We present some considerations on time-oscillatory phenomena in hydrodynamical
models for semiconductors and study the existence of periodic solutions. For the one-dimensional,
viscous, isentropic model, written in Lagrangian mass coordinates, we state a first existence result
and give a sketch of the proof.
It is well known that given a single time series, or image,
it might not be possible to utilize various statistical techniques that for
their implementation require more than a single observation at a fixed
point in time/space. If the researcher has repeated measurements in
form of functions/images, than wavelets can be successfully employed
in a functional-type data analysis. In the first part of this paper we
focus on wavelet based functional ANOVA procedure in which the
noise is separated from the signal for different treatments, and at the
same time the treatment responses are additionally split on the mean
response and the treatment effect, in the spirit of traditional ANOVA.
The key properties utilized are abilities of wavelets to decorrelate and
regularize the inputs. Different strategies for (multivariate) shrinkage
separation of treatment effects and significance testing in the wavelet
domain are discussed.
In the second part of this we propose a method for wavelet-filtering of
noisy images when prior information about their L
2
-energy is available but the researcher has only a single measurement. Assuming the
independence model, according to which the wavelet coefficients are
treated individually, we propose a level dependent shrinkage rule that
turns out to be the ?-minimax rule for a suitable class, say ?, of realistic priors on the wavelet coefficients.
Both methods are illustrated and evaluated on test-functions and images with controlled signal-to-noise ratios
The need for anti-HIV-1 vaccines is universally recognized. Although several potential vaccine formulations are being tested in clinical trials, the complexity of the viral system and the length of the experimentation required and its costs makes the goal of obtaining such a vaccine still elusive. We have built a mathematical model for the simulation of HIV-1 infection spreading into the body, which allows us study in silico the effect of hypothetical anti-HIV-1 vaccines having different properties. In particular, vaccines eliciting a cytolytic T-cell response, a humoral response, or both can be simulated. The vaccines considered can be envisaged either as preventive or therapeutic and can have different strength. The kinetic parameters used for solving the model are those of HIV-1 infection obtained from experimental and clinical observations. The vaccines are instead characterized by parameters that can be varied in order to mimic different behaviors: the rate of killing of the single effector cell and the rate of neutralization of the single antibody molecule; and the level of the immune response raised. The model allows us to predict which characteristics of immunogenicity a preventive or therapeutic vaccine should possess to be efficacious, and which are the key factors that most likely will affect its ability to control the spread of the infection. We discuss here the conclusions that can be drawn from a such a model and some of its limitations.
