Equilibrium in a two-agent assignment problem

In this paper we address a particular generalisation of the Assignment Problem (AP) in a Multi-Agent setting, where distributed agents share common resources. We consider the problem of determining Pareto-optimal solutions that satisfy a fairness criterion (equilibrium). We show that the solution obtained is equivalent to a Kalai Smorodinsky solution of a suitably defined bargaining problem and characterise the computational complexity of finding such an equilibrium. Additionally, we propose an exact solution algorithm based on a branch-and-bound scheme that exploits bounds obtained by suitably rounding the solutions of the corresponding linear relaxation, and give the results of extensive computational experiments. Copyright © 2009, Inderscience Publishers

Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Consider the generalized iterated wreath product $\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k}$ where $r_i \in \mathbb{N}$. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science

Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060

Pseudomonas expression of an oxygen sensing prolyl hydroxylase homologue regulates neutrophil host responses in vitro and in vivo

Background: Pseudomonas species are adapted to evade innate immune responses and can persist at sites of relative tissue hypoxia, including the mucus-plugged airways of patients with cystic fibrosis and bronchiectasis. The ability of these bacteria to directly sense and respond to changes in local oxygen availability is in part consequent upon expression of the 2-oxoglutarate oxygenase, Pseudomonas prolyl hydroxylase (PPHD), which acts on elongation factor Tu (EF-Tu), and is homologous with the human hypoxia inducible factor (HIF) prolyl hydroxylases. We report that PPHD expression regulates the neutrophil response to acute pseudomonal infection. Methods: In vitro co-culture experiments were performed with human neutrophils and PPHD-deficient and wild-type bacteria and supernatants, with viable neutrophil counts determined by flow cytometry. In vivo consequences of infection with PPHD deficient P. aeruginosa were determined in an acute pneumonia mouse model following intra-tracheal challenge. Results: Supernatants of PPHD-deficient bacterial cultures contained higher concentrations of the phenazine exotoxin pyocyanin and induced greater acceleration of neutrophil apoptosis than wild-type PAO1 supernatants in vitro. In vivo infection with PPHD mutants compared to wild-type PAO1 controls resulted in increased levels of neutrophil apoptosis and impaired control of infection, with higher numbers of P. aeruginosa recovered from the lungs of mice infected with the PPHD-deficient strain. This resulted in an overall increase in mortality in mice infected with the PPHD-deficient strain. Conclusions: Our data show that Pseudomonas expression of its prolyl hydroxylase influences the outcome of host-pathogen interactions in vitro and in vivo, demonstrating the importance of considering how both host and pathogen adaptations to hypoxia together define outcomes of infection. Given that inhibitors for the HIF prolyl hydroxylases are in late stage trials for the treatment of anaemia and that the active sites of PPHD and human HIF prolyl hydroxylases are closely related, the results are of current clinical interest

Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica

MHCII-mediated dialog between group 2 innate lymphoid cells and CD4+ T cells potentiates type 2 immunity and promotes parasitic helminth expulsion

Group 2 innate lymphoid cells (ILC2s) release interleukin-13 (IL-13) during protective immunity to helminth infection and detrimentally during allergy and asthma. Using two mouse models to deplete ILC2s in vivo, we demonstrate that T helper 2 (Th2) cell responses are impaired in the absence of ILC2s. We show that MHCII-expressing ILC2s interact with antigen-specific T cells to instigate a dialog in which IL-2 production from T cells promotes ILC2 proliferation and IL-13 production. Deletion of MHCII renders IL-13-expressing ILC2s incapable of efficiently inducing Nippostrongylus brasiliensis expulsion. Thus, during transition to adaptive T cell-mediated immunity, the ILC2 and T cell crosstalk contributes to their mutual maintenance, expansion and cytokine production. This interaction appears to augment dendritic-cell-induced T cell activation and identifies a previously unappreciated pathway in the regulation of type-2 immunity

Unconventional Ubiquitin Recognition by the Ubiquitin-Binding Motif within the Y-Family DNA Polymerases ι and Rev1

Translesion synthesis is an essential cell survival strategy to promote replication after DNA damage. The accumulation of Y family polymerases (pol) ι and Rev1 at the stalled replication machinery is mediated by the ubiquitin-binding motifs (UBMs) of the polymerases and enhanced by PCNA monoubiquitination. We report the solution structures of the C-terminal UBM of human pol ι and its complex with ubiquitin. Distinct from other ubiquitin-binding domains, the UBM binds to the hydrophobic surface of ubiquitin centered at L8. Accordingly, mutation of L8A, but not I44A, of ubiquitin abolishes UBM binding. Human pol ι contains two functional UBMs, both contributing to replication foci formation. In contrast, only the second UBM of Saccharomyces cerevisiae Rev1 binds to ubiquitin and is essential for Rev1-dependent cell survival and mutagenesis. Point mutations disrupting the UBM-ubiquitin interaction also impair the accumulation of pol ι in replication foci and Rev1-mediated DNA damage tolerance in vivo.National Institute of General Medical Sciences (U.S.) (Grant GM-079376)American Cancer Society. Research ProfessorshipNational Institute of Environmental Health Sciences (Grant P30 ES-002109

Hair analysis following chronic smoked-drugs-of-abuse exposure in adults and their toddler: a case report

<p>Abstract</p> <p>Introduction</p> <p>Over the past two decades, the study of chronic cocaine and crack cocaine exposure in the pediatric population has been focused on the potential adverse effects, especially in the prenatal period and early childhood. Non-invasive biological matrices have become an essential tool for the assessment of a long-term history of drug of abuse exposure.</p> <p>Case report</p> <p>We analyze the significance of different biomarker values in hair after chronic crack exposure in a two-year-old Caucasian girl and her parents, who are self-reported crack smokers. The level of benzoylecgonine, the principal metabolite of cocaine, was determined in segmented hair samples (0 cm to 3 cm from the scalp, and > 3 cm from the scalp) following washing to exclude external contamination. Benzoylecgonine was detectable in high concentrations in the child's hair, at 1.9 ng/mg and 7.04 ng/mg, respectively. Benzoylecgonine was also present in the maternal and paternal hair samples at 7.88 ng/mg and 6.39 ng/mg, and 13.06 ng/mg and 12.97 ng/mg, respectively.</p> <p>Conclusion</p> <p>Based on the data from this case and from previously published poisoning cases, as well as on the experience of our research group, we conclude that, using similar matrices for the study of chronic drug exposure, children present with a higher cocaine concentration in hair and they experience more serious deleterious acute effects, probably due to a different and slower cocaine metabolism. Consequently, children must be not exposed to secondhand crack smoke under any circumstance.</p