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Chao Zhu

Publications and source records attributed to Chao Zhu.

At least 55 records · Page 3Linked to original sources

Machine learning driven synthesis of few-layered WTe2

Reducing the lateral scale of two-dimensional (2D) materials to one-dimensional (1D) has attracted substantial research interest not only to achieve competitive electronic device applications but also for the exploration of fundamental physical properties. Controllable synthesis of high-quality 1D nanoribbons (NRs) is thus highly desirable and essential for the further study. Traditional exploration of the optimal synthesis conditions of novel materials is based on the trial-and-error approach, which is time consuming, costly and laborious. Recently, machine learning (ML) has demonstrated promising capability in guiding material synthesis through effectively learning from the past data and then making recommendations. Here, we report the implementation of supervised ML for the chemical vapor deposition (CVD) synthesis of high-quality 1D few-layered WTe2 nanoribbons (NRs). The synthesis parameters of the WTe2 NRs are optimized by the trained ML model. On top of that, the growth mechanism of as-synthesized 1T' few-layered WTe2 NRs is further proposed, which may inspire the growth strategies for other 1D nanostructures. Our findings suggest that ML is a powerful and efficient approach to aid the synthesis of 1D nanostructures, opening up new opportunities for intelligent material development.

cond-mat.mtrl-sci↗

Band Structure Engineering of Interfacial Semiconductors Based on Atomically Thin Lead Iodide Crystals

To explore new constituents in two-dimensional materials and to combine their best in van der Waals heterostructures, are in great demand as being unique platform to discover new physical phenomena and to design novel functionalities in interface-based devices. Herein, PbI2 crystals as thin as few-layers are first synthesized, particularly through a facile low-temperature solution approach with the crystals of large size, regular shape, different thicknesses and high-yields. As a prototypical demonstration of flexible band engineering of PbI2-based interfacial semiconductors, these PbI2 crystals are subsequently assembled with several transition metal dichalcogenide monolayers. The photoluminescence of MoS2 is strongly enhanced in MoS2/PbI2 stacks, while a dramatic photoluminescence quenching of WS2 and WSe2 is revealed in WS2/PbI2 and WSe2/PbI2 stacks. This is attributed to the effective heterojunction formation between PbI2 and these monolayers, but type I band alignment in MoS2/PbI2 stacks where fast-transferred charge carriers accumulate in MoS2 with high emission efficiency, and type II in WS2/PbI2 and WSe2/PbI2 stacks with separated electrons and holes suitable for light harvesting. Our results demonstrate that MoS2, WS2, WSe2 monolayers with very similar electronic structures themselves, show completely distinct light-matter interactions when interfacing with PbI2, providing unprecedent capabilities to engineer the device performance of two-dimensional heterostructures.

cond-mat.mes-hall↗

Design Flow of Accelerating Hybrid Extremely Low Bit-width Neural Network in Embedded FPGA

Neural network accelerators with low latency and low energy consumption are desirable for edge computing. To create such accelerators, we propose a design flow for accelerating the extremely low bit-width neural network (ELB-NN) in embedded FPGAs with hybrid quantization schemes. This flow covers both network training and FPGA-based network deployment, which facilitates the design space exploration and simplifies the tradeoff between network accuracy and computation efficiency. Using this flow helps hardware designers to deliver a network accelerator in edge devices under strict resource and power constraints. We present the proposed flow by supporting hybrid ELB settings within a neural network. Results show that our design can deliver very high performance peaking at 10.3 TOPS and classify up to 325.3 image/s/watt while running large-scale neural networks for less than 5W using embedded FPGA. To the best of our knowledge, it is the most energy efficient solution in comparison to GPU or other FPGA implementations reported so far in the literature.

cs.DC↗

Regime-Switching Jump Diffusions with Non-Lipschitz Coefficients and Countably Many Switching States: Existence and Uniqueness, Feller, and Strong Feller Properties

This work focuses on a class of regime-switching jump diffusion processes, which is a two component Markov processes $(X(t),Λ(t))$, where $Λ(t)$ is a component representing discrete events taking values in a countably infinite set. Considering the corresponding stochastic differential equations, our main focus is on treating those with non-Lipschitz coefficients. We first show that there exists a unique strong solution to the corresponding stochastic differential equation. Then Feller and strong Feller properties are investigated.

math.PR↗

Jump Type Stochastic Differential Equations with Non-Lipschitz Coefficients: Non Confluence, Feller and Strong Feller Properties, and Exponential Ergodicity

This paper considers multidimensional jump type stochastic differential equations with super linear growth and non-Lipschitz coefficients. After establishing a sufficient condition for nonexplosion, this paper presents sufficient non-Lipschitz conditions for pathwise uniqueness. The non confluence property for solutions is investigated. Feller and strong Feller properties under non-Lipschitz conditions are investigated via the coupling method. Sufficient conditions for irreducibility and exponential ergodicity are derived. As applications, this paper also studies multidimensional stochastic differential equations driven by Lévy processes and presents a Feynman-Kac formula for Lévy type operators.

