Investigating the Broad Matrix-Gate Network in the Mitochondrial ADP/ATP Carrier through Molecular Dynamics Simulations

The mitochondrial ADP/ATP carrier (AAC) exports ATP and imports ADP through alternating between cytosol-open (c-) and matrix-open (m-) states. The salt bridge networks near the matrix side (m-gate) and cytosol side (c-gate) are thought to be crucial for state transitions, yet our knowledge on these networks is still limited. In the current work, we focus on more conserved m-gate network in the c-state AAC. All-atom molecular dynamics (MD) simulations on a variety of mutants and the CATR-AAC complex have revealed that: (1) without involvement of other positive residues, the charged residues from the three Px[DE]xx[KR] motifs only are prone to form symmetrical inter-helical network; (2) R235 plays a determinant role for the asymmetry in m-gate network of AAC; (3) R235 significantly strengthens the interactions between H3 and H5; (4) R79 exhibits more significant impact on m-gate than R279; (5) CATR promotes symmetry in m-gate mainly through separating R234 from D231 and fixing R79; (6) vulnerability of the H2-H3 interface near matrix side could be functionally important. Our results provide new insights into the highly conserved yet variable m-gate network in the big mitochondrial carrier family.     

λ-Deformation: A Canonical Framework for Statistical Manifolds of Constant Curvature

This paper systematically presents the λ-deformation as the canonical framework of deformation to the dually flat (Hessian) geometry, which has been well established in information geometry. We show that, based on deforming the Legendre duality, all objects in the Hessian case have their correspondence in the λ-deformed case: λ-convexity, λ-conjugation, λ-biorthogonality, λ-logarithmic divergence, λ-exponential and λ-mixture families, etc. In particular, λ-deformation unifies Tsallis and Rényi deformations by relating them to two manifestations of an identical λ-exponential family, under subtractive or divisive probability normalization, respectively. Unlike the different Hessian geometries of the exponential and mixture families, the λ-exponential family, in turn, coincides with the λ-mixture family after a change of random variables. The resulting statistical manifolds, while still carrying a dualistic structure, replace the Hessian metric and a pair of dually flat conjugate affine connections with a conformal Hessian metric and a pair of projectively flat connections carrying constant (nonzero) curvature. Thus, λ-deformation is a canonical framework in generalizing the well-known dually flat Hessian structure of information geometry.     

强非局域非线性介质中的超高斯空间光孤子族

运用变分法,对任意实对称响应函数泰勒级数展开取至二阶,得到了1 1维强非局域非线性介质中光束传输的超高斯光束的近似分析解,提出了超高斯空间光孤子族模型。分析结果表明:束宽解是三角函数型,相移、空间啁啾以及临界输入功率都正比于超高斯光束的阶数,束宽振荡周期不仅与介质材料有关,而且还与光束和相位因子的阶有关。提出了准方波形空间光孤子的可能性。     

