arXiv subjects

Chao Zhou

Publications and source records attributed to Chao Zhou.

At least 163 records · Page 9Linked to original sources

arXiv2021

Gold nanocrystal-mediated sliding of doublet DNA origami filaments

Sliding is one of the fundamental mechanical movements in machinery. In macroscopic systems, double-rack pinion machines employ gears to slide two linear tracks along opposite directions. In microscopic systems, kinesin-5 proteins crosslink and slide apart antiparallel microtubules, promoting spindle bipolarity and elongation during mitosis. Here we demonstrate an artificial nanoscopic analog, in which gold nanocrystals can mediate coordinated sliding of two antiparallel DNA origami filaments powered by DNA fuels. Stepwise and reversible sliding along opposite directions is in situ monitored and confirmed using fluorescence spectroscopy. A theoretical model including different energy transfer mechanisms is developed to understand the observed fluorescence dynamics. We further show that such sliding can also take place in the presence of multiple DNA sidelocks that are introduced to inhibit the relative movements. Our work enriches the toolbox of DNA-based nanomachinery, taking one step further toward the vision of molecular nanofactories.

physics.bio-ph↗

arXiv2021

Rate compatible reconciliation for continuous-variable quantum key distribution using Raptor-like LDPC codes

In the practical continuous-variable quantum key distribution (CV-QKD) system, the postprocessing process, particularly the error correction part, significantly impacts the system performance. Multi-edge type low-density parity-check (MET-LDPC) codes are suitable for CV-QKD systems because of their Shannon-limit-approaching performance at a low signal-to-noise ratio (SNR). However, the process of designing a low-rate MET-LDPC code with good performance is extremely complicated. Thus, we introduce Raptor-like LDPC (RL-LDPC) codes into the CV-QKD system, exhibiting both the rate compatible property of the Raptor code and capacity-approaching performance of MET-LDPC codes. Moreover, this technique can significantly reduce the cost of constructing a new matrix. We design the RL-LDPC matrix with a code rate of 0.02 and easily and effectively adjust this rate from 0.016 to 0.034. Simulation results show that we can achieve more than 98% reconciliation efficiency in a range of code rate variation using only one RL-LDPC code that can support high-speed decoding with an SNR less than -16.45 dB. This code allows the system to maintain a high key extraction rate under various SNRs, paving the way for practical applications of CV-QKD systems with different transmission distances.

quant-ph↗

arXiv2021

Nearly quantum-limited Josephson-junction Frequency Comb synthesizer

While coherently-driven Kerr microcavities have rapidly matured as a platform for frequency comb formation, such microresonators generally possess weak Kerr coefficients; consequently, triggering comb generation requires millions of photons to be circulating inside the cavity. This suppresses the role of quantum fluctuations in the comb's dynamics. In this paper, we realize a minimal version of coherently-driven Kerr-mediated microwave frequency combs in the circuit QED architecture, where the quantum vacuum's fluctuations are the primary limitation on comb coherence. We achieve a comb phase coherence of up to 35~$μ$s, approaching the theoretical device quantum limit of 55~$μ$s, and vastly longer than the modes' inherent lifetimes of 13~ns. The ability within cQED to engineer stronger nonlinearities than optical microresonators, together with operation at cryogenic temperatures, and excellent agreement of comb dynamics with quantum theory indicates a promising platform for the study of complex dynamics of quantum nonlinear systems

quant-ph↗

arXiv2021

SelectNet: Self-paced Learning for High-dimensional Partial Differential Equations

The least squares method with deep neural networks as function parametrization has been applied to solve certain high-dimensional partial differential equations (PDEs) successfully; however, its convergence is slow and might not be guaranteed even within a simple class of PDEs. To improve the convergence of the network-based least squares model, we introduce a novel self-paced learning framework, SelectNet, which quantifies the difficulty of training samples, treats samples equally in the early stage of training, and slowly explores more challenging samples, e.g., samples with larger residual errors, mimicking the human cognitive process for more efficient learning. In particular, a selection network and the PDE solution network are trained simultaneously; the selection network adaptively weighting the training samples of the solution network achieving the goal of self-paced learning. Numerical examples indicate that the proposed SelectNet model outperforms existing models on the convergence speed and the convergence robustness, especially for low-regularity solutions.

