Smooth Linearization for a Saddle on Banach Spaces

As a continuation of a previous work on linearization of class C¹ of diffeomorphisms and flows in infinite dimensions near a fixed point, in this work we deal with the case of a saddle point with some non-resonance restrictions for the linear part. Our result can be seen as an extension of results by Hartman [Boletin de la Sociedad Matematica Mexicana 5(2), 220–241 (1960)] and Aronson, Belitskii and Zhuzhoma [Introduction to the Qualitative Theory of Dynamical systems on surfaces, AMS Transl. Math. Monog. vol.153, pp. 268–277 (1996)] in dimension two. We also present an application to a system of nonlinear wave equations.AMS Subject Classifications: Primary: 35B05, 34G20. Secondary: 35B40, 34D05.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday     

Comparative analysis of the conformational profile of substance P using simulated annealing and molecular dynamics

The present study describes an extensive conformational search of substance P using two different computational methods. On the one hand, the peptide was studied using the iterative simulated annealing, and on the other, molecular dynamics simulations at 300 and 400 K. With the former method, the peptide was studied in vacuo with a dielectric constant of 80, whereas using the latter study the peptide was studied in a box of TIP3P water molecules. Analysis of the results obtained using both methodologies was carried out using an in-house methodology using a cluster analysis method based on information theory. Comparison of the two sampling methodologies and the different environment used in the calculations is also analyzed. Finally, the conformational motifs that are characteristic of substance P in a hydrophilic environment are presented and compared with the experimental results available in the literature.     

Phase transitions in unstable cancer cell populations

The dynamics of cancer evolution is studied by means of a simple quasispecies model involving cells displaying high levels of genetic instability. Both continuous, mean-field and discrete, bit-string models are analysed. The string model is simulated on a single-peak landscape. It is shown that a phase transition exists at high levels of genetic instability, thus separating two phases of slow and rapid growth. The results suggest that, under a conserved level of genetic instability the cancer cell population will be close to the threshold level. Implications for therapy are outlined.Received: 22 April 2003, Published online: 22 September 2003PACS: 87.10.+e Biological physics: General theory and mathematical aspects - 87.23.Kg Dynamics of evolution - 87.23.-n Ecology and evolution - 89.75.Fb Structures and organization in complex systems     

Anomalous behavior of ideal Fermi gas below two dimensions

Normal behavior of the thermodynamic properties of a Fermi gas in d > 2 dimensions, integer or not, means monotonically increasing or decreasing of its specific heat, chemical potential or isothermal sound velocity, all as functions of temperature. However, for 0 < d < 2 dimensions these properties develop a "hump" (or "trough") which increases (or deepens) as d? 0 d\rightarrow 0 . Though not the phase transition signaled by the sharp features ("cusp" or "jump") in those properties for the ideal Bose gas in d > 2 (known as the Bose-Einstein condensation), it is nevertheless an intriguing structural anomaly which we exhibit in detail.     

Downside Risk analysis applied to the Hedge Funds universe

Hedge Funds are considered as one of the portfolio management sectors which shows a fastest growing for the past decade. An optimal Hedge Fund management requires an appropriate risk metrics. The classic CAPM theory and its Ratio Sharpe fail to capture some crucial aspects due to the strong non-Gaussian character of Hedge Funds statistics. A possible way out to this problem while keeping the CAPM simplicity is the so-called Downside Risk analysis. One important benefit lies in distinguishing between good and bad returns, that is: returns greater or lower than investor's goal. We revisit most popular Downside Risk indicators and provide new analytical results on them. We compute these measures by taking the Credit Suisse/Tremont Investable Hedge Fund Index Data and with the Gaussian case as a benchmark. In this way, an unusual transversal lecture of the existing Downside Risk measures is provided.     

Classification of Dansgaard–Oeschger climatic cycles by the application of similitude signal processing

In this work we have performed a detailed analysis, using signal processing tools, to study time series of data (temperature proxy) extracted from the GRIP ice-core records and we relate it with the evolution of atmospheric CO₂ within the last glacial period. Our method is based in considering the warm periods known as Dansgaard–Oeschger (D/O) events and posterior returns to the cold stage as a climatic cycle. After the warming phase, D/O events relax to the initial cold state in three different ways, what gives rise to three classes of cycles. Also, the Younger/Dryas–Bolling/Allerod (Y/D–B/A) cycle corresponds to one of the classes obtained. We have found that all cycles start with identical warming phases which seem completely unrelated to variations in CO₂ concentration. We discuss on the consequences for global climatology of such steady pattern of cycles.     

The xraylib library for X-ray–matter interactions. Recent developments

This work presents the recent developments of xraylib, an ANSI C library that provides convenient access to a large number of X-ray related databases, with a focus on quantitative X-ray fluorescence applications. The enhancements include improved X-ray fluorescence production cross sections that take into account cascade effects and M-lines, as well as revised line energies, atomic level widths, Compton broadening profiles etc. A full overview of the complete application programming interface is presented.