arXiv subjects
Publications and source records attributed to Chao Zhou.
In this work we investigate an optimal closure problem under Knightian uncertainty. We obtain the value function and an optimal control as the minimal (super-)solution of a second order BSDE with monotone generator and with a singular terminal condition.
Dynamic adaptive streaming over HTTP (DASH) has recently been widely deployed in the Internet and adopted in the industry. It, however, does not impose any adaptation logic for selecting the quality of video fragments requested by clients and suffers from lackluster performance with respect to a number of desirable properties: efficiency, stability, and fairness when multiple players compete for a bottleneck link. In this paper, we propose a throughput-friendly DASH (TFDASH) rate control scheme for video streaming with multiple clients over DASH to well balance the trade-offs among efficiency, stability, and fairness. The core idea behind guaranteeing fairness and high efficiency (bandwidth utilization) is to avoid OFF periods during the downloading process for all clients, i.e., the bandwidth is in perfect-subscription or over-subscription with bandwidth utilization approach to 100\%. We also propose a dual-threshold buffer model to solve the instability problem caused by the above idea. As a result, by integrating these novel components, we also propose a probability-driven rate adaption logic taking into account several key factors that most influence visual quality, including buffer occupancy, video playback quality, video bit-rate switching frequency and amplitude, to guarantee high-quality video streaming. Our experiments evidently demonstrate the superior performance of the proposed method.
It is a common perception that the transport of a spin current in polycrystalline metal is isotropic and independent of the polarization direction, even though spin current is a tensorlike quantity and its polarization direction is a key variable. We demonstrate surprising anisotropic spin relaxation in mesoscopic polycrystalline Cu channels in nonlocal spin valves. For directions in the substrate plane, the spin-relaxation length is longer for spins parallel to the Cu channel than for spins perpendicular to it, by as much as 9% at 10 K. Spin-orbit effects on the surfaces of Cu channels can account for this anisotropic spin relaxation. The finding suggests novel tunability of spin current, not only by its polarization direction but also by electrostatic gating.
Topological defects in magnetism have attracted great attention due to fundamental research interests and potential novel spintronics applications. Rich examples of topological defects can be found in nanoscale non-uniform spin textures, such as monopoles, domain walls, vortices, and skyrmions. Recently, skyrmions stabilized by the Dzyaloshinskii-Moriya interaction have been studied extensively. However, the stabilization of antiskyrmions is less straightforward. Here, using numerical simulations we demonstrate that antiskyrmions can be a stable spin configuration in the presence of anisotropic Dzyaloshinskii-Moriya interaction. We find current-driven antiskyrmion motion that has a transverse component, namely antiskyrmion Hall effect. The antiskyrmion gyroconstant is opposite to that for skyrmion, which allows the current-driven propagation of coupled skyrmion-antiskyrmion pairs without apparent skyrmion Hall effect. The antiskyrmion Hall angle strongly depends on the current direction, and a zero antiskyrmion Hall angle can be achieved at a critic current direction. These results open up possibilities to tailor the spin topology in nanoscale magnetism, which may be useful in the emerging field of skyrmionics.
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are nonlinear generalisations of the traditional (linear) expectations, this problem can be understood as stochastic control of a family of nonlinear expectations, or equivalently of nonlinear kernels. Our first main contribution is to prove a dynamic programming principle for this control problem in an abstract setting, which we then use to provide a semi-martingale characterisation of the value function. We next explore several applications of our results. We first obtain a wellposedness result for second order BSDEs (as introduced in [86]) which does not require any regularity assumption on the terminal condition and the generator. Then we prove a nonlinear optional decomposition in a robust setting, extending recent results of [71], which we then use to obtain a super-hedging duality in uncertain, incomplete and nonlinear financial markets. Finally, we relate, under additional regularity assumptions, the value function to a viscosity solution of an appropriate path-dependent partial differential equation (PPDE).
A phenomenological thermodynamic potential was constructed based on the symmetry analysis and property characterization of bulk DyCo2. An eight-order polynomial of Landau expansion was employed to describe the thermodynamic behavior of DyCo2. Several properties were reproduced including ferromagnetic transition temperature, magnetization curve, temperature dependence of magnetization. The transition behavior was analyzed via the thermodynamic potential. The Landau phenomenological thermodynamic model predicts the correct metamagnetic transition near the Curie temperature.
In this paper, we study an unconventional but practically meaningful reversibility problem of commonly used image filters. We broadly define filters as operations to smooth images or to produce layers via global or local algorithms. And we raise the intriguingly problem if they are reservable to the status before filtering. To answer it, we present a novel strategy to understand general filter via contraction mappings on a metric space. A very simple yet effective zero-order algorithm is proposed. It is able to practically reverse most filters with low computational cost. We present quite a few experiments in the paper and supplementary file to thoroughly verify its performance. This method can also be generalized to solve other inverse problems and enables new applications.
Estimating correspondence between two images and extracting the foreground object are two challenges in computer vision. With dual-lens smart phones, such as iPhone 7Plus and Huawei P9, coming into the market, two images of slightly different views provide us new information to unify the two topics. We propose a joint method to tackle them simultaneously via a joint fully connected conditional random field (CRF) framework. The regional correspondence is used to handle textureless regions in matching and make our CRF system computationally efficient. Our method is evaluated over 2,000 new image pairs, and produces promising results on challenging portrait images.
