Homomorphism polynomials of chemical graphs

We say that a graphG ishomomorphic to a graphH if there is a mappingp from the vertices of G onto the vertices ofH such thatp(u) andp() are adjacent inH wheneveru and are adjacent in G. Thehomomorphism polynomial of a graphG is a polynomial in two variables that counts the number of homomorphisms ofG onto the complete graph of each order. This polynomial can be computed recursively in an analog to the chromatic polynomial. In this paper, we present some results regarding the homomorphism polynomials of the graphs of chemical compounds — in particular, alkane isomers. The coefficients of the homomorphism polynomial can be used to predict the rankings of compounds with respect to several chemical properties. Our results seem to refine those obtained by Randi et al. from path lengths.     

Immunotoxic effects of cis-urocanic acid exposure in C57BL/6N and C3H/HeN mice

Exposure to ultraviolet radiation results in increased levels of intradermal cis-urocanic acid (cUCA) and alters cutaneous immunity by interfering with processing and presentation of antigen by Langerhans cells. Reports on effects of systemic immunotoxicity with 30 day cUCA exposure in laboratory rodents include thymic atrophy, thymic hypocellularity and decreased T-cell-mediated immunity; however, immune effects of single exposure or 5 day cUCA administration, which may better mimic human exposures, are poorly defined. The present study initially evaluated immune effects of single, 5 day, and 4 week cUCA exposure in C57BL/6N mice. Single administration of intradermal cUCA resulted in decreased splenocyte phagocytosis that persisted for 30 days after cUCA exposure. Five day consecutive cUCA exposure decreased numbers of phenotypically mature CD4(+)CD8(-) and CD4(-)CD8(+) (single positive) thymocytes, increased CD4(+)CD8(+) (double positive) immature thymocytes and increased splenocyte proliferation. Prolonged cUCA exposure (4 weeks) caused profound thymic hypocellularity and splenic hypercellularity and increased splenic macrophage chemiluminescence. Because of this apparent sensitivity of C57BL/6N mice to cUCA, thymic hypocellularity was compared between C57BL/6N and C3H/HeN mice dosed with cUCA, and was found to be more pronounced in the C57BL/6N strain. These results are an extension of previous conclusions on immune modulation caused by cUCA in the spleen and thymus. Further, the observed variation in sensitivity between the mouse strains is consistent with known genetic susceptibility of these strains to the immunomodulatory effects of exposure to sunlight.     

2-isohedral triangulations

A triangulations is 2-isohedral iff there are exactly two orbits of triangles under the triangulation's symmetry group. 2-isohedral triangulations are classified using incidence symbols. This also determines the homeomeric types of 2-isohedral triangulation. There are 38 types. The proof is by aggregation into isohedral tilings and by reflection axis splitting.     

Combined dermal exposure to permethrin and cis-urocanic acid suppresses the contact hypersensitivity response in C57BL/6N mice in an additive manner

Cutaneous exposure to the pyrethroid insecticide permethrin significantly suppresses contact hypersensitivity (CH) response to oxazolone in C57BL/6N mice. Additionally, cis-urocanic acid (cUCA), an endogenous cutaneous chromophore isomerized to its active form following exposure to ultraviolet radiation, modulates cell-mediated cutaneous immune responses. This study describes cutaneous immune alterations following combined topical permethrin and intradermal cUCA exposure. Female C57BL/6N mice were administered 5, 50 or 100 microg cUCA daily for 5 consecutive days. CH was then evaluated by the mouse ear swelling test (MEST) response to oxazolone. Decreased responses of 52.3%, 76.3% and 76.3%, respectively, as compared to controls were observed. Then, mice were co-exposed to 5 microg cUCA daily for 5 days and 1.5, 5, 15, or 25 microL permethrin, on either day 1, 3 or 5 of the cUCA treatment to evaluate combined immunomodulatory effects of the two chemicals, or cUCA daily for 5 days followed by permethrin on day 3, 5, or 7 after the last cUCA injection to demonstrate prolonged immunosuppressive effects. Two days after final treatment, mice were sensitized with oxazolone and MEST was performed. Mice receiving five cUCA injections and permethrin topically on cUCA injection day 1 showed up to 93.3% suppression of MEST compared to vehicle control. CH was suppressed by 87.5%, 86.6% and 74.2% in mice treated with 25 muL permethrin on days 3, 5 and 7 after cUCA, respectively, compared to vehicle control. Taken together, these data indicate co-exposure to cUCA and permethrin profoundly suppresses cell-mediated cutaneous immunity.     

An alternate approach to analyzing convergence by Leslie matrices

The process of convergence of a population vector to its stable equivalent under iteration by a Leslie matrix is analyzed. The norm mostly used is an additive norm, called the eigen‐norm. A natural convergence measure S is shown to be monotonic non‐increasing upon matrix iteration. Guaranteed rates of convergence of S for any population are described by functions F and B, and results are obtained for these functions. Analogous measures based upon concepts of spectral decompositions are considered. Corresponding results are presented, and comparisons made between these spectral measures and natural measures from a theoretical approach and from data analyses of samples of modern populations.     

Nachweis, Bestimmung und Trennung des Zirkoniums von anderen Elementen

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