In this paper we present a lattice dynamical system stated by K. Kaneko in [Phys. Rev. Lett., 65, 1391-1394, 1990] which is related to the Belusov-Zhabotinskii reaction. We prove that this CML (Coupled Map Lattice) system has positive topological entropy for zero coupling constant.

Many agriculturally important traits are complex, affected by many genes and the environment. Quantitative trait loci (QTL) mapping is a key tool for studying the genetic structure of complex traits in plants. In the present study QTLs associated with yield and agronomical traits such as leaf number, leaf length, leaf width, plant height, stem and head diameter were identified by using 70 recom...

We extend the Billera–Ehrenborg–Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky’s fundamental results on the number of regions.

The continuum Kardar-Parisi-Zhang equation in one dimension is lattice discretized in such a way that the drift part is divergence free. This allows to determine explicitly the stationary measures. We map the lattice KPZ equation to a bosonic field theory which has a cubic anti-hermitian nonlinearity. Thereby it is established that the stationary two-point function spreads superdiffusively.

Arrhythmias are potentially fatal disruptions to the normal heart rhythm, but their underlying dynamics is still poorly understood. Theoretical modeling an important tool fill this gap. Typical studies often employ detailed multidimensional conductance-based models. We describe cardiac muscle with a three-dimensional map-based membrane potential model in lattices. Although maps retain biophysic...

In [13], Kötter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this alphabet is the map d ∶ (U,V ) ↦ dim(U + V ) − dim(U ∩ V ). In this paper we generalize this model to arbitrary modular lattices, i.e. we consider codes, whic...