Tolerance competition graphs

AbstractThe ø-tolerance competition graph is introduced as a generalization of the p-competition graphs defined by Kim, McKee, McMorris, and Roberts. Let ø be a symmetric function defined from N × N into N, where N denotes the nonnegative integers. G = (V, E) is a ø-tolerance competition graph if there is a directed graph D = (V, A) and an assignment of a nonnegative integer ti to each vertex vi ∈ V such that, for i ≠ j, vivj ∈ E(G) if and only if |O(vi) ∩ O(vj)| ≥ ø(ti, tj), where O(x) = {y : xy ∈ A}. A general characterization of ø-tolerance competition graphs is given, and specific results are obtained when ø is the minimum, maximum, and sum functions

The t-median function on graphs

A median of a sequence pi = x1, x2, … , xk of elements of a finite metric space (X, d ) is an element x for which ∑ k, i=1 d(x, xi) is minimum. The function M with domain the set of all finite sequences on X and defined by M(pi) = {x: x is a median of pi} is called the median function on X, and is one of the most studied consensus functions. Based on previous characterizations of median sets M(pi), a generalization of the median function is introduced and studied on various graphs and ordered sets. In addition, new results are presented for median graphs

An algebraic analysis of cladistic characters

Cladistic characters are used by many numerical axonomists in the estimation of evolutionary history. We make use of semilattice theory to give an algebraic formulation of the ideas involved in this process and to give rigorous proofs of theorems which justify certain operational procedures in current use. In particular, we discuss certain compatibility tests for a collection of charactersPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21663/1/0000050.pd

Sviluppo pre-clinico e clinico di inibitori della cellula staminale leucemica nelle leucemie acute

In Leukemias, recent developments have demonstrated that the Hedgehog pathway plays a key-role in the peculiar ability of self renewal of leukemia stem cells. The aim of this research activity was to investigate, through a first in man, Phase I, open label, clinical trial, the role and the impact, mainly in terms of safety profile, adverse events and pharmacokinetics, of a Sonic Hedgehog inhibitor compound on a population of heavely pretreated patients affected by AML, CML, MF, or MDS, resistant or refractory to standard chemotherapy. Thirty-five patients have been enrolled. The drug was administered orally, in 28 days cycles, without rest periods. The compound showed a good safety profile. The half life was of 17-35 hours, justifying the daily administration. Significant signs of activity, in terms of reduction of bone marrow blast cell amount were seen in most of the patients enrolled. Interestingly, correlative biological studies demonstrated that, comparing the gene expression profyiling signature of separated CD34+ cells before and after one cycle of treatment, the most variably expressed genes were involved in the Hh pathway. Moreover, we observed that many genes involved in MDR (multidrug resistance)were significantly down regulated after treatment. These data might lead to future clinical trials based on combinatory approaches, including, for instance, Hh inhibitors and conventional chemotherapy

Subpath acyclic digraphs

A characterization is given for acyclic digraphs that are the acyclic intersection digraphs of subpaths of a directed tree