A sharp threshold for random graphs with a monochromatic triangle in every edge coloring

Let $\R$ be the set of all finite graphs $G$ with the Ramsey property that every coloring of the edges of $G$ by two colors yields a monochromatic triangle. In this paper we establish a sharp threshold for random graphs with this property. Let $G(n,p)$ be the random graph on $n$ vertices with edge probability $p$. We prove that there exists a function $\hat c=\hat c(n)$ with $0 0$, as $n$ tends to infinity Pr[G(n,(1-\eps)\hat c/\sqrt{n}) \in \R ] \to 0 and Pr [ G(n,(1+\eps)\hat c/\sqrt{n}) \in \R ] \to 1. A crucial tool that is used in the proof and is of independent interest is a generalization of Szemer\'edi's Regularity Lemma to a certain hypergraph setting.Comment: 101 pages, Final version - to appear in Memoirs of the A.M.

The Ramsey Number for 3-Uniform Tight Hypergraph Cycles

Let C(3)n denote the 3-uniform tight cycle, that is, the hypergraph with vertices v1, .–.–., vn and edges v1v2v3, v2v3v4, .–.–., vn−1vnv1, vnv1v2. We prove that the smallest integer N = N(n) for which every red–blue colouring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of C(3)n is asymptotically equal to 4n/3 if n is divisible by 3, and 2n otherwise. The proof uses the regularity lemma for hypergraphs of Frankl and Rödl

The number of cliques in hypergraphs with forbidden subgraphs

We study the maximum number of $r$-vertex cliques in $(r-1)$-uniform hypergraphs not containing complete $r$-partite hypergraphs $K_r^{(r-1)}(a_1, \dots, a_r)$. By using the hypergraph removal lemma, we show that this maximum is $o( n^{r - 1/(a_1 \cdots a_{r-1})} )$. This immediately implies the corresponding results of Mubayi and Mukherjee and of Balogh, Jiang, and Luo for graphs. We also provide a lower bound by using hypergraph Tur\'an numbers

Subgraphs with a positive minimum semidegree in digraphs with large outdegree

We prove that every $n$-vertex directed graph $G$ with the minimum outdegree $δ^+(G) = d$ contains a subgraph $H$ satisfying $$\min\left\{δ^+(H), δ^-(H) \right\} \ge \frac{d(d+1)}{2n} \,.$$ We also show that if $d = o(n)$ then this bound is asymptotically best possible

What punishment expresses

In this article, I consider the question of what punishment expresses and propose a way of approaching the question that overcomes problems in both psychosocial and philosophical expressivist traditions. The problem in both traditions is, I suggest, the need for an adequate moral – neither moralizing nor reductive – psychology, and I argue that Melanie Klein’s work offers such a moral psychology. I offer a reconstruction of Klein’s central claims and begin to sketch some of its potential implications for an expressive account of punishment. I outline a Kleinian interpretation of modern punishment’s expression as of an essentially persecutory nature but also include depressive realizations that have generally proved too difficult for liberal modernity to work through successfully, and the recent ‘persecutory turn’ is a defence against such realizations. I conclude by considering the wider philosophical significance of a Kleinian account for the expressivist theory of punishment

Novel PAMAM-PEG-Peptide Conjugates for siRNA Delivery Targeted to the Transferrin and Epidermal Growth Factor Receptors

The transferrin (TfR) and epidermal growth factor receptors (EGFR) are known to be overexpressed on the surface of a wide variety of tumor cells. Therefore, the peptides B6 (TfR specific) and GE11 (targeted to the EGFR) were linked to the PAMAM (polyamidoamine) structure via a polyethylenglycol (PEG) 2 kDa chain with the aim of improving the silencing capacity of the PAMAM-based dendriplexes. The complexes showed an excellent binding capacity to the siRNA with a maximal condensation at nitrogen/phosphate (N/P) 2. The nanoparticles formed exhibited hydrodynamic diameters below 200 nm. The zeta potential was always positive, despite the complexes containing the PEG chain in the structure showing a drop of the values due to the shielding effect. The gene silencing capacity was assayed in HeLa and LS174T cells stably transfected with the eGFPLuc cassette. The dendriplexes containing a specific anti luciferase siRNA, assayed at different N/P ratios, were able to mediate a mean decrease of the luciferase expression values of 14% for HeLa and 20% in LS174T cells, compared to an unspecific siRNA-control. (p < 0.05). In all the conditions assayed, dendriplexes resulted to be non-toxic and viability was always above 75%