Stochastic Synchronization of Genetic Oscillator Networks

The study of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic networks are intrinsically noisy due to natural random intra- and inter-cellular fluctuations. Therefore, it is important to study the effects of noise perturbation on the synchronous dynamics of genetic oscillators. From the synthetic biology viewpoint, it is also important to implement biological systems that minimizing the negative influence of the perturbations. In this paper, based on systems biology approach, we provide a general theoretical result on the synchronization of genetic oscillators with stochastic perturbations. By exploiting the specific properties of many genetic oscillator models, we provide an easy-verified sufficient condition for the stochastic synchronization of coupled genetic oscillators, based on the Lur'e system approach in control theory. A design principle for minimizing the influence of noise is also presented. To demonstrate the effectiveness of our theoretical results, a population of coupled repressillators is adopted as a numerical example. In summary, we present an efficient theoretical method for analyzing the synchronization of genetic oscillator networks, which is helpful for understanding and testing the synchronization phenomena in biological organisms. Besides, the results are actually applicable to general oscillator networks.Comment: 14 pages, 4 figure

Phase transition problems of conservation laws

In this thesis we study phase transition problems of conservation laws. Phase transition problems arise from various applications such as gas dynamics, mechanics and material science. Conservation laws involving phase change is an attractive field in applied mathematics. Solutions to phase transition problems are complicated for the presence of boundaries between different phases. In addition to entropy condition, criteria such as kinetic relation [1, 3] and nucleation criterion are introduced to determine the configurations of solutions.;In Chapter 1, we construct two numerical procedures to solve the Riemann problems for a system of conservation laws with phase change. We first find the solution with a stationary phase boundary by Newton iteration [ 14]. The configuration of the solution, especially the direction of the propagating phase boundary, is then determined based on the criterion suggested by Hattori [11] given that the speed of a moving phase boundary is much smaller than the speed of a shock or a rarefaction wave. One way to solve the Riemann problem with a moving phase boundary is to list all the relations and find the solution of the resulting nonlinear system. Another is to construct an iterative process to find the intersection of two projection curves.;In Chapter 2, we discuss the well posedness of the initial value problem to Euler equations related to phase transition. The solution contains two phase boundaries moving in opposite directions. Entropy condition and kinetic relationship are used as the main admissibility criteria to select the physically relevant solution. We show the existence of the entropy solution under a suitable Finiteness Condition and a Stability Condition guarantees the stability of the problem in L1∩ BV and the existence of a Lipschitz semigroup of solutions. We also discuss the well posedness of the problem given that the wave speeds do not differ significantly between different phases

Transient Resetting: A Novel Mechanism for Synchrony and Its Biological Examples

The study of synchronization in biological systems is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. In this paper, by using simple dynamical systems theory, we present a novel mechanism, named transient resetting, for the synchronization of uncoupled biological oscillators with stimuli. This mechanism not only can unify and extend many existing results on (deterministic and stochastic) stimulus-induced synchrony, but also may actually play an important role in biological rhythms. We argue that transient resetting is a possible mechanism for the synchronization in many biological organisms, which might also be further used in medical therapy of rhythmic disorders. Examples on the synchronization of neural and circadian oscillators are presented to verify our hypothesis.Comment: 17 pages, 7 figure

Hopf Bifurcation and Chaos in Tabu Learning Neuron Models

In this paper, we consider the nonlinear dynamical behaviors of some tabu leaning neuron models. We first consider a tabu learning single neuron model. By choosing the memory decay rate as a bifurcation parameter, we prove that Hopf bifurcation occurs in the neuron. The stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory. We give a numerical example to verify the theoretical analysis. Then, we demonstrate the chaotic behavior in such a neuron with sinusoidal external input, via computer simulations. Finally, we study the chaotic behaviors in tabu learning two-neuron models, with linear and quadratic proximity functions respectively.Comment: 14 pages, 13 figures, Accepted by International Journal of Bifurcation and Chao

Mean Transverse Energy of Ultrananocrystalline Diamond Photocathode

Nitrogen incorporated ultrananocrystalline diamond ((N)UNCD) could be an enabling material platform for photocathode applications due to its high emissivity. While the quantum efficiency (QE) of UNCD was reported by many groups, no experimental measurements of the intrinsic emittance/mean transverse energy (MTE) have been reported. Here, MTE measurement results for an (N)UNCD photocathode in the photon energy range of 4.41 to 5.26 eV are described. The MTE demonstrates no noticeable dependence on the photon energy, with an average value of 266 meV. This spectral behavior is shown to not to be dependent upon physical or chemical surface roughness and inconsistent with low electron effective mass emission from graphitic grain boundaries, but may be associated with emission from spatially-confined states in the graphite regions between the diamond grains. The combined effect of fast-growing QE and constant MTE with respect to the excess laser energy may pave the way to bright UNCD photocathodes.Comment: 4 pages, 4 figure

Zr-Co-Al bulk metallic glass composites containing B2 ZrCo via rapid quenching and annealing

As a promising remedy for overcoming the limited ductility and work softening of bulk metallic glasses (BMGs), BMG composites incorporating a B2 crystalline phase have attracted considerable attention. Here, we explore the formation of Zr-Co-Al BMG composites by quenching alloys Zr$_{55}$Co$_{31}$Al$_{14}$, Zr$_{54.5}$Co$_{33.5}$Al$_{12}$, Zr$_{53.5}$Co$_{36.5}$Al$_{10}$, Zr$_{52.5}$Co$_{37.5}$Al$_{10}$, and Zr$_{43}$Co$_{43}$Al$_{14}$. We found the first alloy fully amorphous whereas the fifth was fully crystallized upon quenching. The other three were quenched to generate composite structures, with a higher fraction of B2 ZrCo phase with increasing Co/Zr ratio and decreasing Al content. For comparison, the formation of B2 ZrCo in annealed Zr$_{55}$Co$_{31}$Al$_{14}$ was also studied. For both approaches the influence of crystalline phases on hardness was examined