Extended triplet set C343 of DNA sequences and its application to the p53 gene

Recently, much research has indicated that more and more cancers pose a threat to human life. Cancers are caused by oncogenes. Many human oncogenes have been found and most of them are located on chromosomes. The discovery of the oncogene plays a significant role in the treatment of cancer. The p53 tumor suppressor gene has received much attention because it frequently mutates or deletes in tumor cells of most people. Thus, the study of oncogenes is significant. In order to establish the Galois field (GF(7)), the indefinite gene is introduced as D and oncogene is introduced as O, and P. Taking the polynomial coefficients a₀, a₁, a₂ ∈ GF(7) and the bijective function f:GF(7) → {D,A,C,O,G,T,P}, where f(0) = D, f(1) = A, f(2) = C, f(3) = O, f(4) = G, f(5) = T, and f(6) = P, the bijective φ may be written as φ(a₀ + a₁x + a₂x²). Based on the algebraic structure, we can not only analyse the DNA sequence of oncogenes, but also predict possible new cancers.     

K-matrix analysis of the (IJ<Superscript>PC</Superscript> = 00<Superscript>+ +</Superscript>)-wave in the mass region below 1900 MeV

We present the results of the current analysis of the partial wave IJ ^PC = 00^{+ +} based on the available data for meson spectra ( ππ, KˉK,ηη,η,ππππ). In the framework of the K-matrix approach, the analytical amplitude has been reconstructed in the mass region 280 MeV < < 1900 MeV. The following scalar-isoscalar states are seen: comparatively narrow resonances f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750) and the broad state f₀(1200-1600). The positions of the amplitude poles (masses and total widths of the resonances) are determined as well as pole residues (partial widths to meson channels ππ, KˉK,ηη,η,ππππ). The fitted amplitude gives us the positions of the K-matrix poles (bare states) and the values of bare-state couplings to meson channels thus allowing the quark-antiquark nonet classification of bare states. On the basis of the obtained partial widths to the channels ππ, KˉK,ηη,η, we estimate the quark/gluonium content of f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750), f₀(1200-1600). For f ₀(980), f ₀(1300), f ₀(1500) and f ₀(1750), their partial widths testify the qˉq origin of these mesons though being unable to provide precise evaluation of the possible admixture of the gluonium component in these resonances. The ratios of the decay coupling constants for the f₀(1200-1600) support the idea about the gluonium nature of this broad state. Received: 14 May 2002 / Accepted: 20 August 2002 / Published online: 11 February 2003 RID="a" ID="a"e-mail: anisovic@thd.pnpi.spb.ru Communicated by A. Sch?fer     

混沌半导体激光器的弛豫振荡频率对随机序列速率的影响

利用光反馈半导体激光器产生的混沌激光作为随机数发生器的物理熵源, 分析了混沌信号自相关系数与随机序列游程数之间的联系, 在此基础上研究了激光器的弛豫振荡频率f_r与随机序列速率f_n在不同比值时, 序列游程数的变化情况. 研究发现, 当f_r/f_n=(2k+1)/4时, 随机序列的游程数容易满足NIST SP800-22随机数测试标准的要求. 当k=1时, 得到随机序列最大速率为f_n=4f_r/3.     

YH,YD,YT分子基态的结构与势能函数

在Y的有效核势近似下, 对H分别选6-311++G(3df,2pd), AUG-cc-PVTZ, AUG-cc-PVQZ基组, 应用密度泛函理论的B3LYP方法, 优化计算了YH(D,T)分子基态的能量, 平衡结构, 和谐振频率.根据原子分子反应静力学原理, 导出了YH(D,T)分子基态的合理离解极限. 通过优化计算结果和已有的实验和理论数据对比, 得出LANL2TZ/AUG-cc-PVQZ混合基组为对体系进行计算的最优基组. 基于此, 在B3LYP/LANL2TZ/AUG-cc-PVQZ水平对YH(D,T)分子基态的势能面进行了单点能扫描. 并采用最小二乘法拟合得到了相应的Murrell-Sorbie势能函数. 计算出了这些分子的力常数(f₂, f₃, f₄)和光谱常数(B_e, α_e, ω_e, ω_eχ_e, D_e).结果与已有的实验数据符合得很好.     

