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Papers - PENG Linyu

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The Effect of Accuracy of Initial Velocity Discretisations on Discrete Energy in Variational Integration

M Gunji, Y Ono, L Peng

Proceedings of the IUTAM Symposium on Nonlinear Dynamics for Design of … (Springer Cham) 88 - 98 2025.01

Euler--Poincar\'e reduction and the Kelvin--Noether theorem for discrete mechanical systems with advected parameters and additional dynamics

Y Ono, S Fiori, L Peng

arXiv preprint arXiv:2501.12940 2025

Reconstruction of Graph Signals on Complex Manifolds with Kernel Methods

Y Zhang, L Peng, BZ Li

arXiv preprint arXiv:2505.15202 2025

Neural bidomain model for multidimensional ephaptic coupling of neural spike propagation along myelinated fiber bundles with the nodes of Ranvier

S Chun, L Peng, HJ Park

bioRxiv 2024.12

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半離散方程式の対称性と群不変解

彭林玉，富田繁，郡司士

Jxiv, JST プレプリントサーバ 2024.11

半離散方程式（微分差分方程式ともいう）においては，連続独立変数と離散独立変数が非可換のため，対称性とならない非内在（non-intrinsic）（または不規則（irregular））な変換が生じるという問題があった．本論文では，この問題の解決方法を論じるとともに，半離散方程式における対称性理論について紹介する．具体例として，戸田型，ヴォルテラ型，5 点の伊藤・成田・ボゴヤヴレンスキー方程式などのリー点対称性（Lie point symmetry）を求め，群不変解（group-invariant solution）を導出する．

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Discrete Dirac structures and discrete Lagrange--Dirac dynamical systems in mechanics

Linyu Peng, Hiroaki Yoshimura

arXiv preprint arXiv:2411.09530 2024.11

In this paper, we propose the concept of $(\pm)$-discrete Dirac structures
over a manifold, where we define $(\pm)$-discrete two-forms on the manifold and
incorporate discrete constraints using $(\pm)$-finite difference maps.
Specifically, we develop $(\pm)$-discrete induced Dirac structures as discrete
analogues of the induced Dirac structure on the cotangent bundle over a
configuration manifold, as described by Yoshimura and Marsden (2006). We
demonstrate that $(\pm)$-discrete Lagrange--Dirac systems can be naturally
formulated in conjunction with the $(\pm)$-induced Dirac structure on the
cotangent bundle. Furthermore, we show that the resulting equations of motion
are equivalent to the $(\pm)$-discrete Lagrange--d'Alembert equations proposed
in Cort\'es and Mart\'inez (2001) and McLachlan and Perlmutter (2006). We also
clarify the variational structures of the discrete Lagrange--Dirac dynamical
systems within the framework of the $(\pm)$-discrete
Lagrange--d'Alembert--Pontryagin principle. Finally, we validate the proposed
discrete Lagrange--Dirac systems with some illustrative examples of
nonholonomic systems through numerical tests.

Information geometry and alpha-parallel prior of the beta-logistic distribution

L Jiu, L Peng

Communications in Statistics-Theory and Methods 2024.08

The Comparison of Riemannian Geometric Matrix-CFAR Signal Detectors

Y Ono, L Peng

IEEE Transactions on Aerospace and Electronic Systems 60 ( 2 ) 1679 - 1691 2024.04

ISSN 00189251

Essential characteristics of signal data can be captured by the autocovariance matrix, which, in the stationary scenarios, is Toeplitz Hermitian positive definite (HPD). In this paper, several well-known Riemannian geometric structures of HPD matrix manifolds are applied to signal detection, including the affine invariant Riemannian metric, the log-Euclidean metric, and the Bures–Wasserstein (BW) metric, the last of which was recently extended to HPD manifolds. Riemannian gradient descent algorithms are proposed to solve the corresponding geometric means and medians, that play fundamental roles in the detection process. Simulations within the scenario using the ideal steering vector as the target signal provide compelling evidence that the BW detectors outperform the other geometric detectors as well as the conventional adaptive matched filter and adaptive normalized matched filter when observation data are limited. Further simulations demonstrate that the matrix-CFAR is robust in scenarios where the signal is mismatched. In addition to detection performances, robustness of the geometric detectors to outliers and computational complexity of the algorithms are analysed.

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Developing a cloud evidence method for dynamic early warning of tunnel construction safety risk in undersea environment

H Zhou, B Gao, X Zhao, L Peng, S Bai

Developments in the Built Environment 16 100225 2023.12

ISSN 2666-1659

Traditional methods have limitations in achieving precise predictions of risk occurrence at an exact future time and have difficulties transforming between qualitative and quantitative indicators and handling multi-source heterogeneous risk data. This study quantifies and analyzes the multi-source construction safety risks classified into the categories of man, machine, material, method and environment (4M1E), and presents a cloud evidence method that integrates wavelet de-noising algorithm, cloud model, and Dempster-Shafer (D-S) evidence theory. A real-time risk prediction and warning is provided using this method after the fusion of multi-source uncertain information and the transformation between qualitative and quantitative indicators, enabling the timely detection of potential risks for project managers. This method analyzing “uncertainty” with “certainty” is verified by an undersea tunnel construction project. The result shows that this method is effective in early warning risks two days before their actual occurrence, providing reference significance for risk early warning of the tunnel construction project.

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The difference variational bicomplex and multisymplectic systems

Linyu Peng, Peter E. Hydon

arXiv preprint arXiv:2307.13935 2023.07

The difference variational bicomplex, which is the natural setting for
systems of difference equations, is constructed and used to examine the
geometric and algebraic properties of various systems. Exactness of the
bicomplex gives a coordinate-free setting for finite difference variational
problems, Euler--Lagrange equations and Noether's theorem. We also examine the
connection between the condition for existence of a Hamiltonian and the
multisymplecticity of systems of partial difference equations. Furthermore, we
define difference multimomentum maps of multisymplectic systems, which yield
their conservation laws. To conclude, we demonstrate how multisymplectic
integrators can be comprehended even on non-uniform meshes through a
generalized difference variational bicomplex.