math.NA↗

arXiv2021

A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEs

Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional semi-linear parabolic PDEs. This scheme is inspired by the approach coming from machine learning and developed using deep neural networks in Han and al. [32]. Our algorithm is based on a Picard iteration scheme in which a sequence of linear-quadratic optimisation problem is solved by means of stochastic gradient descent (SGD) algorithm. In the framework of a linear specification of the approximation space, we manage to prove a convergence result for our scheme, under some smallness condition. In practice, in order to be able to treat high-dimensional examples, we employ sparse grid approximation spaces. In the case of periodic coefficients and using pre-wavelet basis functions, we obtain an upper bound on the global complexity of our method. It shows in particular that the curse of dimensionality is tamed in the sense that in order to achieve a root mean squared error of order $ε$, for a prescribed precision $ε$, the complexity of the Picard algorithm grows polynomially in $ε^{-1}$ up to some logarithmic factor $ |log(ε)| $ which grows linearly with respect to the PDE dimension. Various numerical results are presented to validate the performance of our method and to compare them with some recent machine learning schemes proposed in Han and al. [20] and Huré and al. [37].

math.NA↗

arXiv2020

Lifetime Ruin under High-watermark Fees and Drift Uncertainty

This paper aims to make a new contribution to the study of lifetime ruin problem by considering investment in two hedge funds with high-watermark fees and drift uncertainty. Due to multi-dimensional performance fees that are charged whenever each fund profit exceeds its historical maximum, the value function is expected to be multi-dimensional. New mathematical challenges arise as the standard dimension reduction cannot be applied, and the convexity of the value function and Isaacs condition may not hold in our ruin probability minimization problem with drift uncertainty. We propose to employ the stochastic Perron's method to characterize the value function as the unique viscosity solution to the associated Hamilton Jacobi Bellman (HJB) equation without resorting to the proof of dynamic programming principle. The required comparison principle is also established in our setting to close the loop of stochastic Perron's method.

q-fin.MF↗

arXiv2020

Corrigendum for "Second-order reflected backward stochastic differential equations" and "Second-order BSDEs with general reflection and game options under uncertainty"

The aim of this short note is to fill in a gap in our earlier paper [16] on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper [15]. We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions [13, 23] in the so--called $G-$framework.

math.PR↗

arXiv2020

Binary Funding Impacts in Derivative Valuation

We discuss the binary nature of funding impact in derivative valuation. Under some conditions, funding is either a cost or a benefit, i.e., one of the lending/borrowing rates does not play a role in pricing derivatives. When derivatives are priced, considering different lending/borrowing rates leads to semi-linear BSDEs and PDEs, and thus it is necessary to solve the equations numerically. However, once it can be guaranteed that only one of the rates affects pricing, linear equations can be recovered and analytical formulae can be derived. Moreover, as a byproduct, our results explain how debt value adjustment (DVA) and funding benefits are dissimilar. It is often believed that considering both DVA and funding benefits results in a double-counting issue but it will be shown that the two components are affected by different mathematical structures of derivative transactions. We find that funding benefit is related to the decreasing property of the payoff function, but this relationship decreases as the funding choices of underlying assets are transferred to repo markets.

q-fin.MF↗

arXiv2020

Relative wealth concerns with partial information and heterogeneous priors

We establish a Nash equilibrium in a market with $ N $ agents with the performance criteria of relative wealth level when the market return is unobservable. Each investor has a random prior belief on the return rate of the risky asset. The investors can be heterogeneous in both the mean and variance of the prior. By a separation result and a martingale argument, we show that the optimal investment strategy under a stochastic return rate model can be characterized by a fully-coupled linear FBSDE. Two sets of deep neural networks are used for the numerical computation to first find each investor's estimate of the mean return rate and then solve the FBSDEs. We establish the existence and uniqueness result for the class of FBSDEs with stochastic coefficients and solve the utility game under partial information using deep neural network function approximators. We demonstrate the efficiency and accuracy by a base-case comparison with the solution from the finite difference scheme in the linear case and apply the algorithm to the general case of nonlinear hidden variable process. Simulations of investment strategies show a herd effect that investors trade more aggressively under relativeness concerns. Statistical properties of the investment strategies and the portfolio performance, including the Sharpe ratios and the Variance Risk ratios (VRRs) are examed. We observe that the agent with the most accurate prior estimate is likely to lead the herd, and the effect of competition on heterogeneous agents varies more with market characteristics compared to the homogeneous case.

