Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity

We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic (SH), including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency.

Differential Persistence of Transmitted HIV-1 Drug Resistance Mutation Classes

Methods. We studied participants with acute and/or early HIV infection and TDR in 2 cohorts (San Francisco, California, and Sao Paulo, Brazil). We followed baseline mutations longitudinally and compared replacement rates between mutation classes with use of a parametric proportional hazards model. Results. Among 75 individuals with 195 TDR mutations, M184V/I became undetectable markedly faster than did nonnucleoside reverse-transcriptase inhibitor (NNRTI) mutations (hazard ratio, 77.5; 95% confidence interval [CI], 14.7-408.2; P < .0001), while protease inhibitor and NNRTI replacement rates were similar. Higher plasma HIV-1 RNA level predicted faster mutation replacement, but this was not statistically significant (hazard ratio, 1.71 log(10) copies/mL; 95% CI, .90-3.25 log(10) copies/mL; P = .11). We found substantial person-to-person variability in mutation replacement rates not accounted for by viral load or mutation class (P < .0001). Conclusions. The rapid replacement of M184V/I mutations is consistent with known fitness costs. The long-term persistence of NNRTI and protease inhibitor mutations suggests a risk for person-to-person propagation. Host and/or viral factors not accounted for by viral load or mutation class are likely influencing mutation replacement and warrant further study.

Introduction to Discounted Cash Flow Analysis and Financial Functions in Excel

The financial and economic analysis of investment projects is typically carried out using the technique of discounted cash flow (DCF) analysis. This module introduces concepts of discounting and DCF analysis for the derivation of project performance criteria such as net present value (NPV), internal rate of return (IRR) and benefit to cost (B/C) ratios. These concepts and criteria are introduced with respect to a simple example, for which calculations using MicroSoft Excel are demonstrated.