Tables of Lamé polynomials

Tables of Lamé Polynomial

Numerical Strategies for Solving Multiparameter Spectral Problems

We focus on the solution of multiparameter spectral problems, and in particular on some strategies to compute coarse approximations of selected eigenparameters depending on the number of oscillations of the associated eigenfunctions. Since the computation of the eigenpa- AQ1 rameters is crucial in codes for multiparameter problems based on finite differences, we herein present two strategies. The first one is an iterative algorithm computing solutions as limit of a set of decoupled problems (much easier to solve). The second one solves problems depending on a parameter σ ∈ [0, 1], that give back the original problem only when σ = 1. We compare the strategies by using well known test problems with two and three parameters

Exosomes are released by bystander cells exposed to radiation-induced biophoton signals: Reconciling the mechanisms mediating the bystander effect

OBJECTIVE:The objective of our study was to explore a possible molecular mechanism by which ultraviolet (UV) biophotons could elicit bystander responses in reporter cells and resolve the problem of seemingly mutually exclusive mechanisms of a physical UV signal & a soluble factor-mediated bystander signal. METHODS:The human colon carcinoma cell line, HCT116 p53 +/+, was directly irradiated with 0.5 Gy tritium beta particles to induce ultraviolet biophoton emission. Bystander cells were not directly irradiated but were exposed to the emitted UV biophotons. Medium was subsequently harvested from UV-exposed bystander cells. The exosomes extracted from this medium were incubated with reporter cell populations. These reporter cells were then assayed for clonogenic survival and mitochondrial membrane potential with and without prior treatment of the exosomes with RNase. RESULTS:Clonogenic cell survival was significantly reduced in reporter cells incubated with exosomes extracted from cells exposed to secondarily-emitted UV. These exosomes also induced significant mitochondrial membrane depolarization in receiving reporter cells. Conversely, exosomes extracted from non-UV-exposed cells did not produce bystander effects in reporter cells. The treatment of exosomes with RNase prior to their incubation with reporter cells effectively abolished bystander effects in reporter cells and this suggests a role for RNA in mediating the bystander response elicited by UV biophotons and their produced exosomes. CONCLUSION:This study supports a role for exosomes released from UV biophoton-exposed bystander cells in eliciting bystander responses and also indicates a reconciliation between the UV-mediated bystander effect and the bystander effect which has been suggested in the literature to be mediated by soluble factors