arXiv subjects
Publications and source records attributed to Xi Zhang.
In this paper, we study Higgs bundles on non-compact Hermitian manifolds. Under some assumptions for the underlying Hermitian manifolds which are not necessarily Kähler, we solve the Hermitian-Einstein equation on analytically stable Higgs bundles.
Non-orthogonal multiple access (NOMA) is a promising radio access technology for the 5G wireless systems. The core of NOMA is to support multiple users in the same resource block via power or code domain multiplexing, which provides great enhancement in spectrum efficiency and connectivity. Meanwhile, with the recent advance in self-interference (SI) cancelation techniques, full duplex (FD) wireless communication has become a feasible technology enabling radios to receive and transmit simultaneously. This article aims to investigate the combination of these two emerging technologies. At first, several typical scenarios and protocols are presented to illustrate the application of FD technique in NOMA systems. Then, a novel NOMA system with FD base stations (BSs) based on centralized radio access networks (C-RAN) is proposed. Furthermore, power allocation policies are discussed for the proposed scheme, and simulation results are provided to demonstrate its superiority. Finally, challenges and research opportunities of FD NOMA systems are also identified to stimulate the future research.
In this paper, we study the stability of the conical Kähler-Ricci flows on Fano manifolds. That is, if there exists a conical Kähler-Einstein metric with cone angle $2πβ$ along the divisor, then for any $β'$ sufficiently close to $β$, the corresponding conical Kähler-Ricci flow converges to a conical Kähler-Einstein metric with cone angle $2πβ'$ along the divisor. Here, we only use the condition that the Log Mabuchi energy is bounded from below. This is a weaker condition than the properness that we have adopted to study the convergence before. As corollaries, we give parabolic proofs of Donaldson's openness theorem and his existence conjecture for the conical Kähler-Einstein metrics with positive Ricci curvatures.
Each hypersurface of a nearly Kähler manifold is naturally equipped with two tensor fields of $(1,1)$-type, namely the shape operator $A$ and the induced almost contact structure $ϕ$. In this paper, we show that, in the homogeneous NK $\mathbb{S}^6$ a hypersurface satisfies the condition $Aϕ+ϕA=0$ if and only if it is totally geodesic; moreover, similar as for the non-flat complex space forms, the homogeneous nearly Kähler manifold $\mathbb{S}^3\times\mathbb{S}^3$ does not admit a hypersurface that satisfies the condition $Aϕ+ϕA=0$.
Thermal light-curve analysis is a powerful approach to probe the thermal structures of exoplanetary atmospheres, which are greatly influenced by the planetary obliquity and eccentricity. Here we investigate the thermal light curves of eccentric-tilted exoplanets across various radiative timescales, eccentricities, obliquities, and viewing geometries using results of shallow-water simulations presented in Ohno $\&$ Zhang (2019). We also achieve an analytical theory of the thermal light curve that can explain general trends in the light curves of tilted exoplanets. For tilted planets in circular orbits, the orbital phase of the flux peak is largely controlled by either the flux from the hot spot projected onto the orbital plane or the pole heated at the summer solstice, depending on the radiative timescale $τ_{\rm rad}$, planetary day $P_{\rm orb}$, and obliquity $θ$. We find that tilted planets potentially produce the flux peak after the secondary eclipse when obliquity is $θ$ > 90 deg for the hot regime $τ_{\rm rad} 18$ deg for the cool regime $τ_{\rm rad} > P_{\rm rot}$. For tilted planets in eccentric orbits, the shape of the light curve is considerably influenced by the heating at the periapse. The flux peak occurring after the secondary eclipse can be used to distinguish tilted planets from nontilted planets when the periapse takes place before the secondary eclipse. Our results could help to constrain exoplanet obliquities in future observations.