Some novel physical structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries system

Yaqing Liu, Linyu Peng

Chaos, Solitons and Fractals 171 113430 2023.06

Corresponding author, Accepted, ISSN 09600779

In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries (KdV) system by its analytic solutions. Its N-soliton solutions are obtained via Hirota's bilinear method, and in particular, the hybrid solutions of lump, breather and line solitons are derived by the long wave limit method. In addition to soliton solutions, similarity reduction, including similarity solutions (also known as group-invariant solutions) and novel non-autonomous rational third-order Painlevé equations, is achieved through symmetry analysis. The analytic results, together with illustrative wave interactions, show interesting physical features, that may shed some light on the study of other variable-coefficient nonlinear systems.

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LDA-MIG Detectors for Maritime Targets in Nonhomogeneous Sea Clutter

X Hua, L Peng, W Liu, Y Cheng, H Wang, H Sun, Z Wang

IEEE Transactions on Geoscience and Remote Sensing 61 5101815 2023.03

Accepted, ISSN 01962892

This article deals with the problem of detecting maritime targets embedded in nonhomogeneous sea clutter, where the limited number of secondary data is available due to the heterogeneity of sea clutter. A class of linear discriminant analysis (LDA)-based matrix information geometry (MIG) detectors is proposed in the supervised scenario. As customary, Hermitian positive-definite (HPD) matrices are used to model the observational sample data, and the clutter covariance matrix of the received dataset is estimated as the geometric mean of the secondary HPD matrices. Given a set of training HPD matrices with class labels, which are elements of a higher dimensional HPD matrix manifold, the LDA manifold projection learns a mapping from the higher dimensional HPD matrix manifold to a lower dimensional one subject to maximum discrimination. In this study, the LDA manifold projection, with the cost function maximizing between-class distance while minimizing within-class distance, is formulated as an optimization problem in the Stiefel manifold. Four robust LDA-MIG detectors corresponding to different geometric measures are proposed. Numerical results based on both simulated radar clutter with interferences and real IPIX radar data show the advantage of the proposed LDA-MIG detectors against their counterparts without using LDA and the state-of-the-art maritime target detection methods in nonhomogeneous sea clutter.

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The target detection method through autocovariance matrices and its robust analysis

Y Ono, L Peng

IEICE Technical Report; IEICE Tech. Rep. 122 ( 388 ) 55 - 60 2023.02

自己共分散行列空間における信号検出手法とそのロバスト性解析

小野悠介，彭林玉

研究報告音声言語情報処理 (SLP) 2023 (14), 1-6 2023-SLP-146 ( 14 ) 1 - 6 2023.02

Lagrangian Multiform Theory and Pluri-Lagrangian Systems (23w5043)

F Nijhoff, L Peng, Y Shi, D Zhang

2023

Towards a simple mathematical model for the legal concept of balancing of interests

Frederike Zufall, Rampei Kimura, Linyu Peng

Artificial Intelligence and Law 31 ( 4 ) 807 - 827 2023

Research paper (scientific journal), Accepted, ISSN 0924-8463

We propose simple nonlinear mathematical models for the legal concept of balancing of interests. Our aim is to bridge the gap between an abstract formalisation of a balancing decision while assuring consistency and ultimately legal certainty across cases. We focus on the conflict between the rights to privacy and to the protection of personal data in Art. 7 and Art. 8 of the EU Charter of Fundamental Rights (EUCh) against the right of access to information derived from Art. 11 EUCh. These competing rights are denoted by (i1) right to privacy and (i2) access to information; mathematically, their indices are respectively assigned by u1∈ [0 , 1] and u2∈ [0 , 1] subject to the constraint u1+ u2= 1. This constraint allows us to use one single index u to resolve the conflict through balancing. The outcome will be concluded by comparing the index u with a prior given threshold u. For simplicity, we assume that the balancing depends on only selected legal criteria such as the social status of affected person, and the sphere from which the information originated, which are represented as inputs of the models, called legal parameters. Additionally, we take “time” into consideration as a legal criterion, building on the European Court of Justice’s ruling on the right to be forgotten: by considering time as a legal parameter, we model how the outcome of the balancing changes over the passage of time. To catch the dependence of the outcome u by these criteria as legal parameters, data were created by a fully-qualified lawyer. By comparison to other approaches based on machine learning, especially neural networks, this approach requires significantly less data. This might come at the price of higher abstraction and simplification, but also provides for higher transparency and explainability. Two mathematical models for u, a time-independent model and a time-dependent model, are proposed, that are fitted by using the data.

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Towards a median signal detector through the total Bregman divergence and its robustness analysis

Y Ono, L Peng

Signal Processing 201 108728 2022.12

Accepted, ISSN 01651684

A novel family of geometric signal detectors are proposed through medians of the total Bregman divergence (TBD), which are shown advantageous over the conventional methods and their mean counterparts. By interpreting the observation data as Hermitian positive-definite matrices, their mean or median play an essential role in signal detection. As is difficult to be solved analytically, we propose numerical solutions through Riemannian gradient descent algorithms or fixed-point algorithms. Beside detection performance, robustness of a detector to outliers is also of vital importance, which can often be analyzed via the influence functions. Introducing an orthogonal basis for Hermitian matrices, we are able to compute the corresponding influence functions analytically and exactly by solving a linear system, which is transformed from the governing matrix equation. Numerical simulations show that the TBD medians are more robust than their mean counterparts.

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A stochastic Hamiltonian formulation applied to dissipative particle dynamics

L Peng, N Arai, K Yasuoka

Applied Mathematics and Computation 426 127126 2022.08

Accepted, ISSN 00963003

In this paper, a stochastic Hamiltonian formulation (SHF) is proposed and applied to dissipative particle dynamics (DPD) simulations. As an extension of Hamiltonian dynamics to stochastic dissipative systems, the SHF provides necessary foundations and great convenience for constructing efficient numerical integrators. As a first attempt, we develop the Störmer–Verlet type of schemes based on the SHF, which are structure-preserving for deterministic Hamiltonian systems without external forces, the dissipative forces in DPD. Long-time behaviour of the schemes is shown numerically by studying the damped Kubo oscillator. In particular, the proposed schemes include the conventional Groot–Warren's modified velocity-Verlet method and a modified version of Gibson–Chen–Chynoweth as special cases. The schemes are applied to DPD simulations and analysed numerically.