q-fin.PM↗

arXiv2020

Mean Field Exponential Utility Game: A Probabilistic Approach

We study an $N$-player and a mean field exponential utility game. Each player manages two stocks; one is driven by an individual shock and the other is driven by a common shock. Moreover, each player is concerned not only with her own terminal wealth but also with the relative performance of her competitors. We use the probabilistic approach to study these two games. We show the unique equilibrium of the $N$-player game and the mean field game can be characterized by a novel multi-dimensional FBSDE with quadratic growth and a novel mean-field FBSDEs, respectively. The well-posedness result and the convergence result are established.

math.OC↗

arXiv2020

Long-Distance Continuous-Variable Quantum Key Distribution over 202.81 km of Fiber

Quantum key distribution provides secure keys resistant to code-breaking quantum computers. The continuous-variable version of quantum key distribution offers the advantages of higher secret key rates in metropolitan areas, as well as the use of standard telecom components that can operate at room temperature. However, the transmission distance of these systems (compared with discrete-variable systems) are currently limited and considered unsuitable for long-distance distribution. Herein, we report the experimental results of long distance continuous-variable quantum key distribution over 202.81 km of ultralow-loss optical fiber by suitably controlling the excess noise and employing highly efficient reconciliation procedures. This record-breaking implementation of the continuous-variable quantum key distribution doubles the previous distance record and shows the road for long-distance and large-scale secure quantum key distribution using room-temperature standard telecom components.

quant-ph↗

arXiv2020

Deep learning for smart fish farming: applications, opportunities and challenges

With the rapid emergence of deep learning (DL) technology, it has been successfully used in various fields including aquaculture. This change can create new opportunities and a series of challenges for information and data processing in smart fish farming. This paper focuses on the applications of DL in aquaculture, including live fish identification, species classification, behavioral analysis, feeding decision-making, size or biomass estimation, water quality prediction. In addition, the technical details of DL methods applied to smart fish farming are also analyzed, including data, algorithms, computing power, and performance. The results of this review show that the most significant contribution of DL is the ability to automatically extract features. However, challenges still exist; DL is still in an era of weak artificial intelligence. A large number of labeled data are needed for training, which has become a bottleneck restricting further DL applications in aquaculture. Nevertheless, DL still offers breakthroughs in the handling of complex data in aquaculture. In brief, our purpose is to provide researchers and practitioners with a better understanding of the current state of the art of DL in aquaculture, which can provide strong support for the implementation of smart fish farming.

cs.CV↗

arXiv2020

Hyperspectral Unmixing Network Inspired by Unfolding an Optimization Problem

The hyperspectral image (HSI) unmixing task is essentially an inverse problem, which is commonly solved by optimization algorithms under a predefined (non-)linear mixture model. Although these optimization algorithms show impressive performance, they are very computational demanding as they often rely on an iterative updating scheme. Recently, the rise of neural networks has inspired lots of learning based algorithms in unmixing literature. However, most of them lack of interpretability and require a large training dataset. One natural question then arises: can one leverage the model based algorithm and learning based algorithm to achieve interpretable and fast algorithm for HSI unmixing problem? In this paper, we propose two novel network architectures, named U-ADMM-AENet and U-ADMM-BUNet, for abundance estimation and blind unmixing respectively, by combining the conventional optimization-model based unmixing method and the rising learning based unmixing method. We first consider a linear mixture model with sparsity constraint, then we unfold Alternating Direction Method of Multipliers (ADMM) algorithm to construct the unmixing network structures. We also show that the unfolded structures can find corresponding interpretations in machine learning literature, which further demonstrates the effectiveness of proposed methods. Benefit from the interpretation, the proposed networks can be initialized by incorporating prior information about the HSI data. Different from traditional unfolding networks, we propose a new training strategy for proposed networks to better fit in the HSI applications. Extensive experiments show that the proposed methods can achieve much faster convergence and competitive performance even with very small size of training data, when compared with state-of-art algorithms.

eess.IV↗

arXiv2020

On Dynamic Programming Principle for Stochastic Control under Expectation Constraints

This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical space at each time t. Motivated by some financial applications, we show that several types of dynamic trading constraints can be reformulated into expectation constraints on paths of controlled state processes. Our results can therefore be employed to recover the dynamic programming principle for these optimal investment problems under dynamic constraints, possibly path-dependent, in a non-Markovian framework.

