日本・アジア青少年サイエンス交流事業

さくらサイエンスプラン
Japan-Asia Youth Exchange Program in Science

JST さくらサイエンスプログラムによる数理科学に関する
日中共同ワークショップ 於松江 2018
Japan–China Joint Workshop on Mathematical Sciences in Matsue 2018
supported by Japan-Asia Youth Exchange Program in Science
島根大学において, 下記の要領で研究集会を開催致しますので, ご案内申し上げます。
世話人

杉江実郎 (島根大学)

記
日時： 2018 年 11 月 17 日 (土) 10:20〜16:30

11 月 18 日 (日) 10:00〜15:20
会 場： 島根大学松江キャンパス
総合理工学部 3 号館数理第 2 総合演習室〒 690-8504 島根県松江市西川津町 1060

Tel: 0852–32–6388 (杉江研究室)
https://www.shimane-u.ac.jp/access/プログラム

11 月 17 日(開会挨拶)
10:30〜10:50 Jiu Li* (北京科技大学)
Hongyan Zang (北京科技大学)
The construction of one-dimensional
discrete chaos theory based on
improved Marotto’s theorem
10:50〜11:10 Yan Yan* (島根大学)
Jitsuro Sugie (島根大学)
Existence regions of positive periodic solutions for a mixed discrete
hematopoiesis model
11:10〜11:30 Li Bingxiu (北京科技大学)
The method research of long non-coding RNA prediction based on
deep learning
11:30〜11:50 Hiroshi Shiozaki* (島根大学)
Jitsuro Sugie (島根大学)
Asymptotic stability for nonlinear diﬀerential equations with timevarying coeﬃcients(昼食)13:30〜14:10 Yukihiko Nakata (島根大学)【特別講演】
Epidemics with waning immunity(休憩)
14:20〜14:40 Rong Qiang* (北京科技大学)
Wanbiao Ma (北京科技大学)
Ke Guo (北京科技大学)
The diﬀerential equation model of pathogenesis of Kawasaki disease
with theoretical analysis
14:40〜15:00 Liu Yang* (島根大学)
Yukihiko Nakata (島根大学)
Epidemics with boosting of immunity
15:00〜15:20 Ke Guo* (北京科技大学)
Wanbiao Ma (北京科技大学)
Global dynamics analysis of a diﬀerential
equation model of Kawasaki disease pathogenesis(休憩)
15:30〜15:50 Na Li* (北京科技大学)
Ping Lin (ダンディー大学)
Fuzheng Gao (山東大学)
An expanded mixed ﬁnite element method for sobolev equations
15:50〜16:10 Yang Liu** (島根大学)
Takeshi Wada (島根大学)
Long range scattering and modiﬁed wave operators for the MaxwellSchrödinger equation in three space dimensions
16:10〜16:30 Kaiqiang Zhang* (北京科技大学)
Baiyu Liu (北京科技大学)
Finite time blow-up and global existence for the nonlocal hyperbolic
equation

11 月 18 日
10:00〜10:40 Hairui Wei (北京科技大学)【特別講演】
Quantum information processing based on artiﬁcial atoms(休憩)10:50〜11:10 Lutao Zhao (北京科技大学)
Guanrong Zeng* (北京科技大学)
Analysis of timeliness of oil price news information based on SVM
11:10〜11:30 Yoshiki Ishihara* (島根大学)
Jitsuro Sugie (島根大学)
Integral averaing technique for oscillation of second-order linear selfadjoint diﬀerential equations with impulsive eﬀect
11:30〜11:50 Chunyan Liu* (北京科技大学)
Liancun Zheng (北京科技大学)
Ping Lin (北京科技大学)
Flow and heat transfer of Bingham plastic ﬂuid over a rotating disk
with variable thickness(昼食)
13:30〜13:50 Kazuki Seto* (島根大学)
Daishi Kuroiwa (島根大学)
Arcwise connected quasiconvex functions and its applications
13:50〜14:10 Xingyan Li* (北京科技大学)
Yan Xu (北京科技大学)
Human age prediction based on DNA methylation using a gradientboosting regressor
14:10〜14:30 Hiroyuki Ohtani* (島根大学)
Koji Okano* (島根大学)
Daishi Kuroiwa (島根大学)
Constraint qualiﬁcations for the Lagrange-duality of extended realvalued convex optimization problems(休憩)
14:40〜15:00 Yingxi Yang* (北京科技大学)
Yan Xu (北京科技大学)
iGlu-Lys: A Predictor for lysine glutarylation through amino acidpair order features
15:00〜15:20 Takumi Murakami* (島根大学)
Yuya Sumida* (島根大学)
Daishi Kuroiwa (島根大学)
Constraint qualiﬁcations for a Lagrange-type duality of extended realvalued DC optimization problems
2018 年 10 月 31 日作成

Japan–China Joint Workshop on Mathematical Sciences in
Matsue 2018 supported by Japan–Asia Youth Exchange
Program in Science
November 17–18, 2018
Room 609, Interdisciplinary Faculty of Science and Engineering 3,
Matsue Campus, Shimane University
Matsue 690-8504, Japan
https://www.shimane-u.ac.jp/en/access/Organizing Committee
Jitsuro Sugie (Shimane University)

Program
November 17(Opening Remarks)
10:30〜10:50 Jiu Li* (University of Science and Technology Beijing)
Hongyan Zang (University of Science and Technology Beijing)
The construction of one-dimensional discrete chaos theory based on
improved Marotto’s theorem
10:50〜11:10 Yan Yan* (Shimane University)
Jitsuro Sugie (Shimane University)
Existence regions of positive periodic solutions for a mixed discrete
hematopoiesis model
11:10〜11:30 Li Bingxiu (University of Science and Technology Beijing)
The method research of long non-coding RNA prediction based on
deep learning
11:30〜11:50 Hiroshi Shiozaki* (Shimane University)
Jitsuro Sugie (Shimane University)
Asymptotic stability for nonlinear diﬀerential equations with timevarying coeﬃcients(Lunch)13:30〜14:10 Yukihiko Nakata (Shimane University)【Special Lecture】
Epidemics with waning immunity(Break)14:20〜14:40 Rong Qiang* (University of Science and Technology Beijing)
Wanbiao Ma (University of Science and Technology Beijing)
Ke Guo (University of Science and Technology Beijing)
The diﬀerential equation model of pathogenesis of Kawasaki disease
with theoretical analysis
14:40〜15:00 Liu Yang* (Northeast Normal University),
Yukihiko Nakata (Shimane University)
Epidemics with boosting of immunity
15:00〜15:20 Ke Guo* (University of Science and Technology Beijing)
Wanbiao Ma (University of Science and Technology Beijing)
Global dynamics analysis of a diﬀerential
equation model of Kawasaki disease pathogenesis(Break)15:30〜15:50 Na Li* (University of Science and Technology Beijing)
Ping Lin (University of Dundee)
Fuzheng Gao (Shandong University)
An expanded mixed ﬁnite element method for sobolev equations
15:50〜16:10 Yang Liu* (Northeast Normal University)
Takeshi Wada (Shimane University)
Long range scattering and modiﬁed wave operators for the MaxwellSchrödinger equation in three space dimensions
16:10〜16:30 Kaiqiang Zhang* (University of Science and Technology Beijing)
Baiyu Liu (University of Science and Technology Beijing)
Finite time blow-up and global existence for the nonlocal hyperbolic
equation

11 月 18 日
10:00〜10:40 Hairui Wei (University of Science and Technology Beijing)【Special
Lecture】
Quantum information processing based on artiﬁcial atoms(Break)10:50〜11:10 Lutao Zhao (University of Science and Technology Beijing)
Guanrong Zeng* (University of Science and Technology Beijing)
Analysis of timeliness of oil price news information based on SVM

