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

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

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 $q>0$, the $q$-transport equation satisfies an $H$-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' $q$-nonextensive velocity distribution.Comment: 4 pages, no figures, corrected some typo

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 $mn$, is considered, the average Tsallis entropy of an $m$-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.

Reply: An inverse association between tumour size and overdiagnosis may explain the results by Bucchi et al

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A novel approach to quantify random error explicitly in epidemiological studies

The most frequently used methods for handling random error are largely misunderstood or misused by researchers. We propose a simple approach to quantify the amount of random error which does not require solid background in statistics for its proper interpretation. This method may help researchers refrain from oversimplistic interpretations relying on statistical significance