Frequency dispersion of dielectric coefficients of layered TlGaS<Subscript>2</Subscript> single crystals

Frequency dependence of the dissipation factor tanδ, the permittivity ɛ, and the ac conductivity σ_ac across the layers in the frequency range f=5×10⁴−3×10⁷ Hz was studied in layered TlGaS₂ single crystals. A significant dispersion in tanδ was observed in the frequency range 10⁶−3×10⁷ Hz. In the range of frequencies studied, the permittivity of TlGaS₂ samples varied from 26 to 30. In the frequency range 5×10⁴−10⁶ Hz, the ac conductivity obeyed the f ^0.8 law, whereas for f>10⁶ Hz σ_ac was proportional to f ². It was established that the mechanism of the ac charge transport across the layers in TlGaS₂ single crystals in the frequency range 5×10⁴−10⁶ Hz is hopping over localized states near the Fermi level. Estimations yielded the following values of the parameters: the density of states at the Fermi level N _F=2.1×10¹⁸ eV⁻¹ cm⁻³, the average time of charge carrier hopping between localized states τ=2 μs, and the average hopping distance R=103 ?. __________ Translated from Fizika Tverdogo Tela, Vol. 46, No. 6, 2004, pp. 979–981. Original Russian Text Copyright ? 2004 by Mustafaeva.     

空间网络上的随机游走

本文以一维均匀环为基础, 通过添加有限数量的长程连接构造出了一维有限能量约束下的空间网络, 环上任意节点i与j之间存在一条长程连接的概率满足p_ijα d_ij^-α (α≥ 0),其中d_ij为节点i与j之间的网格距离, 并且所有长程连接长度总和受到总能量∧=cN(c≥ 0)的约束, N为网络节点总数.通过研究该空间网络上的随机游走过程,存在最优幂指数α₀ 使得陷阱问题的平均首达时间最短.进一步研究发现,平均首达时间与网络规模N之间存在着幂律关系, 随着网络规模N和总能量∧的增加,最优幂指数α₀单调增加,并趋近最优值1.5.     

Regarding the axial-vector mesons

The implications of the f₁(1285)-f₁(1420) mixing for the K₁(³P₁)- K₁(¹P₁) mixing angle are investigated. Based on the f₁(1285)-f₁(1420) mixing angle ∼ 50^° suggested from the analysis for a substantial body of data concerning the f₁(1420) and f₁(1285), the masses of the K₁(³P₁) and K₁(¹P₁) are determined to be ∼ 1307.35±0.63 MeV and 1370.03±9.69 MeV, respectively, which therefore suggests that the K₁(³P₁)- K₁(¹P₁) mixing angle is about ±(59.55±2.81)^°. Also, it is found that the mass of the h^′₁(¹P₁) (mostly of sˉ) state is about 1495.18±8.82 MeV. Comparison of the predicted results and the available experimental information of the h₁(1380) shows that without further confirmation on the h₁(1380), the assignment of the h₁(1380) as the sˉ member of the ¹P₁ meson nonet may be premature.     

关于B0→π－l+ν l衰变过程分支比的计算

通过构造适当的关联函数,计算B→π跃迁形状因子f⁺_Bπ(q²),f _{Bπ(q²)和标量形状因子f⁰(q²),从而就能研究轻子质量对B⁰→π}     

长时间精密锁定的掺Er光纤飞秒光学频率梳

自行研制了基于掺Er光纤飞秒激光器的光学频率梳并实现了重复频率 f_r信号和载波包络偏移频率(Carrier-envelope offset, f_o) 信号的精密锁定, 锁定后的 f_r信号和 f_o 信号的频率抖动量的标准偏差分别为0.515 mHz和93.13 mHz.     

Effects of Fe doping on ac susceptibility of Pr0.75Na0.25MnO3

Ac susceptibility at low temperatures of Pr_0.75Na_0.25Mn_1-xFe_xO₃ (0 ≤ x ≤ 0.30) is investigated. The peak value of the real component of ac susceptibility χ' at the freezing temperature T_f is suppressed with the increasing frequency. The peak value of χ' shows a linear relation between T_f and the logarithm of the frequency ω. The normalized slope P = ΔT_f/T_fΔlgω, which is much lower than canonical insulating spin glass systems in which 0.06 ≤ P ≤ 0.08. The peak value of the imaginary component of the ac susceptibility χ' at T_f for the x = 0, 0.02, 0.30 samples increases with increasing frequency, suggesting a cluster glass ground state with a coexistence of charge-ordered phase and correlated ferromagnetic clusters in spin glass matrix. The peak value of χ' at T_f for the x = 0.10 sample decreases with increasing frequency, suggesting a phase separation ground state. The peak value of χ' at T_f for the x = 0.05 sample decreases with increasing frequency for ω ≤ 52 Hz and increases subsequently till 701 Hz, and then decreases with further increasing frequency for ω ≥ 1501 Hz. This complex behaviour is ascribed to the competition between the effects of large and little ferromagnetic clusters in the sample. The ground state of x = 0.05 sample is a transition state from cluster glass to phase separation.     

