Uwagi o algorytmie sitowym Browkina i Cao

In this paper, we follow our generalisation of the cancellation algorithm described in our previous paper [A. Tomski, M. Zakarczemny, On some cancellation algorithms, NNTDM. 23, 2017, p. 101–114]. For f being a natural-valued function defined on s , s ≥1 we remove the divisors of all possible values of f in the points in which the sum of coordinates is less than or equal to n. The least non-cancelled number is called the discriminator Df(n). We find formulas, or at least an estimation for this discriminator, in the case of a broad class of sequences

Stochastic gene expression revisited

We investigate the model of gene expression in the form of Iterated Function System (IFS), where the probability of choice of any iterated map depends on the state of the phase space. Random jump times of the process mark activation periods of the gene when pre-mRNA molecules are produced before mRNA and protein processing phases occur. The main idea is inspired by the continuous-time piecewise deterministic Markov process describing stochastic gene expression. We show that for our system there exists a unique invariant limit measure. We provide full probabilistic description of the process with a comparison of our results to those obtained for the model with continuous time

Forest recovery in set-aside windthrow is facilitated by fast growth of advance regeneration

Funding This study was conducted as a part of research project 2012/07/ B/NZ8/01908 “Patterns and drivers of the regeneration processes following catastrophic wind disturbances in forests” funded by the Polish National Science Foundation (NCN) and research project Poland N N304 048934 “Comparison of the dynamics of woody species and vascular plants in active and passive protected areas of the Roztoczański National Park” funded by the Ministry of Science and Higher Education of the Republic of Poland. This work was also partially supported by the Ministry of Science and Higher Education of the Republic of Poland (DS 3421/ZBL).The disturbance of a research plot by a windstorm allowed us to study the role of the seedling bank in the regeneration processes. The released advance regeneration dominated among the saplings; taller individuals retained their position until the end of the study. Pioneer species occurred sporadically. Seven years after the disturbance, the windthrow was covered by a dense thicket of young trees. Context: The dominant role played by advance regeneration in natural regeneration processes after intense wind disturbances is still a matter of dispute. Aims: We took advantage of a windstorm in one of our research plots to study the role of the seedling bank released by the disturbance in the regeneration processes. Methods: We collected data in 70 plots, recording the survivorship of seedlings, annual height growth, and signs of browsing. The height ranking was analyzed with Kendall’s concordance coefficient, and the height growth rates were compared using Dunn’s test. Results: The density of seedlings increased from 6.7/m2 in 2008 to 8.1/m2 in 2010 and then decreased to 1.2/m2 in 2015. The density of saplings increased continuously from 0.14 to 1.9/m2. The highest size differentiation occurred in sycamore maple; the individuals which were taller before the windstorm retained their position until the year 2015. The only species that was recruited mainly from germinants was European hornbeam. Conclusion: The advance regeneration released by the windstorm played a major role in the regeneration process, while pioneer species occurred only sporadically. Seven years after the disturbance, the windthrow was already covered by a dense thicket of young trees.NC

Drainage ditches enhance forest succession in a raised bog but do not affect the spatial pattern of tree encroachment

The study was conducted in the raised bog Kusowo (Baltic region, West Pomerania, Poland). Along a transect line crossing two open mires affected by forest succession we analysed tree age distribution. One of those mires had been drained in the past years and still retained some open ditches, while the other one was located far from the ditches. Every 10 meters along the transect line one tree was drilled at the root collar in order to determine its age. We also conducted phytosociological analyses and short-term water level measurements in the sample plots. We expected faster tree encroachment in the undisturbed part of the open mire. The results showed, that there were no significant differences in water table level and in soil moisture indicator values between the formerly drained and undisturbed open mire. There were also no statistically significant differences in tree encroachment between the disturbed and undisturbed mires. Location and the age distribution of the trees suggest that changes in the tree growth conditions cannot be directly explained by the general decreasing of water level in the bog, although periods following drainage works were associated with more numerous establishment of young trees, in the drained part of the bog as well as in the part not directly affected by drainage ditches

