McKean-Vlasov Stochastic Partial Differential Equations: Existence, Uniqueness and Propagation of Chaos

In this paper, we provide a general framework for investigating McKean-Vlasov stochastic partial differential equations. We first show the existence of weak solutions by combining the localizing approximation, Faedo-Galerkin technique, compactness method and the Jakubowski version of the Skorokhod representation theorem. Then under certain locally monotone condition we further investigate the existence and uniqueness of (probabilistically) strong solutions. The applications of the main results include a large class of McKean-Vlasov stochastic partial differential equations such as stochastic 2D/3D Navier-Stokes equations, stochastic Cahn-Hilliard equations and stochastic Kuramoto-Sivashinsky equations. Finally, we show a propagation of chaos result in Wasserstein distance for weakly interacting stochastic 2D Navier-Stokes systems with the interaction term being e.g. {\it{Stokes drag force}} that is proportional to the relative velocity of the particles.Comment: 58 page

Terazosin Analogs Targeting Pgk1 as Neuroprotective Agents: Design, Synthesis, and Evaluation

Nitrogen-containing heterocyclic compounds have shown promising therapeutic effects in a variety of inflammatory and neurodegenerative diseases. Recently, terazosin (TZ), a heterocyclic compound with a quinazoline core, was found to combine with phosphoglycerol kinase 1 (Pgk1) and protect neurons by enhancing Pgk1 activity and promoting glycolysis, thereby slowing, or preventing the neurodegeneration of PD. These findings indicated that terazosin analogs have bright prospects for the development of PD therapeutics. In this study, a series of terazosin analogs were designed and synthesized for neuroprotective effects by targeting Pgk1. Among them, compound 12b was obtained with the best Pgk1 agonistic activity and neuroprotective activity. Further study indicates that it can increase intracellular ATP content and reduce ROS levels by stimulating the activity of Pgk1, thereby playing a role in protecting nerve cells. In conclusion, this study provides a new strategy and reference for the development of neuroprotective drugs

New early oligocene zircon U-Pb dates for the ‘Miocene’ Wenshan Basin, Yunnan, China: Biodiversity and paleoenvironment

The sedimentary basins of Yunnan, Southwest China, record detailed histories of Cenozoic paleoenvironmental change. They track regional tectonic and palaeobiological evolution, both of which are critically important for the development of modern floral diversity in southwestern China and throughout Asia more generally. However, to be useful, the sedimentary archives within the basins have to be placed within a well-constrained timeframe independent of biostratigraphy. Using high resolution U-Pb dating, we redefine the age of fossil-bearing strata in the Wenshan Basin. Regarded as Miocene for the last half century, these basin sediments encompass 30±2 and 32±1 Ma early Oligocene tuffaceous horizons, thus indicating a significantly greater antiquity than previously recognized. Together with other regional age revisions our result points to widespread Yunnan basin and orographic development as largely having taken place by the end Paleogene. This age revision provides an important new perspective on the preserved biotas and their evolution in Yunnan, and especially our understanding of the origin of Asian biodiversity which, regionally, had a near-modern composition by the early Oligocene. Crucially, this revised age evidences late Eocene-early Oligocene regional tectonism, pointing to the rise of eastern Tibet and the Hengduan Mountains before the growth of the Himalaya, and that Asia's high plant diversity has a Paleogene origin

A critical appraisal of the sensitivity of detrital zircon U–Pb provenance data to constrain drainage network evolution in southeast Tibet

Provenance tools, particularly detrital zircon U–Pb analysis, have been widely employed to test drainage network evolution in southeast Tibet and its linkage with the growth of the Tibetan Plateau. Numerous provenance studies have been conducted on the sediments in the paleo-Yangtze and paleo-Red River drainage basins. Nevertheless, it is still hotly debated as to whether a “Mississippi” (dendritic) pattern Greater paleo-Red River, originating from southeast Tibet and draining to the South China Sea, existed in the early Cenozoic, and was subsequently captured by the paleo-lower Yangtze due to uplift of southeastern Tibet. In this study, in addition to presenting new data from the Gonjo and Jianchuan basins along which the Greater paleo-Red River is proposed to have flowed, we compiled all the published detrital zircon U–Pb data from the paleo-upper Yangtze and paleo-Red River drainage basins from Triassic and younger rocks. Our large database of detrital zircon U–Pb analyses shows that the different terranes in the paleo-upper Yangtze and paleo-Red River drainage basins have similar zircon U–Pb signatures since the Late Triassic closure of the Paleo-Tethys Ocean. Therefore, most of the sediments in the Cenozoic sedimentary basins in southeast Tibet could have been either deposited by long-distance transport in large rivers from southeast Tibet or recycled from local bedrock. Given the potential importance of sedimentary recycling that we have demonstrated, this poses challenges to the use of detrital zircon U–Pb analyses to determine paleodrainage in this region. We therefore further explored the previously relatively limited use of Sr–Nd isotopes on mudstones and detrital mica 40Ar/39Ar ages, with new analyses from the Gonjo and Jianchuan Basins, to determine if these techniques were better suited to reconstruct paleodrainage evolution. Whilst these techniques do show some promise, more analyses and strategic sampling are required to obtain a full understanding of the extent of their potential utility. Overall, our integrated provenance study indicates that the available data are not sufficiently conclusive to support or refute the Greater paleo-Red River capture model

Oligocene deformation of the Chuandian terrane in the SE margin of the Tibetan Plateau related to the extrusion of Indochina

Mechanisms driving the tectonic evolution of the southeast (SE) margin of Tibet include the Paleogene extrusion of the coherent Indochina lithospheric block, and the continuous deformation caused by lower crustal flow since the middle Miocene. The timing and style of regional deformations are key to determining the role of each mechanism. Fault-bounded and -controlled Cenozoic basins within the SE margin of Tibet record regional deformation, surface uplift and variations in paleoclimate, but often are poorly dated. New magnetostratigraphy and 40Ar/39Ar dating of volcanic ashes constrain precisely the timing of sedimentation within the Lühe Basin to between ~35 and 26.5 Ma. The basin is located in the Chuandian terrane along the Chuxiong fault, which lies ~70 km north of, and parallel to, the Ailao Shan-Red River fault. The asymmetric syncline of the Lühe Basin suggests syn-contractional sedimentation and the basal age of the basin represents the initiation of the Chuxiong fault and crustal shortening at ~35 Ma. This is coincident with the onset of the Ailao Shan-Red River fault, and supports a kinematic link between them. Our study suggests that, like the Ailao Shan-Red River fault, the Chuxiong fault is a Paleogene transpressional structure that developed during the extrusion and clockwise rotation of Indochina around the Eastern Himalayan Syntaxis, which caused the late Paleogene deformation and surface uplift of the Chuandian terrane and Indochina. Our revised chronostratigraphy of the Lühe Basin provides further evidence that many of the “Neogene” sedimentary basins in the SE margin of Tibet may be much older than previously thought