Orbit Representations from Linear mod 1 Transformations

We show that every point $x_0\in [0,1]$ carries a representation of a $C^*$-algebra that encodes the orbit structure of the linear mod 1 interval map $f_{\beta,\alpha}(x)=\beta x +\alpha$. Such $C^*$-algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map $f_{\beta,\alpha}$. Then we prove that such representation is irreducible. Moreover two such of representations are unitarily equivalent if and only if the points belong to the same generalized orbit, for every $\alpha\in [0,1[$ and $\beta\geq 1$

Internet Marketing for the Wine Business

Apresentação realizada no âmbito do InSITE 2013, Porto, 2 a 5 de julho 2013A keynote presentation about the use of Internet marketing for the wine industr

A discussion on different techniques for GIS data collecting, precision, accuracy and quality of database

Nowadays, is a common sense the importance of geotechnologies in urban planning, transportation engineering and other different areas of knowledge. The Geographic Information System (GIS) is one of the geotechnologies that has been used increasingly. The collection of information and creation of a database are the most expensive, complex and important task in a GIS project. The collection of information results from the direct and indirect measurement of the real world. The reason for creating databases is to register and the maintain the different sources of collecting information. This paper has the objective to present the different techniques for data collection as input in GIS, as well as a brief discussion on the cost associated with the collection of data. Furthermore, comments on precision, accuracy and the quality of database are given.

Backward stochastic differential equation approach to modeling of gene expression

In this article, we introduce a novel backward method to model stochastic gene expression and protein level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of endpoint ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time reversed simulations, allowing, for example, the assessment of the biological conditions (e.g. protein concentrations) that preceded an experimentally measured event of interest (e.g. mitosis, apoptosis, etc.).Comment: Accepted in Physical Review

Memória da obra de Eiffel em Portugal

Livro de homenagem à professora Maria Emília Ricardo Marque

Sexual reproduction vs. clonal propagation in the recovery of a seagrass meadow after an extreme weather event

Marine flowering plants can reproduce sexually and clonally, and the relative contribution of these two modes can be dependent on the environmental conditions. Zostera marina, a seagrass widely distributed in the northern hemisphere, can form annual and perennial meadows with different proportions of sexual versus clonal propagation depending on the environmental disturbance regime. We study the hypothesis that the contribution of sexual propagation varies during the recovery of a seagrass meadow. In this case study, we compare the proportion of sexual versus clonal propagation of a perennial Z. marina meadow before its disappearance due to winter storms and after recovery. Before disturbance, genotypic diversity was high, indicating frequent sexual reproduction events likely to create an abundant seed bank. Seedling germination allowed the population to recover after the extreme disturbance. As months passed, seedlings became rare and finally absent, giving place to adult shoots. In an advanced stage of colonization, the shoots colonized the area by vegetative growth, which lowered the genotypic diversity. Despite this reduction over time, the genotypic diversity of the new meadow is still high, demonstrating the importance of sexual reproduction in meadow recovery and persistence.info:eu-repo/semantics/publishedVersio