Structure of non-negative posets of Dynkin type An\mathbb{A}_n

We study, in terms of directed graphs, partially ordered sets (posets) $I=(\{1,\ldots, n\}, \preceq_I)$ that are non-negative in the sense that their symmetric Gram matrix $G_I:=\frac{1}{2}(C_I + C_I^{tr})\in\mathbb{M}_{|I|}(\mathbb{Q})$ is positive semi-definite, where $C_I\in\mathbb{M}_n(\mathbb{Z})$ is the incidence matrix of $I$ encoding the relation $\preceq_I$. We give a complete, up to isomorphism, structural description of connected posets $I$ of Dynkin type $\mathrm{Dyn}_I=\mathbb{A}_n$ in terms of their Hasse digraphs $\mathcal{H}(I)$ that uniquely determine $I$. One of the main results of the paper is the proof that the matrix $G_I$ is of rank $n$ or $n-1$, i.e., every non-negative poset $I$ with $\mathrm{Dyn}_I=\mathbb{A}_n$ is either positive or principal. Moreover, we depict explicit shapes of Hasse digraphs $\mathcal{H}(I)$ of all non-negative posets $I$ with $\mathrm{Dyn}_I=\mathbb{A}_n$. We show that $\mathcal{H}(I)$ is isomorphic to an oriented path or cycle with at least two sinks. By giving explicit formulae for the number of all possible orientations of the path and cycle graphs, up to the isomorphism of unlabeled digraphs, we devise formulae for the number of non-negative posets of Dynkin type $\mathbb{A}_n$.Comment: 17 pages; Example 2.4 corrected, typos corrected, references adde

Symbolic computations and combinatorial algorithms in spectral classification of finite partially ordered sets

The main subject of the research presented in the dissertation is the Coxeter spectral classification of finite connected partially ordered sets (posets) �, encoded in the form of incidence matrices � � ∈ �| �|(ℤ), by means of symbolic and combinatorial algorithms

Phenotypically exceptional Echiniscus species (Heterotardigrada: Echiniscidae) from Argentina (Neotropics)

One of the most extensive species radiations in the tardigrade evolution took place in the Echiniscus phylogenetic line, which contains the genus Echiniscus with over 120 species described to date. The internal classification of Echiniscus is historically based on two major sources of variability: chaetotaxy, that is the arrangement and the shape of trunk appendages, and the sculpturing of dorsal plates. These two criteria allowed for the delineation of species complexes, such as the blumi-canadensis or the spinulosus group. Recent phylogenetic analyses confirmed that they represent monophyletic lineages. However, the affinities of some species that have not been sequenced are not straightforward given their uncommon morphologies. In this paper, we present five Echiniscus species found in Argentina, two of which constitute such exemplary cases. Echiniscus aonikenk sp. nov. exhibits extraordinarily elongated cirri A, exceeding 50% of the body length, and dorsoventrally flattened trunk spines, including particularly wide spines E. The species is a probable sister group of the spinulosus complex. Furthermore, Echiniscus evelinae de Barros, 1942, reported here only third time ever, is characterised by an extreme elongation of cirri E, often exceeding the body length, and by autapomorphic dorsal sculpturing comprising epicuticular granules, pseudopores, distinct endocuticular reticulum and pillars. Analogously to E. aonikenk sp. nov., E. evelinae apparently constitutes a separate evolutionary lineage. Finally, Echiniscus pellucidus sp. nov. (the merokensis complex), Echiniscus peruvianus Binda & Pilato, 1994 syn. nov. (the testudo complex) and Echiniscus manuelae da Cunha & do Nascimento Ribeiro, 1962 (the spinulosus complex) are analysed. Morphological peculiarities revealed in this study are discussed in the light of the Echiniscus taxonomy

Risk Assessment of Potential Food Chain Threats from Edible Wild Mushrooms Collected in Forest Ecosystems with Heavy Metal Pollution in Upper Silesia, Poland

