Balanced and strongly balanced Pk-designs

AbstractGiven a graph G, a G-decomposition of the complete graph Kv is a set of graphs, all isomorphic to G, whose edge sets partition the edge set of Kv. A G-decomposition of Kv is also called a G-design and the graphs of the partition are said to be the blocks. A G-design is said to be balanced if the number of blocks containing any given vertex of Kv is a constant.In this paper the concept of strongly balanced G-design is introduced and strongly balanced path-designs are studied. Furthermore, we determine the spectrum of those path-designs which are balanced, but not strongly balanced

strongly balanced 4 kite designs nested into oq systems

In this paper we determine the spectrum for octagon quadrangle systems [OQS] which can be partitioned into two strongly balanced 4-kitedesigns

Perfect Octagon Quadrangle Systems with an upper C4-system and a large spectrum

An octagon quadrangle is the graph consisting of an 8-cycle (x1, x2,..., x8) with two additional chords: the edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order ν and index λ [OQS] is a pair (X,H), where X is a finite set of ν vertices and H is a collection of edge disjoint octagon quadrangles (called blocks) which partition the edge set of λKν defined on X. An octagon quadrangle system Σ=(X,H) of order ν and index λ is said to be upper C4-perfect if the collection of all of the upper 4-cycles contained in the octagon quadrangles form a μ-fold 4-cycle system of order ν; it is said to be upper strongly perfect, if the collection of all of the upper 4-cycles contained in the octagon quadrangles form a μ-fold 4-cycle system of order ν and also the collection of all of the outside 8-cycles contained in the octagon quadrangles form a ρ-fold 8-cycle system of order ν. In this paper, the authors determine the spectrum for these systems, in the case that it is the largest possible

Case Report: First Report of Fatal Legionella pneumophila and Klebsiella pneumoniae Coinfection in a Kidney Transplant Recipient

A very rare case of pulmonary Klebsiella pneumoniae-Legionella pneumophila coinfection in a double kidney transplanted man affected by the chronic renal disease is described. Cases of Legionnaires’ disease with an incubation period of 14 days have rarely been documented. Despite the long period of hospitalization, typing of clinical and environmental L. pneumophila strains demonstrated that the patient’s home water distribution system was the source of infection, highlighting that Legionella house contamination can be a hidden risk, especially for immune-compromised people

The role of immune suppression in COVID-19 hospitalization: clinical and epidemiological trends over three years of SARS-CoV-2 epidemic

Specific immune suppression types have been associated with a greater risk of severe COVID-19 disease and death. We analyzed data from patients >17 years that were hospitalized for COVID-19 at the “Fondazione IRCCS Ca′ Granda Ospedale Maggiore Policlinico” in Milan (Lombardy, Northern Italy). The study included 1727 SARS-CoV-2-positive patients (1,131 males, median age of 65 years) hospitalized between February 2020 and November 2022. Of these, 321 (18.6%, CI: 16.8–20.4%) had at least one condition defining immune suppression. Immune suppressed subjects were more likely to have other co-morbidities (80.4% vs. 69.8%, p < 0.001) and be vaccinated (37% vs. 12.7%, p < 0.001). We evaluated the contribution of immune suppression to hospitalization during the various stages of the epidemic and investigated whether immune suppression contributed to severe outcomes and death, also considering the vaccination status of the patients. The proportion of immune suppressed patients among all hospitalizations (initially stable at <20%) started to increase around December 2021, and remained high (30–50%). This change coincided with an increase in the proportions of older patients and patients with co-morbidities and with a decrease in the proportion of patients with severe outcomes. Vaccinated patients showed a lower proportion of severe outcomes; among non-vaccinated patients, severe outcomes were more common in immune suppressed individuals. Immune suppression was a significant predictor of severe outcomes, after adjusting for age, sex, co-morbidities, period of hospitalization, and vaccination status (OR: 1.64; 95% CI: 1.23–2.19), while vaccination was a protective factor (OR: 0.31; 95% IC: 0.20–0.47). However, after November 2021, differences in disease outcomes between vaccinated and non-vaccinated groups (for both immune suppressed and immune competent subjects) disappeared. Since December 2021, the spread of the less virulent Omicron variant and an overall higher level of induced and/or natural immunity likely contributed to the observed shift in hospitalized patient characteristics. Nonetheless, vaccination against SARS-CoV-2, likely in combination with naturally acquired immunity, effectively reduced severe outcomes in both immune competent (73.9% vs. 48.2%, p < 0.001) and immune suppressed (66.4% vs. 35.2%, p < 0.001) patients, confirming previous observations about the value of the vaccine in preventing serious disease

Hyperaffine planes over hyperrings

AbstractThe aim of this paper is to construct a geometric structure over both an hyperring and a multiplicative hyperring. In order to accomplish this goal we will need to define a particular class of planar hyperrings. Moreover, the notions of hyperaffine plane, affine map, translation and homothety are given. Finally, in the first case an hyperaffine plane having all homotheties centered in 0 is obtained; in the second case an hyperaffine translation plane is built