Linear-quadratic Mean Field Control with Non-convex Data

In this manuscript, we study a class of linear-quadratic (LQ) mean field control problems with a common noise and their corresponding $N$-particle systems. The mean field control problems considered are not standard LQ mean field control problems in the sense that their dependence on the mean field terms can be non-linear and non-convex. Therefore, all the existing methods to deal with LQ mean field control problems fail. The key idea to solve our LQ mean field control problem is to utilize the common noise. We first prove the global well-posedness of the corresponding Hamilton-Jacobi equations via the non-degeneracy of the common noise. In contrast to the LQ mean field games master equations, the Hamilton-Jacobi equations for the LQ mean field control problems can not be reduced to finite-dimensional PDEs. We then globally solve the Hamilton-Jacobi equations for $N$-particle systems. As byproducts, we derive the optimal quantitative convergence results from the $N$-particle systems to the mean field control problem and the propagation of chaos property for the related optimal trajectories. This paper extends the results in [{\sc M. Li, C. Mou, Z. Wu and C. Zhou}, \emph{Trans. Amer. Math. Soc.}, 376(06) (2023), pp.~4105--4143] to the LQ mean field control problems.Comment: 35 page

EUCLIA - Exploring the UV/optical continuum lag in active galactic nuclei. I. a model without light echoing

The tight inter-band correlation and the lag-wavelength relation among UV/optical continua of active galactic nuclei have been firmly established. They are usually understood within the widespread reprocessing scenario, however, the implied inter-band lags are generally too small. Furthermore, it is challenged by new evidences, such as the X-ray reprocessing yields too much high frequency UV/optical variations as well as it fails to reproduce the observed timescale-dependent color variations among {\it Swift} lightcurves of NGC 5548. In a different manner, we demonstrate that an upgraded inhomogeneous accretion disk model, whose local {\it independent} temperature fluctuations are subject to a speculated {\it common} large-scale temperature fluctuation, can intrinsically generate the tight inter-band correlation and lag across UV/optical, and be in nice agreement with several observational properties of NGC 5548, including the timescale-dependent color variation. The emergent lag is a result of the {\it differential regression capability} of local temperature fluctuations when responding to the large-scale fluctuation. An average speed of propagations as large as $\gtrsim 15\%$ of the speed of light may be required by this common fluctuation. Several potential physical mechanisms for such propagations are discussed. Our interesting phenomenological scenario may shed new light on comprehending the UV/optical continuum variations of active galactic nuclei.Comment: 18 pages, 8 figures. ApJ accepted. Further comments are very welcome

The universal "heartbeat" oscillations in black hole systems accross the mass-scale

The hyperluminous X-ray source (HLX-1, the peak X-ray luminosity $\sim 10^{42}\rm erg\ s^{-1}$) near the spiral galaxy ESO 243-49 is possibly the best candidate for intermediate mass black hole (IMBH), which underwent recurrent outbursts with a period of $\sim 400$ days. The physical reason for this quasi-periodic variability is still unclear. We explore the possibility of radiation-pressure instability in accretion disk by modeling the light curve of HLX-1, and find that it can roughly reproduce the duration, period and amplitude of the recurrent outbursts HLX-1 with an IMBH of ~10^5Msun. Our result provides a possible mechanism to explain the recurrent outbursts in HLX-1. We further find a universal correlation between the outburst duration and the bolometric luminosity for the BH sources with a very broad mass range (e.g., X-ray binaries, XRBs, HLX-1 and active galactic nuclei, AGNs), which is roughly consistent with the prediction of radiation-pressure instability of the accretion disk. These results imply that "heartbeat" oscillations triggered by radiation-pressure instability may appears in different-scale BH systems.Comment: ApJ in press; 15 pages, 5 Figure

Full-Scale Electromagnetic Transient Modeling and Oscillation Suppression of a Wind Farm with SVG

