A celebrated unresolved conjecture of Erdös and Hajnal states that for every undirected graph H there exists $$ \epsilon (H) > 0 such on n vertices does not contain as an induced subgraph contains a clique or stable set size at least n^{\epsilon (H)} . This has directed equivalent version stating tournament H-free n-vertex T transitive subtournament Recently the was proved all six-vertex tourna...

We use an algebraic description of surfaces with boundary to study covering maps. The focus is on the relationship between automor-phisms in the base and lifted maps. We show how to introduce and/or prohibit additional automorphisms in the lift. Using this control we give proofs of MacBeath's Theorem, Gr unbaum's Conjecture, and settle a conjecture of Nedela and Skoviera.

Let $H$ and $F$ be hypergraphs. We say {\em contains as a trace} if there exists some set $S \subseteq V(H)$ such that $H|_S:=\{E\cap S: E \in E(H)\}$ subhypergraph isomorphic to $F$. In this paper we give an upper bound on the number of edges in $3$-uniform hypergraph does not contain $K_{2,t}$ trace when $t$ is large. particular, show that
 $$\lim_{t\to \infty}\lim_{n\to \infty} \frac{\m...

The aphorism “All models are wrong but some are useful” (Box, 1978) sums up much of what ML is about. The assumptions we make in the Naive Bayes approach to sentimanet classification are wrong, but this is true of the assumptions made in all current formal models of human language (statistical or otherwise), with the possible exception of a few which are very restricted indeed. However, the que...

background and objectives: appropriate attitude about enjoining good and forbidding evil (egfe) as two fundamental topics in islam that are known as a social phenomenon can use as a powerful tool in islamic organizations to promote happiness, management improvement and correction of defficiencies. the objective was to assess attitude of hospital staff regarding enjoining good and forbidding evi...

Random context picture grammars are used to generate pictures through successive refinement. There are three important subclasses of random context picture grammars, namely random permitting context picture grammars, random forbidding context picture grammars and table-driven context-free picture grammars. These grammars generate the random permitting context picture languages, random forbiddin...

How large can a family A ⊂ P[n] be if it does not contain A,B with |A \ B| = 1? Our aim in this paper is to show that any such family has size at most 2+o(1) n ( n bn/2c ) . This is tight up to a multiplicative constant of 2. We also obtain similar results for families A ⊂ P[n] with |A\B| 6 = k, showing that they satisfy |A| ≤ Ck nk ( n bn/2c ) , where Ck is a constant depending only on k.

This paper explicates the complex relationship between contemplative practice and enlightened activity conducted both on off meditative cushion as demonstrated in approach of Sōtō Zen Buddhist founder Dōgen (1200–1253). I examine Dōgen’s intricate views regarding how language, or what refer to just saying, can should be used creative yet often puzzling perplexing ways express experience self-re...