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

Complexity Results for the Spanning Tree Congestion Problem

We study the problem of determining the spanning tree congestion of a graph. We present some sharp contrasts in the complexity of this problem. First, we show that for every fixed k and d the problem to determine whether a given graph has spanning tree congestion at most k can be solved in linear time for graphs of degree at most d. In contrast, if we allow only one vertex of unbounded degree, the problem immediately becomes NP-complete for any fixed k ≥ 10. For very small values of k however, the problem becomes polynomially solvable. We also show that it is NP-hard to approximate the spanning tree congestion within a factor better than 11/10. On planar graphs, we prove the problem is NP-hard in general, but solvable in linear time for fixed k

Collective tree spanners of graphs

In this paper we introduce a new notion of collective tree spanners. We say that a graph G =(V,E) admits a system of µ collective additive tree r-spanners if there is a system T (G) of at most µ spanning trees of G such that for any two vertices x, y of G a spanning tree T ∈T(G) exists such that dT (x, y) ≤ dG(x, y) +r. Among other results, we show that any chordal graph, chordal bipartite graph or cocomparability graph admits a system of at most log 2 n collective additive tree 2–spanners and any c-chordal graph admits a system of at most log 2 n collective additive tree (2⌊c/2⌋)–spanners. Towards establishing these results, we present a general property for graphs, called (α, r)– decomposition, and show that any (α, r)–decomposable graph G with n vertices admits a system of at most log 1/α n collective additive tree 2r– spanners. We discuss also an application of the collective tree spanners to the problem of designing compact and efficient routing schemes in graphs

Navigating in a graph by aid of its spanning tree

Let G =(V,E) be a graph and T be a spanning tree of G. We consider the following strategy in advancing in G from a vertex x towards a target vertex y: from a current vertex z (initially, z = x), unless z = y, gotoaneighborofz in G that is closest to y in T (breaking ties arbitrarily). In this strategy, each vertex has full knowledge of its neighborhood in G and can use the distances in T to navigate in G. Thus, additionally to standard local information (the neighborhood NG(v)), the only global information that is available to each vertex v is the topology of the spanning tree T (in fact, v can know only a very small piece of information about T and still be able to infer from it the necessary tree-distances). For each source vertex x and target vertex y, this way, a path, called a greedy routing path, is produced. Denote by gG,T (x, y) the length of a longest greedy routing path that can be produced for x and y using this strategy and T. We say that a spanning tree T of a graph G is an additive r-carcass for G if gG,T (x, y) ≤ dG(x, y)+r for each ordered pair x, y ∈ V. In this paper, we investigate the problem, given a graph family F, whether a small integer r exists such that any graph G ∈Fadmits an additive r-carcass. We show that rectilinear p × q grids, hypercubes, distance-hereditary graphs, dually chordal graphs (and, therefore, strongly chordal graphs and interval graphs), all admit additive 0-carcasses. Furthermore, every chordal graph G admits an additive (ω(G) + 1)-carcass (where ω(G) is the size of a maximum clique of G), each 3-sun-free chordal graph admits an additive 2-carcass, each chordal bipartite graph admits an additive 4-carcass. In particular, any k-tree admits an additive (k+2)-carcass. All those carcasses are easy to construct

Additive spanners for k-chordal graphs

Abstract. In this paper we show that every chordal graph with n vertices and m edges admits an additive 4-spanner with at most 2n−2 edges and an additive 3-spanner with at most O(n · log n) edges. This significantly improves results of Peleg and Schäffer from [Graph Spanners, J. Graph Theory, 13(1989), 99-116]. Our spanners are additive and easier to construct. An additive 4-spanner can be constructed in linear time while an additive 3-spanner is constructable in O(m · log n) time. Furthermore, our method can be extended to graphs with largest induced cycles of length k. Any such graph admits an additive (k + 1)-spanner with at most 2n − 2 edges which is constructable in O(n · k + m) time. Classification: Algorithms, Sparse Graph Spanners