Department of Applied Mathematics

Department of Applied Maths
Mathematics Building, Block B
Xi'an Jiaotong-Liverpool University
111 Ren'ai Road Suzhou Dushu Lake Science and Education Innovation District , Suzhou Industrial Park
Suzhou,Jiangsu Province,P. R. China,215123

1. Fabricated Pictures Detection with Graph Matching


Source:ACM International Conference Proceeding Series,2020,Vol.

Abstract:Fabricating experimental pictures in research work is a serious academic misconduct, which should better be detected in the reviewing process. However, due to large number of submissions, the detection whether a picture is fabricated or reused is laborious for reviewers, and sometimes is unrecognizable with human eyes. A tool for detecting similarity between images may help to alleviate this problem. Some methods based on local feature points matching work for most of the time, while these methods may result in mess of matchings due to ignorance of global relationship between features. We present a framework to detect similar, or perhaps fabricated, pictures with the graph matching techniques. A new iterative method is proposed, and experiments show that such a graph matching technique is better than the methods based only on local features for some cases.
2. Advances of RRAM Devices: Resistive Switching Mechanisms, Materials and Bionic Synaptic Application

Author:Shen, ZJ;Zhao, C;Qi, YF;Xu, WY;Liu, YN;Mitrovic, IZ;Yang, L;Zhao, CZ


Abstract:Resistive random access memory (RRAM) devices are receiving increasing extensive attention due to their enhanced properties such as fast operation speed, simple device structure, low power consumption, good scalability potential and so on, and are currently considered to be one of the next-generation alternatives to traditional memory. In this review, an overview of RRAM devices is demonstrated in terms of thin film materials investigation on electrode and function layer, switching mechanisms and artificial intelligence applications. Compared with the well-developed application of inorganic thin film materials (oxides, solid electrolyte and two-dimensional (2D) materials) in RRAM devices, organic thin film materials (biological and polymer materials) application is considered to be the candidate with significant potential. The performance of RRAM devices is closely related to the investigation of switching mechanisms in this review, including thermal-chemical mechanism (TCM), valance change mechanism (VCM) and electrochemical metallization (ECM). Finally, the bionic synaptic application of RRAM devices is under intensive consideration, its main characteristics such as potentiation/depression response, short-/long-term plasticity (STP/LTP), transition from short-term memory to long-term memory (STM to LTM) and spike-time-dependent plasticity (STDP) reveal the great potential of RRAM devices in the field of neuromorphic application.
3. Minimum and Maximum Principle Sufficiency for a Nonsmooth Variational Inequality

Author:Wu, ZL;Lu, Y


Abstract:In this paper, the minimum and maximum principle sufficiency properties for a nonsmooth variational inequality problem (NVIP) are studied. We discuss the relationship among the solution set of an NVIP and those defined by its dual problem and relevant gap functions. For a pseudomonotone NVIP, the weaker sharpness of its solution set has been shown to be sufficient for it to have minimum principle sufficiency property. As special cases, pseudomonotonicity(*) and pseudomonotonicity(+) of the relevant bifunction have been characterized, from which the minimum and maximum principle sufficiency properties have also been characterized.
4. Knowledge Discovery and Recommendation With Linear Mixed Model

Author:Chen, ZY;Zhu, SX;Niu, Q;Zuo, TY

Source:IEEE ACCESS,2020,Vol.8

Abstract:We give a concise tutorial on knowledge discovery with linear mixed model in movie recommendation. The versatility of mixed effects model is well explained. Commonly used methods for parameter estimation, confidence interval estimate and evaluation criteria for model selection are briefly reviewed. Mixed effects models produce sound inference based on a series of rigorous analysis. In particular, we analyze millions of movie rating data with LME4 R package and find solid evidences for a general social behavior: the young tend to be more censorious than senior people when evaluating the same object. Such a social behavior phenomenon can be used in recommender systems and business data analysis.
5. Full-shipload tramp ship routing and scheduling with variable speeds