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Unsupervised Learning Discriminative MIG Detectors in Nonhomogeneous Clutter

Xiaoqiang Hua, Yusuke Ono, Linyu Peng, Yuting Xu

IEEE Transactions on Communications 70 ( 6 ) 4107 - 4120 2022.06

Accepted, ISSN 00906778

Principal component analysis (PCA) is a common used pattern analysis method that maps high-dimensional data into a lower-dimensional space maximizing the data variance, that results in the promotion of separability of data. Inspired by the principle of PCA, a novel type of learning discriminative matrix information geometry (MIG) detectors in the unsupervised scenario are developed, and applied to signal detection in nonhomogeneous environments. Hermitian positive-definite (HPD) matrices can be used to model the sample data, while the clutter covariance matrix is estimated by the geometric mean of a set of secondary HPD matrices. We define a projection that maps the HPD matrices in a high-dimensional manifold to a low-dimensional and more discriminative one to increase the degree of separation of HPD matrices by maximizing the data variance. Learning a mapping can be formulated as a two-step mini-max optimization problem in Riemannian manifolds, which can be solved by the Riemannian gradient descent algorithm. Three discriminative MIG detectors are illustrated with respect to different geometric measures, i.e., the Log-Euclidean metric, the Jensen–Bregman LogDet divergence and the symmetrized Kullback–Leibler divergence. Simulation results show that performance improvements of the novel MIG detectors can be achieved compared with the conventional detectors and their state-of-the-art counterparts within nonhomogeneous environments.

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A modified formal Lagrangian formulation for general differential equations

L Peng

Japan Journal of Industrial and Applied Mathematics 39 ( 2 ) 573 - 598 2022.05

Research paper (scientific journal), Accepted, ISSN 0916-7005

In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown.

Fisher–Rao geometry and Jeffreys prior for Pareto distribution

M Li, H Sun, L Peng

Communications in Statistics-Theory and Methods 51 ( 6 ) 1895 - 1910 2022.03

Research paper (scientific journal), Accepted, ISSN 03610926

In this paper, we investigate the Fisher–Rao geometry of the two-parameter family of Pareto distribution. We prove that its geometrical structure is isometric to the Poincaré upper half-plane model, and then study the corresponding geometrical features by presenting explicit expressions for connection, curvature and geodesics. It is then applied to Bayesian inference by considering the Jeffreys prior determined by the volume form. In addition, the posterior distribution from the prior is computed, providing a systematic method to the Bayesian inference for Pareto distribution.

Transformations, symmetries and Noether theorems for differential-difference equations

L Peng, PE Hydon

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 478 ( 2259 ) 20210944 2022.03

Research paper (scientific journal), Joint Work, Accepted, ISSN 13645021

The first part of this paper develops a geometric setting for
differential-difference equations that resolves an open question about the
extent to which continuous symmetries can depend on discrete independent
variables. For general mappings, differentiation and differencing fail to
commute. We prove that there is no such failure for structure-preserving
mappings, and identify a class of equations that allow greater freedom than is
typical.
For variational symmetries, the above results lead to a simple proof of the
differential-difference version of Noether's Theorem. We state and prove the
differential-difference version of Noether's Second Theorem, together with a
Noether-type theorem that spans the gap between the analogues of Noether's two
theorems. These results are applied to various equations from physics.

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Multiple soliton solutions and similarity reduction of a (2+ 1)-dimensional variable-coefficient Korteweg-de Vries system

Y Liu, L Peng

arXiv preprint arXiv:2212.03432 2022

In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg-de Vries (KdV) system by its analytic solutions. Its $N$-soliton solution are obtained via Hirota's bilinear method, and in particular, the hybrid solution of lump, breather and line soliton are derived by the long wave limit method. In addition to soliton solutions, similarity reduction, including similarity solutions (also known as group-invariant solutions) and non-autonomous third-order Painlevé equations, is achieved through symmetry analysis. The analytic results, together with illustrative wave interactions, show interesting physical features, that may shed some light on the study of other variable-coefficient nonlinear systems.

ディラック力学系のモデリングと離散的変分法による定式化

吉村浩明，彭林玉

計算力学講演会講演論文集 (The Japan Society of Mechanical Engineers) 2022.35 ( 0 ) 13-05 2022

ISSN 2424-2799

変分的積分法を用いたベイジアンニューラルネットワークの応用

大竹桃子，彭林玉

計算力学講演会講演論文集 (The Japan Society of Mechanical Engineers) 2022.35 ( 0 ) 13-01 2022

ISSN 2424-2799

<p>In numerical analysis, the conservation of structure, i.e., whether the essential properties of physical phenomena can be reproduced numerically, is of great importance. On the other hand, neural networks that can learn conservation laws has recently received great attention. These models take important structure of physical problems into consideration, which are often ignored in traditional models that directly learn using data, consequently exhibiting long-term accurate prediction and interpretability. In the current study, we construct neural network models based on variational integrator, a typical kind of structure-preserving method. In addition, we introduce Bayesian framework to measure uncertainty of the model and evaluate the models quantitively. Illustrative examples are studied.</p>

MIG Median Detectors with Manifold Filter

Xiaoqiang Hua, Linyu Peng

Signal Processing 188 108176 2021.11

Research paper (scientific journal), Joint Work, Accepted

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A simple mathematical model for the legal concept of balancing of interests

Frederike Zufall, Rampei Kimura, Linyu Peng

Proceedings of the Eighteenth International Conference on Artificial Intelligence and Law 270 - 271 2021.07

Research paper (scientific journal), Joint Work, Accepted

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Target Detection within Nonhomogeneous Clutter via Total Bregman Divergence-Based Matrix Information Geometry Detectors