11:10〜11:30 Yoshiki Ishihara* (Shimane University)
Jitsuro Sugie (Shimane University)
Integral averaing technique for oscillation of second-order linear selfadjoint diﬀerential equations with impulsive eﬀect
11:30〜11:50 Chunyan Liu* (University of Science and Technology Beijing)
Liancun Zheng (University of Science and Technology Beijing)
Ping Lin (University of Science and Technology Beijing)
Flow and heat transfer of Bingham plastic ﬂuid over a rotating disk
with variable thickness(Lunch)13:30〜13:50 Kazuki Seto* (Shimane University)
Daishi Kuroiwa (Shimane University)
Arcwise connected quasiconvex functions and its applications
13:50〜14:10 Xingyan Li* (University of Science and Technology Beijing)
Yan Xu (University of Science and Technology Beijing)
Human age prediction based on DNA methylation using a gradientboosting regressor
14:10〜14:30 Hiroyuki Ohtani* (Shimane University)
Koji Okano* (Shimane University)
Daishi Kuroiwa (Shimane University)
Constraint qualiﬁcations for the Lagrange-duality of extended realvalued convex optimization problems(Break)14:40〜15:00 Yingxi Yang* (University of Science and Technology Beijing)
Yan Xu (University of Science and Technology Beijing)iGlu-Lys: A Predictor for lysine glutarylation through amino acidpair order features
15:00〜15:20 Takumi Murakami* (Shimane University)
Yuya Sumida* (Shimane University)
Daishi Kuroiwa (Shimane University)
Constraint qualiﬁcations for a Lagrange-type duality of extended realvalued DC optimization problems
2018 年 11 月 1 日作成

THE CONSTRUCTION OF ONE-DIMENSIONALDISCRETE CHAOS THEORY BASED ON
IMPROVED MAROTTO’S THEOREM
JIU LI* AND HONGYAN ZANG

In this talk, we consider one-dimensional map in the Chen-Lai alorithm [1] givenby the following discrete-time dynamical system(1)

xk+1 = f (xk ) + (N + ec ) xk (mod1) ,where f (x) ∈ C1 [0, 1], and f (0) = 0, the control parameters N and c are restricted
to be in |f ′ (x)| < 1 ≤ N and c > 0. It is proved that system (1) exists chaos inthe sense of Li-Yorke [2] from the point of chaos anti-control idea. Actually, such
equation (1) is via the origin, namely, let xk = 0 one obtains that xk+1 = 0.
Therefore, this talk intends to deal with the mathematical model with modulo
operation(2)

xk+1 = f (xk ) (mod1) ,where f (x) ∈ C1 [0, 1], and f (0) ∈/ Z. Obviously, let xk = 0 one gets that xk+1 ̸= 0.
We simply mark the derived map from the system (2) to g (x)(3)

g (x) := f (x) (mod1) ,where f (x) ∈ C1 [0, 1], and 0 < g (0) < 1.
In the map (3), given that f (x) is divided into two cases: strictly monotonically increasing and strictly monotonically decreasing, we analyze the existence of
their fixed points separately. And using the improved Marotto’s theorem [3], theconditions for the existence of chaotic properties are given. To be specific, in order to overcome the traditional structural limitations that a chaotic system can be
only through the origin, a one-dimensional discrete-time system with nonzero value
as x equaling 0 is firstly given. a systematic methodology can be developed here
for designing a one-dimensional discrete-time chaotic system which satisfies some
performances.
References[1] G. Chen and D. Lai, Feedback control of Lyapunov exponents for discrete-time dynamicalsystems, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 6 (1996), 1341–1349.
[2] T.Y. Li and J.A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), 985–992.
[3] Y. Shi and G. Chen, Discrete chaos in Banach spaces, Sci. China Ser. A 48 (2005), 222–238.
J. Li: Mathematics and Physics School, University of Science and Technology Beijing, Beijing 100083, China
E-mail address: sharooolooo@163.com
H. Zang: Mathematics and Physics School, University of Science and Technology
Beijing, Beijing 100083, China
E-mail address: zhylixiang@126.com

2010 Mathematics Subject Classification. Primary 34C28, 37C75, 37E10.
Key words and phrases. Chaotic system, Polynomial chaos, Snap-back repeller, Marotto’s
theorem.
*Presenting author.

EXISTENCE REGIONS OF POSITIVE PERIODIC SOLUTIONSFOR A MIXED DISCRETE HEMATOPOIESIS MODELYAN YAN* AND JITSURO SUGIEIn 1977, using ordinary diﬀerential equations, Mackey and Glass [4] proposed
mathematical models to describe the production process of mature blood cells.
Their models are divided into two types according to the characteristics of the production function. Since the regulatory mechanisms in hematopoiesis have not yet
been completely elucidated, they introduced a monotonically Decreasing function
and a Unimodal function in order to express its production process. We call thehematopoiesis models with the former production function and with the latter production function as D-type model (see [1]) and U-type model (see [5]), respectively.
On the other hand, discrete models have attracted attention in biomathematics.
Several researchers have pay attention to the study of discrete models of D-type
and/or U-type. For example, we refer to the works [2, 3, 6, 7].
In this talk, we combine D-type model and U-type model, and consider a mixed
hematopoiesis modelpq∑bi (k)x(k − ri (k)) ∑cj (k)(1)∆x(k) = − a(k)x(k) ++n (k − r (k))
n (k − s (k))
1
+
x
1
+
x
i
j
i=1
j=1
with n > 1 and p, q ∈ N. We assume that(i) a : Z → (0, 1) is an ω-periodic discrete function;(ii) bi : Z → (0, ∞), ri : Z → Z+ are ω-periodic discrete functions for 1 ≤ i ≤ p;(iii) cj : Z → (0, ∞), sj : Z → Z+ are ω-periodic discrete functions for 1 ≤ j ≤ q.
We give a suﬃcient condition for equation (1) to have positive ω-periodic solutions.
We also clarify the existence region of the positive ω-periodic solutions.
References[1] L. Berezansky, E. Braverman and L. Idels, Mackey-Glass model of hematopoiesis with monotone feedback revisited, Appl. Math. Comput. 219 (2013), 4892–4907.
[2] E. Braverman and S.H. Saker, Permanence, oscillation and attractivity of the discrete
hematopoiesis model with variable coeﬃcients, Nonlinear Anal. 67 (2007), 2955–2965.
[3] D. Jiang, D. O’Regan and R.P. Agarwal, Optimal existence theory for single and multiple positive periodic solutions to functional diﬀerence equations, Appl. Math. Comput. 161 (2005),
441–462.
[4] M.C. Mackey and L. Glass, Oscillation and chaos in physiological control system, Science,
New Series, 197 (1977), 287–289.
[5] X.-M. Wu, J.-W. Li and H.-Q. Zhou, A necessary and suﬃcient condition for the existenceof positive periodic solutions of a model of hematopoiesis, Comput. Math. Appl. 54 (2007),
840–849.
[6] Y. Yan and J. Sugie, Existence regions of positive periodic solutions for a discrete hematopoiesis model with unimodal production functions, preprint.
[7] Z. Yao, Existence and global attractivity of the unique positive periodic solution for discrete
hematopoiesis model, Topol. Methods Nonlinear Anal. 45 (2015), 423–437.
Yan Yan: Department of Mathematics, Shimane University, Matsue, Shimane 6908504, Japan
E-mail address: yanyan90811@gmail.com
Jitsuro Sugie: Department of Mathematics, Shimane University, Matsue, Shimane
690-8504, Japan
E-mail address: jsugie@riko.shimane-u.ac.jp
2010 Mathematics Subject Classification. Primary 37N25, 39A23, 92C37.
Key words and phrases. Discrete hematopoiesis model, Unimodal production function, Positive
periodic solutions, Global asymptotic stability, Lyapunov function.
*Presenting author.

