Inductive logic programming (ILP) is a subfield of machine learning which uses first-order logic as a uniform representation for examples, background knowledge and hypotheses (Muggleton and De Raedt, 1994). In this paper we deal with a so called template consistency problem, which is one of essential tasks in ILP (Gottlob et al 1999). In particular, given learning examples and template T, we ar...

We consider a brownian motion on a general graph, that starts at time t = 0 from some vertex O and stops at time t somewhere on the graph. Denoting by g the last time when O is reached, we establish a simple expression for the Laplace Transform, L, of the probability density of g. We discuss this result for some special graphs like star, ring, tree or square lattice. Finally, we show that L can...

We begin by descr ib ing the mode l under cons idera t ion . Let 5 0 = { ( m , n ) e 2 2 : m + n is even} and make 50 into a g raph by d rawing an or iented arc from each z ~ 5 ~ to z + (1, 1 ) and to z + ( 1, l ). Each arc, also called a bond, is independen t ly open with p robab i l i t y p and closed with p robab i l i t y 1 p. An open b o n d indicates that flow is a l lowed in the direct i...

in the complex z = e -2H plane, where H is the reduced external magnetic field. At infinite temperature (T = m) the spins are noninteracting and the partition function reduces to (z 1í2 + z-ìë)~, where N is the total number of spins. The zeros are therefore N-fold degenerate at 8 = a. As the temperature is lowered, the zeros spread into an arc segment of the unit circle centered about 8 = 7r an...

Apoptosis repressor with caspase recruitment domain (ARC) inhibits both death receptorandmitochondrial/ ER-mediated pathways of apoptosis. Although expressed mainly in terminally differentiated cells, ARC is markedly upregulated in a variety of human cancers, where its potential contributions have not yet been defined. In this study, we provide evidence of multiple critical pathophysiologic fun...

If x is a vertex of a digraph D, then we denote by d(x) and d−(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by ig(D) = max{d+(x), d−(x)}−min{d+(y), d−(y)} over all vertices x and y of D (including x = y). If ig(D) = 0, then D is regular and if ig(D) ≤ 1, then D is almost regular. A c-partite tournament is an orientation of a complete c-...

If x is a vertex of a digraph D, then we denote by d(x) and d−(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by ig(D) = max{d+(x), d−(x)}−min{d+(y), d−(y)} over all vertices x and y of D (including x = y). If ig(D) = 0, then D is regular and if ig(D) ≤ 1, then D is almost regular. A c-partite tournament is an orientation of a complete c-...

Given positive integers k £ m £ n, a graph G of order n is (k, m)-pancyclic ordered if for any set of k vertices of G and any integer r with m £ r £ n, there is a cycle of length r encountering the k vertices in a specified order. Minimum degree conditions that imply a graph of sufficiently large order n is (k, m)-pancylic ordered are proved. Examples showing that these constraints are best pos...

We prove the following approximate version of Pósa’s theorem for directed graphs: every directed graph on n vertices whose inand outdegree sequences satisfy di ≥ i+o(n) and d+i ≥ i+o(n) for all i ≤ n/2 has a Hamilton cycle. In fact, we prove that such digraphs are pancyclic (i.e. contain cycles of lengths 2, . . . , n). We also prove an approximate version of Chvátal’s theorem for digraphs. Thi...

In this paper, we consider the intersection graph IΓ(Zn) of gamma sets in the total graph on Zn. We characterize the values of n for which IΓ(Zn) is complete, bipartite, cycle, chordal and planar. Further, we prove that IΓ(Zn) is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivit...