Sequences with long range exclusions

Given an alphabet $S$, we consider the size of the subsets of the full sequence space $S^{\rm {\bf Z}}$ determined by the additional restriction that $x_i\not=x_{i+f(n)},\ i\in {\rm {\bf Z}},\ n\in {\rm {\bf N}}.$ Here $f$ is a positive, strictly increasing function. We review an other, graph theoretic, formulation and then the known results covering various combinations of $f$ and the alphabet size. In the second part of the paper we turn to the fine structure of the allowed sequences in the particular case where $f$ is a suitable polynomial. The generation of sequences leads naturally to consider the problem of their maximal length, which turns out highly random asymptotically in the alphabet size.Comment: 18 pages, 3 figures. Replaces earlier version, submission 1204.3439, major updat

Dense packing on uniform lattices

We study the Hard Core Model on the graphs ${\rm {\bf \scriptstyle G}}$ obtained from Archimedean tilings i.e. configurations in $\scriptstyle \{0,1\}^{{\rm {\bf G}}}$ with the nearest neighbor 1's forbidden. Our particular aim in choosing these graphs is to obtain insight to the geometry of the densest packings in a uniform discrete set-up. We establish density bounds, optimal configurations reaching them in all cases, and introduce a probabilistic cellular automaton that generates the legal configurations. Its rule involves a parameter which can be naturally characterized as packing pressure. It can have a critical value but from packing point of view just as interesting are the noncritical cases. These phenomena are related to the exponential size of the set of densest packings and more specifically whether these packings are maximally symmetric, simple laminated or essentially random packings.Comment: 18 page

Piileväyhteisöt jokivesien ekologisen tilan luokittelussa ja seurannassa – menetelmäohjeet

Piilevämenetelmää käytetään vesipolitiikan puitedirektiivin mukaisessa jokien ekologisen tilan luokittelussa ja seurannassa. Tähän julkaisuun on koottu Suomen oloihin sopiva ohjeistus menetelmän toteutuksesta näytteenotosta piileväpreparaattien valmistukseen ja tulosten tulkintaan. Lisäksi julkaisussa on esitelty pohjalevien ekologiaa

Determination of barley nitrogen status with chlorophyll meter for high β-amylase in grains

The production of β-amylase is of great importance in two-rowed spring barley cv. Kymppi (Hordeum vulgare L.) in the Finland, where long-day conditions favour high enzyme activities. Nitrogen (N) fertilization of a crop is the main means of manipulating barley β-amylase activity for industrial purposes. In this study, leaf chlorophyll content determined with a portable chlorophyll meter (Minolta SPAD-502) in the field, was used to predict N availability of cv. Kymppi for β-amylase production. Critical chlorophyll meter readings (SPAD values) were calculated from data deriving from experiments with various N fertilizer levels using the Cate-Nelson procedure. According to the results of this study it can be stated that the critical SPAD values at pollination (i.e. pollen grains on well-developed stigmatic hairs, GS 52-58) are 37 SPAD units for grain yield and 41 SPAD units for β-amylase activity. The optimum grain yield occurred at 41 SPAD units and optimum P-amylase activity was reached at 45 SPAD units. Determination of leaf chlorophyll content using the chlorophyll meter led to more appropriate fertilizer application recommendations and subsequently increased β-amylase activity in grains. Grain protein concentration could be an effective diagnostic tool for post-harvest evaluation of grain β-amylase activity in cv. Kymppi