THE METHOD RESEARCH OF LONG NON-CODING RNA
PREDICTION BASED ON DEEP LEARNING
LI BINGXIUWith the rapid development of high-throughput transcriptome sequencing technology, a large number of transcript sequences have been discovered, and how to
identify long non-coding RNAs and mRNAs from transcripts is a challenging task.
In this paper, we constructed a deep learning model to eﬀectively distinguish longnon-coding RNAs from mRNAs. First, in order to extract the context information,
we use the unsupervised GloVe algorithm to introduce the feature representationof the RNA sequence and use the k-mer embedding vector instead of the traditional one-hot encoding to get a better feature representation. Then we set up thesupervised deep learning framework, including the Bidirectional Long Short-Term
Memory model (BLSTM) layer and the convolutional neural network layer withthree hidden layers, it is used to extract deep features. Finally, in the supervised
training stage, we consider the binary classiﬁcation as the SoftMax regression of
the feature representation, calculating the category probability without the priorassumption of the data distribution, and complete the ﬁnal classiﬁcation purpose.
We hope that our model will provide eﬀective help in distinguishing between mature RNAs and long non-coding RNAs and become a potential tool to help humans
understand the diseases related to detected lncRNAs.
References[1] R.E. Green, A.S. Malaspinas and J. Krause, et al., A Complete Neandertal Mitochondrial
Genome Sequence Determined by High-Throughput Sequencing, Cell 134 (2008), 416–426.
[2] S. Hochreiter and J. Schmidhuber, Long short-term memory, Neural Comput. 9 (1997), 1735–
1780.
[3] Y. Kim, Convolutional neural networks for sentence classification, Proceedings of the 2014
Conference on Empirical Methods in Natural Language Processing, pp. 1746–1751.
[4] A. Li, J. Zhang and Z. Zhou, PLEK: a tool for predicting long non-coding RNAs and messenger RNAs based on an improved k- mer scheme, BMC Bioinformatics 15 (2014), 311, 10
pp.
[5] X. Min, W. Zeng, N. Chen, et al., Chromatin accessibility prediction via convolutional longshort-term memory networks with k-mer embedding, Bioinformatics 33 (2017), i92–i101.
[6] J. Pennington, R. Socher and C. Manning, GloVe: Global vectors for word representation,
Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing,pp. 1532–1543.
School of Mathematics and Physics, University of Science and Technology Beijing,
Beijing 100083, China
E-mail address: grace41363011@126.com

Key words and phrases. lncRNA, K-mer, Prediction, Deep learning, SoftMax.

ASYMPTOTIC STABILITY FOR NONLINEAR DIFFERENTIAL
EQUATIONS WITH TIME-VARYING COEFFICIENTSHIROSHI SHIOZAKI* AND JITSURO SUGIE

We consider the nonlinear diﬀerential equation()′(1)
ϕp (x′ ) + f (t, x, x′ )ϕp (x′ ) + g(t, x) = 0,
where f is a continuous function on [0, ∞) × R2, g is a continuous function on[0, ∞) × R satisfying xg(t, x) > 0 for (t, x) ∈ [0, ∞) × R\{0} and ϕp is a continuousfunction deﬁned by{|u|p−2 u if u ̸= 0,
ϕp (u) =0
if u = 0,
with p > 1. Equation (1) has the only equilibrium (x, x′ ) = (0, 0).
In the special case that f (t, x, x′ ) = h(t) and g(t, x) = ϕp (x), equation (1)becomes the half-linear diﬀerential equation(2)′(ϕp (x′ )) + h(t)ϕp (x′ ) + ϕp (x) = 0.

Sugie [2] proved that a necessary and suﬃcient condition for the equilibrium of (2)to be (globally) asymptotically stable is∫ ∞ ( ∫ t H(s) )eds(3)
ϕp∗ 0 H(t)dt = ∞e0
under the assumption
(4)

∫ t+d
lim inft→∞h(s)ds > 0,t∫twhere p∗ is a number satisfying (p − 1)(p∗ − 1) = 1 and H(t) = 0 h(s)ds. Notethat ϕp∗ is the inverse function of ϕp . Although the result in [2] is very sharp, for a
concretely given h, it is diﬃcult to judge whether condition (3) is satisﬁed or not.
In this talk, by using the method of Artstein and Infante [1], we give a condition
which can easily guarantee that the equilibrium of (1) (or (2)) is asymptoticallystable.
References[1] Z. Artstain, and E. F. Infante, On the asymptotic stability of oscillators with unbounded
damping, Quart. Appl. Math. 34 (1976), 195–199.
[2] J. Sugie, Global asymptotic stability for damped half-linear oscillators, Nonlinear Anal. 74(2011), 7151–7167.
Hiroshi Shiozaki: Department of Mathematics, Shimane University, Matsue, Shimane
690-8504, Japan
E-mail address: n18m012@matsu.shimane-u.ac.jp
Jitsuro Sugie: Department of Mathematics, Shimane University, Matsue, Shimane
690-8504, Japan
E-mail address: jsugie@riko.shimane-u.ac.jp

2010 Mathematics Subject Classification. Primary 34D05, 34D20.
Key words and phrases. Nonlinear diﬀerential equation, Asymptotic stability.
*Presenting author.

EPIDEMICS WITH WANING IMMUNITYYUKIHIKO NAKATA

We ﬁrst formulate an SIRS type epidemic model by delay diﬀerential equations,to describe disease transmission dynamics in a population. It is assumed thatthe duration of individuals immunity, obtained upon the infection, is ﬁnite, thus
individuals do not acquire lifelong immunity. We analyze stability of equilibria
and show that the endemic equilibrium becomes unstable via Hopf bifurcation, as
model parameters change. For a special case, following the idea by Kaplan andYorke (1974), we study the existence of a periodic solution of period 2.
Yukihiko Nakata: Department of Mathematics, Shimane University, Matsue, Shimane
690-8504, Japan
E-mail address: ynakata@riko.shimane-u.ac.jp

2010 Mathematics Subject Classification. Primary 92D30.
Key words and phrases. Epidemic models, Waning immunity, Stability, Delay diﬀerential
equation.

THE DIFFERENTIAL EQUATION MODEL OF PATHOGENESISOF KAWASAKI DISEASE WITH THEORETICAL ANALYSISRONG QIANG*, WANBIAO MA, AND KE GUO

Kawasaki disease, an autoimmune disease , is a systemic vasculitis mainly aﬀecting children younger than 5 years old [3]. Due to the delayed therapy and diagnosis,
coronary artery abnormalities develop in children with Kawasaki disease, and leads
to a high risk of acquired heart disease. Later, patients may cause myocardial
infarction or even sudden death. Unfortunately, at present, the pathogenesis of
Kawasaki disease remains unknown and this disease lacks of speciﬁc and sensitive
biomarkers, which bring diﬃculties to diagnose and cure [1]. Therefore it is a highly
focused topic to research on the pathogenesis of Kawasaki disease. Some scholars
believe that Kawasaki disease is caused by the cross reaction of external infection
and organ tissue composition, hereby triggering disorder of the immune system andproducing a variety of inﬂammatory factors [1, 2]. On the basis of considering thefactors such as inﬂammatory factors, adhesion factors, endothelial cell growth factors and so on, put forward a kind of dynamic model of pathogenesis of Kawasaki
disease by the theory of ordinary diﬀerential equation. It is found that the dynamic
model can show complex dynamic behavior [4, 5], such as the forward and backward bifurcation of the equilibria. This article reveals the possible complexity of
infection of Kawasaki disease, and provides a theoretical references for the researchof pathogenisis and clinical treatment of Kawasaki disease.
References[1] S. Bayers, S.T. Shulman and A.S. Paller, Kawasaki disease: Part I. Diagnosis, clinical features,and pathogenesis, J. Am. Acad. Dermatol. 69 (2013), 501e1–501e11.
[2] C. Galeotti, S.V. Kaveri, R. Cimaz, I. Kon-Paut and J. Bayry, Predisposing factors, pathogenesis and therapeutic intervention of Kawasaki disease, Drug. Discov. Today. 21 (2016),
1850–1857.
[3] T. Kawasaki, Acute febrile mucocutaneous syndrome with lymphoid involvement with speciﬁcdesquamation of the ﬁngers and toes in children, Arerugi. 16 (1967), 178–222.
[4] M.A. Nowak and C.R.M. Bangham, Population dynamics of immune responses to persistentvirus, Science 272 (1996), 74–79.
[5] M.A. Nowak and R.M. May, Virus Dynamics: Mathematical Principles of Immunology andVirology, Nature Medicine 410 (2001), 412–413.
Rong Qiang : Department of Mathematics, University of Science and Technology
Beijing, Beijing 100083, China
E-mail address: 1292436826@qq.com
Wanbiao Ma : Department of Mathematics, University of Science and Technology
Beijing, Beijing 100083, China
E-mail address: wanbiao ma@ustb.edu.cn
Ke Guo : Department of Mathematics, University of Science and Technology Beijing,
Beijing 100083, China
E-mail address: ke guo@163.com