Reconstruction of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity according to holographic dark energy

We develop the reconstruction of the f(T) gravity model according to the holographic dark energy. T is the torsion scalar and its initial value from the teleparallel gravity is imposed for fitting the initial value of the function f(T). The evolutionary nature of the holographic dark energy is essentially based on two important parameters, Ω _V  and ω _V , respectively, the dimensionless dark energy and the parameter of the equation of state, related to the holographic dark energy. The result shows a polynomial function for f(T), and we also observe that, when Ω _V →1 at the future time, ω _V may cross −1 for some values of the input parameter b. Another interesting aspect of the obtained model is that it provides a unification scenario of dark matter with dark energy.     

Density perturbation of unparticle dark matter in the flat Universe

The unparticle has been suggested as a candidate of dark matter. We investigated the growth rate of the density perturbation for unparticle dark matter in the flat Universe. First, we consider the model in which the unparticle is the sole dark matter and find that the growth factor can be approximated well by f=(1+3ω _u )Ω _u ^γ , where ω _u is the equation of state of unparticle. Our results show that the presence of ω _u modifies the behavior of the growth factor f. For the second model where the unparticle co-exists with cold dark matter, the growth factor has a new approximation f=(1+3ω _u )Ω _u ^γ +α Ω _m and α is a function of ω _u . Thus the growth factor of the unparticle is quite different from that of the usual dark matter. This information can help us know more about unparticle and the early evolution of the Universe.     

Transport Properties of Random Walks on Scale-Free/Regular-Lattice Hybrid Networks

We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds (F) and across network shortcuts (f). For fast shortcuts (f/F≫1) and low shortcut densities, traversal time data collapse onto a universal curve, while a crossover behavior that can be related to the percolation threshold of the scale-free network component is identified at higher shortcut densities, in analogy to similar observations reported recently in Newman-Watts small-world networks. Furthermore, we observe that random walk traversal times are larger for networks with a higher degree of inhomogeneity in their shortcut distribution, and we discuss access time distributions as functions of the initial and final node degrees. These findings are relevant, in particular, when considering the optimization of existing information networks by the addition of a small number of fast shortcut connections.     

The Combined Effect of Connectivity and Dependency Links on Percolation of Networks

Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently developed mathematical framework for analyzing percolation properties of realistic scenarios of networks having links of two types, connectivity and dependency links. This formalism was applied to study Erdős-Rényi (ER) networks that include also dependency links. For an ER network with average degree [`(k)]\bar{k} that is composed of dependency clusters of size s, the fraction of nodes that belong to the giant component, P <sub>∞</sub>, is given by P<sub>￥</sub>=p<sup>s-1</sup>[1-exp(-[`(k)]pP_￥) ]^sP_{\infty}=p^{s-1}[1-\exp{(-\bar{k}pP_{\infty})} ]^{s} where 1−p is the initial fraction of randomly removed nodes. Here, we apply the formalism to the study of random-regular (RR) networks and find a formula for the size of the giant component in the percolation process: P _∞=p ^s−1(1−r ^k ) ^s where r is the solution of r=p ^s (r ^k−1−1)(1−r ^k )+1, and k is the degree of the nodes. These general results coincide, for s=1, with the known equations for percolation in ER and RR networks respectively without dependency links. In contrast to s=1, where the percolation transition is second order, for s>1 it is of first order. Comparing the percolation behavior of ER and RR networks we find a remarkable difference regarding their resilience. We show, analytically and numerically, that in ER networks with low connectivity degree or large dependency clusters, removal of even a finite number (zero fraction) of the infinite network nodes will trigger a cascade of failures that fragments the whole network. Specifically, for any given s there exists a critical degree value, [`(k)]<sub>min</sub>\bar{k}_{\min}, such that an ER network with [`(k)] ￡ [`(k)]_min\bar{k}\leq \bar{k}_{\min} is unstable and collapse when removing even a single node. This result is in contrast to RR networks where such cascades and full fragmentation can be triggered only by removal of a finite fraction of nodes in the network.     