Relatively long-period nonsynchronized planets---such as warm Jupiters---potentially retain the primordial rotation, eccentricity, and obliquity that might encapsulate information on planetary climate and formation processes. To date, there has not been a systematic study on climate patterns on these planets that will significantly influence their observations. Here we investigate the atmospheric dynamics of nonsynchronized, fast-rotating exoplanets across various radiative timescales, eccentricities, and obliquities using a shallow water model. The dynamical pattern can be demarcated into five regimes in terms of radiative timescale $τ_{\rm rad}$ and obliquity $θ$. An atmosphere with $τ_{\rm rad}$ shorter than a planetary day usually exhibits a strong day--night temperature contrast and a day-to-night flow pattern. In the intermediate $τ_{\rm rad}$ regime between a planetary day and a year, the atmosphere is dominated by steady temperature and eastward jet patterns for $θ$ < 18 deg but shows a strong seasonal variation for $θ$ > 18 deg because the polar region undergoes an intense heating at around the summer solstice. If $τ_{\rm rad}$ is longer than a year, seasonal variation is very weak. In this regime, eastward jets are developed for $θ$ < 54 deg and westward jets are developed for $θ$ > 54 deg. These dynamical regimes are also applicable to the planets in eccentric orbits. The large effects of exoplanetary obliquities on circulation patterns might offer observational signatures, which will be investigated in Paper II of this study.
In this paper, we study numerically flat holomorphic vector bundles over a compact non-Kähler manifold $(X, ω)$ with the Hermitian metric $ω$ satisfying the Gauduchon and Astheno-Kähler conditions. We prove that numerically flatness is equivalent to numerically effectiveness with vanishing first Chern number, semistablity with vanishing first and second Chern numbers, approximate Hermitian flatness and the existence of a filtration whose quotients are Hermitian flat. This gives an affirmative answer to the question proposed by Demailly, Peternell and Schneider.
Rotational modulations are observed on brown dwarfs and directly imaged exoplanets, but the underlying mechanism is not well understood. Here, we analyze Jupiter's rotational light curves at 12 wavelengths from the ultraviolet (UV) to the mid-infrared (mid-IR). Peak-to-peak amplitudes of Jupiter's light curves range from sub percent to 4% at most wavelengths, but the amplitude exceeds 20% at 5 $\rm μm$, a wavelength sensing Jupiter's deep troposphere. Jupiter's rotational modulations are primarily caused by discrete patterns in the cloudless belts instead of the cloudy zones. The light-curve amplitude is dominated by the sizes and brightness contrasts of the Great Red Spot (GRS), expansions of the North Equatorial Belt (NEB), patchy clouds in the North Temperate Belt (NTB) and a train of hot spots in the NEB. In reflection, the contrast is controlled by upper tropospheric and stratospheric hazes, clouds, and chromophores in the clouds. In thermal emission, the small rotational variability is caused by the spatial distribution of temperature and opacities of gas and aerosols; the large variation is caused by the $\rm NH_{3}$ cloud holes and thin-thick clouds. The methane-band light curves exhibit opposite-shape behavior compared with the UV and visible wavelengths, caused by wavelength-dependent brightness change of the GRS. Light-curve evolution is induced by periodic events in the belts and longitudinal drifting of the GRS and patchy clouds in the NTB. This study suggests several interesting mechanisms related to distributions of temperature, gas, hazes, and clouds for understanding the observed rotational modulations on brown dwarfs and exoplanets.
Precise segmentation of bladder walls and tumor regions is an essential step towards non-invasive identification of tumor stage and grade, which is critical for treatment decision and prognosis of patients with bladder cancer (BC). However, the automatic delineation of bladder walls and tumor in magnetic resonance images (MRI) is a challenging task, due to important bladder shape variations, strong intensity inhomogeneity in urine and very high variability across population, particularly on tumors appearance. To tackle these issues, we propose to use a deep fully convolutional neural network. The proposed network includes dilated convolutions to increase the receptive field without incurring extra cost nor degrading its performance. Furthermore, we introduce progressive dilations in each convolutional block, thereby enabling extensive receptive fields without the need for large dilation rates. The proposed network is evaluated on 3.0T T2-weighted MRI scans from 60 pathologically confirmed patients with BC. Experiments shows the proposed model to achieve high accuracy, with a mean Dice similarity coefficient of 0.98, 0.84 and 0.69 for inner wall, outer wall and tumor region, respectively. These results represent a very good agreement with reference contours and an increase in performance compared to existing methods. In addition, inference times are less than a second for a whole 3D volume, which is between 2-3 orders of magnitude faster than related state-of-the-art methods for this application. We showed that a CNN can yield precise segmentation of bladder walls and tumors in bladder cancer patients on MRI. The whole segmentation process is fully-automatic and yields results in very good agreement with the reference standard, demonstrating the viability of deep learning models for the automatic multi-region segmentation of bladder cancer MRI images.