Author:Wen, M;Ropke, S;Petersen, HL;Larsen, R;Madsen, OBG


Abstract:This paper investigates the simultaneous optimization problem of routing and sailing speed in the context of full-shipload tramp shipping. In this problem, a set of cargoes can be transported from their load to discharge ports by a fleet of heterogeneous ships of different speed ranges and load-dependent fuel consumption. The objective is to determine which orders to serve and to find the optimal route for each ship and the optimal sailing speed on each leg of the route so that the total profit is maximized. The problem originated from a real-life challenge faced by a Danish tramp shipping company in the tanker business. To solve the problem, a three-index mixed integer linear programming formulation as well as a set packing formulation is presented. A novel Branch-and-Price algorithm with efficient data preprocessing and heuristic column generation is proposed. The computational results on the test instances generated from real-life data show that the heuristic provides optimal solutions for small test instances and near-optimal solutions for larger test instances in a short running time. The effects of speed optimization and the sensitivity of the solutions to the fuel price change are analyzed. It is shown that speed optimization can improve the total profit by 16%% on average and the fuel price has a significant effect on the average sailing speed and total profit. (C) 2015 Elsevier Ltd. All rights reserved.
6. Orthonormal shifted discrete Chebyshev polynomials: Application for a fractal-fractional version of the coupled Schrodinger-Boussinesq system

Author:Heydari, MH;Razzaghi, M;Avazzadeh, Z


Abstract:In this paper, a novel fractal-fractional derivative operator with Mittag-Leffler function as its kernel is introduced. Using this differentiation, the fractal-fractional model of the coupled nonlinear SchrodingerBoussinesq system is defined. The orthonormal shifted discrete Chebyshev polynomials are generated and used for constructing a computational matrix method to solve the defined system. In the established method, using the matrices of the ordinary and fractal-fractional differentiations of these polynomials, the fractal-fractional system transformed into a system of algebraic equations, which is solved readily. Practicability and precision of the method are examined by solving two numerical examples. (c) 2020 Elsevier Ltd. All rights reserved.
7. Optimal control of hyperthermia thermal damage based on tumor configuration

Author:Roohi, R;Heydari, MH;Avazzadeh, Z

Source:RESULTS IN PHYSICS,2021,Vol.23

Abstract:Improvement and optimization of hyperthermia as one of the most effective and conventional cancer treatments have been tackled by many researchers in recent years. The main benchmark for hyperthermia treatment is to elevate the cancerous tissue temperature to a specified level to initiate damage or ablation and simultaneously to prevent any irreversible thermal damage to the surrounding healthy cells. Therefore, the heat source pattern for hyperthermia treatment should be adjusted according to the distribution of cancerous cells. To do this, in the present study the fractional bioheat equation with unknown heat source term is implemented. Two different hyperthermia scenarios with single and dual tumors are considered and the appropriate damage level at both healthy and cancerous tissues is planned according to the Arrhenius model. Moreover, the optimal control criterion is set to simultaneously produce the goal temperature level and minimize the thermal power consumption. The mentioned task is accomplished by the definition of a priority coefficient as a weight function which determines whether the establishment of desired thermal field or the reduction of applied thermal power is more important. Based on the results, the optimal control approach can precisely determine the heat source distribution for single and dual tumor cases (with 1.03 and 0.13%% deviation error, respectively). Whereas, by shifting the priority to the minimization of applied energy, up to 23.1 and 38.7%% deviation is observed in formation of the desired temperature field (while the overall cost function is minimized). In order to investigate the numerical results, a computational method based on the Legendre cardinal functions is proposed. The main advantage of the proposed method is that it transforms solving such fractional models into solving systems of algebraic equations which greatly simplify the problem.
8. Profile Inference from Heterogeneous Data Fundamentals and New Trends

Author:Lu, X;Zhu, SX;Niu, Q;Chen, ZY


Abstract:One of the essential steps in most business is to understand customers' preferences. In a data-centric era, profile inference is more and more relaying on mining increasingly accumulated and usually anonymous (protected) data. Personalized profile (preferences) of an anonymous user can even be recovered by some data technologies. The aim of the paper is to review some commonly used information retrieval techniques in recommendation systems and introduce new trends in heterogeneous information network based and knowledge graph based approaches. Then business developers can get some insights on what kind of data to collect as well as how to store and manage them so that better decisions can be made after analyzing the data and extracting the needed information.
9. Equivalent Extensions to Caristi-Kirk's Fixed Point Theorem, Ekeland's Variational Principle, and Takahashi's Minimization Theorem

Author:Wu, ZL


Abstract:With a recent result of Suzuki (2001) we extend Caristi-Kirk's fixed point theorem, Ekeland's variational principle, and Takahashi's minimization theorem in a complete metric space by replacing the distance with a tau-distance. In addition, these extensions are shown to be equivalent. When the tau-distance is l.s.c. in its second variable, they are applicable to establish more equivalent results about the generalized weak sharp minima and error bounds, which are in turn useful for extending some existing results such as the petal theorem.
10. A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations

Author:Benzi, M;Ng, M;Niu, Q;Wang, Z


Abstract:In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo [7]. Numerical results for a variety of finite element discretizations of both steady and unsteady incompressible flow problems indicate very good behavior of the RDF preconditioner with respect to both mesh size and viscosity. (C) 2011 Elsevier Inc. All rights reserved.
11. Symmetric Sweeping Algorithms for Overlaps of Quadrilateral Meshes of the Same Connectivity

Author:Xu, XH;Zhu, SX

Source:COMPUTATIONAL SCIENCE - ICCS 2018, PT III,2018,Vol.10862

Abstract:We propose a method to calculate intersections of two admissible quadrilateral meshes of the same connectivity. The global quadrilateral polygons intersection problem is reduced to a local problem that how an edge intersects with a local frame which consists 7 connected edges. A classification on the types of intersection is presented. By symmetry, an alternative direction sweep algorithm halves the searching space. It reduces more than 256 possible cases of polygon intersection to 34 (17 when considering symmetry) programmable cases of edge intersections. Besides, we show that the complexity depends on how the old and new mesh intersect.
12. A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics

Author:Nikan, O;Avazzadeh, Z


Abstract:This paper develops a numerical approach for finding the approximate solution of the Sobolev model. This model describes many natural processes, such as thermal conduction for different media and fluid evolution in soils and rocks. The proposed method approximates the unknown solution with the help of two main stages. At a first stage, the time discretization is performed by means of a second-order finite difference procedure. At a second stage, the space discretization is accomplished using the local radial basis function partition of unity collocation method based on the finite difference (LRBF-PUM-FD). The major disadvantage of global techniques is the high computational burden of solving large linear systems. The LRBF-PUM-FD significantly sparsifies the linear system and reduces the computational burden, while simultaneously maintaining a high accuracy level. The time-discrete formulation is studied in terms of the stability and convergence analysis via the energy method. Three examples are illustrated to verify the efficiency and accuracy of the method. (C) 2021 Elsevier Inc. All rights reserved.
13. Spectral analysis of the generalized shift-splitting preconditioned saddle point problem

Author:Ren, ZR;Cao, Y;Niu, Q


Abstract:A shift-splitting preconditioner was recently proposed for saddle point problems, which is based on a generalized shift-splitting of the saddle point matrix. We provide a new analysis to prove that the corresponding shift-splitting iteration method is unconditional convergent. To further show the efficiency of the shift-splitting preconditioner, the eigenvalue distribution of the shift-splitting preconditioned saddle point matrix is investigated. We show that all eigenvalues having nonzero imaginary parts are located in an intersection of two circles and all real eigenvalues are located in a positive interval. Numerical examples are given to confirm our theoretical results. (C) 2016 Elsevier B.V. All rights reserved.
14. Extension of Talenti's Inequality and Maximum Values Relative to Rearrangement Classes

Author:Emamizadeh, B;Liu, YC;Porru, G


Abstract:The article starts by revisiting and extending the Talenti's inequality where the sharpness of the extended inequality is also addressed. The process leading to the extension comprises two steps. First, an observation that the Talenti's inequality indeed can be formulated in terms of a rearrangement class. Second, proving that the inequality holds even when the rearrangement class is replaced by a much bigger (modulo trivial cases) set namely an appropriate closure of the class. The article then continues to introduce and explore a related maximization problem, associated to the classical Poisson equation, where the admissible set is the class of rearrangements of a given function. The article briefly explains the physical interest in this optimization problem. The existence of optimal solutions is proved and the optimality conditions they satisfy are explicitly derived. The particular case where the rearrangement class is built out of a characteristic function is also discussed.
15. Toward self-powered photodetection enabled by triboelectric nanogenerators

Author:Wen, Z;Fu, JJ;Han, L;Liu, YN;Peng, MF;Zheng, L;Zhu, YY;Sun, XH;Zi, YL


Abstract:Photodetectors have been demonstrated to have broad applications in optical communication, environmental protection, biomedical monitoring, and so on. However, the applications of these photodetectors face great challenges due to the difficulties in powering these vastly distributed detectors and their limited photoresponsivity. At the same time, the invention of triboelectric nanogenerators (TENGs) provides a novel way for generating a high-voltage low-current power supply with well-controllable output, making a promising approach to trigger photodetection. This review article summarizes the existing research work on combining TENGs with photodetectors through four different configurations. These research studies achieved self-powered or active photodetectors enabled by TENGs, explored the novel photodetection mechanisms, and demonstrated TENG output for enhancing the photoresponsivity, which will promote the relevant research toward self-powered photodetection with greatly improved performance.
16. Daily Passenger Volume Prediction in the Bus Transportation System using ARIMAX Model with Big Data


Source:Proceedings - 2020 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery, CyberC 2020,2020,Vol.