2010 Mathematics Subject Classification. Primary 34D23, 92B05.
Key words and phrases. Kawasaki disease, Systemic vasculitis, Diﬀerential equation model,
Stability.
*Presenting author.

EPIDEMICS WITH BOOSTING OF IMMUNITY
LIU YANG* AND YUKIHIKO NAKATA

We formulate an epidemic model with waning and boosting of immunity by delay
diﬀerential equations, following the idea by Aron [1, 2]. In the model, recovered
individuals may be reinfected because the immune system does not confer longlasting immunity against a pathogen, thus the immunity wanes. On the other
hand, it is also reported that the natural immunity is enhanced by the continued
exposure to infection which is called boosting eﬀect. Our main purpose is to explore
the eﬀect of the boosting of immunity on the disease transmission dynamics using
an epidemic model. We also compare the transmission dynamic with and without
boosting eﬀect by numerical simulations.
References[1] J.L. Aron, Dynamics of acquired immunity boosted by exposure to infection, Math. Biosci.
64 (1983), 249–259.
[2] J.L. Aron, Acquired immunity dependent upon exposure in an SIRS epidemic model, Math.
Biosci. 88 (1988), 37–47.
Liu Yang: School of Mathematics and Statistics, Northeast Normal University,
Changchun, Jilin 130024, China / Department of Mathematics, Shimane University, Matsue, Shimane 690-8504, Japan
E-mail address: yangl994@nenu.edu.cn
Yukihiko Nakata: Department of Mathematics, Shimane University, Matsue, Shimane
690-8504, Japan
E-mail address: ynakata@riko.shimane-u.ac.jp

2010 Mathematics Subject Classification. Primary 92D30.
Key words and phrases. Reinfection, Boosting immunity, Stability, Lambert W function.
*Presenting author.

GLOBAL DYNAMICS ANALYSIS OF A DIFFERENTIAL
EQUATION MODEL OF KAWASAKIDISEASE PATHOGENESISKE GUO*, WANBIAO MA, AND RONG QIANG

Kawasaki disease, also known as mucocutaneous lymph node syndrome (MCLS),
was first discovered by Japanese Kawasaki physician in 1967. It is a systemic
vasculitis that common occurs in infants and young children [2], if not discovered
and treated in time, may induce acquired heart disease, cause coronary arterydisease [1]. In order to provide a theoretical basis for the research and clinicaltreatment of the pathogenesis of Kawasaki disease, Qiang, Ma and Guo [3] proposedmodel:
k6 V (t)E(t)− k1 E(t)P (t) − d1 E(t),Ė(t) =r +
1 + V (t)V̇ (t) =k2 E(t)P (t) − d2 V (t),(1)
 Ċ(t) =k3 E(t)P (t) + k4 V (t) − d3 C(t),Ṗ (t) =k5 C(t) − d4 P (t),and gave a complete analysis on the local stability of the equilibria. Where E(t),V (t), C(t) and P (t) represent concentration of normal endothelial cells, vascular endothelial growth factors, activated adhesion factors and chemokines, inflammatory
factors in the lesion area at time t in acute stage of Kawasaki disease, respectively.
All the parameters are positive constants.
In this talk, the main purpose is to study the global stability of model (1). Sufficient conditions are obtained for the global asymptotic stability, by constructing
suitable Lyapunov functions and using Lyapunov-LaSalle invariance principle. In
addition, we give some numerical simulations to illustrate our analytical results.
References[1] H. Kato, Cardiovascular complications in Kawasaki disease: coronary artery lumen and longterm consequences, Prog. Pediatr. Cardiol. 19 (2004), 137–145.
[2] T. Kawasaki, Acute febrile mucocutaneous syndrome with lymphoid involvement with speciﬁcdesquamation of the ﬁngers and toes in children, Arerugi. 16 (1967), 178–222. (in Japanese)[3] R. Qiang, W. Ma and K. Guo, The diﬀerential equation model of pathogenesis of Kawasaki
disease with theoretical analysis, Math. Biosci. (submitted)
Ke Guo: School of Mathematics and Physics, University of Science and Technology
Beijing, Beijing100083, PR China
E-mail address: ke guo@163.com
Wanbiao Ma: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
E-mail address: wanbiao ma@ustb.edu.cn
Rong Qiang: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
E-mail address: 1292436826@qq.com

2010 Mathematics Subject Classification. Primary 34D23, 92B05.
Key words and phrases. Kawasaki disease, Diﬀerential equation model, Global stability, Lyapunov function.
*Presenting author.

AN EXPANDED MIXED FINITE ELEMENT METHOD FOR
SOBOLEV EQUATIONSNA LI*, PING LIN, AND FUZHENG GAOLet Ω ⊂ R2 be a bounded domain with piecewise smooth boundary ∂Ω. For
ﬁxed 0 < T < ∞, we consider the following initial and boundary value problem: ut − µ∆ut − γ∆u = f, (x, y, t) ∈ Ω × (0, T ],
(1)




u(x, y, t) = 0,(x, y, t) ∈ ∂Ω × (0, T ],u(x, y, 0) = φ0 (x, y),(x, y) ∈ Ω,

where ut denotes the time derivative of the function u, µ and γ are two positive
constants, the source term f (x, y, t) and the initial value function φ0 (x, y) are sufﬁciently smooth.
The purpose of this talk is to introduce the expanded mixed ﬁnite element
method for the two-dimensional Sobolev equations. We show the existence anduniqueness of the solution of the mixed ﬁnite element method, describe the semidiscrete formulation and the fully discrete formulation for Eq. (1), and provide theerror estimates of the solution. The optimal error estimates are obtained. Finally,
we provide two numerical examples to verify that numerical results are consistent
with theoretical conclusions.
References[1] N. Li, F. Gao and T. Zhang, An expanded mixed ﬁnite element method for Sobolev equation,
J. Comput. Anal. Appl. 15 (2013), 535–543[2] W. Liu, H. Rui and H. Guo, A two-grid method with expanded mixed element for nonlinear
reaction-diﬀusion equations, Acta Math. Appl. Sin. Engl. Ser. 27 (2011), 495–502.
[3] D. Shi and Y. Zhang, High accuracy analysis of a new nonconforming mixed ﬁnite element
scheme for Sobolev equations, Appl. Math. Comput. 218 (2011), 3176–3186.
[4] T. Sun, A Godunov-mixed ﬁnite element method on changing meshes for the nonlinear
Sobolev equations, Abstr. Appl. Anal. 2012, Article ID 413718, 19 pp.
Na Li: School of Mathematics and Physics, University of Science and Technology
Beijing, Beijing 100083, China
E-mail address: dajiena2002@163.com
Ping Lin: Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK
E-mail address: p.lin@dundee.ac.uk
Fuzheng Gao: School of Mathematics, Shandong University, Jinan 250100, China
E-mail address: fzgao@sdu.edu.cn

2010 Mathematics Subject Classification. Primary 65M60, 65N06.
Key words and phrases. Sobolev Equation; Expanded Mixed Finite Element; Error Estimate;
Numerical Experiment.
*Presenting author.

