arXiv subjects

Ye Zhang

Publications and source records attributed to Ye Zhang.

At least 163 records · Page 9Linked to original sources

arXiv2022

Convergence analysis for forward and inverse problems in singularly perturbed time-dependent reaction-advection-diffusion equations

In this paper, by employing the asymptotic expansion method, we prove the existence and uniqueness of a smoothing solution for a time-dependent nonlinear singularly perturbed partial differential equation (PDE) with a small-scale parameter. As a by-product, we obtain an approximate smooth solution, constructed from a sequence of reduced stationary PDEs with vanished high-order derivative terms. We prove that the accuracy of the constructed approximate solution can be in any order of this small-scale parameter in the whole domain, except a negligible transition layer. Furthermore, based on a simpler link equation between this approximate solution and the source function, we propose an efficient algorithm, called the asymptotic expansion regularization (AER), for solving nonlinear inverse source problems governed by the original PDE. The convergence-rate results of AER are proven, and the a posteriori error estimation of AER is also studied under some a priori assumptions of source functions. Various numerical examples are provided to demonstrate the efficiency of our new approach.

math.NA↗

arXiv2022

Discrimination in the Venture Capital Industry: Evidence from Field Experiments

This paper examines discrimination by early-stage investors based on startup founders' gender and race using two complementary field experiments with real U.S. venture capitalists. Results show the following. (i) Discrimination varies depending on the context. Investors implicitly discriminate against female and Asian founders when evaluating attractive startups, but they favor female and Asian founders when evaluating struggling startups. This helps to reconcile the contradictory results in the extant literature and confirms the theoretical predictions of "discrimination reversion" and "pro-cyclical discrimination" phenomena. (ii) Among multiple coexisting sources of discrimination identified, statistical discrimination and implicit discrimination are important reasons for investors' "anti-minority" behaviors. A consistent estimator is developed to measure the polarization of investors' discrimination behaviors and their separate driving forces. (iii) Homophily exists when investors provide anonymous encouragement to startups in a non-investment setting. (iv) There was temporary, stronger discrimination against Asian founders during the COVID-19 outbreak.

econ.GN↗

arXiv2022

N-Grammer: Augmenting Transformers with latent n-grams

Transformer models have recently emerged as one of the foundational models in natural language processing, and as a byproduct, there is significant recent interest and investment in scaling these models. However, the training and inference costs of these large Transformer language models are prohibitive, thus necessitating more research in identifying more efficient variants. In this work, we propose a simple yet effective modification to the Transformer architecture inspired by the literature in statistical language modeling, by augmenting the model with n-grams that are constructed from a discrete latent representation of the text sequence. We evaluate our model, the N-Grammer on language modeling on the C4 data-set as well as text classification on the SuperGLUE data-set, and find that it outperforms several strong baselines such as the Transformer and the Primer. We open-source our model for reproducibility purposes in Jax.

cs.CL↗

arXiv2022

Proxy ensemble geometric phase and proxy index of time-reversal invariant topological insulators at finite temperatures

The ensemble geometric phase (EGP) has been proposed as a topological indicator for finite-temperatures systems. The ensemble Wilson loop, or the transfer matrix, contains the crucial information in the EGP construction. We propose a proxy index and a proxy EGP directly from the transfer matrix and apply them to time-reversal invariant topological insulators exemplified by the Bernevig-Hughes-Zhang (BHZ) and Kane-Mele (KM) models. The quantized proxy index and proxy EGP smoothly generalize the ground-state topological index to finite temperatures. For the BHZ model, a comparison with another topological indicator, the Uhlmann phase, shows different transition behavior with temperature. For the KM model, the EGP have been generalized to the time-reversal EGP previously, but the proxy EGP does not require any splitting of the contributions. The proxy index and proxy EGP thus offer an efficient means for characterizing finite-temperature topological properties.