With the gradual depletion of the earth’s resources and people’s attention to environmental issues, the access of renewable energy has been paid more and more attention by countries around the world. Wind is one of the pollution-free energy sources, and wind power generation is forming a boom in the world, because wind power generation does not need to use fuel, nor does it produce radiation or air pollution. The power of wind power generation is characterized by volatility and intermittence. When there is disturbance in the system, the wind farm is likely to oscillate and challenge the stability of the power grid. Therefore, the wind turbine generator must be connected to SVG system to realize dynamic reactive power compensation function, so as to ensure the stability of its operation in case of fault. In addition, the cause of wind turbine oscillation needs to be analyzed in detail to ensure its stability

Identification and interaction analysis of key genes and microRNAs in hepatocellular carcinoma by bioinformatics analysis

Complete list of differentially expressed genes (DEGs) in GSE22058. (DOCX 183 kb

Relightable and Animatable Neural Avatar from Sparse-View Video

This paper tackles the challenge of creating relightable and animatable neural avatars from sparse-view (or even monocular) videos of dynamic humans under unknown illumination. Compared to studio environments, this setting is more practical and accessible but poses an extremely challenging ill-posed problem. Previous neural human reconstruction methods are able to reconstruct animatable avatars from sparse views using deformed Signed Distance Fields (SDF) but cannot recover material parameters for relighting. While differentiable inverse rendering-based methods have succeeded in material recovery of static objects, it is not straightforward to extend them to dynamic humans as it is computationally intensive to compute pixel-surface intersection and light visibility on deformed SDFs for inverse rendering. To solve this challenge, we propose a Hierarchical Distance Query (HDQ) algorithm to approximate the world space distances under arbitrary human poses. Specifically, we estimate coarse distances based on a parametric human model and compute fine distances by exploiting the local deformation invariance of SDF. Based on the HDQ algorithm, we leverage sphere tracing to efficiently estimate the surface intersection and light visibility. This allows us to develop the first system to recover animatable and relightable neural avatars from sparse view (or monocular) inputs. Experiments demonstrate that our approach is able to produce superior results compared to state-of-the-art methods. Our code will be released for reproducibility.Comment: Project page: https://zju3dv.github.io/relightable_avata

Decreasing carbon allocation belowground in alpine meadow soils by shrubification

Distribution of shrubs expanding in grasslands – shrubification – is ongoing worldwide in grasslands and is common on the Qinghai–Tibetan Plateau (QTP). But the consequences of shrubification for plant carbon (C) input and fate in soil are unclear. We used 13C pulse labelling in a meadow on the QTP to compare photosynthetic capacity and photosynthate distribution in shoots, roots, soil and microbial functional groups between herbaceous plants (herbs) and shrubby Potentilla fruticosa. During 3 h of labeling in 13CO2 atmosphere, the 13C amount assimilated by shrubs (0.81 g C/m−2) was only 38 % of that by herbs. Over 8 days after labeling, 13C amount respired jointly by roots and soil microorganisms under shrubs (0.049 g m−2) was less than half of that under herbs. The mean residence time of 13C for respiration jointly by roots and rhizosphere microorganisms was longer under shrubs (0.61 day) than under herbs (0.44 day). Within 22 days after labelling, 13C amounts in roots, soil, and microorganisms were consistently smaller under shrubs than those under herbs. Consequently, shrub P. fruticosa had not only smaller photosynthetic potential, but also allocated less photosynthate belowground and slowed down C cycling in soil compared with herbs. The distribution of total 13C in microbial functional groups indicated by PLFA analysis was similar between herbs and shrubs. Averaged over vegetation patch types, gram negative bacteria and AMF accounted for 22 % and 4 % of the total microbial PLFAs in the 0–20 cm, respectively, but these two functional groups took up 51 % and 23 % of the total 13C absorbed by microorganisms, respectively. This indicates that gram negative bacteria and AMF are major consumers of rhizodeposits. Concluding, shrubification leads to smaller C allocation belowground and slows down C cycling in the soil