Pattern formation in associative neural networks is related to a
quadratic optimization problem. Biological considerations imply
that the functional is constrained in the L\infty norm and in
the L1 norm. We consider such optimization problems. We derive
the Euler–Lagrange equations, and construct basic properties of
the maximizers. We study in some detail the case where the kernel
of the quadratic functional is finite-dimensional. In this case
the optimization problem can be fully characterized by the
geometry of a certain convex and compact finite-dimensional set. 相似文献
The authors have investigated (a) the self-assembly of single-stranded DNA (ssDNA) on glass surfaces, and (b) the interaction of DNA with liquid crystals (LCs) on solid surfaces. The results suggest that ssDNA (compared to dsDNA) on the solid interface causes particularly different orientations in LCs. The LC molecules assume a uniform homeotropic orientation on the surface with a typical surface ssDNA coverage of ~2.4 × 1012 molecules per square cm. Once complementary DNA is hybridized on the surface, the homotropic orientation of the LCs becomes disrupted. This orientation transition can be visually observed by using a crossed polarizer. The findings were exploiting to design an assay for target DNA (= analyte DNA) that has an ~0.1 nM detection limit. The assay is highly selective and can easily differentiate target DNA from single-base mismatch and non-complementary DNA. In our perception, it represents a powerful, label-free and portable DNA detection scheme.
Graphical abstract Schematic illustration of the mechanism for orientation behavior of a liquid crystal film supported on different surfaces. The homeotropic orientation of LC molecules was induced by ssDNA with appropriate surface coverage and was disrupted by ssDNA with lower or higher surface coverage or P1/T1 complex. 5CB: 4-Cyano-4′-pentylbiphenyl. TEA: Triethoxysilylbutyraldehyde.
The authors describe a method for amperometric determination of chloramine-T that is based on the indirect detection of chloramine-T by detecting p-quinone imine (p-QI) that is generated by oxidation of p-aminophenylboronic acid by chloramine-T. p-QI can be detected with excellent selectivity and at low potential by using a glassy carbon electrode. Hence, the method displays attractive features such as high sensitivity, wide detection range and excellent selectivity. The electrode has two linear responses in the 50 nM to 100 μM concentration range and a 6 nM detection limit. Compared to other electrochemical methods, this assay has a detection limit that is better by three orders of magnitude. The relative standard deviation is 3.4% for the determination of 10 μM of the medical chloramine-T sample, and the recovery of a samples containing chloramine-T at a level of 10 μM is 115%.
Graphical abstract Highly sensitive electrochemical detection of chloramine-T is achieved based on the reaction of chloramine-T with p-aminophenylboronic acid with a detection limit of 6 nM.
A glassy carbon electrode (GCE) was modified with gold nanoparticles (AuNPs) coated on monolayer graphene (AuNP/MG) by direct in situ sputtering of AuNPs on CVD-generated graphene. This process avoids complicated polymer transfer and polymer cleaning processes and affords AuNPs with a clean surface. The monolayer graphene is ductile and well dispersed. The clean surface of the AuNPs renders this sensor superior to GCEs modified with AuNPs on reduced graphene oxide in terms of the amperometric non-enzymatic determination of hydrogen peroxide. The detection limit is 10 nM (S/N = 3) at 0.55 V (vs. SCE), which is lower than that for similar methods, and the response time is as short as 2 s. Another attractive feature of the sensor is its feasibility for large-scale production via CVD and sputtering.
Graphical abstract Gold nanoparticles deposited onto monolayered graphene generated by chemical vapor deposition (CVD) are used for electrochemical sensing of H2O2, with the detection limit of 10 nM (S/N = 3) and response time of less than 2 s.
The effects of three types of electrically-inert fillers, calcium carbonate (CaCO3), talc and glass fiber (GF), on electrical resistivity, crystallization behavior and dynamic mechanical properties of poly(m-xylene adipamide) (MXD6)/multiwalled carbon nanotube (MWCNT) composites are investigated. The electrical resistivity of MXD6/MWCNT composites is significantly reduced with the addition of inert fillers due to the volume-exclusion effect that leads to increased effective concentration of MWCNTs in MXD6 matrix and also due to improved MWCNT dispersion. The crystallization temperature of MXD6 increases with the addition of MWCNTs, indicating that MWCNTs can act as nucleating agent and induce crystallization of MXD6. The incorporation of inert fillers has no further effect on crystallization behavior of MXD6, but significantly improves the storage modulus of MXD6/MWCNT composite, demonstrating that CaCO3, talc and GF filled MXD6/MWCNT composites are very promising materials with not only improved electrical property but also excellent mechanical properties. 相似文献
