1. Native ultrametricity in random sparse systems Sergei Nechaev LPTMS, Orsay, France

2. Spectra of sparse matrices and random operators: from Fibonacci sequences to Anderson localization…and more Sergei Nechaev LPTMS, Orsay, France In collaboration with V. Avetisov (Moscow), P. Krapivsky (Boston)

7. Density of linear subgraphs (chains) at percolation point: Total cluster density: 95% subgraphs at percolation point are linear chains

8. Linear bi-diagonal operators

9. Spectral density of ensembles of linear chains

12. Generic expression of the principle series Principle series of peaks

13. Degeneracy of series of peaks

14. Degeneracy of a principle series of peaks Visibility diagram

15. Spectrum tail for q < 1 Lifshitz tail of 1D Anderson localization

16. Spectrum tail for q  1

17. Asymptotic behavior of the Dedekind function

19. Conjecture about asymptotic behavior of the Dedekind function and spectrum tail for q  1 Direct numeric simulations Limiting eigenvalue density Log of Dedekind 

20. Static and Dynamical Phyllotaxis in Magnetic Cactus C. Nisoli et al: ArXiv: cond-mat/0702335 Thomae (Dirichlet) function

21. Attempts to squeeze the surface in the 3D space Jupe a godets

22. Isometric embedding of an uniform open Cayley tree Lobachevsky plane (space)

23. Explicit construction by conformal maps is realized by the Dedekind eta-function

24. Hyperbolic geometry in Nature coral Relief on the basis of Dedekind  -function

25. Surface cut near maxima of the relief