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Papers - PENG Linyu

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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 simple mathematical model for the legal concept of balancing of interests: F. Zufall et al.

F Zufall, R Kimura, L Peng

Artificial Intelligence and law 31 (4), 807-827 2023

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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