LONG RANGE SCATTERING AND MODIFIED WAVEOPERATORS FOR THE MAXWELL-SCHRÖDINGER
EQUATION IN THREE SPACE DIMENSIONSYANG LIU* AND TAKESHI WADA

We consider the scattering theory for the Maxwell-Schrödinger equations under
the Lorentz gauge conditions in three space dimensions.
i∂t u = −(1/2)∆A u + Ae u
(1)
□Ae = J0
□A = J
where (A, Ae ) is an R3+1 valued function deﬁned in space time R3+1 , ∇A = ∇ − iAand ∆A = ∇2A are the covariant gradient and covariant Laplacian respectively and□ = ∂t2 − ∆ is the d’Alembertian. J0 = |u|2 and J = Imū∇A u. By the current
conservation ∂t J0 + ∇ · J = 0.
We prove the existence of modiﬁed wave operators for the Maxwell-Schrödinger
system, without any restriction on the size of those data. To this end, we solve
this system with prescribed asymptotic behaviour as t → ∞, deﬁned in terms of
Schrödinger and Maxwell asymptotic data. This system belongs to the borderline
between the short range case and the long range one, so that the prescribed asymptotic behaviour for the Schrödinger function includes a suitable phase correction.
The method consists in partially solving the Maxwell equations for the potentials,
substituting the result into the Schrödinger equation, which then becomes bothnonlinear and nonlocal in time. The Schrödinger function is then parametrized interms of an amplitude and a phase satisfying a suitable auxiliary system. Then wesolve the Cauchy problem for this auxiliary system by an energy method.
References[1] J. Ginibre and G. Velo, Long range scattering and modified wave operators for the WaveSchrödinger system, Ann. Henri Poincaré 3 (2002), 537–612.
[2] J. Ginibre and G. Velo, Long range scattering and modified wave operators for the MaxwellSchrödinger system II. The General case, Ann. Henri Poincaeé 8 (2007), 917–994.
[3] M. Nakamura and T. Wada, Local well-posedness for the Maxwell-Schrödinger equations,Math. Ann. 332 (2005), 565–604.
[4] M. Nakamura and T. Wada, Global existence and uniqueness of solutions to the MaxwellSchrödinger equations, Comm. Math. Phys. 276 (2007), 315–339.
Yang Liu: School of Mathematics and Statistics, Northeast Normal University,
Changchun, Jilin 130024, China / Department of Mathematics, Shimane University, Matsue, Shimane 690-8504, Japan
E-mail address: liuy694@nenu.edu.cn
Takeshi Wada: Department of Mathematics, Shimane University, Matsue, Shimane
690-8504, Japan
E-mail address: wada@riko.shimane-u.ac.jp

Key words and phrases. Lorentz gauge, Maxwell-Schrödinger equation, Modified wave operator, Energy method.
*Presenting author.

FINITE TIME BLOW-UP AND GLOBAL EXISTENCE FOR THE
NONLOCAL HYPERBOLIC EQUATIONKAIQIANG ZHANG* AND BAIYU LIU

In this talk, we consider the initial boundary value problem of a hyperbolic
equation with nonlocal nonlinear source on a bounded smooth domain condition:

1
p
p−2
 utt = ∆u + ( |x|n−2 ∗ |u| )|u| u, x ∈ Ω, t > 0;u(x, t) = 0,x ∈ ∂Ω, t > 0;u(x, 0) = u0 (x), ut (x, 0) = u1 (x)x ∈ Ω;
where Ω is a bounded domain in Rn ,n ≥ 3 ,1 < p < (n + 2)/(n − 2). The vacuum
isolation of solutions are obtained by introducing a family of potential well.
Sattinger [8] ﬁrstly studied hyperbolic equation with nonlinear source |u|p−2 u byintroducing potential well method.The potential well method help us understandunder what conditions will the solution exist for all time and under what conditions
will the solution become unstable to collapse. Then,by using potential well method,
we obtain a threshold of global weak solution and blow up for weak solutions with
low initial energy.
When blow-up occurs, the blow-up time Tmax can’t usually be computed exactly.
It is therefore of great importance in practice to determine lower bounds for Tmax .
In this talk, if u(x, t) blow up at time Tmax ,we give a lower bound for Tmax .
References[1] X. Li and B. Liu B, Vacuum isolating, blow up threshold and asymptotic behavior of solutions
for a nonlocal parabolic equation, J. Math. Phys. 58 (2017), 101503, 9 pp.
[2] Y. Liu and R. Xu, Wave equations and reaction-diﬀusion equations with several nonlinear
source terms of diﬀerent sign, Discrete Contin. Dyn. Syst. Ser. B 7 (2007), 171–189.
[3] Y. Liu, R. Xu and T. Yu, Wave equations. and reaction-diﬀusion equations with several
nonlinear source terms, Appl. Math. Mech. 28 (2007), 1209–1218.
[4] L.E. Payne and D.H. Sattinger, Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math. 22 (1975), 273–303.
[5] G.A. Philippin, Lower bounds for blow-up time in a class of nonlinear wave equations, Z.
Angew. Math. Phys. 66 (2015), 129–134.
[6] P. Pucci and J. Serrin, Some new results on global nonexistence for abstract evolution equation with positive initial energy, Topol. Methods Nonlinear Anal. 10 (1997), 241–247.
[7] P. Pucci and J. Serrin, Global nonexistence for abstract evolution equations with positive
initial energy, J. Diﬀerential Equations 150 (1998), 203–214.
[8] D.H. Sattinger, On global solution of nonlinear hyperbolic equations, Arch. Ration. Mech.
Anal. 30 (1968), 148–172.
[9] Y. Wang, A suﬃcient condition for ﬁnite time blow up of the nonlinear Klein-Gordon equations with arbitrary positive initial energy, Proc. Amer. Math. Soc. 136 (2008), 3477–3482.
[10] R. Xu, Initial boundary value problem for semilinear hyperbolic equations and parabolic
equations with critical initial data, Quart. Appl. Math. 68 (2010), 459–468.
Kaiqiang Zhang: Department of Mathematics, University of Science and Technology
Beijing, Beijing 100083, China
E-mail address: cav23@foxmail.com
Baiyu Liu: Department of Mathematics, University of Science and Technology Beijing, Beijing 100083, China
E-mail address: liuby@ustb.edu.cn
2010 Mathematics Subject Classification. Primary 35L20, 35A01, 35B44, 35D30.
Key words and phrases. Nonlocal hyperbolic equation; Vacuum isolation; Global existence;
Finite time blow-up; Lower bound for Tmax .
*Presenting author.

