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Papers - PENG Linyu

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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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