X Hua, Y Ono, L Peng, Y Cheng, H Wang

IEEE Transactions on Signal Processing 69 4326 - 4340 2021.07

Research paper (scientific journal), Joint Work, Accepted, ISSN 1053-587X

Information divergences are commonly used to measure the dissimilarity of two
elements on a statistical manifold. Differentiable manifolds endowed with
different divergences may possess different geometric properties, which can
result in totally different performances in many practical applications. In
this paper, we propose a total Bregman divergence-based matrix information
geometry (TBD-MIG) detector and apply it to detect targets emerged into
nonhomogeneous clutter. In particular, each sample data is assumed to be
modeled as a Hermitian positive-definite (HPD) matrix and the clutter
covariance matrix is estimated by the TBD mean of a set of secondary HPD
matrices. We then reformulate the problem of signal detection as discriminating
two points on the HPD matrix manifold. Three TBD-MIG detectors, referred to as
the total square loss, the total log-determinant and the total von Neumann MIG
detectors, are proposed, and they can achieve great performances due to their
power of discrimination and robustness to interferences. Simulations show the
advantage of the proposed TBD-MIG detectors in comparison with the geometric
detector using an affine invariant Riemannian metric as well as the adaptive
matched filter in nonhomogeneous clutter.

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The matrix-CFAR via total Bregman divergence medians in signal detection

Y Ono, L Peng, H Sato

ASPAI' 2021 18 - 22 2021

Research paper (international conference proceedings), Accepted

Mobile Charging as a Service: A Reservation-Based Approach

X Zhang, Y Cao, L Peng, J Li, N Ahmad, S Yu

IEEE Transactions on Automation Science and Engineering 17 ( 4 ) 1976 - 1988 2020.10

Research paper (scientific journal), Joint Work, Accepted, ISSN 1558-3783

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Towards holistic charging management for urban electric taxi via a hybrid deployment of battery charging and swap stations

X Zhang, L Peng, Y Cao, S Liu, H Zhou, L Huang

Renewable Energy 155 703 - 716 2020.08

Research paper (scientific journal), Joint Work, Accepted, ISSN 09601481

© 2020 Elsevier Ltd While previous studies focused on managing charging demand for private electric vehicles (EVs), we investigate ways of supporting the upgrade of an entire public urban electric taxi (ET) system. Concerning the coexistence of plugin charging stations (CSs) and battery swap stations (BSSs) in practice, it thus requires further efforts to design a holistic charging management especially for ETs. By jointly considering the combination of plug-in charging and battery swapping, a hybrid charging management framework is proposed in this paper. The proposed scheme is capable of guiding ETs to appropriate stations with time-varying requirements depending on how emergent the demand will be. Through the selection of battery charging/swap, the optimization goal is to reduce the trip delay of ET. Results under a Helsinki city scenario with realistic ETs and charging stations show the effectiveness of our enabling technology, in terms of minimized drivers’ trip duration, as well as charging performance gains at the ET and station sides.

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Towards Efficient Battery Swapping Service Operation under Battery Heterogeneity

X Zhang, Y Cao, L Peng, N Ahmad, L Xu

IEEE Transactions on Vehicular Technology 69 ( 6 ) 6107 - 6118 2020.06

Research paper (scientific journal), Joint Work, Accepted, ISSN 1939-9359

© 1967-2012 IEEE. The proliferation of electric vehicles (EVs) has posed significant challenges to the existing power grid infrastructure. It thus becomes of vital importance to efficiently manage the Electro-Mobility for large demand from EVs. Due to limited cruising range of EVs, vehicles have to make frequent stops for recharging, while long charging period is one major concern under plug-in charging. We herein leverage battery swapping (BS) technology to provide an alternative charging service, which substantially reduces the charging duration (from hours down to minutes). Concerning in practice that various battery is generally not compatible with each other, we thus introduce battery heterogeneity into the swapping service, concerning the case that different types of EVs co-exist. A battery heterogeneity-based swapping service framework is then proposed. Further with reservations for swapping service enabled, the demand load can be anticipated at BS stations as a guidance to alleviate service congestion. Therefore, potential hotspots can be avoided. Results show the performance gains under the proposed scheme by comparing to other benchmarks, in terms of service waiting time, etc. In particular, the diversity of battery stock across the network can be effectively managed.

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Application of gradient descent algorithms based on geodesic distances

X Duan, H Sun, L Peng

Science China Information Sciences 63 ( 5 ) 152201 2020.05

Research paper (scientific journal), Joint Work, Accepted, ISSN 1674733X

© 2020, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature. In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the objective function. The first proposed problem is the control for positive definite Hermitian matrix systems whose outputs only depend on their inputs. The geodesic distance is adopted as the difference of the output matrix and the target matrix. The controller to adjust the input is obtained such that the output matrix is as close as possible to the target matrix. We show the trajectory of the control input on the manifold using the Riemannian gradient algorithm. The second application is to compute the Karcher mean of a finite set of given Toeplitz positive definite Hermitian matrices, which is defined as the minimizer of the sum of geodesic distances. To obtain more efficient iterative algorithm than traditional ones, a natural gradient algorithm is proposed to compute the Karcher mean. Illustrative simulations are provided to show the computational behavior of the proposed algorithms.

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Discrete Crum’s theorems and lattice KdV-type equations

C Zhang, L Peng, D Zhang

Theoretical and Mathematical Physics 202 ( 2 ) 165 - 182 2020.03

Research paper (scientific journal), Joint Work, Accepted, ISSN 00405779

© 2020, Pleiades Publishing, Ltd. We develop Darboux transformations (DTs) and their associated Crum’s formulas for two Schrödinger-type difference equations that are themselves discretized versions of the spectral problems of the KdV and modified KdV equations. With DTs viewed as a discretization process, classes of semidiscrete and fully discrete KdV-type systems, including the lattice versions of the potential KdV, potential modified KdV, and Schwarzian KdV equations, arise as the consistency condition for the differential/difference spectral problems and their DTs. The integrability of the underlying lattice models, such as Lax pairs, multidimensional consistency, τ-functions, and soliton solutions, can be easily obtained by directly applying the discrete Crum’s formulas.

