A Data-Driven Approach for Discovering the Most Probable Transition Pathway for a Stochastic Carbon Cycle System

Many natural systems exhibit tipping points where changing environmental conditions spark a sudden shift to a new and sometimes quite different state. Global climate change is often associated with the stability of marine carbon stocks. We consider a stochastic carbonate system of the upper ocean to capture such transition phenomena. Based on the Onsager-Machlup action functional theory, we calculate the most probable transition pathway between the metastable and oscillatory states via a neural shooting method, and further explore the effects of external random carbon input rates on the most probable transition pathway, which provides a basis to recognize naturally occurring tipping points. Particularly, we investigate the effect of the transition time on the transition pathway and further compute the optimal transition time using physics informed neural network, towards the maximum carbonate concentration state in the oscillatory regimes. This work offers some insights on the effects of random carbon input on climate transition in a simple model. Key words: Onsager-Machlup action functional, the most probable transition pathway, neural shooting method, stochastic carbon cycle system

Most Probable Transitions from Metastable to Oscillatory Regimes in a Carbon Cycle System

Global climate changes are related to the ocean's store of carbon. We study a carbonate system of the upper ocean, which has metastable and oscillatory regimes, under small random fluctuations. We calculate the most probable transition path via a geometric minimum action method in the context of the large deviations theory. By examining the most probable transition paths from metastable to oscillatory regimes for various external carbon input rates, we find two different transition patterns, which gives us an early warning sign for the dramatic change in the carbonate state of the ocean

Longitudinal trends in prostate cancer incidence, mortality, and survival of patients from two Shanghai city districts: a retrospective population-based cohort study, 2000-2009.

BackgroundProstate cancer is the fifth most common cancer affecting men of all ages in China, but robust surveillance data on its occurrence and outcome is lacking. The specific objective of this retrospective study was to analyze the longitudinal trends of prostate cancer incidence, mortality, and survival in Shanghai from 2000 to 2009.MethodsA retrospective population-based cohort study was performed using data from a central district (Putuo) and a suburban district (Jiading) of Shanghai. Records of all prostate cancer cases reported to the Shanghai Cancer Registry from 2000 to 2009 for the two districts were reviewed. Prostate cancer outcomes were ascertained by matching cases with individual mortality data (up to 2010) from the National Death Register. The Cox proportional hazards model was used to analyze factors associated with prostate cancer survival.ResultsA total of 1022 prostate cancer cases were diagnosed from 2000 to 2009. The average age of patients was 75 years. A rapid increase in incidence occurred during the study period. Compared with the year 2000, 2009 incidence was 3.28 times higher in Putuo and 5.33 times higher in Jiading. Prostate cancer mortality declined from 4.45 per 105 individuals per year in 2000 to 1.94 per 105 in 2009 in Putuo and from 5.45 per 105 to 3.5 per 105 in Jiading during the same period. One-year and 5-year prostate cancer survival rates were 95% and 56% in Putuo, and 88% and 51% in Jiading, respectively. Staging of disease, Karnofsky Performance Scale Index, and selection of chemotherapy were three independent factors influencing the survival of prostate cancer patients.ConclusionsThe prostate cancer incidence increased rapidly from 2000 to 2009, and prostate cancer survival rates decreased in urban and suburban Chinese populations. Early detection and prompt prostate cancer treatment is important for improving health and for increasing survival rates of the Shanghai male population

The Most Likely Transition Path for a Class of Distribution-Dependent Stochastic Systems

Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, we find that the rate function (or action functional) does not involve with the solution of the skeleton equation, which describes unperturbed deterministic flow of the vector field shifted by the interaction at zero distance. As a result, we are led to study the most likely transition path for a stochastic differential equation without distribution-dependency. This enables the computation of the most likely transition path for these distribution-dependent stochastic dynamical systems by the adaptive minimum action method and we illustrate our approach in two examples.Comment: 10 pages, 2 figure

Features of near-inertial motions observed on the northern South China Sea shelf during the passage of two typhoons

Features of near-inertial motions on the shelf (60 m deep) of the northern South China Sea were observed under the passage of two typhoons during the summer of 2009. There are two peaks in spectra at both sub-inertial and super-inertial frequencies. The super-inertial energy maximizes near the surface, while the sub-inertial energy maximizes at a deeper layer of 15 m. The sub-inertial shift of frequency is induced by the negative background vorticity. The super-inertial shift is probably attributed to the near-inertial wave propagating from higher latitudes. The near-inertial currents exhibit a two-layer pattern being separated at mid-depth (25–30 m), with the phase in the upper layer being nearly opposite to that in the lower layer. The vertical propagation of phase implies that the near-inertial energy is not dominantly downward. The upward flux of the near-inertial energy is more evident at the surface layer (<17 m). There exist two boundaries at 17 and 40 m, where the near-inertial energy is reflected upward and downward. The near-inertial motion is intermittent and can reach a peak of as much as 30 cm/s. The passage of Typhoon Nangka generates an intensive near-inertial event, but Typhoon Linfa does not. This difference is attributed to the relative mooring locations, which is on the right hand side of Nangka’s path (leading to a wind pattern rotating clockwise with time) and is on the left hand side of Linfa’s path (leading to a wind pattern rotating anti-clockwise with time)

Coastal Upwelling Off the China Coasts

Upwelling is an important oceanographic phenomenon that brings cooler and nutrient-rich water upward to the surface, facilitating the growth of phytoplankton and other primary producers, which results in high levels of primary productivity and hence fishery production. This chapter presents a review of recent studies on six major upwelling regions along the China coasts, with a focus on the eastern and southeastern coasts of mainland China, based on in situ measurements, satellite observations and numerical simulations. These upwelling regions result primarily from the summer monsoon winds, though other mechanisms, such as river discharge, baroclinicity, topography, tides, and the presence of mean current, may also be in play. In this review, their impacts on local biogeochemical processes are briefly summarized. Also discussed are their possible responses to the globally changing climate

Data-driven method to learn the most probable transition pathway and stochastic differential equations

Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. In this paper, the physics informed neural networks (PINNs) are presented to compute the most probable transition pathway. It is shown that the expected loss is bounded by the empirical loss. And the convergence result for the empirical loss is obtained. Then, a sampling method of rare events is presented to simulate the transition path by the Markovian bridge process. And we investigate the inverse problem to extract the stochastic differential equation from the most probable transition pathway data and the Markovian bridge process data, respectively. Finally, several numerical experiments are presented to verify the effectiveness of our methods