math.PR↗

A Weak Convergence Approach to Inventory Control Using a Long-term Average Criterion

This paper continues the examination of inventory control in which the inventory is modelled by a diffusion process and a long-term average cost criterion is used to make decisions. The class of such models under consideration have general drift and diffusion coefficients and boundary points that are consistent with the notion that demand should tend to reduce the inventory level. The conditions on the cost functions are greatly relaxed from those in \cite{helm:15b}. Characterization of the cost of a general $(s,S)$ policy as a function of two variables naturally leads to a nonlinear optimization problem over the ordering levels $s$ and $S$. Existence of an optimizing pair $(s_*,S_*)$ is established for these models under very weak conditions; non-existence of an optimizing pair is also discussed. Using average expected occupation and ordering measures and weak convergence arguments, weak conditions are given for the optimality of the $(s_*,S_*)$ ordering policy in the general class of admissible policies. The analysis involves an auxiliary function that is globally $C^2$ and which, together with the infimal cost, solve a particular system of linear equations and inequalities related to but different from the long-term average Hamilton-Jacobi-Bellman equation. This approach provides an analytical solution to the problem rather than a solution involving intricate analysis of the stochastic processes. The range of applicability of these results is illustrated on a drifted Brownian motion inventory model, both unconstrained and reflected, and on a geometric Brownian motion inventory model under three different cost structures.

math.OC↗

On the Martingale Problem and Feller and Strong Feller Properties for Weakly Coupled Lévy Type Operators

This paper considers the martingale problem for a class of weakly coupled Lévy type operators. It is shown that under some mild conditions, the martingale problem is well-posed and uniquely determines a strong Markov process $(X,Λ)$. The process $(X,Λ)$, called a regime-switching jump diffusion with Lévy type jumps, is further shown to posses Feller and strong Feller properties under non-Lipschitz conditions via the coupling method.

math.PR↗

Almost Sure and Moment Exponential Stability of Regime-Switching Jump Diffusions

This work is devoted to almost sure and moment exponential stability of regime-switching jump diffusions. The Lyapunov function method is used to derive sufficient conditions for stabilities for general nonlinear systems; which further helps to derive easily verifiable conditions for linear systems. For one-dimensional linear regime-switching jump diffusions, necessary and sufficient conditions for almost sure and $p$th moment exponential stabilities are presented. Several examples are provided for illustration.

math.PR↗

Certain Properties Related to Well Posedness of Switching Diffusions

This work is devoted to switching diffusions that have two components (a continuous component and a discrete component). Different from the so-called Markovian switching diffusions, in the setup, the discrete component (the switching) depends on the continuous component (the diffusion process). The objective of this paper is to provide a number of properties related to the well posedness. First, the differentiability with respect to initial data of the continuous component is established. Then, further properties including uniform continuity with respect to initial data, and smoothness of certain functionals are obtained. Moreover, Feller property is obtained under only local Lipschitz continuity. Finally, an example of Lotka-Voterra model under regime switching is provided as an illustration.

math.PR↗

The Stochastic Solution to a Cauchy Problem for Degenerate Parabolic Equations

We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process is locally Hölder continuous with exponent $δ\in (0, 1]$, the stochastic solution, which represents the price of a European option, is shown to be a classical solution to the Cauchy problem. This improves the standard requirement $δ\ge 1/2$. Uniqueness results, including a Feynman-Kac formula and a comparison theorem, are established without assuming the usual linear growth condition on the diffusion coefficient. When the stochastic solution is not smooth, it is characterized as the limit of an approximating smooth stochastic solutions. In deriving the main results, we discover a new, probabilistic proof of Kotani's criterion for martingality of a one-dimensional diffusion in natural scale.

math.PR↗

Feynman-Kac Formulas for Regime-Switching Jump Diffusions and their Applications

This work develops Feynman-Kac formulas for a class of regime-switching jump diffusion processes, in which the jump part is driven by a Poisson random measure associated to a general Lévy process and the switching part depends on the jump diffusion processes. Under broad conditions, the connections of such stochastic processes and the corresponding partial integro-differential equations are established. Related initial, terminal, and boundary value problems are also treated. Moreover, based on weak convergence of probability measures, it is demonstrated that a sequence of random variables related to the regime-switching jump diffusion process converges in distribution to the arcsine law.