Weyl families of transformed boundary pairs

Let $(\mathfrak{L},\mathrm{\Gamma })$ be an isometric boundary pair associated with a closed symmetric linear relation T in a Krein space $\mathfrak{H}$. Let $M_{\mathrm{\Gamma }}$ be the Weyl family corresponding to $(\mathfrak{L},\mathrm{\Gamma })$. We cope with two main topics. First, since $M_{\mathrm{\Gamma }}$ need not be (generalized) Nevanlinna, the characterization of the closure and the adjoint of a linear relation $M_{\mathrm{\Gamma }}(z)$, for some $z\in \mathbb{C}\setminus \mathbb{R}$, becomes a nontrivial task. Regarding $M_{\mathrm{\Gamma }}(z)$ as the (Shmul'yan) transform of $zI$ induced by Γ, we give conditions for the equality in $\overline{M_{\mathrm{\Gamma }}(z)}\subseteq \overline{M_{\overline{\mathrm{\Gamma }}}(z)}$ to hold and we compute the adjoint $M_{\overline{\mathrm{\Gamma }}}{(z)}^{\ast }$. As an application, we ask when the resolvent set of the main transform associated with a unitary boundary pair for $T^{+}$ is nonempty. Based on the criterion for the closeness of $M_{\mathrm{\Gamma }}(z)$, we give a sufficient condition for the answer. From this result it follows, for example, that, if T is a standard linear relation in a Pontryagin space, then the Weyl family $M_{\mathrm{\Gamma }}$ corresponding to a boundary relation Γ for $T^{+}$ is a generalized Nevanlinna family; a similar conclusion is already known if T is an operator. In the second topic, we characterize the transformed boundary pair $({\mathfrak{L}}^{\prime },{\mathrm{\Gamma }}^{\prime })$ with its Weyl family $M_{{\mathrm{\Gamma }}^{\prime }}$. The transformation scheme is either ${\mathrm{\Gamma }}^{\prime }=\mathrm{\Gamma }{V}^{-1}$ or ${\mathrm{\Gamma }}^{\prime }=V\mathrm{\Gamma }$ with suitable linear relations V. Results in this direction include but are not limited to: a 1-1 correspondence between $(\mathfrak{L},\mathrm{\Gamma })$ and $({\mathfrak{L}}^{\prime },{\mathrm{\Gamma }}^{\prime })$; the formula for $M_{{\mathrm{\Gamma }}^{\prime }}-M_{\mathrm{\Gamma }}$, for an ordinary boundary triple and a standard unitary operator V (first scheme); construction of a quasi boundary triple from an isometric boundary triple $(\mathfrak{L},{\mathrm{\Gamma }}_0,{\mathrm{\Gamma }}_1)$ with $ker\mathrm{\Gamma }=T$ and $T_0=T_0^{\ast }$ (second scheme, Hilbert space case).     

Rota-Baxter簇系统与Gr\"obner-Shirshov基

从Yang-Baxter簇方程和Volterra积分方程得到的Rota-Baxter簇代数的概念出发,我们引入Rota-Baxter簇系统的概念,推广了Brzezinski提出的Rota-Baxter系统.我们证明这个概念也与结合Yang-Baxter簇对和pre-Lie簇代数有关.此外,作为Rota-Baxter簇系统的一个类比,我们引入平均簇系统的概念,并证明平均簇系统会得到dialgebra簇结构.我们还研究dendriform代数上的Rota-Baxter簇系统,并展示它们如何诱导quadri簇代数结构.最后,我们用Gr\"obner-Shirshov基的方法给出Rota-Baxter簇系统的一个线性基.     

涉及Picard例外值的亚纯函数正规族

本文研究了徐炎等人在文(Xu Y,Wu F Q,Liao L W.Picard values and normal families of meromorphic functions,Proc.R.Soc.Edinburgh,2009,139:1091-1099.)中提出的一个有关亚纯函数正规族猜想,得到了两个正规定则...     

Resolvent family for the evolution process with memory

In this paper, we investigate a class of the linear evolution process with memory in Banach space by a different approach. Suppose that the linear evolution process is well posed, we introduce a family pair of bounded linear operators, $\{(G(t),F(t)),t\ge 0\}$, that is, called the resolvent family for the linear evolution process with memory, the $F(t)$ is called the memory effect family. In this paper, we prove that the families $G(t)$ and $F(t)$ are exponentially bounded, and the family $(G(t),F(t))$ associate with an operator pair $(A,L)$ that is called generator of the resolvent family. Using $(A,L)$, we derive associated differential equation with memory and representation of $F(t)$ via L. These results give necessary conditions of the well-posed linear evolution process with memory. To apply the resolvent family to differential equation with memory, we present a generation theorem of the resolvent family under some restrictions on $(A,L)$. The obtained results can be directly applied to linear delay differential equation, integro-differential equation and functional differential equations.