Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a pefect agreement with numerical simulations.

Prognostic relevance of Masaoka and Müller-Hermelink classification in patients with thymic tumors.

BACKGROUND: To compare the prognostic relevance of Masaoka and Müller-Hermelink classifications. METHODS: We treated 71 patients with thymic tumors at our institution between 1980 and 1997. Complete follow-up was achieved in 69 patients (97%) with a mean follow up-time of 8.3 years (range, 9 months to 17 years). RESULTS: Masaoka stage I was found in 31 patients (44.9%), stage II in 17 (24.6%), stage III in 19 (27.6%), and stage IV in 2 (2.9%). The 10-year overall survival rate was 83.5% for stage I, 100% for stage IIa, 58% for stage IIb, 44% for stage III, and 0% for stage IV. The disease-free survival rates were 100%, 70%, 40%, 38%, and 0%, respectively. Histologic classification according to Müller-Hermelink found medullary tumors in 7 patients (10.1%), mixed in 18 (26.1%), organoid in 14 (20.3%), cortical in 11 (15.9%), well-differentiated thymic carcinoma in 14 (20.3%), and endocrine carcinoma in 5 (7.3%), with 10-year overall survival rates of 100%, 75%, 92%, 87.5%, 30%, and 0%, respectively, and 10-year disease-free survival rates of 100%, 100%, 77%, 75%, 37%, and 0%, respectively. Medullary, mixed, and well-differentiated organoid tumors were correlated with stage I and II, and well-differentiated thymic carcinoma and endocrine carcinoma with stage III and IV (p < 0.001). Multivariate analysis showed age, gender, myasthenia gravis, and postoperative adjuvant therapy not to be significant predictors of overall and disease-free survival after complete resection, whereas the Müller-Hermelink and Masaoka classifications were independent significant predictors for overall (p < 0.05) and disease-free survival (p < 0.004; p < 0.0001). CONCLUSIONS: The consideration of staging and histology in thymic tumors has the potential to improve recurrence prediction and patient selection for combined treatment modalities.