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An assignment model with local constraints: Competitive equilibrium and ascending auction

L Pan, L Peng, Y Zhou

Economics Letters 188 108905 2020.03

Research paper (scientific journal), Joint Work, Accepted, ISSN 01651765

© 2019 Elsevier B.V. We consider an assignment model where each agent has unit-demand quasi-linear preferences and may face some local constraint, i.e., her possible assignment is restricted to a subset of items. Our model takes the assignment models without and with outside options, e.g., Andersson (2007) and Andersson et al. (2013), as special cases. We show that local constraints may lead to the non-existence of competitive equilibrium (CE), and provide a sufficient and necessary condition that ensures its existence. We establish the lattice of CE prices. Besides, an ascending auction is proposed, either finding a CE or validating its non-existence in finitely many steps. It generalizes Andersson et al. (2013)’s auction by adjusting increments stepwise.

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Modified Formal Variational Structures for General Differential Equations

PENG Linyu, OBATA Kenji

日本応用数理学会年会講演予稿集(CD-ROM) 2020 2020

Research paper (other academic), Joint Work, Accepted, ISSN 1345-3378

Regular symmetries of differential-difference equations and Noether's conservation laws

L Peng

数理解析研究所講究録 (RIMS) 2137 130 - 139 2019.12

Research paper (bulletin of university, research institution), Single Work, ISSN 1880-2818

An automatic dynamic balancer in a rotating mechanism with time-varying angular velocity

JA Wright, L Peng

Results in Applied Mathematics 2 100015 2019.12

Research paper (scientific journal), Joint Work, Accepted, ISSN 2590-0374

© 2019 The Author(s) We consider the system of a two ball automatic dynamic balancer attached to a rotating disc with nonconstant angular velocity. We directly compare the scenario of constant angular velocity with that when the acceleration of the rotor is taken into consideration. In doing so we show that there are cases where one must take the acceleration phase into consideration to obtain an accurate picture of the dynamics. Similarly we identify cases where the acceleration phase of the disc may be ignored. Finally, we briefly consider nonmonotonic variations of the angular velocity, with a view of maximising the basin of attraction of the desired solution, corresponding to damped vibrations.

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Statistical Einstein manifolds of exponential families with group-invariant potential functions

L Peng, Z Zhang

Journal of Mathematical Analysis and Applications 479 ( 2 ) 2104 - 2118 2019.11

Research paper (scientific journal), Joint Work, Accepted, ISSN 0022247X

© 2019 Elsevier Inc. This paper mainly contributes to a classification of statistical Einstein manifolds, namely statistical manifolds at the same time are Einstein manifolds. A statistical manifold is a Riemannian manifold, each of whose points is a probability distribution. With the Fisher information metric as a Riemannian metric, information geometry was developed to understand the intrinsic properties of statistical models, which play important roles in statistical inference, etc. Among all these models, exponential families is one of the most important kinds, whose geometric structures are fully determined by their potential functions. To classify statistical Einstein manifolds, we derive partial differential equations for potential functions of exponential families; special solutions of these equations are obtained through the ansatz method as well as group-invariant solutions via reductions using Lie point symmetries.

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Symmetries and reductions of integrable nonlocal partial differential equations

L Peng

Symmetry 11 ( 7 ) 884 2019.07

Research paper (scientific journal), Single Work, Accepted

© 2019 by the authors. In this paper, symmetry analysis is extended to study nonlocal differential equations. In particular, two integrable nonlocal equations are investigated, the nonlocal nonlinear Schrödinger equation and the nonlocal modified Korteweg-de Vries equation. Based on general theory, Lie point symmetries are obtained and used to reduce these equations to nonlocal and local ordinary differential equations, separately; namely, one symmetry may allow reductions to both nonlocal and local equations, depending on how the invariant variables are chosen. For the nonlocal modified Korteweg-de Vries equation, analogously to the local situation, all reduced local equations are integrable. We also define complex transformations to connect nonlocal differential equations and differential-difference equations.

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MEGEE: Mobile Edge computer Geared v2x for E-mobility Ecosystem

Y Cao, C Wu, X Zhang, W Liu, L Peng, M Khalid

2019 IEEE Wireless Communications and Networking Conference (WCNC) (IEEE) 2019-April 1 - 6 2019.04

Research paper (international conference proceedings), Joint Work, Accepted

© 2019 IEEE. The introduction of Electric Vehicles (EVs) leads to new concern on the E-Mobility. Making charging reservation, by considering the EV's arrival time and its expected charging time at Charging Stations (CSs) has been studied to predict the dynamic status of CSs. In this paper, we propose a Mobile Edge computer Geared v2x for E-mobility Ecosystem (MEGEE), as a decentralized alternative to the conventional centralized cloud based architecture. MEGEE enables the Vehicular Delay/Disruption Tolerant Networking (VDTN)-driven anycasting for information delivery, and Mobile Edge Computing (MEC) functioned CSs for information mining and aggregation. MEGEE efficiently and timely processes essential charging reservations and charging control information, through the Internet of EVs and MEC servers. Our studies show that MEGEE can achieve the close charging performance as performed by the centralized system, while offers a significant saving in communications cost.