Abstract:© 2020 IEEE. Based on the real data collected from the bus IC card payment database, firstly a time series of daily passenger volumes in a given bus line was obtained and then two kinds of time series models, ARMA with quadratic trend and ARIMAX, were proposed to do the prediction. The experiment results show that both models can make prediction effectively and especially ARIMAX model, which takes daily temperatures in to consideration, performs better in terms of prediction accuracy.
17. Self-driven photodetection based on impedance matching effect between a triboelectric nanogenerator and a MoS2 nanosheets photodetector

Author:Han, L;Peng, MF;Wen, Z;Liu, YN;Zhang, Y;Zhu, QQ;Lei, H;Liu, SN;Zheng, L;Sun, XH;Li, HX

Source:NANO ENERGY,2019,Vol.59

Abstract:Constructing electronic systems without an external power source is urgently required toward self-powered photodetection. In this work, we proposed a self-driven photodetection system with a MoS2 nanosheets photodetector as light intensity sensor, a vertical contact-separate mode triboelectric nanogenerator (CS-TENG) as power source, and several LEDs as alarm. The MoS2 based planar photodetector was fabricated by conventional photolithography technique and lift-off process. It is highly sensitive for visible light illumination with high current on-off ratio and excellent reproducibility characteristics under light on-off switching. When conjuncting these functional devices, the induced output voltage of the CS-TENG is tuned by the load resistance of the photodetector, which is responded to the light intensity. The mechanism can be ascribed to the impedance matching effect between specific output characteristics of TENG and working status of photodetector. By adding a Zener diode acts as a voltage regulator, the self-driven renders the voltage and current varying from 1.58 to 20.60 V and 0.06-4.78 mu A in a range of light intensity from 0 to 3.19 W/m(2), respectively. Finally, it is demonstrated that the output of CS-TENG varies with the variable working states of the MoS(2 )photodetector and then accurately reflects on the lighted number of LEDs.
18. Generalized Bernoulli Polynomials: Solving Nonlinear 2D Fractional Optimal Control Problems

Author:Hassani, H;Machado, JAT;Avazzadeh, Z;Naraghirad, E;Dahaghin, MS


Abstract:This work develops an optimization method based on a new class of basis function, namely the generalized Bernoulli polynomials (GBP), to solve a class of nonlinear 2-dim fractional optimal control problems. The problem is generated by nonlinear fractional dynamical systems with fractional derivative in the Caputo type and the Goursat-Darboux conditions. First, we use the GBP to approximate the state and control variables with unknown coefficients and parameters. Afterwards, we substitute the obtained values for the variables and parameters in the objective function, nonlinear fractional dynamical system and Goursat-Darboux conditions. The 2-dim Gauss-Legendre quadrature rule together with a fractional operational matrix construct a constrained problem, that is solved by the Lagrange multipliers method. The convergence of the GBP method is proved and its efficiency is demonstrated by several examples.
19. Absolute linear instability in laminar and turbulent gas-liquid two-layer channel flow

Author:Naraigh, LO;Spelt, PDM;Shaw, SJ


Abstract:We study two-phase stratified flow where the bottom layer is a thin laminar liquid and the upper layer is a fully developed gas flow. The gas flow can be laminar or turbulent. To determine the boundary between convective and absolute instability, we use Orr-Sommerfeld stability theory, and a combination of linear modal analysis and ray analysis. For turbulent gas flow, and for the density ratio r = 1000, we find large regions of parameter space that produce absolute instability. These parameter regimes involve viscosity ratios of direct relevance to oil and gas flows. If, instead, the gas layer is laminar, absolute instability persists for the density ratio r = 1000, although the convective/absolute stability boundary occurs at a viscosity ratio that is an order of magnitude smaller than in the turbulent case. Two further unstable temporal modes exist in both the laminar and the turbulent cases, one of which can exclude absolute instability. We compare our results with an experimentally determined flow-regime map, and discuss the potential application of the present method to nonlinear analyses.
20. Goodness of fit test for almost cyclostationary processes

Author:Mahmoudi, MR;Heydari, MH;Avazzadeh, Z;Pho, KH


Abstract:This paper is devoted to present a goodness of fit test for discrete-time almost cyclostationary models. The main strategy is based on the spectral support estimation and the application of multiple testing. The results of applying the presented method on simulated and real datasets confirm that the introduced approach acts well in view of power study. Published by Elsevier Inc.
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