Characterization of Birkhoff’s Conditions by Means of Cover-Preserving and Partially Cover-Preserving Sublattices

In the paper we investigate Birkhoff’s conditions (Bi) and (Bi*). We prove that a discrete lattice L satisfies the condition (Bi) (the condition (Bi*)) if and only if L is a 4-cell lattice not containing a cover-preserving sublattice isomorphic to the lattice S*7 (the lattice S7). As a corollary we obtain a well known result of J. Jakubík from [6]. Furthermore, lattices S7 and S*7 are considered as so-called partially cover-preserving sublattices of a given lattice L, S7 ≪ L and S*7 ≪ L, in symbols. It is shown that an upper continuous lattice L satisfies (Bi*) if and only if L is a 4-cell lattice such that S7 ≪ L. The final corollary is a generalization of Jakubík’s theorem for upper continuous and strongly atomic lattices

A Note on some Characterization of Distributive Lattices of Finite Length

Using known facts we give a simple characterization of the distributivity of lattices of finite length

A Note on Distributive Triples

Even if a lattice L is not distributive, it is still possible that for particular elements x, y, z ∈ L it holds (x∨y) ∧z = (x∧z) ∨ (y ∧z). If this is the case, we say that the triple (x, y, z) is distributive. In this note we provide some sufficient conditions for the distributivity of a given triple

Candida albicans shields the periodontal killer Porphyromonas gingivalis from recognition by the host immune system and supports the bacterial infection of gingival tissue

Candida albicans is a pathogenic fungus capable of switching its morphology between yeast-like cells and filamentous hyphae and can associate with bacteria to form mixed biofilms resistant to antibiotics. In these structures, the fungal milieu can play a protective function for bacteria as has recently been reported for C. albicans and a periodontal pathogen—Porphyromonas gingivalis. Our current study aimed to determine how this type of mutual microbe protection within the mixed biofilm affects the contacting host cells. To analyze C. albicans and P. gingivalis persistence and host infection, several models for host–biofilm interactions were developed, including microbial exposure to a representative monocyte cell line (THP1) and gingival fibroblasts isolated from periodontitis patients. For in vivo experiments, a mouse subcutaneous chamber model was utilized. The persistence of P. gingivalis cells was observed within mixed biofilm with C. albicans. This microbial co-existence influenced host immunity by attenuating macrophage and fibroblast responses. Cytokine and chemokine production decreased compared to pure bacterial infection. The fibroblasts isolated from patients with severe periodontitis were less susceptible to fungal colonization, indicating a modulation of the host environment by the dominating bacterial infection. The results obtained for the mouse model in which a sequential infection was initiated by the fungus showed that this host colonization induced a milder inflammation, leading to a significant reduction in mouse mortality. Moreover, high bacterial counts in animal organisms were noted on a longer time scale in the presence of C. albicans, suggesting the chronic nature of the dual-species infection

Kilka uwag na marginesie książki Andrzeja Kisielewicza „Logika i argumentacja”

A few side notes on Logic and Argumentation by Andrzej KisielewiczIn the paper we discuss selected philosophical theses presented in the book Logic and Argumentation. Practical Course in Critical Thinking by Andrzej Kisielewicz. In particular, we reflect on formal logic and practical reasoning, their merits and limitations, and we ask about a sensible compromise between the generality of the former and the usefulness of the latter. A few side notes on Logic and Argumentation by Andrzej KisielewiczIn the paper we discuss selected philosophical theses presented in the book Logic and Argumentation. Practical Course in Critical Thinking by Andrzej Kisielewicz. In particular, we reflect on formal logic and practical reasoning, their merits and limitations, and we ask about a sensible compromise between the generality of the former and the usefulness of the latter

A Note on some Characterization of Distributive Lattices of Finite Length

Using known facts we give a simple characterization of the distributivity of lattices of finite length