DATA-DRIVEN COMPUTATIONAL METHODS FOR QUASI-STATIONARY DISTRIBUTION AND SENSITIVITY ANALYSIS

The goal of the dissertation is to develop the computational methods for quasi-stationary- distributions(QSDs) and the sensitivity analysis of a QSD against the modification of the boundary conditions and against the diffusion approximation.Many models in various applications are described by Markov chains with absorbing states. For example, any models with mass-action kinetics, such as ecological models, epidemic models, and chemical reaction models, are subject to the population-level randomness called the demographic stochasticity, which may lead to extinction in finite time. There are also many dynamical systems that have interesting short term dynamics but trivial long term dynamics, such as dynamical systems with transient chaos [28]. A common way of capturing asymptotical properties of these transient dynamics is the quasi-stationary distribution (QSD), which is the conditional limiting distribution conditioning on not hitting the absorbing set yet. However, most QSDs do not have a closed form. So numerical solutions are necessary in various applications. This dissertation studies computational methods for quasi-stationary distributions (QSDs). We first proposed a data-driven solver that solves Fokker-Planck equations for QSDs. Moti- vated by the case of Fokker-Planck equations for invariant probability measures, we set up an optimization problem that minimizes the distance from a low-accuracy reference solution, under the constraint of satisfying the linear relation given by the discretized Fokker-Planck operator. Then we use coupling method to study the sensitivity of a QSD against either the change of boundary condition or the diffusion coefficient. The 1-Wasserstein distance between a QSD and the corresponding invariant probability measure can be quantitativelyestimated. Some numerical results about both computation of QSDs and their sensitivity analysis are provided.This dissertation also studies the sensitivity analysis of mass-action systems against their diffusion approximations, particularly the dependence on population sizes. As a continuous time Markov chain, a mass-action system can be described by an equation driven by finite many Poisson processes, which has a diffusion approximation that can be pathwisely matched. The magnitude of noise in mass-action systems is proportional to the square root of the molecular count/population, which makes a large class of mass-action systems have quasi-stationary distributions (QSDs) instead of invariant probability measures. In this thesis we modify the coupling based technique developed in [15] to estimate an upper bound of the 1-Wasserstein distance between two QSDs. Some numerical results for sensitivity with different population sizes are provided

Sensitivity analysis of quasi-stationary-distributions (QSDs)

This paper studies the sensitivity analysis of mass-action systems against their diffusion approximations, particularly the dependence on population sizes. As a continuous time Markov chain, a mass-action system can be described by a equation driven by finite many Poisson processes, which has a diffusion approximation that can be pathwisely matched. The magnitude of noise in mass-action systems is proportional to the square root of the molecule count/population, which makes a large class of mass-action systems have quasi-stationary distributions (QSDs) instead of invariant probability measures. In this paper we modify the coupling based technique developed in [8] to estimate an upper bound of the 1-Wasserstein distance between two QSDs. Some numerical results for sensitivity with different population sizes are provided

Nicotine enhances murine airway contractile responses to kinin receptor agonists via activation of JNK- and PDE4-related intracellular pathways

