Quenched Invariance Principle for the Random Walk on the Penrose Tiling

We consider the simple random walk on the graph corresponding to a Penrose tiling. We prove that the path distribution of the walk converges weakly to that of a non-degenerate Brownian motion for almost every Penrose tiling with respect to the appropriate invariant measure on the set of tilings. Our tool for this is the corrector method.Comment: 15 pages, 1 figur

On new paths in vegetation science and landscape ecology: In memoriam Prof. Gábor Fekete

Gábor Fekete academician respectfully but affectionately called ‘Master’ (“Tanár Úr” in Hungarian, a version of ‘Professor’ that we used with a specific meaning of being not only a Tutor but Father and Master as well) by generations of vegetation scientists passed away on the 29th November 2016. His death deprived us of an experienced and didactic teacher who was loved by all. This warm regard was expressed in many commemorating writings published since his death. The present paper mainly concentrates on his scholarly work and the importance of his scientific findings also showing how particular publications signify stages in his scientific career

Impact of the first COVID–19 lockdown on the lifestyle of elementary school children

Abstract COVID-19 lockdown affects people's daily routine and has an impact on their lifestyle. Recent studies documented associations between body weight changes and children's lifestyle during social isolation. Childhood obesity is associated with a higher risk of COVID-19 severity and mortality. Our aim was to assess the effects of lockdown due to the COVID-19 pandemic on children's sleep, screen time, physical activity, and eating habits. 387 parents of five elementary school students between 16 and 26 June 2020 were interviewed through an online questionnaire. Physical activity level decreased (63.8), sleep (60.9) and screen (5.64 ± 3.05 h/day) times and food intake (39.8) increased. 80.6 of parents reported changes in children's diet: increased consumption of fruits and vegetables (32.4), breakfast (15.5), water and sugar-free beverages (17.6), snacks (40.4), sugary drinks (9.9) was observed. Body weight increased in 44.4 of children. The results of the survey conducted under GYERE®-Children's Health Program are in line with the international literature findings: body weight change during the quarantine is significantly associated with food intake, snacking, sugary drinks, and we also found association with fruit and vegetable consumption and lack of breakfast. Effective strategies and electronic health interventions are needed to prevent sedentary lifestyle and obesity during lockdown

Sudden and gradual responses of phytoplankton to global climate change: case studies from two large, shallow lakes (Balaton, Hungary and the Neusiedlersee Austria/Hungary)

This paper analyses two phytoplankton long-term datasets; both are from large, temperate shallow lakes. The main difference between them is that phytoplankton growth in Lake Balaton remained severely P-limited despite P-driven eutrophication during the last 30 years, whereas extremely high turbidity causes a permanent light limitation in Neusiedlersee and therefore an increase in P-loadings did not result in a similar increase in phytoplankton biomass. Neusiedlersee is a (slightly) saline inland lake. In Lake Balaton, the blue-green alga Cylindrospermopsis raciborskii blooms invariably if the July-august temperature deviates positively from a 30-year average by ca. 2 °C. A supposed global warming is predicted to cause a higher frequency (but not intensity!) of these blooms. Neusiedlersee is very shallow and therefore regulation techniques cannot prevent water levels sinking in successive dry years. Annual averages of phytoplankton seem to follow quite a regular, wave-like cyclicity. Such cycles can be recognised in the population records of the characteristic species. Similar changes were seen in changes of water level, conductivity, inorganic-P, inorganic N-forms and nutrient ratios. How phytoplankton species can follow a climatic cycle that covers 200 to 500 generations has not yet become clear. Because of reasons discussed in the paper, neither of the two cases can be generalised; each is quite individual

Evolution and environment of the eastern linear pottery culture: A case study in the site of Polgár-Piócási-Dűlő

A salvage excavation preceding a major investment project was conducted in 2006–2007, during which associated settlement features of a Middle Neolithic, Eastern Linear Pottery Culture (Alföld Linearbandkeramik – ALBK) were uncovered in an area called Piócási-dűlő on the eastern outskirts of Polgár. The features of the ALBK settlement date from two periods. The cluster of multi-functional pits yielding a rich assortment of finds, the handful of post-holes and an unusual ritual well found in the southern part of the investigated area formed one unit from the earliest phase of the Middle Neolithic (ALBK I). The settlement’s other occupation can be assigned to the late phase of the Middle Neolithic (ALBK IV). Five houseplans representing the remains of timber-framed buildings outlined a distinct area with three multi-functional pits. Associated with the above features were 8 burials. The preliminary archaeobotanical results from Polgár–Piócási-dűlő are based on the plant material found within the sediments of 11 archaeological structures, which mainly represent pits and a welI. It can be stated that the natural environment offered habitats in which oak trees dominated in the local vegetation, forming floodplain forests and wooded steppes. They also provided food in the form of fruits and formed an optimal habitat for domestic animals. Arable fields were probably also established in the vicinity of the settlements, suggested by findings of macroscopic plant remains that represented cultivated species. In both settlement phases lithic production activities are manifested both by the local on-site lithic production and – most importantly – by the presence of imported, mainly mesolocal, raw materials that point to contacts with deposit areas, or off-site preliminary working of obsidian and limnoquartzites. The kit of harvesting tools and a large number of grinding stones – especially in the younger phase – for the preparation of plant food suggest a major role of plant cultivation