Combining deep neural networks with reinforcement learning has shown great potential in the next-generation intelligent control. However, there are challenges in terms of safety and cost in practical applications. In this paper, we propose the Intervention Aided Reinforcement Learning (IARL) framework, which utilizes human intervened robot-environment interaction to improve the policy. We used the Unmanned Aerial Vehicle (UAV) as the test platform. We built neural networks as our policy to map sensor readings to control signals on the UAV. Our experiment scenarios cover both simulation and reality. We show that our approach substantially reduces the human intervention and improves the performance in autonomous navigation, at the same time it ensures safety and keeps training cost acceptable.
Subitizing, or the sense of small natural numbers, is an innate cognitive function of humans and primates; it responds to visual stimuli prior to the development of any symbolic skills, language or arithmetic. Given successes of deep learning (DL) in tasks of visual intelligence and given the primitivity of number sense, a tantalizing question is whether DL can comprehend numbers and perform subitizing. But somewhat disappointingly, extensive experiments of the type of cognitive psychology demonstrate that the examples-driven black box DL cannot see through superficial variations in visual representations and distill the abstract notion of natural number, a task that children perform with high accuracy and confidence. The failure is apparently due to the learning method not the CNN computational machinery itself. A recurrent neural network capable of subitizing does exist, which we construct by encoding a mechanism of mathematical morphology into the CNN convolutional kernels. Also, we investigate, using subitizing as a test bed, the ways to aid the black box DL by cognitive priors derived from human insight. Our findings are mixed and interesting, pointing to both cognitive deficit of pure DL, and some measured successes of boosting DL by predetermined cognitive implements. This case study of DL in cognitive computing is meaningful for visual numerosity represents a minimum level of human intelligence.
Deep convolutional neural networks (DCNN) have enjoyed great successes in many signal processing applications because they can learn complex, non-linear causal relationships from input to output. In this light, DCNNs are well suited for the task of sequential prediction of multidimensional signals, such as images, and have the potential of improving the performance of traditional linear predictors. In this research we investigate how far DCNNs can push the envelop in terms of prediction precision. We propose, in a case study, a two-stage deep regression DCNN framework for nonlinear prediction of two-dimensional image signals. In the first-stage regression, the proposed deep prediction network (PredNet) takes the causal context as input and emits a prediction of the present pixel. Three PredNets are trained with the regression objectives of minimizing $\ell_1$, $\ell_2$ and $\ell_\infty$ norms of prediction residuals, respectively. The second-stage regression combines the outputs of the three PredNets to generate an even more precise and robust prediction. The proposed deep regression model is applied to lossless predictive image coding, and it outperforms the state-of-the-art linear predictors by appreciable margin.
In this paper, we consider the Dirichlet problem of a complex Monge-Ampère equation on a ball in $\mathbb C^n$. With $\mathcal C^{1,α}$ (resp. $\mathcal C^{0,α}$) data, we prove an interior $\mathcal C^{1,α}$ (resp. $\mathcal C^{0,α}$) estimate for the solution. These estimates are generalized versions of the Bedford-Taylor interior $\mathcal C^{1,1}$ estimate.
We examined O:H-O bond relaxation under compression,heating,molecular undercoordination and claimed a universal resolution to the best-known mysteries of water ice such as ice foating, ice slipperiness, relegation and warm water cools faster. progress shows that O:H-O bond segmental disparity and O-O repulsivity form the soul dictating the extraordinary adaptivity, cooperativity, recoverability, and sensitivity of water and ice.