math.OC↗

arXiv2020

Optical imaging of antiferromagnetic domains in ultrathin CoO(001) films

Antiferromagnetic (AFM) domains in ultrathin CoO(001) films are imaged by a wide-field optical microscopy using magneto-optical birefringence effect. The magnetic origin of observed optical contrast is confirmed by the spin orientation manipulation through exchange coupling in Fe/CoO(001) bilayer. The finite size effect of ordering temperature for ultrathin single crystal CoO film is revealed by the thickness and temperature dependent measurement of birefringence contrast. The magneto-optical birefringence effect is found to strongly depend on the photon energy of incident light, and a surprising large polarization rotation angle up to 168.5 mdeg is obtained from a 4.6 nm CoO film with a blue light source, making it possible to further investigate the evolution of AFM domains in AFM ultrathin film under external field.

cond-mat.mtrl-sci↗

arXiv2020

Balance Between Efficient and Effective Learning: Dense2Sparse Reward Shaping for Robot Manipulation with Environment Uncertainty

Efficient and effective learning is one of the ultimate goals of the deep reinforcement learning (DRL), although the compromise has been made in most of the time, especially for the application of robot manipulations. Learning is always expensive for robot manipulation tasks and the learning effectiveness could be affected by the system uncertainty. In order to solve above challenges, in this study, we proposed a simple but powerful reward shaping method, namely Dense2Sparse. It combines the advantage of fast convergence of dense reward and the noise isolation of the sparse reward, to achieve a balance between learning efficiency and effectiveness, which makes it suitable for robot manipulation tasks. We evaluated our Dense2Sparse method with a series of ablation experiments using the state representation model with system uncertainty. The experiment results show that the Dense2Sparse method obtained higher expected reward compared with the ones using standalone dense reward or sparse reward, and it also has a superior tolerance of system uncertainty.

cs.LG↗

arXiv2020

Gasoline Pricing Policies for Transportation Safety

Economic factors can have substantial effects on transportation crash trends. This study makes a comprehensive examination of the relationship between the retail gasoline price (including state and federal fuel taxes) and transportation fatal crashes from 2007 to 2016 in the US. Data on motor vehicle, bicycle and pedestrian fatal crashes come from Fatality Analysis Reporting System (FARS) provided by the National Highway Safety Administration (NHTSA) and the gasoline price data is from U.S. Energy Information Administration (EIA). Random effect negative binomial regression models are used to estimate the impact of inflation-adjusted gasoline prices on trends of transportation fatal crashes. Initial results combined with results of previous studies showed that gender and transportation mean type (motorcycle, non-motorcycle, bicycle and pedestrian) play prominent roles in interpreting the final model, so by using random effect negative binomial regression, seven models are developed to evaluate the effects of gasoline price changes on total population, male, female, motorcyclists, non-motorcyclists, bicyclists and pedestrians separately. Our findings suggest that increasing the gasoline prices will not significantly alter the number of total fatal crashes. However, by looking at different vehicle types, it is estimated that one dollar increase in adjusted gasoline price is associated with 24.2% increase in the number of motorcycle fatal crashes, 1.9% decrease in the number of non-motorcycle fatal crashes, and 0.7% decrease in the number of pedestrian fatal crashes. Also, there is no noticeable difference between male and female in response to the gasoline price changes.

stat.AP↗

arXiv2019

A Risk-Sharing Framework of Bilateral Contracts

We introduce a two-agent problem which is inspired by price asymmetry arising from funding difference. When two parties have different funding rates, the two parties deduce different fair prices for derivative contracts even under the same pricing methodology and parameters. Thus, the two parties should enter the derivative contracts with a negotiated price, and we call the negotiation a risk-sharing problem. This framework defines the negotiation as a problem that maximizes the sum of utilities of the two parties. By the derived optimal price, we provide a theoretical analysis on how the price is determined between the two parties. As well as the price, the risk-sharing framework produces an optimal amount of collateral. The derived optimal collateral can be used for contracts between financial firms and non-financial firms. However, inter-dealers markets are governed by regulations. As recommended in Basel III, it is a convention in inter-dealer contracts to pledge the full amount of a close-out price as collateral. In this case, using the optimal collateral, we interpret conditions for the full margin requirement to be indeed optimal.

q-fin.MF↗