The toy model with two strong players in a weighted voting game

Celem niniejszego artykułu jest porównanie szczególnego typu wyborczego modelu-zabawki z wynikami uzyskanymi przy pomocy metod aproksymacji normalnej przez Słomczyńskiego i innych w poprzednich pracach. Dla tego celu skonstruowaliśmy model, w którym zostaje oszacowany próg optymalny dla większości kwalifikowanej. Próg optymalny jest to próg, który minimalizuje różnicę między siłą głosu członka ciała decyzyjnego, mierzoną za pomocą (znormalizowanego) indeksu Penrose'a-Banzhafa, a jego wagą głosu. Wprowadzamy model 'Francja-Niemcy' z dwoma silnymi graczami, w którym każdy z nich jest c>1 razy silniejszy od reszty i szacujemy próg optymalny w przypadku c=2. Sprawdzamy, że te wyniki są zgodne z oszacowaniem uzyskanym z aproksymacji normalnej, gdzie szukany próg jest punktem przegięcia krzywej gęstości rozkładu normalnego. The aim of this article is to compare a specific toy voting model with the results derived from the normal approximation techniques by Słomczyński et al in the previous papers. For this purpose we have constructed a model in which the optimal quota for the qualified majority has been estimated. The optimal quota is set in such a way that the voting power of each member of the voting body, measured by the (normalised) Penrose-Banzhaf index, is proportional to its voting weight. We present the ‘France-Germany’ model of two strong players each of which is c > 1 times stronger than each of the others and we estimate the quota in the case of c = 2. We check that these results are consistent with a formula derived from the normal approximation, where the quota we are looking for is the inflection point of the density function for this distribution

The problem of optimal quota in weighted voting games

In this paper various toy models of weighted voting games are investigated to find the optimal quota, for which the voting power of each member of the voting body is approximately equal to its voting weight. We first introduce basic definitions, after that, we present a toy model of one strong player, where one of the players is larger than the others who have the same voting weight, and then a toy model of two strong players. The optimal quota is found for some cases and its asymptotic is examined. In the next section we describe also how to obtain voting power indices with the help of minimal voting coalitions. In the last part we consider the normal approximation of the sums of the voting weights and study how it is related to the process of finding the optimal quota for weighted voting games.W pracy badane są różne typy modeli-zabawek w ważonych grach wyborczych, mając na celu znalezienie progu optymalnego, dla którego siła głosu każdego członka ciała decyzyjnego jest w przybliżeniu równa jego wadze głosu. Najpierw podajemy podstawowe definicje, później prezentujemy model-zabawkę z jednym silnym graczem, gdzie jeden z graczy jest silniejszy od mających takie same wagi głosu pozostałych graczy, a następnie model-zabawkę dwóch silnych graczy. Próg optymalny zostaje znaleziony w pewnych przypadkach i zostaje sprawdzona jego asymptotyka. W następnym rozdziale opisujemy jak obliczać wskaźniki siły za pomocą minimalnych zwycięskich koalicji. Na końcu rozważamy aproksymację rozkładem normalnym sum wag głosów i jej związek z procesem znajdowania progu optymalnego w ważonych grach wyborczych

Gutzwiller wave function for finite systems : superconductivity in the Hubbard model

We study the superconducting phase of the Hubbard model using the Gutzwiller variational wave function (GWF) and the recently proposed diagrammatic expansion technique (DE-GWF). The DE-GWF method works on the level of the full GWF and in the thermodynamic limit. Here, we consider a finite-size system to study the accuracy of the results as a function of the system size (which is practically unrestricted). We show that the finite-size scaling used, e.g. in the variational Monte Carlo method can lead to significant, uncontrolled errors. The presented research is the first step towards applying the DE-GWF method in studies of inhomogeneous situations, including systems with impurities, defects, inhomogeneous phases, or disorder