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Moving frames and Noether’s finite difference conservation laws I

EL Mansfield, A Rojo-Echeburua, PE Hydon, L Peng

Transactions of Mathematics and its Applications 3 ( 1 ) tnz004 2019

Research paper (scientific journal), Joint Work, Accepted, ISSN 2398-4945

We consider the calculation of Euler–Lagrange systems of ordinary difference equations, including the difference Noether’s theorem, in the light of the recently-developed calculus of difference invariants and discrete moving frames. We introduce the difference moving frame, a natural discrete moving frame that is adapted to difference equations by prolongation conditions. For any Lagrangian that is invariant under a Lie group action on the space of dependent variables, we show that the Euler–Lagrange equations can be calculated directly in terms of the invariants of the group action. Furthermore, Noether’s conservation laws can be written in terms of a difference moving frame and the invariants. We show that this form of the laws can significantly ease the problem of solving the Euler–Lagrange equations, and we also show how to use a difference frame to integrate Lie group invariant difference equations. In this Part I, we illustrate the theory by applications to Lagrangians invariant under various solvable Lie groups. The theory is also generalized to deal with variational symmetries that do not leave the Lagrangian invariant. Apart from the study of systems that are inherently discrete, one significant application is to obtain geometric (variational) integrators that have finite difference approximations of the continuous conservation laws embedded a priori. This is achieved by taking an invariant finite difference Lagrangian in which the discrete invariants have the correct continuum limit to their smooth counterparts. We show the calculations for a discretization of the Lagrangian for Euler’s elastica, and compare our discrete solution to that of its smooth continuum limit.

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A Stochastic Analytical Modeling Framework on ISP-P2P Collaborations in Multi domain Environments

Zhang Xu, Wang Ning, Cao Yue, Peng Linyu, Meng Haining

IEEE Systems Journal 12 ( 3 ) 2320 - 2331 2018.09

Research paper (scientific journal), Joint Work, Accepted, ISSN 19328184

Cooperation between peer-to-peer (P2P) overlays and underlying networks has been proposed as an effective approach to improve the efficiency of both the applications and the underlying networks. However, fundamental characteristics with respect to Internet service providers (ISP) business relationships and inter-ISP routing information are not sufficiently investigated in the context of collaborative ISP-P2P paradigms in multidomain environments. In this paper, we focus on such issues and develop an analytical modeling framework for analyzing optimized interdomain peer selection schemes concerning ISP policies, with the main purpose of mitigating cross-ISP traffic and enhancing service quality of end users. In addition, we introduce an advanced hybrid scheme for peer selections based on the proposed analytical theory framework, in accordance with practical network scenarios, wherein cooperative and noncooperative behaviors coexisting. Numerical results show that the proposed scheme incorporating ISP policies is able to achieve desirable network efficiency as well as great service quality for P2P users. Our analytical modeling framework can be used as a guide for analyzing and evaluating future network-aware P2P peer selection paradigms in general multidomain scenarios.

Towards autonomy: Cost-effective scheduling for long-range autonomous valet parking (lavp)

M Khalid, Y Cao, X Zhang, C Han, L Peng, N Aslam, N Ahmad

2018 IEEE Wireless Communications and Networking Conference (WCNC) (IEEE) 1 - 6 2018.06

Research paper (international conference proceedings), Joint Work, Accepted

© 2018 IEEE. Continuous and effective developments in Autonomous Vehicles (AVs) are happening on daily basis. Industries nowadays, are interested in introducing less costly and highly controllable AVs to public. Current so-called AVP solutions are still limited to a very short range (e.g., even only work at the entrance of car parks). This paper proposes a parking scheduling scheme for long-range AVP (LAVP) case, by considering mobility of Autonomous Vehicles (AVs), fuel consumption and journey time. In LAVP, Car Parks (CPs) are used to accommodate increasing numbers of AVs, and placed outside city center, in order to avoid traffic congestions and ensure road safety in public places. Furthermore, with positioning of reference points to guide user-centric long-term driving and drop-off/pick-up passengers, simulation results under the Helsinki city scenario shows the benefits of LAVP. The advantage of LAVP system is also reflected through both analysis and simulation.

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Discrete Crum's theorems and integrable lattice equations

C Zhang, L Peng, D Zhang

arXiv preprint arXiv:1802.10044 2018

Research paper (other academic)

In this paper, we develop discrete versions of Darboux transformations and
Crum's theorems for two second order difference equations. The difference
equations are discretised versions (using Darboux transformations) of the
spectral problems of the KdV quation, and of the modified KdV equation or
sine-Gordon equation. Considering the discrete dynamics created by Darboux
transformations for the difference equations, one obtains the lattice potential
KdV equation, the lattice potential modified KdV equation and the lattice
Schwarzian KdV equation, that are prototypes of integrable lattice equations.
It turns out that, along the discretisation processes using Darboux
transformations, two families of integrable systems (the KdV family, and the
modified KdV or sine-Gordon family), including their continuous, semi-discrete
and lattice versions, are explicitly constructed. As direct applications of the
discrete Crum's theorems, multi-soliton solutions of the lattice equations are
obtained.

Variational Integrators for Interconnected Systems with Holonomic Constraints

PENG Linyu, MOMOSE Hiroki, YOSHIMURA Hiroaki

日本応用数理学会年会講演予稿集(CD-ROM) 2017 273‐274 2017.09

Research paper (other academic), Joint Work, Accepted, ISSN 1345-3378

Applying DTN routing for reservation-driven EV Charging management in smart cities

Y Cao, X Zhang, R Wang, L Peng, N Aslam, X Chen

13th International Wireless Communications and Mobile Computing Conference, IWCMC 2017 1471 - 1476 2017.07

Research paper (international conference proceedings), Accepted

© 2017 IEEE. Charging management for Electric Vehicles (EVs) on-the-move (moving on the road with certain trip destinations) is becoming important, concerning the increasing popularity of EVs in urban city. However, the limited battery volume of EV certainly influences its driver's experience. This is mainly because the EV needed for intermediate charging during trip, may experience a long service waiting time at Charging Station (CS). In this paper, we focus on CS-selection decision making to manage EVs' charging plans, aiming to minimize drivers' trip duration through intermediate charging at CSs. The anticipated EVs' charging reservations including their arrival time and expected charging time at CSs, are brought for charging management, in addition to taking the local status of CSs into account. Compared to applying traditionally applying cellular network communication to report EVs' charging reservations, we alternatively study the feasibility of applying Vehicle-to-Vehicle (V2V) communication with Delay/Disruption Tolerant Networking (DTN) nature, due primarily to its flexibility and cost-efficiency in Vehicular Ad hoc NETworks (VANETs). Evaluation results under the realistic Helsinki city scenario show that applying the V2V for reservation reporting is promisingly cost-efficient in terms of communication overhead for reservation making, while achieving a comparable performance in terms of charging waiting time and total trip duration.

