Hitting sets and colorings of hypergraphs

In this paper we study the minimal size of edges in hypergraph families which guarantees the existence of a polychromatic coloring, that is, a $k$-coloring of a vertex set such that every hyperedge contains a vertex of all $k$ color classes. We also investigate the connection of this problem with $c$-shallow hitting sets: sets of vertices that intersect each hyperedge in at least one and at most $c$ vertices. We determine in some hypergraph families the minimal $c$ for which a $c$-shallow hitting set exists. We also study this problem for a special hypergraph family, which is induced by arithmetic progressions with a difference from a given set. We show connections between some geometric hypergraph families and the latter, and prove relations between the set of differences and polychromatic colorability

Guidance on noncorticosteroid systemic immunomodulatory therapy in noninfectious uveitis: fundamentals of care for uveitis (focus) initiative

Topic: An international, expert-led consensus initiative to develop systematic, evidence-based recommendations for the treatment of noninfectious uveitis in the era of biologics. Clinical Relevance: The availability of biologic agents for the treatment of human eye disease has altered practice patterns for the management of noninfectious uveitis. Current guidelines are insufficient to assure optimal use of noncorticosteroid systemic immunomodulatory agents. Methods: An international expert steering committee comprising 9 uveitis specialists (including both ophthalmologists and rheumatologists) identified clinical questions and, together with 6 bibliographic fellows trained in uveitis, conducted a Preferred Reporting Items for Systematic Reviews and Meta-Analyses protocol systematic reviewof the literature (English language studies from January 1996 through June 2016; Medline [OVID], the Central Cochrane library, EMBASE,CINAHL,SCOPUS,BIOSIS, andWeb of Science). Publications included randomized controlled trials, prospective and retrospective studies with sufficient follow-up, case series with 15 cases or more, peer-reviewed articles, and hand-searched conference abstracts from key conferences. The proposed statements were circulated among 130 international uveitis experts for review.Atotal of 44 globally representativegroupmembersmet in late 2016 to refine these guidelines using a modified Delphi technique and assigned Oxford levels of evidence. Results: In total, 10 questions were addressed resulting in 21 evidence-based guidance statements covering the following topics: when to start noncorticosteroid immunomodulatory therapy, including both biologic and nonbiologic agents; what data to collect before treatment; when to modify or withdraw treatment; how to select agents based on individual efficacy and safety profiles; and evidence in specific uveitic conditions. Shared decision-making, communication among providers and safety monitoring also were addressed as part of the recommendations. Pharmacoeconomic considerations were not addressed. Conclusions: Consensus guidelines were developed based on published literature, expert opinion, and practical experience to bridge the gap between clinical needs and medical evidence to support the treatment of patients with noninfectious uveitis with noncorticosteroid immunomodulatory agents

Betekintés a Kakeya-problémakörbe

Szakdolgozatomban a geometriai mértékelmélet egy érdekes ágában, a Kakeya-problémakörben merülök el. Ehhez elengedhetetlen egy tartalmas elméleti bevezető, melyben az alapvető dimenziófogalmak megismertetése mellett egyéb geometriai mértékelméleti fogalmakat is bemutatok. Továbbá egy nem geometriai mértékelméleti szempontból is megvizsgálom a Kakeya-problémakör egy fontos kérdését: Baire-kategória tekintetében. Ehhez szintén szükséges volt egy fejezet az alapokkal