A 2-coloring of a hypergraph is a mapping from its vertex set to a set of two colors such that no edge is monochromatic. Let H = H k n p be a random k-uniform hypergraph on a vertex set V of cardinality n, where each k-subset of V is an edge of H with probability p, independently of all other k-subsets. Let m = p(n k ) denote the expected number of edges in H. Let us say that a sequence of even...

The multi-disciplinary and inter-disciplinary movement studying Collaborative Networks (CNs) introduced terminologies, reference architectures, methodologies and models, with the aim of helping the design, creation, operation and maintenance of CNs, and its virtual organisations (VOs). Almost a decade ago, the IST European VOMap project reported a lack of ‘well founded theory and models’ for su...

The pathogenesis of persistent viral infections depends critically on long-term viral loads. Yet what determines these loads is largely unknown. Here, we show that a single CD8+ T cell epitope sets the long-term latent load of a lymphotropic gamma-herpesvirus, Murid herpesvirus-4 (MuHV-4). The MuHV-4 M2 latency gene contains an H2-Kd -restricted T cell epitope, and wild-type but not M2(-) MuHV-...

Background. Hyperbaric oxygen (HBO) therapy, which is used for many conditions, may also have immunosuppressive effects and could be used for prevention or treatment of graft-versus-host disease (GvHD). If HBO is immunosuppressant, then we hypothesize that HBO therapy will delay the T-cell mediated skin graft rejection. Methods. C57/BL6 black-coated (H2B) mice received skin graft from CBA (H2D)...

Iron accumulation in the liver in hereditary hemochromatosis (HH) has been shown to be highly variable. Some studies point to the importance of major histocompatibility complex (MHC) class I (MHC-I) and CD8(+) cells as modifiers of iron overload. In this report, using mice knockout for H2K(b-/-) and H2D(b-/-) genes, it is demonstrated that lack of classical MHC-I molecules results in a spontane...

For a germ of analytic vector fields, the existence of first integrals, resonance and the convergence of normalization transforming the vector field to a normal form are closely related. In this paper we first provide a link between the number of first integrals and the resonant relations for a quasi-periodic vector field, which generalizes one of the Poincaré’s classical results [18] on autono...

The EKG or electrocardiogram sequence is defined by a(1) = 1, a(2) = 2 and, for n ≥ 3, a(n) is the smallest natural number not already in the sequence with the property that gcd{a(n − 1), a(n)} > 1. In spite of its erratic local behavior, which when plotted resembles an electrocardiogram, its global behavior appears quite regular. We conjecture that almost all a(n) satisfy the asymptotic formul...

Let Φ(N) denote the number of products of matrices [ 1 1 0 1 ] and [ 1 0 1 1 ] of trace equal to N , and Ψ(N) = N n=3 Φ(n) be the number of such products of trace at most N . We prove an asymptotic formula of type Ψ(N) = c1N 2 logN + c2N 2 + Oε(N ) as N → ∞. As a result, the Dirichlet series ∞ n=3 Φ(n)n −s has a meromorphic extension in the half-plane <(s) > 7 4 with a single, order two pole at...

A graph G is called C4-free if it does not contain the cycle C4 as an induced subgraph. Hubenko, Solymosi and the first author proved (answering a question of Erdős) a peculiar property of C4-free graphs: C4 graphs with n vertices and average degree at least cn contain a complete subgraph (clique) of size at least c′n (with c′ = 0.1c2n). We prove here better bounds (c2n/3 in general and (c− 1/3...

We present a method, based on functional equations, to enumerate paths on the square lattice that avoid a horizontal half-line. The corresponding generating functions are algebraic, and sometimes remarkably simple: for instance, the number of paths of length 2n + 1 going from (0; 0) to (1; 0) and avoiding the nonpositive horizontal axis (except at their starting point) is C2n+1 , the (2n + 1)th...