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Optimization of Dynamic Portfolio Insurance Model  [PDF]
Yuan Yao
Journal of Mathematical Finance (JMF) , 2012, DOI: 10.4236/jmf.2012.22019
Abstract: This paper establishes a dynamic portfolio insurance model under the condition of continuous time, based on Meton's optimal investment-consumption model, which combined the method of replicating dynamic synthetic put option using risk-free and risk assets. And it transfers the problem of investor's individual intertemporal dynamic portfolio insurance decision into a problem of static utility maximization under condition of continuous time, and give the optimal capital combination strategies corresponding to the optimal wealth level of the portfolio insurers, and compares the difference of strategies between this model and Merton model. The conclusions show that investors' optimal strategies of portfolio insurance are not dependent on their wealth, but market risk. That is to say, the higher the risk is, the more the demand of portfolio insurance is.
Estimates of sections of determinant line bundles on Moduli spaces of pure sheaves on algebraic surfaces
Yao Yuan
Mathematics , 2010,
Abstract: Let $X$ be any smooth simply connected projective surface. We consider some moduli space of pure sheaves of dimension one on $X$, i.e. $\mhu$ with $u=(0,L,\chi(u)=0)$ and $L$ an effective line bundle on $X$, together with a series of determinant line bundles associated to $r[\mo_X]-n[\mo_{pt}]$ in Grothendieck group of $X$. Let $g_L$ denote the arithmetic genus of curves in the linear system $\ls$. For $g_L\leq2$, we give a upper bound of the dimensions of sections of these line bundles by restricting them to a generic projective line in $\ls$. Our result gives, together with G\"ottsche's computation, a first step of a check for the strange duality for some cases for $X$ a rational surface.
Affine pavings for moduli spaces of pure sheaves on $\mathbb{P}^2$ with degree $\leq 5$
Yao Yuan
Mathematics , 2013,
Abstract: Let $M(d,r)$ be the moduli space of semistable sheaves of rank 0, Euler characteristic $r$ and first Chern class $dH (d>0)$, with $H$ the hyperplane class in $\mathbb{P}^2$. By previous work, we gave an explicit description of the class $[M(d,r)]$ of $M(d,r)$ in the Grothendieck ring of varieties for $d\leq 5$ and $g.c.d(d,r)=1$. In this paper we compute the fixed locus of $M(d,r)$ under some $(\mathbb{C}^{*})^2$-action and show that $M(d,r)$ admits an affine paving for $d\leq 5$ and $g.c.d(d,r)=1$. We also pose a conjecture that for any $d$ and $r$ coprime to $d$, $M(d,r)$ would admit an affine paving.
Motivic measures of moduli spaces of 1-dimensional sheaves on rational surfaces
Yao Yuan
Mathematics , 2015,
Abstract: We study the moduli space of rank 0 semistable sheaves on some rational surfaces. We show the irreducibility and stable rationality of them under some conditions. We also compute several (virtual) Betti numbers of those moduli spaces by computing their motivic measures.
Determinant line bundles on Moduli spaces of pure sheaves on rational surfaces and Strange Duality
Yao Yuan
Mathematics , 2010,
Abstract: Let $\mhu$ be the moduli space of semi-stable pure sheaves of class $u$ on a smooth complex projective surface $X$. We specify $u=(0,L,\chi(u)=0),$ i.e. sheaves in $u$ are of dimension $1$. There is a natural morphism $\pi$ from the moduli space $\mhu$ to the linear system $\ls$. We study a series of determinant line bundles $\lcn$ on $\mhu$ via $\pi.$ Denote $g_L$ the arithmetic genus of curves in $\ls.$ For any $X$ and $g_L\leq0$, we compute the generating function $Z^r(t)=\sum_{n}h^0(\mhu,\lcn)t^n$. For $X$ being $\mathbb{P}^2$ or $\mathbb{P}(\mo_{\pone}\oplus\mo_{\pone}(-e))$ with $e=0,1$, we compute $Z^1(t)$ for $g_L>0$ and $Z^r(t)$ for all $r$ and $g_L=1,2$. Our results provide a numerical check to Strange Duality in these specified situations, together with G\"ottsche's computation. And in addition, we get an interesting corollary in the theory of compactified Jacobian of integral curves.
Motivic measures of the moduli spaces of pure sheaves on $\mathbb{P}^2$ with all degrees
Yao Yuan
Mathematics , 2015,
Abstract: Let $\mathcal{M}(d,\chi)$ be the moduli stack of stable sheaves of rank 0, Euler characteristic $\chi$ and first Chern class $dH~(d>0)$, with $H$ the hyperplane class in $\mathbb{P}^2$. We compute the $A$-valued motivic measure $\mu_A(\mathcal{M}(d,\chi))$ of $\mathcal{M}(d,\chi)$ and get explicit formula in codimension $D:=\rho_d-1$, where $\rho_d$ is $d-1$ for $d=p$ or $2p$ with $p$ prime, and $7$ otherwise. As a corollary, we get the last $2(D+1)$ Betti numbers of the moduli scheme $M(d,\chi)$ when $d$ is coprime to $\chi$.
Moduli spaces of 1-dimensional semi-stable sheaves and Strange duality on $\mathbb{P}^2$
Yao Yuan
Mathematics , 2015,
Abstract: We study Le Potier's strange duality conjecture on $\mathbb{P}^2$. We show the conjecture is true for the pair ($M(2,0,2),~M(d,0)$) with $d>0$, where $M(2,0,2)$ is the moduli space of semistable sheaves of rank 2, zero first Chern class and second Chern class 2, and $M(d,0)$ is the moduli space of 1-dimensional semistable sheaves of first Chern class $dH$ and Euler characteristic 0.
Moduli spaces of semistable sheaves of dimension 1 on $\mathbb{P}^2$
Yao Yuan
Mathematics , 2012,
Abstract: Let $M(d,\chi)$ be the moduli space of semistable sheaves of rank 0, Euler characteristic $\chi$ and first Chern class $dH (d>0)$, with $H$ the hyperplane class in $\mathbb{P}^2$. We give a description of $M(d,\chi)$, viewing each sheaf as a class of matrices with entries in $\bigoplus_{i\geq0}H^0(\mathcal{O}_{\mathbb{P}^2}(i))$. We show that there is a big open subset of $M(d,1)$ isomorphic to a projective bundle over an open subset of a Hilbert scheme of points on $\mathbb{P}^2.$ Finally we compute the classes of M(4,1), M(5,1) and M(5,2) in the Grothendieck group of varieties, especially we conclude that M(5,1) and M(5,2) are of the same class.
A new approach for HIV-1 protease cleavage site prediction combined with feature selection  [PDF]
Yao Yuan, Hui Liu, Guangtao Qiu
Journal of Biomedical Science and Engineering (JBiSE) , 2013, DOI: 10.4236/jbise.2013.612144
Abstract:

