On Bifurcations in Nonlinear Consensus Networks

The theory of consensus dynamics is widely employed to study various linear behaviors in networked control systems. Moreover, nonlinear phenomena have been observed in animal groups, power networks and in other networked systems. These observations inspire the development in this paper of three novel approaches to define distributed nonlinear dynamical interactions. The resulting dynamical systems are akin to higher-order nonlinear consensus systems. Over connected undirected graphs, the resulting dynamical systems exhibit various interesting behaviors that we rigorously characterize.     

Gd(III)[15-metallacrown-5] recognition of chiral α-amino acid analogues

Chiral Ln(III)[15-metallacrown-5] complexes with phenyl side chains have been shown to encapsulate aromatic carboxylates reversibly in their hydrophobic cavities. Given the importance of selective guest binding for applications of supramolecular containers in synthesis, separations, and materials design, the affinity of Gd(III)[15-metallacrown(Cu(II), L-pheHA)-5] hosts for a series of chiral carboxylate guests with varying substitutions on the α-carbon (phenylalanine, N-acetyl-phenylalanine, phenyllactate, mandelate, methoxyphenylacetate) has been investigated. Differential binding of S- and R-phenylalanine was revealed by X-ray crystallography, as the S-enantiomer exclusively forms associative hydrogen bonds with oxygen atoms in the metallacrown ring. Selective guest binding in solution was assessed with isothermal titration calorimetry, which measures the sequential guest binding in the hydrophobic cavity first and the hydrophilic face of the host, and a cyclic voltammetry assay, which quantifies guest binding strength in the hydrophobic cavity of the host exclusively. In solution, the Gd(III)[15-metallacrown(Cu(II), L-pheHA)-5] hydrophobic cavity exhibits modest chiral selectivity for enantiomers of phenylalanine (K(S)/K(R) = 2.4) and mandelate (K(S)/K(R) = 1.22). Weak binding constants of ～100 M(-1) were measured for neutral and -1 charged carboxylates with hydrophilic functional groups (ammonium, N-acetyl, methyl ether). Weaker binding relative to the unsubstituted guests is attributed to unfavorable interactions between the hydrophilic functionalities of the guest and the hydrophobic cavity of the host. In contrast, binding constants greater than 2000 M(-1) were measured for α-hydroxy analogues phenyllactate and mandelate. The significantly increased affinity likely arises from the guests being bound as a -2 anion upon metal-assisted deprotonation in the Gd(III)[15-metallacrown(Cu(II), l-pheHA)-5] cavity. It is established that guest binding affinity in the hydrophobic cavity of the host follows the general trend of neutral zwitterion < monoanion < dianion, with hydrophilic functional groups decreasing the binding affinity. These results have broad implications for the development of metallacrowns as supramolecular catalysts or in chiral separations.     

Synthesis of molybdenum nitrido complexes for triple-bond metathesis of alkynes and nitriles

Complexes of the type N≡Mo(OR)(3) (R = tertiary alkyl, tertiary silyl, bulky aryl) have been synthesized in the search for molybdenum-based nitrile-alkyne cross-metathesis (NACM) catalysts. Protonolysis of known N≡Mo(NMe(2))(3) led to the formation of N≡Mo(O-2,6-(i)Pr(2)C(6)H(3))(3)(NHMe(2)) (12), N≡Mo(OSiPh(3))(3)(NHMe(2)) (5-NHMe(2)), and N≡Mo(OCPh(2)Me)(3)(NHMe(2)) (17-NHMe(2)). The X-ray structure of 12 revealed an NHMe(2) ligand bound cis to the nitrido ligand, while 5-NHMe(2) possessed an NHMe(2) bound trans to the nitride ligand. Consequently, 17-NHMe(2) readily lost its amine ligand to form N≡Mo(OCPh(2)Me)(3) (17), while 12 and 5-NHMe(2) retained their amine ligands in solution. Starting from bulkier tris-anilide complexes, N≡Mo(N[R]Ar)(3) (R = isopropyl, tert-butyl; Ar = 3,5-dimethylphenyl) allowed for the formation of base-free complexes N≡Mo(OSiPh(3))(3) (5) and N≡Mo(OSiPh(2)(t)Bu)(3) (16). Achievement of a NACM cycle requires the nitride complex to react with alkynes to form alkylidyne complexes; therefore the alkyne cross-metathesis (ACM) activity of the complexes was tested. Complex 5 was found to be an efficient catalyst for the ACM of 1-phenyl-1-butyne at room temperature. Complexes 12 and 5-NHMe(2) were also active for ACM at 75 °C, while 17-NHMe(2) and 16 did not show ACM activity. Only 5 proved to be active for the NACM of anisonitrile, which is a reactive substrate in NACM catalyzed by tungsten. NACM with 5 required a reaction temperature of 180 °C in order to initiate the requisite alkylidyne-to-nitride conversion, with slightly more than two turnovers achieved prior to catalyst deactivation. Known molybdenum nitrido complexes were screened for NACM activity under similar conditions, and only N≡Mo(OSiPh(3))(3)(py) (5-py) displayed any trace of NACM activity.     

