The longest path problem is polynomial on interval graphs.

The longest path problem is the problem of finding a path of maximum length in a graph. Polynomial solutions for this problem are known only for small classes of graphs, while it is NP-hard on general graphs, as it is a generalization of the Hamiltonian path problem. Motivated by the work of Uehara and Uno in [20], where they left the longest path problem open for the class of interval graphs, in this paper we show that the problem can be solved in polynomial time on interval graphs. The proposed algorithm runs in O(n 4) time, where n is the number of vertices of the input graph, and bases on a dynamic programming approach

Reduced dynamics of Ward solitons

The moduli space of static finite energy solutions to Ward's integrable chiral model is the space $M_N$ of based rational maps from \CP^1 to itself with degree $N$. The Lagrangian of Ward's model gives rise to a K\"ahler metric and a magnetic vector potential on this space. However, the magnetic field strength vanishes, and the approximate non--relativistic solutions to Ward's model correspond to a geodesic motion on $M_N$. These solutions can be compared with exact solutions which describe non--scattering or scattering solitons.Comment: Final version, to appear in Nonlinearit

Non-trivial Soliton Scattering in Planar Integrable Systems

The behavior of solitons in integrable theories is strongly constrained by the integrability of the theory, that is by the existence of an infinite number of conserved quantities that these theories are known to possess. As a result the soliton scattering of such theories are expected to be trivial (with no change of direction, velocity or shape). In this paper we present an extended review on soliton scattering of two spatial dimensional integrable systems which have been derived as dimensional reductions of the self-dual Yang-Mills-Higgs equations and whose scattering properties are highly non-trivial.Comment: 25 pages + 9 Figures, Review Paper to appear in International Journal of Modern Physics

Complete Supersymmetric Quantum Mechanics of Magnetic Monopoles in N=4 SYM Theory

We find the most general low energy dynamics of 1/2 BPS monopoles in the N=4 supersymmetric Yang-Mills theories (SYM) when all six adjoint Higgs expectation values are turned on. When only one Higgs is turned on, the Lagrangian is purely kinetic. When all six are turned on, however, this moduli space dynamics is augmented by five independent potential terms, each in the form of half the squared norm of a Killing vector field on the moduli space. A generic stationary configuration of the monopoles can be interpreted as stable non BPS dyons, previously found as non-planar string webs connecting D3-branes. The supersymmetric extension is also found explicitly, and gives the complete quantum mechanics of monopoles in N=4 SYM theory. We explore its supersymmetry algebra.Comment: Errors in the SUSY algebra corrected. The version to appear in PR

In Situ Characterization of Follicular Helper CD4 T Cells Using Multiplexed Imaging.

Follicular helper CD4 T (Tfh) cells play an essential role in the formation of germinal centers (GCs), where mature B cells proliferate, differentiate, and provide long-term protective humoral responses. Despite the extensive phenotypic characterization and identification of human Tfh cell subsets, their spatial positioning at tissue level is not well understood. Here, we describe a quantitative multiplexed immunofluorescence approach allowing for the comprehensive in situ characterization of Tfh cells in human tonsils and lymph nodes (LNs) from individuals with angioimmunoblastic T-cell lymphoma (AITL). We have developed eight multiplexed panels comprising a spectrum of Tfh cell markers, like PD-1, CXCR5, and ICOS, along with transcription factors (Bcl6, Tbet, GATA3), to assess their expression, frequencies, spatial distribution and co-localization in a quantitative manner. Combined analysis of relevant markers revealed the presence of several Tfh cell subsets at tissue level based on the differential expression of surface receptors, nuclear factors as well as their distinct localization within the follicular areas. Interestingly, we found a considerable amount of tonsillar Tfh cells expressing high levels of the Th2 regulator GATA3. The co-expression of GATA3, CXCR5, and BCL6, points to an important role of GATA3 for the generation of effector human Tfh cells. Furthermore, our data revealed significantly different Tfh cell profile signatures between health and disease. Therefore, our imaging platform generates meaningful information for the in situ characterization of human Tfh cells and could provide the base for future studies aiming to a comprehensive understanding of Tfh cell tissue heterogeneity

Low Avidity T Cells Do Not Hinder High Avidity T Cell Responses Against Melanoma

The efficacy of T cells depends on their functional avidity, i. e., the strength of T cell interaction with cells presenting cognate antigen. The overall T cell response is composed of multiple T cell clonotypes, involving different T cell receptors and variable levels of functional avidity. Recently, it has been proposed that the presence of low avidity tumor antigen-specific CD8 T cells hinder their high avidity counterparts to protect from tumor growth. Here we analyzed human cytotoxic CD8 T cells specific for the melanoma antigen Melan-A/MART-1. We found that the presence of low avidity T cells did not result in reduced cytotoxicity of tumor cells, nor reduced cytokine production, by high avidity T cells. In vivo in NSG-HLA-A2 mice, the anti-tumor effect of high avidity T cells was similar in presence or absence of low avidity T cells. These data indicate that low avidity T cells are not hindering anti-tumor T cell responses, a finding that is reassuring because low avidity T cells are an integrated part of natural T cell responses