326 research outputs found
Intersecting Architectural Surfaces Between Graphic and Analytic Representations
Representing an architectural shape, mediating design/formal/semantic needs, means respecting its specificity according to the purposes with which one operates; therefore, teaching how to represent an architectural shape is a complex operation, especially if this happens in the first year of the degree course in Architecture where the heterogeneity of students' background requires a preliminary definition of a common language. Students are firstly introduced to theoretical geometries which underlie architectural shapes. So, they have to know the basis of Geometry (both Descriptive and Analytical) in order to proceed within these issues. This process requires to underline the two `souls' of architectural shapes: the theoretical and the build one. Moreover, it also leads to investigate two different types of theoretical shapes: the one that lies behind the design idea and the other one which underlies the built. We propose teaching examples focused on reading architectural shapes as a result of intersections of surfaces
Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics
We uncover the dynamics at the chaos threshold of the logistic
map and find it consists of trajectories made of intertwined power laws that
reproduce the entire period-doubling cascade that occurs for . We corroborate this structure analytically via the Feigenbaum
renormalization group (RG) transformation and find that the sensitivity to
initial conditions has precisely the form of a -exponential, of which we
determine the -index and the -generalized Lyapunov coefficient . Our results are an unequivocal validation of the applicability of the
non-extensive generalization of Boltzmann-Gibbs (BG) statistical mechanics to
critical points of nonlinear maps.Comment: Revtex, 3 figures. Updated references and some general presentation
improvements. To appear published as a Rapid communication of PR
Screen-detected vs clinical breast cancer: the advantage in the relative risk of lymph node metastases decreases with increasing tumour size
Screen-detected (SD) breast cancers are smaller and biologically more indolent than clinically presenting cancers. An often debated question is: if left undiagnosed during their preclinical phase, would they become more aggressive or would they only increase in size? This study considered a registry-based series (1988–1999) of 3329 unifocal, pT1a-pT3 breast cancer cases aged 50–70 years, of which 994 were SD cases and 2335 clinical cases. The rationale was that (1) the average risk of lymph node involvement (N+) is lower for SD cases, (2) nodal status is the product of biological aggressiveness and chronological age of the disease, (3) for any breast cancer, tumour size is an indicator of chronological age, and (4) for SD cases, tumour size is specifically an indicator of the duration of the preclinical phase, that is, an inverse indicator of lead time. The hypothesis was that the relative protection of SD cases from the risk of N+ and, thus, their relative biological indolence decrease with increasing tumour size. The odds ratio (OR) estimate of the risk of N+ was obtained from a multiple logistic regression model that included terms for detection modality, tumour size category, patient age, histological type, and number of lymph nodes recovered. A term for the detection modality-by-tumour size category interaction was entered, and the OR for the main effect of detection by screening vs clinical diagnosis was calculated. This increased linearly from 0.05 (95% confidence interval: 0.01–0.39) in the 2–7 mm size category to 0.95 (0.64–1.40) in the 18–22 mm category. This trend is compatible with the view that biological aggressiveness of breast cancer increases during the preclinical phase
Incidence of nonextensive thermodynamics in temporal scaling at Feigenbaum points
Recently, in Phys. Rev. Lett. 95, 140601 (2005), P. Grassberger addresses the
interesting issue of the applicability of q-statistics to the renowned
Feigenbaum attractor. He concludes there is no genuine connection between the
dynamics at the critical attractor and the generalized statistics and argues
against its usefulness and correctness. Yet, several points are not in line
with our current knowledge, nor are his interpretations. We refer here only to
the dynamics on the attractor to point out that a correct reading of recent
developments invalidates his basic claim.Comment: To be published in Physica
Nonextensive Thermostatistics and the H-Theorem
The kinetic foundations of Tsallis' nonextensive thermostatistics are
investigated through Boltzmann's transport equation approach. Our analysis
follows from a nonextensive generalization of the ``molecular chaos
hypothesis". For , the -transport equation satisfies an -theorem
based on Tsallis entropy. It is also proved that the collisional equilibrium is
given by Tsallis' -nonextensive velocity distribution.Comment: 4 pages, no figures, corrected some typo
Latin America: ripe for cutting-edge research proposals for prevention and control of Helicobacter pylori
L\'{e}vy scaling: the Diffusion Entropy Analysis applied to DNA sequences
We address the problem of the statistical analysis of a time series generated
by complex dynamics with a new method: the Diffusion Entropy Analysis (DEA)
(Fractals, {\bf 9}, 193 (2001)). This method is based on the evaluation of the
Shannon entropy of the diffusion process generated by the time series imagined
as a physical source of fluctuations, rather than on the measurement of the
variance of this diffusion process, as done with the traditional methods. We
compare the DEA to the traditional methods of scaling detection and we prove
that the DEA is the only method that always yields the correct scaling value,
if the scaling condition applies. Furthermore, DEA detects the real scaling of
a time series without requiring any form of de-trending. We show that the joint
use of DEA and variance method allows to assess whether a time series is
characterized by L\'{e}vy or Gauss statistics. We apply the DEA to the study of
DNA sequences, and we prove that their large-time scales are characterized by
L\'{e}vy statistics, regardless of whether they are coding or non-coding
sequences. We show that the DEA is a reliable technique and, at the same time,
we use it to confirm the validity of the dynamic approach to the DNA sequences,
proposed in earlier work.Comment: 24 pages, 9 figure
A Dynamic Approach to the Thermodynamics of Superdiffusion
We address the problem of relating thermodynamics to mechanics in the case of
microscopic dynamics without a finite time scale. The solution is obtained by
expressing the Tsallis entropic index q as a function of the Levy index alpha,
and using dynamical rather than probabilistic arguments.Comment: 4 pages, new revised version resubmitted to Phys. Rev. Let
Average Entropy of a Subsystem from its Average Tsallis Entropy
In the nonextensive Tsallis scenario, Page's conjecture for the average
entropy of a subsystem[Phys. Rev. Lett. {\bf 71}, 1291(1993)] as well as its
demonstration are generalized, i.e., when a pure quantum system, whose Hilbert
space dimension is , is considered, the average Tsallis entropy of an
-dimensional subsystem is obtained. This demonstration is expected to be
useful to study systems where the usual entropy does not give satisfactory
results.Comment: Revtex, 6 pages, 2 figures. To appear in Phys. Rev.
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