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Symmetries, Conservation Laws, and Noether's Theorem for Differential‐Difference Equations

L Peng

Studies in Applied Mathematics 139 ( 3 ) 457 - 502 2017

非ホロノミック拘束を受ける力学系と離散ラグランジュ・ディラック構造

百瀬宏樹, 彭林玉, 吉村浩明

日本応用数理学会年会講演予稿集(CD-ROM) 2016 2016

Research paper (other academic), Joint Work, Accepted, ISSN 1345-3378

Self-adjointness and conservation laws of difference equations

L Peng

Communications in Nonlinear Science and Numerical Simulation 23 ( 1-3 ) 209 - 219 2015.06

Research paper (scientific journal), Accepted, ISSN 10075704

© 2014 Elsevier B.V. A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.

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Entropic dynamical models with unstable Jacobi fields

C Li, L Peng, H Sun

Romanian Journal of Physics 60 ( 9-10 ) 1249 - 1262 2015

Research paper (scientific journal), Accepted, ISSN 1221146X

© 2015, Editura Academiei Romane. All rights reserved. The instability of an entropic dynamical model is considered via Jacobi vector field and the Lyapunov exponent. From the viewpoint of information geometry, geometric structure of the statistical manifold underlying this model is investigated, and we conclude that it is a manifold with constant negative scalar curvature. By use of the Jacobi vector field associated with the geodesics, we study the asymptotic behavior of the geodesic spread on the statistical manifold and reach that it is described by an exponentially divergent Jacobi vector field with respect to time. A positive Lyapunov exponent is also obtained, that explains the local instability of the system as well. Furthermore, submanifolds are studied similarly.

Relations between symmetries and conservation laws for difference systems

L Peng

Journal of Difference Equations and Applications 20 ( 12 ) 1609 - 1626 2014.12

Research paper (scientific journal), Accepted, ISSN 10236198

© 2014, Taylor & Francis. This paper presents a relation between divergence variational symmetries for difference variational problems on lattices and conservation laws for the associated Euler–Lagrange system provided by Noether's theorem. This inspires us to define conservation laws related to symmetries for arbitrary difference equations with or without Lagrangian formulations. These conservation laws are constrained by partial differential equations obtained from the symmetries generators. It is shown that the orders of these partial differential equations have been reduced relative to those used in a general approach. Illustrative examples are presented.

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The α-geometric structures on manifold of positive definite Hermite matrices

XM Duan, HF Sun, LY Peng

Acta Mathematica Sinica, English Series 30 ( 12 ) 2137 - 2145 2014.11

Research paper (scientific journal), Accepted, ISSN 14398516

© 2014, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg. Geometric structures of a manifold of positive definite Hermite matrices are considered from the viewpoint of information geometry. A Riemannian metric is defined and dual α-connections are introduced. Then the fact that the manifold is ±1-flat is shown. Moreover, the divergence of two points on the manifold is given through dual potential functions. Furthermore, the optimal approximation of a point onto the submanifold is gotten. Finally, some simulations are given to illustrate our results.

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A Natural Gradient Algorithm for Stochastic Distribution Systems

Z Zhang, H Sun, L Peng, L Jiu

Entropy 16 ( 8 ) 4338 - 4352 2014.08

Research paper (scientific journal), Joint Work, Accepted, ISSN 1099-4300

In this paper, we propose a steepest descent algorithm based on the natural gradient to design the controller of an open-loop stochastic distribution control system (SDCS) of multi-input and single output with a stochastic noise. Since the control input vector decides the shape of the output probability density function (PDF), the purpose of the controller design is to select a proper control input vector, so that the output PDF of the SDCS can be as close as possible to the target PDF. In virtue of the statistical characterizations of the SDCS, a new framework based on a statistical manifold is proposed to formulate the control design of the input and output SDCSs. Here, the Kullback-Leibler divergence is presented as a cost function to measure the distance between the output PDF and the target PDF. Therefore, an iterative descent algorithm is provided, and the convergence of the algorithm is discussed, followed by an illustrative example of the effectiveness.

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The arc length variational formula on the exponential manifold

F Zhang, H Sun, L Jiu, L Peng

Mathematica Slovaca 63 ( 5 ) 1101 - 1112 2013.10

Research paper (scientific journal), Joint Work, Accepted, ISSN 01399918

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Natural gradient algorithm for stochastic distribution systems with output feedback

Z Zhang, H Sun, L Peng

Differential Geometry and Its Applications (ELSEVIER SCIENCE BV) 31 ( 5 ) 682 - 690 2013.10

Research paper (scientific journal), Joint Work, Accepted, ISSN 09262245

In this paper, we use natural gradient algorithm to control the shape of the conditional output probability density function for the stochastic distribution systems from the viewpoint of information geometry. The considered system here is of multi-input and single output with an output feedback and a stochastic noise. Based on the assumption that the probability density function of the stochastic noise is known, we obtain the conditional output probability density function whose shape is only determined by the control input vector under the condition that the output feedback is known at any sample time. The set of all the conditional output probability density functions forms a statistical manifold (M), and the control input vector and the output feedback are considered as the coordinate system. The Kullback divergence acts as the distance between the conditional output probability density function and the target probability density function. Thus, an iterative formula for the control input vector is proposed in the sense of information geometry. Meanwhile, we consider the convergence of the presented algorithm. At last, an illustrative example is utilized to demonstrate the effectiveness of the algorithm. (c) 2013 Elsevier B.V. All rights reserved.

