Reducing the internal pH of cultured cells by several different protocols that block endocytosis is found to alter the structure of clathrin lattices on the inside of the plasma membrane. Lattices curve inward until they become almost spherical yet remain stubbornly attached to the membrane. Also, the lattices bloom empty "microcages" of clathrin around their edges. Correspondingly, broken-open...

We study the graphs associated with Vicsek sets in higher dimensional settings. First, we eigenvalues of Laplacians on approximating sets, finding a general spectral decimation function. This is an extension earlier results two sets. Second, set lattices, which are natural analogues to Sierpinski lattices. have criterion when different lattices isomorphic.

We address the problem of the continuum limit for a system of Hausdorr lattices (namely lattices of isolated points) approximating a topological space M. The correct framework is that of projective systems. The projective limit is a universal space from which M can be recovered as a quotient. We dualize the construction to approximate the algebra C(M) of continuous functions on M. In a companio...

Let X be a right-angled hyperbolic building. We show that the lattices in Aut(X) share many properties with tree lattices. For example, we characterise the set of covolumes of uniform and of nonuniform lattices in Aut(X), and show that the group Aut(X) admits an infinite ascending tower of uniform and of nonuniform lattices. These results are proved by constructing a functor from graphs of grou...

We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite lattices, similar to Nation’s characterization of a hierarchy of pseudovarieties of finite lattices, progressively generalizing finite distributive lattices. This formal connection is mediated through monotone modal logic. Indeed, we adapt the correspondence algorithm ...

Weakly interacting lattices of coupled maps can be modeled as ordinary coupled map lattices separated from each other by boundary regions with small coupling parameters. We demonstrate that such weakly interacting lattices can nevertheless have unexpected and striking effects on each other. Under specific conditions, particular stability properties of the lattices are significantly influenced b...

We investigate the problem of combining or aggregating several color values given in coding scheme RGB. For this reason, we study the problem of averaging values on lattices, and in particular on discrete product lattices. We study the arithemtic mean and the median on product lattices. We apply these aggregation functions in image reduction and we present a new algorithm based on the minimizat...

The Basic Theorem for Concept Lattices represents one of the fundamental tool for a theoretical study of concept lattices. In this paper the similar assertion for generalized one-sided concept lattices is derived. Mathematics Subject Classification: 06A15

Flow and multicomponent reactive transport in saturated/unsaturated porous media are modeled by ensembles of computational particles moving on regular lattices according to specific random walk rules. The occupation number the lattice sites is updated with a global (GRW) procedure which spreads from site costs comparable those for single step sequential procedures. To cope nonlinearity degenera...

We give a survey of the connection between orthogonal polynomials, Toda lattices and related lattices, Painlevé equations (discrete continuous).