Local resilience of an almost spanning kk-cycle in random graphs

The famous P\'{o}sa-Seymour conjecture, confirmed in 1998 by Koml\'{o}s, S\'{a}rk\"{o}zy, and Szemer\'{e}di, states that for any $k \geq 2$, every graph on $n$ vertices with minimum degree $kn/(k + 1)$ contains the $k$-th power of a Hamilton cycle. We extend this result to a sparse random setting. We show that for every $k \geq 2$ there exists $C > 0$ such that if $p \geq C(\log n/n)^{1/k}$ then w.h.p. every subgraph of a random graph $G_{n, p}$ with minimum degree at least $(k/(k + 1) + o(1))np$, contains the $k$-th power of a cycle on at least $(1 - o(1))n$ vertices, improving upon the recent results of Noever and Steger for $k = 2$, as well as Allen et al. for $k \geq 3$. Our result is almost best possible in three ways: for $p \ll n^{-1/k}$ the random graph $G_{n, p}$ w.h.p. does not contain the $k$-th power of any long cycle; there exist subgraphs of $G_{n, p}$ with minimum degree $(k/(k + 1) + o(1))np$ and $\Omega(p^{-2})$ vertices not belonging to triangles; there exist subgraphs of $G_{n, p}$ with minimum degree $(k/(k + 1) - o(1))np$ which do not contain the $k$-th power of a cycle on $(1 - o(1))n$ vertices.Comment: 24 pages; small updates to the paper after anonymous reviewers' report

Asymptotically false-positive-maximizing attack on non-binary Tardos codes

We use a method recently introduced by Simone and Skoric to study accusation probabilities for non-binary Tardos fingerprinting codes. We generalize the pre-computation steps in this approach to include a broad class of collusion attack strategies. We analytically derive properties of a special attack that asymptotically maximizes false accusation probabilities. We present numerical results on sufficient code lengths for this attack, and explain the abrupt transitions that occur in these results

Celiac disease in the preschool age

Celijakija je kronična i imunološka bolest odnosno nemogućnost probavljanja glutena, proteina koji se nalaze u nekim žitaricama, uključujući pšenicu. Bolest se još zove i glutenska enteropatija. Sastojak glutena koji se zove glijanid uzrokuje upalu tankog crijeva, crijevna stjenka postaje nadražena što dovodi do malapsorpcije drugih hranjivih tvari. Mnogi smatraju da ovakvo oboljenje uzrokuju genetski i vanjski čimbenici o čemu ću detaljnije pisati u sljedećim poglavljima. Glutenska enteropatija ili celijakija javlja se u nekoliko tipova: tipična, atipična, tiha i potencijalna. Tipovi celijakije koji stvaraju najveći problem su atipični i tihi tip jer ne postoje određeni simptomi prilikom pojavljivanja bolesti. Atipični broj slučajeva celijakije znatno je porastao proteklih godina, a do otkrivanja dolazi slučajno, krvnim testovima. Baš kao svaka bolest i celijakija znatno utječe na život oboljelih, naročito oboljele djece. Bezglutenska prehrana je jedini način držanja bolesti pod kontrolom. Takva prehrana može utjecati na psihičko stanje djeteta. Postoje i određene prateće bolesti koje se mogu javiti kao posljedica upale tankog crijeva radi konzumacije glutenskih proizvoda. Celijakiju treba prvenstveno shvatiti ozbiljno, zatim je kontrolirati i pratiti.Celiac disease is a chronic and immune disease, that is an inability to digest gluten, proteins found in some cereals, including wheat. The disease is also called gluten enteropathy. The part of gluten called gliyanide causes inflammation of the small intestine, the intestinal wall becomes irritated, leading to malabsorption of other nutrients. Many think that such an illness is caused by genetic and external factors, was described in previous chapters.. Glutathione enteropathy or celiac disease has several types: typical, atypical, silent and potential. Types of celiac disease that cause the biggest problem are atypical and silent type because there are no specific symptoms when the disease occurs. The number of atypical celiac cases has increased considerably over the past few years, and it is discovered by chance, when doing blood tests. Just like any disease the celiac disease significantly affects the lives of the diseased, especially the sick children. Gluten-free nutrition is the only way to keep the disease under control. Such nutrition can affect the child's mental state. There are certain accompanying diseases that may occur as a result of inflammation of the small intestine as the result of gluten consumation. Celiac disease has to be taken seriously, then controlled and monitored