cond-mat.mes-hall↗

arXiv2022

Stochastic asymptotical regularization for linear inverse problems

We introduce Stochastic Asymptotical Regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in science and engineering. We prove the regularizing properties of SAR with regard to mean-square convergence. We also show that SAR is an optimal-order regularization method for linear ill-posed problems provided that the terminating time of SAR is chosen according to the smoothness of the solution. This result is proven for both a priori and a posteriori stopping rules under general range-type source conditions. Furthermore, some converse results of SAR are verified. Two iterative schemes are developed for the numerical realization of SAR, and the convergence analyses of these two numerical schemes are also provided. A toy example and a real-world problem of biosensor tomography are studied to show the accuracy and the advantages of SAR: compared with the conventional deterministic regularization approaches for deterministic inverse problems, SAR can provide the uncertainty quantification of the quantity of interest, which can in turn be used to reveal and explicate the hidden information about real-world problems, usually obscured by the incomplete mathematical modeling and the ascendence of complex-structured noise.

math.NA↗

arXiv2021

A complete answer to the Gaveau--Brockett problem

The note is dedicated to provide a satisfying and complete answer to the long-standing Gaveau--Brockett open problem. More precisely, we determine the exact formula of the Carnot--Carathéodory distance on arbitrary step-two groups. The basic idea of the proof is combining Varadhan's formulas with the explicit expression for the associated heat kernel $p_h$ and the method of stationary phase. However, we have to introduce a number of original new methods, especially the usage of the concept of "Operator convexity". Next, new integral expressions for $p_h$ by means of properties of Bessel functions will be presented. An unexpected direct proof for the well-known positivity of $p_h$ via its original integral formula, will play an important role. Furthermore, all normal geodesics joining the identity element $o$ to any given $g$ as well as the cut locus can be characterized on every step-two groups. Finally, the corresponding results in Riemannian geometry on step-two groups will be briefly presented as well.

math.CA↗

arXiv2021

High-responsivity, High-detectivity Photomultiplication Organic Photodetector Realized by a Metal-Insulator-Semiconductor Tunneling Junction

Organic photodetectors (OPDs) possess bright prospects in applications of medical imaging and wearable electronics due to the advantages such as low cost, good biocompatibility, and good flexibility. Photomultiplication OPDs (PM-OPDs) enabled by the trap-assisted carrier tunneling injection effect exhibit external quantum efficiencies far greater than unity, thus the acquired responsivities are extremely high. However, the reported PM-OPDs with high responsivity performances are all accompanied by high dark currents due to the introduction of carrier traps, which inevitably results in inferior detectivities. In this work, we modify a P3HT:PCBM donor-rich PM-OPD by introducing an atomically thin Al2O3 interfacial layer through the ALD technique, obtaining a high responsivity of 8294 A/W and high detectivity of 6.76*10^14 Jones, simultaneously, both of which are among the highest reported for bulk heterojunction PM-OPDs. Ascribed to the introduction of the atomically thin Al2O3 layer, the metal-insulator-semiconductor (MIS) tunneling junction is formed, which brings forward a suppressed dark current along with an increased amounts of holes tunneling under forward bias. Meanwhile, the weak light detection limit of the modified PM-OPD within the linear response range reaches the level of nW/cm2. Based on the proposed PM-OPD, a proof-of-concept image sensor with 26*26 pixels is demonstrated, which can respond to both ultraviolet light and visible light. The PM-OPD based sensor arrays can find broad applications for medical imaging, wearable electronics, etc.

physics.app-ph↗

arXiv2021

A note on gradient estimates for the heat semigroup on nonisotropic Heisenberg groups

In this note we obtain gradient estimates for the heat semigroup on nonisotropic Heisenberg groups. More precisely, our aim is to get the H.-Q. Li inequality on nonisotropic Heisenberg groups, which is a generalization of the original result on the classical Heisenberg group of dimension 3 and a counterpart of the inequality on the H-type groups. Our proof is based on a Cheeger type inequality, which is an approach proposed by Bakry et al.

math.AP↗

arXiv2021

Effective Sequence-to-Sequence Dialogue State Tracking

Sequence-to-sequence models have been applied to a wide variety of NLP tasks, but how to properly use them for dialogue state tracking has not been systematically investigated. In this paper, we study this problem from the perspectives of pre-training objectives as well as the formats of context representations. We demonstrate that the choice of pre-training objective makes a significant difference to the state tracking quality. In particular, we find that masked span prediction is more effective than auto-regressive language modeling. We also explore using Pegasus, a span prediction-based pre-training objective for text summarization, for the state tracking model. We found that pre-training for the seemingly distant summarization task works surprisingly well for dialogue state tracking. In addition, we found that while recurrent state context representation works also reasonably well, the model may have a hard time recovering from earlier mistakes. We conducted experiments on the MultiWOZ 2.1-2.4, WOZ 2.0, and DSTC2 datasets with consistent observations.