QUANTUM INFORMATION PROCESSING BASED ON
ARTIFICIAL ATOMSHAIRUI WEI* AND FUGUO DENG

Quantum logic gates play an important role in quantum computation [1]. The
precise control and manipulation of quantum states can be accomplished with quantum gates [5]. We present compact quantum circuits to deterministically implement
universal quantum logic gates on diﬀerent kinds of qubits via artiﬁcial atoms in optical microcavities [3, 7, 8]; Our schemes have some features. (1) The control qubitsof the hybrid universal gates are encoded on the ﬂying photons and they are excellent candidates for quantum communication, and target qubits are encoded on
the solid-state electron spins in artiﬁcial atoms and they are suitable for quantum
information storage and processing. (2) Compared with cross-Kerr-based or theparity-check proposals [2, 4], our schemes for optical gates do not require additional photonic qubits, which reduces quantum resources needed and decreases theerrors taking place on the photonic qubits. (3) Compared with the conventional
synthesis-based programs [6], our schemes for solid-state quantum gates are morecompact and simpler. Our schemes could be performed with high ﬁdelities and higheﬃciencies with current achievable experimental techniques.
References[1] A. Barenco, C. H. Bennett, R. Cleve, D.P. DiVincenzo, N. Margolus, P. Shor, T. Sleator,
J.A. Smolin and H. Weinfurter, Elementary gates for quantum computation, Phys. Rev. A
52 (1995), 3457–3467.
[2] C.W.J. Beenakker, D.P. DiVincenzo, C. Emary and M. Kindermann, Charge detection enables free-electron quantum computation, Phys. Rev. Lett. 93 (2004), 250501, 5 pp.
[3] J.-Z. Liu, H.-R. Wei and N.-Y. Chen, A heralded and error-rejecting three-photon hyperparallel quantum gate through cavity-assisted interactions, Sci. Rep. 8 (2018), 1885, 11 pp.
[4] K. Nemoto and W. J. Munro, Nearly deterministic linear optical controlled-NOT gate, Phys.
Rev. Lett. 93 (2004), 250502.
[5] M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).
[6] V.V. Shende, I.L. Markov and S.S. Bullock, Minimal universal two-qubit controlled-NOTbased circuits, Phys. Rev. A 69 (2004), 062321, 8 pp.
[7] H.-R. Wei and F.-G. Deng, Universal quantum gates for hybrid systems assisted by quantum
dots inside double-sided optical microcavities, Phys. Rev. A 87 (2013), 022305, 11 pp.
[8] H.-R. Wei and G.-L. Long, Universal photonic quantum gates assisted by ancilla diamondnitrogen-vacancy centers coupled to resonators, Phys. Rev. A 91 (2015), 032324.
Hairui Wei: Department of Applied Mathematics, School of Mathematics and Physics,
University of Science and Technology Beijing, Beijing 100083, China
E-mail address: hrwei@ustb.edu.cn
Fuguo Deng: Department of Physics, Applied Optics Beijing Area Major Laboratory,
Beijing Normal University, Beijing 100875, China
E-mail address: fgdeng@bnu.edu.cn

2010 Mathematics Subject Classification. Primary 81V10, 81V65.
Key words and phrases. Quantum information computation, Universal quantum logic gate,
Artificial atom.
*Presenting author.

ANALYSIS OF TIMELINESS OF OIL PRICE NEWSINFORMATION BASED ON SVM
LUTAO ZHAO AND GUANRONG ZENG*International oil price forecasting has always been an important and diﬃcultissue. With the renovation of big data technology, it is a new idea to correct andimprove the oil price forecasting model by collecting and extracting network news
information. However, due to timeliness and other complex factors of the networknews, the ability of online news to predict oil prices is unstable. In this paper, anovel method based on SVM (support vector machines) is proposed to explore thetimeliness of news towards oil price. The timeliness of news can be explained by theaccuracy of SVM. A multi-scale trend discovery method is proposed to more ﬂexibly
extract oil price trends at diﬀerent scales and in diﬀerent directions. The news texts
are marked in 82 diﬀerent ways. With the help of SVM, the text information is
directed and extracted, and the ability of the news to describe ﬂuctuations in oil
price trends is reﬂected by the quality indicators of classiﬁcation. The empiricalresults show that the new multi-scale trend discovery method has high reliability.
The ability of news to describe the short-term oil price trend only lasts for about
one week, and the relatively long-term trend can be maintained for two or eventhree weeks. News is more able to express information on relatively long-term
trends. In addition, information described in the news is more likely to have an
impact on the future rather than on the volatility of past oil prices. This study ofthe interactive relationship between news texts and oil price trends is a powerfulsupport for the application of news texts to forecast oil prices. At the same time, it
is also a powerful complement to the study of discrete correlations and interactions.
References[1] Z. Ding, Z. Liu, Y. Zhang and R. Long, The contagion eﬀect of international crude oil priceﬂuctuations on Chinese stock market investor sentiment, Applied Energy 187 (2017), 27–36.
[2] G.P.C. Fung, J.X. Yu and W. Lam, News sensitive stock trend prediction, in Advances in
Knowledge Discovery and Data Mining, PAKDD 2002, Lecture Notes in Computer Science,(eds. M.S. Chen, P.S. Yu and B. Liu) 2336, Springer (Berlin, Heidelberg 2002), pp. 481–493.
[3] B.S. Kumar and V.Ravi, A survey of the applications of text mining in ﬁnancial domain,
Knowledge-Based Systems 114 (2016), 128–147.
[4] J. Li, Z. Xu, H. Xu, L. Tang and L. Yu, Forecasting oil price trends with sentiment of online
news articles, Procedia Computer Sciences 91 (2016), 1081–1087.
[5] E. Panas and V. Ninni, Are oil markets chaotic? A non-linear dynamic analysis, Energy
Econmics 22 (2000), 549–568.
[6] J. Wang and J. Wang, Forecasting energy market indices with recurrent neural networks:
Case study of crude oil price ﬂuctuations, Energy 102 (2016), 365–374.
[7] L. Yu, S. Wang and K.-K. Lai, A rough-set-reﬁned text mining approach for crude oil market
tendency forecasting, Inter. J. Knowledge Syst. Sci. 2 (2005), 33–46.
[8] W. Zhuang, Y. Ye, Y. Chen and T. Li, Ensemble clustering for internet security applications,
IEEE Trans. Syst. Man Cybernetics 42 (2012), 1784–1796.
Lutao Zhao: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Guanrong Zeng: School of Mathematics and Physics, University of Science andTechnology Beijing, Beijing 100083, China
E-mail address: chashaozgr@163.com
Key words and phrases. Text Mining; International Oil Price; Timeliness; Trend.
*Presenting author.

INTEGRAL AVERAING TECHNIQUE FOR OSCILLATION OFSECOND-ORDER LINEAR SELF-ADJOINT DIFFERENTIAL
EQUATIONS WITH IMPULSIVE EFFECTYOSHIKI ISHIHARA* AND JITSURO SUGIEIn this talk, we consider the second-order linear self-adjoint diﬀerential equation{(r(t)x′ )′ + c(t)x = 0,t ̸= θk ,(1)′∆(r(θk )x (θk )) + bk x(θk ) = 0.
Here, the coeﬃcient r is a left piecewise continuously diﬀerentiable function on[t0 , ∞) and r(t) > 0 for t ≥ t0 ; the coeﬃcient c is a left piecewise continuous function
on [t0 , ∞); the sequence {θk } is strictly increasing and satisﬁes that θ1 ≥ t0 and θktends to ∞ as k → ∞; diﬀerence operator ∆ is deﬁned by ∆y(θk ) = y(θk+ ) − y(θk− );the sequence {dk } is a sequence of real numbers. The second part in the equation (1)is the so-called impulsive eﬀect. Equation (1) is considered to be a model describing a motion that the movement speed of a mass point changes suddenly due tosome inﬂuence.
Many researchers have studied the oscillation problem for self-adjoint diﬀerential
equations without impulsive eﬀect,(2)(r(t)x′ )′ + c(t)x = 0.

For example, we can refer to Li [1]. The purpose of this talk is to report on how
the inﬂuence is exerted on the oscillation of solutions when adding impulsive eﬀect
to equation (2). Very recently, Sugie and Ishihara [2] gave an oscilation criterion
for equation (1) in the special case that r(t) = 1 for t ≥ t0 .
Our results can be obtained using the ideas of Li [1] in addition to Integral
averaging method and Riccati’s technique. We give an example to show that theobtained result includes the oscillation criterion in [2].
References[1] H.-J. Li, Oscillation criteria for second order linear diﬀerential equations, J. Math. Anal .
Appl. 194 (1995), 217–234.
[2] J. Sugie and K. Ishihara, Philos-type oscillation criteria for linear diﬀerential equations with
impulsive eﬀect, accepted for publication in J. Math. Anal. Appl. (https://doi.org/10.1016/
j.jmaa.2018.10.041)[3] Ch.G. Philos, Oscillation theorems for linear diﬀerential equations of second order, Arch.
Math. (Basel) 53 (1989), 483–492.
Yoshiki Ishihara: Department of Mathematics, Shimane University, Matsue, Shimane
690-8504, Japan
E-mail address: ysk.yopoko0206@gmail.com
Jitsuro Sugie: Department of Mathematics, Shimane University, Matsue, Shimane
690-8504, Japan
E-mail address: jsugie@riko.shimane-u.ac.jp

2010 Mathematics Subject Classification. Primary 34C10, 34C29.
Key words and phrases. Oscillation, Implusive, Integral averaging method, Riccati’s technique.
*Presenting author.

