Abstract. We have constructed graphical (qualitative and visual) representations of DNA sequences as 2D maps and their numerical (quantitative and computational) analysis. The maps are obtained by transforming the four-letter sequences (where letters represent the four nucleic bases) via a spiral representation over triangular and square cells grids into a four-color map. The so constructed maps are then represented by distance matrices. We consider the use of several matrix invariants as DNA descriptors for determining the degree of similarity of a selection of DNA sequences.

No abstract

Abstract.A technique for determining the permeability of a phospholipid membrane on a single giant unilamellar vesicle (GUV) is described, which complements the existing methods utilizing either a planar black lipid membrane or sub-micrometre-sized liposomes.A single GUV is transferred using a micropipette from a solution of a nonpermeable solute into an iso-osmolar solution of a solute with a higher membrane permeability. Osmotical swelling of the vesicle is monitored with a CCD camera mounted on a phase contrast microscope, and a sequence of images is obtained. On each image, the points on the vesicle contour are determined using Sobel filtering with adaptive binarization threshold, and from these, the vesicle radius is calculated with a great accuracy. From the time-dependence of the vesicle radius, the membrane permeability is obtained. Using a test set of data, the method provided a consistent estimate of the POPC membrane permeability for glycerol, P = 1.7 × 10 −8 m/s, with individual samples ranging from 1.61 × 10 −8 m/s to 1.98 × 10 −8 m/s. This value is ≈ 40% lower than the one obtained on similar systems. Possible causes for this discrepancy are discussed.

Let G be a simple, connected graph with n vertices and eigenvalues λ 1 > λ 2 ≥ . . . ≥ λ n . If n is even, define H = n/2 and L = H + 1. If n is odd, define H = L = (n + 1)/2. Define the HL-index of G to be R(G) = max(|λ H |, |λ L |). The eigenvalues λ H and λ L appear in chemical graph theory in the study of molecular stability. In this paper, bounds on HL-index for chemical and general graphs are studied. It is shown that there exist graphs with arbitrarily large HL-index.

Abstract. In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic G 2 Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is confirmed.

Abstract. In this paper the problem of geometric interpolation of planar data by parametric polynomial curves is revisited. The conjecture that a parametric polynomial curve of degree ≤ n can interpolate 2n given points in R 2 is confirmed for n ≤ 5 under certain natural restrictions. This conclusion also implies the optimal asymptotic approximation order. More generally, the optimal order 2n can be achieved as soon as the interpolating curve exists.

No abstract

No abstract