Chiral anomaly, a non-conservation of chiral charge pumped by the topological nontrivial gauge fields, has been predicted to exist in Weyl semimetals. However, until now, the experimental signature of this effect exclusively relies on the observation of negative longitudinal magnetoresistance at low temperatures. Here, we report the field-modulated chiral charge pumping process and valley diffusion in Cd3As2. Apart from the conventional negative magnetoresistance, we observe an unusual nonlocal response with negative field dependence up to room temperature, originating from the diffusion of valley polarization. Furthermore, a large magneto-optic Kerr effect generated by parallel electric and magnetic fields is detected. These new experimental approaches provide a quantitative analysis of the chiral anomaly phenomenon which is inaccessible previously. The ability to manipulate the valley polarization in topological semimetal at room temperature opens up a brand-new route towards understanding its fundamental properties and utilizing the chiral fermions.
The energy efficiency of the spin Hall effects (SHE) can be enhanced if the electrical conductivity is decreased without sacrificing the spin Hall conductivity. The resistivity of Pt films can be increased to 150-300 μΩ*cm by mesoscopic lateral confinement, thereby decreasing the conductivity. The SHE and inverse spin Hall effects (ISHE) in these mesoscopic Pt films are explored at 10 K by using the nonlocal spin injection/detection method. All relevant physical quantities are determined in-situ on the same substrate, and a quantitative approach is developed to characterize all processes effectively. Extensive measurements with various Pt thickness values reveal an upper limit for the Pt spin diffusion length: λ_pt<0.8 nm. The average product of λ_pt and the Pt spin Hall angle α_H is substantial: α_H*λ_pt=(0.142 +/- 0.040)nm for 4 nm thick Pt, though a gradual decrease is observed at larger Pt thickness. The results suggest enhanced spin Hall effects in resistive mesoscopic Pt films.
In this work, we report our study on the THz emission in Fe/Pt magnetic heterostructures. We have carried out a comprehensive investigation of THz emission from Fe/Pt magnetic heterostructures, employing time-domain THz spectroscopy. We reveal that by properly tuning the thickness of Fe or Pt layer, THz emission can be greatly improved in this type of heterostructure. We further demonstrate that the THz field strength emitted from a newly designed multilayer (Pt/Fe/MgO)$_n$ with n=3 can reach a value of ~1.6 kV/cm, which is comparable to the values from the conventional GaAs antenna with a bias of 4 kV/cm, and the nonlinear crystals, e.g., 100 micrometer GaP and 2 mm ZnTe. For the first time, the intensity and spectrum of THz wave is demonstrated to be tunable by the magnetic field applied on the patterned magnetic Fe/Pt heterostructures. These findings thus promise novel approaches to fabricate powerful and tunable THz emitters based on magnetic heterostructure.
In this paper, we define a notion of second-order backward stochastic differential equations with jumps (2BSDEJs for short), which generalizes the continuous case considered by Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190]. However, on the contrary to their formulation, where they can define pathwise the density of quadratic variation of the canonical process, in our setting, the compensator of the jump measure associated to the jumps of the canonical process, which is the counterpart of the density in the continuous case, depends on the underlying probability measures. Then in our formulation of 2BSDEJs, the generator of the 2BSDEJs depends also on the underlying probability measures through the compensator. But the solution to the 2BSDEJs can still be defined universally. Moreover, we obtain a representation of the $Y$ component of a solution of a 2BSDEJ as a supremum of solutions of standard backward SDEs with jumps, which ensures the uniqueness of the solution.
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is non-dominated. We propose studying this problem in the framework of second-order backward stochastic differential equations (2BSDEs for short) with quadratic growth generators. We show for exponential, power and logarithmic utilities that the value function of the problem can be written as the initial value of a particular 2BSDE and prove existence of an optimal strategy. Finally several examples which shed more light on the problem and its links with the classical utility maximization one are provided. In particular, we show that in some cases, the upper bound of the volatility interval plays a central role, exactly as in the option pricing problem with uncertain volatility models of [2].
In this article, we build upon the work of Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190] to define a notion of a second order backward stochastic differential equation reflected on a lower càdlàg obstacle. We prove existence and uniqueness of the solution under a Lipschitz-type assumption on the generator, and we investigate some links between our reflected 2BSDEs and nonclassical optimal stopping problems. Finally, we show that reflected 2BSDEs provide a super-hedging price for American options in a market with volatility uncertainty.
In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJs for short) started in our accompanying paper [15]. We prove existence of these equations by a direct method, thus providing complete wellposedness for 2BSDEJs. These equations are a natural candidate for the probabilistic interpretation of some fully non-linear partial integro-differential equations, which is the point of the second part of this work. We prove a non-linear Feynman-Kac formula and show that solutions to 2BSDEJs provide viscosity solutions of the associated PIDEs.
We extend the wellposedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang \cite{stz} to the case of a bounded terminal condition and a generator with quadratic growth in the $z$ variable. More precisely, we obtain uniqueness through a representation of the solution inspired by stochastic control theory, and we obtain two existence results using two different methods. In particular, we obtain the existence of the simplest purely quadratic 2BSDEs through the classical exponential change, which allows us to introduce a quasi-sure version of the entropic risk measure. As an application, we also study robust risk-sensitive control problems. Finally, we prove a Feynman-Kac formula and a probabilistic representation for fully nonlinear PDEs in this setting.
In this article, we prove the existence of bounded solutions of quadratic backward SDEs with jumps, that is to say for which the generator has quadratic growth in the variables (z,u). From a technical point of view, we use a direct fixed point approach as in Tevzadze [38], which allows us to obtain existence and uniqueness of a solution when the terminal condition is small enough. Then, thanks to a well-chosen splitting, we recover an existence result for general bounded solution. Under additional assumptions, we can obtain stability results and a comparison theorem, which as usual implies uniqueness.
In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of their properties. We obtain in particular a non-linear Doob-Meyer decomposition for g-submartingales and a downcrossing inequality which implies their regularity in time. As a consequence of these results, we also obtain a converse comparison theorem for our class of BSDEs. Finally, we provide a dual representation for the corresponding dynamic risk measures, and study the properties of their inf-convolution, giving several explicit examples