arXiv subjects

Yu Du

Publications and source records attributed to Yu Du.

67 records · Page 4Linked to original sources

arXiv2020

Coexistence of Ferromagnetism and Topology by Charge Carrier Engineering in intrinsic magnetic topological insulator MnBi4Te7

Intrinsic magnetic topological insulators (MTIs) MnBi2Te4 and MnBi2Te4/(Bi2Te3)n are expected to realize the high-temperature quantum anomalous Hall effect (QAHE) and dissipationless electrical transport. Extensive efforts have been made on this field but there is still lack of ideal MTI candidate with magnetic ordering of ferromagnetic (FM) ground state. Here, we demonstrate a MTI sample of Mn(Bi0.7Sb0.3)4Te7 which holds the coexistence of FM ground state and topological non-triviality. The dramatic modulation of the magnetism is induced by a charge carrier engineering process by the way of Sb substitution in MnBi4Te7 matrix with AFM ordering. The evolution of magnetism in Mn(Bi1-xSbx)4Te7 is systematically investigated by magnetic measurements and theoretical calculations. The clear topological surface states of the FM sample of x = 0.3 are also verified by angle-resolved photoemission spectra. We also aware that the FM sample of x = 0.3 is close to the charge neutral point. Therefore, the demonstration of intrinsic FM-MTI of Mn(Bi0.7Sb0.3)4Te7 in this work sheds light to the further studies of QAHE realization and optimizations.

cond-mat.mtrl-sci↗

arXiv2020

Zero-Shot Heterogeneous Transfer Learning from Recommender Systems to Cold-Start Search Retrieval

Many recent advances in neural information retrieval models, which predict top-K items given a query, learn directly from a large training set of (query, item) pairs. However, they are often insufficient when there are many previously unseen (query, item) combinations, often referred to as the cold start problem. Furthermore, the search system can be biased towards items that are frequently shown to a query previously, also known as the 'rich get richer' (a.k.a. feedback loop) problem. In light of these problems, we observed that most online content platforms have both a search and a recommender system that, while having heterogeneous input spaces, can be connected through their common output item space and a shared semantic representation. In this paper, we propose a new Zero-Shot Heterogeneous Transfer Learning framework that transfers learned knowledge from the recommender system component to improve the search component of a content platform. First, it learns representations of items and their natural-language features by predicting (item, item) correlation graphs derived from the recommender system as an auxiliary task. Then, the learned representations are transferred to solve the target search retrieval task, performing query-to-item prediction without having seen any (query, item) pairs in training. We conduct online and offline experiments on one of the world's largest search and recommender systems from Google, and present the results and lessons learned. We demonstrate that the proposed approach can achieve high performance on offline search retrieval tasks, and more importantly, achieved significant improvements on relevance and user interactions over the highly-optimized production system in online experiments.

cs.LG↗

arXiv2020

Understanding and adjusting the selection bias from a proof-of-concept study to a more confirmatory study

It has long been noticed that the efficacy observed in small early phase studies is generally better than that observed in later larger studies. Historically, the inflation of the efficacy results from early proof-of-concept studies is either ignored, or adjusted empirically using a frequentist or Bayesian approach. In this article, we systematically explained the underlying reason for the inflation of efficacy results in small early phase studies from the perspectives of measurement error models and selection bias. A systematic method was built to adjust the early phase study results from both frequentist and Bayesian perspectives. A hierarchical model was proposed to estimate the distribution of the efficacy for a portfolio of compounds, which can serve as the prior distribution for the Bayesian approach. We showed through theory that the systematic adjustment provides an unbiased estimator for the true mean efficacy for a portfolio of compounds. The adjustment was applied to paired data for the efficacy in early small and later larger studies for a set of compounds in diabetes and immunology. After the adjustment, the bias in the early phase small studies seems to be diminished.

stat.ME↗

arXiv2020

Quantum Bridge Analytics II: Network Optimization and Combinatorial Chaining for Asset Exchange

Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys key elements of Quantum Bridge Analytics and its applications. Part I focused on the Quadratic Unconstrained Binary Optimization (QUBO) model which is presently the most widely applied optimization model in the quantum computing area, and which unifies a rich variety of combinatorial optimization problems. Part II (the present paper) examines an application that augments the use of QUBO models, by disclosing a context for coordinating QUBO solutions through a model we call the Asset Exchange Problem (AEP). Solutions to the AEP enable individuals or institutions to take fuller advantage of solutions to their QUBO models by exchanges of assets that benefit all participants. Such exchanges are generated by a combination of two optimization technologies, one grounded in network optimization and one based on a new metaheuristic optimization approach called combinatorial chaining. This combination provides a flexibility to solve AEP variants that open the door to additional links to quantum computing applications and additional applications via the Quantum Bridge Analytics perspective. We show how this modeling and solution capability gives rise to an Asset Exchange Technology that embraces a broad range of financial, industrial, scientific and social settings. Examples are presented that show the nature of these processes from a tutorial perspective.

