrons drifting parallel to the magnetic field. Analytical expressions have been derived for the frequency and growth/damping rate of ion cyclotron waves around the first harmonic of both hydrogen and oxygen ion gyrofrequencies. We find that the frequencies and growth/damping rates are dependent on the densities and temperatures of all species of ions. A detailed numerical study, for parameters relevant to comet Halley, shows that the growth rate is dependent on the magnitude of the frequency. The ion cyclotron waves are driven by the electron drift parallel to the magnetic field; the temperature anisotropy of the oxygen ions only slightly enhance the growth rates for small values of temperature anisotropies. A simple explanation, in terms of wave exponentiation times, is offered for the absence of electrostatic ion cyclotron waves in the multi-ion plasma of comet Halley.     

Synthesis and characterization of polylactide‐PAMAM “Janus‐type” linear‐dendritic hybrids

Herein, we present a facile and comprehensive synthetic methodology for the preparation of polyester‐polyamidoamine (PAMAM) (i.e., polyester: polylactide [PLA] (hydrophobic) and polyamidoamine, PAMAM [hydrophilic]) polymers. A library of PLA‐PAMAM linear dendritic block copolymers (LDBCs) in which both l and d , l polylactide were employed in mass ratios of 30:70, 50:50, 70:30, and 90:10 (PLA:PAMAM) were synthesized and analyzed. When placed in aqueous media, the immiscibility of the hydrophilic and hydrophobic segments leads to nanophase‐segregation exhibited as the formation of aggregates (e.g., vesicles, worms, and/or micelles). By employing both stereochemical configurations of PLA, the differentiation in mass ratios of PLA‐PAMAM aided in elucidating the structure–property relationships of the LDBC system and provided a means toward the control of nanoparticle morphology. Transmission electron microscopy and dynamic light scattering afford the size and shape of the nanoparticles with diameters ranging from 10.6 for low mass ratios to 122.4 nm for high mass ratios of PLA‐PAMAM and positive zeta‐potential values between +24.7 mV and +48.2 mV. Furthermore, small‐angle X‐ray scattering (SAXS) studies were employed to obtain more detailed information on the morphological assemblies constructed via direct dissolution. Such insights provide a pathway toward nanomaterials with unique morphologies and tunable properties deemed relevant in the development of next generation biomaterials. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1448–1459     

Emerging techniques for submicrometer particle sizing applied to Stöber silica

The accurate characterization of submicrometer and nanometer sized particles presents a major challenge in the diverse applications envisaged for them including cosmetics, biosensors, renewable energy, and electronics. Size is one of the principal parameters for classifying particles and understanding their behavior, with other particle characteristics usually only quantifiable when size is accounted for. We present a comparative study of emerging and established techniques to size submicrometer particles, evaluating their sizing precision and relative resolution, and demonstrating the variety of physical principles upon which they are based, with the aim of developing a framework in which they can be compared. We used in-house synthesized St?ber silica particles between 100 and 400 nm in diameter as reference materials for this study. The emerging techniques of scanning ion occlusion sensing (SIOS), differential centrifugal sedimentation (DCS), and nanoparticle tracking analysis (NTA) were compared to the established techniques of transmission electron microscopy (TEM), scanning mobility particle sizing (SMPS), and dynamic light scattering (DLS). The size distributions were described using the mode, arithmetic mean, and standard deviation. Uncertainties associated with the six techniques were evaluated, including the statistical uncertainties in the mean sizes measured by the single-particle counting techniques. Q-Q plots were used to analyze the shapes of the size distributions. Through the use of complementary techniques for particle sizing, a more complete characterization of the particles was achieved, with additional information on their density and porosity attained.     

How Lives Measure Up

The quality of a life is typically understood as a function of the actual goods and bads in it, that is, its actual value. Likewise, the value of a population is typically taken to be a function of the actual value of the lives in it. We introduce an alternative understanding of life quality: adjusted value. A life’s adjusted value is a function of its actual value and its ideal value (the best value it could have had). The concept of adjusted value is useful for at least three reasons. First, it fits our judgments about how well lives are going. Second, it allows us to avoid what we call False Equivalence, an error related to the non-identity problem. Third, when we use adjusted value as an input for calculating the value of a population, we can avoid two puzzles that Derek Parfit calls the “Repugnant Conclusion” and the “Mere Addition Paradox.”