Golden gaskets: variations on the Sierpi\'nski sieve

We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor \la\in(0,1). As is well known, for \la=1/2 the invariant set, \S_\la, is a fractal called the Sierpi\'nski sieve, and for \la<1/2 it is also a fractal. Our goal is to study \S_\la for this IFS for 1/2<\la<2/3, i.e., when there are "overlaps" in \S_\la as well as "holes". In this introductory paper we show that despite the overlaps (i.e., the Open Set Condition breaking down completely), the attractor can still be a totally self-similar fractal, although this happens only for a very special family of algebraic \la's (so-called "multinacci numbers"). We evaluate \dim_H(\S_\la) for these special values by showing that \S_\la is essentially the attractor for an infinite IFS which does satisfy the Open Set Condition. We also show that the set of points in the attractor with a unique ``address'' is self-similar, and compute its dimension. For ``non-multinacci'' values of \la we show that if \la is close to 2/3, then \S_\la has a nonempty interior and that if \la<1/\sqrt{3} then \S_\la$ has zero Lebesgue measure. Finally we discuss higher-dimensional analogues of the model in question.Comment: 27 pages, 10 figure

Stability of relative equilibria with singular momentum values in simple mechanical systems

A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.Comment: Partially rewritten. Some mistakes fixed. Exposition improve

Centralized cytogenetic analysis of pediatric acute leukemia: results of an italian collaborative experience

Background and Objective. Cytogenetic analysis of acute leukemia yields important information which has been demonstrated to be correlated to patient survival. A reference laboratory was created in order to perform karyotype analysis on all cases of acute leukemia enrolled in the AIEOP (Associazione Italiana Emato-Oncologia Pediatrica) protocols. Methods. From January 1990 to December 1995, 1115 samples of children with ALL or AML were sent in for cytogenetic analysis. The results of cell cultures were screened in the Reference Laboratory and then the fixed metaphases were sent to one of the six cytogenetic laboratories for analysis. Results. The leukemic karyotypes of 556 patients were successfully analyzed. An abnormal clone was detected in 49% of cases of ALL and in 66% of AML. In ALL the most frequent abnormality was 9p rearrangement. Other recurrent abnormalities were t(9;22), t(4;11) and t(1;19). In AML t(8;21), t(15;17) and 11q23 rearrangement were the most frequent structural abnormalities. These findings are similar to the results obtained in other multicenter studies using a similar approach. Interpretation and Conclusions. Our data confirm the feasibility of performing cytogenetic analysis in a centralized laboratory on mailed samples of bone marrow and/or peripheral blood; this is very important considering that cytogenetic analysis of neoplastic tissue requires a special laboratory and expert staff

Functional imaging studies of cognition using 99mTc-HMPAO SPECT: empirical validation using the n-back working memory paradigm

{Purpose} Functional activation protocols are widely applied for the study of brain-cognition relations. Only few take advantage of the intrinsic characteristics of SPECT, particularly those allowing cognitive assessment outside of the camera, in settings close to the standard clinical or laboratory ones. The purpose of the study was to assess the feasibility of a split-dose activation protocol with 99mTc-HMPAO using low irradiation dose. {Materials and methods} A two-scans protocol was applied to 12 healthy young volunteers using 270 MBq of 99mTc-HMPAO per scan, with each image associated to a particular experimental condition of the verbal {n}-back working memory task (0-back, 2-back). Subtraction method was used to identify regional brain activity related to the task. {Results} Voxel-wise statistical analysis showed left lateralized activity associated with the 2-back task, compared to the 0-back task. Activated regions, mainly prefrontal and parietal, were similar to those observed in previous fMRI and 15O-PET studies. {Conclusion} The results support the use of 99mTc-HMPAO SPECT for the investigation of brain-cognition relations and demonstrate the feasibility of optimal quality images despite low radiopharmaceutical doses. The findings also acknowledge the use of HMPAO as a radioligand to capture neuro-energetic modulations linked to cognitive activity. They encourage extending the application of the described activation protocol to clinical populations