The discretized flow on domains of attraction: a structural stability result

It is well known that, for stepsize sufficiently small, compactattractors of ordinary differential equations persist underdiscretization. The present paper describes the structure ofthe discrete-time dynamical system obtained via discretizationon A(M_h)\M_h where M_h is the approximate attractor and A(M_h)is its domain of attraction. The existence of a smooth embeddinginto a continuous-time parallelizable flow is proved. The constructioncan be used to define sections for discretizations and can beinterpreted as a justification of the method of modified equations.     

Synthesis of the first difunctional N-fluoro perfluoroalkylsulfonylimides, CF3SO2NFSO2(CF2)nSO2NFSO2CF3

Synthesis of difunctional N,N′-difluoro perfluoroalkylsulfonamides, CF₃SO₂NFSO₂(CF₂)_nSO₂NFSO₂CF₃, where n=4, 6 is reported. A related compound with an oxygen linkage CF₃SO₂NFSO₂(CF₂)₂O(CF₂)₂SO₂NFSO₂CF₃ has also been prepared. These reagents showed good activity for electrophilic fluorination.     

Spurious serotonin dimer formation using electrokinetic injection in capillary electrophoresis from small volume biological samples

One normally assumes that the analytical measurement process does not introduce spurious compounds. Capillary electrophoresis is a separation method frequently used for small-volume biological measurements. We demonstrate the potential for creating new peaks in a capillary electropherogram when using electrokinetic injections and illustrate the potential deleterious effects with biological samples involving serotonin and nitric oxide measurements. Specifically, when measuring the serotonin content from individual neurons using electrokinetic injections from 360 nL stainless steel vials, we detect a new peak that we identify as a serotonin dimer. We do not observe this peak when using hydrodynamic injections.     

Error estimates for generalized barycentric interpolation

We prove the optimal convergence estimate for first-order interpolants used in finite element methods based on three major approaches for generalizing barycentric interpolation functions to convex planar polygonal domains. The Wachspress approach explicitly constructs rational functions, the Sibson approach uses Voronoi diagrams on the vertices of the polygon to define the functions, and the Harmonic approach defines the functions as the solution of a PDE. We show that given certain conditions on the geometry of the polygon, each of these constructions can obtain the optimal convergence estimate. In particular, we show that the well-known maximum interior angle condition required for interpolants over triangles is still required for Wachspress functions but not for Sibson functions.     

35Cl NQR spectra of group 1 and silver dichloromethanesulfonates

The dichloromethanesulfonates of silver and other +1-charged cations, M ^?+?(Cl₂CHSO $_{3}^{-})$ (M = Ag, Tl, Li, Na, K, Rb, Cs) were synthesized and studied by ³⁵Cl NQR. Dichloromethanesulfonic acid was prepared by the methanolysis of dichloromethanesulfonyl chloride, and was then neutralized with the carbonates of the +1-charged cations to produce the corresponding dichloromethanesulfonate salt. This NQR study completed the investigation of the chloroacetates and chloromethanesulfonates of silver, Ag^?+?(Cl _x CH_3???x SO $_{3}^{-})$ and Ag^?+?(Cl _x CH_3???x CO $_{2}^{-})$ , and suggests (1) that the ability of organochlorine atoms to coordinate to silver decreases as the number of electron-withdrawing groups (Cl, SO $_{3}^{-}$ , CO $_{2}^{-})$ attached to the carbon atom increases; (2) that the unusually large NQR spectral width found among M ^?+?(Cl₂CHCO $_{2}^{-})$ salts is not present among M ^?+?(Cl₂CHSO $_{3}^{-})$ salts, and therefore is not generally characteristic of the dichloromethyl group in salts.     

Functional optical coherence tomography for detecting neural activity through scattering changes

We have demonstrated functional optical coherence tomography (fOCT) for neural imaging by detecting scattering changes during the propagation of action potentials through neural tissue. OCT images of nerve fibers from the abdominal ganglion of the sea slug Aplysia californica were taken before, during, and after electrical stimulation. Images acquired during stimulation showed localized reversible increases in scattering compared with those acquired before stimulation. Motion-mode OCT images of nerve fibers showed transient scattering changes from spontaneous action potentials. These results demonstrate that OCT is sensitive to the optical changes in electrically active nerve fibers.     

Microfluidic devices for culturing primary mammalian neurons at low densities

Microfluidic devices have been used to study high-density cultures of many cell types. Because cell-to-cell signaling is local, however, there exists a need to develop culture systems that sustain small numbers of neurons and enable analyses of the microenvironments. Such cultures are hard to maintain in stable form, and it is difficult to prevent cell death when using primary mammalian neurons. We demonstrate that postnatal primary hippocampal neurons from rat can be cultured at low densities within nanoliter-volume microdevices fabricated using polydimethylsiloxane (PDMS). Doing so requires an additional fabrication step, serial extractions/washes of PDMS with several solvents, which removes uncrosslinked oligomers, solvent and residues of the platinum catalyst used to cure the polymer. We found this step improves the biocompatibility of the PDMS devices significantly. Whereas neurons survive for > or = 7 days in open channel microdevices, the ability to culture neurons in closed-channel devices made of untreated, native PDMS is limited to < or = 2 days. When the closed-channel PDMS devices are extracted, biocompatibility improves allowing for reliable neuron cultures at low densities for > or = 7 days. Comparisons made to autoclaved PDMS and native, untreated PDMS reveal that the solvent-treated polymer is superior in sustaining low densities of primary neurons in culture. When neuronal affinity for local substrates is observed directly, we find that axons localize to channel corners and prefer PDMS surfaces to glass in hybrid devices. When perfusing the channels with media by gravity flow, cultured hippocampal neurons survive for > or = 11 days. Extracting PDMS improves biocompatibility of microfluidic devices and thus enables the study of differentiation of identifiable neurons and the characterization of local extracellular signals.