Acquired immunodeficiency syndrome (AIDS) is a fatal disease which highly threatens the health of human being. Human immunodeficiency virus (HIV) is the pathogeny for this disease. Investigating HIV-1 protease cleavage sites can help researchers find or develop protease inhibitors which can restrain the replication of HIV-1, thus resisting AIDS. Feature selection is a new approach for solving the HIV-1 protease cleavage site prediction task and it’s a key point in our research. Comparing with the previous work, there are several advantages in our work. First, a filter method is used to eliminate the redundant features. Second, besides traditional orthogonal encoding (OE), two kinds of newly proposed features extracted by conducting principal component analysis (PCA) and non-linear Fisher transformation (NLF) on AAindex database are used. The two new features are proven to perform better than OE. Third, the data set used here is largely expanded to 1922 samples. Also to improve prediction performance, we conduct parameter optimization for SVM, thus the classifier can obtain better prediction capability. We also fuse the three kinds of features to make sure comprehensive feature representation and improve prediction performance. To effectively evaluate the prediction performance of our method, five parameters, which are much more than previous work, are used to conduct complete comparison. The experimental results of our method show that our method gain better performance than the state of art method. This means that the feature selection combined with feature fusion and classifier parameter optimization can effectively improve HIV-1 cleavage site prediction. Moreover, our work can provide useful help for HIV-1 protease inhibitor developing in the future.

 

2,4-Dimethylanilinium chloride
Ji-Yuan Yao
Acta Crystallographica Section E , 2010, DOI: 10.1107/s1600536810020568
Abstract: In the crystal structure of the title compound, C8H12N+·Cl , all H atoms bonded to the ammonium N atom are hydrogen bonded to the chloride ions, with N...Cl distances in the range 3.080 (2)–3.136 (2) , resulting in 16-membered macrocyclic rings involving four formula units of the title compound.
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