cs.DM↗

arXiv2019

A Tutorial on Formulating and Using QUBO Models

The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and has become a subject of study in neuromorphic computing. Through these connections, QUBO models lie at the heart of experimentation carried out with quantum computers developed by D-Wave Systems and neuromorphic computers developed by IBM. Computational experience is being amassed by both the classical and the quantum computing communities that highlights not only the potential of the QUBO model but also its effectiveness as an alternative to traditional modeling and solution methodologies. This tutorial discloses the basic features of the QUBO model that give it the power and flexibility to encompass the range of applications that have thrust it onto center stage of the optimization field. We show how many different types of constraining relationships arising in practice can be embodied within the "unconstrained" QUBO formulation in a very natural manner using penalty functions, yielding exact model representations in contrast to the approximate representations produced by customary uses of penalty functions. Each step of generating such models is illustrated in detail by simple numerical examples, to highlight the convenience of using QUBO models in numerous settings. We also describe recent innovations for solving QUBO models that offer a fertile avenue for integrating classical and quantum computing and for applying these models in machine learning.

cs.DS↗

arXiv2019

A pure source transfer domain decomposition method for Helmholtz equations in unbounded domain

We propose a pure source transfer domain decomposition method (PSTDDM) for solving the truncated perfectly matched layer (PML) approximation in bounded domain of Helmholtz scattering problem. The method is a modification of the STDDM proposed by [Z. Chen and X. Xiang, SIAM J. Numer. Anal., 51 (2013), pp. 2331--2356]. After decomposing the domain into $N$ non-overlapping layers, the STDDM is composed of two series steps of sources transfers and wave expansions, where $N-1$ truncated PML problems on two adjacent layers and $N-2$ truncated half-space PML problems are solved successively. While the PSTDDM consists merely of two parallel source transfer steps in two opposite directions, and in each step $N-1$ truncated PML problems on two adjacent layers are solved successively. One benefit of such a modification is that the truncated PML problems on two adjacent layers can be further solved by the PSTDDM along directions parallel to the layers. And therefore, we obtain a block-wise PSTDDM on the decomposition composed of $N^2$ squares, which reduces the size of subdomain problems and is more suitable for large-scale problems. Convergences of both the layer-wise PSTDDM and the block-wise PSTDDM are proved for the case of constant wave number. Numerical examples are included to show that the PSTDDM gives good approximations to the discrete Helmholtz equations with constant wave numbers and can be used as an efficient preconditioner in the preconditioned GMRES method for solving the discrete Helmholtz equations with constant and heterogeneous wave numbers.

math.NA↗

arXiv2018

SQUAREM: An R Package for Off-the-Shelf Acceleration of EM, MM and Other EM-like Monotone Algorithms

We discuss R package SQUAREM for accelerating iterative algorithms which exhibit slow, monotone convergence. These include the well-known expectation-maximization algorithm, majorize-minimize (MM), and other EM-like algorithms such as expectation conditional maximization, and generalized EM algorithms. We demonstrate the simplicity, generality, and power of SQUAREM through a wide array of applications of EM/MM problems, including binary Poisson mixture, factor analysis, interval censoring, genetics admixture, and logistic regression maximum likelihood estimation (an MM problem). We show that SQUAREM is easy to apply, and can accelerate any fixed-point, smooth, contraction mapping with linear convergence rate. Squared iterative scheme (Squarem) algorithm provides significant speed-up of EM-like algorithms. The margin of the advantage for Squarem is especially huge for high-dimensional problems or when EM step is relatively time-consuming to evaluate. Squarem can be used off-the-shelf since there is no need for the user to tweak any control parameters to optimize performance. Given its remarkable ease of use, Squarem may be considered as a default accelerator for slowly converging EM-like algorithms. All the comparisons of CPU computing time in the paper are made on a quad-core 2.3 GHz Intel Core i7 Mac computer. R Package SQUAREM can be downloaded at https://cran.r-project.org/web/packages/SQUAREM/index.html.

