5,203 research outputs found
Broadcasting Automata and Patterns on Z^2
The Broadcasting Automata model draws inspiration from a variety of sources
such as Ad-Hoc radio networks, cellular automata, neighbourhood se- quences and
nature, employing many of the same pattern forming methods that can be seen in
the superposition of waves and resonance. Algorithms for broad- casting
automata model are in the same vain as those encountered in distributed
algorithms using a simple notion of waves, messages passed from automata to au-
tomata throughout the topology, to construct computations. The waves generated
by activating processes in a digital environment can be used for designing a
vari- ety of wave algorithms. In this chapter we aim to study the geometrical
shapes of informational waves on integer grid generated in broadcasting
automata model as well as their potential use for metric approximation in a
discrete space. An explo- ration of the ability to vary the broadcasting radius
of each node leads to results of categorisations of digital discs, their form,
composition, encodings and gener- ation. Results pertaining to the nodal
patterns generated by arbitrary transmission radii on the plane are explored
with a connection to broadcasting sequences and ap- proximation of discrete
metrics of which results are given for the approximation of astroids, a
previously unachievable concave metric, through a novel application of the
aggregation of waves via a number of explored functions
DP-colorings of uniform hypergraphs and splittings of Boolean hypercube into faces
We develop a connection between DP-colorings of -uniform hypergraphs of
order and coverings of -dimensional Boolean hypercube by pairs of
antipodal -dimensional faces. Bernshteyn and Kostochka established that
the lower bound on edges in a non-2-DP-colorable -uniform hypergraph is
equal to for odd and for even . They proved that
these bounds are tight for . In this paper, we prove that the bound is
achieved for all odd .Comment: The previous versions of paper contains a significant erro
On the number of transversals in latin squares
The logarithm of the maximum number of transversals over all latin squares of
order is greater than
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