FLOW AND HEAT TRANSFER OF BINGHAM PLASTIC FLUIDOVER A ROTATING DISK WITH VARIABLE THICKNESSCHUNYAN LIU*, LIANCUN ZHENG, AND PING LIN

In this talk, we consider the steady ﬂow and heat transfer of Bingham plastic
ﬂuid over a rotating disk of ﬁnite radius with variable thickness radially in boundary layer. The boundary layer ﬂow is caused by the rotating disk when the extra
stress is greater than the yield stress of the Bingham ﬂuid. The analyses of thevelocity and temperature ﬁeld related to the variable thickness disk have not been
investigated in current literatures. The governing equations are ﬁrst simpliﬁed
into ordinary diﬀerential equations owing to the generalized Von Karman transformation for seeking solutions easily. Then semi-similarity approximate analyticalsolutions are obtained by using the homotopy analysis method (HAM) for diﬀerent
physical parameters. It is found that the Bingham number clearly inﬂuences thevelocity ﬁeld distribution and the skin friction coeﬃcient Cf r are nonlinear growthwith respect to the shape parameter m. Additionally, the eﬀects of the involved
parameters (i.e. shape parameter m, variable thickness parameter β, Reynolds
number Rev and Prandtl number P r) on velocity and temperature distribution areinvestigated and analyzed in detail.
References[1] E.C. Bingham and H. Green, Paint, A plastic material and not a viscous liquid; the measurement of its mobility and yield value, Proc. Amer. Soc. Test Mater. II (1919), 640–675.
[2] S. Liao, On the homotopy analysis method for nonlinear problems, Appl. Math. Comput. 2(2004), 499–513.
[3] A.A. Rashaida, D.J. Bergstrom and R.J. Sumner, Mass transfer from a rotating disk to abingham fluid, J. Appl. Mech. 1 (2006), 108–111.
Chunyan Liu: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
E-mail address: liuchunyanbeike@163.com
Liancun Zheng: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
E-mail address: liancunzheng@ustb.edu.cn
Ping Lin: School of Mathematics and Physics, University of Science and Technology
Beijing, Beijing 100083, China
E-mail address: plin@maths.dundee.ac.uk

2010 Mathematics Subject Classification. Primary 76A05, 76N20.
Key words and phrases. Bingham plastic fluid, Homotopy analysis method, Rotating disk, Von
Karman transformation.
*Presenting author.

ARCWISE CONNECTED QUASICONVEX FUNCTIONS AND ITSAPPLICATIONSKAZUKI SETO* AND DAISHI KUROIWA

The minimax theorem guarantee that the max-min inequality is also an equality.
Minimax theorems apply to the game theory in order for us to find solutions. The
first and the most famous one was given by von Neumann [1] and Sion [2] gave ageneralization of von Neumann’s minimax theorem.
In this talk, we give a generalization of Sion’s minimax theorem in terms ofarcwise connected quasiconvex functions.
References[1] J. v.Neumann, Zur theorie der gesellschaftsspiele, Math. Ann. 100 (1928), 295–320.
[2] M. Sion, On general minimax theorems, Pacific J. Math. 8 (1958), 171–176.
[3] H. Komiya, Elementary proof for Sion’s minimax theorem, Kodai Math. J. 11 (1988), 5–7.
[4] D. Kuroiwa and K. Seto, A Sion’s minimax theorem on the product of arcwise topologicalspaces, preprint.
Kazuki Seto: Interdisciplinary Graduate School of Science and Engineering, Shimane University, Matsue, Shimane, 690-8504, Japan
E-mail address: k.seto@math.shimane-u.ac.jp
Daishi Kuroiwa: Major in Interdisciplinary Science and Engineering, Shimane University, Matsue, Shimane, 690-8054, Japan
E-mail address: kuroiwa@math.shimane-u.ac.jp

2010 Mathematics Subject Classification. Primary 26B25; Secondary 49J35.
Key words and phrases. Minimax theorem, Arcwise connected, Set-optimization.
*Presenting author.

HUMAN AGE PREDICTION BASED ON DNA METHYLATIONUSING A GRADIENT BOOSTING REGRESSORXINGYAN LI* AND YAN XU

All tissues of organisms will become old as time goes on. Recent studies haveshown that human aging is related to the alteration of DNA methylation in genome
speciﬁc locations, and these epigenetic modiﬁcations can be used to estimate theindividual age. We analyzed 16 sets of healthy samples and 9 sets of diseased
samples. Six age-related CpG sites were selected through calculating Pearson correlation coeﬃcients between age and DNA methylation values. We built a gradientboosting regressor model for these age-related CpG sites. 70% of the data was
randomly selected as training data and the other 30% as independent data in eachdataset for 25 runs in total. In the training dataset, the healthy samples showedthat the correlation between predicted age and DNA methylation was 0.97, and themean absolute deviation (MAD) was 2.72 years. In the independent dataset, theMAD was 4.06 years. The proposed model was further tested using the diseased
samples. The MAD was 5.44 years for the training dataset and 7.08 years for the
independent dataset. Furthermore, our model worked well when it was applied tosaliva samples. These results illustrated that the age prediction based on six DNA
methylation markers is very eﬀective using the gradient boosting regressor.
References[1] S.D. Din, A. Godfrey, B. Galna, S. Lord and L. Rochester, Free-living gait characteristics
in ageing and Parkinson’s disease: impact of environment and ambulatory bout length, J.
Neuroeng. Rehabil. 13:46 (2016), pp. 12.
[2] A. Vidaki, D. Ballard, A. Aliferi, T.H. Miller, L.P. Barron and S.D. Court, DNA methylationbased forensic age prediction using artificial neural networks and next generation sequencing,
Forensic. Sci. Int. Genet. 28 (2017), 225–236.
[3] S.B. Zaghlool, M. Al-Shafai, W.A. Al Muftah, P. Kumar, M. Falchi and K. Suhre, Associationof DNA methylation with age, gender, and smoking in an Arab population, Clin. Epigenetics
7 (2015), 1–12.
Xingyan Li: Department of Information and Computer Science, University of Scienceand Technology Beijing, Beijing 100083, China
E-mail address: s20170744@xs.ustb.edu.cn
Yan Xu: Department of Information and Computer Science, University of Scienceand Technology Beijing, Beijing 100083, China
E-mail address: xuyan@ustb.edu.cn

Key words and phrases. Aging, DNA methylation, Epigenetics, Age prediction, Gradientboosting regressor.
*Presenting author.

