Undecidable Properties of Limit Set Dynamics of Cellular Automata

Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial properties of limit sets are undecidable. In this paper we consider properties of limit set dynamics, i.e. properties of the dynamics of Cellular Automata restricted to their limit sets. There can be no equivalent of Kari's Theorem for limit set dynamics. Anyway we show that there is a large class of undecidable properties of limit set dynamics, namely all properties of limit set dynamics which imply stability or the existence of a unique subshift attractor. As a consequence we have that it is undecidable whether the cellular automaton map restricted to the limit set is the identity, closing, injective, expansive, positively expansive, transitive

Versal unfoldings for linear retarded functional differential equations

We consider parametrized families of linear retarded functional differential equations (RFDEs) projected onto finite-dimensional invariant manifolds, and address the question of versality of the resulting parametrized family of linear ordinary differential equations. A sufficient criterion for versality is given in terms of readily computable quantities. In the case where the unfolding is not versal, we show how to construct a perturbation of the original linear RFDE (in terms of delay differential operators) whose finite-dimensional projection generates a versal unfolding. We illustrate the theory with several examples, and comment on the applicability of these results to bifurcation analyses of nonlinear RFDEs

Nuovi danni causati in Sardegna da <i>Apate monachus</i> fabr. (<i>Coleoptera Bostrychidae</i>)

In the summer of 1982, a pullulation of Apate monachus Fabr. was observed in the north-eastern coastal region of Sardinia. As well as vineyards, peach, pear and apple trees, a tourist village park was attacked, damaging trees of Melia azedarach and Tamarix gallica so severely that trunks were later broken off in the wind. Several Quercus ilex trees were also attacked. No damage was observed to Quercus suber or Ailanthus glandulosa. To control the attack, a synthetic pyrethroid gave good results

La Lotta microbiologica a difesa delle sugherete. Risultati ottenuti in Sardegna

Si riporta una sintesi delle indagini condotte in sugherete della Sardegna sui principali lepidotteri defogliatori. Le specie che causano danni di un certo rilievo sono Lymantria dispar L. e Malacosoma neustria (L.), con infestazioni di tipo periodico, e Tortrix viridana L., con fluttuazioni di tipo temporaneo. La periodicità delle gradazioni di L. dispar, studiata con il conteggio delle ovature, ha avuto un’ampiezza variabile fra 11 e 5-6 anni nei diversi comprensori subericoli dell’Isola, probabilmente per le differenti condizione di conservazione degli equilibri naturali nei singoli ambienti indagati. Sono inoltre illustrati i risultati di prove di lotta microbiologica condotte contro questo defogliatore con preparati a base di Bacillus thuringiensis kurstaki. Dosi superiori a 30 miliardi di U.I. per ettaro hanno determinato elevate mortalità larvali (anche superiori all’80%) mentre la distribuzione di soli 16 miliardi di U.I./ha non ha garantito un’efficace protezione della vegetazione. I preparati microbiologici saggiati nel corso di 5 anni di sperimentazione non hanno avuto nessun effetto negativo diretto sull’entomofauna utile

Osservazioni sulla densità di popolazione di <i>Lymantria dispar</i> l. nelle principali aree subericole della Sardegna

A two year survey (1980·81) was carried out in zones adjacent to roads running through the principal Sardinian cork growing regions. Every 5 km in each region, egg clusters were counted on 40 trees, i.e. 4 radial lines of 10 trees (each line directed towards one of the cardinal points). The results showed a wide population density variability spectrum, indicating those areas likely to suffer total defoliation; summer observations confirmed correspondence between egg cluster counts and damage. Whereas populations in the north of the island showed the highest levels, in the south they were at latency levels. This staggered population fluctuation may possibily be explanied by different sub-populations having been formed due to the distance and natural barriers between the two regions. The survey not only showed the importance of the insect's active and passive diffusion phenomena in determining defoliation extension, but also verified that food availability is a major factor in controlling population density. The relative scarcity in high density populations limited fecundity and prolificity and at times starvation caused mass mortality in the larvae

La Dinamica di popolazione di <i>Lymantria dispar</i> L. in Sardegna: 1.: indicatori della gradazione ricavati dalle ovideposizioni

The present work, dealing with the egg stage of Lymantria dispar L., forms part of a 9-year (1972-1980) research program on the population dynamics of the insect in a N. E. Sardinian cork-growing region. Egg-cluster counts (per hectare of forest surface) showed that total defoliation is to be expected every 7-9 years, that population density increase is not necessarily concomitant, and that different population densities may occur even in adjacent biotopes. The average egg count per cluster was low .(329 to 353) in peak population years and in the first year of retrogradation (288 to 339), but appreciably higher in years of latency and progradation (674 to 726). Egg sterility showed lower (from 1.7% to 6.0%) in latency years than in years of progradation, peak and retrogradation (from 7.6% to 18.4 %). The height above ground of ovideposition on the cork-oak trunks also varied. In latency years, more than 75% of the c1usters were laid below 2 metres: in progradation years, from 40% to 60% at above 2 m. In peak years, more than 75% were laid above 6 m, and in retrogradation years 40% to 60% between 2 m and 6 m. Information gathered on parasites (Ooencyrtus kuwanai (How.) and Anastatus disparis Ruschka) and predators (Dermestes lardarius L. and Haplocnemus jejunus Kinsenw.), which, at most, reached 27.9% in 1978 - a latency year for L. dispar -, would suggest that these are not of prime significance in controlling the defoliating populations. Statistic correlations are shown between egg-cluster dimensions and egg count per cluster, in particular the linear regression between the length of the egg-cluster major axis and total eggs in the cluster (y = – 11.86 + 11.26 x), in order to enable estimates of population levels to be made more rapidly. If correctly used on a large scale, the indicators analysed taken as a whole should enable sufficiently reliable forecasts to be made of L. dispar population levels and gradation phases, forming the basis of commen· surate programming for the protection of Quercus suber forests from defoliation

Osservazioni sugli afidi <i>Eucallipterus tiliae</i> (L.) e <i>Tinocallis platani</i> (Kalt.) (Homoptera Callaphididae) dannosi al verde pubblico

During the period 1989-90, in the urban avenues of Sassari (North Sardinia), observations on Eucallipterus tiliae (L.) and Tinocallis platani (Kalt.) population fluctuations were carried out. These aphids, which infest rispectively limes and elms. caused the rain of copious quantities of sticky honeydew. Both species showed an annual alternation in population density, which caused the shift of the peack of abundance from late spring in the year of high abundance to the beginning of summer in that of low abundance. That seems to prove the occurrence, also for the populations living in mediterranean environment, of an inverse relationship between the densities of fundatrices and oviparae within each season