cs.CL↗

arXiv2021

Double-bowl State in photonic Dirac nodal line semimetal

The past decade has seen a proliferation of topological materials for both insulators and semimetals in electronic systems and classical waves. Topological semimetals exhibit topologically protected band degeneracies, such as nodal points and nodal lines. Dirac nodal line semimetals (DNLS), which own four-fold line degeneracy, have drawn particular attention. DNLSs have been studied in electronic systems but there is no photonic DNLS. Here in this work, we provide a new mechanism which is unique for photonic systems to investigate a stringent photonic DNLS. When truncated, the photonic DNLS exhibits double-bowl states (DBS), which comprises two sets of perpendicularly polarized surface states. In sharp contrast to nondegenerate surface states in other photonic systems, here the two sets of surface states are almost degenerate over the whole spectrum range. The DBS and the bulk Dirac nodal ring (DNR) dispersion along the relevant directions, are experimentally resolved.

physics.optics↗

arXiv2021

Comparison of finite-temperature topological indicators based on Uhlmann connection

Two indicators of finite-temperature topological properties based on the Uhlmann connection, one generalizing the Wilson loop to the Uhlmann-Wilson loop and the other generalizing the Berry phase to the Uhlmann phase, are constructed explicitly for a time-reversal invariant topological insulators with a $Z_2$ index. While the phases of the eigenvalues of the Wilson loop reflect the $Z_2$ index of the model at zero temperature, it is found that the signature from the Uhlmann-Wilson loop gradually fades away as temperature increases. On the other hand, the Berry phase exhibits quantization due to the underlying holonomy group. The Uhlmann phase retains the quantization at finite temperatures and serves as an indicator of topological properties. A phase diagram showing where jumps of the Uhlmann phase can be found is presented. By modifying the model to allow higher winding numbers, finite-temperature topological regimes sandwiched between trivial regimes at high and low temperatures may emerge.

cond-mat.mes-hall↗

arXiv2021

On the method of differentiation and its application to asymptotics for the heat kernel on H-type groups

The aim of this note is twofold. The first one is to find conditions on the asymptotic sequence which ensures differentiation of a general asymptotic expansion with respect to it. Our method results from the classical one but generalizes it. As an application, our second aim is to give sharp asymptotic estimates at infinity of the heat kernel on H-type groups by the method of differentiation provided we have the result of the isotropic Heisenberg groups.

math.AP↗

arXiv2021

Publicly Auditable MPC-as-a-Service with succinct verification and universal setup

In recent years, multiparty computation as a service (MPCaaS) has gained popularity as a way to build distributed privacy-preserving systems. We argue that for many such applications, we should also require that the MPC protocol is publicly auditable, meaning that anyone can check the given computation is carried out correctly -- even if the server nodes carrying out the computation are all corrupt. In a nutshell, the way to make an MPC protocol auditable is to combine an underlying MPC protocol with verifiable computing proof (in particular, a SNARK). Building a general-purpose MPCaaS from existing constructions would require us to perform a costly "trusted setup" every time we wish to run a new or modified application. To address this, we provide the first efficient construction for auditable MPC that has a one-time universal setup. Despite improving the trusted setup, we match the state-of-the-art in asymptotic performance: the server nodes incur a linear computation overhead and constant round communication overhead compared to the underlying MPC, and the audit size and verification are logarithmic in the application circuit size. We also provide an implementation and benchmarks that support our asymptotic analysis in example applications. Furthermore, compared with existing auditable MPC protocols, besides offering a universal setup our construction also has a 3x smaller proof, 3x faster verification time and comparable prover time.

cs.CR↗

arXiv2021

A new mathematical model for dispersion of Rayleigh wave and a machine learning based inversion solver

In this work, by introducing the seismic impedance tensor we propose a new Rayleigh wave dispersion function in a homogeneous and layered medium of the Earth, which provides an efficient way to compute the dispersion curve -- a relation between the frequencies and the phase velocities. With this newly established forward model, based on the Mixture Density Networks (MDN) we develop a machine learning based inversion approach, named as FW-MDN, for the problem of estimating the S-wave velocity from the dispersion curves. The method FW-MDN deals with the non-uniqueness issue encountered in studies that invert dispersion curves for crust and upper mantle models and attains a satisfactory performance on the dataset with various noise structure. Numerical simulations are performed to show that the FW-MDN possesses the characteristics of easy calculation, efficient computation, and high precision for the model characterization.

