Dynamical Properties of a Two-gene Network with Hysteresis

A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ a hybrid systems model to capture the dynamics of the system. The proposed model incorporates binary hysteresis with different thresholds capturing the interaction between the genes. We analyze properties of the solutions and asymptotic stability of equilibria in the system as a function of its parameters. Our analysis reveals the presence of limit cycles for a certain range of parameters, behavior that is associated with hysteresis. The set of points defining the limit cycle is characterized and its asymptotic stability properties are studied. Furthermore, the stability property of the limit cycle is robust to small perturbations. Numerical simulations are presented to illustrate the results.Comment: 55 pages, 31 figures.Expanded version of paper in Special Issue on Hybrid Systems and Biology, Elsevier Information and Computation, 201

Neural networks based recognition of 3D freeform surface from 2D sketch

In this paper, the Back Propagation (BP) network and Radial Basis Function (RBF) neural network are employed to recognize and reconstruct 3D freeform surface from 2D freehand sketch. Some tests and comparison experiments have been made to evaluate the performance for the reconstruction of freeform surfaces of both networks using simulation data. The experimental results show that both BP and RBF based freeform surface reconstruction methods are feasible; and the RBF network performed better. The RBF average point error between the reconstructed 3D surface data and the desired 3D surface data is less than 0.05 over all our 75 test sample data

Radiative and Collisional Jet Energy Loss in a Quark-Gluon Plasma

We calculate radiative and collisional energy loss of hard partons traversing the quark-gluon plasma created at RHIC and compare the respective size of these contributions. We employ the AMY formalism for radiative energy loss and include additionally energy loss by elastic collisions. Our treatment of both processes is complete at leading order in the coupling, and accounts for the probabilistic nature of jet energy loss. We find that a solution of the Fokker-Planck equation for the probability density distributions of partons is necessary for a complete calculation of the nuclear modification factor $R_{AA}$ for pion production in heavy ion collisions. It is found that the magnitude of $R_{AA}$ is sensitive to the inclusion of both collisional and radiative energy loss, while the average energy is less affected by the addition of collisional contributions. We present a calculation of $R_{AA}$ for $\pi^0$ at RHIC, combining our energy loss formalism with a relativistic (3+1)-dimensional hydrodynamic description of the thermalized medium.Comment: 4 pages, 4 figures, contributed to Quark Matter 2008, Jaipur, Indi

Groundstate with Zero Eigenvalue for Generalized Sombrero-shaped Potential in NN-dimensional Space

Based on an iterative method for solving the goundstate of Schroedinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.Comment: 8 pages, 3 figure