The Poisson Voronoi Tessellation II. Edge Length Distribution Functions

This paper presents a method for the determination of the distribution function of the length of the 'typical' edge of the Poisson Voronoi tessellation. The method is based on distributional properties of the configuration of the centres in the neighbourhood of the 'typical' vertex. The distribution and density functions of the edge lengths are given in double integral form for various dimensions. Analogous characteristics are considered for two-dimensional sections through higher-dimensional Poisson Voronoi tessellations.     

The second volume moment of the typical cell and higher moments of edge lengths of the spatial Poisson–Voronoi tessellation

This paper presents analytical results for higher moments of characteristics of a Voronoi tessellation generated by a homogeneous Poisson point process in the three-dimensional Euclidean space. The second moment of the volume of the typical cell as well as higher moments for the edge length distribution and the linear contact distribution are given. These characteristics are calculated analytically and presented in a unified form.     

Four-regular graphs with rigid vertices associated to DNA recombination

Genome rearrangement and homological recombination processes have been modeled by Angeleska et al. [A. Angeleska, N. Jonoska, M. Saito, DNA recombinations through assembly graphs, Discrete Appl. Math. 157 (2009) 3020–3037] as 4-regular spacial graphs with rigid vertices, called assembly graphs. These graphs can also be represented by double occurrence words called assembly words. The rearranged DNA segments are modeled by certain types of paths in the assembly graphs called polygonal paths. The minimum number of polygonal paths visiting all vertices in a graph is called an assembly number for the graph.In this paper, we give formulas for counting certain types of assembly graphs and assembly words. Some of these formulas produce sequences not previously reported at the Online Encyclopedia of Integer Sequences (http://oeis.org). We provide a sharp upper bound for the number of polygonal paths in Hamiltonian sets of polygonal paths, and present a family of graphs that achieves this bound. We investigate changes in the assembly numbers as a result of graph compositions. Finally, we introduce a polynomial invariant for assembly graphs and show properties of this invariant.     

An approach to the sensitivity of temperature-gradient gel electrophoresis in the detection of clonally expanded T-cells in cutaneous T-cell lymphoma

Detection of T-cell clonality by polymerase chain reaction (PCR) and high-resolution electrophoresis facilitates differentiation of early stages of cutaneous T-cell lymphoma (CTCL) from benign T-cell-rich dermatoses. However, data regarding the sensitivity of the various electrophoresis techniques differ remarkably. In the present study, the capacity of heteroduplex (HD)-loaded temperature-gradient gel electrophoresis (TGGE) to detect clonally expanded T-cells was assessed systematically and modifications to the procedure were defined. Using our standard protocol, HD-TGGE detected clonal T-cell receptor (TCR)-gamma PCR products, generated from the Jurkat cell line, down to a total of 2 ng/microL (14 ng) DNA. However, slowly migrating single strands of the clonal PCR product reduced the amount of the clonality indicating homoduplices. To overcome this single-strand formation, thus decreasing the detection limit, the urea concentration in the gel and the temperature ramp for the HD-formation were altered, as well as the temperature gradient in the gel. Application of the modified protocol resulted in a tenfold lower detection limit of 0.15 ng/microL (1.05 ng) DNA in the clonal band. The sensitivity of the adapted HD-TGGE was investigated by dilution experiments using the well established T-cell lines Jurkat, Molt-4, MyLa and SeAx. By these approaches clonal PCR products diluted in nonclonal PCR products were detectable down to concentrations of 5-10%. Comparably, in the case of mixtures of clonal in nonclonal DNA the detection limit reached 5-10% clonal DNA. However, by dilution of clonal cells in nonclonal peripheral blood mononuclear cells, which corresponds to in vivo conditions, a lower detection limit of approximately 1-5% was observed.     

The second volume moment of the typical cell and higher moments of edge lengths of the spatial Poisson–Voronoi tessellation

This paper presents analytical results for higher moments of characteristics of a Voronoi tessellation generated by a homogeneous Poisson point process in the three-dimensional Euclidean space. The second moment of the volume of the typical cell as well as higher moments for the edge length distribution and the linear contact distribution are given. These characteristics are calculated analytically and presented in a unified form.     

The Poisson Voronoi Tessellation III. Miles' Formula

This paper gives distributional properties of geometrical characteristics of a Voronoi tessellation generated by a stationary Poisson point process. The considerations are based on a well-known formula given by [10] describing size and shape of a cell of the Delaunay tessellation and on the close connection between Delaunay and Voronoi tessellation. Several results are given for the two-dimensional case, but the main part is the investigation of the three-dimensional case. They include the density functions of the angles perpendicular to the ‘typical’ edge, spanned by two neighbouring Poisson points and that spanned by two neighbouring faces, the angle between two edges emanating from the ‘typical’ vertex, the distance of two neighbouring Poisson points, the angle between two edges emanating from the ‘typical’ vertex of the Poisson Voronoi tessellation and some others. These density functions are given partly explicitely and partly in integral form.     

Second‐order properties of the point process of nodes in a stationary Voronoi tessellation

In this paper we derive representation formulae for the second factorial moment measure of the point process of nodes and the second moment of the number of vertices of the typical cell associated with a stationary normal Voronoi tessellation in ?^d . In case the Voronoi tessellation is generated by a stationary Poisson process with intensity λ > 0 the corresponding pair correlation function g_V,λ (r) can be expressed by a weighted sum of d +2 (numerically tractable) multiple parameter integrals. The asymptotic variance of the number of nodes in an increasing cubic domain as well as the second moment of the number of vertices of the typical Poisson Voronoi cell are calculated exactly by means of these parameter integrals. The existence of a (d ? 1)st‐order pole of g_V,λ (r) at r = 0 is proved and the exact value of lim_{r →0} r^{d –1} g_V,λ (r) is determined. In the particular cases d = 2 and d = 3 the graph of g_V,1(r) including its local extreme points, the points of level 1 of gV, 1(r) and other characteristics are computed by numerical integration. Furthermore, an asymptotically exact confidence interval for the intensity of nodes is obtained. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Untersuchungen an oxidischen Katalysatoren. XIX. Über die thermische Alterung eines Al2O3/Cr2O3/K2O-Tränkkatalysators für die Dehydrocyclisierung und seine Regenerierung

Studies on Oxide Catalysts. XIX. On the Thermal Aging of an Al₂O₃/Cr₂O₃/K₂O Dehydrocyclization Catalyst Made by Impregnation and its Regeneration An Al₂O₃/Cr₂O₃/K₂O catalyst was aged at different temperatures in hydrogen flow. These samples and the regenerated ones (prepared by oxidation and subsequent reduction under mild conditions of the aged samples) were investigated by means of reflectance spectroscopy, EPR, oxygen chemisorption, determination of oxidizability and microcatalytic measurements of the activity in the dehydrocyclization of n-hexane. The reversible and irreversible processes occurring during the thermal aging are discussed. The importance of the oxidizability of the chromia for the regenerability of the catalysts is explained.