Projects: 1. Find Fano Factor for a model with two gene copies and fixed concentration of transcriptional factors. 2. Derive system of equations for moments in the stationary state in an autoregulation model with dimerization of protein molecules. 3. Construct infinite-volume Gibbs states for a Hamiltonian with a unique (up to translations) periodic ground-state configurations. Use Peierls contours. 4. Find all ground-state configurations for one-dimensional Ising model with nearest-neighbor and next-nearest-neighbor interactions. A general algorithm is presented in the following paper. The Third Law of Thermodynamics, J. Miękisz i C. Radin, Mod. Phys. Lett. B1: 61-65 (1987) pdf 5. 6. EXAMS and MIDTERMS Exam08 pdf Exam10 pdf Exam11 pdf Exam12 pdf Exam13 pdf Exam14 pdf Midterm09 pdf Midterm10 pdf Midterm13 pdf Midterm14 pdf Midterm15 pdf