Primjena vizualnog menadžmenta u proizvodnim poduzećima

Tema završnog rada je bio vizualni menadžment s posebnim naglaskom na alatima vizualnog menadžmenta i promjenama koje donosi njegova uporaba u nekom poduzeću ili organizaciji. što se alata tiče vidi se kroz priložene primjere da su oni vrlo raznoliki te da njihova upotreba ovisi o ljudskoj volji i maštovitosti. Drugim riječima, mi sami odlučujemo da li će nam neka slika, dijagram, ljepljiva traka, Lego kockice kao u General Motorsu ili nešto drugo biti od značaja kao alat vizualnog menadžmenta. Govoreći o alatima vizualnog menadžmenta dotaknuo sam se i metode 5S. Metoda 5S ima izrazito vizualnu prirodu, sa jakim utjecajem vizualnog menadžmenta. Metoda 5S govori o organizaciji na radnom mjestu, o čistoći i redu, o disciplini te o konstantom održavanju takvoga stanja. Bitno je dakle da na radnom mjestu nema nereda, da su sve komponente i faktori važni za rad pregledni i na svom određenom mjestu kako bi lakše pojedinac ili skupina mogla funkcionirati

Medical Subject Headings – MESH® Thesaurus

Tezaurus Medical Subject Headings (MeSH) nadzirani je rječnik koji izrađuje Nacionalna medicinska knjižnica Sjedinjenih Američkih Država. Koristi se za predmetnu obradu, indeksiranje i pretraživanje publikacija iz područja biomedicine i zdravstva. Tezaurus sačinjavaju nizovi deskriptora organiziranih u abecednu i hijerarhijsku strukturu. Izdanje MesH-a za 2011. godinu sadržava 26.142 deskriptora, više od 177.000 nedeskriptora te više od 199.000 dopunskih pojmova. Zbog iznimne kvalitete, specifične strukture i detaljnog pristupa, tezaurus Medical Subject Headings prihvaćen je širom svijeta i preveden na brojne jezike. Tome pridonosi i činjenica da je od 1997. godine besplatno dostupan u elektroničkom obliku. Stvoren na osnovi praktičnog rada stručnjaka iz područja biomedicine i informacijskih stručnjaka, to je dinamičan popis koji se iz izdanja u izdanje razvija u skladu s razvojem biomedicinskih znanosti. Hrvatske medicinske knjižnice također ga koriste u svom radu, a sudjeluju i u njegovu prevođenju. U ovom članku, povodom pedesete godišnjice prvog izdanja i četrdesete godišnjice korištenja u Hrvatskoj, donosimo pregled povijesti, strukture i primjene MeSH-a.Medical Subject Headings (MeSH) is the United States of America National Library of Medicine controlled vocabulary thesaurus. It is used for subject cataloging, indexing and searching biomedical literature. It consists of sets of descriptors arranged in both alphabetic and hierarchical structures. There are 26.142 descriptors, over 177.000 entry terms, and more than 199.000 Supplementary Concept Records in MeSH 2011. Due to its exquisite quality, elaborate structure and detailed approach, it is used worldwide and translated into many languages. The fact that it has been available for free in the electronic machine-readable form since 1997 has also contributed to its popularity. It was created by both health and information sciences experts who continually revise and update the MeSH vocabulary, so it evolves together with the growth and development of biomedicine. Croatian medical libraries use MeSH in their everyday practice and contribute to its translations. In this article, commemorating fifty years of MeSH and forty years of its use in Croatia, we present the outline of MeSH history, structure, and practice

Sunflower Breeding for Resistance to Abiotic and Biotic Stresses

Due to a specific structure of its main organs (root, stem, leaves, and head), sunflower can be successfully grown on marginal soils and in semiarid conditions, and it is more resistant to abiotic stresses, than other field crops. Unfortunately, it is very sensitive to biotic stresses