Domain structure of cellulose triacetate

The topology of the surface of thin films obtained from cellulose triacetate solutions has been studied using electron microscopy. The domain structure of the physical network of macromolecules (percolation cluster) with the maximum size L ≈ 30 nm of regions with a local orientational order has been established. With an increase in the volume fraction Ω of the cluster to the critical value Ω = 0.91, repacking of domains takes place, which is connected with a decrease in the parameter Ω, L doubling bifurcation of the size L, and formation of regions of long-range orientational order: the mesophase of the polymer.     

Bootstrap Percolation on Homogeneous Trees Has 2 Phase Transitions

We study the threshold θ bootstrap percolation model on the homogeneous tree with degree b+1, 2≤θ≤b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p _f , such that a) for p>p _f , the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p<p _f , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p _c , such that 0<p _c <p _f , with the following properties: 1) if p≤p _c , then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p>p _c , then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p<p _c , the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p=p _c , the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0,p _f ] and analytic on (p _c ,p _f ), admitting an analytic continuation from the right at p _c and, only in the case θ=b, also from the left at p _f . L.R.G. Fontes partially supported by the Brazilians CNPq through grants 475833/2003-1, 307978/2004-4 and 484351/2006-0, and FAPESP through grant 04/07276-2. R.H. Schonmann partially supported by the American N.S.F. through grant DMS-0300672.     

Dark energy degeneracies in the background dynamics

We discuss degeneracies between dark energy and cosmic parameters using a fully non-perturbative and non-parametric approach. This allows us to examine the knock-on bias induced in the reconstructed dark energy equation of state, w(z), if there is a bias in the cosmic curvature or dark matter content. Assuming perfect Hubble, distance and volume measurements, we show that for z > 1, the bias in w(z) is up to two orders of magnitude larger than the corresponding errors in Ω _k or Ω _m .     

Phase space quantization as a moment problem

We consider questions related to the following quantization scheme: a classical variable f: Ω → ℝ on a phase space Ω is associated with a unique semispectral measure E ^f , such that the kth moment operator of E ^f is required to coincide with the operator integral L(f ^k , E) of f ^k with respect to a certain fixed phase space semispectral measure E. Mainly, we take the phase space Ω to be a locally compact unimodular group. In the concrete case where Ω = ℝ² and E is a translation covariant semispectral measure, we determine explicitly the relevant operators L(f ^k , E) for certain variables f. In addition, we consider the question under what conditions a positive operator measure is projection valued. The text was submitted by the author in English.     

A New Class of Cellular Automata with a Discontinuous Glass Transition

We introduce a new class of two-dimensional cellular automata with a bootstrap percolation-like dynamics. Each site can be either empty or occupied by a single particle and the dynamics follows a deterministic updating rule at discrete times which allows only emptying sites. We prove that the threshold density ρ _c for convergence to a completely empty configuration is non trivial, 0<ρ _c <1, contrary to standard bootstrap percolation. Furthermore we prove that in the subcritical regime, ρ<ρ _c , emptying always occurs exponentially fast and that ρ _c coincides with the critical density for two-dimensional oriented site percolation on ℤ². This is known to occur also for some cellular automata with oriented rules for which the transition is continuous in the value of the asymptotic density and the crossover length determining finite size effects diverges as a power law when the critical density is approached from below. Instead for our model we prove that the transition is discontinuous and at the same time the crossover length diverges faster than any power law. The proofs of the discontinuity and the lower bound on the crossover length use a conjecture on the critical behaviour for oriented percolation. The latter is supported by several numerical simulations and by analytical (though non rigorous) works through renormalization techniques. Finally, we will discuss why, due to the peculiar mixed critical/first order character of this transition, the model is particularly relevant to study glassy and jamming transitions. Indeed, we will show that it leads to a dynamical glass transition for a Kinetically Constrained Spin Model. Most of the results that we present are the rigorous proofs of physical arguments developed in a joint work with D.S. Fisher.     

Three-dimensional vortex visualization in stratified spin-up

Abstract  

We present the results of three-dimensional time-dependent numerical simulations of incremental spin-up of a thermally stratified fluid. The fluid inside a vertical cylindrical container of radius R and height 2H is water characterized by the kinematic viscosity ν and thermal diffusivity κ. Initially, its density (temperature) varies linearly with height and is characterized by a constant buoyancy frequency N, which is proportional to the density gradient. The system undergoes an abrupt change in the rotation rate from its initial value Ω_i, when the fluid is in a solid-body rotation state, to the final value Ω_f. The aim of this contribution is to show the formation of columnar vortices in a high Rossby number spin-up flow.