Introduction of the principles of the asymmetrical, short-range O:H-O coupled oscillater pair and the basic rule for water ice, which reconciles the structure and anomalies of water ice.
Traditional stock market prediction methods commonly only utilize the historical trading data, ignoring the fact that stock market fluctuations can be impacted by various other information sources such as stock related events. Although some recent works propose event-driven prediction approaches by considering the event data, how to leverage the joint impacts of multiple data sources still remains an open research problem. In this work, we study how to explore multiple data sources to improve the performance of the stock prediction. We introduce an Extended Coupled Hidden Markov Model incorporating the news events with the historical trading data. To address the data sparsity issue of news events for each single stock, we further study the fluctuation correlations between the stocks and incorporate the correlations into the model to facilitate the prediction task. Evaluations on China A-share market data in 2016 show the superior performance of our model against previous methods.
In Zhang $\&$ Showman (2018, hereafter Paper I), we developed an analytical theory of 1D eddy diffusivity $K_{zz}$ for global-mean vertical tracer transport in a 3D atmosphere. We also presented 2D numerical simulations on fast-rotating planets to validate our theory. On a slowly rotating planet such as Venus or a tidally locked planet (not necessarily a slow-rotator) such as a hot Jupiter, the tracer distribution could exhibit significant longitudinal inhomogeneity and tracer transport is intrinsically 3D. Here we study the global-mean vertical tracer transport on tidally locked planets using 3D tracer-transport simulations. We find that our analytical $K_{zz}$ theory in Paper I is validated on tidally locked planets over a wide parameter space. $K_{zz}$ strongly depends on the large-scale circulation strength, horizontal mixing due to eddies and waves and local tracer sources and sinks due to chemistry and microphysics. As our analytical theory predicted, $K_{zz}$ on tidally locked planets also exhibit three regimes In Regime I where the chemical and microphysical processes are uniformly distributed across the globe, different chemical species should be transported via different eddy diffusivity. In Regime II where the chemical and microphysical processes are non-uniform---for example, photochemistry or cloud formation that exhibits strong day-night contrast---the global-mean vertical tracer mixing does not always behave diffusively. In the third regime where the tracer is long-lived, non-diffusive effects are significant. Using species-dependent eddy diffusivity, we provide a new analytical theory of the dynamical quench points for disequilibrium tracers on tidally locked planets from first principles.
Most chemistry and cloud formation models for planetary atmospheres adopt a one-dimensional (1D) diffusion approach to approximate the global-mean vertical tracer transport. The physical underpinning of the key parameter in this framework, eddy diffusivity $K_{zz}$, is usually obscure. Here we analytically and numerically investigate vertical tracer transport in a 3D stratified atmosphere and predict $K_{zz}$ as a function of the large-scale circulation strength, horizontal mixing due to eddies and waves and local tracer sources and sinks. We find that $K_{zz}$ increases with tracer chemical lifetime and circulation strength but decreases with horizontal eddy mixing efficiency. We demarcated three $K_{zz}$ regimes in planetary atmospheres. In the first regime where the tracer lifetime is short compared with the transport timescale and horizontal tracer distribution under chemical equilibrium ($χ_0$) is uniformly distributed across the globe, global-mean vertical tracer mixing behaves diffusively. But the traditional assumption in current 1D models that all chemical species are transported via the same eddy diffusivity generally breaks down. We show that different chemical species in a single atmosphere should in principle have different eddy diffusion profiles. In the second regime where tracer is short-lived but $χ_0$ is non-uniformly distributed, a significant non-diffusive component might lead to a negative $K_{zz}$ under the diffusive assumption. In the third regime where the tracer is long-lived, global-mean vertical tracer transport is also largely influenced by non-diffusive effects. Numerical simulations of 2D tracer transport on fast-rotating zonally symmetric planets validate our analytical $K_{zz}$ theory over a wide parameter space.