Parameterized Complexity of Finding a Spanning Tree with Minimum Reload Cost Diameter

We study the minimum diameter spanning tree problem under the reload cost model (DIAMETER-TREE for short) introduced by Wirth and Steffan (2001). In this problem, given an undirected edge-colored graph G, reload costs on a path arise at a node where the path uses consecutive edges of different colors. The objective is to find a spanning tree of G of minimum diameter with respect to the reload costs. We initiate a systematic study of the parameterized complexity of the DIAMETER-TREE problem by considering the following parameters: the cost of a solution, and the treewidth and the maximum degree Delta of the input graph. We prove that DIAMETER-TREE is para-np-hard for any combination of two of these three parameters, and that it is FPT parameterized by the three of them. We also prove that the problem can be solved in polynomial time on cactus graphs. This result is somehow surprising since we prove DIAMETER-TREE to be NP-hard on graphs of treewidth two, which is best possible as the problem can be trivially solved on forests. When the reload costs satisfy the triangle inequality, Wirth and Steffan (2001) proved that the problem can be solved in polynomial time on graphs with Delta=3, and Galbiati (2008) proved that it is NP-hard if Delta=4. Our results show, in particular, that without the requirement of the triangle inequality, the problem is NP-hard if Delta=3, which is also best possible. Finally, in the case where the reload costs are polynomially bounded by the size of the input graph, we prove that DIAMETER-TREE is in XP and W[1]-hard parameterized by the treewidth plus Delta

Cortical topological network changes following optic neuritis

OBJECTIVE: To differentiate between visual cortical network topology changes following optic neuritis (ON) stemming from different inflammatory disease types, we used mathematical graph theory-based tools to analyze functional imaging data. METHODS: Sixty-two patients were recruited into this cross-sectional study, 23 of whom had neuromyelitis optica spectrum disorder (NMOSD) with ON, 18 with clinically isolated syndrome (CIS)-ON, and 21 with other CIS episodes. Twenty-six healthy controls (HCs) were also recruited. All participants underwent resting-state functional MRI. Visual networks were defined using 50 visual regions of interest. Analysis included graph theory metrics, including degree, density, modularity, and local and global efficiency. RESULTS: Visual network density shows decreased connectivity in all patient groups compared with controls. A higher degree of connections is seen in both ON groups (CIS and NMOSD) compared with the the non-ON group. This pattern is most pronounced in dorsal-lateral regions. Information transfer efficiency and modularity were reduced in both CIS groups, but not in the NMOSD group, compared with the HC group. CONCLUSIONS: Visual network density appears affected by the neurologic deficit sustained (ON), and connectivity changes are more evident in dorsal-lateral regions. Efficiency and modularity appear to be associated with the specific disease type (CIS vs NMOSD). Thus, topological cortical changes in the visual system are associated with the type of neurologic deficit within the limits set on them by the underlying pathophysiology. We suggest that cortical patterns of activity should be considered in the outcome of the patients despite the localized nature of ON

Placing regenerators in optical networks to satisfy multiple sets of requests

The placement of regenerators in optical networks has become an active area of research during the last years. Given a set of lightpaths in a network G and a positive integer d, regenerators must be placed in such a way that in any lightpath there are no more than d hops without meeting a regenerator. While most of the research has focused on heuristics and simulations, the first theoretical study of the problem has been recently provided in [10], where the considered cost function is the number of locations in the network hosting regenerators. Nevertheless, in many situations a more accurate estimation of the real cost of the network is given by the total number of regenerators placed at the nodes, and this is the cost function we consider. Furthermore, in our model we assume that we are given a finite set of p possible traffic patterns (each given by a set of lightpaths), and our objective is to place the minimum number of regenerators at the nodes so that each of the traffic patterns is satisfied. While this problem can be easily solved when d = 1 or p = 1, we prove that for any fixed d,p ≥ 2 it does not admit a PTASUnknown control sequence '\textsc', even if G has maximum degree at most 3 and the lightpaths have length O(d)(d). We complement this hardness result with a constant-factor approximation algorithm with ratio ln (d ·p). We then study the case where G is a path, proving that the problem is NP-hard for any d,p ≥ 2, even if there are two edges of the path such that any lightpath uses at least one of them. Interestingly, we show that the problem is polynomial-time solvable in paths when all the lightpaths share the first edge of the path, as well as when the number of lightpaths sharing an edge is bounded. Finally, we generalize our model in two natural directions, which allows us to capture the model of [10] as a particular case, and we settle some questions that were left open in [10]

Artificial Atoms

Contains research goals and objectives, reports on six research projects and a list of publications.Joint Services Electronics Program Contract DAAL03-92-C-0001Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Grant ECS 92-0342

Amenability of groups and GG-sets

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; (4) to describe recent classes of examples, and in particular groups acting on Cantor sets and topological full groups

Search for Single Top Production at LEP

Single top production in e+e- annihilations is searched for in data collected by the L3 detector at centre-of-mass energies from 189 to 209 GeV, corresponding to a total integrated luminosity of 634 pb-1. Investigating hadronic and semileptonic top decays, no evidence of single top production at LEP is obtained and upper limits on the single top cross section as a function of the centre-of-mass energy are derived. Limits on possible anomalous couplings, as well as on the scale of contact interactions responsible for single top production are determined

Tumor-Like Stem Cells Derived from Human Keloid Are Governed by the Inflammatory Niche Driven by IL-17/IL-6 Axis

Alterations in the stem cell niche are likely to contribute to tumorigenesis; however, the concept of niche promoted benign tumor growth remains to be explored. Here we use keloid, an exuberant fibroproliferative dermal growth unique to human skin, as a model to characterize benign tumor-like stem cells and delineate the role of their "pathological" niche in the development of the benign tumor.Subclonal assay, flow cytometric and multipotent differentiation analyses demonstrate that keloid contains a new population of stem cells, named keloid derived precursor cells (KPCs), which exhibit clonogenicity, self-renewal, distinct embryonic and mesenchymal stem cell surface markers, and multipotent differentiation. KPCs display elevated telomerase activity and an inherently upregulated proliferation capability as compared to their peripheral normal skin counterparts. A robust elevation of IL-6 and IL-17 expression in keloid is confirmed by cytokine array, western blot and ELISA analyses. The altered biological functions are tightly regulated by the inflammatory niche mediated by an autocrine/paracrine cytokine IL-17/IL-6 axis. Utilizing KPCs transplanted subcutaneously in immunocompromised mice we generate for the first time a human keloid-like tumor model that is driven by the in vivo inflammatory niche and allows testing of the anti-tumor therapeutic effect of antibodies targeting distinct niche components, specifically IL-6 and IL-17.These findings support our hypothesis that the altered niche in keloids, predominantly inflammatory, contributes to the acquirement of a benign tumor-like stem cell phenotype of KPCs characterized by the uncontrolled self-renewal and increased proliferation, supporting the rationale for in vivo modification of the "pathological" stem cell niche as a novel therapy for keloid and other mesenchymal benign tumors