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A natural gradient descent algorithm for the solution of discrete algebraic Lyapunov equations based on the geodesic distance

X Duan, H Sun, L Peng, X Zhao

Applied Mathematics and Computation (ELSEVIER SCIENCE INC) 219 ( 19 ) 9899 - 9905 2013.05

Research paper (scientific journal), Joint Work, Accepted, ISSN 00963003

A new framework to calculate the numerical solution of the discrete algebraic Lyapunov equation is proposed by using the geometric structures on the Riemannian manifold. Specifically, two algorithms based on the manifold of positive definite symmetric matrices are provided. One is a gradient descent algorithm with an objective function of the classical Euclidean distance. The other is a natural gradient descent algorithm with an objective function of the geodesic distance on the curved Riemannian manifold. Furthermore, these two algorithms are compared with a traditional iteration method. Simulation examples show that the convergence speed of the natural gradient descent algorithm is the fastest one among three algorithms. (C) 2013 Elsevier Inc. All rights reserved.

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Information geometry of power spectral

Syed F.S, Peng L.-Y, Sun H.-F, Duan X.-M

Beijing Ligong Daxue Xuebao/Transaction of Beijing Institute of Technology 33 ( 3 ) 327 - 330 2013.03

Research paper (scientific journal), Joint Work, Accepted, ISSN 10010645

From differential to difference: The variational bicomplex and invariant Noether's theorems

L Peng

2013

Doctoral thesis, Accepted

Riemannian means on special Euclidean group and unipotent matrices group

X Duan, H Sun, L Peng

The Scientific World Journal 2013 292787 2013

Research paper (scientific journal), Joint Work, Accepted, ISSN 1537-744X

Among the noncompact matrix Lie groups, the special Euclidean group and the unipotent matrix group play important roles in both theoretic and applied studies. The Riemannian means of a finite set of the given points on the two matrix groups are investigated, respectively. Based on the left invariant metric on the matrix Lie groups, the geodesic between any two points is gotten. And the sum of the geodesic distances is taken as the cost function, whose minimizer is the Riemannian mean. Moreover, a Riemannian gradient algorithm for computing the Riemannian mean on the special Euclidean group and an iterative formula for that on the unipotent matrix group are proposed, respectively. Finally, several numerical simulations in the 3-dimensional case are given to illustrate our results.

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Information geometric characterization of the complexity of fractional Brownian motions

L Peng, H Sun, G Xu

Journal of mathematical physics (AMER INST PHYSICS) 53 ( 12 ) 123305 2012.12

Research paper (scientific journal), Joint Work, Accepted, ISSN 00222488

The complexity of the fractional Brownian motions is investigated from the viewpoint of information geometry. By introducing a Riemannian metric on the space of their power spectral densities, the geometric structure is achieved. Based on the general construction, for an example, whose power spectral density is obtained by use of the normalized Mexican hat wavelet, we show its information geometric structures, e. g., the dual connections, the curvatures, and the geodesics. Furthermore, the instability of the geodesic spreads on this manifold is analyzed via the behaviors of the length between two neighboring geodesics, the average volume element as well as the divergence (or instability) of the Jacobi vector field. Finally, the Lyapunov exponent is obtained. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770047]

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Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric

L Peng, H Sun, X Sun

International Journal of Mathematics and Mathematical Sciences 2011 ( 1 ) 710274 2011.09

Research paper (scientific journal), Joint Work, Accepted, ISSN 01611712

We characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the Jacobi field along the geodesics, and the equations for a certain flow constrained in a family of conformal equivalent nondegenerate metrics are obtained. At last the conformal curvatures, the geodesic equations, the Jacobi equations, and the equations for the flow of the famous models, an N degrees of freedom linear Hamiltonian system and the Hénon-Heiles model are given, and in a special case, numerical solutions of the conformal geodesics, the generalized momenta, and the Jacobi field along the geodesics of the Hénon-Heiles model are obtained. And the numerical results for the Hénon-Heiles model show us the instability of the associated geodesic spreads. © 2011 Linyu Peng et al.

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The geometric structures and instability of entropic dynamical models

L Peng, H Sun, D Sun, J Yi

Advances in Mathematics (ELSEVIER) 227 ( 1 ) 459 - 471 2011.05

Research paper (scientific journal), Joint Work, Accepted, ISSN 00018708

In this paper, we characterize two entropic dynamical (ED) models from the viewpoint of information geometry and give the geometric structures of the associated statistical manifolds of the models. The scalar curvatures and the geodesics are obtained. Also the instability of entropic dynamical models is studied from the behavior of the geodesics lengths, statistical volume elements and Jacobi vector fields. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.

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Information geometry and its applications

Sun H, Peng L, Zhang Z

Advances in Mathematics (China) 40 ( 3 ) 257 - 269 2011

Research paper (scientific journal), Joint Work, Accepted

3D Object Recognition Based on Linear Lie Algebra Model

FX Li, PD Wu, HF Sun, LY Peng

Journal of Beijing Institute of Technology 18 ( 1 ) 46 - 50 2009.03

Research paper (scientific journal), Joint Work, Accepted, ISSN 10040579

A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed. Then an algorithm of 3D object recognition using the linear Lie algebra models is presented. It is a convenient recognition method for the objects which are symmetric about some axis. By using the presented algorithm, the representation matrices of the fibre or the base curve from only finite points of the linear Lie algebra model can be obtained. At last some recognition results of practicalities are given. © A paper published in JBIT is protected by copyright.

On Fibre Bundle Surfaces and Their Curvatures

FX Li, LY Peng, HF Sun

Journal of Beijing Institute of Technology 17 ( 4 ) 451 - 454 2008.12

Research paper (scientific journal), Joint Work, Accepted, ISSN 10040579

The geometric structure of the inverse gamma distribution

T Li, L Peng, H Sun

Contributions to Algebra and Geometry 49 ( 1 ) 217 - 225 2008.04

Research paper (scientific journal), Joint Work, Accepted, ISSN 01384821

Surface model based on a fibre bundle of Hamiltonian Lie algebra and Gaussian curvature

Li F, Wu P, Peng L, Sun H

Science & Technology Review 26 ( 8 ) 37 - 39 2008

Research paper (scientific journal), Joint Work, Accepted

The geometric structure of the Pareto distribution

L Peng, H Sun, L Jiu

Boletın de la Asociación Matemática Venezolana 14 ( 1-2 ) 5 - 13 2007

Research paper (scientific journal), Joint Work, Accepted

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