CONSTRAINT QUALIFICATIONS FOR THE
LAGRANGE-DUALITY OF EXTENDED REAL-VALUEDCONVEX OPTIMIZATION PROBLEMSHIROYUKI OHTANI*, KOJI OKANO*, AND DAISHI KUROIWA

In this talk, we study the following convex optimization problem:(P) minimize
subject tof (x)gi (x) ≤ 0, i = 1, 2, . . . , m,and observe the Lagrange duality of the convex optimization problem. The Slater
condition is the most famous constraint qualiﬁcation for the Lagrange duality andit works when the contraint functions are extended real-valued in the setting 0 ·(+∞) = +∞. Also it is shown that Farkas Minkowski property (FM in short) is anecessary and suﬃcient constraint qualiﬁcation for Lagrange duality in the setting
0 · (+∞) = 0 by Goberna, Jeyakumar and López in 2008, however FM does notcontain the Slater condition. The purpose of this talk is to provide a necessary
and suﬃcient constraint qualiﬁcation for the Lagrange duality which contains the
Slater condition in the setting 0 · (+∞) = +∞.
References[1] V. Jeyakumar, A.M. Rubinov, B.M. Glover and Y. Ishizuka, Inequality systems and global
optimization, J. Math. Anal. Appl. 202 (1996), 900–919.
[2] J.E. Martı́nez-Legaz and M. Volle, Duality in D.C. programming: the case of several D.C.
constraints, J. Math. Anal. Appl. 237 (1999), 657–671.
[3] V. Jeyakumar, Constraint qualiﬁcations characterizing Lagrangian duality in convex optimization, J. Optim. Theory Appl. 136 (2008), 31–41.
[4] M.A. Goberna, V. Jeyakumar, M.A. López, Necessary and suﬃcient constraint qualiﬁcations
for solvability of systems of inﬁnite convex inequalities, Nonlinear Anal. 68 (2008), 1184–1194.
[5] R. Harada and D. Kuroiwa, Lagrange-type duality in DC programming, J. Math. Anal. Appl.
418 (2014), 415–424.
Hiroyuki Ohtani: Graduate School of Natural Science and Technology, Shimane
University, Matsue, Shimane, 690-8504, Japan
E-mail address: n18m007@matsu.shimane-u.ac.jp
Koji Okano: Graduate School of Natural Science and Technology, Shimane University, Matsue, Shimane, 690-8504, Japan
E-mail address: n18m008@matsu.shimane-u.ac.jp
Daishi Kuroiwa: Department of Mathematics, Shimane University, Matsue, Shimane,690-8054, Japan
E-mail address: kuroiwa@math.shimane-u.ac.jp

2010 Mathematics Subject Classification. Primary 90C25; Secondary 49N15.
Key words and phrases. Convex optimization problem, Lagrange duality, Constraint
qualiﬁcation.
*Presenting author.

IGLU-LYS: A PREDICTOR FOR LYSINE GLUTARYLATION
THROUGH AMINO ACID PAIR ORDER FEATURESYINGXI YANG* AND YAN XU

As one of the new posttranslational modiﬁcation(PTM), lysine glutarylation has
been identiﬁed in both prokaryotic and eukaryotic cells. These glutarylated proteins are involved in various cellular functions such as translation, metabolism andexhibited diverse subcellular localizations. Experimental identiﬁcation of lysine
glutarylation sites was in 2014 and also found its deglutarylase sirturn 5(SIRT 5).
Computational prediction of lysine glutarylation could be a complementary way tothe experimental technique. In this work the lysine glutarylation predictor iGlu-Lys
has been developed based on machine learning scheme. We have selected the best
feature scheme which took the amino acid pair order and special-position information into account from four constructions. Machine learning algorithm support
vector machine (SVM) has been adopted and its performance has been measured
for diﬀerent window length of peptides. In the 10-fold cross-validation with window
length 19 the AUC and MCC were 0.8944 and 0.5098, respectively. Diﬀerent ROC
curves in 6-, 8-, and 10-fold cross-validations were very close which illustrated therobustness of our predictor. The results of iGLu-Lys were better than the existing method GlutPred. Meanwhile, a free webserver for iGlu-Lys is accessible at
http://app.aporc.org/iGlu-Lys/.
References[1] W. Deng, Y. Wang, L. Ma, Y. Zhang, et al., Computational prediction of methylation typesof covalently modified lysine and arginine residues in proteins, Brief Bioinform. 18 (2017),
647–658.
[2] Y. Du, Z. Zhai, Y. Li, M. Lu, et al., Prediction of protein lysine acylation by integrating
primary sequence information with multiple functional features, J. Proteome Res. 15 (2016),
4234–4244.
[3] Z. Ju, J.-Z. Cao and H. Gu, Predicting lysine phosphoglycerylation with fuzzy SVM byincorporating k-spaced amino acid pairs into Chou’s general PseAAC, J. Theor. Biol. 397(2016), 145–150.
[4] Z. Ju and J.-J. He, Prediction of lysine glutarylation sites by maximum relevance minimum
redundancy feature selection, Anal. Biochem. 550 (2018), 1–7.
[5] Y. Xu, Y.-X. Ding, J. Ding, L.-Y. Wu and Y. Xue, Mal-Lys: prediction of lysine malonylationsites in proteins integrated sequence-based features with mRMR feature selection, Sci Rep.
6 (2016), 38318, 7 pp.
[6] Z. Ju and J.-J. He, Prediction of lysine glutarylation sites by maximum relevance minimum
redundancy feature selection, Anal. Biochem. 550 (2018), 1–7.
[7] Q. Zhao, Y. Xie, Y. Zheng, S. Jiang, et al, GPS-SUMO: a tool for the prediction of sumoylation sites and SUMO-interaction motifs, Nucleic Acids Res. 42 (2014), W325–W330.
Yingxi Yang: Department of Information and Computer Science, University of Science and Technology Beijing, Beijing 100083, China
E-mail address: 806874768@qq.com
Yan Xu: Department of Information and Computer Science, University of Scienceand Technology Beijing, Beijing 100083, China
E-mail address: xuyan@ustb.edu.cn

Key words and phrases. Posttranslational modification, Glutarylation, Amino acid pair, SVM..
*Presenting author.

CONSTRAINT QUALIFICATIONS FOR A LAGRANGE-TYPE
DUALITY OF EXTENDED REAL-VALUED
DC OPTIMIZATION PROBLEMSTAKUMI MURAKAMI*, YUYA SUMIDA*, AND DAISHI KUROIWA

We study the following optimization problem:(P)

minimizesubject tof0 (x) − g0 (x)fi (x) − gi (x) ≤ 0, i = 1, 2, . . . , m,where f0 , g0 : Rn → R, fi , gi : Rn → R ∪ {+∞} are convex functions for all i =1, 2, . . . , m. In the previous result in [?], a constraint qualification for a Lagrangetype duality of the optimization problem (P) was given when all constraint functions
are real-valued, and the constraint qualification does not work when these functions
are extended real-valued. The purpose of the talk is to give another constraint
qualification for the Lagrange-type duality of the optimization problem (P) whose
constraint functions are extended real-valued in the case 0 · (+∞) = +∞.
References[1] V. Jeyakumar, A.M. Rubinov, B.M. Glover and Y. Ishizuka, Inequality systems and global
optimization. J. Math. Anal. Appl. 202 (1996), 900–919.
[2] J.E. Martı́nez-Legaz and M. Volle, Duality in DC programming: the case of several DC
constraints, J. Math. Anal. Appl. 237 (1999), 657–671.
[3] M.A. Goberna, V. Jeyakumar and M.A. López, Necessary and suﬃcient constraint qualiﬁcations for solvability of systems of inﬁnite convex inequalities, Nonlinear Anal. 68 (2008),
1184–1194.
[4] R. Harada and D. Kuroiwa, Lagrange-type duality in DC programming, J. Math. Anal. Appl.
418 (2014), 415–424.
Takumi Murakami: Department of Mathematics, Interdisciplinary Graduate Schoolof Science and Engineering, Shimane University, Matsue, Shimane, 690-8504, Japan
Yuya Sumida: Department of Mathematics, Interdisciplinary Graduate School of
Science and Engineering, Shimane University, Matsue, Shimane, 690-8504, Japan
Daishi Kuroiwa: Department of Mathematics, Major in Interdisciplinary Science andEngineering, Shimane University, Matsue, Shimane, 690-8504, Japan

2010 Mathematics Subject Classification. Primary 90C26, 49N15.
Key words and phrases. Optimization problem, Ddiﬀerence of convex function, Lagrange duality, Constraint qualiﬁcation.
*Presenting author.