Raman, infrared and XPS study of bamboo phytoliths after chemical digestion

Many phosphate containing minerals are found in the Jenolan Caves. Such minerals are formed by the reaction of bat guano and clays from the caves. Among these cave minerals is the mineral taranakite (K,NH(4))Al(3)(PO(4))(3)(OH)·9(H(2)O) which has been identified by X-ray diffraction. Jenolan Caves taranakite has been characterised by Raman spectroscopy. Raman and infrared bands are assigned to H(2)PO(4), OH and NH stretching vibrations. By using a combination of XRD and Raman spectroscopy, the existence of taranakite in the caves has been proven.     

Multiplex digital PCR: breaking the one target per color barrier of quantitative PCR

Quantitative polymerase chain reactions (qPCR) based on real-time PCR constitute a powerful and sensitive method for the analysis of nucleic acids. However, in qPCR, the ability to multiplex targets using differently colored fluorescent probes is typically limited to 4-fold by the spectral overlap of the fluorophores. Furthermore, multiplexing qPCR assays requires expensive instrumentation and most often lengthy assay development cycles. Digital PCR (dPCR), which is based on the amplification of single target DNA molecules in many separate reactions, is an attractive alternative to qPCR. Here we report a novel and easy method for multiplexing dPCR in picolitre droplets within emulsions-generated and read out in microfluidic devices-that takes advantage of both the very high numbers of reactions possible within emulsions (>10(6)) as well as the high likelihood that the amplification of only a single target DNA molecule will initiate within each droplet. By varying the concentration of different fluorogenic probes of the same color, it is possible to identify the different probes on the basis of fluorescence intensity. Adding multiple colors increases the number of possible reactions geometrically, rather than linearly as with qPCR. Accurate and precise copy numbers of up to sixteen per cell were measured using a model system. A 5-plex assay for spinal muscular atrophy was demonstrated with just two fluorophores to simultaneously measure the copy number of two genes (SMN1 and SMN2) and to genotype a single nucleotide polymorphism (c.815A>G, SMN1). Results of a pilot study with SMA patients are presented.     

Empirically supporting school STEM culture—The creation and validation of the STEM Culture Assessment Tool (STEM‐CAT)

School STEM Culture—an aspect of culture within a school community—is defined as the beliefs, values, practices, and resources in STEM fields as perceived by students, parents, teachers, and administrators and counselors within a school. This study validates the STEM Culture Assessment Tool (STEM‐CAT), an instrument intended to advance the use of the School STEM Culture construct within the research community. Internal consistency was determined through the use of Cronbach's alpha and factor analyses, and the instrument was found to be a reliable measure of School STEM Culture. The instrument can be used in future research to quantify School STEM Culture to determine if interventions change the culture of a school to further STEM education.     

On the possible production and detection of coherent low-energy neutrino beams

Seminal experiments are discussed to prove or disprove the possibility of producing and detecting collimated coherent beams of low-energy neutrinos with the assistance of lasers. Expressions are given for the relative probability that a laser-beam-aligned co- or counter-propagating neutrino-antineutrino pair is emitted instead of a laser photon, during stimulated de-excitations of lasable excited states inside a lasing medium. For a neodymium laser this probability is approximately 10^?7. To detect coherent beams of epithermal neutrinos and antineutrinos emitted from a pulsed high-power laser, it is anticipated that resonant non-absorptive stimulated de-excitations of lasing levels by neutrinos can be exploited to register their fly-through in a second near-threshold laser.     

On lattices with M:obius function ±1, 0

We provide simple arguments of a geometric nature to explain why the Möbius functions of certain lattices take only the values –1, 0, 1.Supported in part by NSF Grant MCS83-01867 and by a Sloan Research Fellowship.