In this study, the contents of selected heavy metals (Zn, Cu, Cd, Pb, Cr, and Ni) and macroelements (C, N, K, P, S, Mg, Na, and Ca) were measured in wild mushrooms growing in a heavily polluted forest ecosystem in the northeastern part of the Upper Silesian Industrial Region. The research was conducted on 10 species of mushrooms belonging to three families: Boletaceae, Russulaceae, and Suillaceae. Using a spatial autoregressive model, the study showed a strong relationship between heavy metal concentrations (especially Zn, Pb, and Cd) and the distance from a source of industrial pollution (a zinc smelter, Huta Miasteczko Śląskie). The concentrations of potentially toxic metals (Pb and Cd) in mushrooms significantly exceeded food-acceptable standards. The bioconcentration factor (BCF), calculated as the ratio between the concentration in mushroom tissues and in forest soils overall, reached the highest values for cadmium (Cd). The highest accumulation capacity for Cd was noted for Imleria badia (BCF = 9.18), which was also the most abundant mushroom species in the study plots. In general, the established threshold values for Pb and Cd concentrations in consumer mushrooms and food products were exceeded up to almost 30-fold in the studied area. We conclude that the potential risk to human health of the toxic elements that enter the food chain through the harvesting and consumption of wild mushrooms from this region is significant

ROADVERT project. Roadside advertisement impact on road safety

Umiejscowienie nośnika reklamy w pobliżu drogi może mieć negatywne konsekwencje dla bezpieczeństwa ruchu drogowego. W Polsce brakuje jasnych wytycznych, na podstawie których można by przeprowadzić ocenę wpływu danej reklamy zewnętrznej na zachowanie użytkowników drogi. W celu opracowania stosownych reguł powstał projekt ROADVERT. W ramach projektu przeprowadzono obiektywną wielokryterialną analizę różnych typów reklam zewnętrznych widzianych z drogi. Analiza ta odnosi się do oceny technicznej (weryfikacji parametrów geometrycznych i świetlnych) oraz uwarunkowań lokalizacji. Przeanalizowane zostały także silnie oddziałujące na bezpieczeństwo ruchu drogowego czynniki związane z treścią reklam i sposobem jej eksponowania, jak również indywidualne predyspozycje kierowców determinujące „wrażliwość” na oddziaływanie reklam. Na podstawie analiz i przeprowadzonych badań w warunkach rzeczywistych i symulacyjnych powstanie zestaw zaleceń oraz innowacyjna, kompleksowa metodyka oceny reklam zewnętrznych w aspekcie wpływu na bezpieczeństwo ruchu drogowego. Dodatkowo w ramach projektu powstanie szereg narzędzi, które pozwolą Generalnej Dyrekcji Dróg Krajowych i Autostrad oraz innym interesariuszom na efektywne zarządzanie bezpieczeństwem ruchu drogowego.Placing the roadside advertisements may cause negative consequences for the road traffic safety. Polish law system lacks clear guidelines upon which road users’ behaviour influence assessment on each outdoor advertisement could be made. In order to develop appropriate rules, the ROADVERT project was created. An objective multicriteria analysis of various types of advertising media noticeable from the road has been performed in the framework of the project. This analysis refers to the technical assessment (verification of geometrical and light parameters) and location conditions. The factors that strongly affect traffic safety, related to the content of advertising mediums and the way it is displayed, as well as individual predispositions of drivers determining “sensitivity” to the impact of advertising will also be analyzed. On the basis of analyzes and conducted research in real and simulation conditions, a set of recommendations and an innovative, comprehensive methodology for the evaluation of advertising mediums in the aspect of impact on road safety will be designed. Additionally, a set of dedicated tools will be designed and provided to the General Directorate for National Roads and Motorways and other stakeholders, so as to enable the efficient management of road traffic safety in respect to the growing advertising industry