Computing weighted Szeged and PI indices from quotient graphs

The weighted (edge-)Szeged index and the weighted (vertex-)PI index are modifications of the (edge-)Szeged index and the (vertex-)PI index, respectively, because they take into account also the vertex degrees. As the main result of this article, we prove that if G is a connected graph, then all these indices can be computed in terms of the corresponding indices of weighted quotient graphs with respect to a partition of the edge set that is coarser than the Θ^*-partition. If G is a benzenoid system or a phenylene, then it is possible to choose a partition of the edge set in such a way that the quotient graphs are trees. As a consequence, it is shown that for a benzenoid system, the mentioned indices can be computed in sublinear time with respect to the number of vertices. Moreover, closed formulas for linear phenylenes are also deduced.     

Spectrally optimal illuminations for diabetic retinopathy detection in retinal imaging

Optical Review - Retinal photography is a standard method for recording retinal diseases for subsequent analysis and diagnosis. However, the currently used white light or red-free retinal imaging...     

New 3,4-Annelated Coumarin Derivatives: Synthesis, Antimicrobial Activity, Antioxidant Capacity, and Molecular Modeling

Summary.  The one pot reaction preparation, spectral analysis, and molecular modeling experiments on the new 3,4-annelated coumarin systems with bioactivity associated structural features are described. These provided the insight into the equilibrium of the respective tautomeric forms making possible the reconciliation of previously published spectral data with the structure assignments as well as the correction of erroneously established structures. The synthesized compounds were tested in a standard disk diffusion assay and displayed strong to moderate antimicrobial activity, with a promising new lead prototype compound (7-amino-9-hydroxy-5-oxa-7a,8,11-triazacyclopenta[b]phenanthren-6-one (5)) possessing greater activity that the antibiotics Ampicillin and Nystatin. Antioxidant capacities of the compounds, determined spectrophotometrically using a phosphomolybdenum method, were greater, and in the case of compound 5 four times the activity of α-tocopherol acetate.     

A lab-on-a-chip compatible bioaffinity assay method for human alpha-fetoprotein

A new lab-on-a-chip compatible binding assay platform is introduced. The platform combines dry-chemistry bioaffinity reagents and the recently introduced ArcDia TPX binding assay technique. The technique employs polymer microspheres as a solid phase reaction carrier, fluorescently labeled antibody conjugates, and detection of fluorescence emission from the surface of individual microspheres by two-photon excitation fluorescence. Signal response of the technique is independent of the reaction volume, thus the technique is particularly well suited for detection of bioaffinity reactions from miniature volumes. Performance of the new assay platform is studied by means of an immunometric assay of human alpha-fetoprotein (hAFP) in 384-plate format, and the results are compared to those of a corresponding wet-chemistry assay method. The results show that the ArcDia TPX detection technique can be combined with dry-chemistry reagents without compromises in assay performance. The microchip field has so far been characterized with a lack of microchip-compatible detection platforms which would allow cost-effective microchip design and sensitive bioaffinity detection. The presented detection technique is expected to provide a solution for this shortage.     

Characterizations of Sets of Finite Perimeter Using Heat Kernels in Metric Spaces

The overarching goal of this paper is to link the notion of sets of finite perimeter (a concept associated with N^1,1-spaces) and the theory of heat semigroups (a concept related to N^1,2-spaces) in the setting of metric measure spaces whose measure is doubling and supports a 1-Poincaré inequality. We prove a characterization of sets of finite perimeter in terms of a short time behavior of the heat semigroup in such metric spaces. We also give a new characterization of BV functions in terms of a near-diagonal energy in this general setting.     

Homeomorphisms of the Heisenberg group preserving BMO

We provide a new geometric proof of Reimann’s theorem characterizing quasiconformal mappings as the ones preserving functions of bounded mean oscillation. While our proof is new already in the Euclidean spaces, it is applicable in Heisenberg groups as well as in more general stratified nilpotent Carnot groups.