stat.CO↗

arXiv2017

Superconvergence analysis of linear FEM based on the polynomial preserving recovery and Richardson extrapolation for Helmholtz equation with high wave number

We study superconvergence property of the linear finite element method with the polynomial preserving recovery (PPR) and Richardson extrapolation for the two dimensional Helmholtz equation. The $H^1$-error estimate with explicit dependence on the wave number $k$ {is} derived. First, we prove that under the assumption $k(kh)^2\leq C_0$ ($h$ is the mesh size) and certain mesh condition, the estimate between the finite element solution and the linear interpolation of the exact solution is superconvergent under the $H^1$-seminorm, although the pollution error still exists. Second, we prove a similar result for the recovered gradient by PPR and found that the PPR can only improve the interpolation error and has no effect on the pollution error. Furthermore, we estimate the error between the finite element gradient and recovered gradient and discovered that the pollution error is canceled between these two quantities. Finally, we apply the Richardson extrapolation to recovered gradient and demonstrate numerically that PPR combined with the Richardson extrapolation can reduce the interpolation and pollution errors simultaneously, and therefore, leads to an asymptotically exact {\it a posteriori} error estimator. All theoretical findings are verified by numerical tests.

math.NA↗

arXiv2016

Superconvergence analysis of DG-FEM based on the polynomial preserving recovery for Helmholtz equation with high wave number

We study superconvergence property of the linear discontinuous Galerkin finite element method with the polynomial preserving recovery (PPR) and Richardson extrapolation for the two dimensional Helmholtz equation. The error estimate with explicit dependence on the wave number $k$, the penalty parameter $μ$ and the mesh condition parameter $α$ is derived. First, we prove that under the assumption $k(kh)^2\leq C_0$ ($h$ is the mesh size) and certain mesh condition, the estimate between the finite element solution and the linear interpolation of the exact solution is superconvergent under the $\norme{\cdot}$-seminorm. Second, we prove a superconvergence result for the recovered gradient by PPR. Furthermore, we estimate the error between the finite element gradient and recovered gradient, which motivate us to define the a posteriori error estimator. Finally, Some numerical examples are provided to confirm the theoretical results of superconvergence analysis. All theoretical findings are verified by numerical tests.

math.NA↗

arXiv2016

Rate of Convergence of the Bundle Method

We prove that the bundle method for nonsmooth optimization achieves solution accuracy $\varepsilon$ in at most $\mathcal{O}\big(\ln(1/\varepsilon)/\varepsilon\big)$ iterations, if the function is strongly convex. The result is true for the versions of the method with multiple cuts and with cut aggregation.

math.OC↗

arXiv2016

Selective Linearization For Multi-Block Convex Optimization

We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple proximal steps. The algorithm is a form of multiple operator splitting in which the order of processing partial functions is not fixed, but rather determined in the course of calculations. Global convergence is proved and estimates of the convergence rate are derived. Specifically, the number of iterations needed to achieve solution accuracy $\varepsilon$ is of order $\mathcal{O}\big(\ln(1/\varepsilon)/\varepsilon\big)$. We also illustrate the operation of the algorithm on structured regularization problems.

math.OC↗

arXiv2014

Preasymptotic error analysis of higher order FEM and CIP-FEM for Helmholtz equation with high wave number

A preasymptotic error analysis of the finite element method (FEM) and some continuous interior penalty finite element method (CIP-FEM) for Helmholtz equation in two and three dimensions is proposed. $H^1$- and $L^2$- error estimates with explicit dependence on the wave number $k$ are derived. In particular, it is shown that if $k^{2p+1}h^{2p}$ is sufficiently small, then the pollution errors of both methods in $H^1$-norm are bounded by $O(k^{2p+1}h^{2p})$, which coincides with the phase error of the FEM obtained by existent dispersion analyses on Cartesian grids, where $h$ is the mesh size, $p$ is the order of the approximation space and is fixed. The CIP-FEM extends the classical one by adding more penalty terms on jumps of higher (up to $p$-th order) normal derivatives in order to reduce efficiently the pollution errors of higher order methods. Numerical tests are provided to verify the theoretical findings and to illustrate great capability of the CIP-FEM in reducing the pollution effect.

math.NA↗

arXiv2005

On Graded Bialgebra Deformations

We introduce the graded bialgebra deformations, which explain Andruskiewitsch-Schneider's liftings method. We also relate this graded bialgebra deformation with the corresponding graded bialgebra cohomology groups, which is the graded version of the one due to Gerstenhaber-Schack.

math.QA↗