math.NA↗

arXiv2021

Improving Longer-range Dialogue State Tracking

Dialogue state tracking (DST) is a pivotal component in task-oriented dialogue systems. While it is relatively easy for a DST model to capture belief states in short conversations, the task of DST becomes more challenging as the length of a dialogue increases due to the injection of more distracting contexts. In this paper, we aim to improve the overall performance of DST with a special focus on handling longer dialogues. We tackle this problem from three perspectives: 1) A model designed to enable hierarchical slot status prediction; 2) Balanced training procedure for generic and task-specific language understanding; 3) Data perturbation which enhances the model's ability in handling longer conversations. We conduct experiments on the MultiWOZ benchmark, and demonstrate the effectiveness of each component via a set of ablation tests, especially on longer conversations.

cs.CL↗

arXiv2021

A unified construction of all-speed HLL-type schemes for hypersonic heating computations

In this paper, a unified framework to develop all-speed HLL-type schemes for hypersonic heating computations is constructed. Such a unified construction method combines two effective improving techniques: a shock robustness improvement and a low-Mach number fix. It is implemented by properly modifying the approximate solutions of the local Riemann problem in the HLL framework, resulting in two all-speed HLL-type schemes, namely ASHLLC and ASHLLEM solvers. Results from both numerical analysis and experiments demonstrate that the newly proposed schemes not only preserve desirable properties of their original versions, but are also able to provide accurate and robust solutions for complex flows ranging from low-Mach number incompressible to hypersonic compressible regimes. Thus, both the ASHLLC and ASHLLEM schemes can be used as reliable methods for hypersonic heating computations.

cs.CE↗

arXiv2021

Sub-Riemannian geometry on some step-two Carnot groups

This paper is a continuation of the previous work of the first author. We characterize a class of step-two groups introduced in \cite{Li19}, saying GM-groups, via some basic sub-Riemannian geometric properties, including the squared Carnot-Carathéodory distance, the cut locus, the classical cut locus, the optimal synthesis, etc. Also, the shortest abnormal set can be exhibited easily in such situation. Some examples of such groups are step-two groups of corank $2$, of Kolmogorov type, or those associated to quadratic CR manifolds. As a byproduct, the main goal in \cite{BBG12} is achieved from the setting of step-two groups of corank $2$ to all possible step-two groups, via a completely different method. A partial answer to the open questions \cite[(29)-(30)]{BR19} is provided in this paper as well. Moreover, we provide a entirely different proof, based yet on \cite{Li19}, for the Gaveau-Brockett optimal control problem on the free step-two Carnot group with three generators. As a byproduct, we provide a new and independent proof for the main results obtained in \cite{MM17}, namely, the exact expression of $d(g)^2$ for $g$ belonging to the classical cut locus of the identity element $o$, as well as the determination of all shortest geodesics joining $o$ to such $g$.

math.DG↗

arXiv2021

Estimating Adsorption Isotherm Parameters in Chromatography via a Virtual Injection Promoting Feed-forward Neural Network

The means to obtain the adsorption isotherms is a fundamental open problem in competitive chromatography. A modern technique of estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides with actual experimental results. However, this identification process is usually ill-posed in the sense that the small noise in the measured response can lead to a large fluctuation in the estimated quantity of adsorption isotherms. The conventional mathematical method of solving this problem is the variational regularization, which is formulated as a non-convex minimization problem with a regularized objective functional. However, in this method, the choice of regularization parameter and the design of a convergent solution algorithm are quite difficult in practice. Moreover, due to the restricted number of injection profiles in experiments, the types of measured data are extremely limited, which may lead to a biased estimation. In order to overcome these difficulties, in this paper, we develop a new inversion method -- the Virtual Injection Promoting Feed-forward Neural Network (VIP-FNN). In this approach, the training data contain various types of artificial injections and synthetic noisy measurement at outlet, generated by a conventional physics model -- a time-dependent convection-diffusion system. Numerical experiments with both artificial and real data from laboratory experiments show that the proposed VIP-FNN is an efficient and robust algorithm.

eess.SP↗