Energy dependent Schrödinger operators and complex Hamiltonian systems on Riemann surfaces

We use so-called energy-dependent Schrödinger operators to establish a link between special classes of solutions on N-component systems of evolution equations and finite dimensional Hamiltonian systems on the moduli spaces of Riemann surfaces. We also investigate the phase-space geometry of these Hamiltonian systems and introduce deformations of the level sets associated to conserved quantities, which results in a new class of solutions with monodromy for N-component systems of PDEs. After constructing a variety of mechanical systems related to the spatial flows of nonlinear evolution equations, we investigate their semiclassical limits. In particular, we obtain semicalssical asymptotics for the Bloch eigenfunctions of the energy dependent Schrödinger operators, which is of importance in investigating zero-dispersion limits of N-component systems of PDEs

On Soliton-type Solutions of Equations Associated with N-component Systems

The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink transitions and multi-peaked soliton solutions is carried out. Transformations are used to connect these solutions to several other equations that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure

MicroRNA100 Inhibits Self-Renewal of Breast Cancer Stem–like Cells and Breast Tumor Development

miRNAs are essential for self-renewal and differentiation of normal and malignant stem cells by regulating the expression of key stem cell regulatory genes. Here, we report evidence implicating the miR100 in self-renewal of cancer stem-like cells (CSC). We found that miR100 expression levels relate to the cellular differentiation state, with lowest expression in cells displaying stem cell markers. Utilizing a tetracycline-inducible lentivirus to elevate expression of miR100 in human cells, we found that increasing miR100 levels decreased the production of breast CSCs. This effect was correlated with an inhibition of cancer cell proliferation in vitro and in mouse tumor xenografts due to attenuated expression of the CSC regulatory genes SMARCA5, SMARCD1, and BMPR2. Furthermore, miR100 induction in breast CSCs immediately upon their orthotopic implantation or intracardiac injection completely blocked tumor growth and metastasis formation. Clinically, we observed a significant association between miR100 expression in breast cancer specimens and patient survival. Our results suggest that miR100 is required to direct CSC self-renewal and differentiation

Cryptosporidium Priming Is More Effective than Vaccine for Protection against Cryptosporidiosis in a Murine Protein Malnutrition Model

Cryptosporidium is a major cause of severe diarrhea, especially in malnourished children. Using a murine model of C. parvum oocyst challenge that recapitulates clinical features of severe cryptosporidiosis during malnutrition, we interrogated the effect of protein malnutrition (PM) on primary and secondary responses to C. parvum challenge, and tested the differential ability of mucosal priming strategies to overcome the PM-induced susceptibility. We determined that while PM fundamentally alters systemic and mucosal primary immune responses to Cryptosporidium, priming with C. parvum (106 oocysts) provides robust protective immunity against re-challenge despite ongoing PM. C. parvum priming restores mucosal Th1-type effectors (CD3+CD8+CD103+ T-cells) and cytokines (IFNγ, and IL12p40) that otherwise decrease with ongoing PM. Vaccination strategies with Cryptosporidium antigens expressed in the S. Typhi vector 908htr, however, do not enhance Th1-type responses to C. parvum challenge during PM, even though vaccination strongly boosts immunity in challenged fully nourished hosts. Remote non-specific exposures to the attenuated S. Typhi vector alone or the TLR9 agonist CpG ODN-1668 can partially attenuate C. parvum severity during PM, but neither as effectively as viable C. parvum priming. We conclude that although PM interferes with basal and vaccine-boosted immune responses to C. parvum, sustained reductions in disease severity are possible through mucosal activators of host defenses, and specifically C. parvum priming can elicit impressively robust Th1-type protective immunity despite ongoing protein malnutrition. These findings add insight into potential correlates of Cryptosporidium immunity and future vaccine strategies in malnourished children

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

Geometric phases, reduction and Lie-Poisson structure for the resonant three-wave interaction

Hamiltonian Lie-Poisson structures of the three-wave equations associated with the Lie algebras su(3) and su(2, 1) are derived and shown to be compatible. Poisson reduction is performed using the method of invariants and geometric phases associated with the reconstruction are calculated. These results can be applied to applications of nonlinear-waves in, for instance, nonlinear optics. Some of the general structures presented in the latter part of this paper are implicit in the literature; our purpose is to put the three-wave interaction in the modern setting of geometric mechanics and to explore some new things, such as explicit geometric phase formulas, as well as some old things, such as integrability, in this context