math.PR↗

A Counterintuitive Example in Inventory Management

The paper \cite{helm:17} studies an inventory management problem under a long-term average cost criterion using weak convergence methods applied to average expected occupation and average expected ordering measures. Under the natural condition of inf-compactness of the holding cost rate function, the average expected occupation measures are seen to be tight and hence have weak limits. However inf-compactness is not a natural assumption to impose on the ordering cost function. For example, the cost function composed of a fixed cost plus proportional (to the size of the order) cost is not inf-compact. Intuitively, it would seem that imposing a requirement that the long-term average cost be finite ought to imply tightness of the average expected ordering measures; a lack of tightness should mean that the inventory process spends large amounts of time in regions that have arbitrarily large holding costs resulting in an infinite long-term average cost. This paper demonstrates that this intuition is incorrect by identifying a model and an ordering policy for which the resulting inventory process has a finite long-term average cost, tightness of the average expected occupation measures but which lacks tightness of the average expected ordering measures.

math.OC↗

On Feller and Strong Feller Properties and Exponential Ergodicity of Regime-Switching Jump Diffusion Processes with Countable Regimes

This work focuses on a class of regime-switching jump diffusion processes, in which the switching component has countably infinite many states or regimes. The existence and uniqueness of the underlying process are obtained by an interlacing procedure. Then the Feller and strong Feller properties of such processes are derived by the coupling method and an appropriate Radon-Nikodym derivative. Finally the paper studies exponential ergodicity of regime-switching jump-diffusion processes.

math.PR↗

Large-area and high-quality 2D transition metal telluride

Atomically thin transitional metal ditellurides like WTe2 and MoTe2 have triggered tremendous research interests because of their intrinsic nontrivial band structure. They are also predicted to be 2D topological insulators and type-II Weyl semimetals. However, most of the studies on ditelluride atomic layers so far rely on the low-yield and time-consuming mechanical exfoliation method. Direct synthesis of large-scale monolayer ditellurides has not yet been achieved. Here, using the chemical vapor deposition (CVD) method, we demonstrate controlled synthesis of high-quality and atom-thin tellurides with lateral size over 300 μm. We found that the as-grown WTe2 maintains two different stacking sequences in the bilayer, where the atomic structure of the stacking boundary is revealed by scanning transmission electron microscope (STEM). The low-temperature transport measurements revealed a novel semimetal-to-insulator transition in WTe2 layers and an enhanced superconductivity in few-layer MoTe2. This work paves the way to the synthesis of atom-thin tellurides and also quantum spin Hall devices.

cond-mat.mtrl-sci↗

Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model

This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, which were only previously treated separately in certain special cases of risk models in the literature. In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding HJB equation, which in turn leads to an optimal restricted payment policy known as the threshold strategy. In the case of unrestricted payment scheme, by solving the associated integro-differential quasi-variational inequality, we obtain the value function as well as an optimal unrestricted dividend payment scheme known as the barrier strategy. When claim sizes are exponentially distributed, we provide easily verifiable conditions under which the threshold and barrier strategies are optimal restricted and unrestricted dividend payment policies, respectively. The main results are illustrated with several examples, including a new example concerning regressive growth rates.

math.OC↗

On Singular Control Problems with State Constraints and Regime-Switching: A Viscosity Solution Approach

This paper investigates a singular stochastic control problem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is to maximize the total expected discounted rewards from exerting the singular control. Such a formulation stems from application areas such as optimal harvesting multiple species and optimal dividends payments schemes in random environments. With the aid of weak dynamic programming principle and an exponential transformation, we characterize the value function to be the unique constrained viscosity solution of a certain system of coupled nonlinear quasi-variational inequalities. Several examples are analyzed in details to demonstrate the main results.

math.OC↗

On Optimal Harvesting Problems in Random Environments

This paper investigates the optimal harvesting strategy for a single species living in random environments whose growth is given by a regime-switching diffusion. Harvesting acts as a (stochastic) control on the size of the population. The objective is to find a harvesting strategy which maximizes the expected total discounted income from harvesting {\em up to the time of extinction} of the species; the income rate is allowed to be state- and environment-dependent. This is a singular stochastic control problem with both the extinction time and the optimal harvesting policy depending on the initial condition. One aspect of receiving payments up to the random time of extinction is that small changes in the initial population size may significantly alter the extinction time when using the same harvesting policy. Consequently, one no longer obtains continuity of the value function using standard arguments for either regular or singular control problems having a fixed time horizon. This paper introduces a new sufficient condition under which the continuity of the value function for the regime-switching model is established. Further, it is shown that the value function is a viscosity solution of a coupled system of quasi-variational inequalities. The paper also establishes a verification theorem and, based on this theorem, an $\varepsilon$-optimal harvesting strategy is constructed under certain conditions on the model. Two examples are analyzed in detail.

math.OC↗

Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation

This paper develops numerical methods for finding optimal dividend pay-out and reinsurance policies. A generalized singular control formulation of surplus and discounted payoff function are introduced, where the surplus is modeled by a regime-switching process subject to both regular and singular controls. To approximate the value function and optimal controls, Markov chain approximation techniques are used to construct a discrete-time controlled Markov chain with two components. The proofs of the convergence of the approximation sequence to the surplus process and the value function are given. Examples of proportional and excess-of-loss reinsurance are presented to illustrate the applicability of the numerical methods.

q-fin.CP↗