<p>Abstract</p> <p>Background</p> <p>Nicotine plays an important role in cigarette-smoke-associated airway disease. The present study was designed to examine if nicotine could induce airway hyperresponsiveness through kinin receptors, and if so, explore the underlying mechanisms involved.</p> <p>Methods</p> <p>Murine tracheal segments were cultured for 1, 2 or 4 days in serum-free DMEM medium in presence of nicotine (1 and 10 μM) or vehicle (DMSO). Contractile responses induced by kinin B₁receptor agonist, des-Arg⁹-bradykinin, and B₂receptor agonist, bradykinin, were monitored with myographs. The B₁and B₂receptor mRNA expressions were semi-quantified using real-time PCR and their corresponding protein expressions assessed with confocal-microscopy-based immunohistochemistry. Various pharmacological inhibitors were used for studying intracellular signaling pathways.</p> <p>Results</p> <p>Four days of organ culture with nicotine concentration-dependently increased kinin B₁and B₂receptor-mediated airway contractions, without altering the kinin receptor-mediated relaxations. No such increase was seen at day 1 or day 2. The airway contractile responses to 5-HT, acetylcholine and endothelin receptor agonists remained unaffected by nicotine. Two different neuronal nicotinic receptor antagonists MG624 and hexamethonium blocked the nicotine-induced effects. The enhanced contractile responses were accompanied by increased mRNA and protein expression for both kinin receptors, suggesting the involvement of transcriptional mechanisms. Confocal-microscopy-based immunohistochemistry showed that 4 days of nicotine treatment induced activation (phosphorylation) of c-Jun N-terminal kinase (JNK), but not extracellular signal-regulated kinase 1 and 2 (ERK1/2) and p38. Inhibition of JNK with its specific inhibitor SP600125 abolished the nicotine-induced effects on kinin receptor-mediated contractions and reverted the enhanced receptor mRNA expression. Administration of phosphodiesterase inhibitors (YM976 and theophylline), glucocorticoid (dexamethasone) or adenylcyclase activator (forskolin) suppressed the nicotine-enhanced airway contractile response to des-Arg⁹-bradykinin and bradykinin.</p> <p>Conclusions</p> <p>Nicotine induces airway hyperresponsiveness via transcriptional up-regulation of airway kinin B₁and B₂receptors, an effect mediated via neuronal nicotinic receptors. The underlying molecular mechanisms involve activation of JNK- and PDE4-mediated intracellular inflammatory signal pathways. Our results might be relevant to active and passive smokers suffering from airway hyperresponsiveness, and suggest new therapeutic targets for the treatment of smoke-associated airway disease.</p

Tryptophan-kynurenine pathway as a novel link between gut microbiota and schizophrenia: A review

Gut microbiota and its metabolite tryptophan play an important role in regulating neurotransmission, immune homeostasis and oxidative stress which are critical for brain development. The kynurenine pathway is the main route of tryptophan catabolism. Kynurenine metabolites regulate many biological processes including host-microbiome communication, immunity and oxidative stress, as well as neuronal excitability. The accumulation of metabolites produced by kynurenine pathway in brain results in the activation of the immune system (increase in the levels of inflammatory factors) and oxidative stress (production of reactive oxygen species, ROS), which are associated with mental disorders, for example schizophrenia. Thus, it was hypothesized that perturbations in kynurenine pathway could cause activation of immunity, and that oxidative stress may be involved in the etiology of schizophrenia. The present work is a review of the latest studies on the possible role of kynurenine pathway in schizophrenia, and mechanism(s) involved

Extreme subradiance from two-band Bloch oscillations in atomic arrays

Atomic arrays provide an important quantum optical platform with photon-mediated dipoledipole interactions, which can be engineered to realize key applications in quantum information processing. A major obstacle for such application is the fast decay of the excited states. By controlling two-band Bloch oscillations in an atomic array under external magnetic field, here we show that exotic subradiance can be realized and maintained at a time scale upto 12 orders of magnitude larger than the spontaneous decay time in atomic arrays with the finite size. The key finding is to show a way for preventing the wavepacket of excited states scattering into the dissipative zone inside the free space light cone, which therefore leads to the excitation staying at a subradiant state for extremely long decay time. We show that such operation can be achieved by introducing a spatially linear potential from external magnetic field in atomic arrays and then manipulating interconnected two-band Bloch oscillations along opposite directions. Our results also point out the possibility of controllable switching between superradiant and subradiant states, which leads to potential applications in quantum storage.Comment: 6 pages, 3 figure

Study of the Effects of Total Flavonoids of Astragalus on Atherosclerosis Formation and Potential Mechanisms

Astragalus mongholicus Bunge has long been used to treat cardiovascular disease in Chinese traditional medicine. However, its mechanisms are not fully understood. In this study, we explored potential mechanisms and protective effects of total flavonoids of Astragalus (TFA) on cardiovascular disease using in vitro experiments and diet-induced atherosclerotic rabbits. We identified six components and their proportion in TFA. The animal experiments showed that TFA significantly reduced plasma levels of total cholesterol and LDL cholesterol (P < 0.05 to 0.01), increased HDL cholesterol levels (P < 0.01), and reduced the aortic fatty streak area by 43.6 to 63.6% (P < 0.01). We also found that TFA scavenged superoxide and hydroxyl radicals and this effect increased with higher TFA concentration. In in vivo experiments, TFA effectively inhibited the free radical spectrum in the ischemia-reperfusion module. In conclusion, TFA was the active component of Astragalus mongholicus Bunge, which benefits cardiovascular disease attributing to the potent antioxidant activity to improve the atherosclerosis profile