Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity

We study the Gross-Pitaevskii equation involving a nonlocal interaction potential. Our aim is to give sufficient conditions that cover a variety of nonlocal interactions such that the associated Cauchy problem is globally well-posed with non-zero boundary condition at infinity, in any dimension. We focus on even potentials that are positive definite or positive tempered distributions.Comment: Communications in Partial Differential Equations (2010

Instantons and Chiral Symmetry on the Lattice

I address the question of how much of QCD in the chiral limit is reproduced by instantons. After reconstructing the instanton content of smoothed Monte Carlo lattice configurations, I compare hadron spectroscopy on this instanton ensemble to the spectroscopy on the original ``physical'' smoothed configurations using a chirally optimised clover fermion action. By studying the zero mode zone in simple instances I find that the optimised action gives a satisfactory description of it. Through the Banks-Casher formula, instantons by themselves are shown to break chiral symmetry but hadron correlators on the instanton backgrounds are strongly influenced by free quark propagation. This results in unnaturally light hadrons and a small splitting between the vector and the pseudoscalar meson channels. Superimposing a perturbative ensemble of zero momentum gauge field fluctuations (torons) on the instantons is found to be enough to eliminate the free quarks and restore the physical hadron correlators. I argue that the torons that are present only in finite volumes, are probably needed to compensate the unnaturally large finite size effects due to the lack of confinement in the instanton ensemble.Comment: 32 pages, LaTeX with 14 eps figure

Traveling waves for nonlinear Schr\"odinger equations with nonzero conditions at infinity, II

We prove the existence of nontrivial finite energy traveling waves for a large class of nonlinear Schr\"odinger equations with nonzero conditions at infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic" equations) in space dimension $N \geq 2$. We show that minimization of the energy at fixed momentum can be used whenever the associated nonlinear potential is nonnegative and it gives a set of orbitally stable traveling waves, while minimization of the action at constant kinetic energy can be used in all cases. We also explore the relationship between the families of traveling waves obtained by different methods and we prove a sharp nonexistence result for traveling waves with small energy.Comment: Final version, accepted for publication in the {\it Archive for Rational Mechanics and Analysis.} The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-017-1131-

Subfactors of index less than 5, part 3: quadruple points

One major obstacle in extending the classification of small index subfactors beyond 3+\sqrt{3} is the appearance of infinite families of candidate principal graphs with 4-valent vertices (in particular, the "weeds" Q and Q' from Part 1 (arXiv:1007.1730)). Thus instead of using triple point obstructions to eliminate candidate graphs, we need to develop new quadruple point obstructions. In this paper we prove two quadruple point obstructions. The first uses quadratic tangles techniques and eliminates the weed Q' immediately. The second uses connections, and when combined with an additional number theoretic argument it eliminates both weeds Q and Q'. Finally, we prove the uniqueness (up to taking duals) of the 3311 Goodman-de la Harpe-Jones subfactor using a combination of planar algebra techniques and connections.Comment: 21 page

PPARγ Controls Dectin-1 Expression Required for Host Antifungal Defense against Candida albicans

We recently showed that IL-13 or peroxisome proliferator activated receptor γ (PPARγ) ligands attenuate Candida albicans colonization of the gastrointestinal tract. Here, using a macrophage-specific Dectin-1 deficient mice model, we demonstrate that Dectin-1 is essential to control fungal gastrointestinal infection by PPARγ ligands. We also show that the phagocytosis of yeast and the release of reactive oxygen intermediates in response to Candida albicans challenge are impaired in macrophages from Dectin-1 deficient mice treated with PPARγ ligands or IL-13. Although the Mannose Receptor is not sufficient to trigger antifungal functions during the alternative activation of macrophages, our data establish the involvement of the Mannose Receptor in the initial recognition of non-opsonized Candida albicans by macrophages. We also demonstrate for the first time that the modulation of Dectin-1 expression by IL-13 involves the PPARγ signaling pathway. These findings are consistent with a crucial role for PPARγ in the alternative activation of macrophages by Th2 cytokines. Altogether these data suggest that PPARγ ligands may be of therapeutic value in esophageal and gastrointestinal candidiasis in patients severely immunocompromised or with metabolic diseases in whom the prevalence of candidiasis is considerable

In Vivo Systematic Analysis of Candida albicans Zn2-Cys6 Transcription Factors Mutants for Mice Organ Colonization

The incidence of fungal infections in immuno-compromised patients increased considerably over the last 30 years. New treatments are therefore needed against pathogenic fungi. With Candida albicans as a model, study of host-fungal pathogen interactions might reveal new sources of therapies. Transcription factors (TF) are of interest since they integrate signals from the host environment and participate in an adapted microbial response. TFs of the Zn2-Cys6 class are specific to fungi and are important regulators of fungal metabolism. This work analyzed the importance of the C. albicans Zn2-Cys6 TF for mice kidney colonization. For this purpose, 77 Zn2-Cys6 TF mutants were screened in a systemic mice model of infection by pools of 10 mutants. We developed a simple barcoding strategy to specifically detect each mutant DNA from mice kidney by quantitative PCR. Among the 77 TF mutant strains tested, eight showed a decreased colonization including mutants for orf19.3405, orf19.255, orf19.5133, RGT1, UGA3, orf19.6182, SEF1 and orf19.2646, and four an increased colonization including mutants for orf19.4166, ZFU2, orf19.1685 and UPC2 as compared to the isogenic wild type strain. Our approach was validated by comparable results obtained with the same animal model using a single mutant and the revertant for an ORF (orf19.2646) with still unknown functions. In an attempt to identify putative involvement of such TFs in already known C. albicans virulence mechanisms, we determined their in vitro susceptibility to pH, heat and oxidative stresses, as well as ability to produce hyphae and invade agar. A poor correlation was found between in vitro and in vivo assays, thus suggesting that TFs needed for mice kidney colonization may involve still unknown mechanisms. This large-scale analysis of mice organ colonization by C. albicans can now be extended to other mutant libraries since our in vivo screening strategy can be adapted to any preexisting mutants